https://wiki.swarma.org/api.php?action=feedcontributions&user=%E5%94%90%E7%B3%96%E7%B3%96&feedformat=atom集智百科 - 复杂系统|人工智能|复杂科学|复杂网络|自组织 - 用户贡献 [zh-cn]2024-03-28T17:40:50Z用户贡献MediaWiki 1.35.0https://wiki.swarma.org/index.php?title=%E5%BC%BA%E5%8C%96%E5%AD%A6%E4%B9%A0&diff=34294强化学习2024-02-21T15:25:21Z<p>唐糖糖:</p>
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<div>此词条暂由Henry翻译<br />
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本词条已有[[用户:Qige96|Ricky]]审校。<br />
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--[[用户:Qige96|Ricky]]:这一词条的行文非常糟糕,但其对应的维基百科原文就是这么糟糕吧。。。强烈希望有第二个审校再审一遍,最好是有点强化学习的背景知识的伙伴。可以考虑用scholarpedia的[http://www.scholarpedia.org/article/Reinforcement_learning 相应词条]作为原文本。<br />
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{{For|reinforcement learning in psychology|Reinforcement|Operant conditioning}}<br />
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'''Reinforcement learning''' ('''RL''') is an area of machine learning concerned with how software agents ought to take actions in an environment in order to maximize the notion of cumulative reward. Reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and unsupervised learning.<br />
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Reinforcement learning (RL) is an area of machine learning concerned with how software agents ought to take actions in an environment in order to maximize the notion of cumulative reward. Reinforcement learning is one of three basic machine learning paradigms, alongside supervised learning and unsupervised learning.<br />
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<font color="#ff8000"> 强化学习Reinforcement learning</font>是机器学习的一个领域,它关注的是[[基于主体的模型|软件主体]](software agent)应该在一个环境中采取何种行动,才能最大化总体收益。强化学习,有监督学习和无监督学习是机器学习的三种基本范式。<br />
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Reinforcement learning differs from supervised learning in not needing labelled input/output pairs be presented, and in not needing sub-optimal actions to be explicitly corrected. Instead the focus is on finding a balance between exploration (of uncharted territory) and exploitation (of current knowledge).<ref name="kaelbling">{{cite journal|last1=Kaelbling|first1=Leslie P.|last2=Littman|first2=Michael L.|authorlink2=Michael L. Littman|last3=Moore|first3=Andrew W.|authorlink3=Andrew W. Moore|year=1996|title=Reinforcement Learning: A Survey|url=http://www.cs.washington.edu/research/jair/abstracts/kaelbling96a.html|url-status=dead|journal=Journal of Artificial Intelligence Research|volume=4|pages=237–285|doi=10.1613/jair.301|archiveurl=http://webarchive.loc.gov/all/20011120234539/http://www.cs.washington.edu/research/jair/abstracts/kaelbling96a.html|archivedate=2001-11-20|ref=harv|authorlink1=Leslie P. Kaelbling|arxiv=cs/9605103}}</ref><br />
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Reinforcement learning differs from supervised learning in not needing labelled input/output pairs be presented, and in not needing sub-optimal actions to be explicitly corrected. Instead the focus is on finding a balance between exploration (of uncharted territory) and exploitation (of current knowledge).<br />
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强化学习与有监督学习的不同之处在于,前者不需要标记输入、输出对,也不需要对次优操作进行显式修正。相反,强化学习的重点是在探索(未知领域)和利用(现有知识)之间找到平衡。<ref name="kaelbling">{{cite journal|last1=Kaelbling|first1=Leslie P.|last2=Littman|first2=Michael L.|authorlink2=Michael L. Littman|last3=Moore|first3=Andrew W.|authorlink3=Andrew W. Moore|year=1996|title=Reinforcement Learning: A Survey|url=http://www.cs.washington.edu/research/jair/abstracts/kaelbling96a.html|url-status=dead|journal=Journal of Artificial Intelligence Research|volume=4|pages=237–285|doi=10.1613/jair.301|archiveurl=http://webarchive.loc.gov/all/20011120234539/http://www.cs.washington.edu/research/jair/abstracts/kaelbling96a.html|archivedate=2001-11-20|ref=harv|authorlink1=Leslie P. Kaelbling|arxiv=cs/9605103}}</ref><br />
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The environment is typically stated in the form of a Markov decision process (MDP), because many reinforcement learning algorithms for this context utilize dynamic programming techniques.<ref>{{Cite book|title=Reinforcement learning and markov decision processes|author1=van Otterlo, M.|author2=Wiering, M.|journal=Reinforcement Learning |volume=12|pages=3–42 |year=2012 |doi=10.1007/978-3-642-27645-3_1|series=Adaptation, Learning, and Optimization|isbn=978-3-642-27644-6}}</ref> The main difference between the classical dynamic programming methods and reinforcement learning algorithms is that the latter do not assume knowledge of an exact mathematical model of the MDP and they target large MDPs where exact methods become infeasible.<br />
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The environment is typically stated in the form of a Markov decision process (MDP), because many reinforcement learning algorithms for this context utilize dynamic programming techniques. The main difference between the classical dynamic programming methods and reinforcement learning algorithms is that the latter do not assume knowledge of an exact mathematical model of the MDP and they target large MDPs where exact methods become infeasible.<br />
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主体所在的环境通常是以<font color="#ff8000"> 马可夫决策过程 Markov decision process</font>(MDP)的形式表示的,因为许多在此情景下的强化学习算法都使用了动态规划方法。经典的动态规划方法和强化学习算法间主要区别在于后者并不假设精确的MDP数学模型的知识,而是关注于那些精确方法不可行的大型MDP场景。<br />
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== 介绍 ==<br />
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[[File:Reinforcement learning diagram.svg|thumb|right|250px| The typical framing of a Reinforcement Learning (RL) scenario: an agent takes actions in an environment, which is interpreted into a reward and a representation of the state, which are fed back into the agent.]]<br />
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The typical framing of a Reinforcement Learning (RL) scenario: an agent takes actions in an environment, which is interpreted into a reward and a representation of the state, which are fed back into the agent.<br />
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强化学习的典型场景: 主体在环境中采取某项行动,这像行动会被程序翻译成收益和状态的表示,而收益和状态又会被反馈回主体。<br />
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Reinforcement learning, due to its generality, is studied in many other disciplines, such as game theory, control theory, operations research, information theory, simulation-based optimization, multi-agent systems, swarm intelligence, statistics and genetic algorithms. In the operations research and control literature, reinforcement learning is called ''approximate dynamic programming,'' or ''neuro-dynamic programming.'' The problems of interest in reinforcement learning have also been studied in the theory of optimal control, which is concerned mostly with the existence and characterization of optimal solutions, and algorithms for their exact computation, and less with learning or approximation, particularly in the absence of a mathematical model of the environment. In economics and game theory, reinforcement learning may be used to explain how equilibrium may arise under bounded rationality.<br />
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Reinforcement learning, due to its generality, is studied in many other disciplines, such as game theory, control theory, operations research, information theory, simulation-based optimization, multi-agent systems, swarm intelligence, statistics and genetic algorithms. In the operations research and control literature, reinforcement learning is called approximate dynamic programming, or neuro-dynamic programming. The problems of interest in reinforcement learning have also been studied in the theory of optimal control, which is concerned mostly with the existence and characterization of optimal solutions, and algorithms for their exact computation, and less with learning or approximation, particularly in the absence of a mathematical model of the environment. In economics and game theory, reinforcement learning may be used to explain how equilibrium may arise under bounded rationality.<br />
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由于它的普遍性,强化学习在许多其他学科中都有所应用,如<font color="#ff8000"> 博弈论 game theory</font>、<font color="#ff8000"> 控制论 control theory</font>、<font color="#ff8000"> 运筹学 operations research</font>、<font color="#ff8000"> 信息论 information theory</font>、基于仿真的优化、多主体系统、群体智能、<font color="#ff8000"> 统计学 statistics </font>和遗传算法等。在运筹学和控制论中,强化学习被称为近似的动态规划,或者神经动态规划。其中最优控制理论也研究了强化学习中一些热点问题。最优控制理论主要关注最优解的存在性、形式及其精确计算的算法,在缺乏环境数学模型的情况下的学习或近似的方法则关注较少。在经济学和<font color="#ff8000"> 博弈论</font>中,强化学习可以用来解释均衡性是如何在有限理性下产生的。<br />
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Basic reinforcement is modeled as a Markov decision process:<br />
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Basic reinforcement is modeled as a Markov decision process:<br />
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基本的强化被模拟成一个<font color="#ff8000"> 马尔可夫决策过程 Markov decision process</font><br />
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* a set of environment and agent states, {{mvar|S}};<br />
* a set of actions, {{mvar|A}}, of the agent;<br />
* <math>P_a(s,s')=\Pr(s_{t+1}=s'\mid s_t=s, a_t=a)</math> is the probability of transition (at time <math>t</math>) from state <math>s</math> to state <math>s'</math> under action <math>a</math>.<br />
* <math>R_a(s,s')</math> is the immediate reward after transition from <math>s</math> to <math>s'</math> with action <math>a</math>.<br />
* rules that describe what the agent observes<br />
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*一组环境和主体集合{{mvar|S}};<br />
*一组主体的行为 {{mvar|A}};<br />
*Pa(s,s′)=Pr(st+1=s′∣st=s,at=a)是在时间t和行为a下从s到 s′ 状态转变的可能性<br />
<math>P_a(s,s')=\Pr(s_{t+1}=s'\mid s_t=s, a_t=a)</math>是在时间<math>t</math>时,主体采取行动<math>a</math>后,状态从<math>s</math>到<math>s'</math>转移的概率<br />
*<math>R_a(s,s')</math>是从s到s′过渡所得到的即时收益<br />
*描述主体要遵守的规则<br />
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Rules are often stochastic. The observation typically involves the scalar, immediate reward associated with the last transition. In many works, the agent is assumed to observe the current environmental state (''full observability''). If not, the agent has ''partial observability''. Sometimes the set of actions available to the agent is restricted (a zero balance cannot be reduced. For example, if the current value of the agent is 3 and the state transition reduces the value by 4, the transition will not be allowed).<br />
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Rules are often stochastic. The observation typically involves the scalar, immediate reward associated with the last transition. In many works, the agent is assumed to observe the current environmental state (full observability). If not, the agent has partial observability. Sometimes the set of actions available to the agent is restricted (a zero balance cannot be reduced. For example, if the current value of the agent is 3 and the state transition reduces the value by 4, the transition will not be allowed).<br />
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强化学习模型中规则往往是带有随机性,观察通常会包括上一次状态转移带来的收益。在许多工作中,主体被假定能够观察当前的环境状态(完全可观察性)。如果不能,则称主体具有部分可观测性。有时,主体可用的操作集会受到限制(比如说,账户余额不能减到0以下。如果主体的当前值为3,而状态转换将该值减少4,这样的转换是不被允许的)。<br />
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A reinforcement learning agent interacts with its environment in discrete time steps. At each time {{mvar|t}}, the agent receives an observation <math>o_t</math>, which typically includes the reward <math>r_t</math>. It then chooses an action <math>a_t</math> from the set of available actions, which is subsequently sent to the environment. The environment moves to a new state <math>s_{t+1}</math> and the reward <math>r_{t+1}</math> associated with the ''transition'' <math>(s_t,a_t,s_{t+1})</math> is determined. The goal of a reinforcement learning agent is to collect as much reward as possible. The agent can (possibly randomly) choose any action as a function of the history.<br />
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A reinforcement learning agent interacts with its environment in discrete time steps. At each time , the agent receives an observation <math>o_t</math>, which typically includes the reward <math>r_t</math>. It then chooses an action <math>a_t</math> from the set of available actions, which is subsequently sent to the environment. The environment moves to a new state <math>s_{t+1}</math> and the reward <math>r_{t+1}</math> associated with the transition <math>(s_t,a_t,s_{t+1})</math> is determined. The goal of a reinforcement learning agent is to collect as much reward as possible. The agent can (possibly randomly) choose any action as a function of the history.<br />
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强化学习中的主体以离散的时间步骤与环境进行交互。在每一个时间步{{mvar|t}},主体都会收到一个观察<math>o_t</math>,这通常包括收益<math>r_t</math>。然后,它从一组可用的操作中选择一个操作 <math>a_t</math>,该操作随后被发送到环境中。环境转移到一个新的状态数学 <math>s_{t+1}</math>,并确定与转换 <math>(s_t,a_t,s_{t+1})</math> 相关的奖励 <math>r_{t+1}</math>。强化学习主体的目标是尽可能多地获取收益。主体可以(可能是随机的)根据历史选择任何操作。<br />
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When the agent's performance is compared to that of an agent that acts optimally, the difference in performance gives rise to the notion of regret. In order to act near optimally, the agent must reason about the long term consequences of its actions (i.e., maximize future income), although the immediate reward associated with this might be negative.<br />
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When the agent's performance is compared to that of an agent that acts optimally, the difference in performance gives rise to the notion of regret. In order to act near optimally, the agent must reason about the long term consequences of its actions (i.e., maximize future income), although the immediate reward associated with this might be negative.<br />
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当某主体的表现与理论最优主体的表现相比较时,表现上的差值就是“后悔”。为了近乎最优地行动,主体必须推理其行动的长期后果(即,最大化未来收入) ,尽管与此相关的短期收益可能是负的。<br />
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Thus, reinforcement learning is particularly well-suited to problems that include a long-term versus short-term reward trade-off. It has been applied successfully to various problems, including robot control, elevator scheduling, telecommunications, backgammon, checkers and Go (AlphaGo).<br />
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Thus, reinforcement learning is particularly well-suited to problems that include a long-term versus short-term reward trade-off. It has been applied successfully to various problems, including robot control, elevator scheduling, telecommunications, backgammon, checkers and Go (AlphaGo).<br />
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因此,强化学习特别适合解决包括长期与短期收益均衡在内的问题。它已成功地应用于各种问题,包括机器人控制、电梯调度、通信、西洋双陆棋、跳棋和围棋(AlphaGo)。<br />
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Two elements make reinforcement learning powerful: the use of samples to optimize performance and the use of function approximation to deal with large environments. Thanks to these two key components, reinforcement learning can be used in large environments in the following situations:<br />
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Two elements make reinforcement learning powerful: the use of samples to optimize performance and the use of function approximation to deal with large environments. Thanks to these two key components, reinforcement learning can be used in large environments in the following situations:<br />
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使得强化学习功能强大的因素有两个: 使用样本来优化性能和使用函数逼近来处理大型环境。正因为有了这两个关键组件,强化学习可以在以下情况下在大型环境中使用:<br />
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* A model of the environment is known, but an analytic solution is not available;<br />
* Only a simulation model of the environment is given (the subject of simulation-based optimization);<ref>{{cite book|url = https://www.springer.com/mathematics/applications/book/978-1-4020-7454-7|title = Simulation-based Optimization: Parametric Optimization Techniques and Reinforcement|last = Gosavi|first = Abhijit|publisher = Springer|year = 2003|isbn = 978-1-4020-7454-7|pages =|ref = harv|authorlink = Abhijit Gosavi|series = Operations Research/Computer Science Interfaces Series}}</ref><br />
* The only way to collect information about the environment is to interact with it.<br />
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*一种环境的模型是已知的,但是无法得到其数学解析式;<br />
*只给出了环境的模拟模型;<ref>{{cite book|url = https://www.springer.com/mathematics/applications/book/978-1-4020-7454-7|title = Simulation-based Optimization: Parametric Optimization Techniques and Reinforcement|last = Gosavi|first = Abhijit|publisher = Springer|year = 2003|isbn = 978-1-4020-7454-7|pages =|ref = harv|authorlink = Abhijit Gosavi|series = Operations Research/Computer Science Interfaces Series}}</ref><br />
*收集环境信息的唯一方法就是去与环境交互;<br />
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The first two of these problems could be considered planning problems (since some form of model is available), while the last one could be considered to be a genuine learning problem. However, reinforcement learning converts both planning problems to machine learning problems.<br />
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The first two of these problems could be considered planning problems (since some form of model is available), while the last one could be considered to be a genuine learning problem. However, reinforcement learning converts both planning problems to machine learning problems.<br />
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前两个问题可以被认为是规划问题(因为某种形式的模型是可用的) ,而后一个问题可以被认为是真正的学习问题。然而,强化学习可以将前两个规划问题转化为机器学习问题。<br />
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== 探索 ==<br />
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The exploration vs. exploitation trade-off has been most thoroughly studied through the multi-armed bandit problem and for finite state space MDPs in Burnetas and Katehakis (1997).<ref>{{citation | last1 = Burnetas|first1 = Apostolos N.|last2 = Katehakis|first2 = Michael N.|authorlink2 = Michael N. Katehakis|year = 1997|title = Optimal adaptive policies for Markov Decision Processes|journal = Mathematics of Operations Research|volume = 22|pages = 222–255|ref = harv|doi=10.1287/moor.22.1.222}}</ref><br />
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The exploration vs. exploitation trade-off has been most thoroughly studied through the multi-armed bandit problem and for finite state space MDPs in Burnetas and Katehakis (1997).<br />
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Burnetas 和 Katehakis (1997)<ref>{{citation | last1 = Burnetas|first1 = Apostolos N.|last2 = Katehakis|first2 = Michael N.|authorlink2 = Michael N. Katehakis|year = 1997|title = Optimal adaptive policies for Markov Decision Processes|journal = Mathematics of Operations Research|volume = 22|pages = 222–255|ref = harv|doi=10.1287/moor.22.1.222}}</ref> 已经通过多臂老虎机问题非常彻底地研究了有限的状态空间MDPs中探索与利用的权衡。<br />
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Reinforcement learning requires clever exploration mechanisms; randomly selecting actions, without reference to an estimated probability distribution, shows poor performance. The case of (small) finite Markov decision processes is relatively well understood. However, due to the lack of algorithms that scale well with the number of states (or scale to problems with infinite state spaces), simple exploration methods are the most practical.<br />
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Reinforcement learning requires clever exploration mechanisms; randomly selecting actions, without reference to an estimated probability distribution, shows poor performance. The case of (small) finite Markov decision processes is relatively well understood. However, due to the lack of algorithms that scale well with the number of states (or scale to problems with infinite state spaces), simple exploration methods are the most practical.<br />
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强化学习需要聪明的探索机制; 不参考概率分布来随机地选择行动,性能表现往往会很糟糕。有限马尔可夫决策过程的情况是相对较好理解的。然而,由于缺乏可以在状态的数量很大时依然高效运行的算法(或者说适用于无限状态空间问题的算法) ,多数情况下简单的探索方法是最实用的。<br />
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One such method is <math>\epsilon</math>-greedy, where <math>0 < \epsilon < 1</math> is a parameter controlling the amount of exploration vs. exploitation. With probability <math>1-\epsilon</math>, exploitation is chosen, and the agent chooses the action that it believes has the best long-term effect (ties between actions are broken uniformly at random). Alternatively, with probability <math>\epsilon</math>, exploration is chosen, and the action is chosen uniformly at random. <math>\epsilon</math> is usually a fixed parameter but can be adjusted either according to a schedule (making the agent explore progressively less), or adaptively based on heuristics.<ref>{{citation | last1 = Tokic | first1 = Michel | last2 = Palm | first2 = Günther | chapter = Value-Difference Based Exploration: Adaptive Control Between Epsilon-Greedy and Softmax | pages = 335–346 | publisher = Springer | series = Lecture Notes in Computer Science | title = KI 2011: Advances in Artificial Intelligence | volume = 7006 | year = 2011 | chapter-url = http://www.tokic.com/www/tokicm/publikationen/papers/KI2011.pdf | isbn = 978-3-642-24455-1}}</ref><br />
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One such method is <math>\epsilon</math>-greedy, where <math>0 < \epsilon < 1</math> is a parameter controlling the amount of exploration vs. exploitation. With probability <math>1-\epsilon</math>, exploitation is chosen, and the agent chooses the action that it believes has the best long-term effect (ties between actions are broken uniformly at random). Alternatively, with probability <math>\epsilon</math>, exploration is chosen, and the action is chosen uniformly at random. <math>\epsilon</math> is usually a fixed parameter but can be adjusted either according to a schedule (making the agent explore progressively less), or adaptively based on heuristics.<br />
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其中一个方法是ϵ-greedy,其中 0<ϵ<1 是一个控制探索与开发的数量的参数。主体有1−ϵ的概率选择“利用”,选择它认为具有最佳长期效果的行动(若几个行动的效果一样好,则均匀地随机选择)。主体还有ϵ的概率选择探索,并随机均匀地选择动作。ϵ通常是一个固定的参数,但可以根据时间进行调整(使主体逐步减少探索) ,或者根据一些启发式信息调整。<br />
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== 控制学习的算法 ==<br />
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Even if the issue of exploration is disregarded and even if the state was observable (assumed hereafter), the problem remains to use past experience to find out which actions lead to higher cumulative rewards.<br />
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Even if the issue of exploration is disregarded and even if the state was observable (assumed hereafter), the problem remains to use past experience to find out which actions lead to higher cumulative rewards.<br />
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即使忽略探索与利用的问题,且状态是可观察的,最大的问题仍然是如何利用过去的经验来找出哪些行动可以带来更高的总体收益。<br />
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===最优性的定义和标准===<br />
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==== 策略 ====<br />
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The agent's action selection is modeled as a map called ''policy'':<br />
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The agent's action selection is modeled as a map called policy:<br />
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主体的行动选择可以被建模为一个称为'''策略(policy)'''的映射:<br />
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:<math>\pi: A \times S \rightarrow [0,1]</math><br />
:<math>\pi(a,s) = \Pr(a_t = a\mid s_t =s)</math><br />
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The policy map gives the probability of taking action <math>a</math> when in state <math>s</math>.<ref name=":0">{{Cite book|url=http://people.inf.elte.hu/lorincz/Files/RL_2006/SuttonBook.pdf|title=Reinforcement learning: An introduction|year=|isbn=|location=|page=|pages=}}</ref>{{Rp|61}} There are also non-probabilistic policies.<br />
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The policy map gives the probability of taking action <math>a</math> when in state <math>s</math>. There are also non-probabilistic policies.<br />
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策略映射给出了在状态<math>s</math>下采取行动<math>a</math>的概率。<ref name=":0">{{Cite book|url=http://people.inf.elte.hu/lorincz/Files/RL_2006/SuttonBook.pdf|title=Reinforcement learning: An introduction|year=|isbn=|location=|page=|pages=}}</ref>{{Rp|61}}此外,也存在一些非概率化的策略。<br />
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==== “状态-价值” 函数 ====<br />
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Value function <math>V_\pi(s)</math> is defined as the ''expected return'' starting with state <math>s</math>, i.e. <math>s_0 = s</math>, and successively following policy <math>\pi</math>. Hence, roughly speaking, the value function estimates "how good" it is to be in a given state.<ref name=":0" />{{Rp|60}}<br />
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Value function <math>V_\pi(s)</math> is defined as the expected return starting with state <math>s</math>, i.e. <math>s_0 = s</math>, and successively following policy <math>\pi</math>. Hence, roughly speaking, the value function estimates "how good" it is to be in a given state.<br />
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价值函数<math>V_\pi(s)</math>定义为从状态<math>s</math>开始的期望收益,即<math>s_0 = s</math>,后续的策略为<math>\pi</math>。因此,粗略地说,价值函数估计一个给定状态有多“好”。<br />
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:<math>V_\pi(s) = \operatorname E[R] = \operatorname E\left[\sum_{t=0}^\infty \gamma^t r_t\mid s_0 = s\right],</math><br />
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where the random variable <math>R</math> denotes the '''return''', and is defined as the sum of future discounted rewards{{clarify|reason=What is a discounted reward?|date=January 2019}}<br />
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where the random variable <math>R</math> denotes the return, and is defined as the sum of future discounted rewards<br />
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其中随机变量<math>R</math>表示收益,而且是未来总体收益的折现。<br />
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:<math>R=\sum_{t=0}^\infty \gamma^t r_t,</math><br />
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where <math>r_t</math> is the reward at step <math>t</math>, <math>\gamma \in [0,1) </math> is the discount-rate.<br />
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<math>r_t</math>是在时间步<math>t</math>的收益,<math>\gamma \in [0,1) </math> 是折现率。<br />
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The algorithm must find a policy with maximum expected return. From the theory of MDPs it is known that, without loss of generality, the search can be restricted to the set of so-called ''stationary'' policies. A policy is ''stationary'' if the action-distribution returned by it depends only on the last state visited (from the observation agent's history). The search can be further restricted to ''deterministic'' stationary policies. A ''deterministic stationary'' policy deterministically selects actions based on the current state. Since any such policy can be identified with a mapping from the set of states to the set of actions, these policies can be identified with such mappings with no loss of generality.<br />
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The algorithm must find a policy with maximum expected return. From the theory of MDPs it is known that, without loss of generality, the search can be restricted to the set of so-called stationary policies. A policy is stationary if the action-distribution returned by it depends only on the last state visited (from the observation agent's history). The search can be further restricted to deterministic stationary policies. A deterministic stationary policy deterministically selects actions based on the current state. Since any such policy can be identified with a mapping from the set of states to the set of actions, these policies can be identified with such mappings with no loss of generality.<br />
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算法必须找到一个期望收益最大的策略。根据 MDPs 理论,我们知道,搜索可以不失一般性地被限制在所谓的平稳政策集合中。如果策略返回的行动分布仅取决于最后访问的状态(主体的历史记录) ,则策略是平稳的。这种搜索可以进一步限制为确定性平稳策略。确定性平稳策略根据当前状态确定地选择操作。不损失一般性地说,任何这样的策略都可以通过从状态集到行动集的映射来标识。<br />
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=== 蛮力方法 ===<br />
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The brute force approach entails two steps:<br />
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蛮力方法包括两个步骤:<br />
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* For each possible policy, sample returns while following it<br />
* Choose the policy with the largest expected return<br />
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*对于每一个可能的策略,记录下每次使用该策略的收益<br />
*选择具有最大期望收益的政策<br />
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One problem with this is that the number of policies can be large, or even infinite. Another is that variance of the returns may be large, which requires many samples to accurately estimate the return of each policy.<br />
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这样做的一个问题是,策略的数量可能很大,甚至可能是无限的。另一个原因是收益的方差可能很大,这需要很多次采样来准确地估计每个策略的收益。<br />
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These problems can be ameliorated if we assume some structure and allow samples generated from one policy to influence the estimates made for others. The two main approaches for achieving this are [[#Value function|value function estimation]] and [[#Direct policy search|direct policy search]].<br />
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如果我们假设某些结构,并允许从一个策略中生成的样本影响为其他策略所做的估计,那么这些问题可以得到改善。实现这一目标的两种主要方法是价值函数估计和直接策略搜索。<br />
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=== 价值函数 ===<br />
{{see also|Value function}}<br />
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Value function approaches attempt to find a policy that maximizes the return by maintaining a set of estimates of expected returns for some policy (usually either the "current" [on-policy] or the optimal [off-policy] one).<br />
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<font color="#ff8000"> 价值函数 Value function</font>方法通过维护一组对某种策略的预期收益的估计值,来找到一个使收益最大化的策略。<br />
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These methods rely on the theory of MDPs, where optimality is defined in a sense that is stronger than the above one: A policy is called optimal if it achieves the best expected return from ''any'' initial state (i.e., initial distributions play no role in this definition). Again, an optimal policy can always be found amongst stationary policies.<br />
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这些方法依赖于 MDPs 理论,其中最优性的定义强于上述各种定义: 如果一个策略从任何初始状态都能获得最佳预期收益(即,初始分配在这个定义中没有任何作用) ,则称其为最优策略。同样,在平稳策略中总能找到最优策略。<br />
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To define optimality in a formal manner, define the value of a policy <math>\pi</math> by<br />
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要以形式化地定义最优性,可通过以下方式定义策略<math>\pi</math>的值<br />
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:<math> V^{\pi} (s) = E[R\mid s,\pi],</math><br />
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where <math>R</math> stands for the return associated with following <math>\pi</math> from the initial state <math>s</math>. Defining <math>V^*(s)</math> as the maximum possible value of <math>V^\pi(s)</math>, where <math>\pi</math> is allowed to change,<br />
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where <math>R</math> stands for the return associated with following <math>\pi</math> from the initial state <math>s</math>. Defining <math>V^*(s)</math> as the maximum possible value of <math>V^\pi(s)</math>, where <math>\pi</math> is allowed to change,<br />
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其中<math>R</math>表示初始状态<math>s</math>与策略<math>\pi</math>相关的收益。<math>V^*(s)</math>则被定义为 <math>V^\pi(s)</math>的最大可能值,其中<math>\pi</math>允许更改,<br />
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:<math>V^*(s) = \max_\pi V^\pi(s).</math><br />
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A policy that achieves these optimal values in each state is called ''optimal''. Clearly, a policy that is optimal in this strong sense is also optimal in the sense that it maximizes the expected return <math>\rho^\pi</math>, since <math>\rho^\pi = E[ V^\pi(S) ]</math>, where <math>S</math> is a state randomly sampled from the distribution <math>\mu</math>{{clarify |date=July 2018 |reason= <math>\mu</math> no previously defined}}.<br />
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A policy that achieves these optimal values in each state is called optimal. Clearly, a policy that is optimal in this strong sense is also optimal in the sense that it maximizes the expected return <math>\rho^\pi</math>, since <math>\rho^\pi = E[ V^\pi(S) ]</math>, where <math>S</math> is a state randomly sampled from the distribution <math>\mu</math>.<br />
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在每个状态下都能达到这些最优值的策略称为最优策略。显然,一个策略如果在这种强定义下是最优,那么它一定也最大化了预期收益率<math>\rho^\pi</math>,因为 <math>\rho^\pi = E[ V^\pi(S) ]</math>,其中<math>S</math>是从分布 <math>\mu</math>随机抽样得到的状态。<br />
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Although state-values suffice to define optimality, it is useful to define action-values. Given a state <math>s</math>, an action <math>a</math> and a policy <math>\pi</math>, the action-value of the pair <math>(s,a)</math> under <math>\pi</math> is defined by<br />
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Although state-values suffice to define optimality, it is useful to define action-values. Given a state <math>s</math>, an action <math>a</math> and a policy <math>\pi</math>, the action-value of the pair <math>(s,a)</math> under <math>\pi</math> is defined by<br />
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尽管“状态-值”足以定义最优性,但定义“行动-值”还是是有用的。给定一个状态<math>s</math>、一个行动<math>a</math>和一个策略<math>\pi</math>,元组(s,a)的“行动-值”的定义是<br />
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:<math>Q^\pi(s,a) = \operatorname E[R\mid s,a,\pi],\,</math><br />
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where <math>R</math> now stands for the random return associated with first taking action <math>a</math> in state <math>s</math> and following <math>\pi</math>, thereafter.<br />
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where <math>R</math> now stands for the random return associated with first taking action <math>a</math> in state <math>s</math> and following <math>\pi</math>, thereafter.<br />
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其中<math>R</math>现在代表的是随机收益,这个收益与第一次在状态<math>s</math>中采取行动的<math>a</math>和之后的策略<math>\pi</math>相关。<br />
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The theory of MDPs states that if <math>\pi^*</math> is an optimal policy, we act optimally (take the optimal action) by choosing the action from <math>Q^{\pi^*}(s,\cdot)</math> with the highest value at each state, <math>s</math>. The ''action-value function'' of such an optimal policy (<math>Q^{\pi^*}</math>) is called the ''optimal action-value function'' and is commonly denoted by <math>Q^*</math>. In summary, the knowledge of the optimal action-value function alone suffices to know how to act optimally.<br />
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The theory of MDPs states that if <math>\pi^*</math> is an optimal policy, we act optimally (take the optimal action) by choosing the action from <math>Q^{\pi^*}(s,\cdot)</math> with the highest value at each state, <math>s</math>. The action-value function of such an optimal policy (<math>Q^{\pi^*}</math>) is called the optimal action-value function and is commonly denoted by <math>Q^*</math>. In summary, the knowledge of the optimal action-value function alone suffices to know how to act optimally.<br />
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MDPs 理论指出,如果<math>\pi^*</math>是一个最优策略,那么我们通过从 <math>Q^{\pi^*}(s,\cdot)</math> 中选择每个状态<math>s</math>下的最大值来优化操作(采取最优操作)。这种最优策略的操作值函数(<math>Q^{\pi^*}</math>)称为最优操作值函数,通常由<math>Q^*</math>表示。总之,仅仅知道最优行动值函数就足以知道如何进行最优行动。<br />
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Assuming full knowledge of the MDP, the two basic approaches to compute the optimal action-value function are [[value iteration]] and [[policy iteration]]. Both algorithms compute a sequence of functions <math>Q_k</math> (<math>k=0,1,2,\ldots</math>) that converge to <math>Q^*</math>. Computing these functions involves computing expectations over the whole state-space, which is impractical for all but the smallest (finite) MDPs. In reinforcement learning methods, expectations are approximated by averaging over samples and using function approximation techniques to cope with the need to represent value functions over large state-action spaces.<br />
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Assuming full knowledge of the MDP, the two basic approaches to compute the optimal action-value function are value iteration and policy iteration. Both algorithms compute a sequence of functions <math>Q_k</math> (<math>k=0,1,2,\ldots</math>) that converge to <math>Q^*</math>. Computing these functions involves computing expectations over the whole state-space, which is impractical for all but the smallest (finite) MDPs. In reinforcement learning methods, expectations are approximated by averaging over samples and using function approximation techniques to cope with the need to represent value functions over large state-action spaces.<br />
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在充分了解 MDP 的前提下,计算最优动作值函数的两种基本方法是值迭代法和策略迭代法。两种算法都计算一个函数序列<math>Q_k</math> (<math>k=0,1,2,\ldots</math>),这个序列收敛于<math>Q^*</math> 。计算这些函数需要计算整个状态空间上的期望值,这对于除了最小(有限) MDP 之外的所有 MDP 都是不切实际的。在强化学习方法中,期望值是近似的,通过对样本进行平均,并使用函数逼近技术来满足在大型状态动作空间上表示值函数的需要。<br />
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====蒙特卡罗方法====<br />
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Monte Carlo methods can be used in an algorithm that mimics policy iteration. Policy iteration consists of two steps: ''policy evaluation'' and ''policy improvement''.<br />
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Monte Carlo methods can be used in an algorithm that mimics policy iteration. Policy iteration consists of two steps: policy evaluation and policy improvement.<br />
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<font color="#ff8000"> 蒙特卡罗方法 Monte Carlo methods</font>可用于模拟策略迭代的算法。策略迭代包括两个步骤: 策略评估和策略改进。<br />
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Monte Carlo is used in the policy evaluation step. In this step, given a stationary, deterministic policy <math>\pi</math>, the goal is to compute the function values <math>Q^\pi(s,a)</math> (or a good approximation to them) for all state-action pairs <math>(s,a)</math>. Assuming (for simplicity) that the MDP is finite, that sufficient memory is available to accommodate the action-values and that the problem is episodic and after each episode a new one starts from some random initial state. Then, the estimate of the value of a given state-action pair <math>(s,a)</math> can be computed by averaging the sampled returns that originated from <math>(s,a)</math> over time. Given sufficient time, this procedure can thus construct a precise estimate <math>Q</math> of the action-value function <math>Q^\pi</math>. This finishes the description of the policy evaluation step.<br />
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Monte Carlo is used in the policy evaluation step. In this step, given a stationary, deterministic policy <math>\pi</math>, the goal is to compute the function values <math>Q^\pi(s,a)</math> (or a good approximation to them) for all state-action pairs <math>(s,a)</math>. Assuming (for simplicity) that the MDP is finite, that sufficient memory is available to accommodate the action-values and that the problem is episodic and after each episode a new one starts from some random initial state. Then, the estimate of the value of a given state-action pair <math>(s,a)</math> can be computed by averaging the sampled returns that originated from <math>(s,a)</math> over time. Given sufficient time, this procedure can thus construct a precise estimate <math>Q</math> of the action-value function <math>Q^\pi</math>. This finishes the description of the policy evaluation step.<br />
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蒙特卡罗方法被用在了策略评估步骤。在这个步骤中,给定一个平稳的、确定性的策略<math>\pi</math>,目标是计算所有状态动作对<math>(s,a)</math>的函数值<math>Q^\pi(s,a)</math>(或者一个很好的近似值)。(为简单起见)假设 MDP 是有限的,且计算机有足够的内存来容纳动作值,问题是分阶段的的,每阶段之后一个新阶段从某个随机的初始状态开始。然后,通过对来自<math>(s,a)</math>随时间变化的抽样收益进行平均,可以计算出给定状态动作对<math>(s,a)</math>的值。给定足够的时间,这个过程可以构造出动作值函数 <math>Q^\pi</math>的一个精确的估计<math>Q</math>。<br />
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In the policy improvement step, the next policy is obtained by computing a greedy policy with respect to <math>Q</math>: Given a state <math>s</math>, this new policy returns an action that maximizes <math>Q(s,\cdot)</math>. In practice lazy evaluation can defer the computation of the maximizing actions to when they are needed.<br />
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在策略改进步骤中,新的策略是通过计算关于<math>Q</math>的贪婪策略获得的: 给定一个状态<math>s</math>,这个新策略返回一个最大化<math>Q(s,\cdot)</math>的行动。实际上,惰懒计算可以将最大化行动的计算推迟到需要使用到它们的时候。<br />
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Problems with this procedure include:<br />
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Problems with this procedure include:<br />
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这一方法的问题包括:<br />
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* The procedure may spend too much time evaluating a suboptimal policy.<br />
* It uses samples inefficiently in that a long trajectory improves the estimate only of the ''single'' state-action pair that started the trajectory.<br />
* When the returns along the trajectories have ''high variance'', convergence is slow.<br />
* It works in <u>episodic problems</u> only;<br />
* It works in small, finite MDPs only.<br />
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*程序可能会花过多的时间在评估次优策略上<br />
*它使用样本的效率很低,因为长过程只会提高对启动轨迹的那一个“状态-行动“元组的估计 <br />
*当过程的收益具有“高方差”时,收敛速度较慢 <br />
*它只适用于分阶段式问题<br />
*它只适用于小的,有限的马尔可夫决策。<br />
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====时序差分方法====<br />
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The first problem is corrected by allowing the procedure to change the policy (at some or all states) before the values settle. This too may be problematic as it might prevent convergence. Most current algorithms do this, giving rise to the class of ''generalized policy iteration'' algorithms. Many ''actor critic'' methods belong to this category.<br />
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The first problem is corrected by allowing the procedure to change the policy (at some or all states) before the values settle. This too may be problematic as it might prevent convergence. Most current algorithms do this, giving rise to the class of generalized policy iteration algorithms. Many actor critic methods belong to this category.<br />
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第一个问题通过允许程序在值确定之前更改策略(在部分或全部状态)来得到纠正。这也可能也是有问题的,因为它可能会阻止收敛。目前大多数算法都是这样做的,所以一类广义策略迭代算法就产生了。许多“行动者-批评者”方法都属于这一范畴。<br />
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TThe second issue can be corrected by allowing trajectories to contribute to any state-action pair in them. This may also help to some extent with the third problem, although a better solution when returns have high variance is Sutton's [[temporal difference]] (TD) methods that are based on the recursive [[Bellman equation]].<ref>{{cite thesis|last = Sutton|first = Richard S.|title= Temporal Credit Assignment in Reinforcement Learning|degree= PhD|publisher = University of Massachusetts, Amherst, MA|url= http://incompleteideas.net/sutton/publications.html#PhDthesis|authorlink = Richard S. Sutton|year= 1984 }}</ref>{{sfn|Sutton|Barto|1998|loc=[http://incompleteideas.net/sutton/book/ebook/node60.html §6. Temporal-Difference Learning]}} The computation in TD methods can be incremental (when after each transition the memory is changed and the transition is thrown away), or batch (when the transitions are batched and the estimates are computed once based on the batch). Batch methods, such as the least-squares temporal difference method,<ref>{{cite journal<br />
| doi = 10.1023/A:1018056104778<br />
| last1 = Bradtke | first1 = Steven J. | authorlink1 = Steven J. Bradtke<br />
| last2 = Barto | first2 = Andrew G. | authorlink2 = Andrew G. Barto<br />
| title = Learning to predict by the method of temporal differences<br />
| journal = Machine Learning<br />
| volume = 22<br />
| pages = 33–57<br />
| year = 1996<br />
| citeseerx = 10.1.1.143.857 | s2cid = 20327856 }}</ref> may use the information in the samples better, while incremental methods are the only choice when batch methods are infeasible due to their high computational or memory complexity. Some methods try to combine the two approaches. Methods based on temporal differences also overcome the fourth issue.<br />
<br />
The second issue can be corrected by allowing trajectories to contribute to any state-action pair in them. This may also help to some extent with the third problem, although a better solution when returns have high variance is Sutton's temporal difference (TD) methods that are based on the recursive Bellman equation. The computation in TD methods can be incremental (when after each transition the memory is changed and the transition is thrown away), or batch (when the transitions are batched and the estimates are computed once based on the batch). Batch methods, such as the least-squares temporal difference method, may use the information in the samples better, while incremental methods are the only choice when batch methods are infeasible due to their high computational or memory complexity. Some methods try to combine the two approaches. Methods based on temporal differences also overcome the fourth issue.<br />
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第二个问题可以通过允许过程对其中的任何“状态-行动”对做出贡献而得到纠正。 尽管收益具有高方差时,更好的解决方案是基于递归Bellman方程的Sutton的时序差分(TD)方法,但这在某种程度上也可以解决第三个问题。 TD方法中的计算可以是增量的(在每次转换后更改内存并丢弃转换),也可以是批处理(对转换进行批处理并且一次完成估算)。 批处理方法(例如最小二乘时差方法)<ref>{{cite journal<br />
| doi = 10.1023/A:1018056104778<br />
| last1 = Bradtke | first1 = Steven J. | authorlink1 = Steven J. Bradtke<br />
| last2 = Barto | first2 = Andrew G. | authorlink2 = Andrew G. Barto<br />
| title = Learning to predict by the method of temporal differences<br />
| journal = Machine Learning<br />
| volume = 22<br />
| pages = 33–57<br />
| year = 1996<br />
| citeseerx = 10.1.1.143.857 | s2cid = 20327856 }}</ref>可能会更好地使用样本中的信息,而增量方法是由于批处理方法的高计算或内存复杂性而无法使用的唯一选择。 一些方法尝试将两种方法结合起来。 基于时序差分的方法也克服了第四个问题。<br />
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In order to address the fifth issue, ''function approximation methods'' are used. ''Linear function approximation'' starts with a mapping <math>\phi</math> that assigns a finite-dimensional vector to each state-action pair. Then, the action values of a state-action pair <math>(s,a)</math> are obtained by linearly combining the components of <math>\phi(s,a)</math> with some ''weights'' <math>\theta</math>:<br />
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In order to address the fifth issue, function approximation methods are used. Linear function approximation starts with a mapping <math>\phi</math> that assigns a finite-dimensional vector to each state-action pair. Then, the action values of a state-action pair <math>(s,a)</math> are obtained by linearly combining the components of <math>\phi(s,a)</math> with some weights <math>\theta</math>:<br />
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为了解决第五个问题,我们使用了函数逼近方法。线性函数逼近从一个映射 <math>\phi</math>开始,它为每个“状态-行动”元组分配一个有限维向量。然后,通过线性组合<math>\phi(s,a)</math>的分量和一些权重 <math>\theta</math> 的分量,得到状态动作对<math>(s,a)</math>的动作值:<br />
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:<math>Q(s,a) = \sum_{i=1}^d \theta_i \phi_i(s,a).</math><br />
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The algorithms then adjust the weights, instead of adjusting the values associated with the individual state-action pairs. Methods based on ideas from nonparametric statistics (which can be seen to construct their own features) have been explored.<br />
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然后,算法会调整权重,而不是调整与各个“状态-行动”对相关联的值。基于无参数统计的方法也被研究过了(可以看出它们构造了自己的特征)。<br />
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Value iteration can also be used as a starting point, giving rise to the Q-learning algorithm and its many variants.<ref>{{cite thesis<br />
| last = Watkins | first = Christopher J.C.H. | authorlink = Christopher J.C.H. Watkins<br />
| degree= PhD<br />
| title= Learning from Delayed Rewards<br />
| year= 1989 <br />
| publisher = King’s College, Cambridge, UK<br />
| url= http://www.cs.rhul.ac.uk/~chrisw/new_thesis.pdf}}</ref><br />
<br />
<br />
值迭代也可以被用作开始点,催生出了Q-学习算法以及它的各种变体。<ref>{{cite thesis<br />
| last = Watkins | first = Christopher J.C.H. | authorlink = Christopher J.C.H. Watkins<br />
| degree= PhD<br />
| title= Learning from Delayed Rewards<br />
| year= 1989 <br />
| publisher = King’s College, Cambridge, UK<br />
| url= http://www.cs.rhul.ac.uk/~chrisw/new_thesis.pdf}}</ref><br />
<br />
<br />
The problem with using action-values is that they may need highly precise estimates of the competing action values that can be hard to obtain when the returns are noisy, though this problem is mitigated to some extent by temporal difference methods. Using the so-called compatible function approximation method compromises generality and efficiency. Another problem specific to TD comes from their reliance on the recursive Bellman equation. Most TD methods have a so-called <math>\lambda</math> parameter <math>(0\le \lambda\le 1)</math> that can continuously interpolate between Monte Carlo methods that do not rely on the Bellman equations and the basic TD methods that rely entirely on the Bellman equations. This can be effective in palliating this issue.<br />
<br />
The problem with using action-values is that they may need highly precise estimates of the competing action values that can be hard to obtain when the returns are noisy, though this problem is mitigated to some extent by temporal difference methods. Using the so-called compatible function approximation method compromises generality and efficiency. Another problem specific to TD comes from their reliance on the recursive Bellman equation. Most TD methods have a so-called <math>\lambda</math> parameter <math>(0\le \lambda\le 1)</math> that can continuously interpolate between Monte Carlo methods that do not rely on the Bellman equations and the basic TD methods that rely entirely on the Bellman equations. This can be effective in palliating this issue.<br />
<br />
使用“行动-值”的问题是,它们可能需要对相互竞争的动作值进行高度精确的估计,而当收益是有噪声时,这个问题可能很难得到,尽管时序差分方法在一定程度上缓解了这个问题。使用所谓的兼容函数逼近方法会损害通用性和效率。另一个特定于 TD 的问题来自于他们对递归贝尔曼方程的依赖。大多数 TD 方法都有一个所谓的λ参数(0≤λ≤1) ,可以在不依赖于 Bellman 方程的 蒙特卡洛方法和完全依赖于 Bellman 方程的基本 TD 方法之间连续插值。这可以有效地缓解这个问题。<br />
<br />
=== 直接策略搜索 ===<br />
<br />
An alternative method is to search directly in (some subset of) the policy space, in which case the problem becomes a case of stochastic optimization. The two approaches available are gradient-based and gradient-free methods.<br />
<br />
另一种方法是直接在策略空间(的子集)中搜索。使用这种方法,问题就变成了随机优化问题。现有的两种方法是基于梯度的方法和无梯度的方法。<br />
<br />
<br />
Gradient-based methods (policy gradient methods) start with a mapping from a finite-dimensional (parameter) space to the space of policies: given the parameter vector <math>\theta</math>, let <math>\pi_\theta</math> denote the policy associated to <math>\theta</math>. Defining the performance function by<br />
<br />
基于梯度的方法(策略梯度方法)从有限维(参数)空间到策略空间的映射开始: 给定参数向量<math>\theta</math>,让<math>\pi_\theta</math>表示与<math>\theta</math>相关的策略。通过以下方式定义性能函数<br />
<br />
<br />
:<math>\rho(\theta) = \rho^{\pi_\theta},</math><br />
<br />
<br />
under mild conditions this function will be differentiable as a function of the parameter vector <math>\theta</math>. If the gradient of <math>\rho</math> was known, one could use gradient ascent. Since an analytic expression for the gradient is not available, only a noisy estimate is available. Such an estimate can be constructed in many ways, giving rise to algorithms such as Williams' REINFORCE method<ref>{{cite conference<br />
| last = Williams | first = Ronald J. | authorlink = Ronald J. Williams <br />
| title = A class of gradient-estimating algorithms for reinforcement learning in neural networks<br />
| booktitle = Proceedings of the IEEE First International Conference on Neural Networks<br />
| year = 1987| citeseerx = 10.1.1.129.8871 }}</ref> (which is known as the likelihood ratio method in the simulation-based optimization literature).<ref>{{cite conference<br />
| last1 = Peters | first1 = Jan | authorlink1 = Jan Peters (researcher)<br />
| last2 = Vijayakumar | first2 = Sethu | authorlink2 = Sethu Vijayakumar<br />
| last3 = Schaal | first3 = Stefan | authorlink3 = Stefan Schaal<br />
| title = Reinforcement Learning for Humanoid Robotics<br />
| booktitle = IEEE-RAS International Conference on Humanoid Robots<br />
| year = 2003<br />
| url = http://www-clmc.usc.edu/publications/p/peters-ICHR2003.pdf}}</ref> Policy search methods have been used in the [[robotics]] context.<ref>{{Cite book|title = A Survey on Policy Search for Robotics|last1 = Deisenroth|first1 = Marc Peter|last2 = Neumann|first2 = Gerhard|last3 = Peters|first3 = Jan|publisher = NOW Publishers|year = 2013|series = Foundations and Trends in Robotics|volume = 2|issue = 1–2|pages = 1–142 |authorlink1 = Marc Peter Deisenroth|authorlink2 = Gerhard Neumann|authorlink3 = Jan Peters (researcher)|hdl = 10044/1/12051|doi = 10.1561/2300000021|url = http://eprints.lincoln.ac.uk/28029/1/PolicySearchReview.pdf}}</ref> Many policy search methods may get stuck in local optima (as they are based on local search).<br />
<br />
通常情况下,这个函数是关于参数<math>\theta</math>可微的。如果已知参数<math>\rho</math>的梯度,则可以直接使用梯度下降法。但是,我们不能得到关于梯度的解析式,只能得到一个有噪的估计量。这个估计量可以通过许多方法来构建,由此诞生了像REINFORCE这样的算法。<ref>{{cite conference<br />
| last = Williams | first = Ronald J. | authorlink = Ronald J. Williams <br />
| title = A class of gradient-estimating algorithms for reinforcement learning in neural networks<br />
| booktitle = Proceedings of the IEEE First International Conference on Neural Networks<br />
| year = 1987| citeseerx = 10.1.1.129.8871 }}</ref> (which is known as the likelihood ratio method in the simulation-based optimization literature).<ref>{{cite conference<br />
| last1 = Peters | first1 = Jan | authorlink1 = Jan Peters (researcher)<br />
| last2 = Vijayakumar | first2 = Sethu | authorlink2 = Sethu Vijayakumar<br />
| last3 = Schaal | first3 = Stefan | authorlink3 = Stefan Schaal<br />
| title = Reinforcement Learning for Humanoid Robotics<br />
| booktitle = IEEE-RAS International Conference on Humanoid Robots<br />
| year = 2003<br />
| url = http://www-clmc.usc.edu/publications/p/peters-ICHR2003.pdf}}</ref> Policy search methods have been used in the robotics context.<ref>{{Cite book|title = A Survey on Policy Search for Robotics|last1 = Deisenroth|first1 = Marc Peter|last2 = Neumann|first2 = Gerhard|last3 = Peters|first3 = Jan|publisher = NOW Publishers|year = 2013|series = Foundations and Trends in Robotics|volume = 2|issue = 1–2|pages = 1–142 |authorlink1 = Marc Peter Deisenroth|authorlink2 = Gerhard Neumann|authorlink3 = Jan Peters (researcher)|hdl = 10044/1/12051|doi = 10.1561/2300000021|url = http://eprints.lincoln.ac.uk/28029/1/PolicySearchReview.pdf}}</ref><br />
许多策略搜索方法会陷入局部最优点(有哪位他们本就是基于局部搜索的优化方法)<br />
<br />
<br />
A large class of methods avoids relying on gradient information. These include [[simulated annealing]], cross-entropy search or methods of evolutionary computation. Many gradient-free methods can achieve (in theory and in the limit) a global optimum.<br />
<br />
A large class of methods avoids relying on gradient information. These include simulated annealing, cross-entropy search or methods of evolutionary computation. Many gradient-free methods can achieve (in theory and in the limit) a global optimum.<br />
<br />
此外,还有大量避免了使用梯度信息的方法。这些方法包括模拟退火、交叉熵搜索或者演化计算搜索方法。许多无梯度方法可以(在理论上和极限的意义上)得到一个全局最优解。<br />
<br />
<br />
<br />
Policy search methods may converge slowly given noisy data. For example, this happens in episodic problems when the trajectories are long and the variance of the returns is large. Value-function based methods that rely on temporal differences might help in this case. In recent years, ''actor–critic methods'' have been proposed and performed well on various problems.<ref>{{Cite web|url=https://medium.com/emergent-future/simple-reinforcement-learning-with-tensorflow-part-8-asynchronous-actor-critic-agents-a3c-c88f72a5e9f2|title=Simple Reinforcement Learning with Tensorflow Part 8: Asynchronous Actor-Critic Agents (A3C)|last=Juliani|first=Arthur|date=2016-12-17|website=Medium|access-date=2018-02-22}}</ref><br />
<br />
Policy search methods may converge slowly given noisy data. For example, this happens in episodic problems when the trajectories are long and the variance of the returns is large. Value-function based methods that rely on temporal differences might help in this case. In recent years, actor–critic methods have been proposed and performed well on various problems.<br />
<br />
政策搜索方法在处理有噪数据时可能会收敛得很缓慢。例如,这种情况在过程较漫长,且收益的方差较大的场景问题中就会发生。依赖于时间差异的基于价值函数的方法在这种情况下可能会有所帮助。近年来,“行动者–批评者”方法被提出,并在各种问题上取得了良好的效果。<br />
<br />
== 理论 ==<br />
<br />
<br />
Both the asymptotic and finite-sample behavior of most algorithms is well understood. Algorithms with provably good online performance (addressing the exploration issue) are known.<br />
<br />
Both the asymptotic and finite-sample behavior of most algorithms is well understood. Algorithms with provably good online performance (addressing the exploration issue) are known.<br />
<br />
人们已经能很好地理解大多数算法的渐近行为和有限样本行为,还知道了被证明具有良好在线性能(解决探索问题)的算法。<br />
<br />
<br />
<br />
Efficient exploration of MDPs is given in Burnetas and Katehakis (1997).<ref>{{citation | last1 = Burnetas|first1 = Apostolos N.|last2 = Katehakis|first2 = Michael N.|authorlink2 = Michael N. Katehakis|year = 1997|title = Optimal adaptive policies for Markov Decision Processes|journal = Mathematics of Operations Research|volume = 22|pages = 222–255|ref = harv|doi=10.1287/moor.22.1.222}}</ref>. Finite-time performance bounds have also appeared for many algorithms, but these bounds are expected to be rather loose and thus more work is needed to better understand the relative advantages and limitations.<br />
<br />
Efficient exploration of MDPs is given in Burnetas and Katehakis (1997).. Finite-time performance bounds have also appeared for many algorithms, but these bounds are expected to be rather loose and thus more work is needed to better understand the relative advantages and limitations.<br />
<br />
Burnetas 和 Katehakis (1997)<ref>{{citation | last1 = Burnetas|first1 = Apostolos N.|last2 = Katehakis|first2 = Michael N.|authorlink2 = Michael N. Katehakis|year = 1997|title = Optimal adaptive policies for Markov Decision Processes|journal = Mathematics of Operations Research|volume = 22|pages = 222–255|ref = harv|doi=10.1287/moor.22.1.222}}</ref>给出了高效探索 MDPs 的方法。许多算法的'''有限时间性能界限'''也已被找到,但这些界限相当宽松,人们还需要做更多的工作,以更好地了解相对优势和局限性。<br />
<br />
<br />
<br />
For incremental algorithms, asymptotic convergence issues have been settled{{Clarify|reason=What are the issues that have been settled?|date=January 2020}}. Temporal-difference-based algorithms converge under a wider set of conditions than was previously possible (for example, when used with arbitrary, smooth function approximation).<br />
<br />
For incremental algorithms, asymptotic convergence issues have been settled. Temporal-difference-based algorithms converge under a wider set of conditions than was previously possible (for example, when used with arbitrary, smooth function approximation).<br />
<br />
增量算法的提出解决了渐近收敛问题。基于时间差异的算法能在比以前更广泛的条件下达到收敛(例如,与任意的、平滑的函数逼近一起使用时)。<br />
<br />
== 研究 ==<br />
<br />
Research topics include <br />
<br />
Research topics include <br />
<br />
现在强化学习的研究课题包括:<br />
<br />
* adaptive methods that work with fewer (or no) parameters under a large number of conditions<br />
* addressing the exploration problem in large MDPs<br />
* large-scale empirical evaluations<br />
* learning and acting under partial information (e.g., using predictive state representation)<br />
* modular and hierarchical reinforcement learning<ref>{{Cite journal|last=Kulkarni|first=Tejas D.|last2=Narasimhan|first2=Karthik R.|last3=Saeedi|first3=Ardavan|last4=Tenenbaum|first4=Joshua B.|date=2016|title=Hierarchical Deep Reinforcement Learning: Integrating Temporal Abstraction and Intrinsic Motivation|url=http://dl.acm.org/citation.cfm?id=3157382.3157509|journal=Proceedings of the 30th International Conference on Neural Information Processing Systems|series=NIPS'16|location=USA|publisher=Curran Associates Inc.|pages=3682–3690|isbn=978-1-5108-3881-9|bibcode=2016arXiv160406057K|arxiv=1604.06057}}</ref><br />
* improving existing value-function and policy search methods<br />
* algorithms that work well with large (or continuous) action spaces<br />
* transfer learning<ref>{{Cite journal|last=George Karimpanal|first=Thommen|last2=Bouffanais|first2=Roland|date=2019|title=Self-organizing maps for storage and transfer of knowledge in reinforcement learning|journal=Adaptive Behavior|language=en|volume=27|issue=2|pages=111–126|doi=10.1177/1059712318818568|issn=1059-7123|arxiv=1811.08318}}</ref><br />
* lifelong learning<br />
* efficient sample-based planning (e.g., based on [[Monte Carlo tree search]]). <br />
*bug detection in software projects<ref>{{Cite web|url=https://cie.acm.org/articles/use-reinforcements-learning-testing-game-mechanics/|title=On the Use of Reinforcement Learning for Testing Game Mechanics : ACM - Computers in Entertainment|website=cie.acm.org|language=en|access-date=2018-11-27}}</ref><br />
* Intrinsic motivation which differentiates information-seeking, curiosity-type behaviours from task-dependent goal-directed behaviours (typically) by introducing a reward function based on maximising novel information<ref name=kaplan2004>Kaplan, F. and Oudeyer, P. (2004). Maximizing learning progress: an internal reward system for development. Embodied artificial intelligence, pages 629–629.</ref><ref name=klyubin2008>Klyubin, A., Polani, D., and Nehaniv, C. (2008). Keep your options open: an information-based driving principle for sensorimotor systems. PloS ONE, 3(12):e4018. https://dx.doi.org/10.1371%2Fjournal.pone.0004018</ref><ref name=barto2013>Barto, A. G. (2013). “Intrinsic motivation and reinforcement learning,” in Intrinsically Motivated Learning in Natural and Artificial Systems (Berlin; Heidelberg: Springer), 17–47</ref><br />
*Multiagent or distributed reinforcement learning is a topic of interest. Applications are expanding.<ref>{{Cite web|url=http://umichrl.pbworks.com/Successes-of-Reinforcement-Learning/|title=Reinforcement Learning / Successes of Reinforcement Learning|website=umichrl.pbworks.com|access-date=2017-08-06}}</ref><br />
* Actor-critic reinforcement learning <br />
* Reinforcement learning algorithms such as TD learning are under investigation as a model for dopamine-based learning in the brain. In this model, the dopaminergic projections from the substantia nigra to the basal ganglia function as the prediction error. Reinforcement learning has been used as a part of the model for human skill learning, especially in relation to the interaction between implicit and explicit learning in skill acquisition (the first publication on this application was in 1995–1996).<ref>[http://incompleteideas.net/sutton/RL-FAQ.html#behaviorism] {{webarchive|url=https://web.archive.org/web/20170426212431/http://incompleteideas.net/sutton/RL-FAQ.html|date=2017-04-26}}</ref><br />
<br />
<br />
*在诸多条件下使用较少(或没有)参数的自适应方法<br />
*解决在大规模MDPs里的探索问题<br />
*大规模实证评价<br />
*部分可观测马尔可夫决策过程下的学习与行动 <br />
*模块化分层的强化学习 <br />
*改进现有的价值函数和策略搜索方法 <br />
*适用于大型(或连续)动作空间的算法 <br />
*迁移学习<ref>{{Cite journal|last=George Karimpanal|first=Thommen|last2=Bouffanais|first2=Roland|date=2019|title=Self-organizing maps for storage and transfer of knowledge in reinforcement learning|journal=Adaptive Behavior|language=en|volume=27|issue=2|pages=111–126|doi=10.1177/1059712318818568|issn=1059-7123|arxiv=1811.08318}}</ref><br />
*终生学习<br />
*基于样本的高效规划算法(比如,基于蒙特卡洛搜索树的方法)<br />
*软件项目中的缺陷检测 s<ref>{{Cite web|url=https://cie.acm.org/articles/use-reinforcements-learning-testing-game-mechanics/|title=On the Use of Reinforcement Learning for Testing Game Mechanics : ACM - Computers in Entertainment|website=cie.acm.org|language=en|access-date=2018-11-27}}</ref><br />
*通过引入最大化新信息的奖励函数来区分主体(agent)信息收集等好奇行为,以及任务导向等有目标行为的不同内在动机 <ref name=kaplan2004>Kaplan, F. and Oudeyer, P. (2004). Maximizing learning progress: an internal reward system for development. Embodied artificial intelligence, pages 629–629.</ref><ref name=klyubin2008>Klyubin, A., Polani, D., and Nehaniv, C. (2008). Keep your options open: an information-based driving principle for sensorimotor systems. PloS ONE, 3(12):e4018. https://dx.doi.org/10.1371%2Fjournal.pone.0004018</ref><ref name=barto2013>Barto, A. G. (2013). “Intrinsic motivation and reinforcement learning,” in Intrinsically Motivated Learning in Natural and Artificial Systems (Berlin; Heidelberg: Springer), 17–47</ref><br />
*多主体或分布式强化学习也是令人感兴趣的话题,这方面的应用正在不断扩大。<br />
*“行动者-批评家”强化学习<br />
*像 TD 学习这样的强化学习学习算法被研究用来建模大脑中基于多巴胺的学习模型。在这个模型中,从黑质到基底神经节的多巴胺能投射可以被视为预测错误。强化学习被用作是人类技能学习模型的一部分,特别是关于技能习得中内隐和外显学习之间的相互作用(这一应用的第一次出版是在1995-1996年)。<br />
<br />
== 强化学习算法比较 ==<br />
<br />
{| class="wikitable"<br />
|-<br />
! Algorithm !! Description !! Model !! Policy !! Action Space !! State Space !! Operator<br />
|-<br />
| [[Monte Carlo method|Monte Carlo]] || Every visit to Monte Carlo || Model-Free || Either || Discrete || Discrete || Sample-means<br />
|-<br />
| Q-learning || State–action–reward–state || Model-Free || Off-policy || Discrete || Discrete || Q-value<br />
|-<br />
| SARSA || State–action–reward–state–action || Model-Free || On-policy || Discrete || Discrete || Q-value<br />
|-<br />
| Q-learning - Lambda || State–action–reward–state with eligibility traces|| Model-Free || Off-policy || Discrete || Discrete || Q-value<br />
|-<br />
| SARSA - Lambda || State–action–reward–state–action with eligibility traces || Model-Free || On-policy || Discrete || Discrete || Q-value<br />
|-<br />
| DQN || Deep Q Network || Model-Free || Off-policy || Discrete || Continuous || Q-value<br />
|-<br />
| DDPG || Deep Deterministic Policy Gradient || Model-Free || Off-policy || Continuous || Continuous || Q-value<br />
|-<br />
| A3C || Asynchronous Advantage Actor-Critic Algorithm || Model-Free || On-policy || Continuous || Continuous || Advantage<br />
|-<br />
| NAF || Q-Learning with Normalized Advantage Functions || Model-Free || Off-policy || Continuous || Continuous || Advantage<br />
|-<br />
| TRPO || Trust Region Policy Optimization || Model-Free || On-policy || Continuous || Continuous || Advantage<br />
|-<br />
| PPO || Proximal Policy Optimization || Model-Free || On-policy || Continuous || Continuous || Advantage<br />
|-<br />
|TD3<br />
|Twin Delayed Deep Deterministic Policy Gradient<br />
|Model-Free<br />
|Off-policy<br />
|Continuous<br />
|Continuous<br />
|Q-value<br />
|-<br />
|SAC<br />
|Soft Actor-Critic<br />
|Model-Free<br />
|Off-policy<br />
|Continuous<br />
|Continuous<br />
|Advantage<br />
|}<br />
<br />
<br />
{| class="wikitable"<br />
|-<br />
! 算法 !! 描述 !! 模型 !! 策略 !! 行动空间 !! 状态空间 !! 操作符<br />
|-<br />
| 蒙特卡洛 || 采样 || 无模型 || Either || 离散 || 离散 || 样本均值<br />
|-<br />
| Q-learning || 状态–行动–奖励–状态 || 无模型 || Off || 离散 || 离散 || Q值<br />
|-<br />
| SARSA || 状态–行动–奖励–状态-行动 || 无模型 || On || 离散 || 离散 || Q值<br />
|-<br />
| Q-learning - Lambda || 带资格痕迹的状态–行动–奖励–状态 || 无模型 || Off || 离散 || 离散 || Q值<br />
|-<br />
| SARSA - Lambda || 带资格痕迹的状态–行动–奖励–状态-行动 || 无模型 || On || 离散 || 离散 || Q值<br />
|-<br />
| DQN || 深度Q网络 || 无模型 || Off || 离散 || 连续 || Q值<br />
|-<br />
| DDPG || 深度确定性策略梯度 || 无模型 || Off || 连续 || 连续 || Q值<br />
|-<br />
| A3C || 异步优势行“动者-批评者”算法 || 无模型 || On || 连续 || 连续 || 优势(Advantage)<br />
|-<br />
| NAF || 带归一化优势函数的Q-学习 || 无模型 || Off || 连续 || 连续 || 优势<br />
|-<br />
| TRPO || 信任区域策略的最优化 || 无模型 || On || 连续 || 连续 || 优势<br />
|-<br />
| PPO || 近端策略最优化 || 无模型 || On || 连续 || 连续 || 优势<br />
|-<br />
|TD3<br />
|双延迟深度确定性策略梯度<br />
|无模型<br />
|Off<br />
|连续<br />
|连续<br />
|Q-值<br />
|-<br />
|SAC<br />
|软“行动者-批评者”<br />
|无模型<br />
|Off<br />
|连续<br />
|连续<br />
|优势<br />
|}<br />
<br />
<br />
<br />
=== 深度强度学习 ===<br />
<br />
This approach extends reinforcement learning by using a deep neural network and without explicitly designing the state space.<ref name="intro_deep_RL">{{cite journal |first= Vincent|display-authors=etal|last= Francois-Lavet |year=2018 |title= An Introduction to Deep Reinforcement Learning |journal=Foundations and Trends in Machine Learning|volume=11 |issue=3–4 |pages=219–354 |doi=10.1561/2200000071|arxiv= 1811.12560 |bibcode=2018arXiv181112560F}}</ref> The work on learning ATARI games by Google DeepMind increased attention to deep reinforcement learning or end-to-end reinforcement learning.<ref name="DQN2">{{cite journal |first= Volodymyr|display-authors=etal|last= Mnih |year=2015 |title= Human-level control through deep reinforcement learning |journal=Nature|volume=518 |issue=7540 |pages=529–533 |doi=10.1038/nature14236|pmid= 25719670 |bibcode=2015Natur.518..529M |url=https://www.semanticscholar.org/paper/e0e9a94c4a6ba219e768b4e59f72c18f0a22e23d}}</ref><br />
<br />
This approach extends reinforcement learning by using a deep neural network and without explicitly designing the state space. The work on learning ATARI games by Google DeepMind increased attention to deep reinforcement learning or end-to-end reinforcement learning.<br />
<br />
这种方法通过使用深层神经网络来扩展强化学习,因此不需要明确地设计状态空间。<ref name="intro_deep_RL">{{cite journal |first= Vincent|display-authors=etal|last= Francois-Lavet |year=2018 |title= An Introduction to Deep Reinforcement Learning |journal=Foundations and Trends in Machine Learning|volume=11 |issue=3–4 |pages=219–354 |doi=10.1561/2200000071|arxiv= 1811.12560 |bibcode=2018arXiv181112560F}}</ref>谷歌 DeepMind 在雅达利游戏上的研究提高了人们对强化学习或端到端强化学习游戏的关注。<ref name="DQN2">{{cite journal |first= Volodymyr|display-authors=etal|last= Mnih |year=2015 |title= Human-level control through deep reinforcement learning |journal=Nature|volume=518 |issue=7540 |pages=529–533 |doi=10.1038/nature14236|pmid= 25719670 |bibcode=2015Natur.518..529M |url=https://www.semanticscholar.org/paper/e0e9a94c4a6ba219e768b4e59f72c18f0a22e23d}}</ref><br />
<br />
<br />
<br />
=== 逆强化学习 ===<br />
<br />
In inverse reinforcement learning (IRL), no reward function is given. Instead, the reward function is inferred given an observed behavior from an expert. The idea is to mimic observed behavior, which is often optimal or close to optimal.<ref>{{cite book |last=Ng |first=A. Y. |last2=Russell |first2=S. J. |year=2000 |chapter=Algorithms for Inverse Reinforcement Learning |title=Proceeding ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning |pages=663–670 |isbn=1-55860-707-2 |chapterurl=https://ai.stanford.edu/~ang/papers/icml00-irl.pdf }}</ref><br />
<br />
In inverse reinforcement learning (IRL), no reward function is given. Instead, the reward function is inferred given an observed behavior from an expert. The idea is to mimic observed behavior, which is often optimal or close to optimal.<br />
<br />
在逆强化学习中,奖励函数是没有给出的。相反,奖励功能是根据观察到的专家的行为推断出来的。这个想法是为了模仿观察到的行为,且通常是最优的或接近最优的。<ref>{{cite book |last=Ng |first=A. Y. |last2=Russell |first2=S. J. |year=2000 |chapter=Algorithms for Inverse Reinforcement Learning |title=Proceeding ICML '00 Proceedings of the Seventeenth International Conference on Machine Learning |pages=663–670 |isbn=1-55860-707-2 |chapterurl=https://ai.stanford.edu/~ang/papers/icml00-irl.pdf }}</ref><br />
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=== 学徒学习 ===<br />
<br />
In apprenticeship learning, an expert demonstrates the target behavior. The system tries to recover the policy via observation.<br />
<br />
In apprenticeship learning, an expert demonstrates the target behavior. The system tries to recover the policy via observation.<br />
<br />
在学徒学习过程中,师傅会展示目标行为,系统(学徒)试图通过观察来还原策略。<br />
<br />
== See also ==<br />
参阅<br />
{{Div col|colwidth=20em}}<br />
<br />
* [[Temporal difference learning]]<br />
<font color="#ff8000"> 时间差分学习</font><br />
* [[Q-learning]]<br />
<font color="#ff8000"> q-学习</font><br />
* [[State–action–reward–state–action]] (SARSA)<br />
<font color="#ff8000"> SARSA算法</font><br />
* [[Fictitious play]]<br />
<font color="#ff8000"> 虚构对策</font><br />
* [[Learning classifier system]]<br />
<font color="#ff8000"> 学习分类器系统</font><br />
* [[Optimal control]]<br />
<font color="#ff8000"> 最优控制</font><br />
* [[Dynamic treatment regimes]]<br />
<font color="#ff8000"> 动态处理方案</font><br />
* [[Error-driven learning]]<br />
<font color="#ff8000"> 错误驱动学习</font><br />
* [[Multi-agent system]]<br />
<font color="#ff8000"> 多主体系统</font><br />
* [[Distributed artificial intelligence]]<br />
<font color="#ff8000"> 分布式人工智能</font><br />
* [[Intrinsic motivation (artificial intelligence)|Intrinsic motivation]]<br />
<font color="#ff8000"> 内在动力(人工智能)</font><br />
{{Div col end}}<br />
<br />
<br />
<br />
== References ==<br />
参考<br />
{{Reflist|30em}}<br />
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<br />
<br />
== 延伸阅读 ==<br />
* {{cite journal|last1 = Auer|first1 = Peter|last2 = Jaksch|first2 = Thomas |last3 = Ortner|first3 = Ronald |year = 2010|title = Near-optimal regret bounds for reinforcement learning|url = http://jmlr.csail.mit.edu/papers/v11/jaksch10a.html|journal = Journal of Machine Learning Research|volume = 11|pages = 1563–1600 |authorlink1 = Peter Auer}}<br />
* {{cite book|url = http://www.dcsc.tudelft.nl/rlbook/|title = Reinforcement Learning and Dynamic Programming using Function Approximators|last1 = Busoniu|first1 = Lucian|last2 = Babuska|first2 = Robert|last3 = De Schutter|first3 = Bart|last4 = Ernst|first4 = Damien|publisher = Taylor & Francis CRC Press|year = 2010|isbn = 978-1-4398-2108-4|pages = |authorlink3 = Bart De Schutter }}<br />
* {{cite journal<br />
| doi = 10.1561/2200000071<br />
| last1 = François-Lavet | first1 = Vincent<br />
| last2 = Henderson | first2 = Peter<br />
| last3 = Islam | first3 = Riashat<br />
| last4 = Bellemare | first4 = Marc G.<br />
| last5 = Pineau | first5 = Joelle<br />
| title = An Introduction to Deep Reinforcement Learning<br />
| journal = Foundations and Trends in Machine Learning<br />
| volume = 11<br />
| issue = 3–4 | pages = 219–354<br />
| year = 2018<br />
| arxiv = 1811.12560 | bibcode = 2018arXiv181112560F | s2cid = 54434537 }}<br />
* {{cite book<br />
| last = Powell | first = Warren<br />
| title = Approximate dynamic programming: solving the curses of dimensionality<br />
| year = 2007<br />
| publisher = Wiley-Interscience<br />
| isbn = 978-0-470-17155-4<br />
| url = http://www.castlelab.princeton.edu/adp.htm}}<br />
* {{cite book|url=http://incompleteideas.net/sutton/book/the-book.html|title=Reinforcement Learning: An Introduction|last1=Sutton|first1=Richard S.|last2=Barto|first2=Andrew G.|publisher=MIT Press|year=2018|isbn=978-0-262-03924-6|edition=2|location=|pages=|authorlink1=Richard S. Sutton|authorlink2=Andrew Barto}}<br />
* {{cite journal<br />
| doi = 10.1007/BF00115009<br />
| last = Sutton | first = Richard S. | authorlink = Richard S. Sutton<br />
| title = Learning to predict by the method of temporal differences<br />
| journal = Machine Learning<br />
| volume = 3<br />
| pages = 9–44<br />
| year = 1988<br />
| url = http://incompleteideas.net/sutton/publications.html#TD_paper | doi-access = free<br />
}}<br />
* {{cite conference|last1 = Szita|first1 = Istvan|last2 = Szepesvari|first2 = Csaba |year = 2010|title = Model-based Reinforcement Learning with Nearly Tight Exploration Complexity Bounds|url = http://www.icml2010.org/papers/546.pdf|publisher = Omnipress|pages = 1031–1038 |booktitle = ICML 2010|url-status = dead|archiveurl = https://web.archive.org/web/20100714095438/http://www.icml2010.org/papers/546.pdf|archivedate = 2010-07-14}}<br />
<br />
== External links ==<br />
<br />
* [http://www-anw.cs.umass.edu/rlr/ 麻省大学阿默斯特分校强化学习实验室]<br />
<br />
* [http://spaces.facsci.ualberta.ca/rlai/ 阿尔伯塔大学强化学习与人工智能实验室]<br />
<br />
* [http://www-all.cs.umass.edu/ 麻省大学阿默斯特分校自动化学习实验室]<br />
<br />
* [http://www.cogsci.rpi.edu/~rsun/hybrid-rl.html 混合强化学习介绍]<br />
<br />
* [http://www.dcsc.tudelft.nl/~robotics/media.html 真实世界中的强化学习实验]<br />
<br />
* [https://www.youtube.com/watch?v=RtxI449ZjSc&feature=relmfu 吴恩达强化学习介绍]<br />
<br />
* [https://mpatacchiola.github.io/blog/2016/12/09/dissecting-reinforcement-learning.html 强化学习剖析] 强化学习系列博客文章及相应Python代码<br />
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{{Computer science}}<br />
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[[Category:Markov models]]<br />
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Category:Markov models<br />
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类别: 马尔科夫模型<br />
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[[Category:Reinforcement learning| ]]<br />
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[[Category:Belief revision]]<br />
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Category:Belief revision<br />
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类别: 信念修正<br />
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<noinclude><br />
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<small>This page was moved from [[wikipedia:en:Reinforcement learning]]. Its edit history can be viewed at [[增强学习/edithistory]]</small></noinclude><br />
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[[Category:待整理页面]]</div>唐糖糖https://wiki.swarma.org/index.php?title=%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B&diff=30651微分方程2022-04-23T14:41:06Z<p>唐糖糖:/* 编者推荐 */</p>
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<div>{{#seo:<br />
|keywords=数学,方程<br />
|description=将一个或多个函数及其导数相互关联的方程。<br />
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[[File:Elmer-pump-heatequation.png|thumb|350px|通过求解热力学方程,我们建立了泵壳内传热的可视化模型。热量在内部产生并在边界冷却,从而为整体提供稳定的温度分布。]]<br />
在数学上,'''微分方程 Differential Equation'''是可以将一个或多个函数及其导数相互关联的方程。<ref name="Zill2012">{{cite book|author=Dennis G. Zill|title=A First Course in Differential Equations with Modeling Applications|url=https://books.google.com/books?id=pasKAAAAQBAJ&printsec=frontcover#v=snippet&q=%22ordinary%20differential%22&f=false|date=15 March 2012|publisher=Cengage Learning|isbn=1-285-40110-7}}</ref>在实际应用中,函数通常代表物理量,导数代表其变化率,而微分方程则定义了两者之间的关系。由于这种关系十分普遍,因此微分方程在包括工程学、物理学、经济学和生物学在内的许多学科中得到了广泛的应用。<br />
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<br />
微分方程的研究主要包括对微分方程解(满足每个方程的函数集)及其解的性质的研究。只有最简单的微分方程才能直接用公式求解;然而,有时无需精确计算便可以确定给定微分方程的解的许多性质。<br />
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一般地,当闭式解不存在时,可以用计算机求方程的近似解。动力系统理论着重于对由微分方程描述的系统进行定性分析。同时,现在已经得出了许多数值方法来计算给定精度下微分方程的解。<br />
<br />
<br />
<br />
==历史==<br />
微分方程是在牛顿和莱布尼茨发明微积分后才出现的。Isaac Newton 艾萨克·牛顿在他1671年的著作《无限的循环与系列 Method of Fluxions》的第二章<ref>Newton, Isaac. (c.1671). Methodus Fluxionum et Serierum Infinitarum (The Method of Fluxions and Infinite Series), published in 1736 [Opuscula, 1744, Vol. I. p. 66].</ref>中列出了三种微分方程:<br />
<br />
<br />
<br />
:<math><br />
\begin{align}<br />
& \frac {dy}{dx} = f(x) \\[5pt]<br />
& \frac {dy}{dx} = f(x,y) \\[5pt]<br />
& x_1 \frac {\partial y}{\partial x_1} + x_2 \frac {\partial y}{\partial x_2} = y<br />
\end{align}<br />
</math><br />
<br />
<br />
在这些例子中,{{mvar|y}}是自变量 {{mvar|x}}(或者是<math>x_1</math> 和 <math>x_2</math>)的未知函数,并且 {{mvar|f}} 是一个给定的函数。<br />
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他利用无穷级数来求解这些以及其他例子,并讨论了解的非唯一性。<br />
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雅可比·伯努利 Jacob Bernoulli在1695年提出了伯努利微分方程。<ref>{{Citation | last1=Bernoulli | first1=Jacob | author1-link=Jacob Bernoulli | title=Explicationes, Annotationes & Additiones ad ea, quae in Actis sup. de Curva Elastica, Isochrona Paracentrica, & Velaria, hinc inde memorata, & paratim controversa legundur; ubi de Linea mediarum directionum, alliisque novis | year=1695 | journal=[[Acta Eruditorum]]}}</ref>这种方程是'''常微分方程 Ordinary Differential Equation'''的一种形式,<br />
<br />
<br />
: <math>y'+ P(x)y = Q(x)y^n\,</math><br />
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莱布尼茨 Leibniz于第二年将方程简化从而得到了方程的解。<ref>{{Citation | last1=Hairer | first1=Ernst | last2=Nørsett | first2=Syvert Paul | last3=Wanner | first3=Gerhard | title=Solving ordinary differential equations I: Nonstiff problems | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-3-540-56670-0 | year=1993}}</ref><br />
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<br />
历史上,让·勒朗·达朗贝尔 Jean le Rond d'Alembert,欧拉 Leonhard Euler,丹尼尔·伯努利 Daniel Bernoulli和约瑟夫·路易斯·拉格朗日 Joseph-Louis Lagrange等都研究过弦(比如乐器的弦)振动问题。<ref>{{cite journal|url = http://homes.chass.utoronto.ca/~cfraser/vibration.pdf |title = Review of ''The evolution of dynamics, vibration theory from 1687 to 1742'', by John T. Cannon and Sigalia Dostrovsky|last= Frasier|first=Craig|journal=Bulletin (New Series) of the American Mathematical Society |date=July 1983 |volume= 9| issue = 1}}</ref><ref>{{cite journal |first=Gerard F. |last=Wheeler |first2=William P. |last2=Crummett |title=The Vibrating String Controversy |journal= [[American Journal of Physics|Am. J. Phys.]] |year=1987 |volume=55 |issue=1 |pages=33–37 |doi=10.1119/1.15311 |bibcode = 1987AmJPh..55...33W }}</ref><ref>For a special collection of the 9 groundbreaking papers by the three authors, see [http://www.lynge.com/item.php?bookid=38975&s_currency=EUR&c_sourcepage= First Appearance of the wave equation: D'Alembert, Leonhard Euler, Daniel Bernoulli. - the controversy about vibrating strings] (retrieved 13 Nov 2012). Herman HJ Lynge and Son.</ref><ref>For de Lagrange's contributions to the acoustic wave equation, can consult [https://books.google.com/books?id=D8GqhULfKfAC&pg=PA18 Acoustics: An Introduction to Its Physical Principles and Applications] Allan D. Pierce, Acoustical Soc of America, 1989; page 18.(retrieved 9 Dec 2012)</ref> 1746年,达朗贝尔发现了一维波动方程,十年之内,欧拉又发现了三维波动方程。<ref name=Speiser>Speiser, David. ''[https://books.google.com/books?id=9uf97reZZCUC&pg=PA191 Discovering the Principles of Mechanics 1600-1800]'', p. 191 (Basel: Birkhäuser, 2008).</ref><br />
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<br />
欧拉-拉格朗日方程式 Euler–Lagrange equation是欧拉和拉格朗日在18世纪50年代结合他们对等时降线问题的研究而发明的。这是一个不考虑起始点的曲线求解问题,其中一个加权的粒子将在一个给定的时间内下降到一个固定的点。拉格朗日在1755年解决了这个问题,并将其寄给欧拉。二人都进一步发展了拉格朗日的方法并将其应用于力学,从而促使了拉格朗日力学的形成。<br />
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1822年,Joseph Fourier 傅立叶在《热的分析理论 Théorie analytique de la chaleur》中发表了他关于热流的研究成果,<ref>{{Cite book | last = Fourier | first = Joseph | title = Théorie analytique de la chaleur | publisher = Firmin Didot Père et Fils | year = 1822 | location = Paris | language = French | url=https://archive.org/details/bub_gb_TDQJAAAAIAAJ | oclc=2688081 }}</ref>其中他以[[牛顿的冷却定律 Newton's law of cooling]]为基础进行推导,即两个相邻分子之间的热流与它们之间微小的温差成正比。这本书中包含了傅立叶关于热传导扩散的热方程式的建议。现在,每一个学习数学物理的学生都需要学习这类偏微分方程。<br />
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==示例==<br />
在经典力学中,物体运动是由其不断随时间变化的位置和速度来描述的。这些变量的表达在牛顿定律中是动态的(给定位置、速度、加速度和作用在物体上的各种力) ,并以时间函数的形式给出了未知物体位置的微分方程。<br />
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在某些情况下,这种微分方程(称为运动方程)可以精确地求解。<br />
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使用微分方程来模拟现实世界问题的一个例子是仅考虑重力和空气阻力来确定球在空中落下的速度。球对地面的加速度是重力加速度减去由于空气阻力提供的加速度。重力被认为是常数,空气阻力可以被模拟为与球的速度成正比。这意味着球的加速度,也就是其速度的导数,取决于速度(而速度取决于时间)。找到时间的函数--速度--需要解决一个微分方程问题并验证其正确性。<br />
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==微分方程的类型==<br />
微分方程可分为以下几种类型。除了描述方程本身的性质之外,微分方程的多种类型为我们选择何种解决方案提供了多种指导。常见的微分方程有: 常微分/偏微分方程、线性/非线性方程和齐次/非齐次方程。微分方程还有许多类型,以及许多在特定的情况下实用的其它性质和子类。<br />
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===常微分方程===<br />
'''常微分方程 ordinary differential equation(ODE)'''是只含有一个实变量或复变量的未知函数,其导数以及此函数的一些方程。未知函数因变量(通常由 {{mvar|y}} 表示),其常常随 {{mvar|x}}的变化而变化 。因此 {{mvar|x}} 通常被称为方程式的自变量。“常微分方程”一词与偏微分方程一词相比,后者涉及一个以上的独立变量。<br />
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线性微分方程是指方程中未知函数及其导数都是线性的微分方程。关于这些方程的理论发展得很好,在多数情况下可以用积分来表示它们的解。<br />
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物理学中遇到的大多数常微分方程都是线性的。因此,大多数特殊函数可以定义为线性微分方程的解(见完整性函数)。<br />
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一般地,微分方程的解不能用解析解表示,而会在计算机上利用数值方法求解。<br />
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===偏微分方程===<br />
'''偏微分方程 Partial Differential Equation(PDE)'''是一种包含多元函数及其偏导数的微分方程函数(这与处理单变量函数及其导数的常微分方程不同)。偏微分方程可用于描述涉及多元函数的问题求闭式解,或者用于创建相关的计算机模型。<br />
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偏微分方程可以用来描述自然界中各种各样的现象,如声音、热量、静电、电动力学、流体流动、弹性和量子力学等。这些看起来截然不同的物理现象其实都可以用相似的偏微分方程表达。正如常微分方程常被用于对一维动力系统进行建模一样,偏微分方程常被用于对多维系统进行建模。随机偏微分方程延伸了偏微分方程在模拟随机性上的应用。<br />
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===非线性微分方程===<br />
<br />
非线性微分方程是微分方程的一种,但它不是关于未知函数及其导数的线性方程(这里不考虑函数本身的线性或非线性)。能够精确求解非线性微分方程的方法很少; 那些已有的方法通常依赖于方程具有某种特定的对称性。非线性微分方程在更长的时间段内表现出非常复杂的行为,具有混沌特性。即使非线性微分方程也有解的存在性、唯一性和可扩展性等基本问题以及初边值问题的适定性问题,但对其研究也是一个难题(可参考纳维-斯托克斯方程的存在性和光滑性)。然而,如果微分方程是一个有意义物理过程的正确表述,那么人们期望它有一个解析解。 <br />
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线性微分方程经常作为非线性方程的近似形式出现。这些近似只有某些限制条件下才有效。例如,谐振子方程是非线性摆方程的近似这一情况只有对于小幅度振荡是有效的(见下文)。<br />
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===方程的阶===<br />
<br />
微分方程的阶数是由它们的导数的最高阶决定的。只含有一阶导数的方程是一阶微分方程,含有二阶导数的方程是二阶微分方程,等等。描述自然现象的微分方程几乎总是只有一阶和二阶导数<ref>[[Eric W Weisstein|Weisstein, Eric W]]. "Ordinary Differential Equation Order." From [[MathWorld]]--A Wolfram Web Resource. http://mathworld.wolfram.com/OrdinaryDifferentialEquationOrder.html</ref><ref>[http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx Order and degree of a differential equation] {{Webarchive|url=https://web.archive.org/web/20160401070512/http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx |date=2016-04-01 }}, accessed Dec 2015.</ref>,但也有一些例外,例如薄膜方程,它是一个四阶偏微分方程。<br />
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===示例===<br />
<br />
在第一组示例中,待求解的''u''是''x''的函数,''c''和''ω''是应该已知的常数。常微分方程和偏微分方程这两种广义分类下还要区分微分方程的线性和非线性,以及区分微分方程的齐次和非齐次。<br />
<br />
<br />
* 非齐次一阶常系数常微分方程:<br />
<br />
<br />
:: <math> \frac{du}{dx} = cu+x^2. </math><br />
<br />
<br />
<br />
* 齐次二阶线性常微分方程:<br />
<br />
<br />
:: <math> \frac{d^2u}{dx^2} - x\frac{du}{dx} + u = 0. </math><br />
<br />
<br />
* 用于描述简谐振动的齐次二阶常系数常系数微分方程:<br />
<br />
:: <math> \frac{d^2u}{dx^2} + \omega^2u = 0. </math><br />
<br />
<br />
* 非齐次一阶非线性常微分方程:<br />
<br />
:: <math> \frac{du}{dx} = u^2 + 4. </math><br />
<br />
<br />
* 用于描述摆长为L的钟摆运动的二阶非线性(因正弦函数产生)常微分方程:<br />
<br />
<br />
:: <math> L\frac{d^2u}{dx^2} + g\sin u = 0. </math><br />
<br />
<br />
<br />
在下一组例子中,未知函数''u''依赖于两个变量''x'' 和 ''t''或者''x''和''y''。<br />
<br />
<br />
<br />
* 齐次一阶线性偏微分方程:<br />
<br />
<br />
:: <math> \frac{\partial u}{\partial t} + t\frac{\partial u}{\partial x} = 0. </math><br />
<br />
<br />
<br />
<br />
*齐次二阶线性常系数椭圆形偏微分方程,也称为拉普拉斯方程:<br />
<br />
<br />
:: <math> \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0. </math><br />
<br />
<br />
*齐次三阶非线性偏微分方程:<br />
<br />
<br />
:: <math> \frac{\partial u}{\partial t} = 6u\frac{\partial u}{\partial x} - \frac{\partial^3 u}{\partial x^3}. </math><br />
<br />
==解的存在性==<br />
<br />
<br />
<br />
解微分方程不同于解代数方程。方程解的情况往往是不确定的,而且解是否唯一或是否存在也是值得关注的问题。<br />
<br />
<br />
对于一阶初值问题,皮亚诺存在性定理给出了一组解存在的情况。给定的x-y平面上的任意点 <math>(a,b)</math> ,定义矩形区域 <math>Z</math> ,如,<math>Z = [l,m]\times[n,p]</math> 而且 <math>(a,b)</math> 是 <math>Z</math> 内部一点。如果我们给出一个微分方程 <math>\frac{dy}{dx} = g(x,y)</math> 和当<math>x=a</math>时<math>y=b</math>,如果<math>g(x,y)</math>和<math>\frac{\partial g}{\partial x}</math>在<math>Z</math>上是连续的,那么这个问题就有一个局部解。这个解在以 <math>a</math> 为中心的某些区间上存在,其可能不是唯一的。(其他结果请参见常微分方程。)<br />
<br />
<br />
然而,这只能帮助我们解决一阶初始值问题。假设我们有一个n阶线性初始值问题:<br />
<br />
<br />
<br />
:<math><br />
f_{n}(x)\frac{d^n y}{dx^n} + \cdots + f_{1}(x)\frac{d y}{dx} + f_{0}(x)y = g(x)<br />
</math><br />
<br />
<br />
其中有<br />
<br />
:<math><br />
y(x_{0})=y_{0}, y'(x_{0}) = y'_{0}, y''(x_{0}) = y''_{0}, \cdots<br />
</math><br />
<br />
<br />
对于任意非零 <math>f_{n}(x)</math> ,如果<math>\{f_{0},f_{1},\cdots\}</math> 和 <math>g</math>在某个包含<math>x_{0}</math>的区间上连续,则<math>y</math>是存在且唯一的。<ref>{{cite book|last1=Zill|first1=Dennis G.|title=A First Course in Differential Equations|publisher=Brooks/Cole|isbn=0-534-37388-7|edition=5th|year=2001}}</ref><br />
<br />
==相关概念==<br />
<br />
<br />
<br />
*延迟微分方程(DDE)是一元函数的方程,变量通常为时间,其中函数在一定时间点的微分会被较早时间点的函数值表达。<br />
<br />
*积分微分方程(IDE)结合了微分方程和积分方程。<br />
<br />
*随机微分方程(SDE)中的未知量处于随机过程,并且涉及一些已知的随机过程,例如,扩散方程中的维纳过程。<br />
<br />
*随机偏微分方程(SPDE)是一种含空间和时间噪声过程的广义随机微分方程,它通常应用于量子场论以及统计力学中。<br />
<br />
* 微分代数方程(DAE)是一种含微分和代数项的微分方程,通常以隐式形式给出。<br />
<br />
==与差分方程之间的联系==<br />
<br />
<br />
微分方程理论与差分方程理论密切相关。在差分方程理论中,坐标系中只假定存在离散值,计算中会涉及到未知函数或已知函数的值以及坐标附近的值。许多求微分方程数值解或研究微分方程性质的方法,都会涉及通过相应差分方程的解来逼近微分方程的解。<br />
<br />
== 应用==<br />
<br />
<br />
<br />
<br />
微分方程的研究可以应用于许多领域,如理论数学、应用数学、物理学和工程学,它们都与各种类型的微分方程的性质有关。理论数学关注解的存在性和唯一性,而应用数学则强调求解方法的严格准确性。从天体运动到桥梁设计,再到神经元之间的相互作用,微分方程在几乎所有物理、技术或生物过程的建模中都扮演着重要的角色。用于解决实际问题的微分方程,不一定是直接可解的,如可能不存在闭式解。但我们可以用数值方法来近似得到方程的解。<br />
<br />
<br />
<br />
许多物理和化学的基本定律都可以用微分方程来表示。在生物学和经济学中,微分方程被用来模拟复杂系统的行为。微分方程理论最初是与其起源并得到应用的科学一起发展起来的。然而,有时完全不同的科学领域,却可能产生相同的微分方程。当这种情况发生时,方程后面的数学理论可以被看作是不同现象背后的统一原则。例如,光和声在大气中的传播,或是池塘表面的水波的传播。所有这些过程都可以用相同的二阶偏微分方程来描述,即波动方程。我们把光和声音想象成与水波相似的形式。由约瑟夫·傅里叶提出的热传导的理论由另一个二阶偏微分方程——热方程所支配。事实证明,许多扩散过程,虽然看上去形式不同,但都可以同一个方程来描述;。例如,金融学中的布莱克-斯科尔斯方程就与热方程有关。<br />
<br />
<br />
事实上,同一类型的微分方程可以应用于不同领域这样的现象屡见不鲜,这足以证明微分方程这一课题的重要性。参见已命名的微分方程列表。<br />
<br />
==参见==<br />
<br />
*复微分方程<br />
*精确微分方程<br />
*<br />
泛函微分方程<br />
*<br />
初始条件<br />
*<br />
积分方程<br />
*<br />
求解常微分方程的数值方法<br />
*求解偏微分方程的数值方法<br />
*关于解的存在性和唯一性的皮卡德–林德洛夫定理<br />
*递推关系,也称为差分方程<br />
*抽象微分方程<br />
*微分方程组<br />
{{div col end}}<br />
<br />
==参考文献==<br />
<br />
{{reflist|30em}}<br />
<br />
==拓展阅读==<br />
<br />
*{{cite book |first=P. |last=Abbott |first2=H. |last2=Neill |title=Teach Yourself Calculus |year=2003 |pages=266–277 }}<br />
<br />
*{{cite book |first=P. |last=Blanchard |authorlink2=Robert L. Devaney |first2=R. L. |last2=Devaney |first3=G. R. |last3=Hall |title=Differential Equations |location= |publisher=Thompson |year=2006 }}<br />
<br />
*{{cite book |first=W. |last=Boyce | first2=R. |last2=DiPrima| first3=D. |last3=Meade| title=Elementary Differential Equations and Boundary Value Problems|publisher=Wiley |year=2017}}<br />
<br />
*{{cite book |first=E. A. |last=Coddington |first2=N. |last2=Levinson |title=Theory of Ordinary Differential Equations |url=https://archive.org/details/theoryofordinary00codd |url-access=registration |publisher=McGraw-Hill |year=1955 }}<br />
<br />
*{{cite book |first=E. L. |last=Ince |title=Ordinary Differential Equations |publisher=Dover |year=1956 }}<br />
<br />
*{{cite book |first=W. |last=Johnson |url=http://www.hti.umich.edu/cgi/b/bib/bibperm?q1=abv5010.0001.001 |title=A Treatise on Ordinary and Partial Differential Equations |publisher=John Wiley and Sons |year=1913 }} In [http://hti.umich.edu/u/umhistmath/ University of Michigan Historical Math Collection]<br />
<br />
*{{cite book |first=A. D. |last=Polyanin |first2=V. F. |last2=Zaitsev |title=Handbook of Exact Solutions for Ordinary Differential Equations |edition=2nd |publisher=Chapman & Hall/CRC Press |location=Boca Raton |year=2003 |isbn=1-58488-297-2 }}<br />
<br />
*{{cite book |first=R. I. |last=Porter |title=Further Elementary Analysis |year=1978 |chapter=XIX Differential Equations }}<br />
<br />
*{{Cite book| last = Teschl| given = Gerald|authorlink=Gerald Teschl| title = Ordinary Differential Equations and Dynamical Systems| publisher=[[American Mathematical Society]]| place = [[Providence, Rhode Island|Providence]]| year = 2012| isbn= 978-0-8218-8328-0| url = http://www.mat.univie.ac.at/~gerald/ftp/book-ode/}}<br />
<br />
*{{cite book|author=Daniel Zwillinger|title=Handbook of Differential Equations|url=https://books.google.com/?id=n7TiBQAAQBAJ&printsec=frontcover&dq=%22Handbook+of+Differential+Equations%22#v=onepage&q=%22Handbook%20of%20Differential%20Equations%22&f=false|date=12 May 2014|publisher=Elsevier Science|isbn=978-1-4832-6396-0}}<br />
<br />
==外部链接==<br />
<br />
{{wikiquote}}<br />
<br />
{{Wikibooks|Ordinary Differential Equations}}<br />
<br />
{{Wikiversity|Differential equations}}<br />
<br />
{{EB1911 poster|Differential Equation}}<br />
<br />
*{{Commonscatinline|Differential equations}}<br />
<br />
*[http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/ Lectures on Differential Equations] [[MIT]] Open CourseWare Videos<br />
<br />
*[http://tutorial.math.lamar.edu/classes/de/de.aspx Online Notes / Differential Equations] Paul Dawkins, [[Lamar University]]<br />
<br />
*[http://www.sosmath.com/diffeq/diffeq.html Differential Equations], S.O.S. Mathematics<br />
<br />
*[http://www.fioravante.patrone.name/mat/u-u/en/differential_equations_intro.htm Introduction to modeling via differential equations] Introduction to modeling by means of differential equations, with critical remarks.<br />
<br />
*[http://user.mendelu.cz/marik/maw/index.php?lang=en&form=ode Mathematical Assistant on Web] Symbolic ODE tool, using [[Maxima (software)|Maxima]]<br />
<br />
*[http://eqworld.ipmnet.ru/en/solutions/ode.htm Exact Solutions of Ordinary Differential Equations]<br />
<br />
*[http://www.hedengren.net/research/models.htm Collection of ODE and DAE models of physical systems] MATLAB models<br />
<br />
*[http://www.jirka.org/diffyqs/ Notes on Diffy Qs: Differential Equations for Engineers] An introductory textbook on differential equations by Jiri Lebl of [[UIUC]]<br />
<br />
*[http://www.khanacademy.org/math/differential-equations Khan Academy Video playlist on differential equations ] Topics covered in a first year course in differential equations.<br />
<br />
*[https://web.archive.org/web/20130607120716/http://math.rareinfos.com/category/courses/solutions-differential-equations/homogeneous-linear-systems/ MathDiscuss Video playlist on differential equations ]<br />
<br />
==编者推荐==<br />
[https://campus.swarma.org/course/1646 Introduction II: Differential Equations]<br />
<br />
<br />
[https://campus.swarma.org/course/2099 常微分方程]<br />
<br />
<br />
[https://campus.swarma.org/course/2003 凯风研读营之“复杂系统自动建模专题”]<br />
<br />
<br />
[https://campus.swarma.org/course/1392 Matlab 基础与应用:微分方程]<br />
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<br />
<br/><br/><br/><br />
----<br />
本中文词条由[[用户:Yuling|Yuling]]编译,[[用户:CecileLi|CecileLi]]审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
<br />
<br />
'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B&diff=30650微分方程2022-04-23T14:40:52Z<p>唐糖糖:/* 编者推荐 */</p>
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<div>{{#seo:<br />
|keywords=数学,方程<br />
|description=将一个或多个函数及其导数相互关联的方程。<br />
}}<br />
[[File:Elmer-pump-heatequation.png|thumb|350px|通过求解热力学方程,我们建立了泵壳内传热的可视化模型。热量在内部产生并在边界冷却,从而为整体提供稳定的温度分布。]]<br />
在数学上,'''微分方程 Differential Equation'''是可以将一个或多个函数及其导数相互关联的方程。<ref name="Zill2012">{{cite book|author=Dennis G. Zill|title=A First Course in Differential Equations with Modeling Applications|url=https://books.google.com/books?id=pasKAAAAQBAJ&printsec=frontcover#v=snippet&q=%22ordinary%20differential%22&f=false|date=15 March 2012|publisher=Cengage Learning|isbn=1-285-40110-7}}</ref>在实际应用中,函数通常代表物理量,导数代表其变化率,而微分方程则定义了两者之间的关系。由于这种关系十分普遍,因此微分方程在包括工程学、物理学、经济学和生物学在内的许多学科中得到了广泛的应用。<br />
<br />
<br />
微分方程的研究主要包括对微分方程解(满足每个方程的函数集)及其解的性质的研究。只有最简单的微分方程才能直接用公式求解;然而,有时无需精确计算便可以确定给定微分方程的解的许多性质。<br />
<br />
<br />
一般地,当闭式解不存在时,可以用计算机求方程的近似解。动力系统理论着重于对由微分方程描述的系统进行定性分析。同时,现在已经得出了许多数值方法来计算给定精度下微分方程的解。<br />
<br />
<br />
<br />
==历史==<br />
微分方程是在牛顿和莱布尼茨发明微积分后才出现的。Isaac Newton 艾萨克·牛顿在他1671年的著作《无限的循环与系列 Method of Fluxions》的第二章<ref>Newton, Isaac. (c.1671). Methodus Fluxionum et Serierum Infinitarum (The Method of Fluxions and Infinite Series), published in 1736 [Opuscula, 1744, Vol. I. p. 66].</ref>中列出了三种微分方程:<br />
<br />
<br />
<br />
:<math><br />
\begin{align}<br />
& \frac {dy}{dx} = f(x) \\[5pt]<br />
& \frac {dy}{dx} = f(x,y) \\[5pt]<br />
& x_1 \frac {\partial y}{\partial x_1} + x_2 \frac {\partial y}{\partial x_2} = y<br />
\end{align}<br />
</math><br />
<br />
<br />
在这些例子中,{{mvar|y}}是自变量 {{mvar|x}}(或者是<math>x_1</math> 和 <math>x_2</math>)的未知函数,并且 {{mvar|f}} 是一个给定的函数。<br />
<br />
<br />
他利用无穷级数来求解这些以及其他例子,并讨论了解的非唯一性。<br />
<br />
<br />
雅可比·伯努利 Jacob Bernoulli在1695年提出了伯努利微分方程。<ref>{{Citation | last1=Bernoulli | first1=Jacob | author1-link=Jacob Bernoulli | title=Explicationes, Annotationes & Additiones ad ea, quae in Actis sup. de Curva Elastica, Isochrona Paracentrica, & Velaria, hinc inde memorata, & paratim controversa legundur; ubi de Linea mediarum directionum, alliisque novis | year=1695 | journal=[[Acta Eruditorum]]}}</ref>这种方程是'''常微分方程 Ordinary Differential Equation'''的一种形式,<br />
<br />
<br />
: <math>y'+ P(x)y = Q(x)y^n\,</math><br />
<br />
<br />
莱布尼茨 Leibniz于第二年将方程简化从而得到了方程的解。<ref>{{Citation | last1=Hairer | first1=Ernst | last2=Nørsett | first2=Syvert Paul | last3=Wanner | first3=Gerhard | title=Solving ordinary differential equations I: Nonstiff problems | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-3-540-56670-0 | year=1993}}</ref><br />
<br />
<br />
历史上,让·勒朗·达朗贝尔 Jean le Rond d'Alembert,欧拉 Leonhard Euler,丹尼尔·伯努利 Daniel Bernoulli和约瑟夫·路易斯·拉格朗日 Joseph-Louis Lagrange等都研究过弦(比如乐器的弦)振动问题。<ref>{{cite journal|url = http://homes.chass.utoronto.ca/~cfraser/vibration.pdf |title = Review of ''The evolution of dynamics, vibration theory from 1687 to 1742'', by John T. Cannon and Sigalia Dostrovsky|last= Frasier|first=Craig|journal=Bulletin (New Series) of the American Mathematical Society |date=July 1983 |volume= 9| issue = 1}}</ref><ref>{{cite journal |first=Gerard F. |last=Wheeler |first2=William P. |last2=Crummett |title=The Vibrating String Controversy |journal= [[American Journal of Physics|Am. J. Phys.]] |year=1987 |volume=55 |issue=1 |pages=33–37 |doi=10.1119/1.15311 |bibcode = 1987AmJPh..55...33W }}</ref><ref>For a special collection of the 9 groundbreaking papers by the three authors, see [http://www.lynge.com/item.php?bookid=38975&s_currency=EUR&c_sourcepage= First Appearance of the wave equation: D'Alembert, Leonhard Euler, Daniel Bernoulli. - the controversy about vibrating strings] (retrieved 13 Nov 2012). Herman HJ Lynge and Son.</ref><ref>For de Lagrange's contributions to the acoustic wave equation, can consult [https://books.google.com/books?id=D8GqhULfKfAC&pg=PA18 Acoustics: An Introduction to Its Physical Principles and Applications] Allan D. Pierce, Acoustical Soc of America, 1989; page 18.(retrieved 9 Dec 2012)</ref> 1746年,达朗贝尔发现了一维波动方程,十年之内,欧拉又发现了三维波动方程。<ref name=Speiser>Speiser, David. ''[https://books.google.com/books?id=9uf97reZZCUC&pg=PA191 Discovering the Principles of Mechanics 1600-1800]'', p. 191 (Basel: Birkhäuser, 2008).</ref><br />
<br />
<br />
欧拉-拉格朗日方程式 Euler–Lagrange equation是欧拉和拉格朗日在18世纪50年代结合他们对等时降线问题的研究而发明的。这是一个不考虑起始点的曲线求解问题,其中一个加权的粒子将在一个给定的时间内下降到一个固定的点。拉格朗日在1755年解决了这个问题,并将其寄给欧拉。二人都进一步发展了拉格朗日的方法并将其应用于力学,从而促使了拉格朗日力学的形成。<br />
<br />
<br />
1822年,Joseph Fourier 傅立叶在《热的分析理论 Théorie analytique de la chaleur》中发表了他关于热流的研究成果,<ref>{{Cite book | last = Fourier | first = Joseph | title = Théorie analytique de la chaleur | publisher = Firmin Didot Père et Fils | year = 1822 | location = Paris | language = French | url=https://archive.org/details/bub_gb_TDQJAAAAIAAJ | oclc=2688081 }}</ref>其中他以[[牛顿的冷却定律 Newton's law of cooling]]为基础进行推导,即两个相邻分子之间的热流与它们之间微小的温差成正比。这本书中包含了傅立叶关于热传导扩散的热方程式的建议。现在,每一个学习数学物理的学生都需要学习这类偏微分方程。<br />
<br />
<br />
==示例==<br />
在经典力学中,物体运动是由其不断随时间变化的位置和速度来描述的。这些变量的表达在牛顿定律中是动态的(给定位置、速度、加速度和作用在物体上的各种力) ,并以时间函数的形式给出了未知物体位置的微分方程。<br />
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在某些情况下,这种微分方程(称为运动方程)可以精确地求解。<br />
<br />
<br />
使用微分方程来模拟现实世界问题的一个例子是仅考虑重力和空气阻力来确定球在空中落下的速度。球对地面的加速度是重力加速度减去由于空气阻力提供的加速度。重力被认为是常数,空气阻力可以被模拟为与球的速度成正比。这意味着球的加速度,也就是其速度的导数,取决于速度(而速度取决于时间)。找到时间的函数--速度--需要解决一个微分方程问题并验证其正确性。<br />
<br />
<br />
==微分方程的类型==<br />
微分方程可分为以下几种类型。除了描述方程本身的性质之外,微分方程的多种类型为我们选择何种解决方案提供了多种指导。常见的微分方程有: 常微分/偏微分方程、线性/非线性方程和齐次/非齐次方程。微分方程还有许多类型,以及许多在特定的情况下实用的其它性质和子类。<br />
<br />
<br />
<br />
===常微分方程===<br />
'''常微分方程 ordinary differential equation(ODE)'''是只含有一个实变量或复变量的未知函数,其导数以及此函数的一些方程。未知函数因变量(通常由 {{mvar|y}} 表示),其常常随 {{mvar|x}}的变化而变化 。因此 {{mvar|x}} 通常被称为方程式的自变量。“常微分方程”一词与偏微分方程一词相比,后者涉及一个以上的独立变量。<br />
<br />
<br />
线性微分方程是指方程中未知函数及其导数都是线性的微分方程。关于这些方程的理论发展得很好,在多数情况下可以用积分来表示它们的解。<br />
<br />
<br />
物理学中遇到的大多数常微分方程都是线性的。因此,大多数特殊函数可以定义为线性微分方程的解(见完整性函数)。<br />
<br />
<br />
一般地,微分方程的解不能用解析解表示,而会在计算机上利用数值方法求解。<br />
<br />
<br />
===偏微分方程===<br />
'''偏微分方程 Partial Differential Equation(PDE)'''是一种包含多元函数及其偏导数的微分方程函数(这与处理单变量函数及其导数的常微分方程不同)。偏微分方程可用于描述涉及多元函数的问题求闭式解,或者用于创建相关的计算机模型。<br />
<br />
<br />
偏微分方程可以用来描述自然界中各种各样的现象,如声音、热量、静电、电动力学、流体流动、弹性和量子力学等。这些看起来截然不同的物理现象其实都可以用相似的偏微分方程表达。正如常微分方程常被用于对一维动力系统进行建模一样,偏微分方程常被用于对多维系统进行建模。随机偏微分方程延伸了偏微分方程在模拟随机性上的应用。<br />
<br />
<br />
===非线性微分方程===<br />
<br />
非线性微分方程是微分方程的一种,但它不是关于未知函数及其导数的线性方程(这里不考虑函数本身的线性或非线性)。能够精确求解非线性微分方程的方法很少; 那些已有的方法通常依赖于方程具有某种特定的对称性。非线性微分方程在更长的时间段内表现出非常复杂的行为,具有混沌特性。即使非线性微分方程也有解的存在性、唯一性和可扩展性等基本问题以及初边值问题的适定性问题,但对其研究也是一个难题(可参考纳维-斯托克斯方程的存在性和光滑性)。然而,如果微分方程是一个有意义物理过程的正确表述,那么人们期望它有一个解析解。 <br />
<br />
<br />
线性微分方程经常作为非线性方程的近似形式出现。这些近似只有某些限制条件下才有效。例如,谐振子方程是非线性摆方程的近似这一情况只有对于小幅度振荡是有效的(见下文)。<br />
<br />
===方程的阶===<br />
<br />
微分方程的阶数是由它们的导数的最高阶决定的。只含有一阶导数的方程是一阶微分方程,含有二阶导数的方程是二阶微分方程,等等。描述自然现象的微分方程几乎总是只有一阶和二阶导数<ref>[[Eric W Weisstein|Weisstein, Eric W]]. "Ordinary Differential Equation Order." From [[MathWorld]]--A Wolfram Web Resource. http://mathworld.wolfram.com/OrdinaryDifferentialEquationOrder.html</ref><ref>[http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx Order and degree of a differential equation] {{Webarchive|url=https://web.archive.org/web/20160401070512/http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx |date=2016-04-01 }}, accessed Dec 2015.</ref>,但也有一些例外,例如薄膜方程,它是一个四阶偏微分方程。<br />
<br />
===示例===<br />
<br />
在第一组示例中,待求解的''u''是''x''的函数,''c''和''ω''是应该已知的常数。常微分方程和偏微分方程这两种广义分类下还要区分微分方程的线性和非线性,以及区分微分方程的齐次和非齐次。<br />
<br />
<br />
* 非齐次一阶常系数常微分方程:<br />
<br />
<br />
:: <math> \frac{du}{dx} = cu+x^2. </math><br />
<br />
<br />
<br />
* 齐次二阶线性常微分方程:<br />
<br />
<br />
:: <math> \frac{d^2u}{dx^2} - x\frac{du}{dx} + u = 0. </math><br />
<br />
<br />
* 用于描述简谐振动的齐次二阶常系数常系数微分方程:<br />
<br />
:: <math> \frac{d^2u}{dx^2} + \omega^2u = 0. </math><br />
<br />
<br />
* 非齐次一阶非线性常微分方程:<br />
<br />
:: <math> \frac{du}{dx} = u^2 + 4. </math><br />
<br />
<br />
* 用于描述摆长为L的钟摆运动的二阶非线性(因正弦函数产生)常微分方程:<br />
<br />
<br />
:: <math> L\frac{d^2u}{dx^2} + g\sin u = 0. </math><br />
<br />
<br />
<br />
在下一组例子中,未知函数''u''依赖于两个变量''x'' 和 ''t''或者''x''和''y''。<br />
<br />
<br />
<br />
* 齐次一阶线性偏微分方程:<br />
<br />
<br />
:: <math> \frac{\partial u}{\partial t} + t\frac{\partial u}{\partial x} = 0. </math><br />
<br />
<br />
<br />
<br />
*齐次二阶线性常系数椭圆形偏微分方程,也称为拉普拉斯方程:<br />
<br />
<br />
:: <math> \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0. </math><br />
<br />
<br />
*齐次三阶非线性偏微分方程:<br />
<br />
<br />
:: <math> \frac{\partial u}{\partial t} = 6u\frac{\partial u}{\partial x} - \frac{\partial^3 u}{\partial x^3}. </math><br />
<br />
==解的存在性==<br />
<br />
<br />
<br />
解微分方程不同于解代数方程。方程解的情况往往是不确定的,而且解是否唯一或是否存在也是值得关注的问题。<br />
<br />
<br />
对于一阶初值问题,皮亚诺存在性定理给出了一组解存在的情况。给定的x-y平面上的任意点 <math>(a,b)</math> ,定义矩形区域 <math>Z</math> ,如,<math>Z = [l,m]\times[n,p]</math> 而且 <math>(a,b)</math> 是 <math>Z</math> 内部一点。如果我们给出一个微分方程 <math>\frac{dy}{dx} = g(x,y)</math> 和当<math>x=a</math>时<math>y=b</math>,如果<math>g(x,y)</math>和<math>\frac{\partial g}{\partial x}</math>在<math>Z</math>上是连续的,那么这个问题就有一个局部解。这个解在以 <math>a</math> 为中心的某些区间上存在,其可能不是唯一的。(其他结果请参见常微分方程。)<br />
<br />
<br />
然而,这只能帮助我们解决一阶初始值问题。假设我们有一个n阶线性初始值问题:<br />
<br />
<br />
<br />
:<math><br />
f_{n}(x)\frac{d^n y}{dx^n} + \cdots + f_{1}(x)\frac{d y}{dx} + f_{0}(x)y = g(x)<br />
</math><br />
<br />
<br />
其中有<br />
<br />
:<math><br />
y(x_{0})=y_{0}, y'(x_{0}) = y'_{0}, y''(x_{0}) = y''_{0}, \cdots<br />
</math><br />
<br />
<br />
对于任意非零 <math>f_{n}(x)</math> ,如果<math>\{f_{0},f_{1},\cdots\}</math> 和 <math>g</math>在某个包含<math>x_{0}</math>的区间上连续,则<math>y</math>是存在且唯一的。<ref>{{cite book|last1=Zill|first1=Dennis G.|title=A First Course in Differential Equations|publisher=Brooks/Cole|isbn=0-534-37388-7|edition=5th|year=2001}}</ref><br />
<br />
==相关概念==<br />
<br />
<br />
<br />
*延迟微分方程(DDE)是一元函数的方程,变量通常为时间,其中函数在一定时间点的微分会被较早时间点的函数值表达。<br />
<br />
*积分微分方程(IDE)结合了微分方程和积分方程。<br />
<br />
*随机微分方程(SDE)中的未知量处于随机过程,并且涉及一些已知的随机过程,例如,扩散方程中的维纳过程。<br />
<br />
*随机偏微分方程(SPDE)是一种含空间和时间噪声过程的广义随机微分方程,它通常应用于量子场论以及统计力学中。<br />
<br />
* 微分代数方程(DAE)是一种含微分和代数项的微分方程,通常以隐式形式给出。<br />
<br />
==与差分方程之间的联系==<br />
<br />
<br />
微分方程理论与差分方程理论密切相关。在差分方程理论中,坐标系中只假定存在离散值,计算中会涉及到未知函数或已知函数的值以及坐标附近的值。许多求微分方程数值解或研究微分方程性质的方法,都会涉及通过相应差分方程的解来逼近微分方程的解。<br />
<br />
== 应用==<br />
<br />
<br />
<br />
<br />
微分方程的研究可以应用于许多领域,如理论数学、应用数学、物理学和工程学,它们都与各种类型的微分方程的性质有关。理论数学关注解的存在性和唯一性,而应用数学则强调求解方法的严格准确性。从天体运动到桥梁设计,再到神经元之间的相互作用,微分方程在几乎所有物理、技术或生物过程的建模中都扮演着重要的角色。用于解决实际问题的微分方程,不一定是直接可解的,如可能不存在闭式解。但我们可以用数值方法来近似得到方程的解。<br />
<br />
<br />
<br />
许多物理和化学的基本定律都可以用微分方程来表示。在生物学和经济学中,微分方程被用来模拟复杂系统的行为。微分方程理论最初是与其起源并得到应用的科学一起发展起来的。然而,有时完全不同的科学领域,却可能产生相同的微分方程。当这种情况发生时,方程后面的数学理论可以被看作是不同现象背后的统一原则。例如,光和声在大气中的传播,或是池塘表面的水波的传播。所有这些过程都可以用相同的二阶偏微分方程来描述,即波动方程。我们把光和声音想象成与水波相似的形式。由约瑟夫·傅里叶提出的热传导的理论由另一个二阶偏微分方程——热方程所支配。事实证明,许多扩散过程,虽然看上去形式不同,但都可以同一个方程来描述;。例如,金融学中的布莱克-斯科尔斯方程就与热方程有关。<br />
<br />
<br />
事实上,同一类型的微分方程可以应用于不同领域这样的现象屡见不鲜,这足以证明微分方程这一课题的重要性。参见已命名的微分方程列表。<br />
<br />
==参见==<br />
<br />
*复微分方程<br />
*精确微分方程<br />
*<br />
泛函微分方程<br />
*<br />
初始条件<br />
*<br />
积分方程<br />
*<br />
求解常微分方程的数值方法<br />
*求解偏微分方程的数值方法<br />
*关于解的存在性和唯一性的皮卡德–林德洛夫定理<br />
*递推关系,也称为差分方程<br />
*抽象微分方程<br />
*微分方程组<br />
{{div col end}}<br />
<br />
==参考文献==<br />
<br />
{{reflist|30em}}<br />
<br />
==拓展阅读==<br />
<br />
*{{cite book |first=P. |last=Abbott |first2=H. |last2=Neill |title=Teach Yourself Calculus |year=2003 |pages=266–277 }}<br />
<br />
*{{cite book |first=P. |last=Blanchard |authorlink2=Robert L. Devaney |first2=R. L. |last2=Devaney |first3=G. R. |last3=Hall |title=Differential Equations |location= |publisher=Thompson |year=2006 }}<br />
<br />
*{{cite book |first=W. |last=Boyce | first2=R. |last2=DiPrima| first3=D. |last3=Meade| title=Elementary Differential Equations and Boundary Value Problems|publisher=Wiley |year=2017}}<br />
<br />
*{{cite book |first=E. A. |last=Coddington |first2=N. |last2=Levinson |title=Theory of Ordinary Differential Equations |url=https://archive.org/details/theoryofordinary00codd |url-access=registration |publisher=McGraw-Hill |year=1955 }}<br />
<br />
*{{cite book |first=E. L. |last=Ince |title=Ordinary Differential Equations |publisher=Dover |year=1956 }}<br />
<br />
*{{cite book |first=W. |last=Johnson |url=http://www.hti.umich.edu/cgi/b/bib/bibperm?q1=abv5010.0001.001 |title=A Treatise on Ordinary and Partial Differential Equations |publisher=John Wiley and Sons |year=1913 }} In [http://hti.umich.edu/u/umhistmath/ University of Michigan Historical Math Collection]<br />
<br />
*{{cite book |first=A. D. |last=Polyanin |first2=V. F. |last2=Zaitsev |title=Handbook of Exact Solutions for Ordinary Differential Equations |edition=2nd |publisher=Chapman & Hall/CRC Press |location=Boca Raton |year=2003 |isbn=1-58488-297-2 }}<br />
<br />
*{{cite book |first=R. I. |last=Porter |title=Further Elementary Analysis |year=1978 |chapter=XIX Differential Equations }}<br />
<br />
*{{Cite book| last = Teschl| given = Gerald|authorlink=Gerald Teschl| title = Ordinary Differential Equations and Dynamical Systems| publisher=[[American Mathematical Society]]| place = [[Providence, Rhode Island|Providence]]| year = 2012| isbn= 978-0-8218-8328-0| url = http://www.mat.univie.ac.at/~gerald/ftp/book-ode/}}<br />
<br />
*{{cite book|author=Daniel Zwillinger|title=Handbook of Differential Equations|url=https://books.google.com/?id=n7TiBQAAQBAJ&printsec=frontcover&dq=%22Handbook+of+Differential+Equations%22#v=onepage&q=%22Handbook%20of%20Differential%20Equations%22&f=false|date=12 May 2014|publisher=Elsevier Science|isbn=978-1-4832-6396-0}}<br />
<br />
==外部链接==<br />
<br />
{{wikiquote}}<br />
<br />
{{Wikibooks|Ordinary Differential Equations}}<br />
<br />
{{Wikiversity|Differential equations}}<br />
<br />
{{EB1911 poster|Differential Equation}}<br />
<br />
*{{Commonscatinline|Differential equations}}<br />
<br />
*[http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/ Lectures on Differential Equations] [[MIT]] Open CourseWare Videos<br />
<br />
*[http://tutorial.math.lamar.edu/classes/de/de.aspx Online Notes / Differential Equations] Paul Dawkins, [[Lamar University]]<br />
<br />
*[http://www.sosmath.com/diffeq/diffeq.html Differential Equations], S.O.S. Mathematics<br />
<br />
*[http://www.fioravante.patrone.name/mat/u-u/en/differential_equations_intro.htm Introduction to modeling via differential equations] Introduction to modeling by means of differential equations, with critical remarks.<br />
<br />
*[http://user.mendelu.cz/marik/maw/index.php?lang=en&form=ode Mathematical Assistant on Web] Symbolic ODE tool, using [[Maxima (software)|Maxima]]<br />
<br />
*[http://eqworld.ipmnet.ru/en/solutions/ode.htm Exact Solutions of Ordinary Differential Equations]<br />
<br />
*[http://www.hedengren.net/research/models.htm Collection of ODE and DAE models of physical systems] MATLAB models<br />
<br />
*[http://www.jirka.org/diffyqs/ Notes on Diffy Qs: Differential Equations for Engineers] An introductory textbook on differential equations by Jiri Lebl of [[UIUC]]<br />
<br />
*[http://www.khanacademy.org/math/differential-equations Khan Academy Video playlist on differential equations ] Topics covered in a first year course in differential equations.<br />
<br />
*[https://web.archive.org/web/20130607120716/http://math.rareinfos.com/category/courses/solutions-differential-equations/homogeneous-linear-systems/ MathDiscuss Video playlist on differential equations ]<br />
<br />
==编者推荐==<br />
[https://campus.swarma.org/course/1646 Introduction II: Differential Equations]<br />
[https://campus.swarma.org/course/2099 常微分方程]<br />
[https://campus.swarma.org/course/2003 凯风研读营之“复杂系统自动建模专题”]<br />
[https://campus.swarma.org/course/1392 Matlab 基础与应用:微分方程]<br />
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本中文词条由[[用户:Yuling|Yuling]]编译,[[用户:CecileLi|CecileLi]]审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B&diff=30649微分方程2022-04-23T14:39:24Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=数学,方程<br />
|description=将一个或多个函数及其导数相互关联的方程。<br />
}}<br />
[[File:Elmer-pump-heatequation.png|thumb|350px|通过求解热力学方程,我们建立了泵壳内传热的可视化模型。热量在内部产生并在边界冷却,从而为整体提供稳定的温度分布。]]<br />
在数学上,'''微分方程 Differential Equation'''是可以将一个或多个函数及其导数相互关联的方程。<ref name="Zill2012">{{cite book|author=Dennis G. Zill|title=A First Course in Differential Equations with Modeling Applications|url=https://books.google.com/books?id=pasKAAAAQBAJ&printsec=frontcover#v=snippet&q=%22ordinary%20differential%22&f=false|date=15 March 2012|publisher=Cengage Learning|isbn=1-285-40110-7}}</ref>在实际应用中,函数通常代表物理量,导数代表其变化率,而微分方程则定义了两者之间的关系。由于这种关系十分普遍,因此微分方程在包括工程学、物理学、经济学和生物学在内的许多学科中得到了广泛的应用。<br />
<br />
<br />
微分方程的研究主要包括对微分方程解(满足每个方程的函数集)及其解的性质的研究。只有最简单的微分方程才能直接用公式求解;然而,有时无需精确计算便可以确定给定微分方程的解的许多性质。<br />
<br />
<br />
一般地,当闭式解不存在时,可以用计算机求方程的近似解。动力系统理论着重于对由微分方程描述的系统进行定性分析。同时,现在已经得出了许多数值方法来计算给定精度下微分方程的解。<br />
<br />
<br />
<br />
==历史==<br />
微分方程是在牛顿和莱布尼茨发明微积分后才出现的。Isaac Newton 艾萨克·牛顿在他1671年的著作《无限的循环与系列 Method of Fluxions》的第二章<ref>Newton, Isaac. (c.1671). Methodus Fluxionum et Serierum Infinitarum (The Method of Fluxions and Infinite Series), published in 1736 [Opuscula, 1744, Vol. I. p. 66].</ref>中列出了三种微分方程:<br />
<br />
<br />
<br />
:<math><br />
\begin{align}<br />
& \frac {dy}{dx} = f(x) \\[5pt]<br />
& \frac {dy}{dx} = f(x,y) \\[5pt]<br />
& x_1 \frac {\partial y}{\partial x_1} + x_2 \frac {\partial y}{\partial x_2} = y<br />
\end{align}<br />
</math><br />
<br />
<br />
在这些例子中,{{mvar|y}}是自变量 {{mvar|x}}(或者是<math>x_1</math> 和 <math>x_2</math>)的未知函数,并且 {{mvar|f}} 是一个给定的函数。<br />
<br />
<br />
他利用无穷级数来求解这些以及其他例子,并讨论了解的非唯一性。<br />
<br />
<br />
雅可比·伯努利 Jacob Bernoulli在1695年提出了伯努利微分方程。<ref>{{Citation | last1=Bernoulli | first1=Jacob | author1-link=Jacob Bernoulli | title=Explicationes, Annotationes & Additiones ad ea, quae in Actis sup. de Curva Elastica, Isochrona Paracentrica, & Velaria, hinc inde memorata, & paratim controversa legundur; ubi de Linea mediarum directionum, alliisque novis | year=1695 | journal=[[Acta Eruditorum]]}}</ref>这种方程是'''常微分方程 Ordinary Differential Equation'''的一种形式,<br />
<br />
<br />
: <math>y'+ P(x)y = Q(x)y^n\,</math><br />
<br />
<br />
莱布尼茨 Leibniz于第二年将方程简化从而得到了方程的解。<ref>{{Citation | last1=Hairer | first1=Ernst | last2=Nørsett | first2=Syvert Paul | last3=Wanner | first3=Gerhard | title=Solving ordinary differential equations I: Nonstiff problems | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-3-540-56670-0 | year=1993}}</ref><br />
<br />
<br />
历史上,让·勒朗·达朗贝尔 Jean le Rond d'Alembert,欧拉 Leonhard Euler,丹尼尔·伯努利 Daniel Bernoulli和约瑟夫·路易斯·拉格朗日 Joseph-Louis Lagrange等都研究过弦(比如乐器的弦)振动问题。<ref>{{cite journal|url = http://homes.chass.utoronto.ca/~cfraser/vibration.pdf |title = Review of ''The evolution of dynamics, vibration theory from 1687 to 1742'', by John T. Cannon and Sigalia Dostrovsky|last= Frasier|first=Craig|journal=Bulletin (New Series) of the American Mathematical Society |date=July 1983 |volume= 9| issue = 1}}</ref><ref>{{cite journal |first=Gerard F. |last=Wheeler |first2=William P. |last2=Crummett |title=The Vibrating String Controversy |journal= [[American Journal of Physics|Am. J. Phys.]] |year=1987 |volume=55 |issue=1 |pages=33–37 |doi=10.1119/1.15311 |bibcode = 1987AmJPh..55...33W }}</ref><ref>For a special collection of the 9 groundbreaking papers by the three authors, see [http://www.lynge.com/item.php?bookid=38975&s_currency=EUR&c_sourcepage= First Appearance of the wave equation: D'Alembert, Leonhard Euler, Daniel Bernoulli. - the controversy about vibrating strings] (retrieved 13 Nov 2012). Herman HJ Lynge and Son.</ref><ref>For de Lagrange's contributions to the acoustic wave equation, can consult [https://books.google.com/books?id=D8GqhULfKfAC&pg=PA18 Acoustics: An Introduction to Its Physical Principles and Applications] Allan D. Pierce, Acoustical Soc of America, 1989; page 18.(retrieved 9 Dec 2012)</ref> 1746年,达朗贝尔发现了一维波动方程,十年之内,欧拉又发现了三维波动方程。<ref name=Speiser>Speiser, David. ''[https://books.google.com/books?id=9uf97reZZCUC&pg=PA191 Discovering the Principles of Mechanics 1600-1800]'', p. 191 (Basel: Birkhäuser, 2008).</ref><br />
<br />
<br />
欧拉-拉格朗日方程式 Euler–Lagrange equation是欧拉和拉格朗日在18世纪50年代结合他们对等时降线问题的研究而发明的。这是一个不考虑起始点的曲线求解问题,其中一个加权的粒子将在一个给定的时间内下降到一个固定的点。拉格朗日在1755年解决了这个问题,并将其寄给欧拉。二人都进一步发展了拉格朗日的方法并将其应用于力学,从而促使了拉格朗日力学的形成。<br />
<br />
<br />
1822年,Joseph Fourier 傅立叶在《热的分析理论 Théorie analytique de la chaleur》中发表了他关于热流的研究成果,<ref>{{Cite book | last = Fourier | first = Joseph | title = Théorie analytique de la chaleur | publisher = Firmin Didot Père et Fils | year = 1822 | location = Paris | language = French | url=https://archive.org/details/bub_gb_TDQJAAAAIAAJ | oclc=2688081 }}</ref>其中他以[[牛顿的冷却定律 Newton's law of cooling]]为基础进行推导,即两个相邻分子之间的热流与它们之间微小的温差成正比。这本书中包含了傅立叶关于热传导扩散的热方程式的建议。现在,每一个学习数学物理的学生都需要学习这类偏微分方程。<br />
<br />
<br />
==示例==<br />
在经典力学中,物体运动是由其不断随时间变化的位置和速度来描述的。这些变量的表达在牛顿定律中是动态的(给定位置、速度、加速度和作用在物体上的各种力) ,并以时间函数的形式给出了未知物体位置的微分方程。<br />
<br />
<br />
在某些情况下,这种微分方程(称为运动方程)可以精确地求解。<br />
<br />
<br />
使用微分方程来模拟现实世界问题的一个例子是仅考虑重力和空气阻力来确定球在空中落下的速度。球对地面的加速度是重力加速度减去由于空气阻力提供的加速度。重力被认为是常数,空气阻力可以被模拟为与球的速度成正比。这意味着球的加速度,也就是其速度的导数,取决于速度(而速度取决于时间)。找到时间的函数--速度--需要解决一个微分方程问题并验证其正确性。<br />
<br />
<br />
==微分方程的类型==<br />
微分方程可分为以下几种类型。除了描述方程本身的性质之外,微分方程的多种类型为我们选择何种解决方案提供了多种指导。常见的微分方程有: 常微分/偏微分方程、线性/非线性方程和齐次/非齐次方程。微分方程还有许多类型,以及许多在特定的情况下实用的其它性质和子类。<br />
<br />
<br />
<br />
===常微分方程===<br />
'''常微分方程 ordinary differential equation(ODE)'''是只含有一个实变量或复变量的未知函数,其导数以及此函数的一些方程。未知函数因变量(通常由 {{mvar|y}} 表示),其常常随 {{mvar|x}}的变化而变化 。因此 {{mvar|x}} 通常被称为方程式的自变量。“常微分方程”一词与偏微分方程一词相比,后者涉及一个以上的独立变量。<br />
<br />
<br />
线性微分方程是指方程中未知函数及其导数都是线性的微分方程。关于这些方程的理论发展得很好,在多数情况下可以用积分来表示它们的解。<br />
<br />
<br />
物理学中遇到的大多数常微分方程都是线性的。因此,大多数特殊函数可以定义为线性微分方程的解(见完整性函数)。<br />
<br />
<br />
一般地,微分方程的解不能用解析解表示,而会在计算机上利用数值方法求解。<br />
<br />
<br />
===偏微分方程===<br />
'''偏微分方程 Partial Differential Equation(PDE)'''是一种包含多元函数及其偏导数的微分方程函数(这与处理单变量函数及其导数的常微分方程不同)。偏微分方程可用于描述涉及多元函数的问题求闭式解,或者用于创建相关的计算机模型。<br />
<br />
<br />
偏微分方程可以用来描述自然界中各种各样的现象,如声音、热量、静电、电动力学、流体流动、弹性和量子力学等。这些看起来截然不同的物理现象其实都可以用相似的偏微分方程表达。正如常微分方程常被用于对一维动力系统进行建模一样,偏微分方程常被用于对多维系统进行建模。随机偏微分方程延伸了偏微分方程在模拟随机性上的应用。<br />
<br />
<br />
===非线性微分方程===<br />
<br />
非线性微分方程是微分方程的一种,但它不是关于未知函数及其导数的线性方程(这里不考虑函数本身的线性或非线性)。能够精确求解非线性微分方程的方法很少; 那些已有的方法通常依赖于方程具有某种特定的对称性。非线性微分方程在更长的时间段内表现出非常复杂的行为,具有混沌特性。即使非线性微分方程也有解的存在性、唯一性和可扩展性等基本问题以及初边值问题的适定性问题,但对其研究也是一个难题(可参考纳维-斯托克斯方程的存在性和光滑性)。然而,如果微分方程是一个有意义物理过程的正确表述,那么人们期望它有一个解析解。 <br />
<br />
<br />
线性微分方程经常作为非线性方程的近似形式出现。这些近似只有某些限制条件下才有效。例如,谐振子方程是非线性摆方程的近似这一情况只有对于小幅度振荡是有效的(见下文)。<br />
<br />
===方程的阶===<br />
<br />
微分方程的阶数是由它们的导数的最高阶决定的。只含有一阶导数的方程是一阶微分方程,含有二阶导数的方程是二阶微分方程,等等。描述自然现象的微分方程几乎总是只有一阶和二阶导数<ref>[[Eric W Weisstein|Weisstein, Eric W]]. "Ordinary Differential Equation Order." From [[MathWorld]]--A Wolfram Web Resource. http://mathworld.wolfram.com/OrdinaryDifferentialEquationOrder.html</ref><ref>[http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx Order and degree of a differential equation] {{Webarchive|url=https://web.archive.org/web/20160401070512/http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx |date=2016-04-01 }}, accessed Dec 2015.</ref>,但也有一些例外,例如薄膜方程,它是一个四阶偏微分方程。<br />
<br />
===示例===<br />
<br />
在第一组示例中,待求解的''u''是''x''的函数,''c''和''ω''是应该已知的常数。常微分方程和偏微分方程这两种广义分类下还要区分微分方程的线性和非线性,以及区分微分方程的齐次和非齐次。<br />
<br />
<br />
* 非齐次一阶常系数常微分方程:<br />
<br />
<br />
:: <math> \frac{du}{dx} = cu+x^2. </math><br />
<br />
<br />
<br />
* 齐次二阶线性常微分方程:<br />
<br />
<br />
:: <math> \frac{d^2u}{dx^2} - x\frac{du}{dx} + u = 0. </math><br />
<br />
<br />
* 用于描述简谐振动的齐次二阶常系数常系数微分方程:<br />
<br />
:: <math> \frac{d^2u}{dx^2} + \omega^2u = 0. </math><br />
<br />
<br />
* 非齐次一阶非线性常微分方程:<br />
<br />
:: <math> \frac{du}{dx} = u^2 + 4. </math><br />
<br />
<br />
* 用于描述摆长为L的钟摆运动的二阶非线性(因正弦函数产生)常微分方程:<br />
<br />
<br />
:: <math> L\frac{d^2u}{dx^2} + g\sin u = 0. </math><br />
<br />
<br />
<br />
在下一组例子中,未知函数''u''依赖于两个变量''x'' 和 ''t''或者''x''和''y''。<br />
<br />
<br />
<br />
* 齐次一阶线性偏微分方程:<br />
<br />
<br />
:: <math> \frac{\partial u}{\partial t} + t\frac{\partial u}{\partial x} = 0. </math><br />
<br />
<br />
<br />
<br />
*齐次二阶线性常系数椭圆形偏微分方程,也称为拉普拉斯方程:<br />
<br />
<br />
:: <math> \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0. </math><br />
<br />
<br />
*齐次三阶非线性偏微分方程:<br />
<br />
<br />
:: <math> \frac{\partial u}{\partial t} = 6u\frac{\partial u}{\partial x} - \frac{\partial^3 u}{\partial x^3}. </math><br />
<br />
==解的存在性==<br />
<br />
<br />
<br />
解微分方程不同于解代数方程。方程解的情况往往是不确定的,而且解是否唯一或是否存在也是值得关注的问题。<br />
<br />
<br />
对于一阶初值问题,皮亚诺存在性定理给出了一组解存在的情况。给定的x-y平面上的任意点 <math>(a,b)</math> ,定义矩形区域 <math>Z</math> ,如,<math>Z = [l,m]\times[n,p]</math> 而且 <math>(a,b)</math> 是 <math>Z</math> 内部一点。如果我们给出一个微分方程 <math>\frac{dy}{dx} = g(x,y)</math> 和当<math>x=a</math>时<math>y=b</math>,如果<math>g(x,y)</math>和<math>\frac{\partial g}{\partial x}</math>在<math>Z</math>上是连续的,那么这个问题就有一个局部解。这个解在以 <math>a</math> 为中心的某些区间上存在,其可能不是唯一的。(其他结果请参见常微分方程。)<br />
<br />
<br />
然而,这只能帮助我们解决一阶初始值问题。假设我们有一个n阶线性初始值问题:<br />
<br />
<br />
<br />
:<math><br />
f_{n}(x)\frac{d^n y}{dx^n} + \cdots + f_{1}(x)\frac{d y}{dx} + f_{0}(x)y = g(x)<br />
</math><br />
<br />
<br />
其中有<br />
<br />
:<math><br />
y(x_{0})=y_{0}, y'(x_{0}) = y'_{0}, y''(x_{0}) = y''_{0}, \cdots<br />
</math><br />
<br />
<br />
对于任意非零 <math>f_{n}(x)</math> ,如果<math>\{f_{0},f_{1},\cdots\}</math> 和 <math>g</math>在某个包含<math>x_{0}</math>的区间上连续,则<math>y</math>是存在且唯一的。<ref>{{cite book|last1=Zill|first1=Dennis G.|title=A First Course in Differential Equations|publisher=Brooks/Cole|isbn=0-534-37388-7|edition=5th|year=2001}}</ref><br />
<br />
==相关概念==<br />
<br />
<br />
<br />
*延迟微分方程(DDE)是一元函数的方程,变量通常为时间,其中函数在一定时间点的微分会被较早时间点的函数值表达。<br />
<br />
*积分微分方程(IDE)结合了微分方程和积分方程。<br />
<br />
*随机微分方程(SDE)中的未知量处于随机过程,并且涉及一些已知的随机过程,例如,扩散方程中的维纳过程。<br />
<br />
*随机偏微分方程(SPDE)是一种含空间和时间噪声过程的广义随机微分方程,它通常应用于量子场论以及统计力学中。<br />
<br />
* 微分代数方程(DAE)是一种含微分和代数项的微分方程,通常以隐式形式给出。<br />
<br />
==与差分方程之间的联系==<br />
<br />
<br />
微分方程理论与差分方程理论密切相关。在差分方程理论中,坐标系中只假定存在离散值,计算中会涉及到未知函数或已知函数的值以及坐标附近的值。许多求微分方程数值解或研究微分方程性质的方法,都会涉及通过相应差分方程的解来逼近微分方程的解。<br />
<br />
== 应用==<br />
<br />
<br />
<br />
<br />
微分方程的研究可以应用于许多领域,如理论数学、应用数学、物理学和工程学,它们都与各种类型的微分方程的性质有关。理论数学关注解的存在性和唯一性,而应用数学则强调求解方法的严格准确性。从天体运动到桥梁设计,再到神经元之间的相互作用,微分方程在几乎所有物理、技术或生物过程的建模中都扮演着重要的角色。用于解决实际问题的微分方程,不一定是直接可解的,如可能不存在闭式解。但我们可以用数值方法来近似得到方程的解。<br />
<br />
<br />
<br />
许多物理和化学的基本定律都可以用微分方程来表示。在生物学和经济学中,微分方程被用来模拟复杂系统的行为。微分方程理论最初是与其起源并得到应用的科学一起发展起来的。然而,有时完全不同的科学领域,却可能产生相同的微分方程。当这种情况发生时,方程后面的数学理论可以被看作是不同现象背后的统一原则。例如,光和声在大气中的传播,或是池塘表面的水波的传播。所有这些过程都可以用相同的二阶偏微分方程来描述,即波动方程。我们把光和声音想象成与水波相似的形式。由约瑟夫·傅里叶提出的热传导的理论由另一个二阶偏微分方程——热方程所支配。事实证明,许多扩散过程,虽然看上去形式不同,但都可以同一个方程来描述;。例如,金融学中的布莱克-斯科尔斯方程就与热方程有关。<br />
<br />
<br />
事实上,同一类型的微分方程可以应用于不同领域这样的现象屡见不鲜,这足以证明微分方程这一课题的重要性。参见已命名的微分方程列表。<br />
<br />
==参见==<br />
<br />
*复微分方程<br />
*精确微分方程<br />
*<br />
泛函微分方程<br />
*<br />
初始条件<br />
*<br />
积分方程<br />
*<br />
求解常微分方程的数值方法<br />
*求解偏微分方程的数值方法<br />
*关于解的存在性和唯一性的皮卡德–林德洛夫定理<br />
*递推关系,也称为差分方程<br />
*抽象微分方程<br />
*微分方程组<br />
{{div col end}}<br />
<br />
==参考文献==<br />
<br />
{{reflist|30em}}<br />
<br />
==拓展阅读==<br />
<br />
*{{cite book |first=P. |last=Abbott |first2=H. |last2=Neill |title=Teach Yourself Calculus |year=2003 |pages=266–277 }}<br />
<br />
*{{cite book |first=P. |last=Blanchard |authorlink2=Robert L. Devaney |first2=R. L. |last2=Devaney |first3=G. R. |last3=Hall |title=Differential Equations |location= |publisher=Thompson |year=2006 }}<br />
<br />
*{{cite book |first=W. |last=Boyce | first2=R. |last2=DiPrima| first3=D. |last3=Meade| title=Elementary Differential Equations and Boundary Value Problems|publisher=Wiley |year=2017}}<br />
<br />
*{{cite book |first=E. A. |last=Coddington |first2=N. |last2=Levinson |title=Theory of Ordinary Differential Equations |url=https://archive.org/details/theoryofordinary00codd |url-access=registration |publisher=McGraw-Hill |year=1955 }}<br />
<br />
*{{cite book |first=E. L. |last=Ince |title=Ordinary Differential Equations |publisher=Dover |year=1956 }}<br />
<br />
*{{cite book |first=W. |last=Johnson |url=http://www.hti.umich.edu/cgi/b/bib/bibperm?q1=abv5010.0001.001 |title=A Treatise on Ordinary and Partial Differential Equations |publisher=John Wiley and Sons |year=1913 }} In [http://hti.umich.edu/u/umhistmath/ University of Michigan Historical Math Collection]<br />
<br />
*{{cite book |first=A. D. |last=Polyanin |first2=V. F. |last2=Zaitsev |title=Handbook of Exact Solutions for Ordinary Differential Equations |edition=2nd |publisher=Chapman & Hall/CRC Press |location=Boca Raton |year=2003 |isbn=1-58488-297-2 }}<br />
<br />
*{{cite book |first=R. I. |last=Porter |title=Further Elementary Analysis |year=1978 |chapter=XIX Differential Equations }}<br />
<br />
*{{Cite book| last = Teschl| given = Gerald|authorlink=Gerald Teschl| title = Ordinary Differential Equations and Dynamical Systems| publisher=[[American Mathematical Society]]| place = [[Providence, Rhode Island|Providence]]| year = 2012| isbn= 978-0-8218-8328-0| url = http://www.mat.univie.ac.at/~gerald/ftp/book-ode/}}<br />
<br />
*{{cite book|author=Daniel Zwillinger|title=Handbook of Differential Equations|url=https://books.google.com/?id=n7TiBQAAQBAJ&printsec=frontcover&dq=%22Handbook+of+Differential+Equations%22#v=onepage&q=%22Handbook%20of%20Differential%20Equations%22&f=false|date=12 May 2014|publisher=Elsevier Science|isbn=978-1-4832-6396-0}}<br />
<br />
==外部链接==<br />
<br />
{{wikiquote}}<br />
<br />
{{Wikibooks|Ordinary Differential Equations}}<br />
<br />
{{Wikiversity|Differential equations}}<br />
<br />
{{EB1911 poster|Differential Equation}}<br />
<br />
*{{Commonscatinline|Differential equations}}<br />
<br />
*[http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/ Lectures on Differential Equations] [[MIT]] Open CourseWare Videos<br />
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*[http://tutorial.math.lamar.edu/classes/de/de.aspx Online Notes / Differential Equations] Paul Dawkins, [[Lamar University]]<br />
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*[http://www.sosmath.com/diffeq/diffeq.html Differential Equations], S.O.S. Mathematics<br />
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*[http://www.fioravante.patrone.name/mat/u-u/en/differential_equations_intro.htm Introduction to modeling via differential equations] Introduction to modeling by means of differential equations, with critical remarks.<br />
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*[http://user.mendelu.cz/marik/maw/index.php?lang=en&form=ode Mathematical Assistant on Web] Symbolic ODE tool, using [[Maxima (software)|Maxima]]<br />
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*[http://eqworld.ipmnet.ru/en/solutions/ode.htm Exact Solutions of Ordinary Differential Equations]<br />
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*[http://www.hedengren.net/research/models.htm Collection of ODE and DAE models of physical systems] MATLAB models<br />
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*[http://www.jirka.org/diffyqs/ Notes on Diffy Qs: Differential Equations for Engineers] An introductory textbook on differential equations by Jiri Lebl of [[UIUC]]<br />
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*[http://www.khanacademy.org/math/differential-equations Khan Academy Video playlist on differential equations ] Topics covered in a first year course in differential equations.<br />
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*[https://web.archive.org/web/20130607120716/http://math.rareinfos.com/category/courses/solutions-differential-equations/homogeneous-linear-systems/ MathDiscuss Video playlist on differential equations ]<br />
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==编者推荐==<br />
[https://campus.swarma.org/course/1646 Introduction II: Differential Equations]<br />
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本中文词条由[[用户:Yuling|Yuling]]编译,[[用户:CecileLi|CecileLi]]审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B&diff=30648微分方程2022-04-23T14:36:11Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=数学,方程<br />
|description=将一个或多个函数及其导数相互关联的方程。<br />
}}<br />
[[File:Elmer-pump-heatequation.png|thumb|350px|通过求解热力学方程,我们建立了泵壳内传热的可视化模型。热量在内部产生并在边界冷却,从而为整体提供稳定的温度分布。]]<br />
在数学上,'''微分方程 Differential Equation'''是可以将一个或多个函数及其导数相互关联的方程。<ref name="Zill2012">{{cite book|author=Dennis G. Zill|title=A First Course in Differential Equations with Modeling Applications|url=https://books.google.com/books?id=pasKAAAAQBAJ&printsec=frontcover#v=snippet&q=%22ordinary%20differential%22&f=false|date=15 March 2012|publisher=Cengage Learning|isbn=1-285-40110-7}}</ref>在实际应用中,函数通常代表物理量,导数代表其变化率,而微分方程则定义了两者之间的关系。由于这种关系十分普遍,因此微分方程在包括工程学、物理学、经济学和生物学在内的许多学科中得到了广泛的应用。<br />
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微分方程的研究主要包括对微分方程解(满足每个方程的函数集)及其解的性质的研究。只有最简单的微分方程才能直接用公式求解;然而,有时无需精确计算便可以确定给定微分方程的解的许多性质。<br />
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一般地,当闭式解不存在时,可以用计算机求方程的近似解。动力系统理论着重于对由微分方程描述的系统进行定性分析。同时,现在已经得出了许多数值方法来计算给定精度下微分方程的解。<br />
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==历史==<br />
微分方程是在牛顿和莱布尼茨发明微积分后才出现的。Isaac Newton 艾萨克·牛顿在他1671年的著作《无限的循环与系列 Method of Fluxions》的第二章<ref>Newton, Isaac. (c.1671). Methodus Fluxionum et Serierum Infinitarum (The Method of Fluxions and Infinite Series), published in 1736 [Opuscula, 1744, Vol. I. p. 66].</ref>中列出了三种微分方程:<br />
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:<math><br />
\begin{align}<br />
& \frac {dy}{dx} = f(x) \\[5pt]<br />
& \frac {dy}{dx} = f(x,y) \\[5pt]<br />
& x_1 \frac {\partial y}{\partial x_1} + x_2 \frac {\partial y}{\partial x_2} = y<br />
\end{align}<br />
</math><br />
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在这些例子中,{{mvar|y}}是自变量 {{mvar|x}}(或者是<math>x_1</math> 和 <math>x_2</math>)的未知函数,并且 {{mvar|f}} 是一个给定的函数。<br />
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他利用无穷级数来求解这些以及其他例子,并讨论了解的非唯一性。<br />
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雅可比·伯努利 Jacob Bernoulli在1695年提出了伯努利微分方程。<ref>{{Citation | last1=Bernoulli | first1=Jacob | author1-link=Jacob Bernoulli | title=Explicationes, Annotationes & Additiones ad ea, quae in Actis sup. de Curva Elastica, Isochrona Paracentrica, & Velaria, hinc inde memorata, & paratim controversa legundur; ubi de Linea mediarum directionum, alliisque novis | year=1695 | journal=[[Acta Eruditorum]]}}</ref>这种方程是'''常微分方程 Ordinary Differential Equation'''的一种形式,<br />
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: <math>y'+ P(x)y = Q(x)y^n\,</math><br />
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莱布尼茨 Leibniz于第二年将方程简化从而得到了方程的解。<ref>{{Citation | last1=Hairer | first1=Ernst | last2=Nørsett | first2=Syvert Paul | last3=Wanner | first3=Gerhard | title=Solving ordinary differential equations I: Nonstiff problems | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-3-540-56670-0 | year=1993}}</ref><br />
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历史上,让·勒朗·达朗贝尔 Jean le Rond d'Alembert,欧拉 Leonhard Euler,丹尼尔·伯努利 Daniel Bernoulli和约瑟夫·路易斯·拉格朗日 Joseph-Louis Lagrange等都研究过弦(比如乐器的弦)振动问题。<ref>{{cite journal|url = http://homes.chass.utoronto.ca/~cfraser/vibration.pdf |title = Review of ''The evolution of dynamics, vibration theory from 1687 to 1742'', by John T. Cannon and Sigalia Dostrovsky|last= Frasier|first=Craig|journal=Bulletin (New Series) of the American Mathematical Society |date=July 1983 |volume= 9| issue = 1}}</ref><ref>{{cite journal |first=Gerard F. |last=Wheeler |first2=William P. |last2=Crummett |title=The Vibrating String Controversy |journal= [[American Journal of Physics|Am. J. Phys.]] |year=1987 |volume=55 |issue=1 |pages=33–37 |doi=10.1119/1.15311 |bibcode = 1987AmJPh..55...33W }}</ref><ref>For a special collection of the 9 groundbreaking papers by the three authors, see [http://www.lynge.com/item.php?bookid=38975&s_currency=EUR&c_sourcepage= First Appearance of the wave equation: D'Alembert, Leonhard Euler, Daniel Bernoulli. - the controversy about vibrating strings] (retrieved 13 Nov 2012). Herman HJ Lynge and Son.</ref><ref>For de Lagrange's contributions to the acoustic wave equation, can consult [https://books.google.com/books?id=D8GqhULfKfAC&pg=PA18 Acoustics: An Introduction to Its Physical Principles and Applications] Allan D. Pierce, Acoustical Soc of America, 1989; page 18.(retrieved 9 Dec 2012)</ref> 1746年,达朗贝尔发现了一维波动方程,十年之内,欧拉又发现了三维波动方程。<ref name=Speiser>Speiser, David. ''[https://books.google.com/books?id=9uf97reZZCUC&pg=PA191 Discovering the Principles of Mechanics 1600-1800]'', p. 191 (Basel: Birkhäuser, 2008).</ref><br />
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欧拉-拉格朗日方程式 Euler–Lagrange equation是欧拉和拉格朗日在18世纪50年代结合他们对等时降线问题的研究而发明的。这是一个不考虑起始点的曲线求解问题,其中一个加权的粒子将在一个给定的时间内下降到一个固定的点。拉格朗日在1755年解决了这个问题,并将其寄给欧拉。二人都进一步发展了拉格朗日的方法并将其应用于力学,从而促使了拉格朗日力学的形成。<br />
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1822年,Joseph Fourier 傅立叶在《热的分析理论 Théorie analytique de la chaleur》中发表了他关于热流的研究成果,<ref>{{Cite book | last = Fourier | first = Joseph | title = Théorie analytique de la chaleur | publisher = Firmin Didot Père et Fils | year = 1822 | location = Paris | language = French | url=https://archive.org/details/bub_gb_TDQJAAAAIAAJ | oclc=2688081 }}</ref>其中他以[[牛顿的冷却定律 Newton's law of cooling]]为基础进行推导,即两个相邻分子之间的热流与它们之间微小的温差成正比。这本书中包含了傅立叶关于热传导扩散的热方程式的建议。现在,每一个学习数学物理的学生都需要学习这类偏微分方程。<br />
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==示例==<br />
在经典力学中,物体运动是由其不断随时间变化的位置和速度来描述的。这些变量的表达在牛顿定律中是动态的(给定位置、速度、加速度和作用在物体上的各种力) ,并以时间函数的形式给出了未知物体位置的微分方程。<br />
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在某些情况下,这种微分方程(称为运动方程)可以精确地求解。<br />
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使用微分方程来模拟现实世界问题的一个例子是仅考虑重力和空气阻力来确定球在空中落下的速度。球对地面的加速度是重力加速度减去由于空气阻力提供的加速度。重力被认为是常数,空气阻力可以被模拟为与球的速度成正比。这意味着球的加速度,也就是其速度的导数,取决于速度(而速度取决于时间)。找到时间的函数--速度--需要解决一个微分方程问题并验证其正确性。<br />
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==微分方程的类型==<br />
微分方程可分为以下几种类型。除了描述方程本身的性质之外,微分方程的多种类型为我们选择何种解决方案提供了多种指导。常见的微分方程有: 常微分/偏微分方程、线性/非线性方程和齐次/非齐次方程。微分方程还有许多类型,以及许多在特定的情况下实用的其它性质和子类。<br />
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===常微分方程===<br />
'''常微分方程 ordinary differential equation(ODE)'''是只含有一个实变量或复变量的未知函数,其导数以及此函数的一些方程。未知函数因变量(通常由 {{mvar|y}} 表示),其常常随 {{mvar|x}}的变化而变化 。因此 {{mvar|x}} 通常被称为方程式的自变量。“常微分方程”一词与偏微分方程一词相比,后者涉及一个以上的独立变量。<br />
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线性微分方程是指方程中未知函数及其导数都是线性的微分方程。关于这些方程的理论发展得很好,在多数情况下可以用积分来表示它们的解。<br />
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物理学中遇到的大多数常微分方程都是线性的。因此,大多数特殊函数可以定义为线性微分方程的解(见完整性函数)。<br />
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一般地,微分方程的解不能用解析解表示,而会在计算机上利用数值方法求解。<br />
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===偏微分方程===<br />
'''偏微分方程 Partial Differential Equation(PDE)'''是一种包含多元函数及其偏导数的微分方程函数(这与处理单变量函数及其导数的常微分方程不同)。偏微分方程可用于描述涉及多元函数的问题求闭式解,或者用于创建相关的计算机模型。<br />
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偏微分方程可以用来描述自然界中各种各样的现象,如声音、热量、静电、电动力学、流体流动、弹性和量子力学等。这些看起来截然不同的物理现象其实都可以用相似的偏微分方程表达。正如常微分方程常被用于对一维动力系统进行建模一样,偏微分方程常被用于对多维系统进行建模。随机偏微分方程延伸了偏微分方程在模拟随机性上的应用。<br />
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===非线性微分方程===<br />
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非线性微分方程是微分方程的一种,但它不是关于未知函数及其导数的线性方程(这里不考虑函数本身的线性或非线性)。能够精确求解非线性微分方程的方法很少; 那些已有的方法通常依赖于方程具有某种特定的对称性。非线性微分方程在更长的时间段内表现出非常复杂的行为,具有混沌特性。即使非线性微分方程也有解的存在性、唯一性和可扩展性等基本问题以及初边值问题的适定性问题,但对其研究也是一个难题(可参考纳维-斯托克斯方程的存在性和光滑性)。然而,如果微分方程是一个有意义物理过程的正确表述,那么人们期望它有一个解析解。 <br />
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线性微分方程经常作为非线性方程的近似形式出现。这些近似只有某些限制条件下才有效。例如,谐振子方程是非线性摆方程的近似这一情况只有对于小幅度振荡是有效的(见下文)。<br />
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===方程的阶===<br />
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微分方程的阶数是由它们的导数的最高阶决定的。只含有一阶导数的方程是一阶微分方程,含有二阶导数的方程是二阶微分方程,等等。描述自然现象的微分方程几乎总是只有一阶和二阶导数<ref>[[Eric W Weisstein|Weisstein, Eric W]]. "Ordinary Differential Equation Order." From [[MathWorld]]--A Wolfram Web Resource. http://mathworld.wolfram.com/OrdinaryDifferentialEquationOrder.html</ref><ref>[http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx Order and degree of a differential equation] {{Webarchive|url=https://web.archive.org/web/20160401070512/http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx |date=2016-04-01 }}, accessed Dec 2015.</ref>,但也有一些例外,例如薄膜方程,它是一个四阶偏微分方程。<br />
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===示例===<br />
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在第一组示例中,待求解的''u''是''x''的函数,''c''和''ω''是应该已知的常数。常微分方程和偏微分方程这两种广义分类下还要区分微分方程的线性和非线性,以及区分微分方程的齐次和非齐次。<br />
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* 非齐次一阶常系数常微分方程:<br />
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:: <math> \frac{du}{dx} = cu+x^2. </math><br />
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* 齐次二阶线性常微分方程:<br />
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:: <math> \frac{d^2u}{dx^2} - x\frac{du}{dx} + u = 0. </math><br />
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* 用于描述简谐振动的齐次二阶常系数常系数微分方程:<br />
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:: <math> \frac{d^2u}{dx^2} + \omega^2u = 0. </math><br />
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* 非齐次一阶非线性常微分方程:<br />
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:: <math> \frac{du}{dx} = u^2 + 4. </math><br />
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* 用于描述摆长为L的钟摆运动的二阶非线性(因正弦函数产生)常微分方程:<br />
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:: <math> L\frac{d^2u}{dx^2} + g\sin u = 0. </math><br />
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在下一组例子中,未知函数''u''依赖于两个变量''x'' 和 ''t''或者''x''和''y''。<br />
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* 齐次一阶线性偏微分方程:<br />
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:: <math> \frac{\partial u}{\partial t} + t\frac{\partial u}{\partial x} = 0. </math><br />
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*齐次二阶线性常系数椭圆形偏微分方程,也称为拉普拉斯方程:<br />
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:: <math> \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0. </math><br />
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*齐次三阶非线性偏微分方程:<br />
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:: <math> \frac{\partial u}{\partial t} = 6u\frac{\partial u}{\partial x} - \frac{\partial^3 u}{\partial x^3}. </math><br />
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==解的存在性==<br />
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解微分方程不同于解代数方程。方程解的情况往往是不确定的,而且解是否唯一或是否存在也是值得关注的问题。<br />
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对于一阶初值问题,皮亚诺存在性定理给出了一组解存在的情况。给定的x-y平面上的任意点 <math>(a,b)</math> ,定义矩形区域 <math>Z</math> ,如,<math>Z = [l,m]\times[n,p]</math> 而且 <math>(a,b)</math> 是 <math>Z</math> 内部一点。如果我们给出一个微分方程 <math>\frac{dy}{dx} = g(x,y)</math> 和当<math>x=a</math>时<math>y=b</math>,如果<math>g(x,y)</math>和<math>\frac{\partial g}{\partial x}</math>在<math>Z</math>上是连续的,那么这个问题就有一个局部解。这个解在以 <math>a</math> 为中心的某些区间上存在,其可能不是唯一的。(其他结果请参见常微分方程。)<br />
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然而,这只能帮助我们解决一阶初始值问题。假设我们有一个n阶线性初始值问题:<br />
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:<math><br />
f_{n}(x)\frac{d^n y}{dx^n} + \cdots + f_{1}(x)\frac{d y}{dx} + f_{0}(x)y = g(x)<br />
</math><br />
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其中有<br />
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:<math><br />
y(x_{0})=y_{0}, y'(x_{0}) = y'_{0}, y''(x_{0}) = y''_{0}, \cdots<br />
</math><br />
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对于任意非零 <math>f_{n}(x)</math> ,如果<math>\{f_{0},f_{1},\cdots\}</math> 和 <math>g</math>在某个包含<math>x_{0}</math>的区间上连续,则<math>y</math>是存在且唯一的。<ref>{{cite book|last1=Zill|first1=Dennis G.|title=A First Course in Differential Equations|publisher=Brooks/Cole|isbn=0-534-37388-7|edition=5th|year=2001}}</ref><br />
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==相关概念==<br />
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*延迟微分方程(DDE)是一元函数的方程,变量通常为时间,其中函数在一定时间点的微分会被较早时间点的函数值表达。<br />
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*积分微分方程(IDE)结合了微分方程和积分方程。<br />
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*随机微分方程(SDE)中的未知量处于随机过程,并且涉及一些已知的随机过程,例如,扩散方程中的维纳过程。<br />
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*随机偏微分方程(SPDE)是一种含空间和时间噪声过程的广义随机微分方程,它通常应用于量子场论以及统计力学中。<br />
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* 微分代数方程(DAE)是一种含微分和代数项的微分方程,通常以隐式形式给出。<br />
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==与差分方程之间的联系==<br />
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微分方程理论与差分方程理论密切相关。在差分方程理论中,坐标系中只假定存在离散值,计算中会涉及到未知函数或已知函数的值以及坐标附近的值。许多求微分方程数值解或研究微分方程性质的方法,都会涉及通过相应差分方程的解来逼近微分方程的解。<br />
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== 应用==<br />
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微分方程的研究可以应用于许多领域,如理论数学、应用数学、物理学和工程学,它们都与各种类型的微分方程的性质有关。理论数学关注解的存在性和唯一性,而应用数学则强调求解方法的严格准确性。从天体运动到桥梁设计,再到神经元之间的相互作用,微分方程在几乎所有物理、技术或生物过程的建模中都扮演着重要的角色。用于解决实际问题的微分方程,不一定是直接可解的,如可能不存在闭式解。但我们可以用数值方法来近似得到方程的解。<br />
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许多物理和化学的基本定律都可以用微分方程来表示。在生物学和经济学中,微分方程被用来模拟复杂系统的行为。微分方程理论最初是与其起源并得到应用的科学一起发展起来的。然而,有时完全不同的科学领域,却可能产生相同的微分方程。当这种情况发生时,方程后面的数学理论可以被看作是不同现象背后的统一原则。例如,光和声在大气中的传播,或是池塘表面的水波的传播。所有这些过程都可以用相同的二阶偏微分方程来描述,即波动方程。我们把光和声音想象成与水波相似的形式。由约瑟夫·傅里叶提出的热传导的理论由另一个二阶偏微分方程——热方程所支配。事实证明,许多扩散过程,虽然看上去形式不同,但都可以同一个方程来描述;。例如,金融学中的布莱克-斯科尔斯方程就与热方程有关。<br />
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事实上,同一类型的微分方程可以应用于不同领域这样的现象屡见不鲜,这足以证明微分方程这一课题的重要性。参见已命名的微分方程列表。<br />
<br />
==参见==<br />
<br />
*复微分方程<br />
*精确微分方程<br />
*<br />
泛函微分方程<br />
*<br />
初始条件<br />
*<br />
积分方程<br />
*<br />
求解常微分方程的数值方法<br />
*求解偏微分方程的数值方法<br />
*关于解的存在性和唯一性的皮卡德–林德洛夫定理<br />
*递推关系,也称为差分方程<br />
*抽象微分方程<br />
*微分方程组<br />
{{div col end}}<br />
<br />
==参考文献==<br />
<br />
{{reflist|30em}}<br />
<br />
==拓展阅读==<br />
<br />
*{{cite book |first=P. |last=Abbott |first2=H. |last2=Neill |title=Teach Yourself Calculus |year=2003 |pages=266–277 }}<br />
<br />
*{{cite book |first=P. |last=Blanchard |authorlink2=Robert L. Devaney |first2=R. L. |last2=Devaney |first3=G. R. |last3=Hall |title=Differential Equations |location= |publisher=Thompson |year=2006 }}<br />
<br />
*{{cite book |first=W. |last=Boyce | first2=R. |last2=DiPrima| first3=D. |last3=Meade| title=Elementary Differential Equations and Boundary Value Problems|publisher=Wiley |year=2017}}<br />
<br />
*{{cite book |first=E. A. |last=Coddington |first2=N. |last2=Levinson |title=Theory of Ordinary Differential Equations |url=https://archive.org/details/theoryofordinary00codd |url-access=registration |publisher=McGraw-Hill |year=1955 }}<br />
<br />
*{{cite book |first=E. L. |last=Ince |title=Ordinary Differential Equations |publisher=Dover |year=1956 }}<br />
<br />
*{{cite book |first=W. |last=Johnson |url=http://www.hti.umich.edu/cgi/b/bib/bibperm?q1=abv5010.0001.001 |title=A Treatise on Ordinary and Partial Differential Equations |publisher=John Wiley and Sons |year=1913 }} In [http://hti.umich.edu/u/umhistmath/ University of Michigan Historical Math Collection]<br />
<br />
*{{cite book |first=A. D. |last=Polyanin |first2=V. F. |last2=Zaitsev |title=Handbook of Exact Solutions for Ordinary Differential Equations |edition=2nd |publisher=Chapman & Hall/CRC Press |location=Boca Raton |year=2003 |isbn=1-58488-297-2 }}<br />
<br />
*{{cite book |first=R. I. |last=Porter |title=Further Elementary Analysis |year=1978 |chapter=XIX Differential Equations }}<br />
<br />
*{{Cite book| last = Teschl| given = Gerald|authorlink=Gerald Teschl| title = Ordinary Differential Equations and Dynamical Systems| publisher=[[American Mathematical Society]]| place = [[Providence, Rhode Island|Providence]]| year = 2012| isbn= 978-0-8218-8328-0| url = http://www.mat.univie.ac.at/~gerald/ftp/book-ode/}}<br />
<br />
*{{cite book|author=Daniel Zwillinger|title=Handbook of Differential Equations|url=https://books.google.com/?id=n7TiBQAAQBAJ&printsec=frontcover&dq=%22Handbook+of+Differential+Equations%22#v=onepage&q=%22Handbook%20of%20Differential%20Equations%22&f=false|date=12 May 2014|publisher=Elsevier Science|isbn=978-1-4832-6396-0}}<br />
<br />
==外部链接==<br />
<br />
{{wikiquote}}<br />
<br />
{{Wikibooks|Ordinary Differential Equations}}<br />
<br />
{{Wikiversity|Differential equations}}<br />
<br />
{{EB1911 poster|Differential Equation}}<br />
<br />
*{{Commonscatinline|Differential equations}}<br />
<br />
*[http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/ Lectures on Differential Equations] [[MIT]] Open CourseWare Videos<br />
<br />
*[http://tutorial.math.lamar.edu/classes/de/de.aspx Online Notes / Differential Equations] Paul Dawkins, [[Lamar University]]<br />
<br />
*[http://www.sosmath.com/diffeq/diffeq.html Differential Equations], S.O.S. Mathematics<br />
<br />
*[http://www.fioravante.patrone.name/mat/u-u/en/differential_equations_intro.htm Introduction to modeling via differential equations] Introduction to modeling by means of differential equations, with critical remarks.<br />
<br />
*[http://user.mendelu.cz/marik/maw/index.php?lang=en&form=ode Mathematical Assistant on Web] Symbolic ODE tool, using [[Maxima (software)|Maxima]]<br />
<br />
*[http://eqworld.ipmnet.ru/en/solutions/ode.htm Exact Solutions of Ordinary Differential Equations]<br />
<br />
*[http://www.hedengren.net/research/models.htm Collection of ODE and DAE models of physical systems] MATLAB models<br />
<br />
*[http://www.jirka.org/diffyqs/ Notes on Diffy Qs: Differential Equations for Engineers] An introductory textbook on differential equations by Jiri Lebl of [[UIUC]]<br />
<br />
*[http://www.khanacademy.org/math/differential-equations Khan Academy Video playlist on differential equations ] Topics covered in a first year course in differential equations.<br />
<br />
*[https://web.archive.org/web/20130607120716/http://math.rareinfos.com/category/courses/solutions-differential-equations/homogeneous-linear-systems/ MathDiscuss Video playlist on differential equations ]<br />
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----<br />
本中文词条由[[用户:Yuling|Yuling]]编译,[[用户:CecileLi|CecileLi]]审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B&diff=30647微分方程2022-04-23T14:27:49Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=数学,方程<br />
|description=将一个或多个函数及其导数相互关联的方程。<br />
}}<br />
[[File:Elmer-pump-heatequation.png|thumb|350px|通过求解热力学方程,我们建立了泵壳内传热的可视化模型。热量在内部产生并在边界冷却,从而为整体提供稳定的温度分布。]]<br />
在数学上,'''微分方程 Differential Equation'''是可以将一个或多个函数及其导数相互关联的方程。<ref name="Zill2012">{{cite book|author=Dennis G. Zill|title=A First Course in Differential Equations with Modeling Applications|url=https://books.google.com/books?id=pasKAAAAQBAJ&printsec=frontcover#v=snippet&q=%22ordinary%20differential%22&f=false|date=15 March 2012|publisher=Cengage Learning|isbn=1-285-40110-7}}</ref>在实际应用中,函数通常代表物理量,导数代表其变化率,而微分方程则定义了两者之间的关系。由于这种关系十分普遍,因此微分方程在包括工程学、物理学、经济学和生物学在内的许多学科中得到了广泛的应用。<br />
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微分方程的研究主要包括对微分方程解(满足每个方程的函数集)及其解的性质的研究。只有最简单的微分方程才能直接用公式求解;然而,有时无需精确计算便可以确定给定微分方程的解的许多性质。<br />
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一般地,当闭式解不存在时,可以用计算机求方程的近似解。动力系统理论着重于对由微分方程描述的系统进行定性分析。同时,现在已经得出了许多数值方法来计算给定精度下微分方程的解。<br />
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<br />
<br />
==历史==<br />
微分方程是在牛顿和莱布尼茨发明微积分后才出现的。Isaac Newton 艾萨克·牛顿在他1671年的著作《无限的循环与系列 Method of Fluxions》的第二章<ref>Newton, Isaac. (c.1671). Methodus Fluxionum et Serierum Infinitarum (The Method of Fluxions and Infinite Series), published in 1736 [Opuscula, 1744, Vol. I. p. 66].</ref>中列出了三种微分方程:<br />
<br />
<br />
<br />
:<math><br />
\begin{align}<br />
& \frac {dy}{dx} = f(x) \\[5pt]<br />
& \frac {dy}{dx} = f(x,y) \\[5pt]<br />
& x_1 \frac {\partial y}{\partial x_1} + x_2 \frac {\partial y}{\partial x_2} = y<br />
\end{align}<br />
</math><br />
<br />
<br />
在这些例子中,{{mvar|y}}是自变量 {{mvar|x}}(或者是<math>x_1</math> 和 <math>x_2</math>)的未知函数,并且 {{mvar|f}} 是一个给定的函数。<br />
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他利用无穷级数来求解这些以及其他例子,并讨论了解的非唯一性。<br />
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雅可比·伯努利 Jacob Bernoulli在1695年提出了伯努利微分方程。<ref>{{Citation | last1=Bernoulli | first1=Jacob | author1-link=Jacob Bernoulli | title=Explicationes, Annotationes & Additiones ad ea, quae in Actis sup. de Curva Elastica, Isochrona Paracentrica, & Velaria, hinc inde memorata, & paratim controversa legundur; ubi de Linea mediarum directionum, alliisque novis | year=1695 | journal=[[Acta Eruditorum]]}}</ref>这种方程是'''常微分方程 Ordinary Differential Equation'''的一种形式,<br />
<br />
<br />
: <math>y'+ P(x)y = Q(x)y^n\,</math><br />
<br />
<br />
莱布尼茨 Leibniz于第二年将方程简化从而得到了方程的解。<ref>{{Citation | last1=Hairer | first1=Ernst | last2=Nørsett | first2=Syvert Paul | last3=Wanner | first3=Gerhard | title=Solving ordinary differential equations I: Nonstiff problems | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-3-540-56670-0 | year=1993}}</ref><br />
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<br />
历史上,让·勒朗·达朗贝尔 Jean le Rond d'Alembert,欧拉 Leonhard Euler,丹尼尔·伯努利 Daniel Bernoulli和约瑟夫·路易斯·拉格朗日 Joseph-Louis Lagrange等都研究过弦(比如乐器的弦)振动问题。<ref>{{cite journal|url = http://homes.chass.utoronto.ca/~cfraser/vibration.pdf |title = Review of ''The evolution of dynamics, vibration theory from 1687 to 1742'', by John T. Cannon and Sigalia Dostrovsky|last= Frasier|first=Craig|journal=Bulletin (New Series) of the American Mathematical Society |date=July 1983 |volume= 9| issue = 1}}</ref><ref>{{cite journal |first=Gerard F. |last=Wheeler |first2=William P. |last2=Crummett |title=The Vibrating String Controversy |journal= [[American Journal of Physics|Am. J. Phys.]] |year=1987 |volume=55 |issue=1 |pages=33–37 |doi=10.1119/1.15311 |bibcode = 1987AmJPh..55...33W }}</ref><ref>For a special collection of the 9 groundbreaking papers by the three authors, see [http://www.lynge.com/item.php?bookid=38975&s_currency=EUR&c_sourcepage= First Appearance of the wave equation: D'Alembert, Leonhard Euler, Daniel Bernoulli. - the controversy about vibrating strings] (retrieved 13 Nov 2012). Herman HJ Lynge and Son.</ref><ref>For de Lagrange's contributions to the acoustic wave equation, can consult [https://books.google.com/books?id=D8GqhULfKfAC&pg=PA18 Acoustics: An Introduction to Its Physical Principles and Applications] Allan D. Pierce, Acoustical Soc of America, 1989; page 18.(retrieved 9 Dec 2012)</ref> 1746年,达朗贝尔发现了一维波动方程,十年之内,欧拉又发现了三维波动方程。<ref name=Speiser>Speiser, David. ''[https://books.google.com/books?id=9uf97reZZCUC&pg=PA191 Discovering the Principles of Mechanics 1600-1800]'', p. 191 (Basel: Birkhäuser, 2008).</ref><br />
<br />
<br />
欧拉-拉格朗日方程式 Euler–Lagrange equation是欧拉和拉格朗日在18世纪50年代结合他们对等时降线问题的研究而发明的。这是一个不考虑起始点的曲线求解问题,其中一个加权的粒子将在一个给定的时间内下降到一个固定的点。拉格朗日在1755年解决了这个问题,并将其寄给欧拉。二人都进一步发展了拉格朗日的方法并将其应用于力学,从而促使了拉格朗日力学的形成。<br />
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1822年,Joseph Fourier 傅立叶在《热的分析理论 Théorie analytique de la chaleur》中发表了他关于热流的研究成果,<ref>{{Cite book | last = Fourier | first = Joseph | title = Théorie analytique de la chaleur | publisher = Firmin Didot Père et Fils | year = 1822 | location = Paris | language = French | url=https://archive.org/details/bub_gb_TDQJAAAAIAAJ | oclc=2688081 }}</ref>其中他以[[牛顿的冷却定律 Newton's law of cooling]]为基础进行推导,即两个相邻分子之间的热流与它们之间微小的温差成正比。这本书中包含了傅立叶关于热传导扩散的热方程式的建议。现在,每一个学习数学物理的学生都需要学习这类偏微分方程。<br />
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==示例==<br />
在经典力学中,物体运动是由其不断随时间变化的位置和速度来描述的。这些变量的表达在牛顿定律中是动态的(给定位置、速度、加速度和作用在物体上的各种力) ,并以时间函数的形式给出了未知物体位置的微分方程。<br />
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在某些情况下,这种微分方程(称为运动方程)可以精确地求解。<br />
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使用微分方程来模拟现实世界问题的一个例子是仅考虑重力和空气阻力来确定球在空中落下的速度。球对地面的加速度是重力加速度减去由于空气阻力提供的加速度。重力被认为是常数,空气阻力可以被模拟为与球的速度成正比。这意味着球的加速度,也就是其速度的导数,取决于速度(而速度取决于时间)。找到时间的函数--速度--需要解决一个微分方程问题并验证其正确性。<br />
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==微分方程的类型==<br />
微分方程可分为以下几种类型。除了描述方程本身的性质之外,微分方程的多种类型为我们选择何种解决方案提供了多种指导。常见的微分方程有: 常微分/偏微分方程、线性/非线性方程和齐次/非齐次方程。微分方程还有许多类型,以及许多在特定的情况下实用的其它性质和子类。<br />
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===常微分方程===<br />
'''常微分方程 ordinary differential equation(ODE)'''是只含有一个实变量或复变量的未知函数,其导数以及此函数的一些方程。未知函数因变量(通常由 {{mvar|y}} 表示),其常常随 {{mvar|x}}的变化而变化 。因此 {{mvar|x}} 通常被称为方程式的自变量。“常微分方程”一词与偏微分方程一词相比,后者涉及一个以上的独立变量。<br />
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线性微分方程是指方程中未知函数及其导数都是线性的微分方程。关于这些方程的理论发展得很好,在多数情况下可以用积分来表示它们的解。<br />
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物理学中遇到的大多数常微分方程都是线性的。因此,大多数特殊函数可以定义为线性微分方程的解(见完整性函数)。<br />
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一般地,微分方程的解不能用解析解表示,而会在计算机上利用数值方法求解。<br />
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===偏微分方程===<br />
'''偏微分方程 Partial Differential Equation(PDE)'''是一种包含多元函数及其偏导数的微分方程函数(这与处理单变量函数及其导数的常微分方程不同)。偏微分方程可用于描述涉及多元函数的问题求闭式解,或者用于创建相关的计算机模型。<br />
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偏微分方程可以用来描述自然界中各种各样的现象,如声音、热量、静电、电动力学、流体流动、弹性和量子力学等。这些看起来截然不同的物理现象其实都可以用相似的偏微分方程表达。正如常微分方程常被用于对一维动力系统进行建模一样,偏微分方程常被用于对多维系统进行建模。随机偏微分方程延伸了偏微分方程在模拟随机性上的应用。<br />
<br />
<br />
===非线性微分方程===<br />
<br />
非线性微分方程是微分方程的一种,但它不是关于未知函数及其导数的线性方程(这里不考虑函数本身的线性或非线性)。能够精确求解非线性微分方程的方法很少; 那些已有的方法通常依赖于方程具有某种特定的对称性。非线性微分方程在更长的时间段内表现出非常复杂的行为,具有混沌特性。即使非线性微分方程也有解的存在性、唯一性和可扩展性等基本问题以及初边值问题的适定性问题,但对其研究也是一个难题(可参考纳维-斯托克斯方程的存在性和光滑性)。然而,如果微分方程是一个有意义物理过程的正确表述,那么人们期望它有一个解析解。 <br />
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线性微分方程经常作为非线性方程的近似形式出现。这些近似只有某些限制条件下才有效。例如,谐振子方程是非线性摆方程的近似这一情况只有对于小幅度振荡是有效的(见下文)。<br />
<br />
===方程的阶===<br />
<br />
微分方程的阶数是由它们的导数的最高阶决定的。只含有一阶导数的方程是一阶微分方程,含有二阶导数的方程是二阶微分方程,等等。描述自然现象的微分方程几乎总是只有一阶和二阶导数<ref>[[Eric W Weisstein|Weisstein, Eric W]]. "Ordinary Differential Equation Order." From [[MathWorld]]--A Wolfram Web Resource. http://mathworld.wolfram.com/OrdinaryDifferentialEquationOrder.html</ref><ref>[http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx Order and degree of a differential equation] {{Webarchive|url=https://web.archive.org/web/20160401070512/http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx |date=2016-04-01 }}, accessed Dec 2015.</ref>,但也有一些例外,例如薄膜方程,它是一个四阶偏微分方程。<br />
<br />
===示例===<br />
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<br />
<br />
In the first group of examples ''u'' is an unknown function of ''x'', and ''c'' and ''ω'' are constants that are supposed to be known. Two broad classifications of both ordinary and partial differential equations consist of distinguishing between ''[[linear differential equation|linear]]'' and ''nonlinear'' differential equations, and between [[homogeneous differential equation|''homogeneous'' differential equation]]s and ''heterogeneous'' ones.<br />
<br />
In the first group of examples u is an unknown function of x, and c and ω are constants that are supposed to be known. Two broad classifications of both ordinary and partial differential equations consist of distinguishing between linear and nonlinear differential equations, and between homogeneous differential equations and heterogeneous ones.<br />
<br />
在第一组示例中,待求解的''u''是''x''的函数,''c''和''ω''是应该已知的常数。常微分方程和偏微分方程这两种广义分类下还要区分微分方程的线性和非线性,以及区分微分方程的齐次和非齐次。<br />
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* Heterogeneous first-order linear constant coefficient ordinary differential equation:<br />
非齐次一阶常系数常微分方程<br />
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:: <math> \frac{du}{dx} = cu+x^2. </math><br />
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* Homogeneous second-order linear ordinary differential equation:<br />
齐次二阶线性常微分方程<br />
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:: <math> \frac{d^2u}{dx^2} - x\frac{du}{dx} + u = 0. </math><br />
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<br />
* Homogeneous second-order linear constant coefficient ordinary differential equation describing the [[harmonic oscillator]]:<br />
用于描述简谐振动的齐次二阶常系数常系数微分方程<br />
<br />
:: <math> \frac{d^2u}{dx^2} + \omega^2u = 0. </math><br />
<br />
<br />
* Heterogeneous first-order nonlinear ordinary differential equation:<br />
非齐次一阶非线性常微分方程<br />
<br />
:: <math> \frac{du}{dx} = u^2 + 4. </math><br />
<br />
<br />
<br />
* Second-order nonlinear (due to sine function) ordinary differential equation describing the motion of a [[pendulum]] of length ''L'':<br />
用于描述摆长为L的钟摆运动的二阶非线性(因正弦函数产生)常微分方程<br />
<br />
<br />
:: <math> L\frac{d^2u}{dx^2} + g\sin u = 0. </math><br />
<br />
<br />
<br />
In the next group of examples, the unknown function ''u'' depends on two variables ''x'' and ''t'' or ''x'' and ''y''.<br />
<br />
In the next group of examples, the unknown function u depends on two variables x and t or x and y.<br />
<br />
在下一组例子中,未知函数''u''依赖于两个变量''x'' 和 ''t''或者''x''和''y''。<br />
<br />
<br />
<br />
* Homogeneous first-order linear partial differential equation:<br />
齐次一阶线性偏微分方程<br />
<br />
<br />
:: <math> \frac{\partial u}{\partial t} + t\frac{\partial u}{\partial x} = 0. </math><br />
<br />
<br />
<br />
<br />
* Homogeneous second-order linear constant coefficient partial differential equation of elliptic type, the [[Laplace equation]]:<br />
齐次二阶线性常系数椭圆形偏微分方程,也称为拉普拉斯方程<br />
<br />
<br />
:: <math> \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0. </math><br />
<br />
<br />
<br />
<br />
* Homogeneous third-order non-linear partial differential equation :<br />
齐次三阶非线性偏微分方程<br />
<br />
<br />
:: <math> \frac{\partial u}{\partial t} = 6u\frac{\partial u}{\partial x} - \frac{\partial^3 u}{\partial x^3}. </math><br />
<br />
==Existence of solutions==<br />
解的存在性<br />
<br />
<br />
Solving differential equations is not like solving [[algebraic equations]]. Not only are their solutions often unclear, but whether solutions are unique or exist at all are also notable subjects of interest.<br />
<br />
Solving differential equations is not like solving algebraic equations. Not only are their solutions often unclear, but whether solutions are unique or exist at all are also notable subjects of interest.<br />
<br />
解微分方程不同于解代数方程。方程解的情况往往是不确定的,而且解是否唯一或是否存在也是值得关注的问题。<br />
<br />
<br />
<br />
For first order initial value problems, the [[Peano existence theorem]] gives one set of circumstances in which a solution exists. Given any point <math>(a,b)</math> in the xy-plane, define some rectangular region <math>Z</math>, such that <math>Z = [l,m]\times[n,p]</math> and <math>(a,b)</math> is in the interior of <math>Z</math>. If we are given a differential equation <math>\frac{dy}{dx} = g(x,y)</math> and the condition that <math>y=b</math> when <math>x=a</math>, then there is locally a solution to this problem if <math>g(x,y)</math> and <math>\frac{\partial g}{\partial x}</math> are both continuous on <math>Z</math>. This solution exists on some interval with its center at <math>a</math>. The solution may not be unique. (See [[Ordinary differential equation]] for other results.)<br />
<br />
For first order initial value problems, the Peano existence theorem gives one set of circumstances in which a solution exists. Given any point <math>(a,b)</math> in the xy-plane, define some rectangular region <math>Z</math>, such that <math>Z = [l,m]\times[n,p]</math> and <math>(a,b)</math> is in the interior of <math>Z</math>. If we are given a differential equation <math>\frac{dy}{dx} = g(x,y)</math> and the condition that <math>y=b</math> when <math>x=a</math>, then there is locally a solution to this problem if <math>g(x,y)</math> and <math>\frac{\partial g}{\partial x}</math> are both continuous on <math>Z</math>. This solution exists on some interval with its center at <math>a</math>. The solution may not be unique. (See Ordinary differential equation for other results.)<br />
<br />
对于一阶初值问题,皮亚诺存在性定理给出了一组解存在的情况。给定的x-y平面上的任意点 <math>(a,b)</math> ,定义矩形区域 <math>Z</math> ,如,<math>Z = [l,m]\times[n,p]</math> 而且 <math>(a,b)</math> 是 <math>Z</math> 内部一点。如果我们给出一个微分方程 <math>\frac{dy}{dx} = g(x,y)</math> 和当<math>x=a</math>时<math>y=b</math>,如果<math>g(x,y)</math>和<math>\frac{\partial g}{\partial x}</math>在<math>Z</math>上是连续的,那么这个问题就有一个局部解。这个解在以 <math>a</math> 为中心的某些区间上存在,其可能不是唯一的。(其他结果请参见常微分方程。)<br />
<br />
<br />
<br />
However, this only helps us with first order [[initial value problem]]s. Suppose we had a linear initial value problem of the nth order:<br />
<br />
However, this only helps us with first order initial value problems. Suppose we had a linear initial value problem of the nth order:<br />
<br />
然而,这只能帮助我们解决一阶初始值问题。假设我们有一个n阶线性初始值问题:<br />
<br />
<br />
<br />
:<math><br />
f_{n}(x)\frac{d^n y}{dx^n} + \cdots + f_{1}(x)\frac{d y}{dx} + f_{0}(x)y = g(x)<br />
</math><br />
<br />
such that<br />
<br />
such that<br />
<br />
其中有<br />
<br />
:<math><br />
y(x_{0})=y_{0}, y'(x_{0}) = y'_{0}, y''(x_{0}) = y''_{0}, \cdots<br />
</math><br />
<br />
<br />
For any nonzero <math>f_{n}(x)</math>, if <math>\{f_{0},f_{1},\cdots\}</math> and <math>g</math> are continuous on some interval containing <math>x_{0}</math>, <math>y</math> is unique and exists.<ref>{{cite book|last1=Zill|first1=Dennis G.|title=A First Course in Differential Equations|publisher=Brooks/Cole|isbn=0-534-37388-7|edition=5th|year=2001}}</ref><br />
<br />
For any nonzero <math>f_{n}(x)</math>, if <math>\{f_{0},f_{1},\cdots\}</math> and <math>g</math> are continuous on some interval containing <math>x_{0}</math>, <math>y</math> is unique and exists.<br />
<br />
对于任意非零 <math>f_{n}(x)</math> ,如果<math>\{f_{0},f_{1},\cdots\}</math> 和 <math>g</math>在某个包含<math>x_{0}</math>的区间上连续,则<math>y</math>是存在且唯一的。<br />
<br />
==Related concepts==<br />
相关概念<br />
<br />
<br />
* A [[delay differential equation]] (DDE) is an equation for a function of a single variable, usually called '''time''', in which the derivative of the function at a certain time is given in terms of the values of the function at earlier times.<br />
延迟微分方程(DDE)是一元函数的方程,变量通常为时间,其中函数在一定时间点的微分会被较早时间点的函数值表达。<br />
<br />
*An [[integro-differential equation]] (IDE) is an equation that combines aspects of a differential equation and an [[integral equation]].<br />
积分微分方程(IDE)结合了微分方程和积分方程。<br />
<br />
* A [[stochastic differential equation]] (SDE) is an equation in which the unknown quantity is a [[stochastic process]] and the equation involves some known stochastic processes, for example, the [[Wiener process]] in the case of diffusion equations.<br />
随机微分方程(SDE)中的未知量处于随机过程,并且涉及一些已知的随机过程,例如,扩散方程中的维纳过程。<br />
<br />
*A [[stochastic partial differential equation]] (SPDE) is an equation that generalizes SDEs to include space-time noise processes, with applications in [[quantum field theory]] and [[statistical mechanics]].<br />
随机偏微分方程(SPDE)是一种含空间和时间噪声过程的广义随机微分方程,它通常应用于量子场论以及统计力学中。<br />
<br />
* A [[differential algebraic equation]] (DAE) is a differential equation comprising differential and algebraic terms, given in implicit form.<br />
微分代数方程(DAE)是一种含微分和代数项的微分方程,通常以隐式形式给出。<br />
<br />
==Connection to difference equations==<br />
与差分方程之间的联系<br />
{{See also|Time scale calculus}}<br />
<br />
<br />
<br />
The theory of differential equations is closely related to the theory of [[difference equations]], in which the coordinates assume only discrete values, and the relationship involves values of the unknown function or functions and values at nearby coordinates. Many methods to compute numerical solutions of differential equations or study the properties of differential equations involve the approximation of the solution of a differential equation by the solution of a corresponding difference equation.<br />
<br />
The theory of differential equations is closely related to the theory of difference equations, in which the coordinates assume only discrete values, and the relationship involves values of the unknown function or functions and values at nearby coordinates. Many methods to compute numerical solutions of differential equations or study the properties of differential equations involve the approximation of the solution of a differential equation by the solution of a corresponding difference equation.<br />
<br />
微分方程理论与差分方程理论密切相关。在差分方程理论中,坐标系中只假定存在离散值,计算中会涉及到未知函数或已知函数的值以及坐标附近的值。许多求微分方程数值解或研究微分方程性质的方法,都会涉及通过相应差分方程的解来逼近微分方程的解。<br />
<br />
==Applications 应用==<br />
<br />
<br />
<br />
The study of differential equations is a wide field in [[pure mathematics|pure]] and [[applied mathematics]], [[physics]], and [[engineering]]. All of these disciplines are concerned with the properties of differential equations of various types. Pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics emphasizes the rigorous justification of the methods for approximating solutions. Differential equations play an important role in modeling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations such as those used to solve real-life problems may not necessarily be directly solvable, i.e. do not have [[closed-form expression|closed form]] solutions. Instead, solutions can be approximated using [[Numerical ordinary differential equations|numerical methods]].<br />
<br />
The study of differential equations is a wide field in pure and applied mathematics, physics, and engineering. All of these disciplines are concerned with the properties of differential equations of various types. Pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics emphasizes the rigorous justification of the methods for approximating solutions. Differential equations play an important role in modeling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations such as those used to solve real-life problems may not necessarily be directly solvable, i.e. do not have closed form solutions. Instead, solutions can be approximated using numerical methods.<br />
<br />
微分方程的研究可以应用于许多领域,如理论数学、应用数学、物理学和工程学,它们都与各种类型的微分方程的性质有关。理论数学关注解的存在性和唯一性,而应用数学则强调求解方法的严格准确性。从天体运动到桥梁设计,再到神经元之间的相互作用,微分方程在几乎所有物理、技术或生物过程的建模中都扮演着重要的角色。用于解决实际问题的微分方程,不一定是直接可解的,如可能不存在闭式解。但我们可以用数值方法来近似得到方程的解。<br />
<br />
<br />
<br />
Many fundamental laws of [[physics]] and [[chemistry]] can be formulated as differential equations. In [[biology]] and [[economics]], differential equations are used to [[mathematical modelling|model]] the behavior of complex systems. The mathematical theory of differential equations first developed together with the sciences where the equations had originated and where the results found application. However, diverse problems, sometimes originating in quite distinct scientific fields, may give rise to identical differential equations. Whenever this happens, mathematical theory behind the equations can be viewed as a unifying principle behind diverse phenomena. As an example, consider the propagation of light and sound in the atmosphere, and of waves on the surface of a pond. All of them may be described by the same second-order [[partial differential equation]], the [[wave equation]], which allows us to think of light and sound as forms of waves, much like familiar waves in the water. Conduction of heat, the theory of which was developed by [[Joseph Fourier]], is governed by another second-order partial differential equation, the [[heat equation]]. It turns out that many [[diffusion]] processes, while seemingly different, are described by the same equation; the [[Black–Scholes]] equation in finance is, for instance, related to the heat equation.<br />
<br />
Many fundamental laws of physics and chemistry can be formulated as differential equations. In biology and economics, differential equations are used to model the behavior of complex systems. The mathematical theory of differential equations first developed together with the sciences where the equations had originated and where the results found application. However, diverse problems, sometimes originating in quite distinct scientific fields, may give rise to identical differential equations. Whenever this happens, mathematical theory behind the equations can be viewed as a unifying principle behind diverse phenomena. As an example, consider the propagation of light and sound in the atmosphere, and of waves on the surface of a pond. All of them may be described by the same second-order partial differential equation, the wave equation, which allows us to think of light and sound as forms of waves, much like familiar waves in the water. Conduction of heat, the theory of which was developed by Joseph Fourier, is governed by another second-order partial differential equation, the heat equation. It turns out that many diffusion processes, while seemingly different, are described by the same equation; the Black–Scholes equation in finance is, for instance, related to the heat equation.<br />
<br />
许多物理和化学的基本定律都可以用微分方程来表示。在生物学和经济学中,微分方程被用来模拟复杂系统的行为。微分方程理论最初是与其起源并得到应用的科学一起发展起来的89。然而,有时完全不同的科学领域,却可能产生相同的微分方程。当这种情况发生时,方程后面的数学理论可以被看作是不同现象背后的统一原则。例如,光和声在大气中的传播,或是池塘表面的水波的传播。所有这些过程都可以用相同的二阶偏微分方程来描述,即波动方程。我们把光和声音想象成与水波相似的形式。由约瑟夫·傅里叶提出的热传导的理论由另一个二阶偏微分方程——热方程所支配。事实证明,许多扩散过程,虽然看上去形式不同,但都可以同一个方程来描述;。例如,金融学中的布莱克-斯科尔斯方程就与热方程有关。<br />
<br />
<br />
==[[用户:Yuling|Yuling]]([[用户讨论:Yuling|讨论]]) "results found application" 翻译为“方程解的搜索”,可能不太准确<br />
<br />
<br />
The number of differential equations that have received a name, in various scientific areas is a witness of the importance of the topic. See [[List of named differential equations]].<br />
<br />
The number of differential equations that have received a name, in various scientific areas is a witness of the importance of the topic. See List of named differential equations.<br />
<br />
事实上,同一类型的微分方程可以应用于不同领域这样的现象屡见不鲜,这足以证明微分方程这一课题的重要性。参见已命名的微分方程列表。<br />
<br />
==See also 另请参见==<br />
<br />
{{Div col|colwidth=22em}}<br />
<br />
*[[Complex differential equation]]<br />
复微分方程<br />
*[[Exact differential equation]]<br />
精确微分方程<br />
*[[Functional differential equation]]<br />
泛函微分方程<br />
*[[Initial condition]]<br />
初始条件<br />
*[[Integral equations]]<br />
积分方程<br />
*[[Numerical methods for ordinary differential equations]]<br />
求解常微分方程的数值方法<br />
*[[Numerical methods for partial differential equations]]<br />
求解偏微分方程的数值方法<br />
*[[Picard–Lindelöf theorem]] on existence and uniqueness of solutions<br />
关于解的存在性和唯一性的皮卡德–林德洛夫定理<br />
*[[Recurrence relation]], also known as 'difference equation'<br />
递推关系,也称为差分方程<br />
*[[Abstract differential equation]]<br />
抽象微分方程<br />
*[[System of differential equations]]<br />
微分方程组<br />
{{div col end}}<br />
<br />
==References 参考文献==<br />
<br />
{{reflist|30em}}<br />
<br />
==Further reading 延伸阅读==<br />
<br />
*{{cite book |first=P. |last=Abbott |first2=H. |last2=Neill |title=Teach Yourself Calculus |year=2003 |pages=266–277 }}<br />
<br />
*{{cite book |first=P. |last=Blanchard |authorlink2=Robert L. Devaney |first2=R. L. |last2=Devaney |first3=G. R. |last3=Hall |title=Differential Equations |location= |publisher=Thompson |year=2006 }}<br />
<br />
*{{cite book |first=W. |last=Boyce | first2=R. |last2=DiPrima| first3=D. |last3=Meade| title=Elementary Differential Equations and Boundary Value Problems|publisher=Wiley |year=2017}}<br />
<br />
*{{cite book |first=E. A. |last=Coddington |first2=N. |last2=Levinson |title=Theory of Ordinary Differential Equations |url=https://archive.org/details/theoryofordinary00codd |url-access=registration |publisher=McGraw-Hill |year=1955 }}<br />
<br />
*{{cite book |first=E. L. |last=Ince |title=Ordinary Differential Equations |publisher=Dover |year=1956 }}<br />
<br />
*{{cite book |first=W. |last=Johnson |url=http://www.hti.umich.edu/cgi/b/bib/bibperm?q1=abv5010.0001.001 |title=A Treatise on Ordinary and Partial Differential Equations |publisher=John Wiley and Sons |year=1913 }} In [http://hti.umich.edu/u/umhistmath/ University of Michigan Historical Math Collection]<br />
<br />
*{{cite book |first=A. D. |last=Polyanin |first2=V. F. |last2=Zaitsev |title=Handbook of Exact Solutions for Ordinary Differential Equations |edition=2nd |publisher=Chapman & Hall/CRC Press |location=Boca Raton |year=2003 |isbn=1-58488-297-2 }}<br />
<br />
*{{cite book |first=R. I. |last=Porter |title=Further Elementary Analysis |year=1978 |chapter=XIX Differential Equations }}<br />
<br />
*{{Cite book| last = Teschl| given = Gerald|authorlink=Gerald Teschl| title = Ordinary Differential Equations and Dynamical Systems| publisher=[[American Mathematical Society]]| place = [[Providence, Rhode Island|Providence]]| year = 2012| isbn= 978-0-8218-8328-0| url = http://www.mat.univie.ac.at/~gerald/ftp/book-ode/}}<br />
<br />
*{{cite book|author=Daniel Zwillinger|title=Handbook of Differential Equations|url=https://books.google.com/?id=n7TiBQAAQBAJ&printsec=frontcover&dq=%22Handbook+of+Differential+Equations%22#v=onepage&q=%22Handbook%20of%20Differential%20Equations%22&f=false|date=12 May 2014|publisher=Elsevier Science|isbn=978-1-4832-6396-0}}<br />
<br />
==External links 外部链接==<br />
<br />
{{wikiquote}}<br />
<br />
{{Wikibooks|Ordinary Differential Equations}}<br />
<br />
{{Wikiversity|Differential equations}}<br />
<br />
{{EB1911 poster|Differential Equation}}<br />
<br />
*{{Commonscatinline|Differential equations}}<br />
<br />
*[http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/ Lectures on Differential Equations] [[MIT]] Open CourseWare Videos<br />
<br />
*[http://tutorial.math.lamar.edu/classes/de/de.aspx Online Notes / Differential Equations] Paul Dawkins, [[Lamar University]]<br />
<br />
*[http://www.sosmath.com/diffeq/diffeq.html Differential Equations], S.O.S. Mathematics<br />
<br />
*[http://www.fioravante.patrone.name/mat/u-u/en/differential_equations_intro.htm Introduction to modeling via differential equations] Introduction to modeling by means of differential equations, with critical remarks.<br />
<br />
*[http://user.mendelu.cz/marik/maw/index.php?lang=en&form=ode Mathematical Assistant on Web] Symbolic ODE tool, using [[Maxima (software)|Maxima]]<br />
<br />
*[http://eqworld.ipmnet.ru/en/solutions/ode.htm Exact Solutions of Ordinary Differential Equations]<br />
<br />
*[http://www.hedengren.net/research/models.htm Collection of ODE and DAE models of physical systems] MATLAB models<br />
<br />
*[http://www.jirka.org/diffyqs/ Notes on Diffy Qs: Differential Equations for Engineers] An introductory textbook on differential equations by Jiri Lebl of [[UIUC]]<br />
<br />
*[http://www.khanacademy.org/math/differential-equations Khan Academy Video playlist on differential equations ] Topics covered in a first year course in differential equations.<br />
<br />
*[https://web.archive.org/web/20130607120716/http://math.rareinfos.com/category/courses/solutions-differential-equations/homogeneous-linear-systems/ MathDiscuss Video playlist on differential equations ]<br />
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本中文词条由[[用户:Yuling|Yuling]]编译,[[用户:CecileLi|CecileLi]]审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B&diff=30646微分方程2022-04-23T14:25:35Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=数学,方程<br />
|description=将一个或多个函数及其导数相互关联的方程。<br />
}}<br />
[[File:Elmer-pump-heatequation.png|thumb|350px|通过求解热力学方程,我们建立了泵壳内传热的可视化模型。热量在内部产生并在边界冷却,从而为整体提供稳定的温度分布。]]<br />
在数学上,'''微分方程 Differential Equation'''是可以将一个或多个函数及其导数相互关联的方程。<ref name="Zill2012">{{cite book|author=Dennis G. Zill|title=A First Course in Differential Equations with Modeling Applications|url=https://books.google.com/books?id=pasKAAAAQBAJ&printsec=frontcover#v=snippet&q=%22ordinary%20differential%22&f=false|date=15 March 2012|publisher=Cengage Learning|isbn=1-285-40110-7}}</ref>在实际应用中,函数通常代表物理量,导数代表其变化率,而微分方程则定义了两者之间的关系。由于这种关系十分普遍,因此微分方程在包括工程学、物理学、经济学和生物学在内的许多学科中得到了广泛的应用。<br />
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微分方程的研究主要包括对微分方程解(满足每个方程的函数集)及其解的性质的研究。只有最简单的微分方程才能直接用公式求解;然而,有时无需精确计算便可以确定给定微分方程的解的许多性质。<br />
<br />
<br />
一般地,当闭式解不存在时,可以用计算机求方程的近似解。动力系统理论着重于对由微分方程描述的系统进行定性分析。同时,现在已经得出了许多数值方法来计算给定精度下微分方程的解。<br />
<br />
<br />
<br />
==历史==<br />
微分方程是在牛顿和莱布尼茨发明微积分后才出现的。Isaac Newton 艾萨克·牛顿在他1671年的著作《无限的循环与系列 Method of Fluxions》的第二章<ref>Newton, Isaac. (c.1671). Methodus Fluxionum et Serierum Infinitarum (The Method of Fluxions and Infinite Series), published in 1736 [Opuscula, 1744, Vol. I. p. 66].</ref>中列出了三种微分方程:<br />
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<br />
:<math><br />
\begin{align}<br />
& \frac {dy}{dx} = f(x) \\[5pt]<br />
& \frac {dy}{dx} = f(x,y) \\[5pt]<br />
& x_1 \frac {\partial y}{\partial x_1} + x_2 \frac {\partial y}{\partial x_2} = y<br />
\end{align}<br />
</math><br />
<br />
<br />
在这些例子中,{{mvar|y}}是自变量 {{mvar|x}}(或者是<math>x_1</math> 和 <math>x_2</math>)的未知函数,并且 {{mvar|f}} 是一个给定的函数。<br />
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他利用无穷级数来求解这些以及其他例子,并讨论了解的非唯一性。<br />
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雅可比·伯努利 Jacob Bernoulli在1695年提出了伯努利微分方程。<ref>{{Citation | last1=Bernoulli | first1=Jacob | author1-link=Jacob Bernoulli | title=Explicationes, Annotationes & Additiones ad ea, quae in Actis sup. de Curva Elastica, Isochrona Paracentrica, & Velaria, hinc inde memorata, & paratim controversa legundur; ubi de Linea mediarum directionum, alliisque novis | year=1695 | journal=[[Acta Eruditorum]]}}</ref>这种方程是'''常微分方程 Ordinary Differential Equation'''的一种形式,<br />
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: <math>y'+ P(x)y = Q(x)y^n\,</math><br />
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莱布尼茨 Leibniz于第二年将方程简化从而得到了方程的解。<ref>{{Citation | last1=Hairer | first1=Ernst | last2=Nørsett | first2=Syvert Paul | last3=Wanner | first3=Gerhard | title=Solving ordinary differential equations I: Nonstiff problems | publisher=[[Springer-Verlag]] | location=Berlin, New York | isbn=978-3-540-56670-0 | year=1993}}</ref><br />
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历史上,让·勒朗·达朗贝尔 Jean le Rond d'Alembert,欧拉 Leonhard Euler,丹尼尔·伯努利 Daniel Bernoulli和约瑟夫·路易斯·拉格朗日 Joseph-Louis Lagrange等都研究过弦(比如乐器的弦)振动问题。<ref>{{cite journal|url = http://homes.chass.utoronto.ca/~cfraser/vibration.pdf |title = Review of ''The evolution of dynamics, vibration theory from 1687 to 1742'', by John T. Cannon and Sigalia Dostrovsky|last= Frasier|first=Craig|journal=Bulletin (New Series) of the American Mathematical Society |date=July 1983 |volume= 9| issue = 1}}</ref><ref>{{cite journal |first=Gerard F. |last=Wheeler |first2=William P. |last2=Crummett |title=The Vibrating String Controversy |journal= [[American Journal of Physics|Am. J. Phys.]] |year=1987 |volume=55 |issue=1 |pages=33–37 |doi=10.1119/1.15311 |bibcode = 1987AmJPh..55...33W }}</ref><ref>For a special collection of the 9 groundbreaking papers by the three authors, see [http://www.lynge.com/item.php?bookid=38975&s_currency=EUR&c_sourcepage= First Appearance of the wave equation: D'Alembert, Leonhard Euler, Daniel Bernoulli. - the controversy about vibrating strings] (retrieved 13 Nov 2012). Herman HJ Lynge and Son.</ref><ref>For de Lagrange's contributions to the acoustic wave equation, can consult [https://books.google.com/books?id=D8GqhULfKfAC&pg=PA18 Acoustics: An Introduction to Its Physical Principles and Applications] Allan D. Pierce, Acoustical Soc of America, 1989; page 18.(retrieved 9 Dec 2012)</ref> 1746年,达朗贝尔发现了一维波动方程,十年之内,欧拉又发现了三维波动方程。<ref name=Speiser>Speiser, David. ''[https://books.google.com/books?id=9uf97reZZCUC&pg=PA191 Discovering the Principles of Mechanics 1600-1800]'', p. 191 (Basel: Birkhäuser, 2008).</ref><br />
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欧拉-拉格朗日方程式 Euler–Lagrange equation是欧拉和拉格朗日在18世纪50年代结合他们对等时降线问题的研究而发明的。这是一个不考虑起始点的曲线求解问题,其中一个加权的粒子将在一个给定的时间内下降到一个固定的点。拉格朗日在1755年解决了这个问题,并将其寄给欧拉。二人都进一步发展了拉格朗日的方法并将其应用于力学,从而促使了拉格朗日力学的形成。<br />
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1822年,Joseph Fourier 傅立叶在《热的分析理论 Théorie analytique de la chaleur》中发表了他关于热流的研究成果,<ref>{{Cite book | last = Fourier | first = Joseph | title = Théorie analytique de la chaleur | publisher = Firmin Didot Père et Fils | year = 1822 | location = Paris | language = French | url=https://archive.org/details/bub_gb_TDQJAAAAIAAJ | oclc=2688081 }}</ref>其中他以[[牛顿的冷却定律 Newton's law of cooling]]为基础进行推导,即两个相邻分子之间的热流与它们之间微小的温差成正比。这本书中包含了傅立叶关于热传导扩散的热方程式的建议。现在,每一个学习数学物理的学生都需要学习这类偏微分方程。<br />
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==示例==<br />
在经典力学中,物体运动是由其不断随时间变化的位置和速度来描述的。这些变量的表达在牛顿定律中是动态的(给定位置、速度、加速度和作用在物体上的各种力) ,并以时间函数的形式给出了未知物体位置的微分方程。<br />
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在某些情况下,这种微分方程(称为运动方程)可以精确地求解。<br />
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使用微分方程来模拟现实世界问题的一个例子是仅考虑重力和空气阻力来确定球在空中落下的速度。球对地面的加速度是重力加速度减去由于空气阻力提供的加速度。重力被认为是常数,空气阻力可以被模拟为与球的速度成正比。这意味着球的加速度,也就是其速度的导数,取决于速度(而速度取决于时间)。找到时间的函数--速度--需要解决一个微分方程问题并验证其正确性。<br />
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==微分方程的类型==<br />
微分方程可分为以下几种类型。除了描述方程本身的性质之外,微分方程的多种类型为我们选择何种解决方案提供了多种指导。常见的微分方程有: 常微分/偏微分方程、线性/非线性方程和齐次/非齐次方程。微分方程还有许多类型,以及许多在特定的情况下实用的其它性质和子类。<br />
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===常微分方程===<br />
'''常微分方程 ordinary differential equation(ODE)'''是只含有一个实变量或复变量的未知函数,其导数以及此函数的一些方程。未知函数因变量(通常由 {{mvar|y}} 表示),其常常随 {{mvar|x}}的变化而变化 。因此 {{mvar|x}} 通常被称为方程式的自变量。“常微分方程”一词与偏微分方程一词相比,后者涉及一个以上的独立变量。<br />
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线性微分方程是指方程中未知函数及其导数都是线性的微分方程。关于这些方程的理论发展得很好,在多数情况下可以用积分来表示它们的解。<br />
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物理学中遇到的大多数常微分方程都是线性的。因此,大多数特殊函数可以定义为线性微分方程的解(见完整性函数)。<br />
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一般地,微分方程的解不能用解析解表示,而会在计算机上利用数值方法求解。<br />
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===偏微分方程===<br />
'''偏微分方程 Partial Differential Equation(PDE)'''是一种包含多元函数及其偏导数的微分方程函数(这与处理单变量函数及其导数的常微分方程不同)。偏微分方程可用于描述涉及多元函数的问题求闭式解,或者用于创建相关的计算机模型。<br />
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偏微分方程可以用来描述自然界中各种各样的现象,如声音、热量、静电、电动力学、流体流动、弹性和量子力学等。这些看起来截然不同的物理现象其实都可以用相似的偏微分方程表达。正如常微分方程常被用于对一维动力系统进行建模一样,偏微分方程常被用于对多维系统进行建模。随机偏微分方程延伸了偏微分方程在模拟随机性上的应用。<br />
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===非线性微分方程===<br />
A '''non-linear differential equation''' is a differential equation that is not a [[linear equation]] in the unknown function and its derivatives (the linearity or non-linearity in the arguments of the function are not considered here). There are very few methods of solving nonlinear differential equations exactly; those that are known typically depend on the equation having particular [[Symmetry|symmetries]]. Nonlinear differential equations can exhibit very complicated behavior over extended time intervals, characteristic of [[chaos theory|chaos]]. Even the fundamental questions of existence, uniqueness, and extendability of solutions for nonlinear differential equations, and well-posedness of initial and boundary value problems for nonlinear PDEs are hard problems and their resolution in special cases is considered to be a significant advance in the mathematical theory (cf. [[Navier–Stokes existence and smoothness]]). However, if the differential equation is a correctly formulated representation of a meaningful physical process, then one expects it to have a solution.<br />
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非线性微分方程是微分方程的一种,但它不是关于未知函数及其导数的线性方程(这里不考虑函数本身的线性或非线性)。能够精确求解非线性微分方程的方法很少; 那些已有的方法通常依赖于方程具有某种特定的对称性。非线性微分方程在更长的时间段内表现出非常复杂的行为,具有混沌特性。即使非线性微分方程也有解的存在性、唯一性和可扩展性等基本问题以及初边值问题的适定性问题,但对其研究也是一个难题(可参考纳维-斯托克斯方程的存在性和光滑性)。然而,如果微分方程是一个有意义物理过程的正确表述,那么人们期望它有一个解析解。 <br />
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Linear differential equations frequently appear as [[linearization|approximations]] to nonlinear equations. These approximations are only valid under restricted conditions. For example, the harmonic oscillator equation is an approximation to the nonlinear pendulum equation that is valid for small amplitude oscillations (see below).<br />
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Linear differential equations frequently appear as approximations to nonlinear equations. These approximations are only valid under restricted conditions. For example, the harmonic oscillator equation is an approximation to the nonlinear pendulum equation that is valid for small amplitude oscillations (see below).<br />
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线性微分方程经常作为非线性方程的近似形式出现。这些近似只有某些限制条件下才有效。例如,谐振子方程是非线性摆方程的近似这一情况只有对于小幅度振荡是有效的(见下文)。<br />
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==={{anchor|Second order}} Equation order===<br />
方程的阶<br />
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Differential equations are described by their order, determined by the term with the [[Derivative#Higher derivatives|highest derivatives]]. An equation containing only first derivatives is a ''first-order differential equation'', an equation containing the [[second derivative]] is a ''second-order differential equation'', and so on.<ref>[[Eric W Weisstein|Weisstein, Eric W]]. "Ordinary Differential Equation Order." From [[MathWorld]]--A Wolfram Web Resource. http://mathworld.wolfram.com/OrdinaryDifferentialEquationOrder.html</ref><ref>[http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx Order and degree of a differential equation] {{Webarchive|url=https://web.archive.org/web/20160401070512/http://www.kshitij-iitjee.com/Maths/Differential-Equations/order-and-degree-of-a-differential-equation.aspx |date=2016-04-01 }}, accessed Dec 2015.</ref> Differential equations that describe natural phenomena almost always have only first and second order derivatives in them, but there are some exceptions, such as the [[Thin-film equation|thin film equation]], which is a fourth order partial differential equation.<br />
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Differential equations are described by their order, determined by the term with the highest derivatives. An equation containing only first derivatives is a first-order differential equation, an equation containing the second derivative is a second-order differential equation, and so on. Differential equations that describe natural phenomena almost always have only first and second order derivatives in them, but there are some exceptions, such as the thin film equation, which is a fourth order partial differential equation.<br />
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微分方程的阶数是由它们的导数的最高阶决定的。只含有一阶导数的方程是一阶微分方程,含有二阶导数的方程是二阶微分方程,等等。描述自然现象的微分方程几乎总是只有一阶和二阶导数,但也有一些例外,例如薄膜方程,它是一个四阶偏微分方程。<br />
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===Examples===<br />
示例<br />
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In the first group of examples ''u'' is an unknown function of ''x'', and ''c'' and ''ω'' are constants that are supposed to be known. Two broad classifications of both ordinary and partial differential equations consist of distinguishing between ''[[linear differential equation|linear]]'' and ''nonlinear'' differential equations, and between [[homogeneous differential equation|''homogeneous'' differential equation]]s and ''heterogeneous'' ones.<br />
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In the first group of examples u is an unknown function of x, and c and ω are constants that are supposed to be known. Two broad classifications of both ordinary and partial differential equations consist of distinguishing between linear and nonlinear differential equations, and between homogeneous differential equations and heterogeneous ones.<br />
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在第一组示例中,待求解的''u''是''x''的函数,''c''和''ω''是应该已知的常数。常微分方程和偏微分方程这两种广义分类下还要区分微分方程的线性和非线性,以及区分微分方程的齐次和非齐次。<br />
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* Heterogeneous first-order linear constant coefficient ordinary differential equation:<br />
非齐次一阶常系数常微分方程<br />
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:: <math> \frac{du}{dx} = cu+x^2. </math><br />
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* Homogeneous second-order linear ordinary differential equation:<br />
齐次二阶线性常微分方程<br />
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:: <math> \frac{d^2u}{dx^2} - x\frac{du}{dx} + u = 0. </math><br />
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* Homogeneous second-order linear constant coefficient ordinary differential equation describing the [[harmonic oscillator]]:<br />
用于描述简谐振动的齐次二阶常系数常系数微分方程<br />
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:: <math> \frac{d^2u}{dx^2} + \omega^2u = 0. </math><br />
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* Heterogeneous first-order nonlinear ordinary differential equation:<br />
非齐次一阶非线性常微分方程<br />
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:: <math> \frac{du}{dx} = u^2 + 4. </math><br />
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* Second-order nonlinear (due to sine function) ordinary differential equation describing the motion of a [[pendulum]] of length ''L'':<br />
用于描述摆长为L的钟摆运动的二阶非线性(因正弦函数产生)常微分方程<br />
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:: <math> L\frac{d^2u}{dx^2} + g\sin u = 0. </math><br />
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In the next group of examples, the unknown function ''u'' depends on two variables ''x'' and ''t'' or ''x'' and ''y''.<br />
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In the next group of examples, the unknown function u depends on two variables x and t or x and y.<br />
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在下一组例子中,未知函数''u''依赖于两个变量''x'' 和 ''t''或者''x''和''y''。<br />
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* Homogeneous first-order linear partial differential equation:<br />
齐次一阶线性偏微分方程<br />
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:: <math> \frac{\partial u}{\partial t} + t\frac{\partial u}{\partial x} = 0. </math><br />
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* Homogeneous second-order linear constant coefficient partial differential equation of elliptic type, the [[Laplace equation]]:<br />
齐次二阶线性常系数椭圆形偏微分方程,也称为拉普拉斯方程<br />
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:: <math> \frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = 0. </math><br />
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* Homogeneous third-order non-linear partial differential equation :<br />
齐次三阶非线性偏微分方程<br />
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:: <math> \frac{\partial u}{\partial t} = 6u\frac{\partial u}{\partial x} - \frac{\partial^3 u}{\partial x^3}. </math><br />
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==Existence of solutions==<br />
解的存在性<br />
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Solving differential equations is not like solving [[algebraic equations]]. Not only are their solutions often unclear, but whether solutions are unique or exist at all are also notable subjects of interest.<br />
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Solving differential equations is not like solving algebraic equations. Not only are their solutions often unclear, but whether solutions are unique or exist at all are also notable subjects of interest.<br />
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解微分方程不同于解代数方程。方程解的情况往往是不确定的,而且解是否唯一或是否存在也是值得关注的问题。<br />
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For first order initial value problems, the [[Peano existence theorem]] gives one set of circumstances in which a solution exists. Given any point <math>(a,b)</math> in the xy-plane, define some rectangular region <math>Z</math>, such that <math>Z = [l,m]\times[n,p]</math> and <math>(a,b)</math> is in the interior of <math>Z</math>. If we are given a differential equation <math>\frac{dy}{dx} = g(x,y)</math> and the condition that <math>y=b</math> when <math>x=a</math>, then there is locally a solution to this problem if <math>g(x,y)</math> and <math>\frac{\partial g}{\partial x}</math> are both continuous on <math>Z</math>. This solution exists on some interval with its center at <math>a</math>. The solution may not be unique. (See [[Ordinary differential equation]] for other results.)<br />
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For first order initial value problems, the Peano existence theorem gives one set of circumstances in which a solution exists. Given any point <math>(a,b)</math> in the xy-plane, define some rectangular region <math>Z</math>, such that <math>Z = [l,m]\times[n,p]</math> and <math>(a,b)</math> is in the interior of <math>Z</math>. If we are given a differential equation <math>\frac{dy}{dx} = g(x,y)</math> and the condition that <math>y=b</math> when <math>x=a</math>, then there is locally a solution to this problem if <math>g(x,y)</math> and <math>\frac{\partial g}{\partial x}</math> are both continuous on <math>Z</math>. This solution exists on some interval with its center at <math>a</math>. The solution may not be unique. (See Ordinary differential equation for other results.)<br />
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对于一阶初值问题,皮亚诺存在性定理给出了一组解存在的情况。给定的x-y平面上的任意点 <math>(a,b)</math> ,定义矩形区域 <math>Z</math> ,如,<math>Z = [l,m]\times[n,p]</math> 而且 <math>(a,b)</math> 是 <math>Z</math> 内部一点。如果我们给出一个微分方程 <math>\frac{dy}{dx} = g(x,y)</math> 和当<math>x=a</math>时<math>y=b</math>,如果<math>g(x,y)</math>和<math>\frac{\partial g}{\partial x}</math>在<math>Z</math>上是连续的,那么这个问题就有一个局部解。这个解在以 <math>a</math> 为中心的某些区间上存在,其可能不是唯一的。(其他结果请参见常微分方程。)<br />
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However, this only helps us with first order [[initial value problem]]s. Suppose we had a linear initial value problem of the nth order:<br />
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However, this only helps us with first order initial value problems. Suppose we had a linear initial value problem of the nth order:<br />
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然而,这只能帮助我们解决一阶初始值问题。假设我们有一个n阶线性初始值问题:<br />
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:<math><br />
f_{n}(x)\frac{d^n y}{dx^n} + \cdots + f_{1}(x)\frac{d y}{dx} + f_{0}(x)y = g(x)<br />
</math><br />
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such that<br />
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such that<br />
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其中有<br />
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:<math><br />
y(x_{0})=y_{0}, y'(x_{0}) = y'_{0}, y''(x_{0}) = y''_{0}, \cdots<br />
</math><br />
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For any nonzero <math>f_{n}(x)</math>, if <math>\{f_{0},f_{1},\cdots\}</math> and <math>g</math> are continuous on some interval containing <math>x_{0}</math>, <math>y</math> is unique and exists.<ref>{{cite book|last1=Zill|first1=Dennis G.|title=A First Course in Differential Equations|publisher=Brooks/Cole|isbn=0-534-37388-7|edition=5th|year=2001}}</ref><br />
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For any nonzero <math>f_{n}(x)</math>, if <math>\{f_{0},f_{1},\cdots\}</math> and <math>g</math> are continuous on some interval containing <math>x_{0}</math>, <math>y</math> is unique and exists.<br />
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对于任意非零 <math>f_{n}(x)</math> ,如果<math>\{f_{0},f_{1},\cdots\}</math> 和 <math>g</math>在某个包含<math>x_{0}</math>的区间上连续,则<math>y</math>是存在且唯一的。<br />
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==Related concepts==<br />
相关概念<br />
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* A [[delay differential equation]] (DDE) is an equation for a function of a single variable, usually called '''time''', in which the derivative of the function at a certain time is given in terms of the values of the function at earlier times.<br />
延迟微分方程(DDE)是一元函数的方程,变量通常为时间,其中函数在一定时间点的微分会被较早时间点的函数值表达。<br />
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*An [[integro-differential equation]] (IDE) is an equation that combines aspects of a differential equation and an [[integral equation]].<br />
积分微分方程(IDE)结合了微分方程和积分方程。<br />
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* A [[stochastic differential equation]] (SDE) is an equation in which the unknown quantity is a [[stochastic process]] and the equation involves some known stochastic processes, for example, the [[Wiener process]] in the case of diffusion equations.<br />
随机微分方程(SDE)中的未知量处于随机过程,并且涉及一些已知的随机过程,例如,扩散方程中的维纳过程。<br />
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*A [[stochastic partial differential equation]] (SPDE) is an equation that generalizes SDEs to include space-time noise processes, with applications in [[quantum field theory]] and [[statistical mechanics]].<br />
随机偏微分方程(SPDE)是一种含空间和时间噪声过程的广义随机微分方程,它通常应用于量子场论以及统计力学中。<br />
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* A [[differential algebraic equation]] (DAE) is a differential equation comprising differential and algebraic terms, given in implicit form.<br />
微分代数方程(DAE)是一种含微分和代数项的微分方程,通常以隐式形式给出。<br />
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==Connection to difference equations==<br />
与差分方程之间的联系<br />
{{See also|Time scale calculus}}<br />
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The theory of differential equations is closely related to the theory of [[difference equations]], in which the coordinates assume only discrete values, and the relationship involves values of the unknown function or functions and values at nearby coordinates. Many methods to compute numerical solutions of differential equations or study the properties of differential equations involve the approximation of the solution of a differential equation by the solution of a corresponding difference equation.<br />
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The theory of differential equations is closely related to the theory of difference equations, in which the coordinates assume only discrete values, and the relationship involves values of the unknown function or functions and values at nearby coordinates. Many methods to compute numerical solutions of differential equations or study the properties of differential equations involve the approximation of the solution of a differential equation by the solution of a corresponding difference equation.<br />
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微分方程理论与差分方程理论密切相关。在差分方程理论中,坐标系中只假定存在离散值,计算中会涉及到未知函数或已知函数的值以及坐标附近的值。许多求微分方程数值解或研究微分方程性质的方法,都会涉及通过相应差分方程的解来逼近微分方程的解。<br />
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==Applications 应用==<br />
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The study of differential equations is a wide field in [[pure mathematics|pure]] and [[applied mathematics]], [[physics]], and [[engineering]]. All of these disciplines are concerned with the properties of differential equations of various types. Pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics emphasizes the rigorous justification of the methods for approximating solutions. Differential equations play an important role in modeling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations such as those used to solve real-life problems may not necessarily be directly solvable, i.e. do not have [[closed-form expression|closed form]] solutions. Instead, solutions can be approximated using [[Numerical ordinary differential equations|numerical methods]].<br />
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The study of differential equations is a wide field in pure and applied mathematics, physics, and engineering. All of these disciplines are concerned with the properties of differential equations of various types. Pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics emphasizes the rigorous justification of the methods for approximating solutions. Differential equations play an important role in modeling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations such as those used to solve real-life problems may not necessarily be directly solvable, i.e. do not have closed form solutions. Instead, solutions can be approximated using numerical methods.<br />
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微分方程的研究可以应用于许多领域,如理论数学、应用数学、物理学和工程学,它们都与各种类型的微分方程的性质有关。理论数学关注解的存在性和唯一性,而应用数学则强调求解方法的严格准确性。从天体运动到桥梁设计,再到神经元之间的相互作用,微分方程在几乎所有物理、技术或生物过程的建模中都扮演着重要的角色。用于解决实际问题的微分方程,不一定是直接可解的,如可能不存在闭式解。但我们可以用数值方法来近似得到方程的解。<br />
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Many fundamental laws of [[physics]] and [[chemistry]] can be formulated as differential equations. In [[biology]] and [[economics]], differential equations are used to [[mathematical modelling|model]] the behavior of complex systems. The mathematical theory of differential equations first developed together with the sciences where the equations had originated and where the results found application. However, diverse problems, sometimes originating in quite distinct scientific fields, may give rise to identical differential equations. Whenever this happens, mathematical theory behind the equations can be viewed as a unifying principle behind diverse phenomena. As an example, consider the propagation of light and sound in the atmosphere, and of waves on the surface of a pond. All of them may be described by the same second-order [[partial differential equation]], the [[wave equation]], which allows us to think of light and sound as forms of waves, much like familiar waves in the water. Conduction of heat, the theory of which was developed by [[Joseph Fourier]], is governed by another second-order partial differential equation, the [[heat equation]]. It turns out that many [[diffusion]] processes, while seemingly different, are described by the same equation; the [[Black–Scholes]] equation in finance is, for instance, related to the heat equation.<br />
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Many fundamental laws of physics and chemistry can be formulated as differential equations. In biology and economics, differential equations are used to model the behavior of complex systems. The mathematical theory of differential equations first developed together with the sciences where the equations had originated and where the results found application. However, diverse problems, sometimes originating in quite distinct scientific fields, may give rise to identical differential equations. Whenever this happens, mathematical theory behind the equations can be viewed as a unifying principle behind diverse phenomena. As an example, consider the propagation of light and sound in the atmosphere, and of waves on the surface of a pond. All of them may be described by the same second-order partial differential equation, the wave equation, which allows us to think of light and sound as forms of waves, much like familiar waves in the water. Conduction of heat, the theory of which was developed by Joseph Fourier, is governed by another second-order partial differential equation, the heat equation. It turns out that many diffusion processes, while seemingly different, are described by the same equation; the Black–Scholes equation in finance is, for instance, related to the heat equation.<br />
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许多物理和化学的基本定律都可以用微分方程来表示。在生物学和经济学中,微分方程被用来模拟复杂系统的行为。微分方程理论最初是与其起源并得到应用的科学一起发展起来的89。然而,有时完全不同的科学领域,却可能产生相同的微分方程。当这种情况发生时,方程后面的数学理论可以被看作是不同现象背后的统一原则。例如,光和声在大气中的传播,或是池塘表面的水波的传播。所有这些过程都可以用相同的二阶偏微分方程来描述,即波动方程。我们把光和声音想象成与水波相似的形式。由约瑟夫·傅里叶提出的热传导的理论由另一个二阶偏微分方程——热方程所支配。事实证明,许多扩散过程,虽然看上去形式不同,但都可以同一个方程来描述;。例如,金融学中的布莱克-斯科尔斯方程就与热方程有关。<br />
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==[[用户:Yuling|Yuling]]([[用户讨论:Yuling|讨论]]) "results found application" 翻译为“方程解的搜索”,可能不太准确<br />
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The number of differential equations that have received a name, in various scientific areas is a witness of the importance of the topic. See [[List of named differential equations]].<br />
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The number of differential equations that have received a name, in various scientific areas is a witness of the importance of the topic. See List of named differential equations.<br />
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事实上,同一类型的微分方程可以应用于不同领域这样的现象屡见不鲜,这足以证明微分方程这一课题的重要性。参见已命名的微分方程列表。<br />
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==See also 另请参见==<br />
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{{Div col|colwidth=22em}}<br />
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*[[Complex differential equation]]<br />
复微分方程<br />
*[[Exact differential equation]]<br />
精确微分方程<br />
*[[Functional differential equation]]<br />
泛函微分方程<br />
*[[Initial condition]]<br />
初始条件<br />
*[[Integral equations]]<br />
积分方程<br />
*[[Numerical methods for ordinary differential equations]]<br />
求解常微分方程的数值方法<br />
*[[Numerical methods for partial differential equations]]<br />
求解偏微分方程的数值方法<br />
*[[Picard–Lindelöf theorem]] on existence and uniqueness of solutions<br />
关于解的存在性和唯一性的皮卡德–林德洛夫定理<br />
*[[Recurrence relation]], also known as 'difference equation'<br />
递推关系,也称为差分方程<br />
*[[Abstract differential equation]]<br />
抽象微分方程<br />
*[[System of differential equations]]<br />
微分方程组<br />
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==References 参考文献==<br />
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{{reflist|30em}}<br />
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==Further reading 延伸阅读==<br />
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*{{cite book |first=P. |last=Abbott |first2=H. |last2=Neill |title=Teach Yourself Calculus |year=2003 |pages=266–277 }}<br />
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*{{cite book |first=P. |last=Blanchard |authorlink2=Robert L. Devaney |first2=R. L. |last2=Devaney |first3=G. R. |last3=Hall |title=Differential Equations |location= |publisher=Thompson |year=2006 }}<br />
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*{{cite book |first=W. |last=Boyce | first2=R. |last2=DiPrima| first3=D. |last3=Meade| title=Elementary Differential Equations and Boundary Value Problems|publisher=Wiley |year=2017}}<br />
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*{{cite book |first=E. A. |last=Coddington |first2=N. |last2=Levinson |title=Theory of Ordinary Differential Equations |url=https://archive.org/details/theoryofordinary00codd |url-access=registration |publisher=McGraw-Hill |year=1955 }}<br />
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*{{cite book |first=E. L. |last=Ince |title=Ordinary Differential Equations |publisher=Dover |year=1956 }}<br />
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*{{cite book |first=W. |last=Johnson |url=http://www.hti.umich.edu/cgi/b/bib/bibperm?q1=abv5010.0001.001 |title=A Treatise on Ordinary and Partial Differential Equations |publisher=John Wiley and Sons |year=1913 }} In [http://hti.umich.edu/u/umhistmath/ University of Michigan Historical Math Collection]<br />
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*{{cite book |first=A. D. |last=Polyanin |first2=V. F. |last2=Zaitsev |title=Handbook of Exact Solutions for Ordinary Differential Equations |edition=2nd |publisher=Chapman & Hall/CRC Press |location=Boca Raton |year=2003 |isbn=1-58488-297-2 }}<br />
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*{{cite book |first=R. I. |last=Porter |title=Further Elementary Analysis |year=1978 |chapter=XIX Differential Equations }}<br />
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*{{Cite book| last = Teschl| given = Gerald|authorlink=Gerald Teschl| title = Ordinary Differential Equations and Dynamical Systems| publisher=[[American Mathematical Society]]| place = [[Providence, Rhode Island|Providence]]| year = 2012| isbn= 978-0-8218-8328-0| url = http://www.mat.univie.ac.at/~gerald/ftp/book-ode/}}<br />
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*{{cite book|author=Daniel Zwillinger|title=Handbook of Differential Equations|url=https://books.google.com/?id=n7TiBQAAQBAJ&printsec=frontcover&dq=%22Handbook+of+Differential+Equations%22#v=onepage&q=%22Handbook%20of%20Differential%20Equations%22&f=false|date=12 May 2014|publisher=Elsevier Science|isbn=978-1-4832-6396-0}}<br />
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==External links 外部链接==<br />
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{{wikiquote}}<br />
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{{Wikibooks|Ordinary Differential Equations}}<br />
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{{Wikiversity|Differential equations}}<br />
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{{EB1911 poster|Differential Equation}}<br />
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*{{Commonscatinline|Differential equations}}<br />
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*[http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/video-lectures/ Lectures on Differential Equations] [[MIT]] Open CourseWare Videos<br />
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*[http://tutorial.math.lamar.edu/classes/de/de.aspx Online Notes / Differential Equations] Paul Dawkins, [[Lamar University]]<br />
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*[http://www.sosmath.com/diffeq/diffeq.html Differential Equations], S.O.S. Mathematics<br />
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*[http://www.fioravante.patrone.name/mat/u-u/en/differential_equations_intro.htm Introduction to modeling via differential equations] Introduction to modeling by means of differential equations, with critical remarks.<br />
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*[http://user.mendelu.cz/marik/maw/index.php?lang=en&form=ode Mathematical Assistant on Web] Symbolic ODE tool, using [[Maxima (software)|Maxima]]<br />
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*[http://eqworld.ipmnet.ru/en/solutions/ode.htm Exact Solutions of Ordinary Differential Equations]<br />
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*[http://www.hedengren.net/research/models.htm Collection of ODE and DAE models of physical systems] MATLAB models<br />
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*[http://www.jirka.org/diffyqs/ Notes on Diffy Qs: Differential Equations for Engineers] An introductory textbook on differential equations by Jiri Lebl of [[UIUC]]<br />
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*[http://www.khanacademy.org/math/differential-equations Khan Academy Video playlist on differential equations ] Topics covered in a first year course in differential equations.<br />
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*[https://web.archive.org/web/20130607120716/http://math.rareinfos.com/category/courses/solutions-differential-equations/homogeneous-linear-systems/ MathDiscuss Video playlist on differential equations ]<br />
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本中文词条由[[用户:Yuling|Yuling]]编译,[[用户:CecileLi|CecileLi]]审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=30408还原论2022-04-18T11:54:18Z<p>唐糖糖:/* 定义 */</p>
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<div>{{#seo:<br />
|keywords=还原论,Reductionism<br />
|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
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[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].<br />
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'''勒内·笛卡尔 René Descartes'''在其1662年出版的《人论 De Homine》中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
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还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
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== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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# <br />
'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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# <br />
'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔 Thomas Nagel和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩 John Polkinghorne所称的“观念”或“认识论”<ref name="Polkinghorne" /> 的还原论是西蒙·布莱克本<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref> Simon Blackburn和金在权<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref> Jaegwon Kim所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯 Richard Jones区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和 <ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref>。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref>。<br />
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== 类型 ==<br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref>。<br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref>。<br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref>。<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref>。<br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref>。<br />
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=== 方法论还原论 ===<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体 <ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref>。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref>。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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=== 理论还原论 ===<br />
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'''理论还原是一个更一般的而理论吸收一个特殊的理论的过程。'''例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论 <ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<br />
量子整体论是一种最低可能的还原理论。<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref>。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref>。<br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref>。当系统表现出历史性时,涌现尤为重要<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref>。涌现与非线性密切相关<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> 。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> <ref name="Clayton2006" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref>。<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref>。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref>。<br />
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== 在数学中 ==<br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。'''<u>策梅洛(Ernst Zermelo)</u>'''是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱'''<u>泽梅洛</u>'''的还原论主张<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref>。<br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref>。<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力。<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref>人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref>。<br />
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== 在语言学中 ==<br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref>。一个例子就是道本语。<br />
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== 在哲学中 == <br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的。<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref>特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制。<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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=== 自由意志 ===<br />
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启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref>。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref>。<br />
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=== 因果关系 ===<br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref>。<br />
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== 批评 ==<br />
=== 反还原论主义 ===<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref><ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref>。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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<blockquote><br />
对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
</blockquote><br />
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<br />
“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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这些观点也引发了对科学方法的许多批评:<br />
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<blockquote><br />
科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref>。<br />
</blockquote><br />
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== 替代方案 ==<br />
<br />
系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref>。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref>。<br />
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在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref>。<br />
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==参见==<br />
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{{Portal|Philosophy|Psychology}}<br />
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{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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}}<br />
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}}<br />
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* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
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{{Reflist}}<br />
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== 拓展阅读 ==<br />
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* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
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* Dawkins, Richard (1976), ''The Selfish Gene''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
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* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* Pinker, Steven (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* Rosenberg, Alexander (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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* Weinberg, Steven (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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* Weinberg, Steven (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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* Capra, Fritjof (1982), ''The Turning Point''.<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=30407还原论2022-04-18T11:52:12Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=还原论,Reductionism<br />
|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
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[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].<br />
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'''勒内·笛卡尔 René Descartes'''在其1662年出版的《人论 De Homine》中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
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还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
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== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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# <br />
'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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# <br />
'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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# <br />
'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔(Thomas Nagel)和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩(John Polkinghorne)所称的“观念”或“认识论”<ref name="Polkinghorne" /> 的还原论是西蒙·布莱克本<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref>(Simon Blackburn)和金在权<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref>(Jaegwon Kim)所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯(Richard Jones)区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和 <ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref>。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref>。<br />
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== 类型 ==<br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref>。<br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref>。<br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref>。<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref>。<br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref>。<br />
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=== 方法论还原论 ===<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体 <ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref>。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref>。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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=== 理论还原论 ===<br />
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'''理论还原是一个更一般的而理论吸收一个特殊的理论的过程。'''例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论 <ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<br />
量子整体论是一种最低可能的还原理论。<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref>。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref>。<br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref>。当系统表现出历史性时,涌现尤为重要<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref>。涌现与非线性密切相关<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> 。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> <ref name="Clayton2006" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref>。<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref>。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref>。<br />
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== 在数学中 ==<br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。'''<u>策梅洛(Ernst Zermelo)</u>'''是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱'''<u>泽梅洛</u>'''的还原论主张<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref>。<br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref>。<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力。<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref>人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref>。<br />
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== 在语言学中 ==<br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref>。一个例子就是道本语。<br />
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== 在哲学中 == <br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的。<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref>特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制。<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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=== 自由意志 ===<br />
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启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref>。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref>。<br />
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=== 因果关系 ===<br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref>。<br />
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== 批评 ==<br />
=== 反还原论主义 ===<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref><ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref>。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
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“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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这些观点也引发了对科学方法的许多批评:<br />
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<blockquote><br />
科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref>。<br />
</blockquote><br />
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== 替代方案 ==<br />
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系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref>。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref>。<br />
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在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref>。<br />
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==参见==<br />
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{{Portal|Philosophy|Psychology}}<br />
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{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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}}<br />
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}}<br />
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* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
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{{Reflist}}<br />
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== 拓展阅读 ==<br />
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* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
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* Dawkins, Richard (1976), ''The Selfish Gene''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
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* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* Pinker, Steven (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* Rosenberg, Alexander (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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* Weinberg, Steven (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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* Weinberg, Steven (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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* Capra, Fritjof (1982), ''The Turning Point''.<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=30406还原论2022-04-18T11:51:52Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
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|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
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[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].<br />
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勒内·笛卡尔 René Descartes在其1662年出版的《人论 De Homine》中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
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还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
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== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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# <br />
'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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# <br />
'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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# <br />
'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔(Thomas Nagel)和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩(John Polkinghorne)所称的“观念”或“认识论”<ref name="Polkinghorne" /> 的还原论是西蒙·布莱克本<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref>(Simon Blackburn)和金在权<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref>(Jaegwon Kim)所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯(Richard Jones)区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和 <ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref>。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref>。<br />
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== 类型 ==<br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref>。<br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref>。<br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref>。<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref>。<br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref>。<br />
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=== 方法论还原论 ===<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体 <ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref>。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref>。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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=== 理论还原论 ===<br />
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'''理论还原是一个更一般的而理论吸收一个特殊的理论的过程。'''例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论 <ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<br />
量子整体论是一种最低可能的还原理论。<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref>。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref>。<br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref>。当系统表现出历史性时,涌现尤为重要<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref>。涌现与非线性密切相关<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> 。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> <ref name="Clayton2006" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref>。<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref>。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref>。<br />
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== 在数学中 ==<br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。'''<u>策梅洛(Ernst Zermelo)</u>'''是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱'''<u>泽梅洛</u>'''的还原论主张<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref>。<br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref>。<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力。<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref>人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref>。<br />
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== 在语言学中 ==<br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref>。一个例子就是道本语。<br />
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== 在哲学中 == <br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的。<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref>特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制。<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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=== 自由意志 ===<br />
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启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref>。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref>。<br />
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=== 因果关系 ===<br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref>。<br />
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== 批评 ==<br />
=== 反还原论主义 ===<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref><ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref>。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
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“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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这些观点也引发了对科学方法的许多批评:<br />
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科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref>。<br />
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== 替代方案 ==<br />
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系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref>。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref>。<br />
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在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref>。<br />
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==参见==<br />
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{{Portal|Philosophy|Psychology}}<br />
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{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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}}<br />
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}}<br />
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* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
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{{Reflist}}<br />
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== 拓展阅读 ==<br />
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* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
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* Dawkins, Richard (1976), ''The Selfish Gene''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
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* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* Pinker, Steven (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* Rosenberg, Alexander (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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* Weinberg, Steven (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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* Weinberg, Steven (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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* Capra, Fritjof (1982), ''The Turning Point''.<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=30405还原论2022-04-18T11:51:19Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
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|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
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[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].<br />
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勒内·笛卡尔 René Descartes在其1662年出版的《人论 De Homine》中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。|链接=Special:FilePath/Digesting_Duck.jpg]]<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
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还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
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== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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# <br />
'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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# <br />
'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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# <br />
'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔(Thomas Nagel)和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩(John Polkinghorne)所称的“观念”或“认识论”<ref name="Polkinghorne" /> 的还原论是西蒙·布莱克本<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref>(Simon Blackburn)和金在权<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref>(Jaegwon Kim)所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯(Richard Jones)区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和 <ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref>。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref>。<br />
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== 类型 ==<br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref>。<br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref>。<br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref>。<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref>。<br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref>。<br />
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=== 方法论还原论 ===<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体 <ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref>。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref>。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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=== 理论还原论 ===<br />
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'''理论还原是一个更一般的而理论吸收一个特殊的理论的过程。'''例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论 <ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<br />
量子整体论是一种最低可能的还原理论。<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref>。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref>。<br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref>。当系统表现出历史性时,涌现尤为重要<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref>。涌现与非线性密切相关<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> 。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> <ref name="Clayton2006" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref>。<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref>。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref>。<br />
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== 在数学中 ==<br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。'''<u>策梅洛(Ernst Zermelo)</u>'''是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱'''<u>泽梅洛</u>'''的还原论主张<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref>。<br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref>。<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力。<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref>人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref>。<br />
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== 在语言学中 ==<br />
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<blockquote><br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref>。一个例子就是道本语。<br />
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== 在哲学中 == <br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的。<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref>特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制。<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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=== 自由意志 ===<br />
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启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref>。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref>。<br />
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=== 因果关系 ===<br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref>。<br />
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== 批评 ==<br />
=== 反还原论主义 ===<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref><ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref>。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
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“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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这些观点也引发了对科学方法的许多批评:<br />
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科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref>。<br />
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== 替代方案 ==<br />
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系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref>。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref>。<br />
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在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref>。<br />
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==参见==<br />
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{{Portal|Philosophy|Psychology}}<br />
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{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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}}<br />
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}}<br />
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* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
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{{Reflist}}<br />
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== 拓展阅读 ==<br />
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* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
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* Dawkins, Richard (1976), ''The Selfish Gene''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
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* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* Pinker, Steven (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* Rosenberg, Alexander (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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* Weinberg, Steven (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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* Weinberg, Steven (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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* Capra, Fritjof (1982), ''The Turning Point''.<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=30404还原论2022-04-18T11:51:03Z<p>唐糖糖:</p>
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|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
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[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].<br />
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勒内·笛卡尔 [[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]]在其1662年出版的《人论 De Homine》中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。|链接=Special:FilePath/Digesting_Duck.jpg]]<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
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还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
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== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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# <br />
'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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# <br />
'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔(Thomas Nagel)和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩(John Polkinghorne)所称的“观念”或“认识论”<ref name="Polkinghorne" /> 的还原论是西蒙·布莱克本<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref>(Simon Blackburn)和金在权<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref>(Jaegwon Kim)所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯(Richard Jones)区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和 <ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref>。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref>。<br />
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== 类型 ==<br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref>。<br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref>。<br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref>。<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref>。<br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref>。<br />
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=== 方法论还原论 ===<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体 <ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref>。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref>。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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=== 理论还原论 ===<br />
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'''理论还原是一个更一般的而理论吸收一个特殊的理论的过程。'''例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论 <ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<br />
量子整体论是一种最低可能的还原理论。<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref>。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref>。<br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref>。当系统表现出历史性时,涌现尤为重要<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref>。涌现与非线性密切相关<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> 。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> <ref name="Clayton2006" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref>。<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref>。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref>。<br />
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== 在数学中 ==<br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。'''<u>策梅洛(Ernst Zermelo)</u>'''是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱'''<u>泽梅洛</u>'''的还原论主张<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref>。<br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref>。<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力。<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref>人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref>。<br />
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== 在语言学中 ==<br />
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<blockquote><br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref>。一个例子就是道本语。<br />
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== 在哲学中 == <br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的。<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref>特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制。<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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=== 自由意志 ===<br />
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启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref>。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref>。<br />
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=== 因果关系 ===<br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref>。<br />
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== 批评 ==<br />
=== 反还原论主义 ===<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref><ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref>。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
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“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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这些观点也引发了对科学方法的许多批评:<br />
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科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref>。<br />
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== 替代方案 ==<br />
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系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref>。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref>。<br />
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在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref>。<br />
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==参见==<br />
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{{Portal|Philosophy|Psychology}}<br />
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{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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}}<br />
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}}<br />
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* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
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{{Reflist}}<br />
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== 拓展阅读 ==<br />
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* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
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* Dawkins, Richard (1976), ''The Selfish Gene''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
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* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* Pinker, Steven (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* Rosenberg, Alexander (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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* Weinberg, Steven (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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* Weinberg, Steven (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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* Capra, Fritjof (1982), ''The Turning Point''.<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=30403还原论2022-04-18T11:49:00Z<p>唐糖糖:/* 理论还原论 */</p>
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<div>{{#seo:<br />
|keywords=还原论,Reductionism<br />
|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
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[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。|链接=Special:FilePath/Digesting_Duck.jpg]]<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
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还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
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== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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# <br />
'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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# <br />
'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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# <br />
'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔(Thomas Nagel)和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩(John Polkinghorne)所称的“观念”或“认识论”<ref name="Polkinghorne" /> 的还原论是西蒙·布莱克本<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref>(Simon Blackburn)和金在权<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref>(Jaegwon Kim)所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯(Richard Jones)区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和 <ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref>。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref>。<br />
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== 类型 ==<br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref>。<br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref>。<br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref>。<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref>。<br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref>。<br />
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=== 方法论还原论 ===<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体 <ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref>。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref>。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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=== 理论还原论 ===<br />
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'''理论还原是一个更一般的而理论吸收一个特殊的理论的过程。'''例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论 <ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<br />
量子整体论是一种最低可能的还原理论。<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref>。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref>。<br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref>。当系统表现出历史性时,涌现尤为重要<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref>。涌现与非线性密切相关<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> 。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> <ref name="Clayton2006" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref>。<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref>。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref>。<br />
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== 在数学中 ==<br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。'''<u>策梅洛(Ernst Zermelo)</u>'''是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱'''<u>泽梅洛</u>'''的还原论主张<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref>。<br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref>。<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力。<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref>人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref>。<br />
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== 在语言学中 ==<br />
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<blockquote><br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref>。一个例子就是道本语。<br />
</blockquote> <br />
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== 在哲学中 == <br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的。<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref>特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制。<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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=== 自由意志 ===<br />
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启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref>。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref>。<br />
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=== 因果关系 ===<br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref>。<br />
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== 批评 ==<br />
=== 反还原论主义 ===<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref><ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref>。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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<blockquote><br />
对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
</blockquote><br />
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“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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这些观点也引发了对科学方法的许多批评:<br />
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<blockquote><br />
科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref>。<br />
</blockquote><br />
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== 替代方案 ==<br />
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系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref>。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref>。<br />
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在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref>。<br />
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==参见==<br />
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{{Portal|Philosophy|Psychology}}<br />
<br />
{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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}}<br />
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}}<br />
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* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
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{{Reflist}}<br />
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== 拓展阅读 ==<br />
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* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
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* Dawkins, Richard (1976), ''The Selfish Gene''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
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* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* Pinker, Steven (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* Rosenberg, Alexander (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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* Weinberg, Steven (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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* Weinberg, Steven (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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* Capra, Fritjof (1982), ''The Turning Point''.<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=30402还原论2022-04-18T11:48:27Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=还原论,Reductionism<br />
|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
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[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。|链接=Special:FilePath/Digesting_Duck.jpg]]<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
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还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
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== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔(Thomas Nagel)和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩(John Polkinghorne)所称的“观念”或“认识论”<ref name="Polkinghorne" /> 的还原论是西蒙·布莱克本<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref>(Simon Blackburn)和金在权<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref>(Jaegwon Kim)所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯(Richard Jones)区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和 <ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref>。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref>。<br />
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== 类型 ==<br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref>。<br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref>。<br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref>。<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref>。<br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref>。<br />
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=== 方法论还原论 ===<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体 <ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref>。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref>。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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=== 理论还原论 ===<br />
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<u>'''理论还原是一个更一般的而理论吸收一个特殊的理论的过程。'''</u><ref name=":0" />例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论 <ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<br />
量子整体论是一种最低可能的还原理论。<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref>。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref>。<br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref>。当系统表现出历史性时,涌现尤为重要<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref>。涌现与非线性密切相关<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> 。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> <ref name="Clayton2006" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref>。<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref>。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref>。<br />
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== 在数学中 ==<br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。'''<u>策梅洛(Ernst Zermelo)</u>'''是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱'''<u>泽梅洛</u>'''的还原论主张<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref>。<br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref>。<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力。<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref>人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref>。<br />
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== 在语言学中 ==<br />
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<blockquote><br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref>。一个例子就是道本语。<br />
</blockquote> <br />
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== 在哲学中 == <br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的。<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref>特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制。<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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=== 自由意志 ===<br />
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启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref>。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref>。<br />
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=== 因果关系 ===<br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref>。<br />
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== 批评 ==<br />
=== 反还原论主义 ===<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref><ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref>。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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<blockquote><br />
对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
</blockquote><br />
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“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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这些观点也引发了对科学方法的许多批评:<br />
<br />
<blockquote><br />
科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref>。<br />
</blockquote><br />
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== 替代方案 ==<br />
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系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref>。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref>。<br />
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在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref>。<br />
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==参见==<br />
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{{Portal|Philosophy|Psychology}}<br />
<br />
{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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}}<br />
<br />
}}<br />
<br />
* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
<br />
{{Reflist}}<br />
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== 拓展阅读 ==<br />
<br />
* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
<br />
* Dawkins, Richard (1976), ''The Selfish Gene''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
<br />
* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* Pinker, Steven (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* Rosenberg, Alexander (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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* Weinberg, Steven (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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* Weinberg, Steven (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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* Capra, Fritjof (1982), ''The Turning Point''.<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=30401还原论2022-04-18T11:44:26Z<p>唐糖糖:</p>
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|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
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[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。|链接=Special:FilePath/Digesting_Duck.jpg]]<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
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还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
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== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔(Thomas Nagel)和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩(John Polkinghorne)所称的“观念”或“认识论”<ref name="Polkinghorne" /> 的还原论是西蒙·布莱克本<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref>(Simon Blackburn)和金在权<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref>(Jaegwon Kim)所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯(Richard Jones)区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和 <ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref>。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref>。<br />
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== 类型 ==<br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref>。<br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref>。<br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref>。<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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Type ontological reductionism is the idea that every type of item is a sum type of item, and that every perceivable type of item is a sum of types of items with a lesser degree of complexity. Type ontological reduction of biological things to chemical things is often rejected.<br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref>。<br />
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[[Michael Ruse]] has criticized ontological reductionism as an improper argument against [[vitalism]].<br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref>。<br />
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=== 方法论还原论 ===<br />
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Methodological reductionism is the position that the best scientific strategy is to attempt to reduce explanations to the smallest possible entities. In a biological context, this means attempting to explain all biological phenomena in terms of their underlying biochemical and molecular processes. Claim of efficacy is demonstrated that the gene – unit of classical heredity – is the deoxyribonucleic acid (DNA), a macro-molecule.<ref name=":1" /><br />
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Statistical mechanics can be considered as a reconciliation of macroscopic thermodynamic laws with the reductionist method of explaining macroscopic properties in terms of microscopic components.<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体 <ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref>。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref>。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
=== 理论还原论 ===<br />
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Theory reduction is the process by which a more general theory absorbs a special theory. For example, both [[Johannes Kepler|Kepler's]] laws of the motion of the [[planet]]s and [[Galileo Galilei|Galileo]]'s theories of motion formulated for terrestrial objects are reducible to Newtonian theories of mechanics because all the explanatory power of the former are contained within the latter. Furthermore, the reduction is considered beneficial because [[Newtonian mechanics]] is a more general theory—that is, it explains more events than Galileo's or Kepler's. Besides scientific theories, theory reduction more generally can be the process by which one explanation subsumes another.<br />
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<u>'''理论还原是一个更一般的而理论吸收一个特殊的理论的过程。'''</u><ref name=":0" />例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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Reductionist thinking and methods form the basis for many of the well-developed topics of modern [[science]], including much of [[physics]], [[chemistry]] and [[molecular biology]]. [[Classical mechanics]] in particular is seen as a reductionist framework. For instance, we understand the solar system in terms of its components (the sun and the planets) and their interactions. [[Statistical mechanics]] can be considered as a reconciliation of [[macroscopic]] [[thermodynamic laws]] with the reductionist method of explaining macroscopic properties in terms of [[microscopic]] components.<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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Some strong reductionists believe that the behavioral sciences should become "genuine" scientific disciplines based on genetic biology, and on the systematic study of culture (see Richard Dawkins's concept of [[memes]]). In his book ''[[The Blind Watchmaker]]'', [[Richard Dawkins|Dawkins]] introduced the term "hierarchical reductionism"to describe the opinion that complex systems can be described with a hierarchy of organizations, each of which is only described in terms of objects one level down in the hierarchy. He provides the example of a computer, which using hierarchical reductionism is explained in terms of the operation of [[hard drive]]s, processors, and memory, but not on the level of [[logic gates]], or on the even simpler level of electrons in a [[semiconductor]] medium.<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论 <ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<br />
量子整体论是一种最低可能的还原理论。<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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Others argue that inappropriate use of reductionism limits our understanding of complex systems. In particular, ecologist [[Robert Ulanowicz]] says that science must develop techniques to study ways in which larger scales of organization influence smaller ones, and also ways in which feedback loops create structure at a given level, independently of details at a lower level of organization. He advocates (and uses) [[information theory]] as a framework to study [[Propensity probability|propensities]] in natural systems. Ulanowicz attributes these criticisms of reductionism to the philosopher [[Karl Popper]] and biologist [[Robert Rosen (theoretical biologist)|Robert Rosen]].<br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref>。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref>。<br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref>。当系统表现出历史性时,涌现尤为重要<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref>。涌现与非线性密切相关<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> 。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> <ref name="Clayton2006" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref>。<br />
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[[Nobel prize in physics|Nobel laureate]] [[Philip Warren Anderson]] used the idea that [[symmetry breaking]] is an example of an emergent phenomenon in his 1972 ''[[Science (journal)|Science]]'' paper "More is different" to make an argument about the limitations of reductionism. One observation he made was that the sciences can be arranged roughly in a linear hierarchy—[[particle physics]], [[solid state physics]], [[chemistry]], [[molecular biology]], [[cellular biology]], [[physiology]], [[psychology]], [[social sciences]]—in that the elementary entities of one science obeys the principles of the science that precedes it in the hierarchy; yet this does not imply that one science is just an applied version of the science that precedes it. He writes that "At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology nor is biology applied chemistry."<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref>。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref>。<br />
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== 在数学中 ==<br />
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In [[mathematics]], reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually [[axiomatic set theory]]. [[Ernst Zermelo]] was one of the major advocates of such an opinion; he also developed much of axiomatic set theory. It has been argued that the generally accepted method of justifying mathematical [[axioms]] by their usefulness in common practice can potentially weaken Zermelo's reductionist claim.<br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。'''<u>策梅洛(Ernst Zermelo)</u>'''是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱'''<u>泽梅洛</u>'''的还原论主张<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref>。<br />
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Jouko Väänänen has argued for [[second-order logic]] as a foundation for mathematics instead of set theory,whereas others have argued for [[category theory]] as a foundation for certain aspects of mathematics.<br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref>。<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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Religious reductionism generally attempts to explain religion by explaining it in terms of nonreligious causes. A few examples of reductionistic explanations for the presence of religion are: that religion can be reduced to humanity's conceptions of right and wrong, that religion is fundamentally a primitive attempt at controlling our environments, that religion is a way to explain the existence of a physical world, and that religion confers an enhanced survivability for members of a group and so is reinforced by [[natural selection]]. Anthropologists [[Edward Burnett Tylor]] and [[James George Frazer]] employed some [[Metatheories of religion in the social sciences#Edward Burnett Tylor and James George Frazer|religious reductionist arguments]].<br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力。<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref>人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref><br />
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== 在语言学中 ==<br />
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Linguistic reductionism is the idea that everything can be described or explained by a language with a limited number of concepts, and combinations of those concepts. An example is the language [[Toki Pona]].<br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref>。一个例子就是道本语。<br />
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== 在哲学中 == <br />
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The concept of [[downward causation]] poses an alternative to reductionism within philosophy. This opinion is developed by [[Peter Bøgh Andersen]], [[Claus Emmeche]], [[Niels Ole Finnemann]], and [[Peder Voetmann Christiansen]], among others. These philosophers explore ways in which one can talk about phenomena at a larger-scale level of organization exerting causal influence on a smaller-scale level, and find that some, but not all proposed types of downward causation are compatible with science. In particular, they find that constraint is one way in which downward causation can operate. The notion of causality as constraint has also been explored as a way to shed light on scientific concepts such as [[self-organization]], [[natural selection]], [[adaptation]], and control.<br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的。<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref>特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制。<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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=== 自由意志 ===<br />
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Philosophers of the [[Age of Enlightenment|Enlightenment]] worked to insulate human free will from reductionism. [[Descartes]] separated the material world of mechanical necessity from the world of mental free will. German philosophers introduced the concept of the "[[Noumenon|noumenal]]" realm that is not governed by the deterministic laws of "[[Phenomena (philosophy)|phenomenal]]" nature, where every event is completely determined by chains of causality. The most influential formulation was by [[Immanuel Kant]], who distinguished between the causal deterministic framework the mind imposes on the world—the phenomenal realm—and the world as it exists for itself, the noumenal realm, which, as he believed, included free will. To insulate theology from reductionism, 19th century post-Enlightenment German theologians, especially [[Friedrich Schleiermacher]] and [[Albrecht Ritschl]], used the [[Romanticism|Romantic]] method of basing religion on the human spirit, so that it is a person's feeling or sensibility about spiritual matters that comprises religion.<br />
启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref>。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref><br />
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=== 因果关系 ===<br />
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Most common philosophical understandings of [[Causality|causation]] involve reducing it to some collection of non-causal facts. Opponents of these reductionist views have given arguments that the non-causal facts in question are insufficient to determine the causal facts.<br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref>。<br />
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== 批评 ==<br />
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=== 反还原论主义 ===<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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An alternative term for ontological reductionism is ''fragmentalism'', often used in a [[pejorative]] sense. [[Anti-realism|Anti-realists]] use the term ''fragmentalism'' in arguments that the world does not exist of separable [[Non-physical entity|entities]], instead consisting of wholes. For example, advocates of this idea claim that:<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref><ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref>。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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The linear deterministic approach to nature and technology promoted a fragmented perception of reality, and a loss of the ability to foresee, to adequately evaluate, in all their complexity, global crises in ecology, civilization and education.<br />
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对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
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“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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这些观点也引发了对科学方法的许多批评:<br />
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<blockquote>The scientific method only acknowledges monophasic consciousness. The method is a specialized system that emphasizes studying small and distinctive parts in isolation, which results in fragmented knowledge.<br />
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科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref>。<br />
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== 替代方案 ==<br />
The development of [[systems thinking]] has provided methods that seek to describe issues in a [[holism|holistic]] rather than a reductionist way, and many scientists use a [[Holism in science|holistic paradigm]]. When the terms are used in a scientific context, holism and reductionism refer primarily to what sorts of [[scientific model|models]] or theories offer valid explanations of the natural world; the scientific method of falsifying hypotheses, checking empirical data against theory, is largely unchanged, but the method guides which theories are considered.<br />
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系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref>。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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[[Alfred North Whitehead]]'s metaphysics opposed reductionism. He refers to this as the "fallacy of the misplaced concreteness". His scheme was to frame a rational, general understanding of phenomena, derived from our reality.<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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[[Ecologist]] [[Sven Erik Jorgensen]] makes both theoretical and practical arguments for a [[holistic]] method in certain topics of science, especially [[ecology]]. He argues that many systems are so complex that they can ever be described in complete detail. In analogy to the Heisenberg [[uncertainty principle]] in physics, he argues that many interesting ecological phenomena cannot be replicated in laboratory conditions, and so cannot be measured or observed without changing the system in some way. He also indicates the importance of inter-connectedness in biological systems. He believes that science can only progress by outlining questions that are unanswerable and by using models that do not try to explain everything in terms of smaller hierarchical levels of organization, but instead model them on the scale of the system itself, taking into account some (but not all) factors from levels higher and lower in the hierarchy.<br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref>。<br />
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In [[cognitive psychology]], [[George Kelly (psychologist)|George Kelly]] developed "constructive alternativism" as a form of [[personal construct psychology]] and an alternative to what he considered "accumulative fragmentalism". For this theory, knowledge is seen as the construction of successful [[mental model]]s of the exterior world, rather than the accumulation of independent "nuggets of truth".<br />
在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref><br />
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==参见==<br />
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{{Portal|Philosophy|Psychology}}<br />
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{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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}}<br />
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}}<br />
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* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
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{{Reflist}}<br />
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== 拓展阅读 ==<br />
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* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
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* Dawkins, Richard (1976), ''The Selfish Gene''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
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* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* Pinker, Steven (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* Rosenberg, Alexander (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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* Weinberg, Steven (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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* Weinberg, Steven (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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* Capra, Fritjof (1982), ''The Turning Point''.<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=30400还原论2022-04-18T11:30:24Z<p>唐糖糖:</p>
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|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
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[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。|链接=Special:FilePath/Digesting_Duck.jpg]]<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
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还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
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== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔(Thomas Nagel)和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩(John Polkinghorne)所称的“观念”或“认识论”<ref name="Polkinghorne" /> 的还原论是西蒙·布莱克本<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref>(Simon Blackburn)和金在权<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref>(Jaegwon Kim)所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯(Richard Jones)区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和 <ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref>。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref>。<br />
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== 类型 ==<br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref>。<br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref>。<br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref>。<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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Type ontological reductionism is the idea that every type of item is a sum type of item, and that every perceivable type of item is a sum of types of items with a lesser degree of complexity. Type ontological reduction of biological things to chemical things is often rejected.<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref><br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7" />。<br />
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[[Michael Ruse]] has criticized ontological reductionism as an improper argument against [[vitalism]].<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref><br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证。<br />
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=== 方法论还原论 ===<br />
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Methodological reductionism is the position that the best scientific strategy is to attempt to reduce explanations to the smallest possible entities.<ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref> In a biological context, this means attempting to explain all biological phenomena in terms of their underlying biochemical and molecular processes.<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref> Claim of efficacy is demonstrated that the gene – unit of classical heredity – is the deoxyribonucleic acid (DNA), a macro-molecule.<ref name=":1" /><br />
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Statistical mechanics can be considered as a reconciliation of macroscopic thermodynamic laws with the reductionist method of explaining macroscopic properties in terms of microscopic components.<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体<ref name=":1" /> 。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6" />。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
=== 理论还原论 ===<br />
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Theory reduction is the process by which a more general theory absorbs a special theory.<ref name=":0" /> For example, both [[Johannes Kepler|Kepler's]] laws of the motion of the [[planet]]s and [[Galileo Galilei|Galileo]]'s theories of motion formulated for terrestrial objects are reducible to Newtonian theories of mechanics because all the explanatory power of the former are contained within the latter. Furthermore, the reduction is considered beneficial because [[Newtonian mechanics]] is a more general theory—that is, it explains more events than Galileo's or Kepler's. Besides scientific theories, theory reduction more generally can be the process by which one explanation subsumes another.<br />
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<u>'''理论还原是一个更一般的而理论吸收一个特殊的理论的过程。'''</u>例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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Reductionist thinking and methods form the basis for many of the well-developed topics of modern [[science]], including much of [[physics]], [[chemistry]] and [[molecular biology]]. [[Classical mechanics]] in particular is seen as a reductionist framework. For instance, we understand the solar system in terms of its components (the sun and the planets) and their interactions.<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> [[Statistical mechanics]] can be considered as a reconciliation of [[macroscopic]] [[thermodynamic laws]] with the reductionist method of explaining macroscopic properties in terms of [[microscopic]] components.<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8" /> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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Some strong reductionists believe that the behavioral sciences should become "genuine" scientific disciplines based on genetic biology, and on the systematic study of culture (see Richard Dawkins's concept of [[memes]]). In his book ''[[The Blind Watchmaker]]'', [[Richard Dawkins|Dawkins]] introduced the term "hierarchical reductionism"<ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> to describe the opinion that complex systems can be described with a hierarchy of organizations, each of which is only described in terms of objects one level down in the hierarchy. He provides the example of a computer, which using hierarchical reductionism is explained in terms of the operation of [[hard drive]]s, processors, and memory, but not on the level of [[logic gates]], or on the even simpler level of electrons in a [[semiconductor]] medium.<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论<ref name=":9" /> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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量子整体论是一种最低可能的还原理论<ref name=":10" /><ref name=":11" />。<br />
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Others argue that inappropriate use of reductionism limits our understanding of complex systems. In particular, ecologist [[Robert Ulanowicz]] says that science must develop techniques to study ways in which larger scales of organization influence smaller ones, and also ways in which feedback loops create structure at a given level, independently of details at a lower level of organization. He advocates (and uses) [[information theory]] as a framework to study [[Propensity probability|propensities]] in natural systems.<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref> Ulanowicz attributes these criticisms of reductionism to the philosopher [[Karl Popper]] and biologist [[Robert Rosen (theoretical biologist)|Robert Rosen]].<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref><br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12" /> 。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13" />。<br />
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[[Stuart Kauffman]] has argued that [[complex systems]] theory and phenomena such as [[emergence]] pose limits to reductionism.<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref> Emergence is especially relevant when systems exhibit historicity.<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref> Emergence is strongly related to [[nonlinearity]].<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> The limits of the application of reductionism are claimed to be especially evident at levels of organization with greater [[complexity]], including living [[Cell (biology)|cells]],<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> [[neural networks]], [[ecosystems]], [[society]], and other systems formed from assemblies of large numbers of diverse components linked by multiple [[feedback loop]]s.<ref name="Huber2013" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref><br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14" />。当系统表现出历史性时,涌现尤为重要<ref name=":15" />。涌现与非线性密切相关<ref name=":16" />。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013" /><ref name="Clayton2006" />。<br />
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[[Nobel prize in physics|Nobel laureate]] [[Philip Warren Anderson]] used the idea that [[symmetry breaking]] is an example of an emergent phenomenon in his 1972 ''[[Science (journal)|Science]]'' paper "More is different" to make an argument about the limitations of reductionism.<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref> One observation he made was that the sciences can be arranged roughly in a linear hierarchy—[[particle physics]], [[solid state physics]], [[chemistry]], [[molecular biology]], [[cellular biology]], [[physiology]], [[psychology]], [[social sciences]]—in that the elementary entities of one science obeys the principles of the science that precedes it in the hierarchy; yet this does not imply that one science is just an applied version of the science that precedes it. He writes that "At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology nor is biology applied chemistry."<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17" /> 。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref><br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18" />。<br />
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== 在数学中 ==<br />
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In [[mathematics]], reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually [[axiomatic set theory]]. [[Ernst Zermelo]] was one of the major advocates of such an opinion; he also developed much of axiomatic set theory. It has been argued that the generally accepted method of justifying mathematical [[axioms]] by their usefulness in common practice can potentially weaken Zermelo's reductionist claim.<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref><br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。'''<u>策梅洛(Ernst Zermelo)</u>'''是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱'''<u>泽梅洛</u>'''的还原论主张<ref name=":19" />。<br />
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Jouko Väänänen has argued for [[second-order logic]] as a foundation for mathematics instead of set theory,<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> whereas others have argued for [[category theory]] as a foundation for certain aspects of mathematics.<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref><br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20" /> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21" /><ref name=":22" />。<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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Religious reductionism generally attempts to explain religion by explaining it in terms of nonreligious causes. A few examples of reductionistic explanations for the presence of religion are: that religion can be reduced to humanity's conceptions of right and wrong, that religion is fundamentally a primitive attempt at controlling our environments, that religion is a way to explain the existence of a physical world, and that religion confers an enhanced survivability for members of a group and so is reinforced by [[natural selection]].<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref> Anthropologists [[Edward Burnett Tylor]] and [[James George Frazer]] employed some [[Metatheories of religion in the social sciences#Edward Burnett Tylor and James George Frazer|religious reductionist arguments]].<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref><br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力<ref name=":25" />。人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26" />。<br />
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== 在语言学中 ==<br />
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Linguistic reductionism is the idea that everything can be described or explained by a language with a limited number of concepts, and combinations of those concepts.<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref> An example is the language [[Toki Pona]].<br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27" /> 。一个例子就是道本语。<br />
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== 在哲学中 == <br />
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The concept of [[downward causation]] poses an alternative to reductionism within philosophy. This opinion is developed by [[Peter Bøgh Andersen]], [[Claus Emmeche]], [[Niels Ole Finnemann]], and [[Peder Voetmann Christiansen]], among others. These philosophers explore ways in which one can talk about phenomena at a larger-scale level of organization exerting causal influence on a smaller-scale level, and find that some, but not all proposed types of downward causation are compatible with science. In particular, they find that constraint is one way in which downward causation can operate.<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref> The notion of causality as constraint has also been explored as a way to shed light on scientific concepts such as [[self-organization]], [[natural selection]], [[adaptation]], and control.<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的<ref name=":28" /> 。特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制<ref name=":29" />。<br />
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=== 自由意志 ===<br />
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Philosophers of the [[Age of Enlightenment|Enlightenment]] worked to insulate human free will from reductionism. [[Descartes]] separated the material world of mechanical necessity from the world of mental free will. German philosophers introduced the concept of the "[[Noumenon|noumenal]]" realm that is not governed by the deterministic laws of "[[Phenomena (philosophy)|phenomenal]]" nature, where every event is completely determined by chains of causality.<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref> The most influential formulation was by [[Immanuel Kant]], who distinguished between the causal deterministic framework the mind imposes on the world—the phenomenal realm—and the world as it exists for itself, the noumenal realm, which, as he believed, included free will. To insulate theology from reductionism, 19th century post-Enlightenment German theologians, especially [[Friedrich Schleiermacher]] and [[Albrecht Ritschl]], used the [[Romanticism|Romantic]] method of basing religion on the human spirit, so that it is a person's feeling or sensibility about spiritual matters that comprises religion.<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref><br />
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启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30" /> 。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31" />。<br />
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=== 因果关系 ===<br />
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Most common philosophical understandings of [[Causality|causation]] involve reducing it to some collection of non-causal facts. Opponents of these reductionist views have given arguments that the non-causal facts in question are insufficient to determine the causal facts.<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref><br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll" />。<br />
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== 批评 ==<br />
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=== 反还原论主义 ===<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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An alternative term for ontological reductionism is ''fragmentalism'',<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref> often used in a [[pejorative]] sense.<ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref> [[Anti-realism|Anti-realists]] use the term ''fragmentalism'' in arguments that the world does not exist of separable [[Non-physical entity|entities]], instead consisting of wholes. For example, advocates of this idea claim that:<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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The linear deterministic approach to nature and technology promoted a fragmented perception of reality, and a loss of the ability to foresee, to adequately evaluate, in all their complexity, global crises in ecology, civilization and education.<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
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对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<br />
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“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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这些观点也引发了对科学方法的许多批评:<br />
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<blockquote>The scientific method only acknowledges monophasic consciousness. The method is a specialized system that emphasizes studying small and distinctive parts in isolation, which results in fragmented knowledge.<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref><br />
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科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin" />。</blockquote><br />
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== 替代方案 ==<br />
The development of [[systems thinking]] has provided methods that seek to describe issues in a [[holism|holistic]] rather than a reductionist way, and many scientists use a [[Holism in science|holistic paradigm]].<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref> When the terms are used in a scientific context, holism and reductionism refer primarily to what sorts of [[scientific model|models]] or theories offer valid explanations of the natural world; the scientific method of falsifying hypotheses, checking empirical data against theory, is largely unchanged, but the method guides which theories are considered.<br />
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系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33" />。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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[[Alfred North Whitehead]]'s metaphysics opposed reductionism. He refers to this as the "fallacy of the misplaced concreteness". His scheme was to frame a rational, general understanding of phenomena, derived from our reality.<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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[[Ecologist]] [[Sven Erik Jorgensen]] makes both theoretical and practical arguments for a [[holistic]] method in certain topics of science, especially [[ecology]]. He argues that many systems are so complex that they can ever be described in complete detail. In analogy to the Heisenberg [[uncertainty principle]] in physics, he argues that many interesting ecological phenomena cannot be replicated in laboratory conditions, and so cannot be measured or observed without changing the system in some way. He also indicates the importance of inter-connectedness in biological systems. He believes that science can only progress by outlining questions that are unanswerable and by using models that do not try to explain everything in terms of smaller hierarchical levels of organization, but instead model them on the scale of the system itself, taking into account some (but not all) factors from levels higher and lower in the hierarchy.<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref><br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34" />。<br />
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In [[cognitive psychology]], [[George Kelly (psychologist)|George Kelly]] developed "constructive alternativism" as a form of [[personal construct psychology]] and an alternative to what he considered "accumulative fragmentalism". For this theory, knowledge is seen as the construction of successful [[mental model]]s of the exterior world, rather than the accumulation of independent "nuggets of truth".<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref><br />
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在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35" />。<br />
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{{Reflist|refs=<br />
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{通货再膨胀 | 参考文献 = <br />
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==参见==<br />
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{{Portal|Philosophy|Psychology}}<br />
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{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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}}<br />
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}}<br />
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* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
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{{Reflist}}<br />
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== 拓展阅读 ==<br />
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* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
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* Dawkins, Richard (1976), ''The Selfish Gene''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
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* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* Pinker, Steven (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* Rosenberg, Alexander (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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* Weinberg, Steven (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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* Weinberg, Steven (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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* Capra, Fritjof (1982), ''The Turning Point''.<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%9C%89%E5%BA%8F%E5%92%8C%E6%97%A0%E5%BA%8F&diff=30399有序和无序2022-04-18T11:19:34Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=物理学,有序,无序,多粒子系统<br />
|description=物理学领域中,多粒子系统中某种对称性或相关性的存在性问题<br />
}} <br />
在'''物理学领域'''中,'''有序'''和'''无序'''指的是多粒子系统中某种'''对称性 symmetry'''或'''相关性 correlation'''的存在性问题。<br />
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在'''凝聚态物理学 condensed matter physics'''中,系统通常在低温下有序;受热后,它们会经历一个或几个'''相变 Phase Transition'''进入无序状态。<br />
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这种'''有序-无序转变'''的例子有:<br />
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* 冰的融化:固-液转变后,有序变无序;<br />
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* 铁在受到'''居里温度 Curie Temperature'''以上温度加热时就会逐渐退磁:铁磁性-顺磁性转变,磁有序变无序。<br />
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有序或无序的自由度可以是平移('''晶体 crystal'''有序)、旋转('''铁电性 ferroelectric'''有序)或自旋状态('''磁 magnetic'''有序)。<br />
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这种顺序既可以是完全晶体'''空间群 space group'''的对称也可以是关联的对称。根据相关系数随距离衰减的程度,我们可以说'''长程有序 long range order'''或'''短程有序 short range order'''。<br />
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如果一个无序的状态不存在于'''热力学平衡 thermodynamic equilibrium'''之中,那么就是'''淬致无序态'''。例如,'''玻璃 glass'''是通过淬火('''过冷却 supercooling''')液体获得的。推而广之,其它淬火态称为'''自旋玻璃态 spin glass'''、'''取向玻璃态 orientational glass'''。在某些情况下,淬致无序态的对立面是'''退火无序态'''。<br />
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==特征化秩序==<br />
===晶格周期性与 x 射线结晶度 ===<br />
固体中最严格的秩序形式是'''晶格周期性''':某种模式( 即'''单元格 unit cell''' 中原子的排列)一次又一次地重复,通过平移形成一个不变的空间'''平铺 tiling'''。这就是'''晶体 crystal'''的定义属性。可能的对称性已在14个'''布拉维斯晶格 bravais lattice'''和230个'''空间群 space group'''中进行了分类。<br />
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格点周期性意味着'''长程有序''':如果我们只知道一个单位单元,那么借助于平移对称性,就有可能在任意距离上精确地预测所有原子的位置。在20世纪的大部分时间里,相反的情况也被认为是合理的——但直到1982年'''准晶体 quasicrystal'''的发现表明,完全确定性的倾斜并不具有晶格周期性。<br />
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除了结构有序外,还有'''电荷有序 charge ordering'''、'''自旋有序 spin ordering'''、'''磁有序 magnetic ordering'''和成分有序。磁有序可以在'''中子衍射 neutron diffraction'''中观察到。<br />
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这是一个热力学'[[熵 Entropy]]的概念,通常表现为一个二阶'''相变 phase transition'''。一般来说,高热能与无序有关,低热能与有序有关,但有违背这一规律的现象存在。在低能衍射实验中,有序峰十分明显。<br />
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===远程有序===<br />
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'''远程有序'''描述了同一样本的远程部分表现出相关行为的物理系统。<br />
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这可以用'''相关函数 correlation function'''(量子场论)来表示,即'''旋转相关函数 spin-spin correlation Function'''(量子场论):<br />
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:<math>G(x,x') = \langle s(x),s(x') \rangle. \, </math><br />
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其中 ''s'' 是自旋量子数,''x'' 是特定系统中的距离函数。<br />
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当<math>x=x'</math>时,这个函数等于单位数量,当距离<math>|x-x'|</math>增加时,函数值减少。通常情况下,当它在很大程度上'''呈指数衰减 Decays Exponentially'''为零时,系统就被认为是无序的。但如果相关函数(量子场论)衰变为一个常数值,那么这个系统就被认为具有远程有序。如果它衰变成为零以作为距离的幂,那么它被称为'''准远程有序'''(详见下面引用的教科书第11章。参见'''Berezinskii–Kosterlitz–Thouless过渡 Berezinskii–Kosterlitz–Thouless Transition''')。请注意,构成较大的<math>|x-x'|</math>的值可以理解为渐近性。<br />
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==淬火无序态==<br />
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在统计物理学 statistical physics中,当定义系统行为的某些参数是不随时间演化的随机变量时,系统称为'''淬火无序态'''。它们被'''淬火 quenched'''或者''冷冻 frozen''。'''自旋玻璃态 spin glass'''就是一个典型的例子。与'''退火无序态 annealed disorder'''相反,它允许随机变量的自我进化。<br />
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在数学中,由于热平均和噪声通常起着非常不同的作用,淬致无序比退火无序更难分析。事实上,这个问题太过困难以至于很少有已知的技术可以处理,而现有的大多数解决方案都依赖于近似值。最常用的是:<br />
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# 一种基于数学解析延拓的技术,被称为'''复制技巧 Replica Trick'''<br />
<br />
# '''谐振腔法 Cavity Method''':虽然这些方法给出的结果与许多问题的实验结果相一致,但它们通常不是一个可证明的严格数学过程。<br />
<br />
<br />
然而,最近人们已经通过严密的方法证明,至少在典型的自旋玻璃模型(所谓的 '''Sherrington–Kirkpatrick 模型 Sherrington–Kirkpatrick Model''')中,基于复制的解确实是精确的。<br />
<br />
<br />
该领域次常用的技术是'''生成函数分析 Generating Functional Analysis'''。这种方法是基于'''路线积分 Path Integrals'''的,虽然这通常比复制过程更难应用,但原则上是完全精确的,<br />
<br />
[[文件:Ordering.png|缩略图|600px|center|从无序(左)状态过渡到有序(右)状态]]<br />
<br />
==退火无序态==<br />
<br />
当一个系统的某些参数进入其定义为随机变量时,称系统呈现'''退火无序态''',但其演化与定义系统的[[自由度 Degrees of Freedom]]有关。它的定义与淬致无序相反,在淬灭无序态中,随机变量可能不会改变其值。<br />
<br />
<br />
退火无序系统通常被认为更容易在数学上处理,因为无序系统的平均值和'''热平均值 thermal average'''可以在同一基础上处理。<br />
<br />
<br />
==参见==<br />
<br />
*在'''高能物理学 High Energy Physics'''中,'''量子色动力学 Quantum Chromodynamics'''中'''手性凝聚物 Chiral Condensate'''的形成是一个有序转变,用'''超选择 Superselection'''来讨论<br />
* [[熵 Entropy]]<br />
* 拓扑有序 Topological order<br />
* 杂质 Impurity<br />
* 上层建筑(物理学) superstructure (physics)<br />
<br />
==延伸阅读==<br />
<br />
* H Kleinert: [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1 ''Gauge Fields in Condensed Matter''] Singapore: World Scientific (1989).<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=14933 学科诞生记:凝聚态物理学的兴起]====<br />
数十年以来,凝聚态物理学都是物理学领域中最大的分支,但是凝聚态物理学的成就直到最近才得以彰显。<br />
<br />
<br />
<br />
<br/><br />
<br />
<br />
<br />
[[Category:统计力学]]<br />
[[Category:结晶学]]<br />
<br />
----<br />
本中文词条由[[用户:小竹凉|小竹凉]]翻译,[[用户:CecileLi|CecileLi]]审校,[[用户:薄荷|薄荷]]欢迎在讨论页面留言。<br />
<br />
<br />
'''本词条内容源自公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%9C%89%E5%BA%8F%E5%92%8C%E6%97%A0%E5%BA%8F&diff=30398有序和无序2022-04-18T11:18:21Z<p>唐糖糖:/* 淬火无序态 Quenched disorder */</p>
<hr />
<div>{{#seo:<br />
|keywords=物理学,有序,无序,多粒子系统<br />
|description=物理学领域中,多粒子系统中某种对称性或相关性的存在性问题<br />
}} <br />
在'''物理学领域 Physics'''中,'''有序'''和'''无序'''指的是多粒子系统中某种'''对称性 symmetry'''或'''相关性 correlation'''的存在性问题。<br />
<br />
<br />
在'''凝聚态物理学 condensed matter physics'''中,系统通常在低温下有序;受热后,它们会经历一个或几个'''相变 Phase Transition'''进入无序状态。<br />
<br />
<br />
这种'''有序-无序转变'''的例子有:<br />
<br />
* 冰的融化:固-液转变后,有序变无序;<br />
<br />
* 铁在受到'''居里温度 Curie Temperature'''以上温度加热时就会逐渐退磁:铁磁性-顺磁性转变,磁有序变无序。<br />
<br />
<br />
有序或无序的自由度可以是平移('''晶体 crystal'''有序)、旋转('''铁电性 ferroelectric'''有序)或自旋状态('''磁 magnetic'''有序)。<br />
<br />
<br />
这种顺序既可以是完全晶体'''空间群 space group'''的对称也可以是关联的对称。根据相关系数随距离衰减的程度,我们可以说'''长程有序 long range order'''或'''短程有序 short range order'''。<br />
<br />
<br />
如果一个无序的状态不存在于'''热力学平衡 thermodynamic equilibrium'''之中,那么就是'''淬致无序态'''。例如,'''玻璃 glass'''是通过淬火('''过冷却 supercooling''')液体获得的。推而广之,其它淬火态称为'''自旋玻璃态 spin glass'''、'''取向玻璃态 orientational glass'''。在某些情况下,淬致无序态的对立面是'''退火无序态'''。<br />
<br />
<br />
==特征化秩序 Characterizing order==<br />
===晶格周期性与 x 射线结晶度 Lattice periodicity and X-ray crystallinity===<br />
固体中最严格的秩序形式是'''晶格周期性''':某种模式( 即'''单元格 unit cell''' 中原子的排列)一次又一次地重复,通过平移形成一个不变的空间'''平铺 tiling'''。这就是'''晶体 crystal'''的定义属性。可能的对称性已在14个'''布拉维斯晶格 bravais lattice'''和230个'''空间群 space group'''中进行了分类。<br />
<br />
<br />
格点周期性意味着'''长程有序''':如果我们只知道一个单位单元,那么借助于平移对称性,就有可能在任意距离上精确地预测所有原子的位置。在20世纪的大部分时间里,相反的情况也被认为是合理的——但直到1982年'''准晶体 quasicrystal'''的发现表明,完全确定性的倾斜并不具有晶格周期性。<br />
<br />
<br />
除了结构有序外,还有'''电荷有序 charge ordering'''、'''自旋有序 spin ordering'''、'''磁有序 magnetic ordering'''和成分有序。磁有序可以在'''中子衍射 neutron diffraction'''中观察到。<br />
<br />
<br />
这是一个热力学'[[熵 Entropy]]的概念,通常表现为一个二阶'''相变 phase transition'''。一般来说,高热能与无序有关,低热能与有序有关,但有违背这一规律的现象存在。在低能衍射实验中,有序峰十分明显。<br />
<br />
<br />
===远程有序 Long-range order===<br />
<br />
'''远程有序'''描述了同一样本的远程部分表现出相关行为的物理系统。<br />
<br />
<br />
这可以用'''相关函数 correlation function'''(量子场论)来表示,即'''旋转相关函数 spin-spin correlation Function'''(量子场论):<br />
<br />
<br />
:<math>G(x,x') = \langle s(x),s(x') \rangle. \, </math><br />
<br />
<br />
其中 ''s'' 是自旋量子数,''x'' 是特定系统中的距离函数。<br />
<br />
<br />
当<math>x=x'</math>时,这个函数等于单位数量,当距离<math>|x-x'|</math>增加时,函数值减少。通常情况下,当它在很大程度上'''呈指数衰减 Decays Exponentially'''为零时,系统就被认为是无序的。但如果相关函数(量子场论)衰变为一个常数值,那么这个系统就被认为具有远程有序。如果它衰变成为零以作为距离的幂,那么它被称为'''准远程有序'''(详见下面引用的教科书第11章。参见'''Berezinskii–Kosterlitz–Thouless过渡 Berezinskii–Kosterlitz–Thouless Transition''')。请注意,构成较大的<math>|x-x'|</math>的值可以理解为渐近性。<br />
<br />
<br />
==淬火无序态 Quenched disorder==<br />
<br />
在统计物理学 statistical physics中,当定义系统行为的某些参数是不随时间演化的随机变量时,系统称为'''淬火无序态'''。它们被'''淬火 quenched'''或者''冷冻 frozen''。'''自旋玻璃态 spin glass'''就是一个典型的例子。与'''退火无序态 annealed disorder'''相反,它允许随机变量的自我进化。<br />
<br />
<br />
在数学中,由于热平均和噪声通常起着非常不同的作用,淬致无序比退火无序更难分析。事实上,这个问题太过困难以至于很少有已知的技术可以处理,而现有的大多数解决方案都依赖于近似值。最常用的是:<br />
<br />
<br />
# 一种基于数学解析延拓的技术,被称为'''复制技巧 Replica Trick'''<br />
<br />
# '''谐振腔法 Cavity Method''':虽然这些方法给出的结果与许多问题的实验结果相一致,但它们通常不是一个可证明的严格数学过程。<br />
<br />
<br />
然而,最近人们已经通过严密的方法证明,至少在典型的自旋玻璃模型(所谓的 '''Sherrington–Kirkpatrick 模型 Sherrington–Kirkpatrick Model''')中,基于复制的解确实是精确的。<br />
<br />
<br />
该领域次常用的技术是'''生成函数分析 Generating Functional Analysis'''。这种方法是基于'''路线积分 Path Integrals'''的,虽然这通常比复制过程更难应用,但原则上是完全精确的,<br />
<br />
[[文件:Ordering.png|缩略图|600px|center|从无序(左)状态过渡到有序(右)状态]]<br />
<br />
==退火无序态 Annealed disorder==<br />
<br />
当一个系统的某些参数进入其定义为随机变量时,称系统呈现'''退火无序态''',但其演化与定义系统的[[自由度 Degrees of Freedom]]有关。它的定义与淬致无序相反,在淬灭无序态中,随机变量可能不会改变其值。<br />
<br />
<br />
退火无序系统通常被认为更容易在数学上处理,因为无序系统的平均值和'''热平均值 thermal average'''可以在同一基础上处理。<br />
<br />
<br />
==参见==<br />
<br />
*在'''高能物理学 High Energy Physics'''中,'''量子色动力学 Quantum Chromodynamics'''中'''手性凝聚物 Chiral Condensate'''的形成是一个有序转变,用'''超选择 Superselection'''来讨论<br />
* [[熵 Entropy]]<br />
* 拓扑有序 Topological order<br />
* 杂质 Impurity<br />
* 上层建筑(物理学) superstructure (physics)<br />
<br />
==延伸阅读==<br />
<br />
* H Kleinert: [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1 ''Gauge Fields in Condensed Matter''] Singapore: World Scientific (1989).<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=14933 学科诞生记:凝聚态物理学的兴起]====<br />
数十年以来,凝聚态物理学都是物理学领域中最大的分支,但是凝聚态物理学的成就直到最近才得以彰显。<br />
<br />
<br />
<br />
<br/><br />
<br />
<br />
<br />
[[Category:统计力学]]<br />
[[Category:结晶学]]<br />
<br />
----<br />
本中文词条由[[用户:小竹凉|小竹凉]]翻译,[[用户:CecileLi|CecileLi]]审校,[[用户:薄荷|薄荷]]欢迎在讨论页面留言。<br />
<br />
<br />
'''本词条内容源自公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%9C%89%E5%BA%8F%E5%92%8C%E6%97%A0%E5%BA%8F&diff=30397有序和无序2022-04-18T11:17:23Z<p>唐糖糖:</p>
<hr />
<div>{{#seo:<br />
|keywords=物理学,有序,无序,多粒子系统<br />
|description=物理学领域中,多粒子系统中某种对称性或相关性的存在性问题<br />
}} <br />
在'''物理学领域 Physics'''中,'''有序'''和'''无序'''指的是多粒子系统中某种'''对称性 symmetry'''或'''相关性 correlation'''的存在性问题。<br />
<br />
<br />
在'''凝聚态物理学 condensed matter physics'''中,系统通常在低温下有序;受热后,它们会经历一个或几个'''相变 Phase Transition'''进入无序状态。<br />
<br />
<br />
这种'''有序-无序转变'''的例子有:<br />
<br />
* 冰的融化:固-液转变后,有序变无序;<br />
<br />
* 铁在受到'''居里温度 Curie Temperature'''以上温度加热时就会逐渐退磁:铁磁性-顺磁性转变,磁有序变无序。<br />
<br />
<br />
有序或无序的自由度可以是平移('''晶体 crystal'''有序)、旋转('''铁电性 ferroelectric'''有序)或自旋状态('''磁 magnetic'''有序)。<br />
<br />
<br />
这种顺序既可以是完全晶体'''空间群 space group'''的对称也可以是关联的对称。根据相关系数随距离衰减的程度,我们可以说'''长程有序 long range order'''或'''短程有序 short range order'''。<br />
<br />
<br />
如果一个无序的状态不存在于'''热力学平衡 thermodynamic equilibrium'''之中,那么就是'''淬致无序态'''。例如,'''玻璃 glass'''是通过淬火('''过冷却 supercooling''')液体获得的。推而广之,其它淬火态称为'''自旋玻璃态 spin glass'''、'''取向玻璃态 orientational glass'''。在某些情况下,淬致无序态的对立面是'''退火无序态'''。<br />
<br />
<br />
==特征化秩序 Characterizing order==<br />
===晶格周期性与 x 射线结晶度 Lattice periodicity and X-ray crystallinity===<br />
固体中最严格的秩序形式是'''晶格周期性''':某种模式( 即'''单元格 unit cell''' 中原子的排列)一次又一次地重复,通过平移形成一个不变的空间'''平铺 tiling'''。这就是'''晶体 crystal'''的定义属性。可能的对称性已在14个'''布拉维斯晶格 bravais lattice'''和230个'''空间群 space group'''中进行了分类。<br />
<br />
<br />
格点周期性意味着'''长程有序''':如果我们只知道一个单位单元,那么借助于平移对称性,就有可能在任意距离上精确地预测所有原子的位置。在20世纪的大部分时间里,相反的情况也被认为是合理的——但直到1982年'''准晶体 quasicrystal'''的发现表明,完全确定性的倾斜并不具有晶格周期性。<br />
<br />
<br />
除了结构有序外,还有'''电荷有序 charge ordering'''、'''自旋有序 spin ordering'''、'''磁有序 magnetic ordering'''和成分有序。磁有序可以在'''中子衍射 neutron diffraction'''中观察到。<br />
<br />
<br />
这是一个热力学'[[熵 Entropy]]的概念,通常表现为一个二阶'''相变 phase transition'''。一般来说,高热能与无序有关,低热能与有序有关,但有违背这一规律的现象存在。在低能衍射实验中,有序峰十分明显。<br />
<br />
<br />
===远程有序 Long-range order===<br />
<br />
'''远程有序'''描述了同一样本的远程部分表现出相关行为的物理系统。<br />
<br />
<br />
这可以用'''相关函数 correlation function'''(量子场论)来表示,即'''旋转相关函数 spin-spin correlation Function'''(量子场论):<br />
<br />
<br />
:<math>G(x,x') = \langle s(x),s(x') \rangle. \, </math><br />
<br />
<br />
其中 ''s'' 是自旋量子数,''x'' 是特定系统中的距离函数。<br />
<br />
<br />
当<math>x=x'</math>时,这个函数等于单位数量,当距离<math>|x-x'|</math>增加时,函数值减少。通常情况下,当它在很大程度上'''呈指数衰减 Decays Exponentially'''为零时,系统就被认为是无序的。但如果相关函数(量子场论)衰变为一个常数值,那么这个系统就被认为具有远程有序。如果它衰变成为零以作为距离的幂,那么它被称为'''准远程有序'''(详见下面引用的教科书第11章。参见'''Berezinskii–Kosterlitz–Thouless过渡 Berezinskii–Kosterlitz–Thouless Transition''')。请注意,构成较大的<math>|x-x'|</math>的值可以理解为渐近性。<br />
<br />
<br />
==淬火无序态 Quenched disorder==<br />
<br />
在[[统计物理学 statistical physics]]中,当定义系统行为的某些参数是不随时间演化的随机变量时,系统称为'''淬火无序态'''。它们被'''淬火 quenched'''或者''冷冻 frozen''。'''自旋玻璃态 spin glass'''就是一个典型的例子。与'''退火无序态 annealed disorder'''相反,它允许随机变量的自我进化。<br />
<br />
<br />
在数学中,由于热平均和噪声通常起着非常不同的作用,淬致无序比退火无序更难分析。事实上,这个问题太过困难以至于很少有已知的技术可以处理,而现有的大多数解决方案都依赖于近似值。最常用的是:<br />
<br />
<br />
# 一种基于数学解析延拓的技术,被称为'''复制技巧 Replica Trick'''<br />
<br />
# '''谐振腔法 Cavity Method''':虽然这些方法给出的结果与许多问题的实验结果相一致,但它们通常不是一个可证明的严格数学过程。<br />
<br />
<br />
然而,最近人们已经通过严密的方法证明,至少在典型的自旋玻璃模型(所谓的 '''Sherrington–Kirkpatrick 模型 Sherrington–Kirkpatrick Model''')中,基于复制的解确实是精确的。<br />
<br />
<br />
该领域次常用的技术是'''生成函数分析 Generating Functional Analysis'''。这种方法是基于'''路线积分 Path Integrals'''的,虽然这通常比复制过程更难应用,但原则上是完全精确的,<br />
<br />
[[文件:Ordering.png|缩略图|600px|center|从无序(左)状态过渡到有序(右)状态]]<br />
<br />
==退火无序态 Annealed disorder==<br />
<br />
当一个系统的某些参数进入其定义为随机变量时,称系统呈现'''退火无序态''',但其演化与定义系统的[[自由度 Degrees of Freedom]]有关。它的定义与淬致无序相反,在淬灭无序态中,随机变量可能不会改变其值。<br />
<br />
<br />
退火无序系统通常被认为更容易在数学上处理,因为无序系统的平均值和'''热平均值 thermal average'''可以在同一基础上处理。<br />
<br />
<br />
==参见==<br />
<br />
*在'''高能物理学 High Energy Physics'''中,'''量子色动力学 Quantum Chromodynamics'''中'''手性凝聚物 Chiral Condensate'''的形成是一个有序转变,用'''超选择 Superselection'''来讨论<br />
* [[熵 Entropy]]<br />
* 拓扑有序 Topological order<br />
* 杂质 Impurity<br />
* 上层建筑(物理学) superstructure (physics)<br />
<br />
==延伸阅读==<br />
<br />
* H Kleinert: [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1 ''Gauge Fields in Condensed Matter''] Singapore: World Scientific (1989).<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=14933 学科诞生记:凝聚态物理学的兴起]====<br />
数十年以来,凝聚态物理学都是物理学领域中最大的分支,但是凝聚态物理学的成就直到最近才得以彰显。<br />
<br />
<br />
<br />
<br/><br />
<br />
<br />
<br />
[[Category:统计力学]]<br />
[[Category:结晶学]]<br />
<br />
----<br />
本中文词条由[[用户:小竹凉|小竹凉]]翻译,[[用户:CecileLi|CecileLi]]审校,[[用户:薄荷|薄荷]]欢迎在讨论页面留言。<br />
<br />
<br />
'''本词条内容源自公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%9C%89%E5%BA%8F%E5%92%8C%E6%97%A0%E5%BA%8F&diff=30396有序和无序2022-04-18T11:16:30Z<p>唐糖糖:</p>
<hr />
<div>{{#seo:<br />
|keywords=物理学,有序,无序,多粒子系统<br />
|description=物理学领域中,多粒子系统中某种对称性或相关性的存在性问题<br />
}} <br />
在'''物理学领域 Physics'''中,'''有序'''和'''无序'''指的是多粒子系统中某种'''对称性 symmetry'''或'''相关性 correlation'''的存在性问题。<br />
<br />
<br />
在'''凝聚态物理学 condensed matter physics'''中,系统通常在低温下有序;受热后,它们会经历一个或几个'''相变 Phase Transition'''进入无序状态。<br />
<br />
<br />
这种'''有序-无序转变'''的例子有:<br />
<br />
* 冰的融化:固-液转变后,有序变无序;<br />
<br />
* 铁在受到'''居里温度 Curie Temperature'''以上温度加热时就会逐渐退磁:铁磁性-顺磁性转变,磁有序变无序。<br />
<br />
<br />
有序或无序的自由度可以是平移('''晶体 crystal'''有序)、旋转('''铁电性 ferroelectric'''有序)或自旋状态('''磁 magnetic'''有序)。<br />
<br />
<br />
这种顺序既可以是完全晶体'''空间群 space group'''的对称的也可以是关联的。根据相关系数随距离衰减的程度,我们可以说'''长程有序 long range order'''或'''短程有序 short range order'''。<br />
<br />
<br />
如果一个无序的状态不存在于'''热力学平衡 thermodynamic equilibrium'''之中,那么就是'''淬致无序态'''。例如,'''玻璃 glass'''是通过淬火('''过冷却 supercooling''')液体获得的。推而广之,其它淬火态称为'''自旋玻璃态 spin glass'''、'''取向玻璃态 orientational glass'''。在某些情况下,淬致无序态的对立面是'''退火无序态'''。<br />
<br />
<br />
==特征化秩序 Characterizing order==<br />
===晶格周期性与 x 射线结晶度 Lattice periodicity and X-ray crystallinity===<br />
固体中最严格的秩序形式是'''晶格周期性''':某种模式( 即'''单元格 unit cell''' 中原子的排列)一次又一次地重复,通过平移形成一个不变的空间'''平铺 tiling'''。这就是'''晶体 crystal'''的定义属性。可能的对称性已在14个'''布拉维斯晶格 bravais lattice'''和230个'''空间群 space group'''中进行了分类。<br />
<br />
<br />
格点周期性意味着'''长程有序''':如果我们只知道一个单位单元,那么借助于平移对称性,就有可能在任意距离上精确地预测所有原子的位置。在20世纪的大部分时间里,相反的情况也被认为是合理的——但直到1982年'''准晶体 quasicrystal'''的发现表明,完全确定性的倾斜并不具有晶格周期性。<br />
<br />
<br />
除了结构有序外,还有'''电荷有序 charge ordering'''、'''自旋有序 spin ordering'''、'''磁有序 magnetic ordering'''和成分有序。磁有序可以在'''中子衍射 neutron diffraction'''中观察到。<br />
<br />
<br />
这是一个热力学'[[熵 Entropy]]的概念,通常表现为一个二阶'''相变 phase transition'''。一般来说,高热能与无序有关,低热能与有序有关,但有违背这一规律的现象存在。在低能衍射实验中,有序峰十分明显。<br />
<br />
<br />
===远程有序 Long-range order===<br />
<br />
'''远程有序'''描述了同一样本的远程部分表现出相关行为的物理系统。<br />
<br />
<br />
这可以用'''相关函数 correlation function'''(量子场论)来表示,即'''旋转相关函数 spin-spin correlation Function'''(量子场论):<br />
<br />
<br />
:<math>G(x,x') = \langle s(x),s(x') \rangle. \, </math><br />
<br />
<br />
其中 ''s'' 是自旋量子数,''x'' 是特定系统中的距离函数。<br />
<br />
<br />
当<math>x=x'</math>时,这个函数等于单位数量,当距离<math>|x-x'|</math>增加时,函数值减少。通常情况下,当它在很大程度上'''呈指数衰减 Decays Exponentially'''为零时,系统就被认为是无序的。但如果相关函数(量子场论)衰变为一个常数值,那么这个系统就被认为具有远程有序。如果它衰变成为零以作为距离的幂,那么它被称为'''准远程有序'''(详见下面引用的教科书第11章。参见'''Berezinskii–Kosterlitz–Thouless过渡 Berezinskii–Kosterlitz–Thouless Transition''')。请注意,构成较大的<math>|x-x'|</math>的值可以理解为渐近性。<br />
<br />
<br />
==淬火无序态 Quenched disorder==<br />
<br />
在[[统计物理学 statistical physics]]中,当定义系统行为的某些参数是不随时间演化的随机变量时,系统称为'''淬火无序态'''。它们被'''淬火 quenched'''或者''冷冻 frozen''。'''自旋玻璃态 spin glass'''就是一个典型的例子。与'''退火无序态 annealed disorder'''相反,它允许随机变量的自我进化。<br />
<br />
<br />
在数学中,由于热平均和噪声通常起着非常不同的作用,淬致无序比退火无序更难分析。事实上,这个问题太过困难以至于很少有已知的技术可以处理,而现有的大多数解决方案都依赖于近似值。最常用的是:<br />
<br />
<br />
# 一种基于数学解析延拓的技术,被称为'''复制技巧 Replica Trick'''<br />
<br />
# '''谐振腔法 Cavity Method''':虽然这些方法给出的结果与许多问题的实验结果相一致,但它们通常不是一个可证明的严格数学过程。<br />
<br />
<br />
然而,最近人们已经通过严密的方法证明,至少在典型的自旋玻璃模型(所谓的 '''Sherrington–Kirkpatrick 模型 Sherrington–Kirkpatrick Model''')中,基于复制的解确实是精确的。<br />
<br />
<br />
该领域次常用的技术是'''生成函数分析 Generating Functional Analysis'''。这种方法是基于'''路线积分 Path Integrals'''的,虽然这通常比复制过程更难应用,但原则上是完全精确的,<br />
<br />
[[文件:Ordering.png|缩略图|600px|center|从无序(左)状态过渡到有序(右)状态]]<br />
<br />
==退火无序态 Annealed disorder==<br />
<br />
当一个系统的某些参数进入其定义为随机变量时,称系统呈现'''退火无序态''',但其演化与定义系统的[[自由度 Degrees of Freedom]]有关。它的定义与淬致无序相反,在淬灭无序态中,随机变量可能不会改变其值。<br />
<br />
<br />
退火无序系统通常被认为更容易在数学上处理,因为无序系统的平均值和'''热平均值 thermal average'''可以在同一基础上处理。<br />
<br />
<br />
==参见==<br />
<br />
*在'''高能物理学 High Energy Physics'''中,'''量子色动力学 Quantum Chromodynamics'''中'''手性凝聚物 Chiral Condensate'''的形成是一个有序转变,用'''超选择 Superselection'''来讨论<br />
* [[熵 Entropy]]<br />
* 拓扑有序 Topological order<br />
* 杂质 Impurity<br />
* 上层建筑(物理学) superstructure (physics)<br />
<br />
==延伸阅读==<br />
<br />
* H Kleinert: [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1 ''Gauge Fields in Condensed Matter''] Singapore: World Scientific (1989).<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=14933 学科诞生记:凝聚态物理学的兴起]====<br />
数十年以来,凝聚态物理学都是物理学领域中最大的分支,但是凝聚态物理学的成就直到最近才得以彰显。<br />
<br />
<br />
<br />
<br/><br />
<br />
<br />
<br />
[[Category:统计力学]]<br />
[[Category:结晶学]]<br />
<br />
----<br />
本中文词条由[[用户:小竹凉|小竹凉]]翻译,[[用户:CecileLi|CecileLi]]审校,[[用户:薄荷|薄荷]]欢迎在讨论页面留言。<br />
<br />
<br />
'''本词条内容源自公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%9C%89%E5%BA%8F%E5%92%8C%E6%97%A0%E5%BA%8F&diff=30395有序和无序2022-04-18T11:15:14Z<p>唐糖糖:/* 参见 */</p>
<hr />
<div>{{#seo:<br />
|keywords=物理学,有序,无序,多粒子系统<br />
|description=物理学领域中,多粒子系统中某种对称性或相关性的存在性问题<br />
}}<br />
在'''<font color="#ff8000">物理学领域 Physics</font>'''中,'''有序'''和'''无序'''指的是多粒子系统中某种'''<font color="#ff8000">对称性 symmetry</font>'''或'''<font color="#ff8000">相关性 correlation</font>'''的存在性问题。<br />
<br />
<br />
在'''<font color="#ff8000">凝聚态物理学 condensed matter physics</font>'''中,系统通常在低温下有序;受热后,它们会经历一个或几个'''<font color="#ff8000">相变 Phase Transition</font>'''进入无序状态。<br />
<br />
<br />
这种'''有序-无序转变'''的例子有:<br />
<br />
* 冰的融化:固-液转变后,有序变无序;<br />
<br />
* 铁在受到'''<font color="#ff8000">居里温度 Curie Temperature</font>'''以上温度加热时就会逐渐退磁:铁磁性-顺磁性转变,磁有序变无序。<br />
<br />
<br />
有序或无序的自由度可以是平移('''<font color="#ff8000">晶体 crystal</font>'''有序)、旋转('''<font color="#ff8000">铁电性 ferroelectric</font>'''有序)或自旋状态('''<font color="#ff8000">磁 magnetic</font>'''有序)。<br />
<br />
<br />
这种顺序既可以是完全晶体'''<font color="#ff8000">空间群 space group</font>'''的对称的也可以是关联的。根据相关系数随距离衰减的程度,我们可以说'''<font color="#ff8000">长程有序 long range order</font>'''或'''<font color="#ff8000">短程有序 short range order</font>'''。<br />
<br />
<br />
如果一个无序的状态不存在于'''<font color="#ff8000">热力学平衡 thermodynamic equilibrium</font>'''之中,那么就是'''淬致无序态'''。例如,'''<font color="#ff8000">玻璃 glass</font>'''是通过淬火('''<font color="#ff8000">过冷却 supercooling</font>''')液体获得的。推而广之,其它淬火态称为'''<font color="#ff8000">自旋玻璃态 spin glass</font>'''、'''<font color="#ff8000">取向玻璃态 orientational glass</font>'''。在某些情况下,淬致无序态的对立面是'''退火无序态'''。<br />
<br />
<br />
==特征化秩序 Characterizing order==<br />
===晶格周期性与 x 射线结晶度 Lattice periodicity and X-ray crystallinity===<br />
固体中最严格的秩序形式是'''晶格周期性''':某种模式( 即'''<font color="#ff8000">单元格 unit cell</font>''' 中原子的排列)一次又一次地重复,通过平移形成一个不变的空间'''<font color="#ff8000">平铺 tiling</font>'''。这就是'''<font color="#ff8000">晶体 crystal</font>'''的定义属性。可能的对称性已在14个'''<font color="#ff8000">布拉维斯晶格 bravais lattice</font>'''和230个'''<font color="#ff8000">空间群 space group</font>'''中进行了分类。<br />
<br />
<br />
格点周期性意味着'''长程有序''':如果我们只知道一个单位单元,那么借助于平移对称性,就有可能在任意距离上精确地预测所有原子的位置。在20世纪的大部分时间里,相反的情况也被认为是合理的——但直到1982年'''<font color="#ff8000">准晶体 quasicrystal</font>'''的发现表明,完全确定性的倾斜并不具有晶格周期性。<br />
<br />
<br />
除了结构有序外,还有'''电荷有序 charge ordering'''、'''自旋有序 spin ordering'''、'''磁有序 magnetic ordering'''和成分有序。磁有序可以在'''<font color="#ff8000">中子衍射 neutron diffraction</font>'''中观察到。<br />
<br />
<br />
这是一个热力学'[[熵 Entropy]]的概念,通常表现为一个二阶'''<font color="#ff8000">相变 phase transition</font>'''。一般来说,高热能与无序有关,低热能与有序有关,但有违背这一规律的现象存在。在低能衍射实验中,有序峰十分明显。<br />
<br />
<br />
===远程有序 Long-range order===<br />
<br />
'''远程有序'''描述了同一样本的远程部分表现出相关行为的物理系统。<br />
<br />
<br />
这可以用'''<font color="#ff8000">相关函数 correlation function</font>'''(量子场论)来表示,即'''<font color="#ff8000">旋转相关函数 spin-spin correlation Function</font>'''(量子场论):<br />
<br />
<br />
:<math>G(x,x') = \langle s(x),s(x') \rangle. \, </math><br />
<br />
<br />
其中 ''s'' 是自旋量子数,''x'' 是特定系统中的距离函数。<br />
<br />
<br />
当<math>x=x'</math>时,这个函数等于单位数量,当距离<math>|x-x'|</math>增加时,函数值减少。通常情况下,当它在很大程度上'''<font color="#ff8000">呈指数衰减 Decays Exponentially</font>'''为零时,系统就被认为是无序的。但如果相关函数(量子场论)衰变为一个常数值,那么这个系统就被认为具有远程有序。如果它衰变成为零以作为距离的幂,那么它被称为'''准远程有序'''(详见下面引用的教科书第11章。参见'''<font color="#ff8000">Berezinskii–Kosterlitz–Thouless过渡 Berezinskii–Kosterlitz–Thouless Transition</font>''')。请注意,构成较大的<math>|x-x'|</math>的值可以理解为渐近性。<br />
<br />
<br />
==淬火无序态 Quenched disorder==<br />
<br />
在[[统计物理学 statistical physics]]中,当定义系统行为的某些参数是不随时间演化的随机变量时,系统称为'''淬火无序态'''。它们被'''<font color="#ff8000">淬火 quenched</font>'''或者''冷冻 frozen''。'''<font color="#ff8000">自旋玻璃态 spin glass</font>'''就是一个典型的例子。与'''<font color="#ff8000">退火无序态 annealed disorder</font>'''相反,它允许随机变量的自我进化。<br />
<br />
<br />
在数学中,由于热平均和噪声通常起着非常不同的作用,淬致无序比退火无序更难分析。事实上,这个问题太过困难以至于很少有已知的技术可以处理,而现有的大多数解决方案都依赖于近似值。最常用的是:<br />
<br />
<br />
# 一种基于数学解析延拓的技术,被称为'''<font color="#ff8000">复制技巧 Replica Trick</font>'''<br />
<br />
# '''<font color="#ff8000">谐振腔法 Cavity Method</font>''':虽然这些方法给出的结果与许多问题的实验结果相一致,但它们通常不是一个可证明的严格数学过程。<br />
<br />
<br />
然而,最近人们已经通过严密的方法证明,至少在典型的自旋玻璃模型(所谓的 '''<font color="#ff8000">Sherrington–Kirkpatrick 模型 Sherrington–Kirkpatrick Model</font>''')中,基于复制的解确实是精确的。<br />
<br />
<br />
该领域次常用的技术是'''<font color="#ff8000">生成函数分析 Generating Functional Analysis</font>'''。这种方法是基于'''<font color="#ff8000">路线积分 Path Integrals</font>'''的,虽然这通常比复制过程更难应用,但原则上是完全精确的,<br />
<br />
[[文件:Ordering.png|缩略图|600px|center|从无序(左)状态过渡到有序(右)状态]]<br />
<br />
==退火无序态 Annealed disorder==<br />
<br />
当一个系统的某些参数进入其定义为随机变量时,称系统呈现'''退火无序态''',但其演化与定义系统的[[自由度 Degrees of Freedom]]有关。它的定义与淬致无序相反,在淬灭无序态中,随机变量可能不会改变其值。<br />
<br />
<br />
退火无序系统通常被认为更容易在数学上处理,因为无序系统的平均值和'''<font color="#ff8000">热平均值 thermal average</font>'''可以在同一基础上处理。<br />
<br />
<br />
==参见==<br />
<br />
*在'''<font color="#ff8000">高能物理学 High Energy Physics</font>'''中,'''<font color="#ff8000">量子色动力学 Quantum Chromodynamics</font>'''中'''<font color="#ff8000">手性凝聚物 Chiral Condensate</font>'''的形成是一个有序转变,用'''<font color="#ff8000">超选择 Superselection</font>'''来讨论<br />
* [[熵 Entropy]]<br />
* 拓扑有序 Topological order<br />
* 杂质 Impurity<br />
* 上层建筑(物理学) superstructure (physics)<br />
<br />
==延伸阅读==<br />
<br />
* H Kleinert: [http://www.physik.fu-berlin.de/~kleinert/kleiner_reb1 ''Gauge Fields in Condensed Matter''] Singapore: World Scientific (1989).<br />
<br />
== 编者推荐 ==<br />
===集智文章推荐===<br />
<br />
====[https://swarma.org/?p=14933 学科诞生记:凝聚态物理学的兴起]====<br />
数十年以来,凝聚态物理学都是物理学领域中最大的分支,但是凝聚态物理学的成就直到最近才得以彰显。<br />
<br />
<br />
<br />
<br/><br />
<br />
<br />
<br />
[[Category:统计力学]]<br />
[[Category:结晶学]]<br />
<br />
----<br />
本中文词条由[[用户:小竹凉|小竹凉]]翻译,[[用户:CecileLi|CecileLi]]审校,[[用户:薄荷|薄荷]]欢迎在讨论页面留言。<br />
<br />
<br />
'''本词条内容源自公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=29729还原论2022-03-27T14:15:20Z<p>唐糖糖:/* 参考文献 */</p>
<hr />
<div>{{#seo:<br />
|keywords=还原论,Reductionism<br />
|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
<br />
<br />
<br />
[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].|链接=Special:FilePath/Digesting_Duck.jpg]]<br />
<br />
<br />
<br />
勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
<br />
<br />
还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
<br />
<br />
<br />
== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔(Thomas Nagel)和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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Other definitions are used by other authors. For example, what [[John Polkinghorne]] terms 'conceptual' or 'epistemological' reductionism<ref name="Polkinghorne" /> is the definition provided by [[Simon Blackburn]]<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref> and by [[Jaegwon Kim]]:<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref> that form of reductionism which concerns a program of replacing the facts or entities involved in one type of discourse with other facts or entities from another type, thereby providing a relationship between them. Richard Jones distinguishes ontological and epistemological reductionism, arguing that many ontological and epistemological reductionists affirm the need for different concepts for different degrees of complexity while affirming a reduction of theories.<ref name="Jones" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩(John Polkinghorne)所称的“观念”或“认识论”的还原论是西蒙·布莱克本<ref name="Blackburn" /> (Simon Blackburn)和金在权<ref name="Kim" /> (Jaegwon Kim)所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯(Richard Jones)区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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The idea of reductionism can be expressed by "levels" of explanation, with higher levels reducible if need be to lower levels. This use of levels of understanding in part expresses our human limitations in remembering detail. However, "most philosophers would insist that our role in conceptualizing reality [our need for a hierarchy of "levels" of understanding] does not change the fact that different levels of organization in reality do have different 'properties'."<ref name="Jones" /><br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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Reductionism should be distinguished from [[Eliminative materialism|eliminationism]]: reductionists do not deny the existence of phenomena, but explain them in terms of another reality; eliminationists deny the existence of the phenomena themselves. For example, eliminationists deny the existence of life by their explanation in terms of physical and chemical processes.<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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Reductionism does not preclude the existence of what might be termed [[Emergence|emergent phenomena]], but it does imply the ability to understand those phenomena completely in terms of the processes from which they are composed. This reductionist understanding is very different from ontological or strong [[emergentism]], which intends that what emerges in "emergence" is more than the sum of the processes from which it emerges, respectively either in the ontological sense or in the epistemological sense.<ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref> Some physicists, however, claim that reductionism and emergentism are complementary: both are needed to explain natural processes.<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref><br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和<ref name=":23" /> 。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24" />。<br />
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== 类型 ==<br />
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Most philosophers delineate three types of reductionism and anti-reductionism.<ref name="Ruse" /><br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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Ontological reductionism is the belief that reality is composed of a minimum number of kinds of entities or substances.<ref name=":0" /> This claim is usually [[metaphysics|metaphysical]], and is most commonly a form of [[monism]], in effect claiming that all objects, properties and events are reducible to a single substance. (A [[mind-body dualism|dualist]] who is an ontological reductionist would believe that everything is reducible to two substances—as one possible example, a dualist might claim that reality is composed of "[[matter]]" and "[[spirit]]".)<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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Richard Jones divides ontological reductionism into two: the reductionism of substances (e.g., the reduction of mind to matter) and the reduction of the number of structures operating in nature (e.g., the reduction of one physical force to another). This permits scientists and philosophers to affirm the former while being anti-reductionists regarding the latter.<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref><br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3" />。<br />
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[[Nancey Murphy]] has claimed that there are two species of ontological reductionism: one that claims that wholes are nothing more than their parts; and atomist reductionism, claiming that wholes are not "really real". She admits that the phrase "really real" is apparently senseless but she has tried to explicate the supposed difference between the two.<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref><br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4" />。<br />
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Ontological reductionism denies the idea of ontological [[emergence]], and claims that emergence is an [[Epistemology|epistemological]] phenomenon that only exists through analysis or description of a system, and does not exist fundamentally.<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref><br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5" />。<br />
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Ontological reductionism takes two forms: '''token ontological reductionism''' and '''type ontological reductionism'''.{{Citation needed|date=July 2020}}<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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Token ontological reductionism is the idea that every item that exists is a sum item. For perceivable items, it affirms that every perceivable item is a sum of items with a lesser degree of complexity. Token ontological reduction of biological things to chemical things is generally accepted.<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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Type ontological reductionism is the idea that every type of item is a sum type of item, and that every perceivable type of item is a sum of types of items with a lesser degree of complexity. Type ontological reduction of biological things to chemical things is often rejected.<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref><br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7" />。<br />
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[[Michael Ruse]] has criticized ontological reductionism as an improper argument against [[vitalism]].<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref><br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证。<br />
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=== 方法论还原论 ===<br />
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Methodological reductionism is the position that the best scientific strategy is to attempt to reduce explanations to the smallest possible entities.<ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref> In a biological context, this means attempting to explain all biological phenomena in terms of their underlying biochemical and molecular processes.<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref> Claim of efficacy is demonstrated that the gene – unit of classical heredity – is the deoxyribonucleic acid (DNA), a macro-molecule.<ref name=":1" /><br />
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Statistical mechanics can be considered as a reconciliation of macroscopic thermodynamic laws with the reductionist method of explaining macroscopic properties in terms of microscopic components.<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体<ref name=":1" /> 。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6" />。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
=== 理论还原论 ===<br />
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Theory reduction is the process by which a more general theory absorbs a special theory.<ref name=":0" /> For example, both [[Johannes Kepler|Kepler's]] laws of the motion of the [[planet]]s and [[Galileo Galilei|Galileo]]'s theories of motion formulated for terrestrial objects are reducible to Newtonian theories of mechanics because all the explanatory power of the former are contained within the latter. Furthermore, the reduction is considered beneficial because [[Newtonian mechanics]] is a more general theory—that is, it explains more events than Galileo's or Kepler's. Besides scientific theories, theory reduction more generally can be the process by which one explanation subsumes another.<br />
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理论还原是一个更一般的而理论吸收一个特殊的理论的过程。例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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Reductionist thinking and methods form the basis for many of the well-developed topics of modern [[science]], including much of [[physics]], [[chemistry]] and [[molecular biology]]. [[Classical mechanics]] in particular is seen as a reductionist framework. For instance, we understand the solar system in terms of its components (the sun and the planets) and their interactions.<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> [[Statistical mechanics]] can be considered as a reconciliation of [[macroscopic]] [[thermodynamic laws]] with the reductionist method of explaining macroscopic properties in terms of [[microscopic]] components.<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8" /> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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In science, reductionism implies that certain topics of study are based on areas that study smaller spatial scales or organizational units. While it is commonly accepted that the foundations of [[chemistry]] are based in [[physics]], and [[molecular biology]] is based on chemistry, similar statements become controversial when one considers less rigorously defined intellectual pursuits. For example, claims that [[sociology]] is based on [[psychology]], or that [[economics]] is based on [[sociology]] and [[psychology]] would be met with reservations. These claims are difficult to substantiate even though there are obvious associations between these topics (for instance, most would agree that [[psychology]] can affect and inform [[economics]]). The limit of reductionism's usefulness stems from [[Emergence#Emergent properties and processes|emergent properties]] of [[complex systems]], which are more common at certain levels of organization. For example, certain aspects of [[evolutionary psychology]] and [[sociobiology]] are rejected by some who claim that complex systems are inherently irreducible and that a [[holistic]] method is needed to understand them.<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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Some strong reductionists believe that the behavioral sciences should become "genuine" scientific disciplines based on genetic biology, and on the systematic study of culture (see Richard Dawkins's concept of [[memes]]). In his book ''[[The Blind Watchmaker]]'', [[Richard Dawkins|Dawkins]] introduced the term "hierarchical reductionism"<ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> to describe the opinion that complex systems can be described with a hierarchy of organizations, each of which is only described in terms of objects one level down in the hierarchy. He provides the example of a computer, which using hierarchical reductionism is explained in terms of the operation of [[hard drive]]s, processors, and memory, but not on the level of [[logic gates]], or on the even simpler level of electrons in a [[semiconductor]] medium.<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论<ref name=":9" /> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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量子整体论是一种最低可能的还原理论<ref name=":10" /><ref name=":11" />。<br />
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Others argue that inappropriate use of reductionism limits our understanding of complex systems. In particular, ecologist [[Robert Ulanowicz]] says that science must develop techniques to study ways in which larger scales of organization influence smaller ones, and also ways in which feedback loops create structure at a given level, independently of details at a lower level of organization. He advocates (and uses) [[information theory]] as a framework to study [[Propensity probability|propensities]] in natural systems.<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref> Ulanowicz attributes these criticisms of reductionism to the philosopher [[Karl Popper]] and biologist [[Robert Rosen (theoretical biologist)|Robert Rosen]].<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref><br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12" /> 。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13" />。<br />
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[[Stuart Kauffman]] has argued that [[complex systems]] theory and phenomena such as [[emergence]] pose limits to reductionism.<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref> Emergence is especially relevant when systems exhibit historicity.<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref> Emergence is strongly related to [[nonlinearity]].<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> The limits of the application of reductionism are claimed to be especially evident at levels of organization with greater [[complexity]], including living [[Cell (biology)|cells]],<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> [[neural networks]], [[ecosystems]], [[society]], and other systems formed from assemblies of large numbers of diverse components linked by multiple [[feedback loop]]s.<ref name="Huber2013" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref><br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14" />。当系统表现出历史性时,涌现尤为重要<ref name=":15" />。涌现与非线性密切相关<ref name=":16" />。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013" /><ref name="Clayton2006" />。<br />
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[[Nobel prize in physics|Nobel laureate]] [[Philip Warren Anderson]] used the idea that [[symmetry breaking]] is an example of an emergent phenomenon in his 1972 ''[[Science (journal)|Science]]'' paper "More is different" to make an argument about the limitations of reductionism.<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref> One observation he made was that the sciences can be arranged roughly in a linear hierarchy—[[particle physics]], [[solid state physics]], [[chemistry]], [[molecular biology]], [[cellular biology]], [[physiology]], [[psychology]], [[social sciences]]—in that the elementary entities of one science obeys the principles of the science that precedes it in the hierarchy; yet this does not imply that one science is just an applied version of the science that precedes it. He writes that "At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology nor is biology applied chemistry."<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17" /> 。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref><br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18" />。<br />
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== 在数学中 ==<br />
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In [[mathematics]], reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually [[axiomatic set theory]]. [[Ernst Zermelo]] was one of the major advocates of such an opinion; he also developed much of axiomatic set theory. It has been argued that the generally accepted method of justifying mathematical [[axioms]] by their usefulness in common practice can potentially weaken Zermelo's reductionist claim.<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref><br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。策梅洛(Ernst Zermelo)是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱泽梅洛的还原论主张<ref name=":19" />。<br />
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Jouko Väänänen has argued for [[second-order logic]] as a foundation for mathematics instead of set theory,<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> whereas others have argued for [[category theory]] as a foundation for certain aspects of mathematics.<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref><br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20" /> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21" /><ref name=":22" />。<br />
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The [[Gödel's incompleteness theorems|incompleteness theorems]] of [[Kurt Gödel]], published in 1931, caused doubt about the attainability of an axiomatic foundation for all of mathematics. Any such foundation would have to include axioms powerful enough to describe the arithmetic of the natural numbers (a subset of all mathematics). Yet Gödel proved that, for any ''consistent'' recursively enumerable axiomatic system powerful enough to describe the arithmetic of the natural numbers, there are (model-theoretically) ''true'' propositions about the natural numbers that cannot be proved from the axioms. Such propositions are known as formally [[Undecidable problem|undecidable propositions]]. For example, the [[continuum hypothesis]] is undecidable in the [[Zermelo–Fraenkel set theory]] as shown by [[Forcing (mathematics)|Cohen]].<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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The role of reduction in [[computer science]] can be thought as a precise and unambiguous mathematical formalization of the philosophical idea of "[[#Types|theory reductionism]]". In a general sense, a problem (or set) is said to be reducible to another problem (or set), if there is a computable/feasible method to translate the questions of the former into the latter, so that, if one knows how to computably/feasibly solve the latter problem, then one can computably/feasibly solve the former. Thus, the latter can only be at least as "[[NP-hardness|hard]]" to solve as the former.<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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Reduction in [[theoretical computer science]] is pervasive in both: the mathematical abstract foundations of computation; and in real-world [[Analysis of algorithms|performance or capability analysis of algorithms]]. More specifically, reduction is a foundational and central concept, not only in the realm of mathematical logic and abstract computation in [[Computability theory|computability (or recursive) theory]], where it assumes the form of e.g. [[Turing reduction]], but also in the realm of real-world computation in time (or space) complexity analysis of algorithms, where it assumes the form of e.g. [[polynomial-time reduction]].<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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Religious reductionism generally attempts to explain religion by explaining it in terms of nonreligious causes. A few examples of reductionistic explanations for the presence of religion are: that religion can be reduced to humanity's conceptions of right and wrong, that religion is fundamentally a primitive attempt at controlling our environments, that religion is a way to explain the existence of a physical world, and that religion confers an enhanced survivability for members of a group and so is reinforced by [[natural selection]].<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref> Anthropologists [[Edward Burnett Tylor]] and [[James George Frazer]] employed some [[Metatheories of religion in the social sciences#Edward Burnett Tylor and James George Frazer|religious reductionist arguments]].<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref><br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力<ref name=":25" />。人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26" />。<br />
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== 在语言学中 ==<br />
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Linguistic reductionism is the idea that everything can be described or explained by a language with a limited number of concepts, and combinations of those concepts.<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref> An example is the language [[Toki Pona]].<br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27" /> 。一个例子就是道本语。<br />
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== 在哲学中 == <br />
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The concept of [[downward causation]] poses an alternative to reductionism within philosophy. This opinion is developed by [[Peter Bøgh Andersen]], [[Claus Emmeche]], [[Niels Ole Finnemann]], and [[Peder Voetmann Christiansen]], among others. These philosophers explore ways in which one can talk about phenomena at a larger-scale level of organization exerting causal influence on a smaller-scale level, and find that some, but not all proposed types of downward causation are compatible with science. In particular, they find that constraint is one way in which downward causation can operate.<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref> The notion of causality as constraint has also been explored as a way to shed light on scientific concepts such as [[self-organization]], [[natural selection]], [[adaptation]], and control.<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的<ref name=":28" /> 。特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制<ref name=":29" />。<br />
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=== 自由意志 ===<br />
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{{Main|Free will}}<br />
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Philosophers of the [[Age of Enlightenment|Enlightenment]] worked to insulate human free will from reductionism. [[Descartes]] separated the material world of mechanical necessity from the world of mental free will. German philosophers introduced the concept of the "[[Noumenon|noumenal]]" realm that is not governed by the deterministic laws of "[[Phenomena (philosophy)|phenomenal]]" nature, where every event is completely determined by chains of causality.<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref> The most influential formulation was by [[Immanuel Kant]], who distinguished between the causal deterministic framework the mind imposes on the world—the phenomenal realm—and the world as it exists for itself, the noumenal realm, which, as he believed, included free will. To insulate theology from reductionism, 19th century post-Enlightenment German theologians, especially [[Friedrich Schleiermacher]] and [[Albrecht Ritschl]], used the [[Romanticism|Romantic]] method of basing religion on the human spirit, so that it is a person's feeling or sensibility about spiritual matters that comprises religion.<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref><br />
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启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30" /> 。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31" />。<br />
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=== 因果关系 ===<br />
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Most common philosophical understandings of [[Causality|causation]] involve reducing it to some collection of non-causal facts. Opponents of these reductionist views have given arguments that the non-causal facts in question are insufficient to determine the causal facts.<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref><br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll" />。<br />
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== 批评 ==<br />
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=== 反还原论主义 ===<br />
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{{Main|Antireductionism}}<br />
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A contrast to reductionism is [[holism]] or [[emergentism]]. Holism is the idea that, in the whole, items can have properties, known as ''emergent properties'', that are not explainable from the sum of their parts. The principle of holism was summarized concisely by [[Aristotle]] in the [[Metaphysics (Aristotle)|Metaphysics]]: "The whole is more than the sum of its parts".<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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An alternative term for ontological reductionism is ''fragmentalism'',<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref> often used in a [[pejorative]] sense.<ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref> [[Anti-realism|Anti-realists]] use the term ''fragmentalism'' in arguments that the world does not exist of separable [[Non-physical entity|entities]], instead consisting of wholes. For example, advocates of this idea claim that:<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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The linear deterministic approach to nature and technology promoted a fragmented perception of reality, and a loss of the ability to foresee, to adequately evaluate, in all their complexity, global crises in ecology, civilization and education.<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
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对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<br />
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The term ''fragmentalism'' is usually applied to reductionist modes of thought, often with the related pejorative term ''[[scientism]]''. This usage is popular among some ecological activists: <br />
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“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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Such opinions also motivate many criticisms of the scientific method:<br />
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这些观点也引发了对科学方法的许多批评:<br />
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<blockquote>The scientific method only acknowledges monophasic consciousness. The method is a specialized system that emphasizes studying small and distinctive parts in isolation, which results in fragmented knowledge.<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref><br />
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科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin" />。</blockquote><br />
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== 替代方案 ==<br />
The development of [[systems thinking]] has provided methods that seek to describe issues in a [[holism|holistic]] rather than a reductionist way, and many scientists use a [[Holism in science|holistic paradigm]].<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref> When the terms are used in a scientific context, holism and reductionism refer primarily to what sorts of [[scientific model|models]] or theories offer valid explanations of the natural world; the scientific method of falsifying hypotheses, checking empirical data against theory, is largely unchanged, but the method guides which theories are considered.<br />
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系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33" />。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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In many cases (such as the [[kinetic theory of gases]]), given a good understanding of the components of the system, one can predict all the important properties of the system as a whole. In other systems, especially concerned with life and life's emergent properties ([[morphogenesis]], [[autopoiesis]], and [[metabolism]]), [[emergent properties]] of the system are said to be almost impossible to predict from knowledge of the parts of the system. [[Complex systems|Complexity theory]] studies systems and properties of the latter type.<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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[[Alfred North Whitehead]]'s metaphysics opposed reductionism. He refers to this as the "fallacy of the misplaced concreteness". His scheme was to frame a rational, general understanding of phenomena, derived from our reality.<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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[[Ecologist]] [[Sven Erik Jorgensen]] makes both theoretical and practical arguments for a [[holistic]] method in certain topics of science, especially [[ecology]]. He argues that many systems are so complex that they can ever be described in complete detail. In analogy to the Heisenberg [[uncertainty principle]] in physics, he argues that many interesting ecological phenomena cannot be replicated in laboratory conditions, and so cannot be measured or observed without changing the system in some way. He also indicates the importance of inter-connectedness in biological systems. He believes that science can only progress by outlining questions that are unanswerable and by using models that do not try to explain everything in terms of smaller hierarchical levels of organization, but instead model them on the scale of the system itself, taking into account some (but not all) factors from levels higher and lower in the hierarchy.<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref><br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34" />。<br />
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In [[cognitive psychology]], [[George Kelly (psychologist)|George Kelly]] developed "constructive alternativism" as a form of [[personal construct psychology]] and an alternative to what he considered "accumulative fragmentalism". For this theory, knowledge is seen as the construction of successful [[mental model]]s of the exterior world, rather than the accumulation of independent "nuggets of truth".<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref><br />
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在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35" />。<br />
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{{Reflist|refs=<br />
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{通货再膨胀 | 参考文献 = <br />
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== See also ==<br />
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{{Portal|Philosophy|Psychology}}<br />
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{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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}}<br />
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}}<br />
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* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
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{{Reflist}}<br />
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== 拓展阅读 ==<br />
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* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
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* Dawkins, Richard (1976), ''The Selfish Gene''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
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* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* Pinker, Steven (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* Rosenberg, Alexander (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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* Weinberg, Steven (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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* Weinberg, Steven (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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* Capra, Fritjof (1982), ''The Turning Point''.<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=29728还原论2022-03-27T14:14:19Z<p>唐糖糖:/* 拓展阅读 */</p>
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|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
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[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].|链接=Special:FilePath/Digesting_Duck.jpg]]<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
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还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
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== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔(Thomas Nagel)和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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Other definitions are used by other authors. For example, what [[John Polkinghorne]] terms 'conceptual' or 'epistemological' reductionism<ref name="Polkinghorne" /> is the definition provided by [[Simon Blackburn]]<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref> and by [[Jaegwon Kim]]:<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref> that form of reductionism which concerns a program of replacing the facts or entities involved in one type of discourse with other facts or entities from another type, thereby providing a relationship between them. Richard Jones distinguishes ontological and epistemological reductionism, arguing that many ontological and epistemological reductionists affirm the need for different concepts for different degrees of complexity while affirming a reduction of theories.<ref name="Jones" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩(John Polkinghorne)所称的“观念”或“认识论”的还原论是西蒙·布莱克本<ref name="Blackburn" /> (Simon Blackburn)和金在权<ref name="Kim" /> (Jaegwon Kim)所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯(Richard Jones)区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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The idea of reductionism can be expressed by "levels" of explanation, with higher levels reducible if need be to lower levels. This use of levels of understanding in part expresses our human limitations in remembering detail. However, "most philosophers would insist that our role in conceptualizing reality [our need for a hierarchy of "levels" of understanding] does not change the fact that different levels of organization in reality do have different 'properties'."<ref name="Jones" /><br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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Reductionism should be distinguished from [[Eliminative materialism|eliminationism]]: reductionists do not deny the existence of phenomena, but explain them in terms of another reality; eliminationists deny the existence of the phenomena themselves. For example, eliminationists deny the existence of life by their explanation in terms of physical and chemical processes.<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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Reductionism does not preclude the existence of what might be termed [[Emergence|emergent phenomena]], but it does imply the ability to understand those phenomena completely in terms of the processes from which they are composed. This reductionist understanding is very different from ontological or strong [[emergentism]], which intends that what emerges in "emergence" is more than the sum of the processes from which it emerges, respectively either in the ontological sense or in the epistemological sense.<ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref> Some physicists, however, claim that reductionism and emergentism are complementary: both are needed to explain natural processes.<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref><br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和<ref name=":23" /> 。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24" />。<br />
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== 类型 ==<br />
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Most philosophers delineate three types of reductionism and anti-reductionism.<ref name="Ruse" /><br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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Ontological reductionism is the belief that reality is composed of a minimum number of kinds of entities or substances.<ref name=":0" /> This claim is usually [[metaphysics|metaphysical]], and is most commonly a form of [[monism]], in effect claiming that all objects, properties and events are reducible to a single substance. (A [[mind-body dualism|dualist]] who is an ontological reductionist would believe that everything is reducible to two substances—as one possible example, a dualist might claim that reality is composed of "[[matter]]" and "[[spirit]]".)<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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Richard Jones divides ontological reductionism into two: the reductionism of substances (e.g., the reduction of mind to matter) and the reduction of the number of structures operating in nature (e.g., the reduction of one physical force to another). This permits scientists and philosophers to affirm the former while being anti-reductionists regarding the latter.<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref><br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3" />。<br />
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[[Nancey Murphy]] has claimed that there are two species of ontological reductionism: one that claims that wholes are nothing more than their parts; and atomist reductionism, claiming that wholes are not "really real". She admits that the phrase "really real" is apparently senseless but she has tried to explicate the supposed difference between the two.<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref><br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4" />。<br />
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Ontological reductionism denies the idea of ontological [[emergence]], and claims that emergence is an [[Epistemology|epistemological]] phenomenon that only exists through analysis or description of a system, and does not exist fundamentally.<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref><br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5" />。<br />
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Ontological reductionism takes two forms: '''token ontological reductionism''' and '''type ontological reductionism'''.{{Citation needed|date=July 2020}}<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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Token ontological reductionism is the idea that every item that exists is a sum item. For perceivable items, it affirms that every perceivable item is a sum of items with a lesser degree of complexity. Token ontological reduction of biological things to chemical things is generally accepted.<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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Type ontological reductionism is the idea that every type of item is a sum type of item, and that every perceivable type of item is a sum of types of items with a lesser degree of complexity. Type ontological reduction of biological things to chemical things is often rejected.<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref><br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7" />。<br />
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[[Michael Ruse]] has criticized ontological reductionism as an improper argument against [[vitalism]].<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref><br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证。<br />
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=== 方法论还原论 ===<br />
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Methodological reductionism is the position that the best scientific strategy is to attempt to reduce explanations to the smallest possible entities.<ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref> In a biological context, this means attempting to explain all biological phenomena in terms of their underlying biochemical and molecular processes.<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref> Claim of efficacy is demonstrated that the gene – unit of classical heredity – is the deoxyribonucleic acid (DNA), a macro-molecule.<ref name=":1" /><br />
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Statistical mechanics can be considered as a reconciliation of macroscopic thermodynamic laws with the reductionist method of explaining macroscopic properties in terms of microscopic components.<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体<ref name=":1" /> 。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6" />。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
=== 理论还原论 ===<br />
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Theory reduction is the process by which a more general theory absorbs a special theory.<ref name=":0" /> For example, both [[Johannes Kepler|Kepler's]] laws of the motion of the [[planet]]s and [[Galileo Galilei|Galileo]]'s theories of motion formulated for terrestrial objects are reducible to Newtonian theories of mechanics because all the explanatory power of the former are contained within the latter. Furthermore, the reduction is considered beneficial because [[Newtonian mechanics]] is a more general theory—that is, it explains more events than Galileo's or Kepler's. Besides scientific theories, theory reduction more generally can be the process by which one explanation subsumes another.<br />
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理论还原是一个更一般的而理论吸收一个特殊的理论的过程。例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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{{More citations needed section|date=August 2011}}<br />
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Reductionist thinking and methods form the basis for many of the well-developed topics of modern [[science]], including much of [[physics]], [[chemistry]] and [[molecular biology]]. [[Classical mechanics]] in particular is seen as a reductionist framework. For instance, we understand the solar system in terms of its components (the sun and the planets) and their interactions.<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> [[Statistical mechanics]] can be considered as a reconciliation of [[macroscopic]] [[thermodynamic laws]] with the reductionist method of explaining macroscopic properties in terms of [[microscopic]] components.<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8" /> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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In science, reductionism implies that certain topics of study are based on areas that study smaller spatial scales or organizational units. While it is commonly accepted that the foundations of [[chemistry]] are based in [[physics]], and [[molecular biology]] is based on chemistry, similar statements become controversial when one considers less rigorously defined intellectual pursuits. For example, claims that [[sociology]] is based on [[psychology]], or that [[economics]] is based on [[sociology]] and [[psychology]] would be met with reservations. These claims are difficult to substantiate even though there are obvious associations between these topics (for instance, most would agree that [[psychology]] can affect and inform [[economics]]). The limit of reductionism's usefulness stems from [[Emergence#Emergent properties and processes|emergent properties]] of [[complex systems]], which are more common at certain levels of organization. For example, certain aspects of [[evolutionary psychology]] and [[sociobiology]] are rejected by some who claim that complex systems are inherently irreducible and that a [[holistic]] method is needed to understand them.<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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Some strong reductionists believe that the behavioral sciences should become "genuine" scientific disciplines based on genetic biology, and on the systematic study of culture (see Richard Dawkins's concept of [[memes]]). In his book ''[[The Blind Watchmaker]]'', [[Richard Dawkins|Dawkins]] introduced the term "hierarchical reductionism"<ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> to describe the opinion that complex systems can be described with a hierarchy of organizations, each of which is only described in terms of objects one level down in the hierarchy. He provides the example of a computer, which using hierarchical reductionism is explained in terms of the operation of [[hard drive]]s, processors, and memory, but not on the level of [[logic gates]], or on the even simpler level of electrons in a [[semiconductor]] medium.<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论<ref name=":9" /> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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量子整体论是一种最低可能的还原理论<ref name=":10" /><ref name=":11" />。<br />
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Others argue that inappropriate use of reductionism limits our understanding of complex systems. In particular, ecologist [[Robert Ulanowicz]] says that science must develop techniques to study ways in which larger scales of organization influence smaller ones, and also ways in which feedback loops create structure at a given level, independently of details at a lower level of organization. He advocates (and uses) [[information theory]] as a framework to study [[Propensity probability|propensities]] in natural systems.<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref> Ulanowicz attributes these criticisms of reductionism to the philosopher [[Karl Popper]] and biologist [[Robert Rosen (theoretical biologist)|Robert Rosen]].<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref><br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12" /> 。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13" />。<br />
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[[Stuart Kauffman]] has argued that [[complex systems]] theory and phenomena such as [[emergence]] pose limits to reductionism.<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref> Emergence is especially relevant when systems exhibit historicity.<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref> Emergence is strongly related to [[nonlinearity]].<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> The limits of the application of reductionism are claimed to be especially evident at levels of organization with greater [[complexity]], including living [[Cell (biology)|cells]],<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> [[neural networks]], [[ecosystems]], [[society]], and other systems formed from assemblies of large numbers of diverse components linked by multiple [[feedback loop]]s.<ref name="Huber2013" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref><br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14" />。当系统表现出历史性时,涌现尤为重要<ref name=":15" />。涌现与非线性密切相关<ref name=":16" />。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013" /><ref name="Clayton2006" />。<br />
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[[Nobel prize in physics|Nobel laureate]] [[Philip Warren Anderson]] used the idea that [[symmetry breaking]] is an example of an emergent phenomenon in his 1972 ''[[Science (journal)|Science]]'' paper "More is different" to make an argument about the limitations of reductionism.<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref> One observation he made was that the sciences can be arranged roughly in a linear hierarchy—[[particle physics]], [[solid state physics]], [[chemistry]], [[molecular biology]], [[cellular biology]], [[physiology]], [[psychology]], [[social sciences]]—in that the elementary entities of one science obeys the principles of the science that precedes it in the hierarchy; yet this does not imply that one science is just an applied version of the science that precedes it. He writes that "At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology nor is biology applied chemistry."<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17" /> 。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref><br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18" />。<br />
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== 在数学中 ==<br />
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In [[mathematics]], reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually [[axiomatic set theory]]. [[Ernst Zermelo]] was one of the major advocates of such an opinion; he also developed much of axiomatic set theory. It has been argued that the generally accepted method of justifying mathematical [[axioms]] by their usefulness in common practice can potentially weaken Zermelo's reductionist claim.<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref><br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。策梅洛(Ernst Zermelo)是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱泽梅洛的还原论主张<ref name=":19" />。<br />
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Jouko Väänänen has argued for [[second-order logic]] as a foundation for mathematics instead of set theory,<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> whereas others have argued for [[category theory]] as a foundation for certain aspects of mathematics.<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref><br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20" /> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21" /><ref name=":22" />。<br />
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The [[Gödel's incompleteness theorems|incompleteness theorems]] of [[Kurt Gödel]], published in 1931, caused doubt about the attainability of an axiomatic foundation for all of mathematics. Any such foundation would have to include axioms powerful enough to describe the arithmetic of the natural numbers (a subset of all mathematics). Yet Gödel proved that, for any ''consistent'' recursively enumerable axiomatic system powerful enough to describe the arithmetic of the natural numbers, there are (model-theoretically) ''true'' propositions about the natural numbers that cannot be proved from the axioms. Such propositions are known as formally [[Undecidable problem|undecidable propositions]]. For example, the [[continuum hypothesis]] is undecidable in the [[Zermelo–Fraenkel set theory]] as shown by [[Forcing (mathematics)|Cohen]].<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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The role of reduction in [[computer science]] can be thought as a precise and unambiguous mathematical formalization of the philosophical idea of "[[#Types|theory reductionism]]". In a general sense, a problem (or set) is said to be reducible to another problem (or set), if there is a computable/feasible method to translate the questions of the former into the latter, so that, if one knows how to computably/feasibly solve the latter problem, then one can computably/feasibly solve the former. Thus, the latter can only be at least as "[[NP-hardness|hard]]" to solve as the former.<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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Reduction in [[theoretical computer science]] is pervasive in both: the mathematical abstract foundations of computation; and in real-world [[Analysis of algorithms|performance or capability analysis of algorithms]]. More specifically, reduction is a foundational and central concept, not only in the realm of mathematical logic and abstract computation in [[Computability theory|computability (or recursive) theory]], where it assumes the form of e.g. [[Turing reduction]], but also in the realm of real-world computation in time (or space) complexity analysis of algorithms, where it assumes the form of e.g. [[polynomial-time reduction]].<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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Religious reductionism generally attempts to explain religion by explaining it in terms of nonreligious causes. A few examples of reductionistic explanations for the presence of religion are: that religion can be reduced to humanity's conceptions of right and wrong, that religion is fundamentally a primitive attempt at controlling our environments, that religion is a way to explain the existence of a physical world, and that religion confers an enhanced survivability for members of a group and so is reinforced by [[natural selection]].<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref> Anthropologists [[Edward Burnett Tylor]] and [[James George Frazer]] employed some [[Metatheories of religion in the social sciences#Edward Burnett Tylor and James George Frazer|religious reductionist arguments]].<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref><br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力<ref name=":25" />。人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26" />。<br />
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== 在语言学中 ==<br />
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Linguistic reductionism is the idea that everything can be described or explained by a language with a limited number of concepts, and combinations of those concepts.<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref> An example is the language [[Toki Pona]].<br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27" /> 。一个例子就是道本语。<br />
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== 在哲学中 == <br />
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The concept of [[downward causation]] poses an alternative to reductionism within philosophy. This opinion is developed by [[Peter Bøgh Andersen]], [[Claus Emmeche]], [[Niels Ole Finnemann]], and [[Peder Voetmann Christiansen]], among others. These philosophers explore ways in which one can talk about phenomena at a larger-scale level of organization exerting causal influence on a smaller-scale level, and find that some, but not all proposed types of downward causation are compatible with science. In particular, they find that constraint is one way in which downward causation can operate.<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref> The notion of causality as constraint has also been explored as a way to shed light on scientific concepts such as [[self-organization]], [[natural selection]], [[adaptation]], and control.<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的<ref name=":28" /> 。特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制<ref name=":29" />。<br />
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=== 自由意志 ===<br />
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{{Main|Free will}}<br />
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Philosophers of the [[Age of Enlightenment|Enlightenment]] worked to insulate human free will from reductionism. [[Descartes]] separated the material world of mechanical necessity from the world of mental free will. German philosophers introduced the concept of the "[[Noumenon|noumenal]]" realm that is not governed by the deterministic laws of "[[Phenomena (philosophy)|phenomenal]]" nature, where every event is completely determined by chains of causality.<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref> The most influential formulation was by [[Immanuel Kant]], who distinguished between the causal deterministic framework the mind imposes on the world—the phenomenal realm—and the world as it exists for itself, the noumenal realm, which, as he believed, included free will. To insulate theology from reductionism, 19th century post-Enlightenment German theologians, especially [[Friedrich Schleiermacher]] and [[Albrecht Ritschl]], used the [[Romanticism|Romantic]] method of basing religion on the human spirit, so that it is a person's feeling or sensibility about spiritual matters that comprises religion.<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref><br />
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启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30" /> 。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31" />。<br />
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=== 因果关系 ===<br />
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Most common philosophical understandings of [[Causality|causation]] involve reducing it to some collection of non-causal facts. Opponents of these reductionist views have given arguments that the non-causal facts in question are insufficient to determine the causal facts.<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref><br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll" />。<br />
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== 批评 ==<br />
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=== 反还原论主义 ===<br />
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{{Main|Antireductionism}}<br />
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A contrast to reductionism is [[holism]] or [[emergentism]]. Holism is the idea that, in the whole, items can have properties, known as ''emergent properties'', that are not explainable from the sum of their parts. The principle of holism was summarized concisely by [[Aristotle]] in the [[Metaphysics (Aristotle)|Metaphysics]]: "The whole is more than the sum of its parts".<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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An alternative term for ontological reductionism is ''fragmentalism'',<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref> often used in a [[pejorative]] sense.<ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref> [[Anti-realism|Anti-realists]] use the term ''fragmentalism'' in arguments that the world does not exist of separable [[Non-physical entity|entities]], instead consisting of wholes. For example, advocates of this idea claim that:<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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The linear deterministic approach to nature and technology promoted a fragmented perception of reality, and a loss of the ability to foresee, to adequately evaluate, in all their complexity, global crises in ecology, civilization and education.<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
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对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<br />
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The term ''fragmentalism'' is usually applied to reductionist modes of thought, often with the related pejorative term ''[[scientism]]''. This usage is popular among some ecological activists: <br />
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“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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Such opinions also motivate many criticisms of the scientific method:<br />
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这些观点也引发了对科学方法的许多批评:<br />
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<blockquote>The scientific method only acknowledges monophasic consciousness. The method is a specialized system that emphasizes studying small and distinctive parts in isolation, which results in fragmented knowledge.<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref><br />
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科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin" />。</blockquote><br />
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== 替代方案 ==<br />
The development of [[systems thinking]] has provided methods that seek to describe issues in a [[holism|holistic]] rather than a reductionist way, and many scientists use a [[Holism in science|holistic paradigm]].<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref> When the terms are used in a scientific context, holism and reductionism refer primarily to what sorts of [[scientific model|models]] or theories offer valid explanations of the natural world; the scientific method of falsifying hypotheses, checking empirical data against theory, is largely unchanged, but the method guides which theories are considered.<br />
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系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33" />。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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In many cases (such as the [[kinetic theory of gases]]), given a good understanding of the components of the system, one can predict all the important properties of the system as a whole. In other systems, especially concerned with life and life's emergent properties ([[morphogenesis]], [[autopoiesis]], and [[metabolism]]), [[emergent properties]] of the system are said to be almost impossible to predict from knowledge of the parts of the system. [[Complex systems|Complexity theory]] studies systems and properties of the latter type.<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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[[Alfred North Whitehead]]'s metaphysics opposed reductionism. He refers to this as the "fallacy of the misplaced concreteness". His scheme was to frame a rational, general understanding of phenomena, derived from our reality.<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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[[Ecologist]] [[Sven Erik Jorgensen]] makes both theoretical and practical arguments for a [[holistic]] method in certain topics of science, especially [[ecology]]. He argues that many systems are so complex that they can ever be described in complete detail. In analogy to the Heisenberg [[uncertainty principle]] in physics, he argues that many interesting ecological phenomena cannot be replicated in laboratory conditions, and so cannot be measured or observed without changing the system in some way. He also indicates the importance of inter-connectedness in biological systems. He believes that science can only progress by outlining questions that are unanswerable and by using models that do not try to explain everything in terms of smaller hierarchical levels of organization, but instead model them on the scale of the system itself, taking into account some (but not all) factors from levels higher and lower in the hierarchy.<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref><br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34" />。<br />
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In [[cognitive psychology]], [[George Kelly (psychologist)|George Kelly]] developed "constructive alternativism" as a form of [[personal construct psychology]] and an alternative to what he considered "accumulative fragmentalism". For this theory, knowledge is seen as the construction of successful [[mental model]]s of the exterior world, rather than the accumulation of independent "nuggets of truth".<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref><br />
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在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35" />。<br />
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{通货再膨胀 | 参考文献 = <br />
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== See also ==<br />
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{{Portal|Philosophy|Psychology}}<br />
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{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
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{{Reflist|refs=<br />
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<ref name=GodfreySmith>{{cite book |title=Philosophy of Biology |author=Peter Godfrey-Smith |isbn= 978-1-4008-5044-0 |year=2013 |publisher=Princeton University Press |url=https://books.google.com/books?id=hfvsAQAAQBAJ&pg=PA16 |page=16}}</ref><br />
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<ref name=Jones>{{cite book |title=Reductionism: Analysis and the Fullness of Reality |author= Richard H. Jones |chapter=Clarification of terminology |publisher=Bucknell University Press |year=2000 |isbn= 978-0-8387-5439-9 |chapter-url=https://books.google.com/books?id=sUgnio874NUC&q=%22+has+some+properties+that+other+levels+do+not+share%22&pg=PA19 |at=Pages 19–, with focus on 27–28, 32}}</ref><br />
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<ref name=MerriamWebster>{{cite book |title=Merriam-Webster's Encyclopedia of World Religions |chapter=Reductionism |chapter-url=https://books.google.com/books?id=ZP_f9icf2roC&q=reductionism+%22simpler+or+more+basic%22&pg=PA911 |isbn=978-0-87779-044-0 |year=1999 |editor=Wendy Doniger |publisher=Merriam-Webster |page=[https://archive.org/details/isbn_9780877790440/page/911 911] |url=https://archive.org/details/isbn_9780877790440/page/911 }}</ref><br />
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<ref name=Nagel>{{cite book |title=Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature is Almost Certainly False |author=Thomas Nagel |year=2012 |publisher=Oxford University Press |isbn=978-0-19-991975-8 |pages=4–5 |url=https://books.google.com/books?id=sFRpAgAAQBAJ&q=%22psychophysical+reductionism,+a+position+in+the+philosophy+of+mind%22&pg=PA4}}</ref><br />
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<ref name=Ney>{{cite encyclopedia |encyclopedia=Internet Encyclopedia of Philosophy |author=Alyssa Ney |title=Reductionism |url=http://www.iep.utm.edu/red-ism/ |access-date=March 13, 2015 |publisher=IEP, University of Tennessee}}</ref><br />
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== 拓展阅读 ==<br />
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* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
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* Dawkins, Richard (1976), ''The Selfish Gene''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
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* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* Pinker, Steven (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* Rosenberg, Alexander (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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* Weinberg, Steven (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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* Weinberg, Steven (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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* Capra, Fritjof (1982), ''The Turning Point''.<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=29727还原论2022-03-27T14:12:36Z<p>唐糖糖:/* 延伸阅读 */</p>
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|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
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[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].|链接=Special:FilePath/Digesting_Duck.jpg]]<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
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还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
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== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔(Thomas Nagel)和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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Other definitions are used by other authors. For example, what [[John Polkinghorne]] terms 'conceptual' or 'epistemological' reductionism<ref name="Polkinghorne" /> is the definition provided by [[Simon Blackburn]]<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref> and by [[Jaegwon Kim]]:<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref> that form of reductionism which concerns a program of replacing the facts or entities involved in one type of discourse with other facts or entities from another type, thereby providing a relationship between them. Richard Jones distinguishes ontological and epistemological reductionism, arguing that many ontological and epistemological reductionists affirm the need for different concepts for different degrees of complexity while affirming a reduction of theories.<ref name="Jones" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩(John Polkinghorne)所称的“观念”或“认识论”的还原论是西蒙·布莱克本<ref name="Blackburn" /> (Simon Blackburn)和金在权<ref name="Kim" /> (Jaegwon Kim)所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯(Richard Jones)区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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The idea of reductionism can be expressed by "levels" of explanation, with higher levels reducible if need be to lower levels. This use of levels of understanding in part expresses our human limitations in remembering detail. However, "most philosophers would insist that our role in conceptualizing reality [our need for a hierarchy of "levels" of understanding] does not change the fact that different levels of organization in reality do have different 'properties'."<ref name="Jones" /><br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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Reductionism should be distinguished from [[Eliminative materialism|eliminationism]]: reductionists do not deny the existence of phenomena, but explain them in terms of another reality; eliminationists deny the existence of the phenomena themselves. For example, eliminationists deny the existence of life by their explanation in terms of physical and chemical processes.<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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Reductionism does not preclude the existence of what might be termed [[Emergence|emergent phenomena]], but it does imply the ability to understand those phenomena completely in terms of the processes from which they are composed. This reductionist understanding is very different from ontological or strong [[emergentism]], which intends that what emerges in "emergence" is more than the sum of the processes from which it emerges, respectively either in the ontological sense or in the epistemological sense.<ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref> Some physicists, however, claim that reductionism and emergentism are complementary: both are needed to explain natural processes.<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref><br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和<ref name=":23" /> 。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24" />。<br />
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== 类型 ==<br />
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Most philosophers delineate three types of reductionism and anti-reductionism.<ref name="Ruse" /><br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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Ontological reductionism is the belief that reality is composed of a minimum number of kinds of entities or substances.<ref name=":0" /> This claim is usually [[metaphysics|metaphysical]], and is most commonly a form of [[monism]], in effect claiming that all objects, properties and events are reducible to a single substance. (A [[mind-body dualism|dualist]] who is an ontological reductionist would believe that everything is reducible to two substances—as one possible example, a dualist might claim that reality is composed of "[[matter]]" and "[[spirit]]".)<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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Richard Jones divides ontological reductionism into two: the reductionism of substances (e.g., the reduction of mind to matter) and the reduction of the number of structures operating in nature (e.g., the reduction of one physical force to another). This permits scientists and philosophers to affirm the former while being anti-reductionists regarding the latter.<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref><br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3" />。<br />
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[[Nancey Murphy]] has claimed that there are two species of ontological reductionism: one that claims that wholes are nothing more than their parts; and atomist reductionism, claiming that wholes are not "really real". She admits that the phrase "really real" is apparently senseless but she has tried to explicate the supposed difference between the two.<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref><br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4" />。<br />
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Ontological reductionism denies the idea of ontological [[emergence]], and claims that emergence is an [[Epistemology|epistemological]] phenomenon that only exists through analysis or description of a system, and does not exist fundamentally.<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref><br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5" />。<br />
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Ontological reductionism takes two forms: '''token ontological reductionism''' and '''type ontological reductionism'''.{{Citation needed|date=July 2020}}<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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Token ontological reductionism is the idea that every item that exists is a sum item. For perceivable items, it affirms that every perceivable item is a sum of items with a lesser degree of complexity. Token ontological reduction of biological things to chemical things is generally accepted.<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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Type ontological reductionism is the idea that every type of item is a sum type of item, and that every perceivable type of item is a sum of types of items with a lesser degree of complexity. Type ontological reduction of biological things to chemical things is often rejected.<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref><br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7" />。<br />
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[[Michael Ruse]] has criticized ontological reductionism as an improper argument against [[vitalism]].<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref><br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证。<br />
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=== 方法论还原论 ===<br />
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Methodological reductionism is the position that the best scientific strategy is to attempt to reduce explanations to the smallest possible entities.<ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref> In a biological context, this means attempting to explain all biological phenomena in terms of their underlying biochemical and molecular processes.<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref> Claim of efficacy is demonstrated that the gene – unit of classical heredity – is the deoxyribonucleic acid (DNA), a macro-molecule.<ref name=":1" /><br />
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Statistical mechanics can be considered as a reconciliation of macroscopic thermodynamic laws with the reductionist method of explaining macroscopic properties in terms of microscopic components.<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体<ref name=":1" /> 。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6" />。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
=== 理论还原论 ===<br />
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Theory reduction is the process by which a more general theory absorbs a special theory.<ref name=":0" /> For example, both [[Johannes Kepler|Kepler's]] laws of the motion of the [[planet]]s and [[Galileo Galilei|Galileo]]'s theories of motion formulated for terrestrial objects are reducible to Newtonian theories of mechanics because all the explanatory power of the former are contained within the latter. Furthermore, the reduction is considered beneficial because [[Newtonian mechanics]] is a more general theory—that is, it explains more events than Galileo's or Kepler's. Besides scientific theories, theory reduction more generally can be the process by which one explanation subsumes another.<br />
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理论还原是一个更一般的而理论吸收一个特殊的理论的过程。例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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{{More citations needed section|date=August 2011}}<br />
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Reductionist thinking and methods form the basis for many of the well-developed topics of modern [[science]], including much of [[physics]], [[chemistry]] and [[molecular biology]]. [[Classical mechanics]] in particular is seen as a reductionist framework. For instance, we understand the solar system in terms of its components (the sun and the planets) and their interactions.<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> [[Statistical mechanics]] can be considered as a reconciliation of [[macroscopic]] [[thermodynamic laws]] with the reductionist method of explaining macroscopic properties in terms of [[microscopic]] components.<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8" /> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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In science, reductionism implies that certain topics of study are based on areas that study smaller spatial scales or organizational units. While it is commonly accepted that the foundations of [[chemistry]] are based in [[physics]], and [[molecular biology]] is based on chemistry, similar statements become controversial when one considers less rigorously defined intellectual pursuits. For example, claims that [[sociology]] is based on [[psychology]], or that [[economics]] is based on [[sociology]] and [[psychology]] would be met with reservations. These claims are difficult to substantiate even though there are obvious associations between these topics (for instance, most would agree that [[psychology]] can affect and inform [[economics]]). The limit of reductionism's usefulness stems from [[Emergence#Emergent properties and processes|emergent properties]] of [[complex systems]], which are more common at certain levels of organization. For example, certain aspects of [[evolutionary psychology]] and [[sociobiology]] are rejected by some who claim that complex systems are inherently irreducible and that a [[holistic]] method is needed to understand them.<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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Some strong reductionists believe that the behavioral sciences should become "genuine" scientific disciplines based on genetic biology, and on the systematic study of culture (see Richard Dawkins's concept of [[memes]]). In his book ''[[The Blind Watchmaker]]'', [[Richard Dawkins|Dawkins]] introduced the term "hierarchical reductionism"<ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> to describe the opinion that complex systems can be described with a hierarchy of organizations, each of which is only described in terms of objects one level down in the hierarchy. He provides the example of a computer, which using hierarchical reductionism is explained in terms of the operation of [[hard drive]]s, processors, and memory, but not on the level of [[logic gates]], or on the even simpler level of electrons in a [[semiconductor]] medium.<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论<ref name=":9" /> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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量子整体论是一种最低可能的还原理论<ref name=":10" /><ref name=":11" />。<br />
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Others argue that inappropriate use of reductionism limits our understanding of complex systems. In particular, ecologist [[Robert Ulanowicz]] says that science must develop techniques to study ways in which larger scales of organization influence smaller ones, and also ways in which feedback loops create structure at a given level, independently of details at a lower level of organization. He advocates (and uses) [[information theory]] as a framework to study [[Propensity probability|propensities]] in natural systems.<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref> Ulanowicz attributes these criticisms of reductionism to the philosopher [[Karl Popper]] and biologist [[Robert Rosen (theoretical biologist)|Robert Rosen]].<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref><br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12" /> 。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13" />。<br />
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[[Stuart Kauffman]] has argued that [[complex systems]] theory and phenomena such as [[emergence]] pose limits to reductionism.<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref> Emergence is especially relevant when systems exhibit historicity.<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref> Emergence is strongly related to [[nonlinearity]].<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> The limits of the application of reductionism are claimed to be especially evident at levels of organization with greater [[complexity]], including living [[Cell (biology)|cells]],<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> [[neural networks]], [[ecosystems]], [[society]], and other systems formed from assemblies of large numbers of diverse components linked by multiple [[feedback loop]]s.<ref name="Huber2013" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref><br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14" />。当系统表现出历史性时,涌现尤为重要<ref name=":15" />。涌现与非线性密切相关<ref name=":16" />。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013" /><ref name="Clayton2006" />。<br />
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[[Nobel prize in physics|Nobel laureate]] [[Philip Warren Anderson]] used the idea that [[symmetry breaking]] is an example of an emergent phenomenon in his 1972 ''[[Science (journal)|Science]]'' paper "More is different" to make an argument about the limitations of reductionism.<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref> One observation he made was that the sciences can be arranged roughly in a linear hierarchy—[[particle physics]], [[solid state physics]], [[chemistry]], [[molecular biology]], [[cellular biology]], [[physiology]], [[psychology]], [[social sciences]]—in that the elementary entities of one science obeys the principles of the science that precedes it in the hierarchy; yet this does not imply that one science is just an applied version of the science that precedes it. He writes that "At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology nor is biology applied chemistry."<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17" /> 。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref><br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18" />。<br />
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== 在数学中 ==<br />
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In [[mathematics]], reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually [[axiomatic set theory]]. [[Ernst Zermelo]] was one of the major advocates of such an opinion; he also developed much of axiomatic set theory. It has been argued that the generally accepted method of justifying mathematical [[axioms]] by their usefulness in common practice can potentially weaken Zermelo's reductionist claim.<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref><br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。策梅洛(Ernst Zermelo)是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱泽梅洛的还原论主张<ref name=":19" />。<br />
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Jouko Väänänen has argued for [[second-order logic]] as a foundation for mathematics instead of set theory,<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> whereas others have argued for [[category theory]] as a foundation for certain aspects of mathematics.<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref><br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20" /> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21" /><ref name=":22" />。<br />
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The [[Gödel's incompleteness theorems|incompleteness theorems]] of [[Kurt Gödel]], published in 1931, caused doubt about the attainability of an axiomatic foundation for all of mathematics. Any such foundation would have to include axioms powerful enough to describe the arithmetic of the natural numbers (a subset of all mathematics). Yet Gödel proved that, for any ''consistent'' recursively enumerable axiomatic system powerful enough to describe the arithmetic of the natural numbers, there are (model-theoretically) ''true'' propositions about the natural numbers that cannot be proved from the axioms. Such propositions are known as formally [[Undecidable problem|undecidable propositions]]. For example, the [[continuum hypothesis]] is undecidable in the [[Zermelo–Fraenkel set theory]] as shown by [[Forcing (mathematics)|Cohen]].<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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The role of reduction in [[computer science]] can be thought as a precise and unambiguous mathematical formalization of the philosophical idea of "[[#Types|theory reductionism]]". In a general sense, a problem (or set) is said to be reducible to another problem (or set), if there is a computable/feasible method to translate the questions of the former into the latter, so that, if one knows how to computably/feasibly solve the latter problem, then one can computably/feasibly solve the former. Thus, the latter can only be at least as "[[NP-hardness|hard]]" to solve as the former.<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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Reduction in [[theoretical computer science]] is pervasive in both: the mathematical abstract foundations of computation; and in real-world [[Analysis of algorithms|performance or capability analysis of algorithms]]. More specifically, reduction is a foundational and central concept, not only in the realm of mathematical logic and abstract computation in [[Computability theory|computability (or recursive) theory]], where it assumes the form of e.g. [[Turing reduction]], but also in the realm of real-world computation in time (or space) complexity analysis of algorithms, where it assumes the form of e.g. [[polynomial-time reduction]].<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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Religious reductionism generally attempts to explain religion by explaining it in terms of nonreligious causes. A few examples of reductionistic explanations for the presence of religion are: that religion can be reduced to humanity's conceptions of right and wrong, that religion is fundamentally a primitive attempt at controlling our environments, that religion is a way to explain the existence of a physical world, and that religion confers an enhanced survivability for members of a group and so is reinforced by [[natural selection]].<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref> Anthropologists [[Edward Burnett Tylor]] and [[James George Frazer]] employed some [[Metatheories of religion in the social sciences#Edward Burnett Tylor and James George Frazer|religious reductionist arguments]].<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref><br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力<ref name=":25" />。人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26" />。<br />
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== 在语言学中 ==<br />
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Linguistic reductionism is the idea that everything can be described or explained by a language with a limited number of concepts, and combinations of those concepts.<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref> An example is the language [[Toki Pona]].<br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27" /> 。一个例子就是道本语。<br />
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== 在哲学中 == <br />
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The concept of [[downward causation]] poses an alternative to reductionism within philosophy. This opinion is developed by [[Peter Bøgh Andersen]], [[Claus Emmeche]], [[Niels Ole Finnemann]], and [[Peder Voetmann Christiansen]], among others. These philosophers explore ways in which one can talk about phenomena at a larger-scale level of organization exerting causal influence on a smaller-scale level, and find that some, but not all proposed types of downward causation are compatible with science. In particular, they find that constraint is one way in which downward causation can operate.<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref> The notion of causality as constraint has also been explored as a way to shed light on scientific concepts such as [[self-organization]], [[natural selection]], [[adaptation]], and control.<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的<ref name=":28" /> 。特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制<ref name=":29" />。<br />
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=== 自由意志 ===<br />
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{{Main|Free will}}<br />
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Philosophers of the [[Age of Enlightenment|Enlightenment]] worked to insulate human free will from reductionism. [[Descartes]] separated the material world of mechanical necessity from the world of mental free will. German philosophers introduced the concept of the "[[Noumenon|noumenal]]" realm that is not governed by the deterministic laws of "[[Phenomena (philosophy)|phenomenal]]" nature, where every event is completely determined by chains of causality.<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref> The most influential formulation was by [[Immanuel Kant]], who distinguished between the causal deterministic framework the mind imposes on the world—the phenomenal realm—and the world as it exists for itself, the noumenal realm, which, as he believed, included free will. To insulate theology from reductionism, 19th century post-Enlightenment German theologians, especially [[Friedrich Schleiermacher]] and [[Albrecht Ritschl]], used the [[Romanticism|Romantic]] method of basing religion on the human spirit, so that it is a person's feeling or sensibility about spiritual matters that comprises religion.<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref><br />
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启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30" /> 。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31" />。<br />
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=== 因果关系 ===<br />
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Most common philosophical understandings of [[Causality|causation]] involve reducing it to some collection of non-causal facts. Opponents of these reductionist views have given arguments that the non-causal facts in question are insufficient to determine the causal facts.<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref><br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll" />。<br />
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== 批评 ==<br />
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=== 反还原论主义 ===<br />
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{{Main|Antireductionism}}<br />
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A contrast to reductionism is [[holism]] or [[emergentism]]. Holism is the idea that, in the whole, items can have properties, known as ''emergent properties'', that are not explainable from the sum of their parts. The principle of holism was summarized concisely by [[Aristotle]] in the [[Metaphysics (Aristotle)|Metaphysics]]: "The whole is more than the sum of its parts".<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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An alternative term for ontological reductionism is ''fragmentalism'',<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref> often used in a [[pejorative]] sense.<ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref> [[Anti-realism|Anti-realists]] use the term ''fragmentalism'' in arguments that the world does not exist of separable [[Non-physical entity|entities]], instead consisting of wholes. For example, advocates of this idea claim that:<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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The linear deterministic approach to nature and technology promoted a fragmented perception of reality, and a loss of the ability to foresee, to adequately evaluate, in all their complexity, global crises in ecology, civilization and education.<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
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对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<br />
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The term ''fragmentalism'' is usually applied to reductionist modes of thought, often with the related pejorative term ''[[scientism]]''. This usage is popular among some ecological activists: <br />
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“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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Such opinions also motivate many criticisms of the scientific method:<br />
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这些观点也引发了对科学方法的许多批评:<br />
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<blockquote>The scientific method only acknowledges monophasic consciousness. The method is a specialized system that emphasizes studying small and distinctive parts in isolation, which results in fragmented knowledge.<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref><br />
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科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin" />。</blockquote><br />
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== 替代方案 ==<br />
The development of [[systems thinking]] has provided methods that seek to describe issues in a [[holism|holistic]] rather than a reductionist way, and many scientists use a [[Holism in science|holistic paradigm]].<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref> When the terms are used in a scientific context, holism and reductionism refer primarily to what sorts of [[scientific model|models]] or theories offer valid explanations of the natural world; the scientific method of falsifying hypotheses, checking empirical data against theory, is largely unchanged, but the method guides which theories are considered.<br />
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系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33" />。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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In many cases (such as the [[kinetic theory of gases]]), given a good understanding of the components of the system, one can predict all the important properties of the system as a whole. In other systems, especially concerned with life and life's emergent properties ([[morphogenesis]], [[autopoiesis]], and [[metabolism]]), [[emergent properties]] of the system are said to be almost impossible to predict from knowledge of the parts of the system. [[Complex systems|Complexity theory]] studies systems and properties of the latter type.<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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[[Alfred North Whitehead]]'s metaphysics opposed reductionism. He refers to this as the "fallacy of the misplaced concreteness". His scheme was to frame a rational, general understanding of phenomena, derived from our reality.<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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[[Ecologist]] [[Sven Erik Jorgensen]] makes both theoretical and practical arguments for a [[holistic]] method in certain topics of science, especially [[ecology]]. He argues that many systems are so complex that they can ever be described in complete detail. In analogy to the Heisenberg [[uncertainty principle]] in physics, he argues that many interesting ecological phenomena cannot be replicated in laboratory conditions, and so cannot be measured or observed without changing the system in some way. He also indicates the importance of inter-connectedness in biological systems. He believes that science can only progress by outlining questions that are unanswerable and by using models that do not try to explain everything in terms of smaller hierarchical levels of organization, but instead model them on the scale of the system itself, taking into account some (but not all) factors from levels higher and lower in the hierarchy.<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref><br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34" />。<br />
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In [[cognitive psychology]], [[George Kelly (psychologist)|George Kelly]] developed "constructive alternativism" as a form of [[personal construct psychology]] and an alternative to what he considered "accumulative fragmentalism". For this theory, knowledge is seen as the construction of successful [[mental model]]s of the exterior world, rather than the accumulation of independent "nuggets of truth".<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref><br />
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在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35" />。<br />
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{{Reflist|refs=<br />
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{通货再膨胀 | 参考文献 = <br />
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== See also ==<br />
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{{Portal|Philosophy|Psychology}}<br />
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{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
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{{Reflist|refs=<br />
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<ref name=GodfreySmith>{{cite book |title=Philosophy of Biology |author=Peter Godfrey-Smith |isbn= 978-1-4008-5044-0 |year=2013 |publisher=Princeton University Press |url=https://books.google.com/books?id=hfvsAQAAQBAJ&pg=PA16 |page=16}}</ref><br />
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<ref name=Jones>{{cite book |title=Reductionism: Analysis and the Fullness of Reality |author= Richard H. Jones |chapter=Clarification of terminology |publisher=Bucknell University Press |year=2000 |isbn= 978-0-8387-5439-9 |chapter-url=https://books.google.com/books?id=sUgnio874NUC&q=%22+has+some+properties+that+other+levels+do+not+share%22&pg=PA19 |at=Pages 19–, with focus on 27–28, 32}}</ref><br />
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<ref name=MerriamWebster>{{cite book |title=Merriam-Webster's Encyclopedia of World Religions |chapter=Reductionism |chapter-url=https://books.google.com/books?id=ZP_f9icf2roC&q=reductionism+%22simpler+or+more+basic%22&pg=PA911 |isbn=978-0-87779-044-0 |year=1999 |editor=Wendy Doniger |publisher=Merriam-Webster |page=[https://archive.org/details/isbn_9780877790440/page/911 911] |url=https://archive.org/details/isbn_9780877790440/page/911 }}</ref><br />
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<ref name=Nagel>{{cite book |title=Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature is Almost Certainly False |author=Thomas Nagel |year=2012 |publisher=Oxford University Press |isbn=978-0-19-991975-8 |pages=4–5 |url=https://books.google.com/books?id=sFRpAgAAQBAJ&q=%22psychophysical+reductionism,+a+position+in+the+philosophy+of+mind%22&pg=PA4}}</ref><br />
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<ref name=Ney>{{cite encyclopedia |encyclopedia=Internet Encyclopedia of Philosophy |author=Alyssa Ney |title=Reductionism |url=http://www.iep.utm.edu/red-ism/ |access-date=March 13, 2015 |publisher=IEP, University of Tennessee}}</ref><br />
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== 拓展阅读 ==<br />
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* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
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* Dawkins, Richard (1976), ''[[The Selfish Gene]]''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
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* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* [[Pinker, Steven]] (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* [[Rosenberg, Alexander]] (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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* [[Weinberg, Steven]] (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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* [[Weinberg, Steven]] (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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* [[Fritjof Capra|Capra, Fritjof]] (1982), ''The Turning Point''.<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E8%BF%98%E5%8E%9F%E8%AE%BA&diff=29726还原论2022-03-27T14:10:13Z<p>唐糖糖:</p>
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|description=还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述,它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场。}}<br />
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[[File:Digesting Duck.jpg|thumb|300px|[[René Descartes]], in [[The World (Descartes)|De homine]] (1662), claimed that non-human animals could be explained reductively as [[automaton|automata]]; meaning essentially as more mechanically complex versions of this [[Digesting Duck]].|链接=Special:FilePath/Digesting_Duck.jpg]]<br />
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勒内·笛卡尔([[René Descartes, in De homine (1662), claimed that non-human animals could be explained reductively as automata; meaning essentially as more mechanically complex versions of this Digesting Duck.|René Descartes]])在其1662年出版的《人论》(De Homine,1662)中宣称:非人类动物可以被简化为自动机,从本质上讲,是这种消化鸭的机械复杂版本。<br />
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还原论是一种有关现象之间的联系的哲学观点,认为现象可以用其他更简单或更基本的现象来描述<ref name="MerriamWebster" /> 。它是一种将一个复杂的系统解释为其各部分的总和的思想和哲学立场<ref name=":0">{{Cite book|last=Kricheldorf|first=Hans R.|title=Getting It Right in Science and Medicine: Can Science Progress through Errors? Fallacies and Facts|publisher=Springer|year=2016|isbn=978-3-319-30386-4|location=Cham|pages=63|language=en}}</ref>。<br />
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== 定义 ==<br />
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《牛津哲学指南》指出,还原论是“哲学词汇中最常用和最常被滥用的术语之一”,并将其划分为三部分:<ref name="Ruse">{{cite book |title=The Oxford Companion to Philosophy |author=Michael Ruse |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for "reductionism" |publisher=Oxford University Press |page=793 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1884}}</ref><br />
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'''本体论还原论''': 一种认为所有现实均是由最小数量的部分组成的信念。<br />
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'''方法论还原论''': 一种用尽可能小的对象来提供解释的科学尝试。<br />
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# <br />
'''理论还原论''': 认为新的理论不会取代或吸收旧的理论,而是将其简化为更基本的术语。理论还原本身可以分为翻译、推导和解释三个部分<ref name="Ney" />。<br />
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还原论可以应用于任何现象,包括对象、问题、解释、理论和意义<ref name=Ney /><ref name=Polkinghorne>{{cite encyclopedia |title=Reductionism |author=John Polkinghorne |url=http://www.disf.org/en/Voci/104.asp |encyclopedia=Interdisciplinary Encyclopedia of Religion and Science|date=2002 |publisher=Advanced School for Interdisciplinary Research; Pontifical University of the Holy Cross}}</ref><ref name=":2">For reductionism referred to [[explanation]]s, [[theory|theories]], and meanings, see [[Willard Van Orman Quine]]'s ''[[Two Dogmas of Empiricism]]''. Quine objected to the [[positivism|positivistic]], reductionist "belief that each meaningful statement is equivalent to some logical construct upon terms which refer to immediate experience" as an intractable problem.</ref>。<br />
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对于科学而言,方法论还原论试图从个体、组成部分及其相互作用的角度对整个系统进行解释。例如,对气体温度的降低不能超过其运动着的分子的平均动能。托马斯 · 内格尔(Thomas Nagel)和其他人还谈到了“心理物理学还原论”(试图将心理现象还原为物理和化学)和“物理化学还原论”(试图将生物学还原为物理和化学)<ref name="Nagel" />。<br />
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在一种非常简化的,有时是有争议的形式中,还原论被认为暗示一个系统只是它的部分的总和<ref name="Polkinghorne" /><ref name="GodfreySmith" />。然而,与之有着细微差别的观点是,一个系统完全由它的部分组成,但该系统将具有任何部分都没有的特征(这在本质上是涌现论的基础)<ref name="Jones" />。“机械论则侧重于解释整体更高层次的特征是如何从部分中产生的。”<ref name="GodfreySmith" /><br />
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Other definitions are used by other authors. For example, what [[John Polkinghorne]] terms 'conceptual' or 'epistemological' reductionism<ref name="Polkinghorne" /> is the definition provided by [[Simon Blackburn]]<ref name="Blackburn">{{cite book |author=Simon Blackburn |title= Oxford Dictionary of Philosophy |chapter=Entry on ‘reductionism’ |date= 27 October 2005 |page=311 |isbn= 978-0-19-861013-7 |chapter-url=https://books.google.com/books?id=5wTQtwB1NdgC&pg=PA311}}</ref> and by [[Jaegwon Kim]]:<ref name="Kim">{{cite book |author=Jaegwon Kim |title=The Oxford Companion to Philosophy |editor=Ted Honderich |isbn=978-0-19-103747-4 |year=2005 |edition=2nd |chapter=Entry for ‘mental reductionism’ |publisher=Oxford University Press |page=794 |chapter-url=https://books.google.com/books?id=bJFCAwAAQBAJ&pg=PT1885}}</ref> that form of reductionism which concerns a program of replacing the facts or entities involved in one type of discourse with other facts or entities from another type, thereby providing a relationship between them. Richard Jones distinguishes ontological and epistemological reductionism, arguing that many ontological and epistemological reductionists affirm the need for different concepts for different degrees of complexity while affirming a reduction of theories.<ref name="Jones" /><br />
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不过也有作者使用另外的定义。例如,约翰·鲍金霍恩(John Polkinghorne)所称的“观念”或“认识论”的还原论是西蒙·布莱克本<ref name="Blackburn" /> (Simon Blackburn)和金在权<ref name="Kim" /> (Jaegwon Kim)所使用的定义: 还原论从形式上用另一类型的其他事实或实体替换论述中提及的某种类型的事实或实体,从而在它们之间提供一种联系。理查德 · 琼斯(Richard Jones)区分了本体论和认识论的还原论,他认为许多本体论和认识论的还原论者在肯定理论还原的同时,也肯定了不同程度的复杂性需要不同的概念<ref name="Jones" />。<br />
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The idea of reductionism can be expressed by "levels" of explanation, with higher levels reducible if need be to lower levels. This use of levels of understanding in part expresses our human limitations in remembering detail. However, "most philosophers would insist that our role in conceptualizing reality [our need for a hierarchy of "levels" of understanding] does not change the fact that different levels of organization in reality do have different 'properties'."<ref name="Jones" /><br />
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还原论的观点可以用解释的“层次”来表达,根据需要可以将较高的层次还原到较低的层次。这种对理解层次的使用在一定程度上反映了人类在记忆细节方面的局限性。然而,“大多数哲学家会坚持认为,我们在概念化现实中的角色(我们对理解层次的需要)不会改变现实中不同层次的组织确实有不同的‘属性’这一事实<ref name="Jones" />。”<br />
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Reductionism should be distinguished from [[Eliminative materialism|eliminationism]]: reductionists do not deny the existence of phenomena, but explain them in terms of another reality; eliminationists deny the existence of the phenomena themselves. For example, eliminationists deny the existence of life by their explanation in terms of physical and chemical processes.<br />
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还原论还应与消除论区别开来:还原论者不否认现象的存在,而是用另一种现实来解释现象。消除论者否认现象本身的存在。例如,消除论者通过解释物理和化学过程来否认生命的存在。<br />
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Reductionism does not preclude the existence of what might be termed [[Emergence|emergent phenomena]], but it does imply the ability to understand those phenomena completely in terms of the processes from which they are composed. This reductionist understanding is very different from ontological or strong [[emergentism]], which intends that what emerges in "emergence" is more than the sum of the processes from which it emerges, respectively either in the ontological sense or in the epistemological sense.<ref name=":23">Axelrod and Cohen "Harnessing Complexity"</ref> Some physicists, however, claim that reductionism and emergentism are complementary: both are needed to explain natural processes.<ref name=":24">Piers Coleman, Center for Materials Theory, Rutgers, Hubbard Theory Consortium and Physics Department, Royal Holloway, University of London; contribution to [https://www.d-iep.org/diep DIEP]-conference "Emergence at all lengthscales" 22-01-2019</ref><br />
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还原论并没有排除所谓涌现现象的存在,但它确实暗示了完全理解这些现象的能力,从它们组成的过程来看。这种还原论的理解与本体论或强涌现论有很大的不同,本体论或强涌现论认为,在“涌现”中出现的东西不仅仅是它从本体论意义上或认识论意义上出现的过程的总和<ref name=":23" /> 。然而,一些物理学家声称还原论和涌现论是互补的: 对自然过程的解释二者都是必需的<ref name=":24" />。<br />
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== 类型 ==<br />
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Most philosophers delineate three types of reductionism and anti-reductionism.<ref name="Ruse" /><br />
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大多数哲学家将还原论和反还原论分为三种类型<ref name="Ruse" />。<br />
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=== 本体论还原论 ===<br />
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Ontological reductionism is the belief that reality is composed of a minimum number of kinds of entities or substances.<ref name=":0" /> This claim is usually [[metaphysics|metaphysical]], and is most commonly a form of [[monism]], in effect claiming that all objects, properties and events are reducible to a single substance. (A [[mind-body dualism|dualist]] who is an ontological reductionist would believe that everything is reducible to two substances—as one possible example, a dualist might claim that reality is composed of "[[matter]]" and "[[spirit]]".)<br />
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本体论还原论认为现实是由最少数量的实体或物质组成的<ref name=":0" />。这种说法通常是形而上学的,是一元论最常见的一种形式,这实际上是断言所有的对象、属性和事件都可以简化为一个单一的实体。(本体论还原论者的二元论者则会认为一切事物都可以简化为两个实体——举个可能的例子,二元论者可能会声称现实是由“物质”和“精神”组成的。)<br />
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Richard Jones divides ontological reductionism into two: the reductionism of substances (e.g., the reduction of mind to matter) and the reduction of the number of structures operating in nature (e.g., the reduction of one physical force to another). This permits scientists and philosophers to affirm the former while being anti-reductionists regarding the latter.<ref name=":3">Richard H. Jones (2000), ''Reductionism: Analysis and the Fuullness of Reality'', pp. 24-26, 29-31. Lewisburg, Pa.: Bucknell University Press.</ref><br />
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理查德·琼斯将本体论还原论分为两种:物质还原论(例如,将精神还原为物质)和在自然界中运作的结构数量的减少(例如,将一种物理作用力还原为另一种)。这种划分使得科学家和哲学家们在对后者持反对态度的同时不得不承认前者<ref name=":3" />。<br />
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[[Nancey Murphy]] has claimed that there are two species of ontological reductionism: one that claims that wholes are nothing more than their parts; and atomist reductionism, claiming that wholes are not "really real". She admits that the phrase "really real" is apparently senseless but she has tried to explicate the supposed difference between the two.<ref name=":4">Nancey Murphy, "Reductionism and Emergence. A Critical Perspective." In ''Human Identity at the Intersection of Science, Technology and Religion''. Edited by Nancey Murphy, and Christopher C. Knight. Burlington, VT: Ashgate, 2010. P. 82.</ref><br />
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南希·墨菲(Nancey Murphy) 断言有两种本体论还原论: 一种声称整体不过是它们的部分;而另一种则是原子论还原论,认为整体不是“真实的真实(really real)”。她承认,“真实的真实(really real)”这个短语显然毫无意义,但她试图解释这两种还原论之间假定的差异<ref name=":4" />。<br />
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Ontological reductionism denies the idea of ontological [[emergence]], and claims that emergence is an [[Epistemology|epistemological]] phenomenon that only exists through analysis or description of a system, and does not exist fundamentally.<ref name=":5">[https://onlinelibrary.wiley.com/doi/abs/10.1111/1467-9213.00136 Michael Silberstein, John McGeever, "The Search for Ontological Emergence", ''The Philosophical Quarterly'', Vol. 49, No. 195 (April 1999)], ({{ISSN|0031-8094}}).</ref><br />
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本体论还原论否定了本体涌现的观点,认为涌现是一种仅仅通过对系统的分析或描述而存在的认识论现象,根本上是不存在的<ref name=":5" />。<br />
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Ontological reductionism takes two forms: '''token ontological reductionism''' and '''type ontological reductionism'''.{{Citation needed|date=July 2020}}<br />
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本体论还原论有两种形式: 表征本体论还原论和类型本体论还原论。<br />
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Token ontological reductionism is the idea that every item that exists is a sum item. For perceivable items, it affirms that every perceivable item is a sum of items with a lesser degree of complexity. Token ontological reduction of biological things to chemical things is generally accepted.<br />
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表征本体论还原论是认为存在的每一项都是一个和项。它确信每个可感知的事物是复杂程度较低的事物的总和。将生物事物还原为化学事物的表征本体论已被普遍接受。<br />
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Type ontological reductionism is the idea that every type of item is a sum type of item, and that every perceivable type of item is a sum of types of items with a lesser degree of complexity. Type ontological reduction of biological things to chemical things is often rejected.<ref name=":7">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|work=philosophybasics.com}}</ref><br />
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类型本体论还原论的观点是,每一种类型的事物都是事物的总和,每一种可感知的事物类型都是复杂程度较低的事物类型的和。将生物事物还原为化学事物的类型本体论已被普遍摒弃<ref name=":7" />。<br />
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[[Michael Ruse]] has criticized ontological reductionism as an improper argument against [[vitalism]].<ref>[http://icb.oxfordjournals.org/cgi/reprint/29/3/1061.pdf] Michael Ruse, "Do Organisms Exist?", Am. Zool., 29: 1061–1066 (1989)</ref><br />
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迈克尔·鲁斯([[Michael Ruse]])批评本体论还原论是对活力论的一种不恰当的论证。<br />
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=== 方法论还原论 ===<br />
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Methodological reductionism is the position that the best scientific strategy is to attempt to reduce explanations to the smallest possible entities.<ref name=":1">{{Cite book|last=Montague|first=Gerard P.|title=Who Am I? Who Is She?: A Naturalistic, Holistic, Somatic Approach to Personal Identity|publisher=Transaction Books|year=2012|isbn=978-3-86838-144-3|location=Piscataway, NJ|pages=308}}</ref> In a biological context, this means attempting to explain all biological phenomena in terms of their underlying biochemical and molecular processes.<ref name=":6">{{Cite encyclopedia |title=Reductionism in Biology |encyclopedia=Stanford Encyclopedia of Philosophy |publisher=Metaphysics Research Lab, Stanford University |url=https://plato.stanford.edu/archives/spr2017/entries/reduction-biology/ |last1=Brigandt |first1=Ingo |date=2017 |editor-last=Zalta |editor-first=Edward N. |last2=Love |first2=Alan |access-date=2019-04-28}}</ref> Claim of efficacy is demonstrated that the gene – unit of classical heredity – is the deoxyribonucleic acid (DNA), a macro-molecule.<ref name=":1" /><br />
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Statistical mechanics can be considered as a reconciliation of macroscopic thermodynamic laws with the reductionist method of explaining macroscopic properties in terms of microscopic components.<br />
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方法论还原论认为,最好的科学策略是试图将解释减少为最小的可能实体<ref name=":1" /> 。在生物学的背景下,这意味着从其潜在的生物化学和分子过程来解释所有生物现象<ref name=":6" />。有力的证明是,基因(经典遗传单位)实质上是一种大分子——脱氧核糖核酸(DNA)<ref name=":1" />。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
=== 理论还原论 ===<br />
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Theory reduction is the process by which a more general theory absorbs a special theory.<ref name=":0" /> For example, both [[Johannes Kepler|Kepler's]] laws of the motion of the [[planet]]s and [[Galileo Galilei|Galileo]]'s theories of motion formulated for terrestrial objects are reducible to Newtonian theories of mechanics because all the explanatory power of the former are contained within the latter. Furthermore, the reduction is considered beneficial because [[Newtonian mechanics]] is a more general theory—that is, it explains more events than Galileo's or Kepler's. Besides scientific theories, theory reduction more generally can be the process by which one explanation subsumes another.<br />
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理论还原是一个更一般的而理论吸收一个特殊的理论的过程。例如,开普勒的行星运动定律和伽利略的地球物体运动理论都可以还原为牛顿力学理论,因为前者的所有解释力都包含在后者之中。此外,这种还原被认为是有好处的,因为牛顿力学是一个更普遍的理论——也就是说,它比伽利略或开普勒的理论解释了更多的事件。除了科学理论之外,理论归纳通常是一种解释包含另一种解释的过程。<br />
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== 在科学中 ==<br />
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{{More citations needed section|date=August 2011}}<br />
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Reductionist thinking and methods form the basis for many of the well-developed topics of modern [[science]], including much of [[physics]], [[chemistry]] and [[molecular biology]]. [[Classical mechanics]] in particular is seen as a reductionist framework. For instance, we understand the solar system in terms of its components (the sun and the planets) and their interactions.<ref name=":8">{{Cite book|last=McCauley|first=Joseph L.|title=Dynamics of Markets: The New Financial Economics, Second Edition|publisher=Cambridge University Press|year=2009|isbn=978-0-521-42962-7|location=Cambridge|pages=241}}</ref> [[Statistical mechanics]] can be considered as a reconciliation of [[macroscopic]] [[thermodynamic laws]] with the reductionist method of explaining macroscopic properties in terms of [[microscopic]] components.<br />
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还原论的思想和方法构成了许多现代科学发展良好的主题的基础,包括许多物理、化学和分子生物学。经典力学尤其可以被看作是一种还原论的框架。例如,我们根据太阳系的组成部分(太阳和行星)及其相互作用来理解太阳系<ref name=":8" /> 。统计力学则可以被认为是宏观热力学定律与用微观组分解释宏观性质的还原方法的调和。<br />
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In science, reductionism implies that certain topics of study are based on areas that study smaller spatial scales or organizational units. While it is commonly accepted that the foundations of [[chemistry]] are based in [[physics]], and [[molecular biology]] is based on chemistry, similar statements become controversial when one considers less rigorously defined intellectual pursuits. For example, claims that [[sociology]] is based on [[psychology]], or that [[economics]] is based on [[sociology]] and [[psychology]] would be met with reservations. These claims are difficult to substantiate even though there are obvious associations between these topics (for instance, most would agree that [[psychology]] can affect and inform [[economics]]). The limit of reductionism's usefulness stems from [[Emergence#Emergent properties and processes|emergent properties]] of [[complex systems]], which are more common at certain levels of organization. For example, certain aspects of [[evolutionary psychology]] and [[sociobiology]] are rejected by some who claim that complex systems are inherently irreducible and that a [[holistic]] method is needed to understand them.<br />
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在科学中,还原论意味着某些研究主题是基于研究更小的空间尺度或组织单位的领域。虽然人们普遍认为化学的基础是基于物理,分子生物学是基于化学,但当一个人思考不那么严格定义的知识领域时,类似的陈述就会变得有争议。例如,人们对声称社会学是以心理学为基础,或者经济学是以社会学和心理学为基础的说法往往会持保留意见。尽管这些话题之间存在明显的联系(例如,大多数人会同意心理学可以影响并影响经济学),但这些说法很难得到证实。还原论效用的限制源于复杂系统的涌现特性,这种特性在组织的某些层次上更为常见。例如,一些人声称复杂的系统从本质上是不可简化的,需要一个整体的方法来理解它们,因而不同意进化心理学和社会生物学的某些观点。<br />
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Some strong reductionists believe that the behavioral sciences should become "genuine" scientific disciplines based on genetic biology, and on the systematic study of culture (see Richard Dawkins's concept of [[memes]]). In his book ''[[The Blind Watchmaker]]'', [[Richard Dawkins|Dawkins]] introduced the term "hierarchical reductionism"<ref name=":9">Interview with magazine ''[[Third Way (magazine)|Third Way]]'' in which [[Richard Dawkins]] discusses reductionism and religion, February 28, 1995</ref> to describe the opinion that complex systems can be described with a hierarchy of organizations, each of which is only described in terms of objects one level down in the hierarchy. He provides the example of a computer, which using hierarchical reductionism is explained in terms of the operation of [[hard drive]]s, processors, and memory, but not on the level of [[logic gates]], or on the even simpler level of electrons in a [[semiconductor]] medium.<br />
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一些强还原论者认为,行为科学应该成为基于遗传生物学和文化系统研究的“真正的”科学分支(参见理查德·道金斯(Richard Dawkins)的模因概念)。在他的《盲眼钟表匠》一书中,道金斯引入了“层次还原论<ref name=":9" /> ”来描述这样一种观点,即复杂系统可以用组织的层次来描述,而每一个组织的层次结构只能用层次结构的下一级对象来描述。他以计算机为例,从硬盘、处理器和内存的角度阐释了层次还原论,而不是基于逻辑门的层次,或者更简单的半导体介质中的电子层次。<br />
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Quantum Holonomy theory is a theory of the lowest possible reduction.<ref name=":10">{{cite web|url=https://youtube.com/watch?v=fSVbWwivu5g|website=youtube|title=Does reductionism End? Quantum Holonomy theory says YES|year=2021}}</ref><ref name=":11">{{cite arXiv|eprint=2008.09356|last1=Aastrup|first1=Johannes|last2=Grimstrup|first2=Jesper M.|title=The Metric Nature of Matter|year=2020|class=hep-th}}</ref><br />
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量子整体论是一种最低可能的还原理论<ref name=":10" /><ref name=":11" />。<br />
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Others argue that inappropriate use of reductionism limits our understanding of complex systems. In particular, ecologist [[Robert Ulanowicz]] says that science must develop techniques to study ways in which larger scales of organization influence smaller ones, and also ways in which feedback loops create structure at a given level, independently of details at a lower level of organization. He advocates (and uses) [[information theory]] as a framework to study [[Propensity probability|propensities]] in natural systems.<ref name=":12">R.E. Ulanowicz, ''Ecology: The Ascendant Perspective'', Columbia University Press (1997) ({{ISBN|0-231-10828-1}})</ref> Ulanowicz attributes these criticisms of reductionism to the philosopher [[Karl Popper]] and biologist [[Robert Rosen (theoretical biologist)|Robert Rosen]].<ref name=":13">{{cite journal | last1 = Ulanowicz | first1 = R.E. | year = 1996 | title = Ecosystem Development: Symmetry Arising? | url = http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | journal = Symmetry: Culture and Science | volume = 7 | issue = 3 | pages = 321–334 | url-status = dead | archive-url = https://web.archive.org/web/20130530212418/http://people.biology.ufl.edu/ulan/pubs/Symmetry.PDF | archive-date = 2013-05-30 }}</ref><br />
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其他人认为,不恰当使用还原论限制了我们对复杂系统的理解。特别是,生态学家罗伯特·尤兰维奇(Robert Ulanowicz)说,科学必须发展技术来研究大规模组织影响小规模组织的方式,以及反馈循环在给定层次上创造结构的方式,而不受较低层次的组织细节的影响。他提倡使用信息理论作为研究自然系统倾向的框架<ref name=":12" /> 。乌兰诺维茨(Ulanowicz)把这些还原论的批评归因于哲学家卡尔 · 波普尔( Karl Popper )和生物学家罗伯特 · 罗森(Robert Rosen)<ref name=":13" />。<br />
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[[Stuart Kauffman]] has argued that [[complex systems]] theory and phenomena such as [[emergence]] pose limits to reductionism.<ref name=":14">[http://www.edge.org/3rd_culture/kauffman06/kauffman06_index.html Beyond Reductionism: Reinventing the Sacred] by Stuart Kauffman</ref> Emergence is especially relevant when systems exhibit historicity.<ref name=":15">{{Cite book|last1=Longo|first1=Giuseppe|last2=Montévil|first2=Maël|last3=Kauffman|first3=Stuart|date=2012-01-01|title=No Entailing Laws, but Enablement in the Evolution of the Biosphere|url=https://www.academia.edu/11720588|journal=Proceedings of the 14th Annual Conference Companion on Genetic and Evolutionary Computation|series=GECCO '12|location=New York, NY, USA|publisher=ACM|pages=1379–1392|doi=10.1145/2330784.2330946|isbn=978-1-4503-1178-6|arxiv=1201.2069|citeseerx=10.1.1.701.3838|s2cid=15609415}}</ref> Emergence is strongly related to [[nonlinearity]].<ref name=":16">[http://personal.riverusers.com/~rover/RedRev.pdf A. Scott, ''Reductionism Revisited'', Journal of Consciousness Studies, 11, No. 2, 2004 pp. 51–68]</ref> The limits of the application of reductionism are claimed to be especially evident at levels of organization with greater [[complexity]], including living [[Cell (biology)|cells]],<ref name="Huber2013">{{cite journal |last1=Huber |first1=F |last2=Schnauss |first2=J |last3=Roenicke |first3=S |last4=Rauch |first4=P |last5=Mueller |first5=K |last6=Fuetterer |first6=C |last7=Kaes |first7=J |title=Emergent complexity of the cytoskeleton: from single filaments to tissue |journal=Advances in Physics |volume=62 |issue=1 |pages=1–112 |year=2013 |doi=10.1080/00018732.2013.771509|bibcode = 2013AdPhy..62....1H |pmid=24748680 |pmc=3985726}} [http://www.tandfonline.com/doi/full/10.1080/00018732.2013.771509 online]</ref> [[neural networks]], [[ecosystems]], [[society]], and other systems formed from assemblies of large numbers of diverse components linked by multiple [[feedback loop]]s.<ref name="Huber2013" /><ref name="Clayton2006">{{cite journal |editor1-last= Clayton |editor1-first= P |editor2-last= Davies |editor2-first= P |title=The Re-emergence of Emergence: The Emergentist Hypothesis from Science to Religion |publisher=Oxford University Press |location=New York |year=2006}}</ref><br />
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斯图尔特 · 考夫曼(Stuart Kauffman)认为复杂系统理论和涌现现象对还原论构成了限制<ref name=":14" />。当系统表现出历史性时,涌现尤为重要<ref name=":15" />。涌现与非线性密切相关<ref name=":16" />。还原论应用的局限性在更复杂的组织层次上尤其明显,包括活细胞<ref name="Huber2013" /> 、神经网络、生态系统、社会,以及由多个反馈回路连接的大量不同组成部分组成的其他系统<ref name="Huber2013" /><ref name="Clayton2006" />。<br />
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[[Nobel prize in physics|Nobel laureate]] [[Philip Warren Anderson]] used the idea that [[symmetry breaking]] is an example of an emergent phenomenon in his 1972 ''[[Science (journal)|Science]]'' paper "More is different" to make an argument about the limitations of reductionism.<ref name=":17">[http://www.sccs.swarthmore.edu/users/08/bblonder/phys120/docs/anderson.pdf Link] {{cite journal|last=Anderson|first=P.W.|title=More is Different|journal=Science|volume=177|issue=4047| pages=393–396|year=1972|doi=10.1126/science.177.4047.393|pmid=17796623|bibcode=1972Sci...177..393A|s2cid=34548824|url=https://semanticscholar.org/paper/8019560143abeb6145ed95aa04ad8ddf9898178d}}</ref> One observation he made was that the sciences can be arranged roughly in a linear hierarchy—[[particle physics]], [[solid state physics]], [[chemistry]], [[molecular biology]], [[cellular biology]], [[physiology]], [[psychology]], [[social sciences]]—in that the elementary entities of one science obeys the principles of the science that precedes it in the hierarchy; yet this does not imply that one science is just an applied version of the science that precedes it. He writes that "At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one. Psychology is not applied biology nor is biology applied chemistry."<br />
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诺贝尔经济学奖获得者菲利普·沃伦·安德森(Philip Warren Anderson)在他1972年发表在《科学》(Science)杂志的论文《More is different》中使用了对称性破缺是一个涌现现象的例子来论证还原论的局限性<ref name=":17" /> 。他观察到,科学可以大致按线性层次排列——粒子物理学、固体物理学、化学、分子生物学、细胞生物学、生理学、心理学、社会科学——一门科学的基本实体遵循在层次中先于它的科学原理的原则。然而,这并不意味着一门科学只是先于它的科学的应用版本。他写道: “在每一个阶段,全新的法则、概念和概括都是必要的,需要灵感和创造力,就像前一个阶段一样。心理学不是应用生物学,生物学也不是应用化学。”<br />
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Disciplines such as [[cybernetics]] and [[systems theory]] imply non-reductionism, sometimes to the extent of explaining phenomena at a given level of hierarchy in terms of phenomena at a higher level, in a sense, the opposite of reductionism.<ref name=":18">{{cite web|url=http://pespmc1.vub.ac.be/DOWNCAUS.html|title=Downward Causation|work=vub.ac.be}}</ref><br />
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诸如控制论和系统论这样的学科隐含着非还原论,有时达到了用更高层次的现象来解释特定层次上的现象的程度,在某种意义上,这是还原论的对立面<ref name=":18" />。<br />
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== 在数学中 ==<br />
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In [[mathematics]], reductionism can be interpreted as the philosophy that all mathematics can (or ought to) be based on a common foundation, which for modern mathematics is usually [[axiomatic set theory]]. [[Ernst Zermelo]] was one of the major advocates of such an opinion; he also developed much of axiomatic set theory. It has been argued that the generally accepted method of justifying mathematical [[axioms]] by their usefulness in common practice can potentially weaken Zermelo's reductionist claim.<ref name=":19">{{cite journal |doi=10.1305/ndjfl/1093633905 |first=R. Gregory |last=Taylor |title=Zermelo, Reductionism, and the Philosophy of Mathematics |journal=Notre Dame Journal of Formal Logic |volume=34 |issue=4 |year=1993 |pages=539–563 |doi-access=free }}</ref><br />
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在数学中,还原论可以解释为所有数学都可以或应该建立在一个共同基础上的哲学,而对于现代数学来说,这个基础通常是公理化集合论。策梅洛(Ernst Zermelo)是这种观点的主要倡导者之一,他也对公理化集合论做出了许多发展。有人认为,用数学公理在普通实践中的有用性来证明数学公理的普遍接受的方法,可能会削弱泽梅洛的还原论主张<ref name=":19" />。<br />
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Jouko Väänänen has argued for [[second-order logic]] as a foundation for mathematics instead of set theory,<ref name=":20">{{cite journal |first=J. |last=Väänänen |title=Second-Order Logic and Foundations of Mathematics |journal=Bulletin of Symbolic Logic |volume=7 |issue=4 |pages=504–520 |year=2001 |doi=10.2307/2687796 |jstor=2687796 |s2cid=7465054 }}</ref> whereas others have argued for [[category theory]] as a foundation for certain aspects of mathematics.<ref name=":21">{{cite journal |first=S. |last=Awodey |title=Structure in Mathematics and Logic: A Categorical Perspective |journal=Philos. Math. |series=Series III |volume=4 |issue=3 |year=1996 |pages=209–237 |doi=10.1093/philmat/4.3.209 }}</ref><ref name=":22">{{cite book |first=F. W. |last=Lawvere |chapter=The Category of Categories as a Foundation for Mathematics |title=Proceedings of the Conference on Categorical Algebra (La Jolla, Calif., 1965) |pages=1–20 |publisher=Springer-Verlag |location=New York |year=1966 }}</ref><br />
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Jouko Väänänen 认为二阶逻辑是数学的基础,而不是集合论<ref name=":20" /> ,而其他人则认为范畴论是数学某些方面的基础<ref name=":21" /><ref name=":22" />。<br />
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The [[Gödel's incompleteness theorems|incompleteness theorems]] of [[Kurt Gödel]], published in 1931, caused doubt about the attainability of an axiomatic foundation for all of mathematics. Any such foundation would have to include axioms powerful enough to describe the arithmetic of the natural numbers (a subset of all mathematics). Yet Gödel proved that, for any ''consistent'' recursively enumerable axiomatic system powerful enough to describe the arithmetic of the natural numbers, there are (model-theoretically) ''true'' propositions about the natural numbers that cannot be proved from the axioms. Such propositions are known as formally [[Undecidable problem|undecidable propositions]]. For example, the [[continuum hypothesis]] is undecidable in the [[Zermelo–Fraenkel set theory]] as shown by [[Forcing (mathematics)|Cohen]].<br />
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1931年发表的库尔特 · 哥德尔(Kurt Gödel)的不完备性定理,引起了对所有数学公理化基础的可达性的怀疑,任何这样的基础都必须包含足够强大的公理来描述所有自然数的算术(所有数学的子集)。然而,哥德尔证明了,对于足以描述自然数算数的任何一致的可递归枚举的公理系统,有关于自然数的真命题(模型-理论)是不能从公理中证明的。这样的命题称为形式上的不可判定的命题。例如,在科恩(Cohen)提出的 Zermelo-Fraenkel 集合论中,连续统假设是不可判定的。<br />
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=== 在计算机科学中 ===<br />
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The role of reduction in [[computer science]] can be thought as a precise and unambiguous mathematical formalization of the philosophical idea of "[[#Types|theory reductionism]]". In a general sense, a problem (or set) is said to be reducible to another problem (or set), if there is a computable/feasible method to translate the questions of the former into the latter, so that, if one knows how to computably/feasibly solve the latter problem, then one can computably/feasibly solve the former. Thus, the latter can only be at least as "[[NP-hardness|hard]]" to solve as the former.<br />
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还原在计算机科学中的作用可以看作是“理论还原论”哲学思想的精确和明确的数学形式化。一般意义上,如果有一个可计算/可行的方法将一个问题或集合转化为另一个问题或集合,那么那么这个问题或集合就是可约化的。如果一个人知道如何可计算/可行地解决后一个问题,那么他就可以可计算/可行地解决前者。因此,后者至少像前者一样“难”解决。<br />
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Reduction in [[theoretical computer science]] is pervasive in both: the mathematical abstract foundations of computation; and in real-world [[Analysis of algorithms|performance or capability analysis of algorithms]]. More specifically, reduction is a foundational and central concept, not only in the realm of mathematical logic and abstract computation in [[Computability theory|computability (or recursive) theory]], where it assumes the form of e.g. [[Turing reduction]], but also in the realm of real-world computation in time (or space) complexity analysis of algorithms, where it assumes the form of e.g. [[polynomial-time reduction]].<br />
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理论计算机科学的还原在两个方面都很普遍:计算的数学抽象基础;以及在现实世界中算法的性能或能力分析。更具体地说,还原是一个基础和核心的概念,不但出现在数学逻辑和可计算性(或递归)理论的抽象计算领域(在这些领域里它呈现出图灵还原的形式),而且出现在现实世界的计算领域,比如在时间(或空间)算法复杂性分析中,它呈现出多项式时间还原的形式。<br />
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== 在宗教中 ==<br />
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Religious reductionism generally attempts to explain religion by explaining it in terms of nonreligious causes. A few examples of reductionistic explanations for the presence of religion are: that religion can be reduced to humanity's conceptions of right and wrong, that religion is fundamentally a primitive attempt at controlling our environments, that religion is a way to explain the existence of a physical world, and that religion confers an enhanced survivability for members of a group and so is reinforced by [[natural selection]].<ref name=":25">{{cite web|url=http://evolution-of-religion.com/|title=Evolution-of-religion.com}}</ref> Anthropologists [[Edward Burnett Tylor]] and [[James George Frazer]] employed some [[Metatheories of religion in the social sciences#Edward Burnett Tylor and James George Frazer|religious reductionist arguments]].<ref name=":26">Strenski, Ivan. "Classic Twentieth-Century Theorist of the Study of Religion: Defending the Inner Sanctum of Religious Experience or Storming It." Pages 176–209 in ''Thinking About Religion: An Historical Introduction to Theories of Religion''. Malden: Blackwell, 2006.</ref><br />
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宗教还原论通常试图用非宗教的原因来解释宗教。关于宗教存在的还原论解释的几个例子是:宗教可以被还原为人类是或非的概念,从根本上说,宗教是控制环境的一种原始尝试,宗教是解释物质世界存在的一种方式,宗教赋予一个群体成员更强的生存能力,自然选择也加强了这种能力<ref name=":25" />。人类学家爱德华·伯内特·泰勒(Edward Burnett tyler)和詹姆斯·弗雷泽(James George fraser)就采用了一些宗教还原论的观点<ref name=":26" />。<br />
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== 在语言学中 ==<br />
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Linguistic reductionism is the idea that everything can be described or explained by a language with a limited number of concepts, and combinations of those concepts.<ref name=":27">{{cite web|url=http://www.philosophybasics.com/branch_reductionism.html|title=Reductionism – By Branch / Doctrine – The Basics of Philosophy|website=www.philosophybasics.com}}</ref> An example is the language [[Toki Pona]].<br />
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语言还原论的观点是,任何事物都可以只用有限数量的概念,以及这些概念的组合来描述或解释<ref name=":27" /> 。一个例子就是道本语。<br />
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== 在哲学中 == <br />
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The concept of [[downward causation]] poses an alternative to reductionism within philosophy. This opinion is developed by [[Peter Bøgh Andersen]], [[Claus Emmeche]], [[Niels Ole Finnemann]], and [[Peder Voetmann Christiansen]], among others. These philosophers explore ways in which one can talk about phenomena at a larger-scale level of organization exerting causal influence on a smaller-scale level, and find that some, but not all proposed types of downward causation are compatible with science. In particular, they find that constraint is one way in which downward causation can operate.<ref name=":28">P.B. Andersen, C. Emmeche, N.O. Finnemann, P.V. Christiansen, ''Downward Causation: Minds, Bodies and Matter'', Aarhus University Press ({{ISBN|87-7288-814-8}}) (2001)</ref> The notion of causality as constraint has also been explored as a way to shed light on scientific concepts such as [[self-organization]], [[natural selection]], [[adaptation]], and control.<ref name=":29">{{cite web|url=http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |first1=A |last1=Juarrero |title=Causality as Constraint |url-status=dead |archive-url=https://web.archive.org/web/20110612013407/http://pespmc1.vub.ac.be/Einmag_Abstr/AJuarrero.html |archive-date=June 12, 2011 }}</ref><br />
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在哲学中,向下因果关系的概念提供了一种还原论的替代方法。这个观点是由彼得·博格·安徒生([[Peter Bøgh Andersen]]),克劳斯([[Claus Emmeche]]),尼尔斯·奥立(Niels Ole Finnemann),和 彼得·克里斯蒂安森(Peder Voetmann Christiansen )等人提出的。这些哲学家探索人们可以在更大范围的组织层面上谈论的现象,在更小范围的组织层面上施加因果影响的方式,并发现一些(但不是所有)向下的因果类型与科学是相容的<ref name=":28" /> 。特别地,他们发现约束是向下因果关系的一种运作方式。因果关系作为约束的概念也作为一种阐明科学概念的方式,例如自组织、自然选择、适应和控制<ref name=":29" />。<br />
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=== 自由意志 ===<br />
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{{Main|Free will}}<br />
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Philosophers of the [[Age of Enlightenment|Enlightenment]] worked to insulate human free will from reductionism. [[Descartes]] separated the material world of mechanical necessity from the world of mental free will. German philosophers introduced the concept of the "[[Noumenon|noumenal]]" realm that is not governed by the deterministic laws of "[[Phenomena (philosophy)|phenomenal]]" nature, where every event is completely determined by chains of causality.<ref name=":30">Paul Guyer, "18th Century German Aesthetics," [http://plato.stanford.edu/entries/aesthetics-18th-german/ ''Stanford Encyclopedia of Philosophy'']</ref> The most influential formulation was by [[Immanuel Kant]], who distinguished between the causal deterministic framework the mind imposes on the world—the phenomenal realm—and the world as it exists for itself, the noumenal realm, which, as he believed, included free will. To insulate theology from reductionism, 19th century post-Enlightenment German theologians, especially [[Friedrich Schleiermacher]] and [[Albrecht Ritschl]], used the [[Romanticism|Romantic]] method of basing religion on the human spirit, so that it is a person's feeling or sensibility about spiritual matters that comprises religion.<ref name=":31">Philip Clayton and Zachary Simpson, eds. ''The Oxford Handbook of Religion and Science'' (2006) p. 161</ref><br />
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启蒙运动时期的哲学家致力于将人类的自由意志与还原论分割开来。笛卡尔将机械必然性的物质世界与精神自由意志的世界分开。德国哲学家引入了“本体”领域的概念,这一领域不受“现象”自然的决定论法则的控制,在“现象”自然中,每一个事件都完全由一系列因果关系所决定<ref name=":30" /> 。最有影响力的是伊曼努尔·康德(Immanuel Kant),他区分了思维强加于世界(现象界)的因果决定论框架和它自己存在的世界(本体界),他认为本体界包括自由意志。为了将神学与还原论相互剥离开来,19世纪后启蒙时代的德国神学家们,特别是施莱马赫(Friedrich Schleiermacher)和阿尔布雷希特·里施(Albrecht Ritschl)采用了浪漫主义的方法,将宗教建立在人类精神的基础上——一个人对精神事物的感觉或情感形成了宗教<ref name=":31" />。<br />
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=== 因果关系 ===<br />
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Most common philosophical understandings of [[Causality|causation]] involve reducing it to some collection of non-causal facts. Opponents of these reductionist views have given arguments that the non-causal facts in question are insufficient to determine the causal facts.<ref name="Carroll">{{cite book |title=The Oxford Handbook of Causation |chapter-url=https://books.google.com/books?id=xGnZtUtG-nIC&pg=PA292 |page=292 |author=John W Carroll |chapter=Chapter 13: Anti-reductionism |isbn=978-0-19-927973-9 |publisher=Oxford Handbooks Online |year=2009 |editor1=Helen Beebee |editor2=Christopher Hitchcock |editor3=Peter Menzies }}</ref><br />
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大多数关于因果关系的哲学理解都将因果关系还原为一些非因果事实的集合。对这些还原论观点持反对意见的人认为,所讨论的非因果事实不足以确定因果事实<ref name="Carroll" />。<br />
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== 批评 ==<br />
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=== 反还原论主义 ===<br />
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{{Main|Antireductionism}}<br />
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A contrast to reductionism is [[holism]] or [[emergentism]]. Holism is the idea that, in the whole, items can have properties, known as ''emergent properties'', that are not explainable from the sum of their parts. The principle of holism was summarized concisely by [[Aristotle]] in the [[Metaphysics (Aristotle)|Metaphysics]]: "The whole is more than the sum of its parts".<br />
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与还原论相对的是整体论或涌现论。整体论认为,事物从整体上看具有的一些属性——即所谓的涌现属性,这些属性不能用各个部分的和来解释。亚里士多德在《形而上学》一书中对整体主义的原则进行了简明的概括: “整体大于部分之和”。<br />
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=== 碎片主义 ===<br />
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An alternative term for ontological reductionism is ''fragmentalism'',<ref>{{cite journal|author=Kukla A|title=Antirealist Explanations of the Success of Science|journal=Philosophy of Science|volume=63|issue=1|pages=S298–S305|year=1996|doi=10.1086/289964|jstor=188539|s2cid=171074337}}</ref> often used in a [[pejorative]] sense.<ref>{{cite journal|author=Pope ML|title=Personal construction of formal knowledge|journal=Interchange|volume=13|issue=4|pages=3–14|year=1982|doi=10.1007/BF01191417|s2cid=198195182}}</ref> [[Anti-realism|Anti-realists]] use the term ''fragmentalism'' in arguments that the world does not exist of separable [[Non-physical entity|entities]], instead consisting of wholes. For example, advocates of this idea claim that:<br />
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本体论还原论的另一个术语是碎片主义,通常带有贬义色彩。反现实主义者使用碎片主义这个术语来论证世界不是由可分离的实体存在的,而是由整体组成的。例如,这种观点的支持者声称:<br />
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The linear deterministic approach to nature and technology promoted a fragmented perception of reality, and a loss of the ability to foresee, to adequately evaluate, in all their complexity, global crises in ecology, civilization and education.<ref>{{cite web|url=http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|title=Global education as a trend reflecting the problems of today and meeting the requirements of tomorrow|website=Indiana University Bloomington|archive-url=https://web.archive.org/web/19991003182135/http://www.indiana.edu/~isre/NEWSLETTER/vol6no2/global.htm|archive-date=3 October 1999|author=Anatoly P. Liferov}}</ref><br />
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对自然和技术的线性决定论方法促进了对现实的碎片化感知,并使人们丧失了预见和充分评估全球生态、文明和教育危机复杂性的能力。<br />
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The term ''fragmentalism'' is usually applied to reductionist modes of thought, often with the related pejorative term ''[[scientism]]''. This usage is popular among some ecological activists: <br />
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“碎片主义”一词通常用来指还原主义的思维模式,通常与贬义的“科学主义”相关。这种用法在一些生态活动家中很流行: <blockquote>There is a need now to move away from [[scientism]] and the ideology of cause-and-effect determinism toward a radical [[empiricism]], such as [[William James]] proposed, as an [[epistemology]] of science.<ref name=":32">{{cite web|url=http://bioregionalanimism.blogspot.com/|title=Redirecting|website=bioregionalanimism.blogspot.com}}</ref><br />
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现在有必要摆脱科学主义和因果决定论的思想,转向彻底的经验主义,如威廉·詹姆斯([[William James]] )提出的科学认识论<ref name=":32" />。</blockquote> These perspectives are not new; during the early 20th century, [[William James]] noted that rationalist science emphasized what he called fragmentation and disconnection.<ref name=Lumpkin /><br />
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这些观点并不新鲜; 在20世纪早期,威廉 · 詹姆斯注意到理性主义科学强调他所谓的分裂和脱节<ref name="Lumpkin" />。<br />
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Such opinions also motivate many criticisms of the scientific method:<br />
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这些观点也引发了对科学方法的许多批评:<br />
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<blockquote>The scientific method only acknowledges monophasic consciousness. The method is a specialized system that emphasizes studying small and distinctive parts in isolation, which results in fragmented knowledge.<ref name="Lumpkin">[http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006]</ref><br />
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科学方法只承认单相意识(monophasic consciousness)。这种方法强调孤立地研究小而独特的部分特定系统,从而导致知识的碎片化<ref name="Lumpkin" />。</blockquote><br />
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== 替代方案 ==<br />
The development of [[systems thinking]] has provided methods that seek to describe issues in a [[holism|holistic]] rather than a reductionist way, and many scientists use a [[Holism in science|holistic paradigm]].<ref name=":33">[[Dossey, Larry]]. ''Reinventing Medicine: Beyond Mind-Body to a New Era of Healing.'' ({{ISBN|0-06-251622-1}}) HarperSanFrancisco. (1999)</ref> When the terms are used in a scientific context, holism and reductionism refer primarily to what sorts of [[scientific model|models]] or theories offer valid explanations of the natural world; the scientific method of falsifying hypotheses, checking empirical data against theory, is largely unchanged, but the method guides which theories are considered.<br />
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系统思维的发展提供了寻求以整体而非简化的方式来描述问题的方法,并且许多科学家开始使用整体范式<ref name=":33" />。在科学语境中使用这些术语时,整体论和还原论主要指的是什么样的模型或理论提供了对自然世界的有效解释。证伪假设、根据理论检验经验数据的科学方法在大体上是不变的,但这些方法指导哪些理论是值得考虑的。<br />
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In many cases (such as the [[kinetic theory of gases]]), given a good understanding of the components of the system, one can predict all the important properties of the system as a whole. In other systems, especially concerned with life and life's emergent properties ([[morphogenesis]], [[autopoiesis]], and [[metabolism]]), [[emergent properties]] of the system are said to be almost impossible to predict from knowledge of the parts of the system. [[Complex systems|Complexity theory]] studies systems and properties of the latter type.<br />
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在许多情况下(例如气体动力学理论) ,只要对系统的组成部分有很好的了解,就可以预测系统作为一个整体的所有重要性质。在其他系统中,特别是与生命或与有关生命的涌现特性(形态发生、自生成和新陈代谢) ,从系统各部分的知识来预测系统的涌现特性被认为几乎是不可能的。复杂性理论研究系统和后一种类型的性质。<br />
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[[Alfred North Whitehead]]'s metaphysics opposed reductionism. He refers to this as the "fallacy of the misplaced concreteness". His scheme was to frame a rational, general understanding of phenomena, derived from our reality.<br />
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阿尔弗雷德·诺思·怀特黑德([[Alfred North Whitehead]])的形而上学反对还原论。他将此称为“错位的具体性谬误”。他的计划是从我们的现实出发,对现象建立一种理性的、普遍的理解。<br />
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[[Ecologist]] [[Sven Erik Jorgensen]] makes both theoretical and practical arguments for a [[holistic]] method in certain topics of science, especially [[ecology]]. He argues that many systems are so complex that they can ever be described in complete detail. In analogy to the Heisenberg [[uncertainty principle]] in physics, he argues that many interesting ecological phenomena cannot be replicated in laboratory conditions, and so cannot be measured or observed without changing the system in some way. He also indicates the importance of inter-connectedness in biological systems. He believes that science can only progress by outlining questions that are unanswerable and by using models that do not try to explain everything in terms of smaller hierarchical levels of organization, but instead model them on the scale of the system itself, taking into account some (but not all) factors from levels higher and lower in the hierarchy.<ref name=":34">S. E. Jørgensen, ''Integration of Ecosystem Theories: A Pattern'', 3rd ed. Kluwer Academic Publishers, ({{ISBN|1-4020-0651-9}}) (2002) Chapters 1 & 2.</ref><br />
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生态学家斯文 · 埃里克 · 乔根森([[Sven Erik Jorgensen]] )在某些科学领域,特别是生态学领域,为整体方法提供了理论和实践两方面的论据。他认为,许多系统是如此复杂,以至于永远无法完全详细地描述它们。与物理学中的海森堡不确定性原理类似,他认为许多有趣的生态现象无法在实验室条件下复制,因此如果不以某种方式改变系统,就无法测量或观察。他还指出了生物系统中相互联系的重要性。他认为,科学只能通过概述无法回答的问题,并使用模型来进步,并且这些模型不是试图从较小的组织层次来解释一切,而是根据系统本身的规模来模拟它们,同时考虑到来自层次结构中更高和更低层次的一些(但不是全部)因素<ref name=":34" />。<br />
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In [[cognitive psychology]], [[George Kelly (psychologist)|George Kelly]] developed "constructive alternativism" as a form of [[personal construct psychology]] and an alternative to what he considered "accumulative fragmentalism". For this theory, knowledge is seen as the construction of successful [[mental model]]s of the exterior world, rather than the accumulation of independent "nuggets of truth".<ref name=":35">{{cite journal|vauthors=Pope ML, Watts M |title=Constructivist Goggles: Implications for Process in Teaching and Learning Physics|journal=Eur. J. Phys.|volume=9|pages=101–109|year=1988|doi=10.1088/0143-0807/9/2/004|issue=2|bibcode = 1988EJPh....9..101P }}</ref><br />
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在认知心理学领域,乔治 · 凯利(George Kelly)发展了“构建替代主义”作为个人建构心理学的一种形式,也是他所认为的“累积碎片主义”的替代。在这一理论中,知识被看作是外部世界的成功的心理模型的构建,而不是独立的“真理金块”的累积<ref name=":35" />。<br />
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{{Reflist|refs=<br />
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{通货再膨胀 | 参考文献 = <br />
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== See also ==<br />
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{{Portal|Philosophy|Psychology}}<br />
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{{div col|colwidth=30em}}<br />
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* [[Antireductionism]]<br />
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* [[Antiscience]]<br />
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* [[Aristotle]]<br />
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* [[Eliminativism]]<br />
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* [[Emergentism]]<br />
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* [[Fallacy of composition]]<br />
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* [[Further facts]]<br />
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}}<br />
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}}<br />
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* [[Holism]]<br />
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* [[Holistic science]]<br />
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* [[Materialism]]<br />
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* [[Multiple realizability]] was used as a source of arguments against reductionism.<br />
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* [[Philosophy of mind]]<br />
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* [[Physicalism]]<br />
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* [[Physical ontology]]<br />
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* [[Scientism]]<br />
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* [[Symmetry breaking]]<br />
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* [[Theology]]<br />
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* ''[[Two Dogmas of Empiricism]]''<br />
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== 参考文献 ==<br />
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{{Reflist|refs=<br />
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<ref name=GodfreySmith>{{cite book |title=Philosophy of Biology |author=Peter Godfrey-Smith |isbn= 978-1-4008-5044-0 |year=2013 |publisher=Princeton University Press |url=https://books.google.com/books?id=hfvsAQAAQBAJ&pg=PA16 |page=16}}</ref><br />
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<ref name=Jones>{{cite book |title=Reductionism: Analysis and the Fullness of Reality |author= Richard H. Jones |chapter=Clarification of terminology |publisher=Bucknell University Press |year=2000 |isbn= 978-0-8387-5439-9 |chapter-url=https://books.google.com/books?id=sUgnio874NUC&q=%22+has+some+properties+that+other+levels+do+not+share%22&pg=PA19 |at=Pages 19–, with focus on 27–28, 32}}</ref><br />
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<ref name=MerriamWebster>{{cite book |title=Merriam-Webster's Encyclopedia of World Religions |chapter=Reductionism |chapter-url=https://books.google.com/books?id=ZP_f9icf2roC&q=reductionism+%22simpler+or+more+basic%22&pg=PA911 |isbn=978-0-87779-044-0 |year=1999 |editor=Wendy Doniger |publisher=Merriam-Webster |page=[https://archive.org/details/isbn_9780877790440/page/911 911] |url=https://archive.org/details/isbn_9780877790440/page/911 }}</ref><br />
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<ref name=Nagel>{{cite book |title=Mind and Cosmos: Why the Materialist Neo-Darwinian Conception of Nature is Almost Certainly False |author=Thomas Nagel |year=2012 |publisher=Oxford University Press |isbn=978-0-19-991975-8 |pages=4–5 |url=https://books.google.com/books?id=sFRpAgAAQBAJ&q=%22psychophysical+reductionism,+a+position+in+the+philosophy+of+mind%22&pg=PA4}}</ref><br />
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<ref name=Ney>{{cite encyclopedia |encyclopedia=Internet Encyclopedia of Philosophy |author=Alyssa Ney |title=Reductionism |url=http://www.iep.utm.edu/red-ism/ |access-date=March 13, 2015 |publisher=IEP, University of Tennessee}}</ref><br />
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}}<br />
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== 延伸阅读 ==<br />
<br />
* Churchland, Patricia (1986), ''[https://books.google.com/books?id=hAeFMFW3rDUC&printsec=frontcover#v=onepage&q=reductionism&f=false Neurophilosophy: Toward a Unified Science of the Mind-Brain]''. MIT Press.<br />
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* Dawkins, Richard (1976), ''[[The Selfish Gene]]''. Oxford University Press; 2nd edition, December 1989.<br />
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* Dennett, Daniel C. (1995) ''Darwin's Dangerous Idea''. Simon & Schuster.<br />
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* Descartes (1637), ''Discourses'', Part V.<br />
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* Dupre, John (1993), ''[https://books.google.com/books?id=Ev3HvgSjb1EC&printsec=frontcover#v=onepage&q=reductionism&f=false The Disorder of Things]''. Harvard University Press.<br />
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* Galison, Peter and David J. Stump, eds. (1996), ''The Disunity of the Sciences: Boundaries, Contexts, and Power''. Stanford University Press.<br />
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* Jones, Richard H. (2013), ''Analysis & the Fullness of Reality: An Introduction to Reductionism & Emergence''. Jackson Square Books.<br />
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* Laughlin, Robert (2005), ''A Different Universe: Reinventing Physics from the Bottom Down.'' Basic Books.<br />
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* Nagel, Ernest (1961), ''The Structure of Science''. New York.<br />
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* [[Pinker, Steven]] (2002), ''The Blank Slate: The Modern Denial of Human Nature''. Viking Penguin.<br />
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* Ruse, Michael (1988), ''Philosophy of Biology''. Albany, NY.<br />
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* [[Rosenberg, Alexander]] (2006), ''Darwinian Reductionism or How to Stop Worrying and Love Molecular Biology''. University of Chicago Press.<br />
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Category:Metatheory of science<br />
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范畴: 科学元理论<br />
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* Eric Scerri The reduction of chemistry to physics has become a central aspect of the philosophy of chemistry. See several articles by this author.<br />
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Category:Metaphysical theories<br />
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范畴: 形而上学理论<br />
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* [[Weinberg, Steven]] (1992), ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature'', Pantheon Books.<br />
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Category:Sociological theories<br />
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范畴: 社会学理论<br />
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* [[Weinberg, Steven]] (2002) describes what he terms the culture war among physicists in his review of ''[[A New Kind of Science (book)|A New Kind of Science]]''.<br />
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Category:Analytic philosophy<br />
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类别: 分析哲学<br />
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* [[Fritjof Capra|Capra, Fritjof]] (1982), ''The Turning Point''.<br />
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Category:Epistemology of science<br />
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范畴: 科学认识论<br />
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* Lopez, F., Il pensiero olistico di Ippocrate. Riduzionismo, antiriduzionismo, scienza della complessità nel trattato sull'Antica Medicina, vol. IIA, Ed. Pubblisfera, Cosenza Italy 2008.<br />
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Category:Cognition<br />
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类别: 认知<br />
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* Maureen L Pope, ''Personal construction of formal knowledge,'' Humanities Social Science and Law, 13.4, December, 1982, pp.&nbsp;3–14<br />
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Category:Epistemological theories<br />
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范畴: 认识论理论<br />
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* Tara W. Lumpkin, ''Perceptual Diversity: Is Polyphasic Consciousness Necessary for Global Survival?'' December 28, 2006, http://www.bioregionalanimism.com/2006/12/is-polyphasic-consciousness-necessary.html<br />
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本中文词条由[[用户:潮升阶|潮升阶]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%AD%A3%E5%8F%8D%E9%A6%88&diff=29644正反馈2022-03-26T10:43:14Z<p>唐糖糖:/* 开关 */</p>
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<div>{{#seo:<br />
|keywords=positive feedback,正反馈,反馈,加剧反馈,自我强化反馈<br />
|description=在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。正反馈的一个重要特点是小扰动变大,当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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[[File:Herdwick Stampede.jpg|thumb|right|【图1:有时,警报或恐慌会通过正反馈在一群动物之间传播,从而引起踩踏事件。】.|链接=Special:FilePath/Herdwick_Stampede.jpg]]<br />
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[[File:Stampede loop.png|thumb|【图2:Causal loop diagram that depicts the causes of a stampede as a positive feedback loop. 在因果环路图中,踩踏事件的发生是一个正反馈循环。】|链接=Special:FilePath/Stampede_loop.png]]<br />
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[[File:Birmingham Northern Rock bank run 2007.jpg|thumb|right|300px|【图3: 在社会学中,网络效应可以迅速产生银行挤兑的正反馈效应。上图是2007年英国北岩银行挤兑事件的照片。】|链接=Special:FilePath/Birmingham_Northern_Rock_bank_run_2007.jpg]]<br />
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==回顾==<br />
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'''正反馈'''(加剧反馈,自我强化反馈) 是一种在反馈循环中加剧微小扰动影响的过程。也就是说,一个扰动对系统的影响包括它自身扰动幅度的增大。或者说,A会产生更多的B,而B又会产生更多的A,与之相反的是,[[负反馈]]指的是一个系统中,变化的结果会减少或抵消它自己的影响。<ref name="theorymodelling" />这两个概念在科学和工程等领域中发挥着重要作用,包括生物学、化学和控制论。<br />
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在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。<ref name="zuckerman" /><ref>Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". ''Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems''. Academic Press. p. 55. ISBN <bdi>9780127784557</bdi>. Archived from the original on 2017-01-03. <q>A positive feedback loop is one with an even number of negative influences [around the loop].</q></ref><ref name="zuckerman" /> 从结果到始发过程的反馈可以是直接的,也可以通过其他状态变量<ref name="theorymodelling" />。这样的系统可以给出丰富的定性行为,但反馈的瞬时信号是正向还是负向,对结果有极其重要的影响。<ref name="theorymodelling" /> 正反馈强化原过程,而负反馈调节原过程。在这个含义下,''正''和''负''指的是大于或小于零的循环收益,并不代表着最终结果或效果的正负性。<ref name=":0">{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>因此,正反馈的一个重要特点是小扰动变大。当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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===基础===<br />
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[[File:Ideal feedback model.svg|thumb|【图4:A basic feedback system can be represented by this block diagram. In the diagram the + symbol is an adder and A and B are arbitrary causal functions. 一个基本的反馈系统可以用这个框图来表示。在图中,+号是加法器,A和B是任意因果函数。】|链接=Special:FilePath/Ideal_feedback_model.svg]]<br />
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图中显示了一个简单的反馈回路。 如果环增益AB为正值,则存在'正'或'再生'反馈的条件。<br />
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如果函数A和B是线性的,且AB小于1,那么系统从输入到输出的整体增益是有限的,但当AB接近1时,系统的增益可以非常大。<ref name="smith"> Electronics circuits and devices second edition. Ralph J. Smith</ref> 在这种情况下,可以表明从输入到输出的整体或 "闭环 "增益为:<br />
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:<math>G_c = A/(1-AB)</math><br />
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当AB>1时,系统是不稳定的,因此不具有明确的增益;增益可称为无限。<br />
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所以系统状态的变化根据反馈可以是收敛的,也可以是发散的。 而正反馈的结果是增强变化,因此小的扰动就可能导致大的变化。<br />
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对于一个当前处于平衡状态的系统,如果其状态的任何变化都发生了正反馈,从而造成了状态的不稳定,那么这个系统就是一个不稳定平衡的系统。使这种系统远离其平衡状态的力的大小是状态与平衡状态之间的距离的递增函数。<br />
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正反馈并不一定意味着平衡的不稳定性,例如,在正反馈结构中可能存在稳定的开关状态<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>。<br />
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=== 迟滞 ===<br />
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[[File:Hysteresis sharp curve.svg|thumb|【图5 Hysteresis causes the output value to depend on the history of the input 迟滞现象会导致输出值取决于输入的历史记录。】|链接=Special:FilePath/Hysteresis_sharp_curve.svg]]<br />
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[[File:Op-Amp Schmitt Trigger.svg|thumb|【图6 In a Schmitt trigger circuit, feedback to the non-inverting input of an amplifier pushes the output directly away from the applied voltage towards the maximum or minimum voltage the amplifier can generate. 在施密特触发器电路中,利用放大器的非反相输入端口产生的反馈,可以直接将电路的输出从原本的外加电压值推向到放大器所能产生的极值电压。】|链接=Special:FilePath/Op-Amp_Schmitt_Trigger.svg]]<br />
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在现实世界中,正反馈循环通常不会引起不断增长,而是通过某种限制效应来改变。根据Donella Meadows的说法:<br />
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正反馈回路是系统增长、爆炸、腐蚀和崩溃的根源。一个系统如果有一个不受控制的正反馈,最终将会自我毁灭。这就是为什么正反馈如此稀少的原因。通常情况下,负反馈迟早会发生。<ref>Donella Meadows, ''[http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf Leverage Points: Places to Intervene in a System]''2013-10-08 at the Wayback Machine, 1999</ref><br />
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[[迟滞]],即起点影响系统的终点的现象,可以通过正反馈产生。当反馈循环的增益高于1时,那么输出就会远离输入:如果大于输入,则向最近的正极限移动,而如果小于输入,则向最近的负极限移动。<br />
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一旦达到极限,它就会稳定下来。但是,如果输入超过极限,那么反馈将改变符号,输出将向相反的方向移动,直到达到相反的极限。因此,该系统表现出'''双稳态行为bistable behavior'''。<br />
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== 术语由来==<br />
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正反馈和负反馈这两个名词最早应用于反馈是在二战前。正反馈的概念随着再生电路的问世,在20世纪20年代已经出现。<br />
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Friis 和 Jensen在1924年描述了一种在电子放大器中发生的"回馈 "是正的情况,这一情况与他们顺便提到的负回馈作用相反。到了1934年,Harold Stephen Black在他的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法:<br />
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正反馈会增加放大器的增益,负反馈会降低增益<br />
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据Mindell(2002年)说,术语上的混乱是在这之后不久产生的:<br />
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“ ... ... Friis 和 Jensen 对 Black 在对"正反馈 "和 "负反馈 "的区分方法是一样的,都不是基于反馈本身的符号,而是基于它对放大器增益的影响。与之相反的是,当Nyquist和Bode基于Black的工作基础时,将负反馈称为符号相反的反馈。Black难以说服其他人相信他的发明的实用性,有一部分原因是在基本的定义问题上存在混乱。"<br />
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==实例与应用==<br />
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=== 电子电路===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|【图7 A vintage style regenerative radio receiver. Due to the controlled use of positive feedback, sufficient amplification can be derived from a single [[vacuum tube]] or valve (centre). 一个老式的再生无线电接收器。由于使用正反馈的控制,真空管或阀门(中心)就可以产生足够的放大效果。】|链接=Special:FilePath/Regenerartive_Receiver-S7300056.JPG]]<br />
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'''再生电路Regenerative circuit'''于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>,用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈,可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此,一个信号可以在一个阶段被放大20000甚至100000倍,而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定,开始振荡。无线电操作员必须不断地调整反馈量,以获得良好的接收效果。而现代无线电接收机采用超异构设计,多了许多放大级,去掉了正反馈并使其工作更稳定。<br />
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在再生无线电电路中产生的振荡还可以被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英),经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计,包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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许多电子电路,特别是放大器,都采用了负反馈。这降低了放大器的信号增益,但改善了它的线性度、输入阻抗、输出阻抗和带宽,并稳定了包括闭环增益等参数。同时,这些参数也变得不那么依赖于放大器件本身的细节,而更多地依赖于反馈元件,因为反馈元件一般不随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位:如果信号反馈失相,则反馈为负,如果相位一致,则反馈为正。对于需要使用负反馈放大器的设计者来说,引入负反馈放大器的问题是,电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°,那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波来做到这一点)。如果任何频率下的环增益(放大器增益与正反馈程度的乘积)大于1,那么放大器将在该频率下发生振荡(巴克豪森稳定性准则)。这种振荡有时被称为寄生振荡:在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化,前板(用户界面)的变化,甚至是由于人或其他导电物品的接近。<br />
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放大器可能会以示波器很难检测到的方式轻轻振荡,有时的振荡也可能非常大,只有非常扭曲或根本没有真正的信号,甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似,因此低频寄生振荡也被称为 "汽艇"。<br />
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【图8 The effect of using a Schmitt trigger (B) instead of a comparator (A) 使用施密特触发器(b)代替比较器(a)的效果】<br />
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许多常见的数字电路都采用正反馈。一般简单的布尔逻辑门通常只是依靠增益将数字信号电压从中间值推到代表布尔值0和1的值上,但许多更复杂的门都采用了反馈。当输入的模拟电压发生变化,但后期数字处理需要尖锐阈值时,施密特触发电路通过正反馈机制确保当输入电压轻微超过阈值时,输出电压可以巧妙而迅速地从一个逻辑状态转移到另一个逻辑状态。施密特触发器使用正反馈的一个必然结果是,如果输入电压再次缓慢下降,超过了相同的阈值,由于正反馈的机制,输出电压将保持在相同的逻辑状态而不改变。这种效应被称为滞后: 输入电压必须降到一个不同的、较低的阈值,才能“解锁”输出,并将其重置为原始数字。通过减小正反馈的程度,可以减小滞后宽度,但宽度不能被完全消除。施密特触发器在某种程度上是一个闭锁电路。<br />
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【图9 Positive feedback is a mechanism by which an output is enhanced, such as protein levels. However, in order to avoid any fluctuation in the protein level, the mechanism is inhibited stochastically (I), therefore when the concentration of the activated protein (A) is past the threshold ([I]), the loop mechanism is activated and the concentration of A increases exponentially if d[A]=k [A] 正反馈是一种增强输出的机制,如蛋白质水平。但为了避免蛋白质水平的波动,该机制是随机抑制的(I),因此只有当激活的蛋白质(A)浓度超过阈值([I])时,循环机制被激活,如果d[A]=k[A],A的浓度就会成倍增加。】<br />
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【图10 Illustration of an R-S ('reset-set') flip-flop made from two digital nor gates with positive feedback. Red and black mean logical '1' and '0', respectively. R-S("复位-设置")触发器的说明,由两个带正反馈的数字诺尔门组成。红色和黑色分别表示逻辑上的 "1 "和 "0"。】<br />
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电子触发器,或“锁存器” ,或“双稳态多谐振荡器” ,是一种由于高正反馈而不稳定于平衡或中间状态的电路。这样的双稳态电路是一位电子存储器的基础。 触发器使用一对放大器、晶体管或逻辑门相互连接,正反馈机制使得输入信号被去除后,电路可以维持在两种非平衡稳定状态中的一种,直到一个合适的替代信号重新作为输入,以改变电路状态。计算机随机存取存储器(RAM)可以用这种方式运作,每位存储器有一个锁存电路。<br />
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电子系统中发生'''热失控Thermal runaway'''的原因是,当电路的某些方面变得更热时,它被允许通过更多的电流,然后它越热,通过的电流就越多,这就使它更热一些,因此它又通过更多的电流。这种现象对有关器件来说通常是灾难性的。如果器件不得不在接近其最大功率处理能力的情况下工作,那么某些条件下就可能出现热失控,这通常可以通过精心设计来改进。<br />
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[[File:Technics SL-1210MK2.jpg|thumb|left|【图11 A phonograph turntable is prone to acoustic feedback. 留声机转盘容易受到声反馈的影响。】|链接=Special:FilePath/Technics_SL-1210MK2.jpg]]<br />
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音频和视频系统可以表现出正反馈。如果麦克风录入了同一电路中扬声器的放大声音输出,那么就会听到音频反馈的嚎叫和尖叫声(在放大器的最大功率容量下),因为随机噪声被音频系统和房间的特性所过滤后,通过正反馈重新放大。<br />
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===音频与现场音频===<br />
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音频反馈(也称为声反馈,简称反馈,或拉森效应)是一种特殊的正反馈,当音频输入(例如,麦克风或吉他拾音器)和音频输出(例如,大声放大的扬声器)之间存在声音回路时,就会出现这种反馈。在这个例子中,麦克风接收到的信号被放大并从扬声器传出。然后,来自扬声器的声音可以再次被麦克风接收,进一步放大,然后再次通过扬声器传递出去。 所产生的声音的频率由传声器、放大器和扬声器的共振频率、房间的声学特性、传声器和扬声器的定向拾音和发射模式以及它们之间的距离决定。对于小型的扩声系统来说,这种声音很容易的体现的响亮的吱吱声或尖叫声。<br />
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在歌手或公众演讲者使用扩声系统或扩音系统的活动中,麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来,音频工程师使用各种电子设备,如均衡器或者自动反馈检测设备,来防止这些不受欢迎的尖叫声或尖叫声,这些声音影响了观众对活动的享受。另一方面,自20世纪60年代以来,摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果,有意制造吉他中的正反馈,以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈,但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中,他说,“我敢说任何人都找不到这样的唱片,除非是1922年这张用这种方式录制的老蓝调唱片。”<br />
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音频反馈的原理是由丹麦科学家Søren Absalon Larsen首先发现的。麦克风并不是唯一受此影响的传感器。录音板拾音器也会产生正反馈,通常是在100赫兹以下的低频范围内表现出低沉的轰鸣声。Jimi Hendrix是一个创新者,在他的吉他独奏中有意使用吉他正反馈来创造独特的声音效果。他帮助发展了电吉他演奏中音频反馈的可控性和音乐性,后来Brian May也是这种技术的著名支持者。<br />
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[[File:Adam Savage HOPE.jpg|thumb|right|220px|[[Video feedback]]【图12 视频反馈】.|链接=Special:FilePath/Adam_Savage_HOPE.jpg]]<br />
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===视频===<br />
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同样,如果一台摄像机对准一个正在显示摄像机自身信号的监控屏幕,那么通过正反馈就可以在屏幕上形成重复的图案。这种视频反馈效果在电视剧《神秘博士》前十季的开场白中就被使用了。<br />
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===开关===<br />
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在电气开关中,包括双金属条型恒温器,开关通常在开关动作中具有滞后性。在这些情况下,滞后是通过一个临界点机构内的正反馈来实现的。正反馈作用可最大限度地减少开关过程中发生电弧的时间,并使触点保持在断开或闭合状态。<br />
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=== 生物学===<br />
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[[File:Positive Feedback- Childbirth (1).svg|thumb|生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。|链接=Special:FilePath/Positive_Feedback-_Childbirth_(1).svg]]<br />
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生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。<br />
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==== 生理学====<br />
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在生理学中可以找到一些正反馈系统的例子。<br />
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其中一个例子是分娩时宫缩的发生,称为弗格森反射。当宫缩发生时,激素催产素会引起神经刺激,刺激下丘脑产生更多的催产素,从而增加子宫收缩。这就导致宫缩的幅度和频率增加。<br />
<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders. {{ISBN|0-7216-3994-1}}</ref><br />
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另一个例子是血液凝固的过程。当受伤的组织释放出信号化学物质,激活血液中的血小板时,这个循环就启动了。被激活的血小板释放化学物质,激活更多的血小板,引起快速的级联反应,形成血栓。<ref name=Guyton1991/><br />
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哺乳也涉及正反馈,当婴儿吸吮乳头时,会有神经反应进入脊髓,并上传到大脑的下丘脑,然后刺激垂体产生更多的催乳素以产生更多的乳汁<ref name=Guyton1991/>。<br />
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在月经周期的卵泡期期间,雌激素的飙升会导致排卵<ref name=Guyton1991/>。<br />
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神经信号的产生是另一个例子,神经纤维的膜使钠离子通过钠通道轻微渗漏,导致膜电位的变化,进而引起更多通道的开放(Hodgkin循环)。所以,最初的轻微渗漏会导致钠渗漏的爆发,从而产生神经动作电位<ref name=Guyton1991/>。<br />
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在心脏的兴奋收缩耦合中,肌浆网膜中的兰尼碱受体检测到心肌细胞内钙离子的增加,该受体以正反馈生理反应将钙运出到细胞质中。<br />
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在大多数情况下,这种反馈循环最终会释放出反信号,从而抑制或破坏循环。分娩宫缩在宝宝离开母体时停止。化学物质分解血凝块。当婴儿不再需要被哺乳时,泌乳停止<ref name=Guyton1991/>。<br />
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====基因调控====<br />
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正反馈是基因调控中研究较好的一种现象,其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时,就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络,以证明双稳态的概念。<ref name=Hasty2002/><br />
正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用,因此,基因调控中的正反馈可以产生显著的生理结果。分子动力学中的随机运动加上正反馈可以引发有趣的效应,例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/> 这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中,如酶动力学或代谢途径。<ref name=Christoph2001/><br />
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==== 进化生物学 ====<br />
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在进化生物学中正反馈循环被用来描述生物进化中变化动态的各个方面。 例如,在宏观层面,Alfred J. Lotka(1945)认为,物种的演变最重要的是选择反馈能量流动以捕获越来越多的能源系统的能量。<ref name=Lotka1945/>在人类层面,Richard D. Alexander(1989)提出,人类群体之间和群体内部的社会竞争会影响智力的选择,从而时不时地会产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子<ref name=Crespi2004/>。通过与军备竞赛进行类比,给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/><br />
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[[File:Phanerozoic Biodiversity.svg|300px|right|thumb|显生宙[[生物多样性]]呈现稳定而非单调的增长,从接近于零一直增长到有几千个属。|链接=Special:FilePath/Phanerozoic_Biodiversity.svg]]<br />
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研究表明,在'''显生宙 ''',生物多样性的变化与双曲模型(广泛用于人口学和宏观社会学)的相关性要比指数模型和逻辑斯特模型(传统上用于人口生物学,并广泛用于生物多样性化石)的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈(更多的祖先,更多的后代)和资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为,生物多样性和人口曲线之间的相似性可能来自这样一个事实,即两者都是由双曲趋势(由正反馈产生)与周期性和随机性的动态干扰而产生的。<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref><br />
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==== 免疫系统====<br />
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细胞因子风暴,或称高细胞因子血症,是一种潜在的致命性免疫反应,表现为各种细胞因子水平高度升高,这是由细胞因子和免疫细胞之间的正反馈环组成。[36]在正常的免疫功能中,可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后,就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合,当B细胞的抗体与C3结合后,就会加快该B细胞分泌更多的抗体和更多的C3蛋白,从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
<br />
====细胞凋亡====<br />
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细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程,其目的是清除长寿或受损的细胞。这一过程的失效与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活,它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时,无论效应子胱天蛋白酶的中间激活步骤数量有多少,这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/> 当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时,该过程呈现双稳态,从而模拟细胞的存活和死亡状态。<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref><br />
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=== 心理学===<br />
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Winner(1996)将有天赋的孩子描述为受到正反馈循环的驱动,这些反馈循环体现在他们自己的课程学习上,通过反馈自己的满意程度,从而进一步将他们的学习目标提高到更高水平等。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a,2009b)提出,神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释,工作记忆中的思维/表现输出被反馈到小脑,在那里被精简,然后再反馈到工作记忆中,从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/> <br />
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=== 经济学===<br />
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====市场上的社会影响====<br />
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事实证明,产品推荐和消费者先前的购买信息对消费者的选择影响很大,无论是音乐、电影、书籍、电子产品还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象(马太效应),即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
<br />
====市场动向====<br />
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根据George Soros提出的反射性理论,价格变化是由一个正反馈过程驱动的,即投资者的预期受到价格变动的影响,因此他们的行为会强化这个方向的价格变动,直到价格的变化变得不可持续,于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
<br />
==== 系统风险====<br />
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系统性风险是指放大效应或杠杆或正反馈过程给系统带来的风险。这通常是未知的,在某些条件下,这个过程会成倍放大,并迅速导致破坏性或混乱的行为。 庞氏骗局就是正反馈系统的一个很好的例子:来自新投资者的资金被用来支付异常高的回报,反过来又吸引了更多的新投资者,导致快速增长进而走向崩溃。W. Brian Arthur 也对经济中的正反馈进行了研究和著述(如W. Brian Arthur,1990)。Hyman Minsky提出了一个理论,认为某些信用扩张行为会使市场经济变成一个 "偏差放大系统",从而可能会突然崩溃,这有时被称为 "明斯基时刻"。<br />
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输入和输出明确分开的简单系统不容易发生系统性风险。 随着系统复杂性的增加,这种风险更容易发生,因为即使在详细的压力测试条件下,也更难看到或分析系统中所有可能的变量组合。 一个复杂系统的效率越高,就越容易发生系统性风险,因为只需要很小的偏差就可以破坏系统。 因此,设计良好的复杂系统一般都会有一些内在的功能来避免这种情况的发生,比如在系统内有少量的摩擦力,或阻力,或惯性,或时间延迟来使输出与输入脱钩。这些因素造成了低效率,但它们是避免不稳定的必要条件。<br />
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2010年的闪崩事件被归咎于高频交易(HFT)的做法,不过HFT是否真的会增加系统性风险仍然存在争议。<br />
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====人口与环境危机====<br />
<br />
可以认为农业和人口之间处于一种正反馈模式,这意味着双方越来越强烈地推动彼此。有人认为,这种正反馈系统终将在某一时刻以灾难结束,因为现代农业正在耗尽所有容易获得的磷酸盐,并且进行高效的单一栽培,使得现代农业更容易受到系统性风险影响。<br />
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技术创新和人类人口也可以有类似的考虑,这也是过去人类人口明显的双曲线增长,而不是简单的指数增长的一个解释。<br />
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有人提出,由于人口和技术之间的二阶正反馈,增长速度正在加快。技术增长增加了土地对人的承载能力,从而导致人口增长,而这反过来又推动了技术的进一步增长。<br />
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==== 偏见、社会制度与贫困====<br />
<br />
Gunnar Myrdal描述了一个不平等和贫困加剧的恶性循环,这就是所谓的”循环累积诱因”。<br />
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===气象学===<br />
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干旱通过正反馈效应加剧。缺雨会降低土壤湿度,从而杀死植物,使它们通过蒸腾作用释放更少的水分。这两个因素都限制了水蒸气从地表加到大气中的过程,并使吸收水分的干燥灰尘进入大气。水汽少了,既意味着露点温度低,白天的供暖效率也高,减少了大气中湿度导致云的形成的机会。最后,没有云,就不会有雨,这个正反馈循环就形成了。<br />
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=== 气候学===<br />
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气候中的"诱因 "可能会将气候系统推向变暖或变冷的方向,例如,大气中温室气体浓度的增加会导致地表变暖。诱因是气候系统的外部因素,而反馈是系统的内部过程。一些反馈机制与气候系统的其他部分相对孤立地发挥作用,而另一些则是紧密耦合的。气候系统的作用力、反馈和动态决定了气候变化的程度和速度。全球变暖中的主要正反馈是变暖使大气中的水汽量增加,进而导致进一步变暖。主要的负反馈来自Stefan-Boltzmann定律,从地球辐射到空间的热量与地球表面和大气温度的四次方成正比。<br />
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气候学中正反馈子系统的其他例子包括:<br />
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大气变暖会使冰融化,从而改变反照率,从而使大气进一步变暖。<br />
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甲烷水合物可能是不稳定的,所以海洋变暖可能会释放更多的温室气体之一的甲烷。<br />
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泥炭,天然存在于泥炭沼泽中,含有碳。当泥炭干燥时,它会分解,并可能额外燃烧。泥炭还会释放一氧化二氮。<br />
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全球变暖会影响云的分布。高空的云层会增强温室效应,而低空的云层则主要反射太阳光,对温度产生相反的影响。<br />
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政府间气候变化专门委员会(气专委)第四次评估报告指出,"人类活动的变暖可能导致一些突然或不可逆转的影响,这取决于气候变化的速度和程度"。<br />
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=== 社会学===<br />
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自我应验预言是信念和行为之间的一个社会正反馈循环: 如果有足够多的人相信某件事是真的,他们的行为就能让它变成真的,而对他们行为的观察又可能反过来增加信念。一个典型的例子是银行挤兑。<br />
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正反馈的另一个社会学例子是网络效应。当更多的人被鼓励加入一个网络时,这就增加了网络的覆盖面,因此网络扩张得越来越快。病毒视频就是网络效应的一个例子,在这个例子中,一个热门视频的链接被分享和再传播,确保更多的人看到这个视频,然后重新发布链接。这是许多社会现象的基础,包括庞氏骗局和连锁信。在许多情况下,人口量是反馈效应的限制因素。<br />
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=== 化学===<br />
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如果化学反应引起热量的释放,而反应本身在较高的温度下发生得更快,那么就很有可能出现正反馈。如果产生的热量没有足够快地从反应物中排除,就会发生热失控,并很快导致化学爆炸。<br />
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=== 自然保护===<br />
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许多野生动物被猎杀的原因是它们身体的某些部位可能相当有价值。目标物种越是接近灭绝,其身体部位的价格就越高。这就是正反馈的一个例子。<br />
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==参见==<br />
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* Chain reaction – Sequence of reactions 链式反应 -- -- 反应的顺序<br />
* Donella Meadows' twelve leverage points to intervene in a system Donella Meadows干预系统的十二个杠杆点<br />
* Hyperbolic growth 双曲增长<br />
* Reflexivity (social theory)反射性(社会理论)<br />
* Stability criterion稳定性标准<br />
* Strategic complements战略补充<br />
* System dynamics 系统动力学<br />
* Technological singularity – Hypothetical point in time at which technological growth becomes uncontrollable and irreversible 技术奇点 -- -- 假设技术增长变得不可控制和不可逆转的时间点<br />
* Thermal runaway 热失控<br />
* Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop. 恶性/恶性循环:在社会和金融系统中,是通过反馈循环自我强化的事件综合体。<br />
* Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour. 正强化:在操作性条件下,结果会增加行为的频率。<br />
* Praise of performance: a term often applied in the context of performance appraisal,although this usage is disputed 绩效表扬:这个词经常被应用于绩效评估中,尽管这种用法有争议。<br />
* Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage 自我强化反馈:系统动力学中使用的术语,以避免与 "表扬 "的用法相混淆。<br />
* Matthew effect – Effect originally observed by Robert K. Merton 马太效应 -- -- 罗伯特-K-默顿最初观察到的效应。<br />
* Self-fulfilling prophecy – Prediction that causes itself to become true 自证预言 -- -- 导致自己成为现实的预言<br />
* Virtuous circle and vicious circle 良性循环和恶性循环<br />
* Autocatalysis 自催化<br />
* Meander – Sinuous bend in a series in the channel of a river 蜿蜒曲折 -- -- 河道中一系列蜿蜒曲折的弯道。<br />
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==参考文献==<br />
{{Reflist|2}}<br />
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==拓展阅读==<br />
* Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.<br />
* Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.<br />
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本中文词条由[[用户:Solitude|Solitude]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%AD%A3%E5%8F%8D%E9%A6%88&diff=29643正反馈2022-03-26T10:41:01Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=positive feedback,正反馈,反馈,加剧反馈,自我强化反馈<br />
|description=在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。正反馈的一个重要特点是小扰动变大,当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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[[File:Herdwick Stampede.jpg|thumb|right|【图1:有时,警报或恐慌会通过正反馈在一群动物之间传播,从而引起踩踏事件。】.|链接=Special:FilePath/Herdwick_Stampede.jpg]]<br />
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[[File:Stampede loop.png|thumb|【图2:Causal loop diagram that depicts the causes of a stampede as a positive feedback loop. 在因果环路图中,踩踏事件的发生是一个正反馈循环。】|链接=Special:FilePath/Stampede_loop.png]]<br />
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[[File:Birmingham Northern Rock bank run 2007.jpg|thumb|right|300px|【图3: 在社会学中,网络效应可以迅速产生银行挤兑的正反馈效应。上图是2007年英国北岩银行挤兑事件的照片。】|链接=Special:FilePath/Birmingham_Northern_Rock_bank_run_2007.jpg]]<br />
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==回顾==<br />
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'''正反馈'''(加剧反馈,自我强化反馈) 是一种在反馈循环中加剧微小扰动影响的过程。也就是说,一个扰动对系统的影响包括它自身扰动幅度的增大。或者说,A会产生更多的B,而B又会产生更多的A,与之相反的是,[[负反馈]]指的是一个系统中,变化的结果会减少或抵消它自己的影响。<ref name="theorymodelling" />这两个概念在科学和工程等领域中发挥着重要作用,包括生物学、化学和控制论。<br />
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在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。<ref name="zuckerman" /><ref>Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". ''Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems''. Academic Press. p. 55. ISBN <bdi>9780127784557</bdi>. Archived from the original on 2017-01-03. <q>A positive feedback loop is one with an even number of negative influences [around the loop].</q></ref><ref name="zuckerman" /> 从结果到始发过程的反馈可以是直接的,也可以通过其他状态变量<ref name="theorymodelling" />。这样的系统可以给出丰富的定性行为,但反馈的瞬时信号是正向还是负向,对结果有极其重要的影响。<ref name="theorymodelling" /> 正反馈强化原过程,而负反馈调节原过程。在这个含义下,''正''和''负''指的是大于或小于零的循环收益,并不代表着最终结果或效果的正负性。<ref name=":0">{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>因此,正反馈的一个重要特点是小扰动变大。当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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===基础===<br />
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[[File:Ideal feedback model.svg|thumb|【图4:A basic feedback system can be represented by this block diagram. In the diagram the + symbol is an adder and A and B are arbitrary causal functions. 一个基本的反馈系统可以用这个框图来表示。在图中,+号是加法器,A和B是任意因果函数。】|链接=Special:FilePath/Ideal_feedback_model.svg]]<br />
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图中显示了一个简单的反馈回路。 如果环增益AB为正值,则存在'正'或'再生'反馈的条件。<br />
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如果函数A和B是线性的,且AB小于1,那么系统从输入到输出的整体增益是有限的,但当AB接近1时,系统的增益可以非常大。<ref name="smith"> Electronics circuits and devices second edition. Ralph J. Smith</ref> 在这种情况下,可以表明从输入到输出的整体或 "闭环 "增益为:<br />
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:<math>G_c = A/(1-AB)</math><br />
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当AB>1时,系统是不稳定的,因此不具有明确的增益;增益可称为无限。<br />
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所以系统状态的变化根据反馈可以是收敛的,也可以是发散的。 而正反馈的结果是增强变化,因此小的扰动就可能导致大的变化。<br />
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对于一个当前处于平衡状态的系统,如果其状态的任何变化都发生了正反馈,从而造成了状态的不稳定,那么这个系统就是一个不稳定平衡的系统。使这种系统远离其平衡状态的力的大小是状态与平衡状态之间的距离的递增函数。<br />
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正反馈并不一定意味着平衡的不稳定性,例如,在正反馈结构中可能存在稳定的开关状态<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>。<br />
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=== 迟滞 ===<br />
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[[File:Hysteresis sharp curve.svg|thumb|【图5 Hysteresis causes the output value to depend on the history of the input 迟滞现象会导致输出值取决于输入的历史记录。】|链接=Special:FilePath/Hysteresis_sharp_curve.svg]]<br />
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[[File:Op-Amp Schmitt Trigger.svg|thumb|【图6 In a Schmitt trigger circuit, feedback to the non-inverting input of an amplifier pushes the output directly away from the applied voltage towards the maximum or minimum voltage the amplifier can generate. 在施密特触发器电路中,利用放大器的非反相输入端口产生的反馈,可以直接将电路的输出从原本的外加电压值推向到放大器所能产生的极值电压。】|链接=Special:FilePath/Op-Amp_Schmitt_Trigger.svg]]<br />
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在现实世界中,正反馈循环通常不会引起不断增长,而是通过某种限制效应来改变。根据Donella Meadows的说法:<br />
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正反馈回路是系统增长、爆炸、腐蚀和崩溃的根源。一个系统如果有一个不受控制的正反馈,最终将会自我毁灭。这就是为什么正反馈如此稀少的原因。通常情况下,负反馈迟早会发生。<ref>Donella Meadows, ''[http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf Leverage Points: Places to Intervene in a System]''2013-10-08 at the Wayback Machine, 1999</ref><br />
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[[迟滞]],即起点影响系统的终点的现象,可以通过正反馈产生。当反馈循环的增益高于1时,那么输出就会远离输入:如果大于输入,则向最近的正极限移动,而如果小于输入,则向最近的负极限移动。<br />
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一旦达到极限,它就会稳定下来。但是,如果输入超过极限,那么反馈将改变符号,输出将向相反的方向移动,直到达到相反的极限。因此,该系统表现出'''双稳态行为bistable behavior'''。<br />
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== 术语由来==<br />
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正反馈和负反馈这两个名词最早应用于反馈是在二战前。正反馈的概念随着再生电路的问世,在20世纪20年代已经出现。<br />
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Friis 和 Jensen在1924年描述了一种在电子放大器中发生的"回馈 "是正的情况,这一情况与他们顺便提到的负回馈作用相反。到了1934年,Harold Stephen Black在他的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法:<br />
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正反馈会增加放大器的增益,负反馈会降低增益<br />
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据Mindell(2002年)说,术语上的混乱是在这之后不久产生的:<br />
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“ ... ... Friis 和 Jensen 对 Black 在对"正反馈 "和 "负反馈 "的区分方法是一样的,都不是基于反馈本身的符号,而是基于它对放大器增益的影响。与之相反的是,当Nyquist和Bode基于Black的工作基础时,将负反馈称为符号相反的反馈。Black难以说服其他人相信他的发明的实用性,有一部分原因是在基本的定义问题上存在混乱。"<br />
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==实例与应用==<br />
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=== 电子电路===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|【图7 A vintage style regenerative radio receiver. Due to the controlled use of positive feedback, sufficient amplification can be derived from a single [[vacuum tube]] or valve (centre). 一个老式的再生无线电接收器。由于使用正反馈的控制,真空管或阀门(中心)就可以产生足够的放大效果。】|链接=Special:FilePath/Regenerartive_Receiver-S7300056.JPG]]<br />
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'''再生电路Regenerative circuit'''于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>,用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈,可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此,一个信号可以在一个阶段被放大20000甚至100000倍,而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定,开始振荡。无线电操作员必须不断地调整反馈量,以获得良好的接收效果。而现代无线电接收机采用超异构设计,多了许多放大级,去掉了正反馈并使其工作更稳定。<br />
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在再生无线电电路中产生的振荡还可以被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英),经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计,包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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许多电子电路,特别是放大器,都采用了负反馈。这降低了放大器的信号增益,但改善了它的线性度、输入阻抗、输出阻抗和带宽,并稳定了包括闭环增益等参数。同时,这些参数也变得不那么依赖于放大器件本身的细节,而更多地依赖于反馈元件,因为反馈元件一般不随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位:如果信号反馈失相,则反馈为负,如果相位一致,则反馈为正。对于需要使用负反馈放大器的设计者来说,引入负反馈放大器的问题是,电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°,那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波来做到这一点)。如果任何频率下的环增益(放大器增益与正反馈程度的乘积)大于1,那么放大器将在该频率下发生振荡(巴克豪森稳定性准则)。这种振荡有时被称为寄生振荡:在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化,前板(用户界面)的变化,甚至是由于人或其他导电物品的接近。<br />
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放大器可能会以示波器很难检测到的方式轻轻振荡,有时的振荡也可能非常大,只有非常扭曲或根本没有真正的信号,甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似,因此低频寄生振荡也被称为 "汽艇"。<br />
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【图8 The effect of using a Schmitt trigger (B) instead of a comparator (A) 使用施密特触发器(b)代替比较器(a)的效果】<br />
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许多常见的数字电路都采用正反馈。一般简单的布尔逻辑门通常只是依靠增益将数字信号电压从中间值推到代表布尔值0和1的值上,但许多更复杂的门都采用了反馈。当输入的模拟电压发生变化,但后期数字处理需要尖锐阈值时,施密特触发电路通过正反馈机制确保当输入电压轻微超过阈值时,输出电压可以巧妙而迅速地从一个逻辑状态转移到另一个逻辑状态。施密特触发器使用正反馈的一个必然结果是,如果输入电压再次缓慢下降,超过了相同的阈值,由于正反馈的机制,输出电压将保持在相同的逻辑状态而不改变。这种效应被称为滞后: 输入电压必须降到一个不同的、较低的阈值,才能“解锁”输出,并将其重置为原始数字。通过减小正反馈的程度,可以减小滞后宽度,但宽度不能被完全消除。施密特触发器在某种程度上是一个闭锁电路。<br />
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【图9 Positive feedback is a mechanism by which an output is enhanced, such as protein levels. However, in order to avoid any fluctuation in the protein level, the mechanism is inhibited stochastically (I), therefore when the concentration of the activated protein (A) is past the threshold ([I]), the loop mechanism is activated and the concentration of A increases exponentially if d[A]=k [A] 正反馈是一种增强输出的机制,如蛋白质水平。但为了避免蛋白质水平的波动,该机制是随机抑制的(I),因此只有当激活的蛋白质(A)浓度超过阈值([I])时,循环机制被激活,如果d[A]=k[A],A的浓度就会成倍增加。】<br />
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【图10 Illustration of an R-S ('reset-set') flip-flop made from two digital nor gates with positive feedback. Red and black mean logical '1' and '0', respectively. R-S("复位-设置")触发器的说明,由两个带正反馈的数字诺尔门组成。红色和黑色分别表示逻辑上的 "1 "和 "0"。】<br />
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电子触发器,或“锁存器” ,或“双稳态多谐振荡器” ,是一种由于高正反馈而不稳定于平衡或中间状态的电路。这样的双稳态电路是一位电子存储器的基础。 触发器使用一对放大器、晶体管或逻辑门相互连接,正反馈机制使得输入信号被去除后,电路可以维持在两种非平衡稳定状态中的一种,直到一个合适的替代信号重新作为输入,以改变电路状态。计算机随机存取存储器(RAM)可以用这种方式运作,每位存储器有一个锁存电路。<br />
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电子系统中发生'''热失控Thermal runaway'''的原因是,当电路的某些方面变得更热时,它被允许通过更多的电流,然后它越热,通过的电流就越多,这就使它更热一些,因此它又通过更多的电流。这种现象对有关器件来说通常是灾难性的。如果器件不得不在接近其最大功率处理能力的情况下工作,那么某些条件下就可能出现热失控,这通常可以通过精心设计来改进。<br />
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[[File:Technics SL-1210MK2.jpg|thumb|left|【图11 A phonograph turntable is prone to acoustic feedback. 留声机转盘容易受到声反馈的影响。】|链接=Special:FilePath/Technics_SL-1210MK2.jpg]]<br />
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音频和视频系统可以表现出正反馈。如果麦克风录入了同一电路中扬声器的放大声音输出,那么就会听到音频反馈的嚎叫和尖叫声(在放大器的最大功率容量下),因为随机噪声被音频系统和房间的特性所过滤后,通过正反馈重新放大。<br />
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===音频与现场音频===<br />
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音频反馈(也称为声反馈,简称反馈,或拉森效应)是一种特殊的正反馈,当音频输入(例如,麦克风或吉他拾音器)和音频输出(例如,大声放大的扬声器)之间存在声音回路时,就会出现这种反馈。在这个例子中,麦克风接收到的信号被放大并从扬声器传出。然后,来自扬声器的声音可以再次被麦克风接收,进一步放大,然后再次通过扬声器传递出去。 所产生的声音的频率由传声器、放大器和扬声器的共振频率、房间的声学特性、传声器和扬声器的定向拾音和发射模式以及它们之间的距离决定。对于小型的扩声系统来说,这种声音很容易的体现的响亮的吱吱声或尖叫声。<br />
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在歌手或公众演讲者使用扩声系统或扩音系统的活动中,麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来,音频工程师使用各种电子设备,如均衡器或者自动反馈检测设备,来防止这些不受欢迎的尖叫声或尖叫声,这些声音影响了观众对活动的享受。另一方面,自20世纪60年代以来,摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果,有意制造吉他中的正反馈,以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈,但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中,他说,“我敢说任何人都找不到这样的唱片,除非是1922年这张用这种方式录制的老蓝调唱片。”<br />
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音频反馈的原理是由丹麦科学家Søren Absalon Larsen首先发现的。麦克风并不是唯一受此影响的传感器。录音板拾音器也会产生正反馈,通常是在100赫兹以下的低频范围内表现出低沉的轰鸣声。Jimi Hendrix是一个创新者,在他的吉他独奏中有意使用吉他正反馈来创造独特的声音效果。他帮助发展了电吉他演奏中音频反馈的可控性和音乐性,后来Brian May也是这种技术的著名支持者。<br />
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[[File:Adam Savage HOPE.jpg|thumb|right|220px|[[Video feedback]]【图12 视频反馈】.|链接=Special:FilePath/Adam_Savage_HOPE.jpg]]<br />
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===视频===<br />
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同样,如果一台摄像机对准一个正在显示摄像机自身信号的监控屏幕,那么通过正反馈就可以在屏幕上形成重复的图案。这种视频反馈效果在电视剧《神秘博士》前十季的开场白中就被使用了。<br />
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===开关===<br />
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In [[electrical switch]]es, including [[bimetallic strip]] based thermostats, the switch usually has hysteresis in the switching action. In these cases hysteresis is mechanically achieved via positive feedback within a tipping point mechanism. The positive feedback action minimises the length of time arcing occurs for during the switching and also holds the contacts in an open or closed state.<br />
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在电气开关中,包括双金属条型恒温器,开关通常在开关动作中具有滞后性。在这些情况下,滞后是通过一个临界点机构内的正反馈来实现的。正反馈作用可最大限度地减少开关过程中发生电弧的时间,并使触点保持在断开或闭合状态。<br />
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=== 生物学===<br />
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[[File:Positive Feedback- Childbirth (1).svg|thumb|生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。|链接=Special:FilePath/Positive_Feedback-_Childbirth_(1).svg]]<br />
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生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。<br />
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==== 生理学====<br />
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在生理学中可以找到一些正反馈系统的例子。<br />
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其中一个例子是分娩时宫缩的发生,称为弗格森反射。当宫缩发生时,激素催产素会引起神经刺激,刺激下丘脑产生更多的催产素,从而增加子宫收缩。这就导致宫缩的幅度和频率增加。<br />
<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders. {{ISBN|0-7216-3994-1}}</ref><br />
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另一个例子是血液凝固的过程。当受伤的组织释放出信号化学物质,激活血液中的血小板时,这个循环就启动了。被激活的血小板释放化学物质,激活更多的血小板,引起快速的级联反应,形成血栓。<ref name=Guyton1991/><br />
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哺乳也涉及正反馈,当婴儿吸吮乳头时,会有神经反应进入脊髓,并上传到大脑的下丘脑,然后刺激垂体产生更多的催乳素以产生更多的乳汁<ref name=Guyton1991/>。<br />
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在月经周期的卵泡期期间,雌激素的飙升会导致排卵<ref name=Guyton1991/>。<br />
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神经信号的产生是另一个例子,神经纤维的膜使钠离子通过钠通道轻微渗漏,导致膜电位的变化,进而引起更多通道的开放(Hodgkin循环)。所以,最初的轻微渗漏会导致钠渗漏的爆发,从而产生神经动作电位<ref name=Guyton1991/>。<br />
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在心脏的兴奋收缩耦合中,肌浆网膜中的兰尼碱受体检测到心肌细胞内钙离子的增加,该受体以正反馈生理反应将钙运出到细胞质中。<br />
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在大多数情况下,这种反馈循环最终会释放出反信号,从而抑制或破坏循环。分娩宫缩在宝宝离开母体时停止。化学物质分解血凝块。当婴儿不再需要被哺乳时,泌乳停止<ref name=Guyton1991/>。<br />
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====基因调控====<br />
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正反馈是基因调控中研究较好的一种现象,其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时,就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络,以证明双稳态的概念。<ref name=Hasty2002/><br />
正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用,因此,基因调控中的正反馈可以产生显著的生理结果。分子动力学中的随机运动加上正反馈可以引发有趣的效应,例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/> 这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中,如酶动力学或代谢途径。<ref name=Christoph2001/><br />
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<br />
==== 进化生物学 ====<br />
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<br />
在进化生物学中正反馈循环被用来描述生物进化中变化动态的各个方面。 例如,在宏观层面,Alfred J. Lotka(1945)认为,物种的演变最重要的是选择反馈能量流动以捕获越来越多的能源系统的能量。<ref name=Lotka1945/>在人类层面,Richard D. Alexander(1989)提出,人类群体之间和群体内部的社会竞争会影响智力的选择,从而时不时地会产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子<ref name=Crespi2004/>。通过与军备竞赛进行类比,给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/><br />
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[[File:Phanerozoic Biodiversity.svg|300px|right|thumb|显生宙[[生物多样性]]呈现稳定而非单调的增长,从接近于零一直增长到有几千个属。|链接=Special:FilePath/Phanerozoic_Biodiversity.svg]]<br />
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研究表明,在'''显生宙 ''',生物多样性的变化与双曲模型(广泛用于人口学和宏观社会学)的相关性要比指数模型和逻辑斯特模型(传统上用于人口生物学,并广泛用于生物多样性化石)的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈(更多的祖先,更多的后代)和资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为,生物多样性和人口曲线之间的相似性可能来自这样一个事实,即两者都是由双曲趋势(由正反馈产生)与周期性和随机性的动态干扰而产生的。<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref><br />
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<br />
==== 免疫系统====<br />
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细胞因子风暴,或称高细胞因子血症,是一种潜在的致命性免疫反应,表现为各种细胞因子水平高度升高,这是由细胞因子和免疫细胞之间的正反馈环组成。[36]在正常的免疫功能中,可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后,就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合,当B细胞的抗体与C3结合后,就会加快该B细胞分泌更多的抗体和更多的C3蛋白,从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
<br />
====细胞凋亡====<br />
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细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程,其目的是清除长寿或受损的细胞。这一过程的失效与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活,它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时,无论效应子胱天蛋白酶的中间激活步骤数量有多少,这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/> 当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时,该过程呈现双稳态,从而模拟细胞的存活和死亡状态。<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref><br />
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=== 心理学===<br />
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Winner(1996)将有天赋的孩子描述为受到正反馈循环的驱动,这些反馈循环体现在他们自己的课程学习上,通过反馈自己的满意程度,从而进一步将他们的学习目标提高到更高水平等。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a,2009b)提出,神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释,工作记忆中的思维/表现输出被反馈到小脑,在那里被精简,然后再反馈到工作记忆中,从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/> <br />
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=== 经济学===<br />
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====市场上的社会影响====<br />
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事实证明,产品推荐和消费者先前的购买信息对消费者的选择影响很大,无论是音乐、电影、书籍、电子产品还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象(马太效应),即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
<br />
====市场动向====<br />
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根据George Soros提出的反射性理论,价格变化是由一个正反馈过程驱动的,即投资者的预期受到价格变动的影响,因此他们的行为会强化这个方向的价格变动,直到价格的变化变得不可持续,于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
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==== 系统风险====<br />
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系统性风险是指放大效应或杠杆或正反馈过程给系统带来的风险。这通常是未知的,在某些条件下,这个过程会成倍放大,并迅速导致破坏性或混乱的行为。 庞氏骗局就是正反馈系统的一个很好的例子:来自新投资者的资金被用来支付异常高的回报,反过来又吸引了更多的新投资者,导致快速增长进而走向崩溃。W. Brian Arthur 也对经济中的正反馈进行了研究和著述(如W. Brian Arthur,1990)。Hyman Minsky提出了一个理论,认为某些信用扩张行为会使市场经济变成一个 "偏差放大系统",从而可能会突然崩溃,这有时被称为 "明斯基时刻"。<br />
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输入和输出明确分开的简单系统不容易发生系统性风险。 随着系统复杂性的增加,这种风险更容易发生,因为即使在详细的压力测试条件下,也更难看到或分析系统中所有可能的变量组合。 一个复杂系统的效率越高,就越容易发生系统性风险,因为只需要很小的偏差就可以破坏系统。 因此,设计良好的复杂系统一般都会有一些内在的功能来避免这种情况的发生,比如在系统内有少量的摩擦力,或阻力,或惯性,或时间延迟来使输出与输入脱钩。这些因素造成了低效率,但它们是避免不稳定的必要条件。<br />
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2010年的闪崩事件被归咎于高频交易(HFT)的做法,不过HFT是否真的会增加系统性风险仍然存在争议。<br />
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<br />
====人口与环境危机====<br />
<br />
可以认为农业和人口之间处于一种正反馈模式,这意味着双方越来越强烈地推动彼此。有人认为,这种正反馈系统终将在某一时刻以灾难结束,因为现代农业正在耗尽所有容易获得的磷酸盐,并且进行高效的单一栽培,使得现代农业更容易受到系统性风险影响。<br />
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技术创新和人类人口也可以有类似的考虑,这也是过去人类人口明显的双曲线增长,而不是简单的指数增长的一个解释。<br />
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有人提出,由于人口和技术之间的二阶正反馈,增长速度正在加快。技术增长增加了土地对人的承载能力,从而导致人口增长,而这反过来又推动了技术的进一步增长。<br />
<br />
==== 偏见、社会制度与贫困====<br />
<br />
Gunnar Myrdal描述了一个不平等和贫困加剧的恶性循环,这就是所谓的”循环累积诱因”。<br />
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===气象学===<br />
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干旱通过正反馈效应加剧。缺雨会降低土壤湿度,从而杀死植物,使它们通过蒸腾作用释放更少的水分。这两个因素都限制了水蒸气从地表加到大气中的过程,并使吸收水分的干燥灰尘进入大气。水汽少了,既意味着露点温度低,白天的供暖效率也高,减少了大气中湿度导致云的形成的机会。最后,没有云,就不会有雨,这个正反馈循环就形成了。<br />
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=== 气候学===<br />
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气候中的"诱因 "可能会将气候系统推向变暖或变冷的方向,例如,大气中温室气体浓度的增加会导致地表变暖。诱因是气候系统的外部因素,而反馈是系统的内部过程。一些反馈机制与气候系统的其他部分相对孤立地发挥作用,而另一些则是紧密耦合的。气候系统的作用力、反馈和动态决定了气候变化的程度和速度。全球变暖中的主要正反馈是变暖使大气中的水汽量增加,进而导致进一步变暖。主要的负反馈来自Stefan-Boltzmann定律,从地球辐射到空间的热量与地球表面和大气温度的四次方成正比。<br />
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气候学中正反馈子系统的其他例子包括:<br />
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大气变暖会使冰融化,从而改变反照率,从而使大气进一步变暖。<br />
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甲烷水合物可能是不稳定的,所以海洋变暖可能会释放更多的温室气体之一的甲烷。<br />
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泥炭,天然存在于泥炭沼泽中,含有碳。当泥炭干燥时,它会分解,并可能额外燃烧。泥炭还会释放一氧化二氮。<br />
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全球变暖会影响云的分布。高空的云层会增强温室效应,而低空的云层则主要反射太阳光,对温度产生相反的影响。<br />
<br />
政府间气候变化专门委员会(气专委)第四次评估报告指出,"人类活动的变暖可能导致一些突然或不可逆转的影响,这取决于气候变化的速度和程度"。<br />
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=== 社会学===<br />
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自我应验预言是信念和行为之间的一个社会正反馈循环: 如果有足够多的人相信某件事是真的,他们的行为就能让它变成真的,而对他们行为的观察又可能反过来增加信念。一个典型的例子是银行挤兑。<br />
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正反馈的另一个社会学例子是网络效应。当更多的人被鼓励加入一个网络时,这就增加了网络的覆盖面,因此网络扩张得越来越快。病毒视频就是网络效应的一个例子,在这个例子中,一个热门视频的链接被分享和再传播,确保更多的人看到这个视频,然后重新发布链接。这是许多社会现象的基础,包括庞氏骗局和连锁信。在许多情况下,人口量是反馈效应的限制因素。<br />
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=== 化学===<br />
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如果化学反应引起热量的释放,而反应本身在较高的温度下发生得更快,那么就很有可能出现正反馈。如果产生的热量没有足够快地从反应物中排除,就会发生热失控,并很快导致化学爆炸。<br />
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=== 自然保护===<br />
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许多野生动物被猎杀的原因是它们身体的某些部位可能相当有价值。目标物种越是接近灭绝,其身体部位的价格就越高。这就是正反馈的一个例子。<br />
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==参见==<br />
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* Chain reaction – Sequence of reactions 链式反应 -- -- 反应的顺序<br />
* Donella Meadows' twelve leverage points to intervene in a system Donella Meadows干预系统的十二个杠杆点<br />
* Hyperbolic growth 双曲增长<br />
* Reflexivity (social theory)反射性(社会理论)<br />
* Stability criterion稳定性标准<br />
* Strategic complements战略补充<br />
* System dynamics 系统动力学<br />
* Technological singularity – Hypothetical point in time at which technological growth becomes uncontrollable and irreversible 技术奇点 -- -- 假设技术增长变得不可控制和不可逆转的时间点<br />
* Thermal runaway 热失控<br />
* Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop. 恶性/恶性循环:在社会和金融系统中,是通过反馈循环自我强化的事件综合体。<br />
* Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour. 正强化:在操作性条件下,结果会增加行为的频率。<br />
* Praise of performance: a term often applied in the context of performance appraisal,although this usage is disputed 绩效表扬:这个词经常被应用于绩效评估中,尽管这种用法有争议。<br />
* Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage 自我强化反馈:系统动力学中使用的术语,以避免与 "表扬 "的用法相混淆。<br />
* Matthew effect – Effect originally observed by Robert K. Merton 马太效应 -- -- 罗伯特-K-默顿最初观察到的效应。<br />
* Self-fulfilling prophecy – Prediction that causes itself to become true 自证预言 -- -- 导致自己成为现实的预言<br />
* Virtuous circle and vicious circle 良性循环和恶性循环<br />
* Autocatalysis 自催化<br />
* Meander – Sinuous bend in a series in the channel of a river 蜿蜒曲折 -- -- 河道中一系列蜿蜒曲折的弯道。<br />
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==参考文献==<br />
{{Reflist|2}}<br />
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==拓展阅读==<br />
* Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.<br />
* Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.<br />
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本中文词条由[[用户:Solitude|Solitude]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%AD%A3%E5%8F%8D%E9%A6%88&diff=29642正反馈2022-03-26T10:12:04Z<p>唐糖糖:</p>
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|keywords=自相似性,共形对称,膨胀<br />
|description=在物理学、数学和统计学中,标度不变性是物体或者物理定律的一种特征,如果长度、能量或者其他变量的标度与一个公因子相乘,而不发生改变,因此也就代表某种普遍性。<br />
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[[File:Wiener process animated.gif|thumb|right|500px|<br />
维纳过程具有标度不变性。|链接=Special:FilePath/Wiener_process_animated.gif]]<br />
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[[File:Herdwick Stampede.jpg|thumb|right|【图1:有时,警报或恐慌会通过正反馈在一群动物之间传播,从而引起踩踏事件。】.|链接=Special:FilePath/Herdwick_Stampede.jpg]]<br />
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[[File:Stampede loop.png|thumb|【图2:Causal loop diagram that depicts the causes of a stampede as a positive feedback loop. 在因果环路图中,踩踏事件的发生是一个正反馈循环。】|链接=Special:FilePath/Stampede_loop.png]]<br />
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[[File:Birmingham Northern Rock bank run 2007.jpg|thumb|right|300px|【图3: 在社会学中,网络效应可以迅速产生银行挤兑的正反馈效应。上图是2007年英国北岩银行挤兑事件的照片。】|链接=Special:FilePath/Birmingham_Northern_Rock_bank_run_2007.jpg]]<br />
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==回顾==<br />
'''Positive feedback''' ('''exacerbating feedback''', '''self-reinforcing feedback''') is a process that occurs in a [[feedback loop]] which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation.Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback.<ref name="theorymodelling" /> Both concepts play an important role in science and engineering, including biology, chemistry, and [[cybernetics]] .<br />
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正反馈(加剧反馈,自我强化反馈) 是一种在反馈循环中加剧微小扰动影响的过程。也就是说,一个扰动对系统的影响包括它自身扰动幅度的增大。或者说,A会产生更多的B,而B又会产生更多的A,与之相反的是,[[负反馈]]指的是一个系统中,变化的结果会减少或抵消它自己的影响。<ref name="theorymodelling" />这两个概念在科学和工程等领域中发挥着重要作用,包括生物学、化学和控制论。<br />
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在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。<ref name="zuckerman" /><ref>Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". ''Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems''. Academic Press. p. 55. ISBN <bdi>9780127784557</bdi>. Archived from the original on 2017-01-03. <q>A positive feedback loop is one with an even number of negative influences [around the loop].</q></ref><ref name="zuckerman" /> 从结果到始发过程的反馈可以是直接的,也可以通过其他状态变量<ref name="theorymodelling" />。这样的系统可以给出丰富的定性行为,但反馈的瞬时信号是正向还是负向,对结果有极其重要的影响。<ref name="theorymodelling" /> 正反馈强化原过程,而负反馈调节原过程。在这个含义下,''正''和''负''指的是大于或小于零的循环收益,并不代表着最终结果或效果的正负性。<ref name=":0">{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>因此,正反馈的一个重要特点是小扰动变大。当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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===基础===<br />
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[[File:Ideal feedback model.svg|thumb|【图4:A basic feedback system can be represented by this block diagram. In the diagram the + symbol is an adder and A and B are arbitrary causal functions. 一个基本的反馈系统可以用这个框图来表示。在图中,+号是加法器,A和B是任意因果函数。】|链接=Special:FilePath/Ideal_feedback_model.svg]]<br />
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图中显示了一个简单的反馈回路。 如果环增益AB为正值,则存在'正'或'再生'反馈的条件。<br />
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如果函数A和B是线性的,且AB小于1,那么系统从输入到输出的整体增益是有限的,但当AB接近1时,系统的增益可以非常大。<ref name="smith"> Electronics circuits and devices second edition. Ralph J. Smith</ref> 在这种情况下,可以表明从输入到输出的整体或 "闭环 "增益为:<br />
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:<math>G_c = A/(1-AB)</math><br />
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当AB>1时,系统是不稳定的,因此不具有明确的增益;增益可称为无限。<br />
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所以系统状态的变化根据反馈可以是收敛的,也可以是发散的。 而正反馈的结果是增强变化,因此小的扰动就可能导致大的变化。<br />
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对于一个当前处于平衡状态的系统,如果其状态的任何变化都发生了正反馈,从而造成了状态的不稳定,那么这个系统就是一个不稳定平衡的系统。使这种系统远离其平衡状态的力的大小是状态与平衡状态之间的距离的递增函数。<br />
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正反馈并不一定意味着平衡的不稳定性,例如,在正反馈结构中可能存在稳定的开关状态<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>。<br />
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=== 迟滞 ===<br />
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[[File:Hysteresis sharp curve.svg|thumb|【图5 Hysteresis causes the output value to depend on the history of the input 迟滞现象会导致输出值取决于输入的历史记录。】|链接=Special:FilePath/Hysteresis_sharp_curve.svg]]<br />
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[[File:Op-Amp Schmitt Trigger.svg|thumb|【图6 In a Schmitt trigger circuit, feedback to the non-inverting input of an amplifier pushes the output directly away from the applied voltage towards the maximum or minimum voltage the amplifier can generate. 在施密特触发器电路中,利用放大器的非反相输入端口产生的反馈,可以直接将电路的输出从原本的外加电压值推向到放大器所能产生的极值电压。】|链接=Special:FilePath/Op-Amp_Schmitt_Trigger.svg]]<br />
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在现实世界中,正反馈循环通常不会引起不断增长,而是通过某种限制效应来改变。根据Donella Meadows的说法:<br />
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正反馈回路是系统增长、爆炸、腐蚀和崩溃的根源。一个系统如果有一个不受控制的正反馈,最终将会自我毁灭。这就是为什么正反馈如此稀少的原因。通常情况下,负反馈迟早会发生。<ref>Donella Meadows, ''[http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf Leverage Points: Places to Intervene in a System]''2013-10-08 at the Wayback Machine, 1999</ref><br />
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[[迟滞]],即起点影响系统的终点的现象,可以通过正反馈产生。当反馈循环的增益高于1时,那么输出就会远离输入:如果大于输入,则向最近的正极限移动,而如果小于输入,则向最近的负极限移动。<br />
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一旦达到极限,它就会稳定下来。但是,如果输入超过极限,那么反馈将改变符号,输出将向相反的方向移动,直到达到相反的极限。因此,该系统表现出'''双稳态行为bistable behavior'''。<br />
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== 术语由来==<br />
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正反馈和负反馈这两个名词最早应用于反馈是在二战前。正反馈的概念随着再生电路的问世,在20世纪20年代已经出现。<br />
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Friis 和 Jensen在1924年描述了一种在电子放大器中发生的"回馈 "是正的情况,这一情况与他们顺便提到的负回馈作用相反。到了1934年,Harold Stephen Black在他的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法:<br />
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正反馈会增加放大器的增益,负反馈会降低增益<br />
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据Mindell(2002年)说,术语上的混乱是在这之后不久产生的:<br />
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“ ... ... Friis 和 Jensen 对 Black 在对"正反馈 "和 "负反馈 "的区分方法是一样的,都不是基于反馈本身的符号,而是基于它对放大器增益的影响。与之相反的是,当Nyquist和Bode基于Black的工作基础时,将负反馈称为符号相反的反馈。Black难以说服其他人相信他的发明的实用性,有一部分原因是在基本的定义问题上存在混乱。"<br />
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==实例与应用==<br />
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=== 电子电路===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|【图7 A vintage style regenerative radio receiver. Due to the controlled use of positive feedback, sufficient amplification can be derived from a single [[vacuum tube]] or valve (centre). 一个老式的再生无线电接收器。由于使用正反馈的控制,真空管或阀门(中心)就可以产生足够的放大效果。】|链接=Special:FilePath/Regenerartive_Receiver-S7300056.JPG]]<br />
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'''再生电路Regenerative circuit'''于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>,用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈,可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此,一个信号可以在一个阶段被放大20000甚至100000倍,而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定,开始振荡。无线电操作员必须不断地调整反馈量,以获得良好的接收效果。而现代无线电接收机采用超异构设计,多了许多放大级,去掉了正反馈并使其工作更稳定。<br />
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在再生无线电电路中产生的振荡还可以被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英),经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计,包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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许多电子电路,特别是放大器,都采用了负反馈。这降低了放大器的信号增益,但改善了它的线性度、输入阻抗、输出阻抗和带宽,并稳定了包括闭环增益等参数。同时,这些参数也变得不那么依赖于放大器件本身的细节,而更多地依赖于反馈元件,因为反馈元件一般不随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位:如果信号反馈失相,则反馈为负,如果相位一致,则反馈为正。对于需要使用负反馈放大器的设计者来说,引入负反馈放大器的问题是,电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°,那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波来做到这一点)。如果任何频率下的环增益(放大器增益与正反馈程度的乘积)大于1,那么放大器将在该频率下发生振荡(巴克豪森稳定性准则)。这种振荡有时被称为寄生振荡:在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化,前板(用户界面)的变化,甚至是由于人或其他导电物品的接近。<br />
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放大器可能会以示波器很难检测到的方式轻轻振荡,有时的振荡也可能非常大,只有非常扭曲或根本没有真正的信号,甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似,因此低频寄生振荡也被称为 "汽艇"。<br />
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【图8 The effect of using a Schmitt trigger (B) instead of a comparator (A) 使用施密特触发器(b)代替比较器(a)的效果】<br />
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许多常见的数字电路都采用正反馈。一般简单的布尔逻辑门通常只是依靠增益将数字信号电压从中间值推到代表布尔值0和1的值上,但许多更复杂的门都采用了反馈。当输入的模拟电压发生变化,但后期数字处理需要尖锐阈值时,施密特触发电路通过正反馈机制确保当输入电压轻微超过阈值时,输出电压可以巧妙而迅速地从一个逻辑状态转移到另一个逻辑状态。施密特触发器使用正反馈的一个必然结果是,如果输入电压再次缓慢下降,超过了相同的阈值,由于正反馈的机制,输出电压将保持在相同的逻辑状态而不改变。这种效应被称为滞后: 输入电压必须降到一个不同的、较低的阈值,才能“解锁”输出,并将其重置为原始数字。通过减小正反馈的程度,可以减小滞后宽度,但宽度不能被完全消除。施密特触发器在某种程度上是一个闭锁电路。<br />
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【图9 Positive feedback is a mechanism by which an output is enhanced, such as protein levels. However, in order to avoid any fluctuation in the protein level, the mechanism is inhibited stochastically (I), therefore when the concentration of the activated protein (A) is past the threshold ([I]), the loop mechanism is activated and the concentration of A increases exponentially if d[A]=k [A] 正反馈是一种增强输出的机制,如蛋白质水平。但为了避免蛋白质水平的波动,该机制是随机抑制的(I),因此只有当激活的蛋白质(A)浓度超过阈值([I])时,循环机制被激活,如果d[A]=k[A],A的浓度就会成倍增加。】<br />
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【图10 Illustration of an R-S ('reset-set') flip-flop made from two digital nor gates with positive feedback. Red and black mean logical '1' and '0', respectively. R-S("复位-设置")触发器的说明,由两个带正反馈的数字诺尔门组成。红色和黑色分别表示逻辑上的 "1 "和 "0"。】<br />
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电子触发器,或“锁存器” ,或“双稳态多谐振荡器” ,是一种由于高正反馈而不稳定于平衡或中间状态的电路。这样的双稳态电路是一位电子存储器的基础。 触发器使用一对放大器、晶体管或逻辑门相互连接,正反馈机制使得输入信号被去除后,电路可以维持在两种非平衡稳定状态中的一种,直到一个合适的替代信号重新作为输入,以改变电路状态。计算机随机存取存储器(RAM)可以用这种方式运作,每位存储器有一个锁存电路。<br />
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电子系统中发生'''热失控Thermal runaway'''的原因是,当电路的某些方面变得更热时,它被允许通过更多的电流,然后它越热,通过的电流就越多,这就使它更热一些,因此它又通过更多的电流。这种现象对有关器件来说通常是灾难性的。如果器件不得不在接近其最大功率处理能力的情况下工作,那么某些条件下就可能出现热失控,这通常可以通过精心设计来改进。<br />
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[[File:Technics SL-1210MK2.jpg|thumb|left|【图11 A phonograph turntable is prone to acoustic feedback. 留声机转盘容易受到声反馈的影响。】|链接=Special:FilePath/Technics_SL-1210MK2.jpg]]<br />
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音频和视频系统可以表现出正反馈。如果麦克风录入了同一电路中扬声器的放大声音输出,那么就会听到音频反馈的嚎叫和尖叫声(在放大器的最大功率容量下),因为随机噪声被音频系统和房间的特性所过滤后,通过正反馈重新放大。<br />
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===音频与现场音频===<br />
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音频反馈(也称为声反馈,简称反馈,或拉森效应)是一种特殊的正反馈,当音频输入(例如,麦克风或吉他拾音器)和音频输出(例如,大声放大的扬声器)之间存在声音回路时,就会出现这种反馈。在这个例子中,麦克风接收到的信号被放大并从扬声器传出。然后,来自扬声器的声音可以再次被麦克风接收,进一步放大,然后再次通过扬声器传递出去。 所产生的声音的频率由传声器、放大器和扬声器的共振频率、房间的声学特性、传声器和扬声器的定向拾音和发射模式以及它们之间的距离决定。对于小型的扩声系统来说,这种声音很容易的体现的响亮的吱吱声或尖叫声。<br />
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在歌手或公众演讲者使用扩声系统或扩音系统的活动中,麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来,音频工程师使用各种电子设备,如均衡器或者自动反馈检测设备,来防止这些不受欢迎的尖叫声或尖叫声,这些声音影响了观众对活动的享受。另一方面,自20世纪60年代以来,摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果,有意制造吉他中的正反馈,以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈,但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中,他说,“我敢说任何人都找不到这样的唱片,除非是1922年这张用这种方式录制的老蓝调唱片。”<br />
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音频反馈的原理是由丹麦科学家Søren Absalon Larsen首先发现的。麦克风并不是唯一受此影响的传感器。录音板拾音器也会产生正反馈,通常是在100赫兹以下的低频范围内表现出低沉的轰鸣声。Jimi Hendrix是一个创新者,在他的吉他独奏中有意使用吉他正反馈来创造独特的声音效果。他帮助发展了电吉他演奏中音频反馈的可控性和音乐性,后来Brian May也是这种技术的著名支持者。<br />
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[[File:Adam Savage HOPE.jpg|thumb|right|220px|[[Video feedback]]【图12 视频反馈】.|链接=Special:FilePath/Adam_Savage_HOPE.jpg]]<br />
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===视频===<br />
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同样,如果一台摄像机对准一个正在显示摄像机自身信号的监控屏幕,那么通过正反馈就可以在屏幕上形成重复的图案。这种视频反馈效果在电视剧《神秘博士》前十季的开场白中就被使用了。<br />
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===开关===<br />
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In [[electrical switch]]es, including [[bimetallic strip]] based thermostats, the switch usually has hysteresis in the switching action. In these cases hysteresis is mechanically achieved via positive feedback within a tipping point mechanism. The positive feedback action minimises the length of time arcing occurs for during the switching and also holds the contacts in an open or closed state.<br />
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在电气开关中,包括双金属条型恒温器,开关通常在开关动作中具有滞后性。在这些情况下,滞后是通过一个临界点机构内的正反馈来实现的。正反馈作用可最大限度地减少开关过程中发生电弧的时间,并使触点保持在断开或闭合状态。<br />
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=== 生物学===<br />
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[[File:Positive Feedback- Childbirth (1).svg|thumb|生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。|链接=Special:FilePath/Positive_Feedback-_Childbirth_(1).svg]]<br />
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生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。<br />
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==== 生理学====<br />
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在生理学中可以找到一些正反馈系统的例子。<br />
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其中一个例子是分娩时宫缩的发生,称为弗格森反射。当宫缩发生时,激素催产素会引起神经刺激,刺激下丘脑产生更多的催产素,从而增加子宫收缩。这就导致宫缩的幅度和频率增加。<br />
<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders. {{ISBN|0-7216-3994-1}}</ref><br />
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另一个例子是血液凝固的过程。当受伤的组织释放出信号化学物质,激活血液中的血小板时,这个循环就启动了。被激活的血小板释放化学物质,激活更多的血小板,引起快速的级联反应,形成血栓。<ref name=Guyton1991/><br />
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哺乳也涉及正反馈,当婴儿吸吮乳头时,会有神经反应进入脊髓,并上传到大脑的下丘脑,然后刺激垂体产生更多的催乳素以产生更多的乳汁<ref name=Guyton1991/>。<br />
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在月经周期的卵泡期期间,雌激素的飙升会导致排卵<ref name=Guyton1991/>。<br />
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神经信号的产生是另一个例子,神经纤维的膜使钠离子通过钠通道轻微渗漏,导致膜电位的变化,进而引起更多通道的开放(Hodgkin循环)。所以,最初的轻微渗漏会导致钠渗漏的爆发,从而产生神经动作电位<ref name=Guyton1991/>。<br />
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在心脏的兴奋收缩耦合中,肌浆网膜中的兰尼碱受体检测到心肌细胞内钙离子的增加,该受体以正反馈生理反应将钙运出到细胞质中。<br />
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在大多数情况下,这种反馈循环最终会释放出反信号,从而抑制或破坏循环。分娩宫缩在宝宝离开母体时停止。化学物质分解血凝块。当婴儿不再需要被哺乳时,泌乳停止<ref name=Guyton1991/>。<br />
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====基因调控====<br />
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正反馈是基因调控中研究较好的一种现象,其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时,就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络,以证明双稳态的概念。<ref name=Hasty2002/><br />
正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用,因此,基因调控中的正反馈可以产生显著的生理结果。分子动力学中的随机运动加上正反馈可以引发有趣的效应,例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/> 这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中,如酶动力学或代谢途径。<ref name=Christoph2001/><br />
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==== 进化生物学 ====<br />
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在进化生物学中正反馈循环被用来描述生物进化中变化动态的各个方面。 例如,在宏观层面,Alfred J. Lotka(1945)认为,物种的演变最重要的是选择反馈能量流动以捕获越来越多的能源系统的能量。<ref name=Lotka1945/>在人类层面,Richard D. Alexander(1989)提出,人类群体之间和群体内部的社会竞争会影响智力的选择,从而时不时地会产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子<ref name=Crespi2004/>。通过与军备竞赛进行类比,给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/><br />
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[[File:Phanerozoic Biodiversity.svg|300px|right|thumb|显生宙[[生物多样性]]呈现稳定而非单调的增长,从接近于零一直增长到有几千个属。|链接=Special:FilePath/Phanerozoic_Biodiversity.svg]]<br />
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研究表明,在<font color="#32CD32"> 显生宙 ''',生物多样性的变化与双曲模型(广泛用于人口学和宏观社会学)的相关性要比指数模型和逻辑斯特模型(传统上用于人口生物学,并广泛用于生物多样性化石)的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈(更多的祖先,更多的后代)和资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为,生物多样性和人口曲线之间的相似性可能来自这样一个事实,即两者都是由双曲趋势(由正反馈产生)与周期性和随机性的动态干扰而产生的。<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref><br />
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==== 免疫系统====<br />
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细胞因子风暴,或称高细胞因子血症,是一种潜在的致命性免疫反应,表现为各种细胞因子水平高度升高,这是由细胞因子和免疫细胞之间的正反馈环组成。[36]在正常的免疫功能中,可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后,就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合,当B细胞的抗体与C3结合后,就会加快该B细胞分泌更多的抗体和更多的C3蛋白,从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
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====细胞凋亡====<br />
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细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程,其目的是清除长寿或受损的细胞。这一过程的失效与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活,它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时,无论效应子胱天蛋白酶的中间激活步骤数量有多少,这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/> 当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时,该过程呈现双稳态,从而模拟细胞的存活和死亡状态。<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref><br />
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=== 心理学===<br />
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Winner(1996)将有天赋的孩子描述为受到正反馈循环的驱动,这些反馈循环体现在他们自己的课程学习上,通过反馈自己的满意程度,从而进一步将他们的学习目标提高到更高水平等。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a,2009b)提出,神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释,工作记忆中的思维/表现输出被反馈到小脑,在那里被精简,然后再反馈到工作记忆中,从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/> <br />
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=== 经济学===<br />
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====市场上的社会影响====<br />
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事实证明,产品推荐和消费者先前的购买信息对消费者的选择影响很大,无论是音乐、电影、书籍、电子产品还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象(马太效应),即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
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====市场动向====<br />
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根据George Soros提出的反射性理论,价格变化是由一个正反馈过程驱动的,即投资者的预期受到价格变动的影响,因此他们的行为会强化这个方向的价格变动,直到价格的变化变得不可持续,于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
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==== 系统风险====<br />
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系统性风险是指放大效应或杠杆或正反馈过程给系统带来的风险。这通常是未知的,在某些条件下,这个过程会成倍放大,并迅速导致破坏性或混乱的行为。 庞氏骗局就是正反馈系统的一个很好的例子:来自新投资者的资金被用来支付异常高的回报,反过来又吸引了更多的新投资者,导致快速增长进而走向崩溃。W. Brian Arthur 也对经济中的正反馈进行了研究和著述(如W. Brian Arthur,1990)。Hyman Minsky提出了一个理论,认为某些信用扩张行为会使市场经济变成一个 "偏差放大系统",从而可能会突然崩溃,这有时被称为 "明斯基时刻"。<br />
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输入和输出明确分开的简单系统不容易发生系统性风险。 随着系统复杂性的增加,这种风险更容易发生,因为即使在详细的压力测试条件下,也更难看到或分析系统中所有可能的变量组合。 一个复杂系统的效率越高,就越容易发生系统性风险,因为只需要很小的偏差就可以破坏系统。 因此,设计良好的复杂系统一般都会有一些内在的功能来避免这种情况的发生,比如在系统内有少量的摩擦力,或阻力,或惯性,或时间延迟来使输出与输入脱钩。这些因素造成了低效率,但它们是避免不稳定的必要条件。<br />
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2010年的闪崩事件被归咎于高频交易(HFT)的做法,不过HFT是否真的会增加系统性风险仍然存在争议。<br />
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====人口与环境危机====<br />
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可以认为农业和人口之间处于一种正反馈模式,这意味着双方越来越强烈地推动彼此。有人认为,这种正反馈系统终将在某一时刻以灾难结束,因为现代农业正在耗尽所有容易获得的磷酸盐,并且进行高效的单一栽培,使得现代农业更容易受到系统性风险影响。<br />
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技术创新和人类人口也可以有类似的考虑,这也是过去人类人口明显的双曲线增长,而不是简单的指数增长的一个解释。<br />
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有人提出,由于人口和技术之间的二阶正反馈,增长速度正在加快。技术增长增加了土地对人的承载能力,从而导致人口增长,而这反过来又推动了技术的进一步增长。<br />
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==== 偏见、社会制度与贫困====<br />
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Gunnar Myrdal描述了一个不平等和贫困加剧的恶性循环,这就是所谓的”循环累积诱因”。<br />
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===气象学===<br />
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干旱通过正反馈效应加剧。缺雨会降低土壤湿度,从而杀死植物,使它们通过蒸腾作用释放更少的水分。这两个因素都限制了水蒸气从地表加到大气中的过程,并使吸收水分的干燥灰尘进入大气。水汽少了,既意味着露点温度低,白天的供暖效率也高,减少了大气中湿度导致云的形成的机会。最后,没有云,就不会有雨,这个正反馈循环就形成了。<br />
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=== 气候学===<br />
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气候中的"诱因 "可能会将气候系统推向变暖或变冷的方向,例如,大气中温室气体浓度的增加会导致地表变暖。诱因是气候系统的外部因素,而反馈是系统的内部过程。一些反馈机制与气候系统的其他部分相对孤立地发挥作用,而另一些则是紧密耦合的。气候系统的作用力、反馈和动态决定了气候变化的程度和速度。全球变暖中的主要正反馈是变暖使大气中的水汽量增加,进而导致进一步变暖。主要的负反馈来自Stefan-Boltzmann定律,从地球辐射到空间的热量与地球表面和大气温度的四次方成正比。<br />
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气候学中正反馈子系统的其他例子包括:<br />
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大气变暖会使冰融化,从而改变反照率,从而使大气进一步变暖。<br />
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甲烷水合物可能是不稳定的,所以海洋变暖可能会释放更多的温室气体之一的甲烷。<br />
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泥炭,天然存在于泥炭沼泽中,含有碳。当泥炭干燥时,它会分解,并可能额外燃烧。泥炭还会释放一氧化二氮。<br />
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全球变暖会影响云的分布。高空的云层会增强温室效应,而低空的云层则主要反射太阳光,对温度产生相反的影响。<br />
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政府间气候变化专门委员会(气专委)第四次评估报告指出,"人类活动的变暖可能导致一些突然或不可逆转的影响,这取决于气候变化的速度和程度"。<br />
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=== 社会学===<br />
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自我应验预言是信念和行为之间的一个社会正反馈循环: 如果有足够多的人相信某件事是真的,他们的行为就能让它变成真的,而对他们行为的观察又可能反过来增加信念。一个典型的例子是银行挤兑。<br />
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正反馈的另一个社会学例子是网络效应。当更多的人被鼓励加入一个网络时,这就增加了网络的覆盖面,因此网络扩张得越来越快。病毒视频就是网络效应的一个例子,在这个例子中,一个热门视频的链接被分享和再传播,确保更多的人看到这个视频,然后重新发布链接。这是许多社会现象的基础,包括庞氏骗局和连锁信。在许多情况下,人口量是反馈效应的限制因素。<br />
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=== 化学===<br />
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如果化学反应引起热量的释放,而反应本身在较高的温度下发生得更快,那么就很有可能出现正反馈。如果产生的热量没有足够快地从反应物中排除,就会发生热失控,并很快导致化学爆炸。<br />
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=== 自然保护===<br />
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许多野生动物被猎杀的原因是它们身体的某些部位可能相当有价值。目标物种越是接近灭绝,其身体部位的价格就越高。这就是正反馈的一个例子。<br />
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==参见==<br />
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* Chain reaction – Sequence of reactions 链式反应 -- -- 反应的顺序<br />
* Donella Meadows' twelve leverage points to intervene in a system Donella Meadows干预系统的十二个杠杆点<br />
* Hyperbolic growth 双曲增长<br />
* Reflexivity (social theory)反射性(社会理论)<br />
* Stability criterion稳定性标准<br />
* Strategic complements战略补充<br />
* System dynamics 系统动力学<br />
* Technological singularity – Hypothetical point in time at which technological growth becomes uncontrollable and irreversible 技术奇点 -- -- 假设技术增长变得不可控制和不可逆转的时间点<br />
* Thermal runaway 热失控<br />
* Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop. 恶性/恶性循环:在社会和金融系统中,是通过反馈循环自我强化的事件综合体。<br />
* Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour. 正强化:在操作性条件下,结果会增加行为的频率。<br />
* Praise of performance: a term often applied in the context of performance appraisal,although this usage is disputed 绩效表扬:这个词经常被应用于绩效评估中,尽管这种用法有争议。<br />
* Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage 自我强化反馈:系统动力学中使用的术语,以避免与 "表扬 "的用法相混淆。<br />
* Matthew effect – Effect originally observed by Robert K. Merton 马太效应 -- -- 罗伯特-K-默顿最初观察到的效应。<br />
* Self-fulfilling prophecy – Prediction that causes itself to become true 自证预言 -- -- 导致自己成为现实的预言<br />
* Virtuous circle and vicious circle 良性循环和恶性循环<br />
* Autocatalysis 自催化<br />
* Meander – Sinuous bend in a series in the channel of a river 蜿蜒曲折 -- -- 河道中一系列蜿蜒曲折的弯道。<br />
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==参考文献==<br />
{{Reflist|2}}<br />
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==拓展阅读==<br />
* Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.<br />
* Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.<br />
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本中文词条由[[用户:Solitude|Solitude]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%AD%A3%E5%8F%8D%E9%A6%88&diff=29638正反馈2022-03-26T09:39:19Z<p>唐糖糖:撤销唐糖糖(讨论)的版本29626</p>
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<div>{{#seo:<br />
|keywords=自相似性,共形对称,膨胀<br />
|description=在物理学、数学和统计学中,标度不变性是物体或者物理定律的一种特征,如果长度、能量或者其他变量的标度与一个公因子相乘,而不发生改变,因此也就代表某种普遍性。<br />
}}<br />
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[[File:Wiener process animated.gif|thumb|right|500px|<br />
维纳过程具有标度不变性。|链接=Special:FilePath/Wiener_process_animated.gif]]<br />
<br />
<br />
<br />
[[File:Herdwick Stampede.jpg|thumb|right|【图1:有时,警报或恐慌会通过正反馈在一群动物之间传播,从而引起踩踏事件。】.|链接=Special:FilePath/Herdwick_Stampede.jpg]]<br />
<br />
[[File:Stampede loop.png|thumb|【图2:Causal loop diagram that depicts the causes of a stampede as a positive feedback loop. 在因果环路图中,踩踏事件的发生是一个正反馈循环。】|链接=Special:FilePath/Stampede_loop.png]]<br />
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[[File:Birmingham Northern Rock bank run 2007.jpg|thumb|right|【图3:In sociology a network effect can quickly create the positive feedback of a bank run. The above photo is of the UK Northern Rock 2007 bank run. 在社会学中,网络效应可以迅速产生银行挤兑的正反馈效应。上图是2007年英国北岩银行挤兑事件的照片。】|链接=Special:FilePath/Birmingham_Northern_Rock_bank_run_2007.jpg]]<br />
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==回顾==<br />
'''Positive feedback''' ('''exacerbating feedback''', '''self-reinforcing feedback''') is a process that occurs in a [[feedback loop]] which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation.Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback.<ref name="theorymodelling" /> Both concepts play an important role in science and engineering, including biology, chemistry, and [[cybernetics]] .<br />
<br />
正反馈(加剧反馈,自我强化反馈) 是一种在反馈循环中加剧微小扰动影响的过程。也就是说,一个扰动对系统的影响包括它自身扰动幅度的增大。或者说,A会产生更多的B,而B又会产生更多的A,与之相反的是,[[负反馈]]指的是一个系统中,变化的结果会减少或抵消它自己的影响。<ref name="theorymodelling" />这两个概念在科学和工程等领域中发挥着重要作用,包括生物学、化学和控制论。<br />
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在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。<ref name="zuckerman" /><ref>Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". ''Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems''. Academic Press. p. 55. ISBN <bdi>9780127784557</bdi>. Archived from the original on 2017-01-03. <q>A positive feedback loop is one with an even number of negative influences [around the loop].</q></ref><ref name="zuckerman" /> 从结果到始发过程的反馈可以是直接的,也可以通过其他状态变量<ref name="theorymodelling" />。这样的系统可以给出丰富的定性行为,但反馈的瞬时信号是正向还是负向,对结果有极其重要的影响。<ref name="theorymodelling" /> 正反馈强化原过程,而负反馈调节原过程。在这个含义下,''正''和''负''指的是大于或小于零的循环收益,并不代表着最终结果或效果的正负性。<ref name=":0">{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>因此,正反馈的一个重要特点是小扰动变大。当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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===基础===<br />
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[[File:Ideal feedback model.svg|thumb|【图4:A basic feedback system can be represented by this block diagram. In the diagram the + symbol is an adder and A and B are arbitrary causal functions. 一个基本的反馈系统可以用这个框图来表示。在图中,+号是加法器,A和B是任意因果函数。】|链接=Special:FilePath/Ideal_feedback_model.svg]]<br />
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图中显示了一个简单的反馈回路。 如果环增益AB为正值,则存在'正'或'再生'反馈的条件。<br />
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<br />
如果函数A和B是线性的,且AB小于1,那么系统从输入到输出的整体增益是有限的,但当AB接近1时,系统的增益可以非常大。<ref name="smith"> Electronics circuits and devices second edition. Ralph J. Smith</ref> 在这种情况下,可以表明从输入到输出的整体或 "闭环 "增益为:<br />
<br />
:<math>G_c = A/(1-AB)</math><br />
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当AB>1时,系统是不稳定的,因此不具有明确的增益;增益可称为无限。<br />
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所以系统状态的变化根据反馈可以是收敛的,也可以是发散的。 而正反馈的结果是增强变化,因此小的扰动就可能导致大的变化。<br />
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对于一个当前处于平衡状态的系统,如果其状态的任何变化都发生了正反馈,从而造成了状态的不稳定,那么这个系统就是一个不稳定平衡的系统。使这种系统远离其平衡状态的力的大小是状态与平衡状态之间的距离的递增函数。<br />
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正反馈并不一定意味着平衡的不稳定性,例如,在正反馈结构中可能存在稳定的开关状态<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>。<br />
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=== 迟滞 ===<br />
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[[File:Hysteresis sharp curve.svg|thumb|【图5 Hysteresis causes the output value to depend on the history of the input 迟滞现象会导致输出值取决于输入的历史记录。】|链接=Special:FilePath/Hysteresis_sharp_curve.svg]]<br />
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[[File:Op-Amp Schmitt Trigger.svg|thumb|【图6 In a Schmitt trigger circuit, feedback to the non-inverting input of an amplifier pushes the output directly away from the applied voltage towards the maximum or minimum voltage the amplifier can generate. 在施密特触发器电路中,利用放大器的非反相输入端口产生的反馈,可以直接将电路的输出从原本的外加电压值推向到放大器所能产生的极值电压。】|链接=Special:FilePath/Op-Amp_Schmitt_Trigger.svg]]<br />
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在现实世界中,正反馈循环通常不会引起不断增长,而是通过某种限制效应来改变。根据Donella Meadows的说法:<br />
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正反馈回路是系统增长、爆炸、腐蚀和崩溃的根源。一个系统如果有一个不受控制的正反馈,最终将会自我毁灭。这就是为什么正反馈如此稀少的原因。通常情况下,负反馈迟早会发生。<ref>Donella Meadows, ''[http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf Leverage Points: Places to Intervene in a System]''2013-10-08 at the Wayback Machine, 1999</ref><br />
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[[迟滞]],即起点影响系统的终点的现象,可以通过正反馈产生。当反馈循环的增益高于1时,那么输出就会远离输入:如果大于输入,则向最近的正极限移动,而如果小于输入,则向最近的负极限移动。<br />
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一旦达到极限,它就会稳定下来。但是,如果输入超过极限,那么反馈将改变符号,输出将向相反的方向移动,直到达到相反的极限。因此,该系统表现出'''双稳态行为bistable behavior'''。<br />
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== 术语由来==<br />
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正反馈和负反馈这两个名词最早应用于反馈是在二战前。正反馈的概念随着再生电路的问世,在20世纪20年代已经出现。<br />
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Friis 和 Jensen在1924年描述了一种在电子放大器中发生的"回馈 "是正的情况,这一情况与他们顺便提到的负回馈作用相反。到了1934年,Harold Stephen Black在他的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法:<br />
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正反馈会增加放大器的增益,负反馈会降低增益<br />
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据Mindell(2002年)说,术语上的混乱是在这之后不久产生的:<br />
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“ ... ... Friis 和 Jensen 对 Black 在对"正反馈 "和 "负反馈 "的区分方法是一样的,都不是基于反馈本身的符号,而是基于它对放大器增益的影响。与之相反的是,当Nyquist和Bode基于Black的工作基础时,将负反馈称为符号相反的反馈。Black难以说服其他人相信他的发明的实用性,有一部分原因是在基本的定义问题上存在混乱。"<br />
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==实例与应用==<br />
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=== 电子电路===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|【图7 A vintage style regenerative radio receiver. Due to the controlled use of positive feedback, sufficient amplification can be derived from a single [[vacuum tube]] or valve (centre). 一个老式的再生无线电接收器。由于使用正反馈的控制,真空管或阀门(中心)就可以产生足够的放大效果。】|链接=Special:FilePath/Regenerartive_Receiver-S7300056.JPG]]<br />
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'''再生电路Regenerative circuit'''于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>,用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈,可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此,一个信号可以在一个阶段被放大20000甚至100000倍,而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定,开始振荡。无线电操作员必须不断地调整反馈量,以获得良好的接收效果。而现代无线电接收机采用超异构设计,多了许多放大级,去掉了正反馈并使其工作更稳定。<br />
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在再生无线电电路中产生的振荡还可以被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英),经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计,包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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许多电子电路,特别是放大器,都采用了负反馈。这降低了放大器的信号增益,但改善了它的线性度、输入阻抗、输出阻抗和带宽,并稳定了包括闭环增益等参数。同时,这些参数也变得不那么依赖于放大器件本身的细节,而更多地依赖于反馈元件,因为反馈元件一般不随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位:如果信号反馈失相,则反馈为负,如果相位一致,则反馈为正。对于需要使用负反馈放大器的设计者来说,引入负反馈放大器的问题是,电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°,那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波来做到这一点)。如果任何频率下的环增益(放大器增益与正反馈程度的乘积)大于1,那么放大器将在该频率下发生振荡(巴克豪森稳定性准则)。这种振荡有时被称为寄生振荡:在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化,前板(用户界面)的变化,甚至是由于人或其他导电物品的接近。<br />
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放大器可能会以示波器很难检测到的方式轻轻振荡,有时的振荡也可能非常大,只有非常扭曲或根本没有真正的信号,甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似,因此低频寄生振荡也被称为 "汽艇"。<br />
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【图8 The effect of using a Schmitt trigger (B) instead of a comparator (A) 使用施密特触发器(b)代替比较器(a)的效果】<br />
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许多常见的数字电路都采用正反馈。一般简单的布尔逻辑门通常只是依靠增益将数字信号电压从中间值推到代表布尔值0和1的值上,但许多更复杂的门都采用了反馈。当输入的模拟电压发生变化,但后期数字处理需要尖锐阈值时,施密特触发电路通过正反馈机制确保当输入电压轻微超过阈值时,输出电压可以巧妙而迅速地从一个逻辑状态转移到另一个逻辑状态。施密特触发器使用正反馈的一个必然结果是,如果输入电压再次缓慢下降,超过了相同的阈值,由于正反馈的机制,输出电压将保持在相同的逻辑状态而不改变。这种效应被称为滞后: 输入电压必须降到一个不同的、较低的阈值,才能“解锁”输出,并将其重置为原始数字。通过减小正反馈的程度,可以减小滞后宽度,但宽度不能被完全消除。施密特触发器在某种程度上是一个闭锁电路。<br />
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【图9 Positive feedback is a mechanism by which an output is enhanced, such as protein levels. However, in order to avoid any fluctuation in the protein level, the mechanism is inhibited stochastically (I), therefore when the concentration of the activated protein (A) is past the threshold ([I]), the loop mechanism is activated and the concentration of A increases exponentially if d[A]=k [A] 正反馈是一种增强输出的机制,如蛋白质水平。但为了避免蛋白质水平的波动,该机制是随机抑制的(I),因此只有当激活的蛋白质(A)浓度超过阈值([I])时,循环机制被激活,如果d[A]=k[A],A的浓度就会成倍增加。】<br />
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【图10 Illustration of an R-S ('reset-set') flip-flop made from two digital nor gates with positive feedback. Red and black mean logical '1' and '0', respectively. R-S("复位-设置")触发器的说明,由两个带正反馈的数字诺尔门组成。红色和黑色分别表示逻辑上的 "1 "和 "0"。】<br />
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电子触发器,或“锁存器” ,或“双稳态多谐振荡器” ,是一种由于高正反馈而不稳定于平衡或中间状态的电路。这样的双稳态电路是一位电子存储器的基础。 触发器使用一对放大器、晶体管或逻辑门相互连接,正反馈机制使得输入信号被去除后,电路可以维持在两种非平衡稳定状态中的一种,直到一个合适的替代信号重新作为输入,以改变电路状态。计算机随机存取存储器(RAM)可以用这种方式运作,每位存储器有一个锁存电路。<br />
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电子系统中发生'''热失控Thermal runaway'''的原因是,当电路的某些方面变得更热时,它被允许通过更多的电流,然后它越热,通过的电流就越多,这就使它更热一些,因此它又通过更多的电流。这种现象对有关器件来说通常是灾难性的。如果器件不得不在接近其最大功率处理能力的情况下工作,那么某些条件下就可能出现热失控,这通常可以通过精心设计来改进。<br />
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[[File:Technics SL-1210MK2.jpg|thumb|left|【图11 A phonograph turntable is prone to acoustic feedback. 留声机转盘容易受到声反馈的影响。】|链接=Special:FilePath/Technics_SL-1210MK2.jpg]]<br />
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音频和视频系统可以表现出正反馈。如果麦克风录入了同一电路中扬声器的放大声音输出,那么就会听到音频反馈的嚎叫和尖叫声(在放大器的最大功率容量下),因为随机噪声被音频系统和房间的特性所过滤后,通过正反馈重新放大。<br />
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===音频与现场音频===<br />
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音频反馈(也称为声反馈,简称反馈,或拉森效应)是一种特殊的正反馈,当音频输入(例如,麦克风或吉他拾音器)和音频输出(例如,大声放大的扬声器)之间存在声音回路时,就会出现这种反馈。在这个例子中,麦克风接收到的信号被放大并从扬声器传出。然后,来自扬声器的声音可以再次被麦克风接收,进一步放大,然后再次通过扬声器传递出去。 所产生的声音的频率由传声器、放大器和扬声器的共振频率、房间的声学特性、传声器和扬声器的定向拾音和发射模式以及它们之间的距离决定。对于小型的扩声系统来说,这种声音很容易的体现的响亮的吱吱声或尖叫声。<br />
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在歌手或公众演讲者使用扩声系统或扩音系统的活动中,麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来,音频工程师使用各种电子设备,如均衡器或者自动反馈检测设备,来防止这些不受欢迎的尖叫声或尖叫声,这些声音影响了观众对活动的享受。另一方面,自20世纪60年代以来,摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果,有意制造吉他中的正反馈,以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈,但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中,他说,“我敢说任何人都找不到这样的唱片,除非是1922年这张用这种方式录制的老蓝调唱片。”<br />
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音频反馈的原理是由丹麦科学家Søren Absalon Larsen首先发现的。麦克风并不是唯一受此影响的传感器。录音板拾音器也会产生正反馈,通常是在100赫兹以下的低频范围内表现出低沉的轰鸣声。Jimi Hendrix是一个创新者,在他的吉他独奏中有意使用吉他正反馈来创造独特的声音效果。他帮助发展了电吉他演奏中音频反馈的可控性和音乐性,后来Brian May也是这种技术的著名支持者。<br />
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[[File:Adam Savage HOPE.jpg|thumb|right|220px|[[Video feedback]]【图12 视频反馈】.|链接=Special:FilePath/Adam_Savage_HOPE.jpg]]<br />
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===视频===<br />
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同样,如果一台摄像机对准一个正在显示摄像机自身信号的监控屏幕,那么通过正反馈就可以在屏幕上形成重复的图案。这种视频反馈效果在电视剧《神秘博士》前十季的开场白中就被使用了。<br />
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===开关===<br />
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In [[electrical switch]]es, including [[bimetallic strip]] based thermostats, the switch usually has hysteresis in the switching action. In these cases hysteresis is mechanically achieved via positive feedback within a tipping point mechanism. The positive feedback action minimises the length of time arcing occurs for during the switching and also holds the contacts in an open or closed state.<br />
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在电气开关中,包括双金属条型恒温器,开关通常在开关动作中具有滞后性。在这些情况下,滞后是通过一个临界点机构内的正反馈来实现的。正反馈作用可最大限度地减少开关过程中发生电弧的时间,并使触点保持在断开或闭合状态。<br />
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=== 生物学===<br />
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[[File:Positive Feedback- Childbirth (1).svg|thumb|生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。|链接=Special:FilePath/Positive_Feedback-_Childbirth_(1).svg]]<br />
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生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。<br />
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==== 生理学====<br />
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在生理学中可以找到一些正反馈系统的例子。<br />
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其中一个例子是分娩时宫缩的发生,称为弗格森反射。当宫缩发生时,激素催产素会引起神经刺激,刺激下丘脑产生更多的催产素,从而增加子宫收缩。这就导致宫缩的幅度和频率增加。<br />
<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders. {{ISBN|0-7216-3994-1}}</ref><br />
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另一个例子是血液凝固的过程。当受伤的组织释放出信号化学物质,激活血液中的血小板时,这个循环就启动了。被激活的血小板释放化学物质,激活更多的血小板,引起快速的级联反应,形成血栓。<ref name=Guyton1991/><br />
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哺乳也涉及正反馈,当婴儿吸吮乳头时,会有神经反应进入脊髓,并上传到大脑的下丘脑,然后刺激垂体产生更多的催乳素以产生更多的乳汁<ref name=Guyton1991/>。<br />
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在月经周期的卵泡期期间,雌激素的飙升会导致排卵<ref name=Guyton1991/>。<br />
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神经信号的产生是另一个例子,神经纤维的膜使钠离子通过钠通道轻微渗漏,导致膜电位的变化,进而引起更多通道的开放(Hodgkin循环)。所以,最初的轻微渗漏会导致钠渗漏的爆发,从而产生神经动作电位<ref name=Guyton1991/>。<br />
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在心脏的兴奋收缩耦合中,肌浆网膜中的兰尼碱受体检测到心肌细胞内钙离子的增加,该受体以正反馈生理反应将钙运出到细胞质中。<br />
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在大多数情况下,这种反馈循环最终会释放出反信号,从而抑制或破坏循环。分娩宫缩在宝宝离开母体时停止。化学物质分解血凝块。当婴儿不再需要被哺乳时,泌乳停止<ref name=Guyton1991/>。<br />
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====基因调控====<br />
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正反馈是基因调控中研究较好的一种现象,其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时,就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络,以证明双稳态的概念。<ref name=Hasty2002/><br />
正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用,因此,基因调控中的正反馈可以产生显著的生理结果。分子动力学中的随机运动加上正反馈可以引发有趣的效应,例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/> 这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中,如酶动力学或代谢途径。<ref name=Christoph2001/><br />
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==== 进化生物学 ====<br />
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在进化生物学中正反馈循环被用来描述生物进化中变化动态的各个方面。 例如,在宏观层面,Alfred J. Lotka(1945)认为,物种的演变最重要的是选择反馈能量流动以捕获越来越多的能源系统的能量。<ref name=Lotka1945/>在人类层面,Richard D. Alexander(1989)提出,人类群体之间和群体内部的社会竞争会影响智力的选择,从而时不时地会产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子<ref name=Crespi2004/>。通过与军备竞赛进行类比,给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/><br />
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[[File:Phanerozoic Biodiversity.svg|300px|right|thumb|显生宙[[生物多样性]]呈现稳定而非单调的增长,从接近于零一直增长到有几千个属。|链接=Special:FilePath/Phanerozoic_Biodiversity.svg]]<br />
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研究表明,在<font color="#32CD32"> 显生宙 ''',生物多样性的变化与双曲模型(广泛用于人口学和宏观社会学)的相关性要比指数模型和逻辑斯特模型(传统上用于人口生物学,并广泛用于生物多样性化石)的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈(更多的祖先,更多的后代)和资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为,生物多样性和人口曲线之间的相似性可能来自这样一个事实,即两者都是由双曲趋势(由正反馈产生)与周期性和随机性的动态干扰而产生的。<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref><br />
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==== 免疫系统====<br />
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细胞因子风暴,或称高细胞因子血症,是一种潜在的致命性免疫反应,表现为各种细胞因子水平高度升高,这是由细胞因子和免疫细胞之间的正反馈环组成。[36]在正常的免疫功能中,可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后,就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合,当B细胞的抗体与C3结合后,就会加快该B细胞分泌更多的抗体和更多的C3蛋白,从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
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====细胞凋亡====<br />
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细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程,其目的是清除长寿或受损的细胞。这一过程的失效与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活,它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时,无论效应子胱天蛋白酶的中间激活步骤数量有多少,这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/> 当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时,该过程呈现双稳态,从而模拟细胞的存活和死亡状态。<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref><br />
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=== 心理学===<br />
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Winner(1996)将有天赋的孩子描述为受到正反馈循环的驱动,这些反馈循环体现在他们自己的课程学习上,通过反馈自己的满意程度,从而进一步将他们的学习目标提高到更高水平等。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a,2009b)提出,神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释,工作记忆中的思维/表现输出被反馈到小脑,在那里被精简,然后再反馈到工作记忆中,从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/> <br />
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=== 经济学===<br />
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====市场上的社会影响====<br />
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事实证明,产品推荐和消费者先前的购买信息对消费者的选择影响很大,无论是音乐、电影、书籍、电子产品还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象(马太效应),即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
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====市场动向====<br />
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根据George Soros提出的反射性理论,价格变化是由一个正反馈过程驱动的,即投资者的预期受到价格变动的影响,因此他们的行为会强化这个方向的价格变动,直到价格的变化变得不可持续,于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
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==== 系统风险====<br />
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系统性风险是指放大效应或杠杆或正反馈过程给系统带来的风险。这通常是未知的,在某些条件下,这个过程会成倍放大,并迅速导致破坏性或混乱的行为。 庞氏骗局就是正反馈系统的一个很好的例子:来自新投资者的资金被用来支付异常高的回报,反过来又吸引了更多的新投资者,导致快速增长进而走向崩溃。W. Brian Arthur 也对经济中的正反馈进行了研究和著述(如W. Brian Arthur,1990)。Hyman Minsky提出了一个理论,认为某些信用扩张行为会使市场经济变成一个 "偏差放大系统",从而可能会突然崩溃,这有时被称为 "明斯基时刻"。<br />
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输入和输出明确分开的简单系统不容易发生系统性风险。 随着系统复杂性的增加,这种风险更容易发生,因为即使在详细的压力测试条件下,也更难看到或分析系统中所有可能的变量组合。 一个复杂系统的效率越高,就越容易发生系统性风险,因为只需要很小的偏差就可以破坏系统。 因此,设计良好的复杂系统一般都会有一些内在的功能来避免这种情况的发生,比如在系统内有少量的摩擦力,或阻力,或惯性,或时间延迟来使输出与输入脱钩。这些因素造成了低效率,但它们是避免不稳定的必要条件。<br />
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2010年的闪崩事件被归咎于高频交易(HFT)的做法,不过HFT是否真的会增加系统性风险仍然存在争议。<br />
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====人口与环境危机====<br />
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可以认为农业和人口之间处于一种正反馈模式,这意味着双方越来越强烈地推动彼此。有人认为,这种正反馈系统终将在某一时刻以灾难结束,因为现代农业正在耗尽所有容易获得的磷酸盐,并且进行高效的单一栽培,使得现代农业更容易受到系统性风险影响。<br />
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技术创新和人类人口也可以有类似的考虑,这也是过去人类人口明显的双曲线增长,而不是简单的指数增长的一个解释。<br />
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有人提出,由于人口和技术之间的二阶正反馈,增长速度正在加快。技术增长增加了土地对人的承载能力,从而导致人口增长,而这反过来又推动了技术的进一步增长。<br />
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==== 偏见、社会制度与贫困====<br />
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Gunnar Myrdal描述了一个不平等和贫困加剧的恶性循环,这就是所谓的”循环累积诱因”。<br />
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===气象学===<br />
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干旱通过正反馈效应加剧。缺雨会降低土壤湿度,从而杀死植物,使它们通过蒸腾作用释放更少的水分。这两个因素都限制了水蒸气从地表加到大气中的过程,并使吸收水分的干燥灰尘进入大气。水汽少了,既意味着露点温度低,白天的供暖效率也高,减少了大气中湿度导致云的形成的机会。最后,没有云,就不会有雨,这个正反馈循环就形成了。<br />
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=== 气候学===<br />
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气候中的"诱因 "可能会将气候系统推向变暖或变冷的方向,例如,大气中温室气体浓度的增加会导致地表变暖。诱因是气候系统的外部因素,而反馈是系统的内部过程。一些反馈机制与气候系统的其他部分相对孤立地发挥作用,而另一些则是紧密耦合的。气候系统的作用力、反馈和动态决定了气候变化的程度和速度。全球变暖中的主要正反馈是变暖使大气中的水汽量增加,进而导致进一步变暖。主要的负反馈来自Stefan-Boltzmann定律,从地球辐射到空间的热量与地球表面和大气温度的四次方成正比。<br />
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气候学中正反馈子系统的其他例子包括:<br />
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大气变暖会使冰融化,从而改变反照率,从而使大气进一步变暖。<br />
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甲烷水合物可能是不稳定的,所以海洋变暖可能会释放更多的温室气体之一的甲烷。<br />
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泥炭,天然存在于泥炭沼泽中,含有碳。当泥炭干燥时,它会分解,并可能额外燃烧。泥炭还会释放一氧化二氮。<br />
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全球变暖会影响云的分布。高空的云层会增强温室效应,而低空的云层则主要反射太阳光,对温度产生相反的影响。<br />
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政府间气候变化专门委员会(气专委)第四次评估报告指出,"人类活动的变暖可能导致一些突然或不可逆转的影响,这取决于气候变化的速度和程度"。<br />
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=== 社会学===<br />
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自我应验预言是信念和行为之间的一个社会正反馈循环: 如果有足够多的人相信某件事是真的,他们的行为就能让它变成真的,而对他们行为的观察又可能反过来增加信念。一个典型的例子是银行挤兑。<br />
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正反馈的另一个社会学例子是网络效应。当更多的人被鼓励加入一个网络时,这就增加了网络的覆盖面,因此网络扩张得越来越快。病毒视频就是网络效应的一个例子,在这个例子中,一个热门视频的链接被分享和再传播,确保更多的人看到这个视频,然后重新发布链接。这是许多社会现象的基础,包括庞氏骗局和连锁信。在许多情况下,人口量是反馈效应的限制因素。<br />
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=== 化学===<br />
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如果化学反应引起热量的释放,而反应本身在较高的温度下发生得更快,那么就很有可能出现正反馈。如果产生的热量没有足够快地从反应物中排除,就会发生热失控,并很快导致化学爆炸。<br />
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=== 自然保护===<br />
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许多野生动物被猎杀的原因是它们身体的某些部位可能相当有价值。目标物种越是接近灭绝,其身体部位的价格就越高。这就是正反馈的一个例子。<br />
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==参见==<br />
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* Chain reaction – Sequence of reactions 链式反应 -- -- 反应的顺序<br />
* Donella Meadows' twelve leverage points to intervene in a system Donella Meadows干预系统的十二个杠杆点<br />
* Hyperbolic growth 双曲增长<br />
* Reflexivity (social theory)反射性(社会理论)<br />
* Stability criterion稳定性标准<br />
* Strategic complements战略补充<br />
* System dynamics 系统动力学<br />
* Technological singularity – Hypothetical point in time at which technological growth becomes uncontrollable and irreversible 技术奇点 -- -- 假设技术增长变得不可控制和不可逆转的时间点<br />
* Thermal runaway 热失控<br />
* Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop. 恶性/恶性循环:在社会和金融系统中,是通过反馈循环自我强化的事件综合体。<br />
* Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour. 正强化:在操作性条件下,结果会增加行为的频率。<br />
* Praise of performance: a term often applied in the context of performance appraisal,although this usage is disputed 绩效表扬:这个词经常被应用于绩效评估中,尽管这种用法有争议。<br />
* Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage 自我强化反馈:系统动力学中使用的术语,以避免与 "表扬 "的用法相混淆。<br />
* Matthew effect – Effect originally observed by Robert K. Merton 马太效应 -- -- 罗伯特-K-默顿最初观察到的效应。<br />
* Self-fulfilling prophecy – Prediction that causes itself to become true 自证预言 -- -- 导致自己成为现实的预言<br />
* Virtuous circle and vicious circle 良性循环和恶性循环<br />
* Autocatalysis 自催化<br />
* Meander – Sinuous bend in a series in the channel of a river 蜿蜒曲折 -- -- 河道中一系列蜿蜒曲折的弯道。<br />
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==参考文献==<br />
{{Reflist|2}}<br />
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==拓展阅读==<br />
* Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.<br />
* Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.<br />
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本中文词条由[[用户:Solitude|Solitude]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%AD%A3%E5%8F%8D%E9%A6%88&diff=29633正反馈2022-03-26T09:29:51Z<p>唐糖糖:撤销唐糖糖(讨论)的版本29629</p>
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<div>{{#seo:<br />
|keywords=反馈,正反馈,Positive feedback,加剧反馈,自我强化反馈<br />
|description=在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。正反馈的一个重要特点是小扰动变大,当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
}}<br />
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[[File:Herdwick Stampede.jpg|thumb|right|图1:有时,警报或恐慌会通过正反馈在一群动物之间传播,从而引起踩踏事件。]]<br />
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[[File:Stampede loop.png|thumb|图2:在因果环路图中,踩踏事件的发生是一个正反馈循环。]]<br />
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[[File:Birmingham Northern Rock bank run 2007.jpg|thumb|right|图3:在社会学中,网络效应可以迅速产生银行挤兑的正反馈效应。上图是2007年英国北岩银行挤兑事件的照片。]]<br />
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==回顾==<br />
'''Positive feedback''' ('''exacerbating feedback''', '''self-reinforcing feedback''') is a process that occurs in a [[feedback loop]] which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation.Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback.<ref name="theorymodelling" /> Both concepts play an important role in science and engineering, including biology, chemistry, and [[cybernetics]] .<br />
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正反馈(加剧反馈,自我强化反馈) 是一种在反馈循环中加剧微小扰动影响的过程。也就是说,一个扰动对系统的影响包括它自身扰动幅度的增大。或者说,A会产生更多的B,而B又会产生更多的A,与之相反的是,[[负反馈]]指的是一个系统中,变化的结果会减少或抵消它自己的影响。<ref name="theorymodelling" />这两个概念在科学和工程等领域中发挥着重要作用,包括生物学、化学和控制论。<br />
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在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。<ref name="zuckerman" /><ref>Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". ''Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems''. Academic Press. p. 55. ISBN <bdi>9780127784557</bdi>. Archived from the original on 2017-01-03. <q>A positive feedback loop is one with an even number of negative influences [around the loop].</q></ref><ref name="zuckerman" /> 从结果到始发过程的反馈可以是直接的,也可以通过其他状态变量<ref name="theorymodelling" />。这样的系统可以给出丰富的定性行为,但反馈的瞬时信号是正向还是负向,对结果有极其重要的影响。<ref name="theorymodelling" /> 正反馈强化原过程,而负反馈调节原过程。在这个含义下,''正''和''负''指的是大于或小于零的循环收益,并不代表着最终结果或效果的正负性。<ref name=":0">{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>因此,正反馈的一个重要特点是小扰动变大。当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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===基础===<br />
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[[File:Ideal feedback model.svg|thumb|图4:一个基本的反馈系统可以用这个框图来表示。在图中,+号是加法器,A和B是任意因果函数。]]<br />
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图中显示了一个简单的反馈回路。 如果环增益AB为正值,则存在'正'或'再生'反馈的条件。<br />
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如果函数A和B是线性的,且AB小于1,那么系统从输入到输出的整体增益是有限的,但当AB接近1时,系统的增益可以非常大。<ref name="smith"> Electronics circuits and devices second edition. Ralph J. Smith</ref> 在这种情况下,可以表明从输入到输出的整体或 "闭环 "增益为:<br />
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:<math>G_c = A/(1-AB)</math><br />
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当AB>1时,系统是不稳定的,因此不具有明确的增益;增益可称为无限。<br />
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所以系统状态的变化根据反馈可以是收敛的,也可以是发散的。 而正反馈的结果是增强变化,因此小的扰动就可能导致大的变化。<br />
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对于一个当前处于平衡状态的系统,如果其状态的任何变化都发生了正反馈,从而造成了状态的不稳定,那么这个系统就是一个不稳定平衡的系统。使这种系统远离其平衡状态的力的大小是状态与平衡状态之间的距离的递增函数。<br />
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正反馈并不一定意味着平衡的不稳定性,例如,在正反馈结构中可能存在稳定的开关状态<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>。<br />
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=== 迟滞 ===<br />
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[[File:Hysteresis sharp curve.svg|thumb|图5:迟滞现象会导致输出值取决于输入的历史记录。]]<br />
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[[File:Op-Amp Schmitt Trigger.svg|thumb|图6:在施密特触发器电路中,利用放大器的非反相输入端口产生的反馈,可以直接将电路的输出从原本的外加电压值推向到放大器所能产生的极值电压。]]<br />
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在现实世界中,正反馈循环通常不会引起不断增长,而是通过某种限制效应来改变。根据Donella Meadows的说法:<br />
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正反馈回路是系统增长、爆炸、腐蚀和崩溃的根源。一个系统如果有一个不受控制的正反馈,最终将会自我毁灭。这就是为什么正反馈如此稀少的原因。通常情况下,负反馈迟早会发生。<ref>Donella Meadows, ''[http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf Leverage Points: Places to Intervene in a System]''2013-10-08 at the Wayback Machine, 1999</ref><br />
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[[迟滞]],即起点影响系统的终点的现象,可以通过正反馈产生。当反馈循环的增益高于1时,那么输出就会远离输入:如果大于输入,则向最近的正极限移动,而如果小于输入,则向最近的负极限移动。<br />
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一旦达到极限,它就会稳定下来。但是,如果输入超过极限,那么反馈将改变符号,输出将向相反的方向移动,直到达到相反的极限。因此,该系统表现出'''双稳态行为bistable behavior'''。<br />
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== 术语由来==<br />
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正反馈和负反馈这两个名词最早应用于反馈是在二战前。正反馈的概念随着再生电路的问世,在20世纪20年代已经出现。<br />
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Friis 和 Jensen在1924年描述了一种在电子放大器中发生的"回馈 "是正的情况,这一情况与他们顺便提到的负回馈作用相反。到了1934年,Harold Stephen Black在他的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法:<br />
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正反馈会增加放大器的增益,负反馈会降低增益<br />
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据Mindell(2002年)说,术语上的混乱是在这之后不久产生的:<br />
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“ ... ... Friis 和 Jensen 对 Black 在对"正反馈 "和 "负反馈 "的区分方法是一样的,都不是基于反馈本身的符号,而是基于它对放大器增益的影响。与之相反的是,当Nyquist和Bode基于Black的工作基础时,将负反馈称为符号相反的反馈。Black难以说服其他人相信他的发明的实用性,有一部分原因是在基本的定义问题上存在混乱。"<br />
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==实例与应用==<br />
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=== 电子电路===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|图7:一个老式的再生无线电接收器。由于使用正反馈的控制,真空管或阀门(中心)就可以产生足够的放大效果。]]<br />
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'''再生电路Regenerative circuit'''于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>,用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈,可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此,一个信号可以在一个阶段被放大20000甚至100000倍,而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定,开始振荡。无线电操作员必须不断地调整反馈量,以获得良好的接收效果。而现代无线电接收机采用超异构设计,多了许多放大级,去掉了正反馈并使其工作更稳定。<br />
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在再生无线电电路中产生的振荡还可以被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英),经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计,包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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许多电子电路,特别是放大器,都采用了负反馈。这降低了放大器的信号增益,但改善了它的线性度、输入阻抗、输出阻抗和带宽,并稳定了包括闭环增益等参数。同时,这些参数也变得不那么依赖于放大器件本身的细节,而更多地依赖于反馈元件,因为反馈元件一般不随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位:如果信号反馈失相,则反馈为负,如果相位一致,则反馈为正。对于需要使用负反馈放大器的设计者来说,引入负反馈放大器的问题是,电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°,那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波来做到这一点)。如果任何频率下的环增益(放大器增益与正反馈程度的乘积)大于1,那么放大器将在该频率下发生振荡(巴克豪森稳定性准则)。这种振荡有时被称为寄生振荡:在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化,前板(用户界面)的变化,甚至是由于人或其他导电物品的接近。<br />
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放大器可能会以示波器很难检测到的方式轻轻振荡,有时的振荡也可能非常大,只有非常扭曲或根本没有真正的信号,甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似,因此低频寄生振荡也被称为 "汽艇"。<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|图8:使用施密特触发器(b)代替比较器(a)的效果]]<br />
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许多常见的数字电路都采用正反馈。一般简单的布尔逻辑门通常只是依靠增益将数字信号电压从中间值推到代表布尔值0和1的值上,但许多更复杂的门都采用了反馈。当输入的模拟电压发生变化,但后期数字处理需要尖锐阈值时,施密特触发电路通过正反馈机制确保当输入电压轻微超过阈值时,输出电压可以巧妙而迅速地从一个逻辑状态转移到另一个逻辑状态。施密特触发器使用正反馈的一个必然结果是,如果输入电压再次缓慢下降,超过了相同的阈值,由于正反馈的机制,输出电压将保持在相同的逻辑状态而不改变。这种效应被称为滞后: 输入电压必须降到一个不同的、较低的阈值,才能“解锁”输出,并将其重置为原始数字。通过减小正反馈的程度,可以减小滞后宽度,但宽度不能被完全消除。施密特触发器在某种程度上是一个闭锁电路。<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|图9:正反馈是一种增强输出的机制,如蛋白质水平。但为了避免蛋白质水平的波动,该机制是随机抑制的(I),因此只有当激活的蛋白质(A)浓度超过阈值([I])时,循环机制被激活,如果d[A]=k[A],A的浓度就会成倍增加。]]<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|图10 :R-S("复位-设置")触发器的说明,由两个带正反馈的数字诺尔门组成。红色和黑色分别表示逻辑上的 "1 "和 "0"。]]<br />
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电子触发器,或“锁存器” ,或“双稳态多谐振荡器” ,是一种由于高正反馈而不稳定于平衡或中间状态的电路。这样的双稳态电路是一位电子存储器的基础。 触发器使用一对放大器、晶体管或逻辑门相互连接,正反馈机制使得输入信号被去除后,电路可以维持在两种非平衡稳定状态中的一种,直到一个合适的替代信号重新作为输入,以改变电路状态。计算机随机存取存储器(RAM)可以用这种方式运作,每位存储器有一个锁存电路。<br />
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电子系统中发生'''热失控Thermal runaway'''的原因是,当电路的某些方面变得更热时,它被允许通过更多的电流,然后它越热,通过的电流就越多,这就使它更热一些,因此它又通过更多的电流。这种现象对有关器件来说通常是灾难性的。如果器件不得不在接近其最大功率处理能力的情况下工作,那么某些条件下就可能出现热失控,这通常可以通过精心设计来改进。<br />
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[[File:Technics SL-1210MK2.jpg|thumb|left|图11:A phonograph turntable is prone to acoustic feedback. 留声机转盘容易受到声反馈的影响。]]<br />
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音频和视频系统可以表现出正反馈。如果麦克风录入了同一电路中扬声器的放大声音输出,那么就会听到音频反馈的嚎叫和尖叫声(在放大器的最大功率容量下),因为随机噪声被音频系统和房间的特性所过滤后,通过正反馈重新放大。<br />
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===音频与现场音频===<br />
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音频反馈(也称为声反馈,简称反馈,或拉森效应)是一种特殊的正反馈,当音频输入(例如,麦克风或吉他拾音器)和音频输出(例如,大声放大的扬声器)之间存在声音回路时,就会出现这种反馈。在这个例子中,麦克风接收到的信号被放大并从扬声器传出。然后,来自扬声器的声音可以再次被麦克风接收,进一步放大,然后再次通过扬声器传递出去。 所产生的声音的频率由传声器、放大器和扬声器的共振频率、房间的声学特性、传声器和扬声器的定向拾音和发射模式以及它们之间的距离决定。对于小型的扩声系统来说,这种声音很容易的体现的响亮的吱吱声或尖叫声。<br />
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在歌手或公众演讲者使用扩声系统或扩音系统的活动中,麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来,音频工程师使用各种电子设备,如均衡器或者自动反馈检测设备,来防止这些不受欢迎的尖叫声或尖叫声,这些声音影响了观众对活动的享受。另一方面,自20世纪60年代以来,摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果,有意制造吉他中的正反馈,以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈,但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中,他说,“我敢说任何人都找不到这样的唱片,除非是1922年这张用这种方式录制的老蓝调唱片。”<br />
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音频反馈的原理是由丹麦科学家Søren Absalon Larsen首先发现的。麦克风并不是唯一受此影响的传感器。录音板拾音器也会产生正反馈,通常是在100赫兹以下的低频范围内表现出低沉的轰鸣声。Jimi Hendrix是一个创新者,在他的吉他独奏中有意使用吉他正反馈来创造独特的声音效果。他帮助发展了电吉他演奏中音频反馈的可控性和音乐性,后来Brian May也是这种技术的著名支持者。<br />
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[[File:Adam Savage HOPE.jpg|thumb|right|220px|图12:视频反馈]]<br />
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===视频===<br />
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同样,如果一台摄像机对准一个正在显示摄像机自身信号的监控屏幕,那么通过正反馈就可以在屏幕上形成重复的图案。这种视频反馈效果在电视剧《神秘博士》前十季的开场白中就被使用了。<br />
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===开关===<br />
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In [[electrical switch]]es, including [[bimetallic strip]] based thermostats, the switch usually has hysteresis in the switching action. In these cases hysteresis is mechanically achieved via positive feedback within a tipping point mechanism. The positive feedback action minimises the length of time arcing occurs for during the switching and also holds the contacts in an open or closed state.<br />
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在电气开关中,包括双金属条型恒温器,开关通常在开关动作中具有滞后性。在这些情况下,滞后是通过一个临界点机构内的正反馈来实现的。正反馈作用可最大限度地减少开关过程中发生电弧的时间,并使触点保持在断开或闭合状态。<br />
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=== 生物学===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。]]<br />
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生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。<br />
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==== 生理学====<br />
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在生理学中可以找到一些正反馈系统的例子。<br />
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* <br />
其中一个例子是分娩时宫缩的发生,称为弗格森反射。当宫缩发生时,激素催产素会引起神经刺激,刺激下丘脑产生更多的催产素,从而增加子宫收缩。这就导致宫缩的幅度和频率增加。<br />
<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders. {{ISBN|0-7216-3994-1}}</ref><br />
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另一个例子是血液凝固的过程。当受伤的组织释放出信号化学物质,激活血液中的血小板时,这个循环就启动了。被激活的血小板释放化学物质,激活更多的血小板,引起快速的级联反应,形成血栓。<ref name=Guyton1991/><br />
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哺乳也涉及正反馈,当婴儿吸吮乳头时,会有神经反应进入脊髓,并上传到大脑的下丘脑,然后刺激垂体产生更多的催乳素以产生更多的乳汁<ref name=Guyton1991/>。<br />
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在月经周期的卵泡期期间,雌激素的飙升会导致排卵<ref name=Guyton1991/>。<br />
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神经信号的产生是另一个例子,神经纤维的膜使钠离子通过钠通道轻微渗漏,导致膜电位的变化,进而引起更多通道的开放(Hodgkin循环)。所以,最初的轻微渗漏会导致钠渗漏的爆发,从而产生神经动作电位<ref name=Guyton1991/>。<br />
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在心脏的兴奋收缩耦合中,肌浆网膜中的兰尼碱受体检测到心肌细胞内钙离子的增加,该受体以正反馈生理反应将钙运出到细胞质中。<br />
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在大多数情况下,这种反馈循环最终会释放出反信号,从而抑制或破坏循环。分娩宫缩在宝宝离开母体时停止。化学物质分解血凝块。当婴儿不再需要被哺乳时,泌乳停止<ref name=Guyton1991/>。<br />
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====基因调控====<br />
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正反馈是基因调控中研究较好的一种现象,其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时,就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络,以证明双稳态的概念。<ref name=Hasty2002/><br />
正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用,因此,基因调控中的正反馈可以产生显著的生理结果。分子动力学中的随机运动加上正反馈可以引发有趣的效应,例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/> 这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中,如酶动力学或代谢途径。<ref name=Christoph2001/><br />
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==== 进化生物学 ====<br />
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在进化生物学中正反馈循环被用来描述生物进化中变化动态的各个方面。 例如,在宏观层面,Alfred J. Lotka(1945)认为,物种的演变最重要的是选择反馈能量流动以捕获越来越多的能源系统的能量。<ref name=Lotka1945/>在人类层面,Richard D. Alexander(1989)提出,人类群体之间和群体内部的社会竞争会影响智力的选择,从而时不时地会产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子<ref name=Crespi2004/>。通过与军备竞赛进行类比,给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/><br />
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[[File:Phanerozoic Biodiversity.svg|300px|right|thumb|显生宙[[生物多样性]]呈现稳定而非单调的增长,从接近于零一直增长到有几千个属。|链接=Special:FilePath/Phanerozoic_Biodiversity.svg]]<br />
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研究表明,在<font color="#32CD32"> 显生宙 ''',生物多样性的变化与双曲模型(广泛用于人口学和宏观社会学)的相关性要比指数模型和逻辑斯特模型(传统上用于人口生物学,并广泛用于生物多样性化石)的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈(更多的祖先,更多的后代)和资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为,生物多样性和人口曲线之间的相似性可能来自这样一个事实,即两者都是由双曲趋势(由正反馈产生)与周期性和随机性的动态干扰而产生的。<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref><br />
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==== 免疫系统====<br />
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细胞因子风暴,或称高细胞因子血症,是一种潜在的致命性免疫反应,表现为各种细胞因子水平高度升高,这是由细胞因子和免疫细胞之间的正反馈环组成。[36]在正常的免疫功能中,可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后,就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合,当B细胞的抗体与C3结合后,就会加快该B细胞分泌更多的抗体和更多的C3蛋白,从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
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====细胞凋亡====<br />
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细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程,其目的是清除长寿或受损的细胞。这一过程的失效与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活,它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时,无论效应子胱天蛋白酶的中间激活步骤数量有多少,这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/> 当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时,该过程呈现双稳态,从而模拟细胞的存活和死亡状态。<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref><br />
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=== 心理学===<br />
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Winner(1996)将有天赋的孩子描述为受到正反馈循环的驱动,这些反馈循环体现在他们自己的课程学习上,通过反馈自己的满意程度,从而进一步将他们的学习目标提高到更高水平等。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a,2009b)提出,神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释,工作记忆中的思维/表现输出被反馈到小脑,在那里被精简,然后再反馈到工作记忆中,从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/> <br />
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=== 经济学===<br />
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====市场上的社会影响====<br />
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事实证明,产品推荐和消费者先前的购买信息对消费者的选择影响很大,无论是音乐、电影、书籍、电子产品还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象(马太效应),即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
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====市场动向====<br />
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根据George Soros提出的反射性理论,价格变化是由一个正反馈过程驱动的,即投资者的预期受到价格变动的影响,因此他们的行为会强化这个方向的价格变动,直到价格的变化变得不可持续,于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
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==== 系统风险====<br />
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系统性风险是指放大效应或杠杆或正反馈过程给系统带来的风险。这通常是未知的,在某些条件下,这个过程会成倍放大,并迅速导致破坏性或混乱的行为。 庞氏骗局就是正反馈系统的一个很好的例子:来自新投资者的资金被用来支付异常高的回报,反过来又吸引了更多的新投资者,导致快速增长进而走向崩溃。W. Brian Arthur 也对经济中的正反馈进行了研究和著述(如W. Brian Arthur,1990)。Hyman Minsky提出了一个理论,认为某些信用扩张行为会使市场经济变成一个 "偏差放大系统",从而可能会突然崩溃,这有时被称为 "明斯基时刻"。<br />
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输入和输出明确分开的简单系统不容易发生系统性风险。 随着系统复杂性的增加,这种风险更容易发生,因为即使在详细的压力测试条件下,也更难看到或分析系统中所有可能的变量组合。 一个复杂系统的效率越高,就越容易发生系统性风险,因为只需要很小的偏差就可以破坏系统。 因此,设计良好的复杂系统一般都会有一些内在的功能来避免这种情况的发生,比如在系统内有少量的摩擦力,或阻力,或惯性,或时间延迟来使输出与输入脱钩。这些因素造成了低效率,但它们是避免不稳定的必要条件。<br />
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2010年的闪崩事件被归咎于高频交易(HFT)的做法,不过HFT是否真的会增加系统性风险仍然存在争议。<br />
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====人口与环境危机====<br />
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可以认为农业和人口之间处于一种正反馈模式,这意味着双方越来越强烈地推动彼此。有人认为,这种正反馈系统终将在某一时刻以灾难结束,因为现代农业正在耗尽所有容易获得的磷酸盐,并且进行高效的单一栽培,使得现代农业更容易受到系统性风险影响。<br />
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技术创新和人类人口也可以有类似的考虑,这也是过去人类人口明显的双曲线增长,而不是简单的指数增长的一个解释。<br />
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有人提出,由于人口和技术之间的二阶正反馈,增长速度正在加快。技术增长增加了土地对人的承载能力,从而导致人口增长,而这反过来又推动了技术的进一步增长。<br />
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==== 偏见、社会制度与贫困====<br />
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Gunnar Myrdal描述了一个不平等和贫困加剧的恶性循环,这就是所谓的”循环累积诱因”。<br />
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===气象学===<br />
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干旱通过正反馈效应加剧。缺雨会降低土壤湿度,从而杀死植物,使它们通过蒸腾作用释放更少的水分。这两个因素都限制了水蒸气从地表加到大气中的过程,并使吸收水分的干燥灰尘进入大气。水汽少了,既意味着露点温度低,白天的供暖效率也高,减少了大气中湿度导致云的形成的机会。最后,没有云,就不会有雨,这个正反馈循环就形成了。<br />
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=== 气候学===<br />
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气候中的"诱因 "可能会将气候系统推向变暖或变冷的方向,例如,大气中温室气体浓度的增加会导致地表变暖。诱因是气候系统的外部因素,而反馈是系统的内部过程。一些反馈机制与气候系统的其他部分相对孤立地发挥作用,而另一些则是紧密耦合的。气候系统的作用力、反馈和动态决定了气候变化的程度和速度。全球变暖中的主要正反馈是变暖使大气中的水汽量增加,进而导致进一步变暖。主要的负反馈来自Stefan-Boltzmann定律,从地球辐射到空间的热量与地球表面和大气温度的四次方成正比。<br />
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气候学中正反馈子系统的其他例子包括:<br />
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大气变暖会使冰融化,从而改变反照率,从而使大气进一步变暖。<br />
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甲烷水合物可能是不稳定的,所以海洋变暖可能会释放更多的温室气体之一的甲烷。<br />
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泥炭,天然存在于泥炭沼泽中,含有碳。当泥炭干燥时,它会分解,并可能额外燃烧。泥炭还会释放一氧化二氮。<br />
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全球变暖会影响云的分布。高空的云层会增强温室效应,而低空的云层则主要反射太阳光,对温度产生相反的影响。<br />
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政府间气候变化专门委员会(气专委)第四次评估报告指出,"人类活动的变暖可能导致一些突然或不可逆转的影响,这取决于气候变化的速度和程度"。<br />
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=== 社会学===<br />
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自我应验预言是信念和行为之间的一个社会正反馈循环: 如果有足够多的人相信某件事是真的,他们的行为就能让它变成真的,而对他们行为的观察又可能反过来增加信念。一个典型的例子是银行挤兑。<br />
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正反馈的另一个社会学例子是网络效应。当更多的人被鼓励加入一个网络时,这就增加了网络的覆盖面,因此网络扩张得越来越快。病毒视频就是网络效应的一个例子,在这个例子中,一个热门视频的链接被分享和再传播,确保更多的人看到这个视频,然后重新发布链接。这是许多社会现象的基础,包括庞氏骗局和连锁信。在许多情况下,人口量是反馈效应的限制因素。<br />
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=== 化学===<br />
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如果化学反应引起热量的释放,而反应本身在较高的温度下发生得更快,那么就很有可能出现正反馈。如果产生的热量没有足够快地从反应物中排除,就会发生热失控,并很快导致化学爆炸。<br />
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=== 自然保护===<br />
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许多野生动物被猎杀的原因是它们身体的某些部位可能相当有价值。目标物种越是接近灭绝,其身体部位的价格就越高。这就是正反馈的一个例子。<br />
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==参见==<br />
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* Chain reaction – Sequence of reactions 链式反应 -- -- 反应的顺序<br />
* Donella Meadows' twelve leverage points to intervene in a system Donella Meadows干预系统的十二个杠杆点<br />
* Hyperbolic growth 双曲增长<br />
* Reflexivity (social theory)反射性(社会理论)<br />
* Stability criterion稳定性标准<br />
* Strategic complements战略补充<br />
* System dynamics 系统动力学<br />
* Technological singularity – Hypothetical point in time at which technological growth becomes uncontrollable and irreversible 技术奇点 -- -- 假设技术增长变得不可控制和不可逆转的时间点<br />
* Thermal runaway 热失控<br />
* Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop. 恶性/恶性循环:在社会和金融系统中,是通过反馈循环自我强化的事件综合体。<br />
* Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour. 正强化:在操作性条件下,结果会增加行为的频率。<br />
* Praise of performance: a term often applied in the context of performance appraisal,although this usage is disputed 绩效表扬:这个词经常被应用于绩效评估中,尽管这种用法有争议。<br />
* Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage 自我强化反馈:系统动力学中使用的术语,以避免与 "表扬 "的用法相混淆。<br />
* Matthew effect – Effect originally observed by Robert K. Merton 马太效应 -- -- 罗伯特-K-默顿最初观察到的效应。<br />
* Self-fulfilling prophecy – Prediction that causes itself to become true 自证预言 -- -- 导致自己成为现实的预言<br />
* Virtuous circle and vicious circle 良性循环和恶性循环<br />
* Autocatalysis 自催化<br />
* Meander – Sinuous bend in a series in the channel of a river 蜿蜒曲折 -- -- 河道中一系列蜿蜒曲折的弯道。<br />
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==参考文献==<br />
{{Reflist|2}}<br />
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==拓展阅读==<br />
* Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.<br />
* Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.<br />
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本中文词条由[[用户:Solitude|Solitude]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%AD%A3%E5%8F%8D%E9%A6%88&diff=29629正反馈2022-03-26T09:24:42Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=反馈,正反馈,Positive feedback,加剧反馈,自我强化反馈<br />
|description=在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。正反馈的一个重要特点是小扰动变大,当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
}}<br />
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[[File:330px-Herdwick_Stampede.jpg|thumb|right|图1:有时,警报或恐慌会通过正反馈在一群动物之间传播,从而引起踩踏事件。]]<br />
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[[File:330px-Stampede_loop.png|thumb|图2:在因果环路图中,踩踏事件的发生是一个正反馈循环。]]<br />
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[[File:330px-Birmingham_Northern_Rock_bank_run_2007.jpg|thumb|right|图3:在社会学中,网络效应可以迅速产生银行挤兑的正反馈效应。上图是2007年英国北岩银行挤兑事件的照片。]]<br />
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==回顾==<br />
'''Positive feedback''' ('''exacerbating feedback''', '''self-reinforcing feedback''') is a process that occurs in a [[feedback loop]] which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation.Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback.<ref name="theorymodelling" /> Both concepts play an important role in science and engineering, including biology, chemistry, and [[cybernetics]] .<br />
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正反馈(加剧反馈,自我强化反馈) 是一种在反馈循环中加剧微小扰动影响的过程。也就是说,一个扰动对系统的影响包括它自身扰动幅度的增大。或者说,A会产生更多的B,而B又会产生更多的A,与之相反的是,[[负反馈]]指的是一个系统中,变化的结果会减少或抵消它自己的影响。<ref name="theorymodelling" />这两个概念在科学和工程等领域中发挥着重要作用,包括生物学、化学和控制论。<br />
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在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。<ref name="zuckerman" /><ref>Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". ''Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems''. Academic Press. p. 55. ISBN <bdi>9780127784557</bdi>. Archived from the original on 2017-01-03. <q>A positive feedback loop is one with an even number of negative influences [around the loop].</q></ref><ref name="zuckerman" /> 从结果到始发过程的反馈可以是直接的,也可以通过其他状态变量<ref name="theorymodelling" />。这样的系统可以给出丰富的定性行为,但反馈的瞬时信号是正向还是负向,对结果有极其重要的影响。<ref name="theorymodelling" /> 正反馈强化原过程,而负反馈调节原过程。在这个含义下,''正''和''负''指的是大于或小于零的循环收益,并不代表着最终结果或效果的正负性。<ref name=":0">{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>因此,正反馈的一个重要特点是小扰动变大。当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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===基础===<br />
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[[File:330px-Positive_Feedback_Diagram_(2).svg.png|thumb|图4:一个基本的反馈系统可以用这个框图来表示。在图中,+号是加法器,A和B是任意因果函数。]]<br />
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图中显示了一个简单的反馈回路。 如果环增益AB为正值,则存在'正'或'再生'反馈的条件。<br />
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如果函数A和B是线性的,且AB小于1,那么系统从输入到输出的整体增益是有限的,但当AB接近1时,系统的增益可以非常大。<ref name="smith"> Electronics circuits and devices second edition. Ralph J. Smith</ref> 在这种情况下,可以表明从输入到输出的整体或 "闭环 "增益为:<br />
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:<math>G_c = A/(1-AB)</math><br />
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当AB>1时,系统是不稳定的,因此不具有明确的增益;增益可称为无限。<br />
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所以系统状态的变化根据反馈可以是收敛的,也可以是发散的。 而正反馈的结果是增强变化,因此小的扰动就可能导致大的变化。<br />
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对于一个当前处于平衡状态的系统,如果其状态的任何变化都发生了正反馈,从而造成了状态的不稳定,那么这个系统就是一个不稳定平衡的系统。使这种系统远离其平衡状态的力的大小是状态与平衡状态之间的距离的递增函数。<br />
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正反馈并不一定意味着平衡的不稳定性,例如,在正反馈结构中可能存在稳定的开关状态<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>。<br />
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=== 迟滞 ===<br />
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[[File:330px-Ideal_feedback_model.svg.png|thumb|图5:迟滞现象会导致输出值取决于输入的历史记录。]]<br />
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[[File:330px-Hysteresis_sharp_curve.svg.png|thumb|图6:在施密特触发器电路中,利用放大器的非反相输入端口产生的反馈,可以直接将电路的输出从原本的外加电压值推向到放大器所能产生的极值电压。]]<br />
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在现实世界中,正反馈循环通常不会引起不断增长,而是通过某种限制效应来改变。根据Donella Meadows的说法:<br />
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正反馈回路是系统增长、爆炸、腐蚀和崩溃的根源。一个系统如果有一个不受控制的正反馈,最终将会自我毁灭。这就是为什么正反馈如此稀少的原因。通常情况下,负反馈迟早会发生。<ref>Donella Meadows, ''[http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf Leverage Points: Places to Intervene in a System]''2013-10-08 at the Wayback Machine, 1999</ref><br />
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[[迟滞]],即起点影响系统的终点的现象,可以通过正反馈产生。当反馈循环的增益高于1时,那么输出就会远离输入:如果大于输入,则向最近的正极限移动,而如果小于输入,则向最近的负极限移动。<br />
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一旦达到极限,它就会稳定下来。但是,如果输入超过极限,那么反馈将改变符号,输出将向相反的方向移动,直到达到相反的极限。因此,该系统表现出'''双稳态行为bistable behavior'''。<br />
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== 术语由来==<br />
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正反馈和负反馈这两个名词最早应用于反馈是在二战前。正反馈的概念随着再生电路的问世,在20世纪20年代已经出现。<br />
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Friis 和 Jensen在1924年描述了一种在电子放大器中发生的"回馈 "是正的情况,这一情况与他们顺便提到的负回馈作用相反。到了1934年,Harold Stephen Black在他的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法:<br />
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正反馈会增加放大器的增益,负反馈会降低增益<br />
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据Mindell(2002年)说,术语上的混乱是在这之后不久产生的:<br />
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“ ... ... Friis 和 Jensen 对 Black 在对"正反馈 "和 "负反馈 "的区分方法是一样的,都不是基于反馈本身的符号,而是基于它对放大器增益的影响。与之相反的是,当Nyquist和Bode基于Black的工作基础时,将负反馈称为符号相反的反馈。Black难以说服其他人相信他的发明的实用性,有一部分原因是在基本的定义问题上存在混乱。"<br />
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==实例与应用==<br />
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=== 电子电路===<br />
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[[File:330px-Op-Amp_Schmitt_Trigger.svg.png|thumb|right|图7:一个老式的再生无线电接收器。由于使用正反馈的控制,真空管或阀门(中心)就可以产生足够的放大效果。]]<br />
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'''再生电路Regenerative circuit'''于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>,用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈,可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此,一个信号可以在一个阶段被放大20000甚至100000倍,而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定,开始振荡。无线电操作员必须不断地调整反馈量,以获得良好的接收效果。而现代无线电接收机采用超异构设计,多了许多放大级,去掉了正反馈并使其工作更稳定。<br />
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在再生无线电电路中产生的振荡还可以被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英),经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计,包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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许多电子电路,特别是放大器,都采用了负反馈。这降低了放大器的信号增益,但改善了它的线性度、输入阻抗、输出阻抗和带宽,并稳定了包括闭环增益等参数。同时,这些参数也变得不那么依赖于放大器件本身的细节,而更多地依赖于反馈元件,因为反馈元件一般不随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位:如果信号反馈失相,则反馈为负,如果相位一致,则反馈为正。对于需要使用负反馈放大器的设计者来说,引入负反馈放大器的问题是,电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°,那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波来做到这一点)。如果任何频率下的环增益(放大器增益与正反馈程度的乘积)大于1,那么放大器将在该频率下发生振荡(巴克豪森稳定性准则)。这种振荡有时被称为寄生振荡:在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化,前板(用户界面)的变化,甚至是由于人或其他导电物品的接近。<br />
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放大器可能会以示波器很难检测到的方式轻轻振荡,有时的振荡也可能非常大,只有非常扭曲或根本没有真正的信号,甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似,因此低频寄生振荡也被称为 "汽艇"。<br />
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[[File:330px-Regenerartive_Receiver-S7300056.jpg|thumb|right|图8:使用施密特触发器(b)代替比较器(a)的效果]]<br />
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许多常见的数字电路都采用正反馈。一般简单的布尔逻辑门通常只是依靠增益将数字信号电压从中间值推到代表布尔值0和1的值上,但许多更复杂的门都采用了反馈。当输入的模拟电压发生变化,但后期数字处理需要尖锐阈值时,施密特触发电路通过正反馈机制确保当输入电压轻微超过阈值时,输出电压可以巧妙而迅速地从一个逻辑状态转移到另一个逻辑状态。施密特触发器使用正反馈的一个必然结果是,如果输入电压再次缓慢下降,超过了相同的阈值,由于正反馈的机制,输出电压将保持在相同的逻辑状态而不改变。这种效应被称为滞后: 输入电压必须降到一个不同的、较低的阈值,才能“解锁”输出,并将其重置为原始数字。通过减小正反馈的程度,可以减小滞后宽度,但宽度不能被完全消除。施密特触发器在某种程度上是一个闭锁电路。<br />
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[[File:330px-Smitt_hysteresis_graph.svg.png|thumb|right|图9:正反馈是一种增强输出的机制,如蛋白质水平。但为了避免蛋白质水平的波动,该机制是随机抑制的(I),因此只有当激活的蛋白质(A)浓度超过阈值([I])时,循环机制被激活,如果d[A]=k[A],A的浓度就会成倍增加。]]<br />
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[[File:330px-Positive_feedback_bistable_switch.svg.png|thumb|right|图10 :R-S("复位-设置")触发器的说明,由两个带正反馈的数字诺尔门组成。红色和黑色分别表示逻辑上的 "1 "和 "0"。]]<br />
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电子触发器,或“锁存器” ,或“双稳态多谐振荡器” ,是一种由于高正反馈而不稳定于平衡或中间状态的电路。这样的双稳态电路是一位电子存储器的基础。 触发器使用一对放大器、晶体管或逻辑门相互连接,正反馈机制使得输入信号被去除后,电路可以维持在两种非平衡稳定状态中的一种,直到一个合适的替代信号重新作为输入,以改变电路状态。计算机随机存取存储器(RAM)可以用这种方式运作,每位存储器有一个锁存电路。<br />
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电子系统中发生'''热失控Thermal runaway'''的原因是,当电路的某些方面变得更热时,它被允许通过更多的电流,然后它越热,通过的电流就越多,这就使它更热一些,因此它又通过更多的电流。这种现象对有关器件来说通常是灾难性的。如果器件不得不在接近其最大功率处理能力的情况下工作,那么某些条件下就可能出现热失控,这通常可以通过精心设计来改进。<br />
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[[File:330px-R-S_mk2.gif|thumb|left|图11:A phonograph turntable is prone to acoustic feedback. 留声机转盘容易受到声反馈的影响。]]<br />
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音频和视频系统可以表现出正反馈。如果麦克风录入了同一电路中扬声器的放大声音输出,那么就会听到音频反馈的嚎叫和尖叫声(在放大器的最大功率容量下),因为随机噪声被音频系统和房间的特性所过滤后,通过正反馈重新放大。<br />
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===音频与现场音频===<br />
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音频反馈(也称为声反馈,简称反馈,或拉森效应)是一种特殊的正反馈,当音频输入(例如,麦克风或吉他拾音器)和音频输出(例如,大声放大的扬声器)之间存在声音回路时,就会出现这种反馈。在这个例子中,麦克风接收到的信号被放大并从扬声器传出。然后,来自扬声器的声音可以再次被麦克风接收,进一步放大,然后再次通过扬声器传递出去。 所产生的声音的频率由传声器、放大器和扬声器的共振频率、房间的声学特性、传声器和扬声器的定向拾音和发射模式以及它们之间的距离决定。对于小型的扩声系统来说,这种声音很容易的体现的响亮的吱吱声或尖叫声。<br />
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在歌手或公众演讲者使用扩声系统或扩音系统的活动中,麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来,音频工程师使用各种电子设备,如均衡器或者自动反馈检测设备,来防止这些不受欢迎的尖叫声或尖叫声,这些声音影响了观众对活动的享受。另一方面,自20世纪60年代以来,摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果,有意制造吉他中的正反馈,以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈,但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中,他说,“我敢说任何人都找不到这样的唱片,除非是1922年这张用这种方式录制的老蓝调唱片。”<br />
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音频反馈的原理是由丹麦科学家Søren Absalon Larsen首先发现的。麦克风并不是唯一受此影响的传感器。录音板拾音器也会产生正反馈,通常是在100赫兹以下的低频范围内表现出低沉的轰鸣声。Jimi Hendrix是一个创新者,在他的吉他独奏中有意使用吉他正反馈来创造独特的声音效果。他帮助发展了电吉他演奏中音频反馈的可控性和音乐性,后来Brian May也是这种技术的著名支持者。<br />
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[[File:330px-Technics_SL-1210MK2.jpg|thumb|right|220px|图12:视频反馈]]<br />
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===视频===<br />
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同样,如果一台摄像机对准一个正在显示摄像机自身信号的监控屏幕,那么通过正反馈就可以在屏幕上形成重复的图案。这种视频反馈效果在电视剧《神秘博士》前十季的开场白中就被使用了。<br />
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===开关===<br />
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In [[electrical switch]]es, including [[bimetallic strip]] based thermostats, the switch usually has hysteresis in the switching action. In these cases hysteresis is mechanically achieved via positive feedback within a tipping point mechanism. The positive feedback action minimises the length of time arcing occurs for during the switching and also holds the contacts in an open or closed state.<br />
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在电气开关中,包括双金属条型恒温器,开关通常在开关动作中具有滞后性。在这些情况下,滞后是通过一个临界点机构内的正反馈来实现的。正反馈作用可最大限度地减少开关过程中发生电弧的时间,并使触点保持在断开或闭合状态。<br />
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=== 生物学===<br />
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[[File:330px-Positive_Feedback-_Childbirth_(1).svg (1).png|thumb|right|生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。]]<br />
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生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。<br />
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==== 生理学====<br />
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在生理学中可以找到一些正反馈系统的例子。<br />
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其中一个例子是分娩时宫缩的发生,称为弗格森反射。当宫缩发生时,激素催产素会引起神经刺激,刺激下丘脑产生更多的催产素,从而增加子宫收缩。这就导致宫缩的幅度和频率增加。<br />
<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders.</ref><br />
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另一个例子是血液凝固的过程。当受伤的组织释放出信号化学物质,激活血液中的血小板时,这个循环就启动了。被激活的血小板释放化学物质,激活更多的血小板,引起快速的级联反应,形成血栓。<ref name=Guyton1991/><br />
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哺乳也涉及正反馈,当婴儿吸吮乳头时,会有神经反应进入脊髓,并上传到大脑的下丘脑,然后刺激垂体产生更多的催乳素以产生更多的乳汁<ref name=Guyton1991/>。<br />
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在月经周期的卵泡期期间,雌激素的飙升会导致排卵<ref name=Guyton1991/>。<br />
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神经信号的产生是另一个例子,神经纤维的膜使钠离子通过钠通道轻微渗漏,导致膜电位的变化,进而引起更多通道的开放(Hodgkin循环)。所以,最初的轻微渗漏会导致钠渗漏的爆发,从而产生神经动作电位<ref name=Guyton1991/>。<br />
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在心脏的兴奋收缩耦合中,肌浆网膜中的兰尼碱受体检测到心肌细胞内钙离子的增加,该受体以正反馈生理反应将钙运出到细胞质中。<br />
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在大多数情况下,这种反馈循环最终会释放出反信号,从而抑制或破坏循环。分娩宫缩在宝宝离开母体时停止。化学物质分解血凝块。当婴儿不再需要被哺乳时,泌乳停止<ref name=Guyton1991/>。<br />
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====基因调控====<br />
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正反馈是基因调控中研究较好的一种现象,其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时,就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络,以证明双稳态的概念。<ref name=Hasty2002/><br />
正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用,因此,基因调控中的正反馈可以产生显著的生理结果。分子动力学中的随机运动加上正反馈可以引发有趣的效应,例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/> 这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中,如酶动力学或代谢途径。<ref name=Christoph2001/><br />
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==== 进化生物学 ====<br />
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在进化生物学中正反馈循环被用来描述生物进化中变化动态的各个方面。 例如,在宏观层面,Alfred J. Lotka(1945)认为,物种的演变最重要的是选择反馈能量流动以捕获越来越多的能源系统的能量。<ref name=Lotka1945/>在人类层面,Richard D. Alexander(1989)提出,人类群体之间和群体内部的社会竞争会影响智力的选择,从而时不时地会产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子<ref name=Crespi2004/>。通过与军备竞赛进行类比,给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/><br />
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[[File:Phanerozoic Biodiversity.svg|300px|right|thumb|显生宙[[生物多样性]]呈现稳定而非单调的增长,从接近于零一直增长到有几千个属。|链接=Special:FilePath/Phanerozoic_Biodiversity.svg]]<br />
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研究表明,在<font color="#32CD32"> 显生宙 ''',生物多样性的变化与双曲模型(广泛用于人口学和宏观社会学)的相关性要比指数模型和逻辑斯特模型(传统上用于人口生物学,并广泛用于生物多样性化石)的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈(更多的祖先,更多的后代)和资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为,生物多样性和人口曲线之间的相似性可能来自这样一个事实,即两者都是由双曲趋势(由正反馈产生)与周期性和随机性的动态干扰而产生的。<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref><br />
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==== 免疫系统====<br />
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细胞因子风暴,或称高细胞因子血症,是一种潜在的致命性免疫反应,表现为各种细胞因子水平高度升高,这是由细胞因子和免疫细胞之间的正反馈环组成。[36]在正常的免疫功能中,可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后,就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合,当B细胞的抗体与C3结合后,就会加快该B细胞分泌更多的抗体和更多的C3蛋白,从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
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====细胞凋亡====<br />
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细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程,其目的是清除长寿或受损的细胞。这一过程的失效与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活,它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时,无论效应子胱天蛋白酶的中间激活步骤数量有多少,这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/> 当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时,该过程呈现双稳态,从而模拟细胞的存活和死亡状态。<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref><br />
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=== 心理学===<br />
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Winner(1996)将有天赋的孩子描述为受到正反馈循环的驱动,这些反馈循环体现在他们自己的课程学习上,通过反馈自己的满意程度,从而进一步将他们的学习目标提高到更高水平等。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a,2009b)提出,神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释,工作记忆中的思维/表现输出被反馈到小脑,在那里被精简,然后再反馈到工作记忆中,从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/> <br />
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=== 经济学===<br />
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====市场上的社会影响====<br />
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事实证明,产品推荐和消费者先前的购买信息对消费者的选择影响很大,无论是音乐、电影、书籍、电子产品还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象(马太效应),即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
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====市场动向====<br />
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根据George Soros提出的反射性理论,价格变化是由一个正反馈过程驱动的,即投资者的预期受到价格变动的影响,因此他们的行为会强化这个方向的价格变动,直到价格的变化变得不可持续,于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
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==== 系统风险====<br />
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系统性风险是指放大效应或杠杆或正反馈过程给系统带来的风险。这通常是未知的,在某些条件下,这个过程会成倍放大,并迅速导致破坏性或混乱的行为。 庞氏骗局就是正反馈系统的一个很好的例子:来自新投资者的资金被用来支付异常高的回报,反过来又吸引了更多的新投资者,导致快速增长进而走向崩溃。W. Brian Arthur 也对经济中的正反馈进行了研究和著述(如W. Brian Arthur,1990)。Hyman Minsky提出了一个理论,认为某些信用扩张行为会使市场经济变成一个 "偏差放大系统",从而可能会突然崩溃,这有时被称为 "明斯基时刻"。<br />
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输入和输出明确分开的简单系统不容易发生系统性风险。 随着系统复杂性的增加,这种风险更容易发生,因为即使在详细的压力测试条件下,也更难看到或分析系统中所有可能的变量组合。 一个复杂系统的效率越高,就越容易发生系统性风险,因为只需要很小的偏差就可以破坏系统。 因此,设计良好的复杂系统一般都会有一些内在的功能来避免这种情况的发生,比如在系统内有少量的摩擦力,或阻力,或惯性,或时间延迟来使输出与输入脱钩。这些因素造成了低效率,但它们是避免不稳定的必要条件。<br />
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2010年的闪崩事件被归咎于高频交易(HFT)的做法,不过HFT是否真的会增加系统性风险仍然存在争议。<br />
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====人口与环境危机====<br />
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可以认为农业和人口之间处于一种正反馈模式,这意味着双方越来越强烈地推动彼此。有人认为,这种正反馈系统终将在某一时刻以灾难结束,因为现代农业正在耗尽所有容易获得的磷酸盐,并且进行高效的单一栽培,使得现代农业更容易受到系统性风险影响。<br />
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技术创新和人类人口也可以有类似的考虑,这也是过去人类人口明显的双曲线增长,而不是简单的指数增长的一个解释。<br />
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有人提出,由于人口和技术之间的二阶正反馈,增长速度正在加快。技术增长增加了土地对人的承载能力,从而导致人口增长,而这反过来又推动了技术的进一步增长。<br />
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==== 偏见、社会制度与贫困====<br />
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Gunnar Myrdal描述了一个不平等和贫困加剧的恶性循环,这就是所谓的”循环累积诱因”。<br />
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===气象学===<br />
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干旱通过正反馈效应加剧。缺雨会降低土壤湿度,从而杀死植物,使它们通过蒸腾作用释放更少的水分。这两个因素都限制了水蒸气从地表加到大气中的过程,并使吸收水分的干燥灰尘进入大气。水汽少了,既意味着露点温度低,白天的供暖效率也高,减少了大气中湿度导致云的形成的机会。最后,没有云,就不会有雨,这个正反馈循环就形成了。<br />
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=== 气候学===<br />
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气候中的"诱因 "可能会将气候系统推向变暖或变冷的方向,例如,大气中温室气体浓度的增加会导致地表变暖。诱因是气候系统的外部因素,而反馈是系统的内部过程。一些反馈机制与气候系统的其他部分相对孤立地发挥作用,而另一些则是紧密耦合的。气候系统的作用力、反馈和动态决定了气候变化的程度和速度。全球变暖中的主要正反馈是变暖使大气中的水汽量增加,进而导致进一步变暖。主要的负反馈来自Stefan-Boltzmann定律,从地球辐射到空间的热量与地球表面和大气温度的四次方成正比。<br />
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气候学中正反馈子系统的其他例子包括:<br />
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大气变暖会使冰融化,从而改变反照率,从而使大气进一步变暖。<br />
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甲烷水合物可能是不稳定的,所以海洋变暖可能会释放更多的温室气体之一的甲烷。<br />
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泥炭,天然存在于泥炭沼泽中,含有碳。当泥炭干燥时,它会分解,并可能额外燃烧。泥炭还会释放一氧化二氮。<br />
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全球变暖会影响云的分布。高空的云层会增强温室效应,而低空的云层则主要反射太阳光,对温度产生相反的影响。<br />
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政府间气候变化专门委员会(气专委)第四次评估报告指出,"人类活动的变暖可能导致一些突然或不可逆转的影响,这取决于气候变化的速度和程度"。<br />
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=== 社会学===<br />
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自我应验预言是信念和行为之间的一个社会正反馈循环: 如果有足够多的人相信某件事是真的,他们的行为就能让它变成真的,而对他们行为的观察又可能反过来增加信念。一个典型的例子是银行挤兑。<br />
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正反馈的另一个社会学例子是网络效应。当更多的人被鼓励加入一个网络时,这就增加了网络的覆盖面,因此网络扩张得越来越快。病毒视频就是网络效应的一个例子,在这个例子中,一个热门视频的链接被分享和再传播,确保更多的人看到这个视频,然后重新发布链接。这是许多社会现象的基础,包括庞氏骗局和连锁信。在许多情况下,人口量是反馈效应的限制因素。<br />
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=== 化学===<br />
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如果化学反应引起热量的释放,而反应本身在较高的温度下发生得更快,那么就很有可能出现正反馈。如果产生的热量没有足够快地从反应物中排除,就会发生热失控,并很快导致化学爆炸。<br />
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=== 自然保护===<br />
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许多野生动物被猎杀的原因是它们身体的某些部位可能相当有价值。目标物种越是接近灭绝,其身体部位的价格就越高。这就是正反馈的一个例子。<br />
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==参见==<br />
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* Chain reaction – Sequence of reactions 链式反应 -- -- 反应的顺序<br />
* Donella Meadows' twelve leverage points to intervene in a system Donella Meadows干预系统的十二个杠杆点<br />
* Hyperbolic growth 双曲增长<br />
* Reflexivity (social theory)反射性(社会理论)<br />
* Stability criterion稳定性标准<br />
* Strategic complements战略补充<br />
* System dynamics 系统动力学<br />
* Technological singularity – Hypothetical point in time at which technological growth becomes uncontrollable and irreversible 技术奇点 -- -- 假设技术增长变得不可控制和不可逆转的时间点<br />
* Thermal runaway 热失控<br />
* Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop. 恶性/恶性循环:在社会和金融系统中,是通过反馈循环自我强化的事件综合体。<br />
* Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour. 正强化:在操作性条件下,结果会增加行为的频率。<br />
* Praise of performance: a term often applied in the context of performance appraisal,although this usage is disputed 绩效表扬:这个词经常被应用于绩效评估中,尽管这种用法有争议。<br />
* Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage 自我强化反馈:系统动力学中使用的术语,以避免与 "表扬 "的用法相混淆。<br />
* Matthew effect – Effect originally observed by Robert K. Merton 马太效应 -- -- 罗伯特-K-默顿最初观察到的效应。<br />
* Self-fulfilling prophecy – Prediction that causes itself to become true 自证预言 -- -- 导致自己成为现实的预言<br />
* Virtuous circle and vicious circle 良性循环和恶性循环<br />
* Autocatalysis 自催化<br />
* Meander – Sinuous bend in a series in the channel of a river 蜿蜒曲折 -- -- 河道中一系列蜿蜒曲折的弯道。<br />
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==参考文献==<br />
{{Reflist|2}}<br />
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==拓展阅读==<br />
* Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.<br />
* Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN0-262-24045-9. Chapter 18: Games as Cybernetic Systems.<br />
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本中文词条由[[用户:Solitude|Solitude]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%AD%A3%E5%8F%8D%E9%A6%88&diff=29628正反馈2022-03-26T09:10:30Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=反馈,正反馈,Positive feedback,加剧反馈,自我强化反馈<br />
|description=在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。正反馈的一个重要特点是小扰动变大,当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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[[File:Herdwick Stampede.jpg|thumb|right|图1:有时,警报或恐慌会通过正反馈在一群动物之间传播,从而引起踩踏事件。]]<br />
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[[File:Stampede loop.png|thumb|图2:在因果环路图中,踩踏事件的发生是一个正反馈循环。]]<br />
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[[File:Birmingham Northern Rock bank run 2007.jpg|thumb|right|图3:在社会学中,网络效应可以迅速产生银行挤兑的正反馈效应。上图是2007年英国北岩银行挤兑事件的照片。]]<br />
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==回顾==<br />
'''Positive feedback''' ('''exacerbating feedback''', '''self-reinforcing feedback''') is a process that occurs in a [[feedback loop]] which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation.Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback.<ref name="theorymodelling" /> Both concepts play an important role in science and engineering, including biology, chemistry, and [[cybernetics]] .<br />
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正反馈(加剧反馈,自我强化反馈) 是一种在反馈循环中加剧微小扰动影响的过程。也就是说,一个扰动对系统的影响包括它自身扰动幅度的增大。或者说,A会产生更多的B,而B又会产生更多的A,与之相反的是,[[负反馈]]指的是一个系统中,变化的结果会减少或抵消它自己的影响。<ref name="theorymodelling" />这两个概念在科学和工程等领域中发挥着重要作用,包括生物学、化学和控制论。<br />
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在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。<ref name="zuckerman" /><ref>Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". ''Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems''. Academic Press. p. 55. ISBN <bdi>9780127784557</bdi>. Archived from the original on 2017-01-03. <q>A positive feedback loop is one with an even number of negative influences [around the loop].</q></ref><ref name="zuckerman" /> 从结果到始发过程的反馈可以是直接的,也可以通过其他状态变量<ref name="theorymodelling" />。这样的系统可以给出丰富的定性行为,但反馈的瞬时信号是正向还是负向,对结果有极其重要的影响。<ref name="theorymodelling" /> 正反馈强化原过程,而负反馈调节原过程。在这个含义下,''正''和''负''指的是大于或小于零的循环收益,并不代表着最终结果或效果的正负性。<ref name=":0">{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>因此,正反馈的一个重要特点是小扰动变大。当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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===基础===<br />
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[[File:Ideal feedback model.svg|thumb|图4:一个基本的反馈系统可以用这个框图来表示。在图中,+号是加法器,A和B是任意因果函数。]]<br />
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图中显示了一个简单的反馈回路。 如果环增益AB为正值,则存在'正'或'再生'反馈的条件。<br />
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如果函数A和B是线性的,且AB小于1,那么系统从输入到输出的整体增益是有限的,但当AB接近1时,系统的增益可以非常大。<ref name="smith"> Electronics circuits and devices second edition. Ralph J. Smith</ref> 在这种情况下,可以表明从输入到输出的整体或 "闭环 "增益为:<br />
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:<math>G_c = A/(1-AB)</math><br />
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当AB>1时,系统是不稳定的,因此不具有明确的增益;增益可称为无限。<br />
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所以系统状态的变化根据反馈可以是收敛的,也可以是发散的。 而正反馈的结果是增强变化,因此小的扰动就可能导致大的变化。<br />
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对于一个当前处于平衡状态的系统,如果其状态的任何变化都发生了正反馈,从而造成了状态的不稳定,那么这个系统就是一个不稳定平衡的系统。使这种系统远离其平衡状态的力的大小是状态与平衡状态之间的距离的递增函数。<br />
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正反馈并不一定意味着平衡的不稳定性,例如,在正反馈结构中可能存在稳定的开关状态<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>。<br />
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=== 迟滞 ===<br />
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[[File:Hysteresis sharp curve.svg|thumb|图5:迟滞现象会导致输出值取决于输入的历史记录。]]<br />
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[[File:Op-Amp Schmitt Trigger.svg|thumb|图6:在施密特触发器电路中,利用放大器的非反相输入端口产生的反馈,可以直接将电路的输出从原本的外加电压值推向到放大器所能产生的极值电压。]]<br />
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在现实世界中,正反馈循环通常不会引起不断增长,而是通过某种限制效应来改变。根据Donella Meadows的说法:<br />
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正反馈回路是系统增长、爆炸、腐蚀和崩溃的根源。一个系统如果有一个不受控制的正反馈,最终将会自我毁灭。这就是为什么正反馈如此稀少的原因。通常情况下,负反馈迟早会发生。<ref>Donella Meadows, ''[http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf Leverage Points: Places to Intervene in a System]''2013-10-08 at the Wayback Machine, 1999</ref><br />
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[[迟滞]],即起点影响系统的终点的现象,可以通过正反馈产生。当反馈循环的增益高于1时,那么输出就会远离输入:如果大于输入,则向最近的正极限移动,而如果小于输入,则向最近的负极限移动。<br />
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一旦达到极限,它就会稳定下来。但是,如果输入超过极限,那么反馈将改变符号,输出将向相反的方向移动,直到达到相反的极限。因此,该系统表现出'''双稳态行为bistable behavior'''。<br />
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== 术语由来==<br />
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正反馈和负反馈这两个名词最早应用于反馈是在二战前。正反馈的概念随着再生电路的问世,在20世纪20年代已经出现。<br />
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Friis 和 Jensen在1924年描述了一种在电子放大器中发生的"回馈 "是正的情况,这一情况与他们顺便提到的负回馈作用相反。到了1934年,Harold Stephen Black在他的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法:<br />
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正反馈会增加放大器的增益,负反馈会降低增益<br />
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据Mindell(2002年)说,术语上的混乱是在这之后不久产生的:<br />
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“ ... ... Friis 和 Jensen 对 Black 在对"正反馈 "和 "负反馈 "的区分方法是一样的,都不是基于反馈本身的符号,而是基于它对放大器增益的影响。与之相反的是,当Nyquist和Bode基于Black的工作基础时,将负反馈称为符号相反的反馈。Black难以说服其他人相信他的发明的实用性,有一部分原因是在基本的定义问题上存在混乱。"<br />
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==实例与应用==<br />
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=== 电子电路===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|图7:一个老式的再生无线电接收器。由于使用正反馈的控制,真空管或阀门(中心)就可以产生足够的放大效果。]]<br />
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'''再生电路Regenerative circuit'''于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>,用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈,可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此,一个信号可以在一个阶段被放大20000甚至100000倍,而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定,开始振荡。无线电操作员必须不断地调整反馈量,以获得良好的接收效果。而现代无线电接收机采用超异构设计,多了许多放大级,去掉了正反馈并使其工作更稳定。<br />
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在再生无线电电路中产生的振荡还可以被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英),经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计,包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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许多电子电路,特别是放大器,都采用了负反馈。这降低了放大器的信号增益,但改善了它的线性度、输入阻抗、输出阻抗和带宽,并稳定了包括闭环增益等参数。同时,这些参数也变得不那么依赖于放大器件本身的细节,而更多地依赖于反馈元件,因为反馈元件一般不随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位:如果信号反馈失相,则反馈为负,如果相位一致,则反馈为正。对于需要使用负反馈放大器的设计者来说,引入负反馈放大器的问题是,电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°,那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波来做到这一点)。如果任何频率下的环增益(放大器增益与正反馈程度的乘积)大于1,那么放大器将在该频率下发生振荡(巴克豪森稳定性准则)。这种振荡有时被称为寄生振荡:在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化,前板(用户界面)的变化,甚至是由于人或其他导电物品的接近。<br />
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放大器可能会以示波器很难检测到的方式轻轻振荡,有时的振荡也可能非常大,只有非常扭曲或根本没有真正的信号,甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似,因此低频寄生振荡也被称为 "汽艇"。<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|图8:使用施密特触发器(b)代替比较器(a)的效果]]<br />
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许多常见的数字电路都采用正反馈。一般简单的布尔逻辑门通常只是依靠增益将数字信号电压从中间值推到代表布尔值0和1的值上,但许多更复杂的门都采用了反馈。当输入的模拟电压发生变化,但后期数字处理需要尖锐阈值时,施密特触发电路通过正反馈机制确保当输入电压轻微超过阈值时,输出电压可以巧妙而迅速地从一个逻辑状态转移到另一个逻辑状态。施密特触发器使用正反馈的一个必然结果是,如果输入电压再次缓慢下降,超过了相同的阈值,由于正反馈的机制,输出电压将保持在相同的逻辑状态而不改变。这种效应被称为滞后: 输入电压必须降到一个不同的、较低的阈值,才能“解锁”输出,并将其重置为原始数字。通过减小正反馈的程度,可以减小滞后宽度,但宽度不能被完全消除。施密特触发器在某种程度上是一个闭锁电路。<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|图9:正反馈是一种增强输出的机制,如蛋白质水平。但为了避免蛋白质水平的波动,该机制是随机抑制的(I),因此只有当激活的蛋白质(A)浓度超过阈值([I])时,循环机制被激活,如果d[A]=k[A],A的浓度就会成倍增加。]]<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|图10 :R-S("复位-设置")触发器的说明,由两个带正反馈的数字诺尔门组成。红色和黑色分别表示逻辑上的 "1 "和 "0"。]]<br />
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电子触发器,或“锁存器” ,或“双稳态多谐振荡器” ,是一种由于高正反馈而不稳定于平衡或中间状态的电路。这样的双稳态电路是一位电子存储器的基础。 触发器使用一对放大器、晶体管或逻辑门相互连接,正反馈机制使得输入信号被去除后,电路可以维持在两种非平衡稳定状态中的一种,直到一个合适的替代信号重新作为输入,以改变电路状态。计算机随机存取存储器(RAM)可以用这种方式运作,每位存储器有一个锁存电路。<br />
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电子系统中发生'''热失控Thermal runaway'''的原因是,当电路的某些方面变得更热时,它被允许通过更多的电流,然后它越热,通过的电流就越多,这就使它更热一些,因此它又通过更多的电流。这种现象对有关器件来说通常是灾难性的。如果器件不得不在接近其最大功率处理能力的情况下工作,那么某些条件下就可能出现热失控,这通常可以通过精心设计来改进。<br />
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[[File:Technics SL-1210MK2.jpg|thumb|left|图11:A phonograph turntable is prone to acoustic feedback. 留声机转盘容易受到声反馈的影响。]]<br />
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音频和视频系统可以表现出正反馈。如果麦克风录入了同一电路中扬声器的放大声音输出,那么就会听到音频反馈的嚎叫和尖叫声(在放大器的最大功率容量下),因为随机噪声被音频系统和房间的特性所过滤后,通过正反馈重新放大。<br />
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===音频与现场音频===<br />
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音频反馈(也称为声反馈,简称反馈,或拉森效应)是一种特殊的正反馈,当音频输入(例如,麦克风或吉他拾音器)和音频输出(例如,大声放大的扬声器)之间存在声音回路时,就会出现这种反馈。在这个例子中,麦克风接收到的信号被放大并从扬声器传出。然后,来自扬声器的声音可以再次被麦克风接收,进一步放大,然后再次通过扬声器传递出去。 所产生的声音的频率由传声器、放大器和扬声器的共振频率、房间的声学特性、传声器和扬声器的定向拾音和发射模式以及它们之间的距离决定。对于小型的扩声系统来说,这种声音很容易的体现的响亮的吱吱声或尖叫声。<br />
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在歌手或公众演讲者使用扩声系统或扩音系统的活动中,麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来,音频工程师使用各种电子设备,如均衡器或者自动反馈检测设备,来防止这些不受欢迎的尖叫声或尖叫声,这些声音影响了观众对活动的享受。另一方面,自20世纪60年代以来,摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果,有意制造吉他中的正反馈,以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈,但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中,他说,“我敢说任何人都找不到这样的唱片,除非是1922年这张用这种方式录制的老蓝调唱片。”<br />
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音频反馈的原理是由丹麦科学家Søren Absalon Larsen首先发现的。麦克风并不是唯一受此影响的传感器。录音板拾音器也会产生正反馈,通常是在100赫兹以下的低频范围内表现出低沉的轰鸣声。Jimi Hendrix是一个创新者,在他的吉他独奏中有意使用吉他正反馈来创造独特的声音效果。他帮助发展了电吉他演奏中音频反馈的可控性和音乐性,后来Brian May也是这种技术的著名支持者。<br />
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[[File:Adam Savage HOPE.jpg|thumb|right|220px|图12:视频反馈]]<br />
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===视频===<br />
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同样,如果一台摄像机对准一个正在显示摄像机自身信号的监控屏幕,那么通过正反馈就可以在屏幕上形成重复的图案。这种视频反馈效果在电视剧《神秘博士》前十季的开场白中就被使用了。<br />
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===开关===<br />
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In [[electrical switch]]es, including [[bimetallic strip]] based thermostats, the switch usually has hysteresis in the switching action. In these cases hysteresis is mechanically achieved via positive feedback within a tipping point mechanism. The positive feedback action minimises the length of time arcing occurs for during the switching and also holds the contacts in an open or closed state.<br />
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在电气开关中,包括双金属条型恒温器,开关通常在开关动作中具有滞后性。在这些情况下,滞后是通过一个临界点机构内的正反馈来实现的。正反馈作用可最大限度地减少开关过程中发生电弧的时间,并使触点保持在断开或闭合状态。<br />
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=== 生物学===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。]]<br />
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生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。<br />
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==== 生理学====<br />
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在生理学中可以找到一些正反馈系统的例子。<br />
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* <br />
其中一个例子是分娩时宫缩的发生,称为弗格森反射。当宫缩发生时,激素催产素会引起神经刺激,刺激下丘脑产生更多的催产素,从而增加子宫收缩。这就导致宫缩的幅度和频率增加。<br />
<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders. {{ISBN|0-7216-3994-1}}</ref><br />
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另一个例子是血液凝固的过程。当受伤的组织释放出信号化学物质,激活血液中的血小板时,这个循环就启动了。被激活的血小板释放化学物质,激活更多的血小板,引起快速的级联反应,形成血栓。<ref name=Guyton1991/><br />
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哺乳也涉及正反馈,当婴儿吸吮乳头时,会有神经反应进入脊髓,并上传到大脑的下丘脑,然后刺激垂体产生更多的催乳素以产生更多的乳汁<ref name=Guyton1991/>。<br />
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在月经周期的卵泡期期间,雌激素的飙升会导致排卵<ref name=Guyton1991/>。<br />
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神经信号的产生是另一个例子,神经纤维的膜使钠离子通过钠通道轻微渗漏,导致膜电位的变化,进而引起更多通道的开放(Hodgkin循环)。所以,最初的轻微渗漏会导致钠渗漏的爆发,从而产生神经动作电位<ref name=Guyton1991/>。<br />
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在心脏的兴奋收缩耦合中,肌浆网膜中的兰尼碱受体检测到心肌细胞内钙离子的增加,该受体以正反馈生理反应将钙运出到细胞质中。<br />
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在大多数情况下,这种反馈循环最终会释放出反信号,从而抑制或破坏循环。分娩宫缩在宝宝离开母体时停止。化学物质分解血凝块。当婴儿不再需要被哺乳时,泌乳停止<ref name=Guyton1991/>。<br />
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====基因调控====<br />
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正反馈是基因调控中研究较好的一种现象,其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时,就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络,以证明双稳态的概念。<ref name=Hasty2002/><br />
正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用,因此,基因调控中的正反馈可以产生显著的生理结果。分子动力学中的随机运动加上正反馈可以引发有趣的效应,例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/> 这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中,如酶动力学或代谢途径。<ref name=Christoph2001/><br />
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==== 进化生物学 ====<br />
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在进化生物学中正反馈循环被用来描述生物进化中变化动态的各个方面。 例如,在宏观层面,Alfred J. Lotka(1945)认为,物种的演变最重要的是选择反馈能量流动以捕获越来越多的能源系统的能量。<ref name=Lotka1945/>在人类层面,Richard D. Alexander(1989)提出,人类群体之间和群体内部的社会竞争会影响智力的选择,从而时不时地会产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子<ref name=Crespi2004/>。通过与军备竞赛进行类比,给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/><br />
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[[File:Phanerozoic Biodiversity.svg|300px|right|thumb|显生宙[[生物多样性]]呈现稳定而非单调的增长,从接近于零一直增长到有几千个属。|链接=Special:FilePath/Phanerozoic_Biodiversity.svg]]<br />
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研究表明,在<font color="#32CD32"> 显生宙 ''',生物多样性的变化与双曲模型(广泛用于人口学和宏观社会学)的相关性要比指数模型和逻辑斯特模型(传统上用于人口生物学,并广泛用于生物多样性化石)的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈(更多的祖先,更多的后代)和资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为,生物多样性和人口曲线之间的相似性可能来自这样一个事实,即两者都是由双曲趋势(由正反馈产生)与周期性和随机性的动态干扰而产生的。<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref><br />
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==== 免疫系统====<br />
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细胞因子风暴,或称高细胞因子血症,是一种潜在的致命性免疫反应,表现为各种细胞因子水平高度升高,这是由细胞因子和免疫细胞之间的正反馈环组成。[36]在正常的免疫功能中,可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后,就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合,当B细胞的抗体与C3结合后,就会加快该B细胞分泌更多的抗体和更多的C3蛋白,从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
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====细胞凋亡====<br />
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细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程,其目的是清除长寿或受损的细胞。这一过程的失效与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活,它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时,无论效应子胱天蛋白酶的中间激活步骤数量有多少,这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/> 当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时,该过程呈现双稳态,从而模拟细胞的存活和死亡状态。<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref><br />
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=== 心理学===<br />
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Winner(1996)将有天赋的孩子描述为受到正反馈循环的驱动,这些反馈循环体现在他们自己的课程学习上,通过反馈自己的满意程度,从而进一步将他们的学习目标提高到更高水平等。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a,2009b)提出,神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释,工作记忆中的思维/表现输出被反馈到小脑,在那里被精简,然后再反馈到工作记忆中,从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/> <br />
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=== 经济学===<br />
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====市场上的社会影响====<br />
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事实证明,产品推荐和消费者先前的购买信息对消费者的选择影响很大,无论是音乐、电影、书籍、电子产品还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象(马太效应),即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
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====市场动向====<br />
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根据George Soros提出的反射性理论,价格变化是由一个正反馈过程驱动的,即投资者的预期受到价格变动的影响,因此他们的行为会强化这个方向的价格变动,直到价格的变化变得不可持续,于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
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==== 系统风险====<br />
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系统性风险是指放大效应或杠杆或正反馈过程给系统带来的风险。这通常是未知的,在某些条件下,这个过程会成倍放大,并迅速导致破坏性或混乱的行为。 庞氏骗局就是正反馈系统的一个很好的例子:来自新投资者的资金被用来支付异常高的回报,反过来又吸引了更多的新投资者,导致快速增长进而走向崩溃。W. Brian Arthur 也对经济中的正反馈进行了研究和著述(如W. Brian Arthur,1990)。Hyman Minsky提出了一个理论,认为某些信用扩张行为会使市场经济变成一个 "偏差放大系统",从而可能会突然崩溃,这有时被称为 "明斯基时刻"。<br />
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输入和输出明确分开的简单系统不容易发生系统性风险。 随着系统复杂性的增加,这种风险更容易发生,因为即使在详细的压力测试条件下,也更难看到或分析系统中所有可能的变量组合。 一个复杂系统的效率越高,就越容易发生系统性风险,因为只需要很小的偏差就可以破坏系统。 因此,设计良好的复杂系统一般都会有一些内在的功能来避免这种情况的发生,比如在系统内有少量的摩擦力,或阻力,或惯性,或时间延迟来使输出与输入脱钩。这些因素造成了低效率,但它们是避免不稳定的必要条件。<br />
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2010年的闪崩事件被归咎于高频交易(HFT)的做法,不过HFT是否真的会增加系统性风险仍然存在争议。<br />
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====人口与环境危机====<br />
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可以认为农业和人口之间处于一种正反馈模式,这意味着双方越来越强烈地推动彼此。有人认为,这种正反馈系统终将在某一时刻以灾难结束,因为现代农业正在耗尽所有容易获得的磷酸盐,并且进行高效的单一栽培,使得现代农业更容易受到系统性风险影响。<br />
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技术创新和人类人口也可以有类似的考虑,这也是过去人类人口明显的双曲线增长,而不是简单的指数增长的一个解释。<br />
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有人提出,由于人口和技术之间的二阶正反馈,增长速度正在加快。技术增长增加了土地对人的承载能力,从而导致人口增长,而这反过来又推动了技术的进一步增长。<br />
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==== 偏见、社会制度与贫困====<br />
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Gunnar Myrdal描述了一个不平等和贫困加剧的恶性循环,这就是所谓的”循环累积诱因”。<br />
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===气象学===<br />
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干旱通过正反馈效应加剧。缺雨会降低土壤湿度,从而杀死植物,使它们通过蒸腾作用释放更少的水分。这两个因素都限制了水蒸气从地表加到大气中的过程,并使吸收水分的干燥灰尘进入大气。水汽少了,既意味着露点温度低,白天的供暖效率也高,减少了大气中湿度导致云的形成的机会。最后,没有云,就不会有雨,这个正反馈循环就形成了。<br />
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=== 气候学===<br />
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气候中的"诱因 "可能会将气候系统推向变暖或变冷的方向,例如,大气中温室气体浓度的增加会导致地表变暖。诱因是气候系统的外部因素,而反馈是系统的内部过程。一些反馈机制与气候系统的其他部分相对孤立地发挥作用,而另一些则是紧密耦合的。气候系统的作用力、反馈和动态决定了气候变化的程度和速度。全球变暖中的主要正反馈是变暖使大气中的水汽量增加,进而导致进一步变暖。主要的负反馈来自Stefan-Boltzmann定律,从地球辐射到空间的热量与地球表面和大气温度的四次方成正比。<br />
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气候学中正反馈子系统的其他例子包括:<br />
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大气变暖会使冰融化,从而改变反照率,从而使大气进一步变暖。<br />
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甲烷水合物可能是不稳定的,所以海洋变暖可能会释放更多的温室气体之一的甲烷。<br />
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泥炭,天然存在于泥炭沼泽中,含有碳。当泥炭干燥时,它会分解,并可能额外燃烧。泥炭还会释放一氧化二氮。<br />
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全球变暖会影响云的分布。高空的云层会增强温室效应,而低空的云层则主要反射太阳光,对温度产生相反的影响。<br />
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政府间气候变化专门委员会(气专委)第四次评估报告指出,"人类活动的变暖可能导致一些突然或不可逆转的影响,这取决于气候变化的速度和程度"。<br />
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=== 社会学===<br />
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自我应验预言是信念和行为之间的一个社会正反馈循环: 如果有足够多的人相信某件事是真的,他们的行为就能让它变成真的,而对他们行为的观察又可能反过来增加信念。一个典型的例子是银行挤兑。<br />
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正反馈的另一个社会学例子是网络效应。当更多的人被鼓励加入一个网络时,这就增加了网络的覆盖面,因此网络扩张得越来越快。病毒视频就是网络效应的一个例子,在这个例子中,一个热门视频的链接被分享和再传播,确保更多的人看到这个视频,然后重新发布链接。这是许多社会现象的基础,包括庞氏骗局和连锁信。在许多情况下,人口量是反馈效应的限制因素。<br />
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=== 化学===<br />
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如果化学反应引起热量的释放,而反应本身在较高的温度下发生得更快,那么就很有可能出现正反馈。如果产生的热量没有足够快地从反应物中排除,就会发生热失控,并很快导致化学爆炸。<br />
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=== 自然保护===<br />
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许多野生动物被猎杀的原因是它们身体的某些部位可能相当有价值。目标物种越是接近灭绝,其身体部位的价格就越高。这就是正反馈的一个例子。<br />
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==参见==<br />
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* Chain reaction – Sequence of reactions 链式反应 -- -- 反应的顺序<br />
* Donella Meadows' twelve leverage points to intervene in a system Donella Meadows干预系统的十二个杠杆点<br />
* Hyperbolic growth 双曲增长<br />
* Reflexivity (social theory)反射性(社会理论)<br />
* Stability criterion稳定性标准<br />
* Strategic complements战略补充<br />
* System dynamics 系统动力学<br />
* Technological singularity – Hypothetical point in time at which technological growth becomes uncontrollable and irreversible 技术奇点 -- -- 假设技术增长变得不可控制和不可逆转的时间点<br />
* Thermal runaway 热失控<br />
* Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop. 恶性/恶性循环:在社会和金融系统中,是通过反馈循环自我强化的事件综合体。<br />
* Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour. 正强化:在操作性条件下,结果会增加行为的频率。<br />
* Praise of performance: a term often applied in the context of performance appraisal,although this usage is disputed 绩效表扬:这个词经常被应用于绩效评估中,尽管这种用法有争议。<br />
* Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage 自我强化反馈:系统动力学中使用的术语,以避免与 "表扬 "的用法相混淆。<br />
* Matthew effect – Effect originally observed by Robert K. Merton 马太效应 -- -- 罗伯特-K-默顿最初观察到的效应。<br />
* Self-fulfilling prophecy – Prediction that causes itself to become true 自证预言 -- -- 导致自己成为现实的预言<br />
* Virtuous circle and vicious circle 良性循环和恶性循环<br />
* Autocatalysis 自催化<br />
* Meander – Sinuous bend in a series in the channel of a river 蜿蜒曲折 -- -- 河道中一系列蜿蜒曲折的弯道。<br />
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==参考文献==<br />
{{Reflist|2}}<br />
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==拓展阅读==<br />
* Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.<br />
* Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.<br />
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本中文词条由[[用户:Solitude|Solitude]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%AD%A3%E5%8F%8D%E9%A6%88&diff=29626正反馈2022-03-26T09:09:09Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=反馈,正反馈,Positive feedback,加剧反馈,自我强化反馈<br />
|description=在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。正反馈的一个重要特点是小扰动变大,当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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[[File:Herdwick Stampede.jpg|thumb|right|图1:有时,警报或恐慌会通过正反馈在一群动物之间传播,从而引起踩踏事件。]]<br />
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[[File:Stampede loop.png|thumb|图2:在因果环路图中,踩踏事件的发生是一个正反馈循环。]]<br />
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[[File:Birmingham Northern Rock bank run 2007.jpg|thumb|right|图3:在社会学中,网络效应可以迅速产生银行挤兑的正反馈效应。上图是2007年英国北岩银行挤兑事件的照片。]]<br />
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==回顾==<br />
'''Positive feedback''' ('''exacerbating feedback''', '''self-reinforcing feedback''') is a process that occurs in a [[feedback loop]] which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation.Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback.<ref name="theorymodelling" /> Both concepts play an important role in science and engineering, including biology, chemistry, and [[cybernetics]] .<br />
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正反馈(加剧反馈,自我强化反馈) 是一种在反馈循环中加剧微小扰动影响的过程。也就是说,一个扰动对系统的影响包括它自身扰动幅度的增大。或者说,A会产生更多的B,而B又会产生更多的A,与之相反的是,[[负反馈]]指的是一个系统中,变化的结果会减少或抵消它自己的影响。<ref name="theorymodelling" />这两个概念在科学和工程等领域中发挥着重要作用,包括生物学、化学和控制论。<br />
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在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。<ref name="zuckerman" /><ref>Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". ''Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems''. Academic Press. p. 55. ISBN <bdi>9780127784557</bdi>. Archived from the original on 2017-01-03. <q>A positive feedback loop is one with an even number of negative influences [around the loop].</q></ref><ref name="zuckerman" /> 从结果到始发过程的反馈可以是直接的,也可以通过其他状态变量<ref name="theorymodelling" />。这样的系统可以给出丰富的定性行为,但反馈的瞬时信号是正向还是负向,对结果有极其重要的影响。<ref name="theorymodelling" /> 正反馈强化原过程,而负反馈调节原过程。在这个含义下,''正''和''负''指的是大于或小于零的循环收益,并不代表着最终结果或效果的正负性。<ref name=":0">{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>因此,正反馈的一个重要特点是小扰动变大。当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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===基础===<br />
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[[File:Ideal feedback model.svg|thumb|图4:一个基本的反馈系统可以用这个框图来表示。在图中,+号是加法器,A和B是任意因果函数。]]<br />
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图中显示了一个简单的反馈回路。 如果环增益AB为正值,则存在'正'或'再生'反馈的条件。<br />
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如果函数A和B是线性的,且AB小于1,那么系统从输入到输出的整体增益是有限的,但当AB接近1时,系统的增益可以非常大。<ref name="smith"> Electronics circuits and devices second edition. Ralph J. Smith</ref> 在这种情况下,可以表明从输入到输出的整体或 "闭环 "增益为:<br />
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:<math>G_c = A/(1-AB)</math><br />
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当AB>1时,系统是不稳定的,因此不具有明确的增益;增益可称为无限。<br />
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所以系统状态的变化根据反馈可以是收敛的,也可以是发散的。 而正反馈的结果是增强变化,因此小的扰动就可能导致大的变化。<br />
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对于一个当前处于平衡状态的系统,如果其状态的任何变化都发生了正反馈,从而造成了状态的不稳定,那么这个系统就是一个不稳定平衡的系统。使这种系统远离其平衡状态的力的大小是状态与平衡状态之间的距离的递增函数。<br />
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正反馈并不一定意味着平衡的不稳定性,例如,在正反馈结构中可能存在稳定的开关状态<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>。<br />
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=== 迟滞 ===<br />
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[[File:Hysteresis sharp curve.svg|thumb|图5:迟滞现象会导致输出值取决于输入的历史记录。]]<br />
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[[File:Op-Amp Schmitt Trigger.svg|thumb|图6:在施密特触发器电路中,利用放大器的非反相输入端口产生的反馈,可以直接将电路的输出从原本的外加电压值推向到放大器所能产生的极值电压。]]<br />
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在现实世界中,正反馈循环通常不会引起不断增长,而是通过某种限制效应来改变。根据Donella Meadows的说法:<br />
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正反馈回路是系统增长、爆炸、腐蚀和崩溃的根源。一个系统如果有一个不受控制的正反馈,最终将会自我毁灭。这就是为什么正反馈如此稀少的原因。通常情况下,负反馈迟早会发生。<ref>Donella Meadows, ''[http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf Leverage Points: Places to Intervene in a System]''2013-10-08 at the Wayback Machine, 1999</ref><br />
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[[迟滞]],即起点影响系统的终点的现象,可以通过正反馈产生。当反馈循环的增益高于1时,那么输出就会远离输入:如果大于输入,则向最近的正极限移动,而如果小于输入,则向最近的负极限移动。<br />
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一旦达到极限,它就会稳定下来。但是,如果输入超过极限,那么反馈将改变符号,输出将向相反的方向移动,直到达到相反的极限。因此,该系统表现出'''双稳态行为bistable behavior'''。<br />
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== 术语由来==<br />
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正反馈和负反馈这两个名词最早应用于反馈是在二战前。正反馈的概念随着再生电路的问世,在20世纪20年代已经出现。<br />
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Friis 和 Jensen在1924年描述了一种在电子放大器中发生的"回馈 "是正的情况,这一情况与他们顺便提到的负回馈作用相反。到了1934年,Harold Stephen Black在他的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法:<br />
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正反馈会增加放大器的增益,负反馈会降低增益<br />
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据Mindell(2002年)说,术语上的混乱是在这之后不久产生的:<br />
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“ ... ... Friis 和 Jensen 对 Black 在对"正反馈 "和 "负反馈 "的区分方法是一样的,都不是基于反馈本身的符号,而是基于它对放大器增益的影响。与之相反的是,当Nyquist和Bode基于Black的工作基础时,将负反馈称为符号相反的反馈。Black难以说服其他人相信他的发明的实用性,有一部分原因是在基本的定义问题上存在混乱。"<br />
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==实例与应用==<br />
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=== 电子电路===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|图7:一个老式的再生无线电接收器。由于使用正反馈的控制,真空管或阀门(中心)就可以产生足够的放大效果。]]<br />
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'''再生电路Regenerative circuit'''于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>,用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈,可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此,一个信号可以在一个阶段被放大20000甚至100000倍,而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定,开始振荡。无线电操作员必须不断地调整反馈量,以获得良好的接收效果。而现代无线电接收机采用超异构设计,多了许多放大级,去掉了正反馈并使其工作更稳定。<br />
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在再生无线电电路中产生的振荡还可以被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英),经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计,包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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许多电子电路,特别是放大器,都采用了负反馈。这降低了放大器的信号增益,但改善了它的线性度、输入阻抗、输出阻抗和带宽,并稳定了包括闭环增益等参数。同时,这些参数也变得不那么依赖于放大器件本身的细节,而更多地依赖于反馈元件,因为反馈元件一般不随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位:如果信号反馈失相,则反馈为负,如果相位一致,则反馈为正。对于需要使用负反馈放大器的设计者来说,引入负反馈放大器的问题是,电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°,那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波来做到这一点)。如果任何频率下的环增益(放大器增益与正反馈程度的乘积)大于1,那么放大器将在该频率下发生振荡(巴克豪森稳定性准则)。这种振荡有时被称为寄生振荡:在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化,前板(用户界面)的变化,甚至是由于人或其他导电物品的接近。<br />
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放大器可能会以示波器很难检测到的方式轻轻振荡,有时的振荡也可能非常大,只有非常扭曲或根本没有真正的信号,甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似,因此低频寄生振荡也被称为 "汽艇"。<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|图8:使用施密特触发器(b)代替比较器(a)的效果]]<br />
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许多常见的数字电路都采用正反馈。一般简单的布尔逻辑门通常只是依靠增益将数字信号电压从中间值推到代表布尔值0和1的值上,但许多更复杂的门都采用了反馈。当输入的模拟电压发生变化,但后期数字处理需要尖锐阈值时,施密特触发电路通过正反馈机制确保当输入电压轻微超过阈值时,输出电压可以巧妙而迅速地从一个逻辑状态转移到另一个逻辑状态。施密特触发器使用正反馈的一个必然结果是,如果输入电压再次缓慢下降,超过了相同的阈值,由于正反馈的机制,输出电压将保持在相同的逻辑状态而不改变。这种效应被称为滞后: 输入电压必须降到一个不同的、较低的阈值,才能“解锁”输出,并将其重置为原始数字。通过减小正反馈的程度,可以减小滞后宽度,但宽度不能被完全消除。施密特触发器在某种程度上是一个闭锁电路。<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|图9:正反馈是一种增强输出的机制,如蛋白质水平。但为了避免蛋白质水平的波动,该机制是随机抑制的(I),因此只有当激活的蛋白质(A)浓度超过阈值([I])时,循环机制被激活,如果d[A]=k[A],A的浓度就会成倍增加。]]<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|图10 :R-S("复位-设置")触发器的说明,由两个带正反馈的数字诺尔门组成。红色和黑色分别表示逻辑上的 "1 "和 "0"。]]<br />
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电子触发器,或“锁存器” ,或“双稳态多谐振荡器” ,是一种由于高正反馈而不稳定于平衡或中间状态的电路。这样的双稳态电路是一位电子存储器的基础。 触发器使用一对放大器、晶体管或逻辑门相互连接,正反馈机制使得输入信号被去除后,电路可以维持在两种非平衡稳定状态中的一种,直到一个合适的替代信号重新作为输入,以改变电路状态。计算机随机存取存储器(RAM)可以用这种方式运作,每位存储器有一个锁存电路。<br />
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电子系统中发生'''热失控Thermal runaway'''的原因是,当电路的某些方面变得更热时,它被允许通过更多的电流,然后它越热,通过的电流就越多,这就使它更热一些,因此它又通过更多的电流。这种现象对有关器件来说通常是灾难性的。如果器件不得不在接近其最大功率处理能力的情况下工作,那么某些条件下就可能出现热失控,这通常可以通过精心设计来改进。<br />
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[[File:Technics SL-1210MK2.jpg|thumb|left|图11:A phonograph turntable is prone to acoustic feedback. 留声机转盘容易受到声反馈的影响。]]<br />
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音频和视频系统可以表现出正反馈。如果麦克风录入了同一电路中扬声器的放大声音输出,那么就会听到音频反馈的嚎叫和尖叫声(在放大器的最大功率容量下),因为随机噪声被音频系统和房间的特性所过滤后,通过正反馈重新放大。<br />
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===音频与现场音频===<br />
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音频反馈(也称为声反馈,简称反馈,或拉森效应)是一种特殊的正反馈,当音频输入(例如,麦克风或吉他拾音器)和音频输出(例如,大声放大的扬声器)之间存在声音回路时,就会出现这种反馈。在这个例子中,麦克风接收到的信号被放大并从扬声器传出。然后,来自扬声器的声音可以再次被麦克风接收,进一步放大,然后再次通过扬声器传递出去。 所产生的声音的频率由传声器、放大器和扬声器的共振频率、房间的声学特性、传声器和扬声器的定向拾音和发射模式以及它们之间的距离决定。对于小型的扩声系统来说,这种声音很容易的体现的响亮的吱吱声或尖叫声。<br />
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在歌手或公众演讲者使用扩声系统或扩音系统的活动中,麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来,音频工程师使用各种电子设备,如均衡器或者自动反馈检测设备,来防止这些不受欢迎的尖叫声或尖叫声,这些声音影响了观众对活动的享受。另一方面,自20世纪60年代以来,摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果,有意制造吉他中的正反馈,以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈,但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中,他说,“我敢说任何人都找不到这样的唱片,除非是1922年这张用这种方式录制的老蓝调唱片。”<br />
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音频反馈的原理是由丹麦科学家Søren Absalon Larsen首先发现的。麦克风并不是唯一受此影响的传感器。录音板拾音器也会产生正反馈,通常是在100赫兹以下的低频范围内表现出低沉的轰鸣声。Jimi Hendrix是一个创新者,在他的吉他独奏中有意使用吉他正反馈来创造独特的声音效果。他帮助发展了电吉他演奏中音频反馈的可控性和音乐性,后来Brian May也是这种技术的著名支持者。<br />
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[[File:Adam Savage HOPE.jpg|thumb|right|220px|图12:视频反馈]]<br />
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===视频===<br />
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同样,如果一台摄像机对准一个正在显示摄像机自身信号的监控屏幕,那么通过正反馈就可以在屏幕上形成重复的图案。这种视频反馈效果在电视剧《神秘博士》前十季的开场白中就被使用了。<br />
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===开关===<br />
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In [[electrical switch]]es, including [[bimetallic strip]] based thermostats, the switch usually has hysteresis in the switching action. In these cases hysteresis is mechanically achieved via positive feedback within a tipping point mechanism. The positive feedback action minimises the length of time arcing occurs for during the switching and also holds the contacts in an open or closed state.<br />
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在电气开关中,包括双金属条型恒温器,开关通常在开关动作中具有滞后性。在这些情况下,滞后是通过一个临界点机构内的正反馈来实现的。正反馈作用可最大限度地减少开关过程中发生电弧的时间,并使触点保持在断开或闭合状态。<br />
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=== 生物学===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。]]<br />
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生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。<br />
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==== 生理学====<br />
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在生理学中可以找到一些正反馈系统的例子。<br />
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* <br />
其中一个例子是分娩时宫缩的发生,称为弗格森反射。当宫缩发生时,激素催产素会引起神经刺激,刺激下丘脑产生更多的催产素,从而增加子宫收缩。这就导致宫缩的幅度和频率增加。<br />
<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders. {{ISBN|0-7216-3994-1}}</ref><br />
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* <br />
另一个例子是血液凝固的过程。当受伤的组织释放出信号化学物质,激活血液中的血小板时,这个循环就启动了。被激活的血小板释放化学物质,激活更多的血小板,引起快速的级联反应,形成血栓。<ref name=Guyton1991/><br />
<br />
* <br />
哺乳也涉及正反馈,当婴儿吸吮乳头时,会有神经反应进入脊髓,并上传到大脑的下丘脑,然后刺激垂体产生更多的催乳素以产生更多的乳汁<ref name=Guyton1991/>。<br />
<br />
* <br />
在月经周期的卵泡期期间,雌激素的飙升会导致排卵<ref name=Guyton1991/>。<br />
<br />
* <br />
神经信号的产生是另一个例子,神经纤维的膜使钠离子通过钠通道轻微渗漏,导致膜电位的变化,进而引起更多通道的开放(Hodgkin循环)。所以,最初的轻微渗漏会导致钠渗漏的爆发,从而产生神经动作电位<ref name=Guyton1991/>。<br />
<br />
* <br />
在心脏的兴奋收缩耦合中,肌浆网膜中的兰尼碱受体检测到心肌细胞内钙离子的增加,该受体以正反馈生理反应将钙运出到细胞质中。<br />
<br />
在大多数情况下,这种反馈循环最终会释放出反信号,从而抑制或破坏循环。分娩宫缩在宝宝离开母体时停止。化学物质分解血凝块。当婴儿不再需要被哺乳时,泌乳停止<ref name=Guyton1991/>。<br />
<br />
<br />
====基因调控====<br />
<br />
正反馈是基因调控中研究较好的一种现象,其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时,就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络,以证明双稳态的概念。<ref name=Hasty2002/><br />
正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用,因此,基因调控中的正反馈可以产生显著的生理结果。分子动力学中的随机运动加上正反馈可以引发有趣的效应,例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/> 这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中,如酶动力学或代谢途径。<ref name=Christoph2001/><br />
<br />
<br />
==== 进化生物学 ====<br />
<br />
<br />
在进化生物学中正反馈循环被用来描述生物进化中变化动态的各个方面。 例如,在宏观层面,Alfred J. Lotka(1945)认为,物种的演变最重要的是选择反馈能量流动以捕获越来越多的能源系统的能量。<ref name=Lotka1945/>在人类层面,Richard D. Alexander(1989)提出,人类群体之间和群体内部的社会竞争会影响智力的选择,从而时不时地会产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子<ref name=Crespi2004/>。通过与军备竞赛进行类比,给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/><br />
<br />
<br />
[[File:Phanerozoic Biodiversity.svg|300px|right|thumb|显生宙[[生物多样性]]呈现稳定而非单调的增长,从接近于零一直增长到有几千个属。|链接=Special:FilePath/Phanerozoic_Biodiversity.svg]]<br />
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<br />
研究表明,在<font color="#32CD32"> 显生宙 ''',生物多样性的变化与双曲模型(广泛用于人口学和宏观社会学)的相关性要比指数模型和逻辑斯特模型(传统上用于人口生物学,并广泛用于生物多样性化石)的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈(更多的祖先,更多的后代)和资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为,生物多样性和人口曲线之间的相似性可能来自这样一个事实,即两者都是由双曲趋势(由正反馈产生)与周期性和随机性的动态干扰而产生的。<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref><br />
<br />
<br />
==== 免疫系统====<br />
<br />
<br />
细胞因子风暴,或称高细胞因子血症,是一种潜在的致命性免疫反应,表现为各种细胞因子水平高度升高,这是由细胞因子和免疫细胞之间的正反馈环组成。[36]在正常的免疫功能中,可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后,就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合,当B细胞的抗体与C3结合后,就会加快该B细胞分泌更多的抗体和更多的C3蛋白,从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
<br />
====细胞凋亡====<br />
<br />
<br />
细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程,其目的是清除长寿或受损的细胞。这一过程的失效与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活,它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时,无论效应子胱天蛋白酶的中间激活步骤数量有多少,这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/> 当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时,该过程呈现双稳态,从而模拟细胞的存活和死亡状态。<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref><br />
<br />
<br />
<br />
=== 心理学===<br />
<br />
<br />
Winner(1996)将有天赋的孩子描述为受到正反馈循环的驱动,这些反馈循环体现在他们自己的课程学习上,通过反馈自己的满意程度,从而进一步将他们的学习目标提高到更高水平等。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a,2009b)提出,神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释,工作记忆中的思维/表现输出被反馈到小脑,在那里被精简,然后再反馈到工作记忆中,从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/> <br />
<br />
=== 经济学===<br />
<br />
<br />
<br />
<br />
====市场上的社会影响====<br />
<br />
<br />
事实证明,产品推荐和消费者先前的购买信息对消费者的选择影响很大,无论是音乐、电影、书籍、电子产品还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象(马太效应),即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
<br />
====市场动向====<br />
<br />
<br />
根据George Soros提出的反射性理论,价格变化是由一个正反馈过程驱动的,即投资者的预期受到价格变动的影响,因此他们的行为会强化这个方向的价格变动,直到价格的变化变得不可持续,于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
<br />
==== 系统风险====<br />
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<br />
系统性风险是指放大效应或杠杆或正反馈过程给系统带来的风险。这通常是未知的,在某些条件下,这个过程会成倍放大,并迅速导致破坏性或混乱的行为。 庞氏骗局就是正反馈系统的一个很好的例子:来自新投资者的资金被用来支付异常高的回报,反过来又吸引了更多的新投资者,导致快速增长进而走向崩溃。W. Brian Arthur 也对经济中的正反馈进行了研究和著述(如W. Brian Arthur,1990)。Hyman Minsky提出了一个理论,认为某些信用扩张行为会使市场经济变成一个 "偏差放大系统",从而可能会突然崩溃,这有时被称为 "明斯基时刻"。<br />
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<br />
输入和输出明确分开的简单系统不容易发生系统性风险。 随着系统复杂性的增加,这种风险更容易发生,因为即使在详细的压力测试条件下,也更难看到或分析系统中所有可能的变量组合。 一个复杂系统的效率越高,就越容易发生系统性风险,因为只需要很小的偏差就可以破坏系统。 因此,设计良好的复杂系统一般都会有一些内在的功能来避免这种情况的发生,比如在系统内有少量的摩擦力,或阻力,或惯性,或时间延迟来使输出与输入脱钩。这些因素造成了低效率,但它们是避免不稳定的必要条件。<br />
<br />
<br />
2010年的闪崩事件被归咎于高频交易(HFT)的做法,不过HFT是否真的会增加系统性风险仍然存在争议。<br />
<br />
<br />
====人口与环境危机====<br />
<br />
可以认为农业和人口之间处于一种正反馈模式,这意味着双方越来越强烈地推动彼此。有人认为,这种正反馈系统终将在某一时刻以灾难结束,因为现代农业正在耗尽所有容易获得的磷酸盐,并且进行高效的单一栽培,使得现代农业更容易受到系统性风险影响。<br />
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<br />
技术创新和人类人口也可以有类似的考虑,这也是过去人类人口明显的双曲线增长,而不是简单的指数增长的一个解释。<br />
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<br />
有人提出,由于人口和技术之间的二阶正反馈,增长速度正在加快。技术增长增加了土地对人的承载能力,从而导致人口增长,而这反过来又推动了技术的进一步增长。<br />
<br />
==== 偏见、社会制度与贫困====<br />
<br />
Gunnar Myrdal描述了一个不平等和贫困加剧的恶性循环,这就是所谓的”循环累积诱因”。<br />
<br />
===气象学===<br />
<br />
干旱通过正反馈效应加剧。缺雨会降低土壤湿度,从而杀死植物,使它们通过蒸腾作用释放更少的水分。这两个因素都限制了水蒸气从地表加到大气中的过程,并使吸收水分的干燥灰尘进入大气。水汽少了,既意味着露点温度低,白天的供暖效率也高,减少了大气中湿度导致云的形成的机会。最后,没有云,就不会有雨,这个正反馈循环就形成了。<br />
<br />
=== 气候学===<br />
<br />
气候中的"诱因 "可能会将气候系统推向变暖或变冷的方向,例如,大气中温室气体浓度的增加会导致地表变暖。诱因是气候系统的外部因素,而反馈是系统的内部过程。一些反馈机制与气候系统的其他部分相对孤立地发挥作用,而另一些则是紧密耦合的。气候系统的作用力、反馈和动态决定了气候变化的程度和速度。全球变暖中的主要正反馈是变暖使大气中的水汽量增加,进而导致进一步变暖。主要的负反馈来自Stefan-Boltzmann定律,从地球辐射到空间的热量与地球表面和大气温度的四次方成正比。<br />
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<br />
气候学中正反馈子系统的其他例子包括:<br />
<br />
大气变暖会使冰融化,从而改变反照率,从而使大气进一步变暖。<br />
<br />
<br />
甲烷水合物可能是不稳定的,所以海洋变暖可能会释放更多的温室气体之一的甲烷。<br />
<br />
<br />
泥炭,天然存在于泥炭沼泽中,含有碳。当泥炭干燥时,它会分解,并可能额外燃烧。泥炭还会释放一氧化二氮。<br />
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<br />
全球变暖会影响云的分布。高空的云层会增强温室效应,而低空的云层则主要反射太阳光,对温度产生相反的影响。<br />
<br />
政府间气候变化专门委员会(气专委)第四次评估报告指出,"人类活动的变暖可能导致一些突然或不可逆转的影响,这取决于气候变化的速度和程度"。<br />
<br />
=== 社会学===<br />
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<br />
自我应验预言是信念和行为之间的一个社会正反馈循环: 如果有足够多的人相信某件事是真的,他们的行为就能让它变成真的,而对他们行为的观察又可能反过来增加信念。一个典型的例子是银行挤兑。<br />
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正反馈的另一个社会学例子是网络效应。当更多的人被鼓励加入一个网络时,这就增加了网络的覆盖面,因此网络扩张得越来越快。病毒视频就是网络效应的一个例子,在这个例子中,一个热门视频的链接被分享和再传播,确保更多的人看到这个视频,然后重新发布链接。这是许多社会现象的基础,包括庞氏骗局和连锁信。在许多情况下,人口量是反馈效应的限制因素。<br />
<br />
=== 化学===<br />
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<br />
如果化学反应引起热量的释放,而反应本身在较高的温度下发生得更快,那么就很有可能出现正反馈。如果产生的热量没有足够快地从反应物中排除,就会发生热失控,并很快导致化学爆炸。<br />
<br />
=== 自然保护===<br />
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许多野生动物被猎杀的原因是它们身体的某些部位可能相当有价值。目标物种越是接近灭绝,其身体部位的价格就越高。这就是正反馈的一个例子。<br />
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==参见==<br />
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* Chain reaction – Sequence of reactions 链式反应 -- -- 反应的顺序<br />
* Donella Meadows' twelve leverage points to intervene in a system Donella Meadows干预系统的十二个杠杆点<br />
* Hyperbolic growth 双曲增长<br />
* Reflexivity (social theory)反射性(社会理论)<br />
* Stability criterion稳定性标准<br />
* Strategic complements战略补充<br />
* System dynamics 系统动力学<br />
* Technological singularity – Hypothetical point in time at which technological growth becomes uncontrollable and irreversible 技术奇点 -- -- 假设技术增长变得不可控制和不可逆转的时间点<br />
* Thermal runaway 热失控<br />
* Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop. 恶性/恶性循环:在社会和金融系统中,是通过反馈循环自我强化的事件综合体。<br />
* Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour. 正强化:在操作性条件下,结果会增加行为的频率。<br />
* Praise of performance: a term often applied in the context of performance appraisal,although this usage is disputed 绩效表扬:这个词经常被应用于绩效评估中,尽管这种用法有争议。<br />
* Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage 自我强化反馈:系统动力学中使用的术语,以避免与 "表扬 "的用法相混淆。<br />
* Matthew effect – Effect originally observed by Robert K. Merton 马太效应 -- -- 罗伯特-K-默顿最初观察到的效应。<br />
* Self-fulfilling prophecy – Prediction that causes itself to become true 自证预言 -- -- 导致自己成为现实的预言<br />
* Virtuous circle and vicious circle 良性循环和恶性循环<br />
* Autocatalysis 自催化<br />
* Meander – Sinuous bend in a series in the channel of a river 蜿蜒曲折 -- -- 河道中一系列蜿蜒曲折的弯道。<br />
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<br />
==参考文献==<br />
1. ^ a b c Ben Zuckerman & David Jefferson (1996). Human Population and the Environmental Crisis. Jones & Bartlett Learning. p. 42. ISBN 9780867209662. Archived from the original on 2018-01-06.<br />
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2. ^ Keesing, R.M. (1981). Cultural anthropology: A contemporary perspective (2nd ed.) p.149. Sydney: Holt, Rinehard & Winston, Inc.<br />
<br />
3. ^ a b c d e Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems. Academic Press. p. 55. ISBN 9780127784557. Archived from the original on 2017-01-03. “A positive feedback loop is one with an even number of negative influences [around the loop].”<br />
<br />
4. ^ S W Amos; R W Amos (2002). Newnes Dictionary of Electronics (4th ed.). Newnes. p. 247. ISBN 9780750656429. Archived from the original on 2017-03-29.<br />
<br />
5. ^ Rudolf F. Graf (1999). Modern Dictionary of Electronics (7th ed.). Newnes. p. 276. ISBN 9780750698665. Archived from the original on 2017-03-29.<br />
<br />
6. ^ "Positive feedback". Oxford English Dictionary. Oxford University Press. Archived from the original on 2 March 2014. Retrieved 15 April 2014.<br />
<br />
7. ^ "Feedback". Glossary. Metadesigners Network. Archived from the original on 16 April 2014. Retrieved 15 April 2014.<br />
<br />
8. ^ Electronics circuits and devices second edition. Ralph J. Smith<br />
<br />
9. ^ a b Lopez-Caamal, Fernando; Middleton, Richard H.; Huber, Heinrich (February 2014). "Equilibria and stability of a class of positive feedback loops". Journal of Mathematical Biology. 68 (3): 609–645. doi:10.1007/s00285-013-0644-z. PMID 23358701.<br />
<br />
10. ^ Donella Meadows, Leverage Points: Places to Intervene in a System Archived 2013-10-08 at the Wayback Machine, 1999<br />
<br />
11. ^ a b Mindell, David A. (2002). Between Human and Machine : Feedback, Control, and Computing before Cybernetics.Baltimore, MD: Johns Hopkins University Press. ISBN 9780801868955. Archived from the original on 2018-01-06.<br />
<br />
12. ^ Friis, H. T.; Jensen, A. G. (April 1924), "High Frequency Amplifiers", Bell System Technical Journal, 3 (2): 181–205, doi:10.1002/j.1538-7305.1924.tb01354.x<br />
<br />
13. ^ Black, H. S. (January 1934), "Stabilized feed-back amplifiers", Electrical Engineering, 53: 114–120, doi:10.1109/ee.1934.6540374<br />
<br />
14. ^ US 1113149, Armstrong, E. H., "Wireless receiving system"<br />
<br />
15. ^ Kitchin, Charles. "A Short Wave Regenerative Receiver Project". Archived from the original on 10 July 2010. Retrieved 23 September 2010.<br />
<br />
16. ^ "Sinewave oscillators". EDUCYPEDIA - electronics. Archived from the original on 27 September 2010. Retrieved 23 September 2010.<br />
<br />
17. ^ Self, Douglas (2009). Audio Power Amplifier Design Handbook. Focal Press. pp. 254–255. ISBN 978-0-240-52162-6. Archived from the original on 2014-01-29.<br />
<br />
18. ^ "CMOS Schmitt Trigger—A Uniquely Versatile Design Component" (PDF). Fairchild Semiconductor Application Note 140. Fairchild Semiconductors. 1975. Archived (PDF) from the original on 22 November 2010. Retrieved 29 September 2010.<br />
<br />
19. ^ Strandh, Robert. "Latches and flip-flops". Laboratoire Bordelais de Recherche en Informatique. Archived from the original on 16 July 2011. Retrieved 4 November 2010.<br />
<br />
20. ^ Wayne, Storr. "Sequential Logic Basics: SR Flip-Flop". Electronics-Tutorials.ws. Archived from the original on 16 September 2010. Retrieved 29 September 2010.<br />
<br />
21. ^ Sharma, Bijay Kumar (2009). "Analog Electronics Lecture 4 Part C RC coupled Amplifier Design Procedure". Retrieved 29 September 2010.<br />
<br />
22. ^ Sheff, David (2000). All We Are Saying. New York, New York: St. Martin's Press. p. 173. ISBN 978-0-312-25464-3.<br />
<br />
23. ^ Shadwick, Keith (2003). Jimi Hendrix, Musician. Backbeat Books. p. 92. ISBN 978-0-87930-764-6.<br />
<br />
24. ^ May, Brian. "Burns Brian May Tri-Sonic Pickups". House Music & Duck Productions. Archived from the original on 20 November 2010. Retrieved 2 February 2011.<br />
<br />
25. ^ "Positive Feedback and Bistable Systems" (PDF). University of Washington. Archived (PDF) from the original on 2015-04-13. “* Non-Hysteretic Switches, Memoryless Switches: These systems have no memory, that is, once the input signal is removed, the system returns to its original state. * Hysteretic Switches, Bistability: Bistable systems, in contrast, have memory. That is, when switched to one state or another, these systems remain in that state unless forced to change back. The light switch is a common example of a bistable system from everyday life. All bistable systems are based around some form of positive feedback loop.”<br />
<br />
26. ^ a b c d e f Guyton, Arthur C. (1991) Textbook of Medical Physiology. (8th ed). Philadelphia: W.B. Saunders. ISBN 0-7216-3994-1<br />
<br />
27. ^ Hasty, J.; McMillen, D.; Collins, J. J. (2002). "Engineered gene circuits". Nature. 420 (6912): 224–230. Bibcode:2002Natur.420..224H. doi:10.1038/nature01257. PMID 12432407.<br />
<br />
28. ^ Veening, J.; Smits, W. K.; Kuipers, O. P. (2008). "Bistability, Epigenetics, and Bet-Hedging in Bacteria" (PDF). Annual Review of Microbiology. 62 (1): 193–210. doi:10.1146/annurev.micro.62.081307.163002. hdl:11370/59bec46a-4434-4eaa-aaae-03461dd02bbb. PMID 18537474.<br />
<br />
29. ^ Bagowski, C. P.; Ferrell, J. E. (2001). "Bistability in the JNK cascade". Current Biology. 11 (15): 1176–1182. doi:10.1016/S0960-9822(01)00330-X. PMID 11516948.<br />
<br />
30. ^ Lotka, A (1945). "The law of evolution as a maximal principle". Human Biology. 17: 168–194.<br />
<br />
31. ^ Alexander, R. (1989). Evolution of the human psyche. In P. Millar & C. Stringer (Eds.), The human revolution: Behavioral and biological perspectives on the origins of modern humans (pp. 455-513). Princeton: Princeton University Press.<br />
<br />
32. ^ Crespi, B. J. (2004). "Vicious circles: positive feedback in major evolutionary and ecological transitions". Trends in Ecology and Evolution. 19 (12): 627–633. doi:10.1016/j.tree.2004.10.001. PMID 16701324.<br />
<br />
33. ^ Dawkins, R. 1991. The Blind Watchmaker London: Penguin. Note: W.W. Norton also published this book, and some citations may refer to that publication. However, the text is identical, so it depends on which book is at hand<br />
<br />
34. ^ Markov A., Korotayev A. "Phanerozoic marine biodiversity follows a hyperbolic trend." Palaeoworld. Volume 16, Issue 4, December 2007, Pages 311-318<br />
<br />
35. ^ Markov, A.; Korotayev, A. (2008). "Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution". Journal of General Biology. 69 (3): 175–194. PMID 18677962. Archived from the original on 2009-12-25.<br />
<br />
36. ^ Osterholm, Michael T. (2005-05-05). "Preparing for the Next Pandemic". The New England Journal of Medicine. 352 (18): 1839–1842. CiteSeerX 10.1.1.608.6200. doi:10.1056/NEJMp058068. PMID 15872196.<br />
<br />
37. ^ Paul, William E. (September 1993). "Infectious Diseases and the Immune System". Scientific American. 269 (3): 93. Bibcode:1993SciAm.269c..90P. doi:10.1038/scientificamerican0993-90. PMID 8211095.<br />
<br />
38. ^ Eissing, Thomas (2014). "Bistability analyses of a caspase activation model for receptor-induced apoptosis". Journal of Biological Chemistry. 279 (35): 36892–36897. doi:10.1074/jbc.M404893200. PMID 15208304.<br />
<br />
39. ^ Winner, E. (1996). Gifted children: Myths and Realities. New York: Basic Books. ISBN 978-0465017607.<br />
<br />
40. ^ Vandervert, L. (2009a). Working memory, the cognitive functions of the cerebellum and the child prodigy. In L.V. Shavinina (Ed.), International handbook on giftedness (pp. 295-316). The Netherlands: Springer Science.<br />
<br />
41. ^ Vandervert, L. (2009b). "The emergence of the child prodigy 10,000 years ago: An evolutionary and developmental explanation". Journal of Mind and Behavior. 30 (1–2): 15–32.<br />
<br />
42. ^ Altszyler, E; Berbeglia, F.; Berbeglia, G.; Van Hentenryck, P. (2017). "Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality". PLOS ONE. 12 (7): e0180040. Bibcode:2017PLoSO..1280040A. doi:10.1371/journal.pone.0180040. PMC 5528888. PMID 28746334.<br />
<br />
43. ^ Azzopardi, Paul V. (2010), Behavioural Technical Analysis, Harriman House Limited, p. 116, ISBN 9780857190680, archived from the original on 2017-03-29<br />
<br />
44. ^ Arthur, W. Brian (1990). "Positive Feedbacks in the Economy". Scientific American. 262 (2): 80. Bibcode:1990SciAm.262b..92A. doi:10.1038/scientificamerican0290-92.<br />
<br />
45. ^ The Financial Instability Hypothesis Archived 2009-10-09 at the Wayback Machine by Hyman P. Minsky, Working Paper No. 74, May 1992, pp. 6–8<br />
<br />
46. ^ "Findings Regarding the Market Events of May 6, 2010" (PDF). 2010-09-30. Archived (PDF) from the original on August 15, 2017.<br />
<br />
47. ^ Brown, A. Duncan (2003), Feed or Feedback: Agriculture, Population Dynamics and the State of the Planet, Utrecht: International Books, ISBN 978-90-5727-048-2<br />
<br />
48. ^ Dolgonosov, B.M. (2010). "On the reasons of hyperbolic growth in the biological and human world systems". Ecological Modelling. 221 (13–14): 1702–1709. doi:10.1016/j.ecolmodel.2010.03.028.<br />
<br />
49. ^ a b Korotayev A. Compact Mathematical Models of World System Development, and How they can Help us to Clarify our Understanding of Globalization Processes Archived 2018-01-06 at the Wayback Machine. Globalization as Evolutionary Process: Modeling Global Change. Edited by George Modelski, Tessaleno Devezas, and William R. Thompson. London: Routledge, 2007. P. 133-160.<br />
<br />
50. ^ Korotayev, A. V., & Malkov, A. S. A Compact Mathematical Model of the World System Economic and Demographic Growth, 1 CE–1973 CE // INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES Volume 10, 2016. P. 200-209 Archived 2018-01-06 at the Wayback Machine.<br />
<br />
51. ^ Berger, Sebastian. "Circular Cumulative Causation (CCC) à la Myrdal and Kapp — Political Institutionalism for Minimizing Social Costs" (PDF). Archived (PDF) from the original on 26 April 2012. Retrieved 26 November 2011.<br />
<br />
52. ^ S.-Y. Simon Wang; Jin-Ho Yoon; Christopher C. Funk; Robert R. Gillies, eds. (2017). Climate Extremes: Patterns and Mechanisms. Wiley. pp. 81–82. ISBN 9781119068037.<br />
<br />
53. ^ US NRC (2012), Climate Change: Evidence, Impacts, and Choices, US National Research Council (US NRC), archived from the original on 2016-05-03, p.9. Also available as PDF Archived 2013-02-20 at the Wayback Machine<br />
<br />
54. ^ Understanding Climate Change Feedbacks, U.S. National Academy of Sciences Archived 2012-02-10 at the Wayback Machine<br />
<br />
55. ^ "8.6.3.1 Water Vapour and Lapse Rate - AR4 WGI Chapter 8: Climate Models and their Evaluation". Archived from the original on 2010-04-09. Retrieved 2010-04-23.<br />
<br />
56. ^ IPCC. "Climate Change 2007: Synthesis Report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Pg 53" (PDF). Archived (PDF) from the original on 2010-02-09.<br />
<br />
57. ^ Holden, Matthew H.; McDonald-Madden, Eve (2017). "High prices for rare species can drive large populations extinct: The anthropogenic Allee effect revisited". Journal of Theoretical Biology. 429: 170–180. arXiv:1703.06736. Bibcode:2017arXiv170306736H. doi:10.1016/j.jtbi.2017.06.019. PMID 28669883.<br />
<br />
58. ^ Positive feedback occurs when one is told he has done something well or correctly. Tom Coens and Mary Jenkins, "Abolishing Performance Appraisals", p116.<br />
<br />
==拓展阅读==<br />
* Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.<br />
* Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.<br />
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本中文词条由[[用户:Solitude|Solitude]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%AD%A3%E5%8F%8D%E9%A6%88&diff=29624正反馈2022-03-26T09:01:56Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=自相似性,共形对称,膨胀<br />
|description=在物理学、数学和统计学中,标度不变性是物体或者物理定律的一种特征,如果长度、能量或者其他变量的标度与一个公因子相乘,而不发生改变,因此也就代表某种普遍性。<br />
}}<br />
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[[File:Wiener process animated.gif|thumb|right|500px|<br />
维纳过程具有标度不变性。|链接=Special:FilePath/Wiener_process_animated.gif]]<br />
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[[File:Herdwick Stampede.jpg|thumb|right|【图1:有时,警报或恐慌会通过正反馈在一群动物之间传播,从而引起踩踏事件。】.|链接=Special:FilePath/Herdwick_Stampede.jpg]]<br />
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[[File:Stampede loop.png|thumb|【图2:Causal loop diagram that depicts the causes of a stampede as a positive feedback loop. 在因果环路图中,踩踏事件的发生是一个正反馈循环。】|链接=Special:FilePath/Stampede_loop.png]]<br />
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[[File:Birmingham Northern Rock bank run 2007.jpg|thumb|right|【图3:In sociology a network effect can quickly create the positive feedback of a bank run. The above photo is of the UK Northern Rock 2007 bank run. 在社会学中,网络效应可以迅速产生银行挤兑的正反馈效应。上图是2007年英国北岩银行挤兑事件的照片。】|链接=Special:FilePath/Birmingham_Northern_Rock_bank_run_2007.jpg]]<br />
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==回顾==<br />
'''Positive feedback''' ('''exacerbating feedback''', '''self-reinforcing feedback''') is a process that occurs in a [[feedback loop]] which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation.Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback.<ref name="theorymodelling" /> Both concepts play an important role in science and engineering, including biology, chemistry, and [[cybernetics]] .<br />
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正反馈(加剧反馈,自我强化反馈) 是一种在反馈循环中加剧微小扰动影响的过程。也就是说,一个扰动对系统的影响包括它自身扰动幅度的增大。或者说,A会产生更多的B,而B又会产生更多的A,与之相反的是,[[负反馈]]指的是一个系统中,变化的结果会减少或抵消它自己的影响。<ref name="theorymodelling" />这两个概念在科学和工程等领域中发挥着重要作用,包括生物学、化学和控制论。<br />
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在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。<ref name="zuckerman" /><ref>Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". ''Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems''. Academic Press. p. 55. ISBN <bdi>9780127784557</bdi>. Archived from the original on 2017-01-03. <q>A positive feedback loop is one with an even number of negative influences [around the loop].</q></ref><ref name="zuckerman" /> 从结果到始发过程的反馈可以是直接的,也可以通过其他状态变量<ref name="theorymodelling" />。这样的系统可以给出丰富的定性行为,但反馈的瞬时信号是正向还是负向,对结果有极其重要的影响。<ref name="theorymodelling" /> 正反馈强化原过程,而负反馈调节原过程。在这个含义下,''正''和''负''指的是大于或小于零的循环收益,并不代表着最终结果或效果的正负性。<ref name=":0">{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>因此,正反馈的一个重要特点是小扰动变大。当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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===基础===<br />
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[[File:Ideal feedback model.svg|thumb|【图4:A basic feedback system can be represented by this block diagram. In the diagram the + symbol is an adder and A and B are arbitrary causal functions. 一个基本的反馈系统可以用这个框图来表示。在图中,+号是加法器,A和B是任意因果函数。】|链接=Special:FilePath/Ideal_feedback_model.svg]]<br />
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图中显示了一个简单的反馈回路。 如果环增益AB为正值,则存在'正'或'再生'反馈的条件。<br />
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如果函数A和B是线性的,且AB小于1,那么系统从输入到输出的整体增益是有限的,但当AB接近1时,系统的增益可以非常大。<ref name="smith"> Electronics circuits and devices second edition. Ralph J. Smith</ref> 在这种情况下,可以表明从输入到输出的整体或 "闭环 "增益为:<br />
<br />
:<math>G_c = A/(1-AB)</math><br />
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当AB>1时,系统是不稳定的,因此不具有明确的增益;增益可称为无限。<br />
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<br />
所以系统状态的变化根据反馈可以是收敛的,也可以是发散的。 而正反馈的结果是增强变化,因此小的扰动就可能导致大的变化。<br />
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对于一个当前处于平衡状态的系统,如果其状态的任何变化都发生了正反馈,从而造成了状态的不稳定,那么这个系统就是一个不稳定平衡的系统。使这种系统远离其平衡状态的力的大小是状态与平衡状态之间的距离的递增函数。<br />
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正反馈并不一定意味着平衡的不稳定性,例如,在正反馈结构中可能存在稳定的开关状态<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>。<br />
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=== 迟滞 ===<br />
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[[File:Hysteresis sharp curve.svg|thumb|【图5 Hysteresis causes the output value to depend on the history of the input 迟滞现象会导致输出值取决于输入的历史记录。】|链接=Special:FilePath/Hysteresis_sharp_curve.svg]]<br />
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[[File:Op-Amp Schmitt Trigger.svg|thumb|【图6 In a Schmitt trigger circuit, feedback to the non-inverting input of an amplifier pushes the output directly away from the applied voltage towards the maximum or minimum voltage the amplifier can generate. 在施密特触发器电路中,利用放大器的非反相输入端口产生的反馈,可以直接将电路的输出从原本的外加电压值推向到放大器所能产生的极值电压。】|链接=Special:FilePath/Op-Amp_Schmitt_Trigger.svg]]<br />
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在现实世界中,正反馈循环通常不会引起不断增长,而是通过某种限制效应来改变。根据Donella Meadows的说法:<br />
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正反馈回路是系统增长、爆炸、腐蚀和崩溃的根源。一个系统如果有一个不受控制的正反馈,最终将会自我毁灭。这就是为什么正反馈如此稀少的原因。通常情况下,负反馈迟早会发生。<ref>Donella Meadows, ''[http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf Leverage Points: Places to Intervene in a System]''2013-10-08 at the Wayback Machine, 1999</ref><br />
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[[迟滞]],即起点影响系统的终点的现象,可以通过正反馈产生。当反馈循环的增益高于1时,那么输出就会远离输入:如果大于输入,则向最近的正极限移动,而如果小于输入,则向最近的负极限移动。<br />
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一旦达到极限,它就会稳定下来。但是,如果输入超过极限,那么反馈将改变符号,输出将向相反的方向移动,直到达到相反的极限。因此,该系统表现出'''双稳态行为bistable behavior'''。<br />
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== 术语由来==<br />
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正反馈和负反馈这两个名词最早应用于反馈是在二战前。正反馈的概念随着再生电路的问世,在20世纪20年代已经出现。<br />
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Friis 和 Jensen在1924年描述了一种在电子放大器中发生的"回馈 "是正的情况,这一情况与他们顺便提到的负回馈作用相反。到了1934年,Harold Stephen Black在他的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法:<br />
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正反馈会增加放大器的增益,负反馈会降低增益<br />
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据Mindell(2002年)说,术语上的混乱是在这之后不久产生的:<br />
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“ ... ... Friis 和 Jensen 对 Black 在对"正反馈 "和 "负反馈 "的区分方法是一样的,都不是基于反馈本身的符号,而是基于它对放大器增益的影响。与之相反的是,当Nyquist和Bode基于Black的工作基础时,将负反馈称为符号相反的反馈。Black难以说服其他人相信他的发明的实用性,有一部分原因是在基本的定义问题上存在混乱。"<br />
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==实例与应用==<br />
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=== 电子电路===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|【图7 A vintage style regenerative radio receiver. Due to the controlled use of positive feedback, sufficient amplification can be derived from a single [[vacuum tube]] or valve (centre). 一个老式的再生无线电接收器。由于使用正反馈的控制,真空管或阀门(中心)就可以产生足够的放大效果。】|链接=Special:FilePath/Regenerartive_Receiver-S7300056.JPG]]<br />
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'''再生电路Regenerative circuit'''于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>,用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈,可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此,一个信号可以在一个阶段被放大20000甚至100000倍,而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定,开始振荡。无线电操作员必须不断地调整反馈量,以获得良好的接收效果。而现代无线电接收机采用超异构设计,多了许多放大级,去掉了正反馈并使其工作更稳定。<br />
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在再生无线电电路中产生的振荡还可以被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英),经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计,包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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许多电子电路,特别是放大器,都采用了负反馈。这降低了放大器的信号增益,但改善了它的线性度、输入阻抗、输出阻抗和带宽,并稳定了包括闭环增益等参数。同时,这些参数也变得不那么依赖于放大器件本身的细节,而更多地依赖于反馈元件,因为反馈元件一般不随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位:如果信号反馈失相,则反馈为负,如果相位一致,则反馈为正。对于需要使用负反馈放大器的设计者来说,引入负反馈放大器的问题是,电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°,那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波来做到这一点)。如果任何频率下的环增益(放大器增益与正反馈程度的乘积)大于1,那么放大器将在该频率下发生振荡(巴克豪森稳定性准则)。这种振荡有时被称为寄生振荡:在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化,前板(用户界面)的变化,甚至是由于人或其他导电物品的接近。<br />
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放大器可能会以示波器很难检测到的方式轻轻振荡,有时的振荡也可能非常大,只有非常扭曲或根本没有真正的信号,甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似,因此低频寄生振荡也被称为 "汽艇"。<br />
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【图8 The effect of using a Schmitt trigger (B) instead of a comparator (A) 使用施密特触发器(b)代替比较器(a)的效果】<br />
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许多常见的数字电路都采用正反馈。一般简单的布尔逻辑门通常只是依靠增益将数字信号电压从中间值推到代表布尔值0和1的值上,但许多更复杂的门都采用了反馈。当输入的模拟电压发生变化,但后期数字处理需要尖锐阈值时,施密特触发电路通过正反馈机制确保当输入电压轻微超过阈值时,输出电压可以巧妙而迅速地从一个逻辑状态转移到另一个逻辑状态。施密特触发器使用正反馈的一个必然结果是,如果输入电压再次缓慢下降,超过了相同的阈值,由于正反馈的机制,输出电压将保持在相同的逻辑状态而不改变。这种效应被称为滞后: 输入电压必须降到一个不同的、较低的阈值,才能“解锁”输出,并将其重置为原始数字。通过减小正反馈的程度,可以减小滞后宽度,但宽度不能被完全消除。施密特触发器在某种程度上是一个闭锁电路。<br />
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【图9 Positive feedback is a mechanism by which an output is enhanced, such as protein levels. However, in order to avoid any fluctuation in the protein level, the mechanism is inhibited stochastically (I), therefore when the concentration of the activated protein (A) is past the threshold ([I]), the loop mechanism is activated and the concentration of A increases exponentially if d[A]=k [A] 正反馈是一种增强输出的机制,如蛋白质水平。但为了避免蛋白质水平的波动,该机制是随机抑制的(I),因此只有当激活的蛋白质(A)浓度超过阈值([I])时,循环机制被激活,如果d[A]=k[A],A的浓度就会成倍增加。】<br />
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【图10 Illustration of an R-S ('reset-set') flip-flop made from two digital nor gates with positive feedback. Red and black mean logical '1' and '0', respectively. R-S("复位-设置")触发器的说明,由两个带正反馈的数字诺尔门组成。红色和黑色分别表示逻辑上的 "1 "和 "0"。】<br />
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电子触发器,或“锁存器” ,或“双稳态多谐振荡器” ,是一种由于高正反馈而不稳定于平衡或中间状态的电路。这样的双稳态电路是一位电子存储器的基础。 触发器使用一对放大器、晶体管或逻辑门相互连接,正反馈机制使得输入信号被去除后,电路可以维持在两种非平衡稳定状态中的一种,直到一个合适的替代信号重新作为输入,以改变电路状态。计算机随机存取存储器(RAM)可以用这种方式运作,每位存储器有一个锁存电路。<br />
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电子系统中发生'''热失控Thermal runaway'''的原因是,当电路的某些方面变得更热时,它被允许通过更多的电流,然后它越热,通过的电流就越多,这就使它更热一些,因此它又通过更多的电流。这种现象对有关器件来说通常是灾难性的。如果器件不得不在接近其最大功率处理能力的情况下工作,那么某些条件下就可能出现热失控,这通常可以通过精心设计来改进。<br />
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[[File:Technics SL-1210MK2.jpg|thumb|left|【图11 A phonograph turntable is prone to acoustic feedback. 留声机转盘容易受到声反馈的影响。】|链接=Special:FilePath/Technics_SL-1210MK2.jpg]]<br />
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音频和视频系统可以表现出正反馈。如果麦克风录入了同一电路中扬声器的放大声音输出,那么就会听到音频反馈的嚎叫和尖叫声(在放大器的最大功率容量下),因为随机噪声被音频系统和房间的特性所过滤后,通过正反馈重新放大。<br />
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===音频与现场音频===<br />
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音频反馈(也称为声反馈,简称反馈,或拉森效应)是一种特殊的正反馈,当音频输入(例如,麦克风或吉他拾音器)和音频输出(例如,大声放大的扬声器)之间存在声音回路时,就会出现这种反馈。在这个例子中,麦克风接收到的信号被放大并从扬声器传出。然后,来自扬声器的声音可以再次被麦克风接收,进一步放大,然后再次通过扬声器传递出去。 所产生的声音的频率由传声器、放大器和扬声器的共振频率、房间的声学特性、传声器和扬声器的定向拾音和发射模式以及它们之间的距离决定。对于小型的扩声系统来说,这种声音很容易的体现的响亮的吱吱声或尖叫声。<br />
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在歌手或公众演讲者使用扩声系统或扩音系统的活动中,麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来,音频工程师使用各种电子设备,如均衡器或者自动反馈检测设备,来防止这些不受欢迎的尖叫声或尖叫声,这些声音影响了观众对活动的享受。另一方面,自20世纪60年代以来,摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果,有意制造吉他中的正反馈,以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈,但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中,他说,“我敢说任何人都找不到这样的唱片,除非是1922年这张用这种方式录制的老蓝调唱片。”<br />
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音频反馈的原理是由丹麦科学家Søren Absalon Larsen首先发现的。麦克风并不是唯一受此影响的传感器。录音板拾音器也会产生正反馈,通常是在100赫兹以下的低频范围内表现出低沉的轰鸣声。Jimi Hendrix是一个创新者,在他的吉他独奏中有意使用吉他正反馈来创造独特的声音效果。他帮助发展了电吉他演奏中音频反馈的可控性和音乐性,后来Brian May也是这种技术的著名支持者。<br />
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[[File:Adam Savage HOPE.jpg|thumb|right|220px|[[Video feedback]]【图12 视频反馈】.|链接=Special:FilePath/Adam_Savage_HOPE.jpg]]<br />
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===视频===<br />
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同样,如果一台摄像机对准一个正在显示摄像机自身信号的监控屏幕,那么通过正反馈就可以在屏幕上形成重复的图案。这种视频反馈效果在电视剧《神秘博士》前十季的开场白中就被使用了。<br />
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===开关===<br />
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In [[electrical switch]]es, including [[bimetallic strip]] based thermostats, the switch usually has hysteresis in the switching action. In these cases hysteresis is mechanically achieved via positive feedback within a tipping point mechanism. The positive feedback action minimises the length of time arcing occurs for during the switching and also holds the contacts in an open or closed state.<br />
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在电气开关中,包括双金属条型恒温器,开关通常在开关动作中具有滞后性。在这些情况下,滞后是通过一个临界点机构内的正反馈来实现的。正反馈作用可最大限度地减少开关过程中发生电弧的时间,并使触点保持在断开或闭合状态。<br />
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=== 生物学===<br />
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[[File:Positive Feedback- Childbirth (1).svg|thumb|生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。|链接=Special:FilePath/Positive_Feedback-_Childbirth_(1).svg]]<br />
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生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。<br />
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==== 生理学====<br />
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在生理学中可以找到一些正反馈系统的例子。<br />
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其中一个例子是分娩时宫缩的发生,称为弗格森反射。当宫缩发生时,激素催产素会引起神经刺激,刺激下丘脑产生更多的催产素,从而增加子宫收缩。这就导致宫缩的幅度和频率增加。<br />
<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders. {{ISBN|0-7216-3994-1}}</ref><br />
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另一个例子是血液凝固的过程。当受伤的组织释放出信号化学物质,激活血液中的血小板时,这个循环就启动了。被激活的血小板释放化学物质,激活更多的血小板,引起快速的级联反应,形成血栓。<ref name=Guyton1991/><br />
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哺乳也涉及正反馈,当婴儿吸吮乳头时,会有神经反应进入脊髓,并上传到大脑的下丘脑,然后刺激垂体产生更多的催乳素以产生更多的乳汁<ref name=Guyton1991/>。<br />
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在月经周期的卵泡期期间,雌激素的飙升会导致排卵<ref name=Guyton1991/>。<br />
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神经信号的产生是另一个例子,神经纤维的膜使钠离子通过钠通道轻微渗漏,导致膜电位的变化,进而引起更多通道的开放(Hodgkin循环)。所以,最初的轻微渗漏会导致钠渗漏的爆发,从而产生神经动作电位<ref name=Guyton1991/>。<br />
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在心脏的兴奋收缩耦合中,肌浆网膜中的兰尼碱受体检测到心肌细胞内钙离子的增加,该受体以正反馈生理反应将钙运出到细胞质中。<br />
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在大多数情况下,这种反馈循环最终会释放出反信号,从而抑制或破坏循环。分娩宫缩在宝宝离开母体时停止。化学物质分解血凝块。当婴儿不再需要被哺乳时,泌乳停止<ref name=Guyton1991/>。<br />
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====基因调控====<br />
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正反馈是基因调控中研究较好的一种现象,其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时,就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络,以证明双稳态的概念。<ref name=Hasty2002/><br />
正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用,因此,基因调控中的正反馈可以产生显著的生理结果。分子动力学中的随机运动加上正反馈可以引发有趣的效应,例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/> 这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中,如酶动力学或代谢途径。<ref name=Christoph2001/><br />
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==== 进化生物学 ====<br />
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在进化生物学中正反馈循环被用来描述生物进化中变化动态的各个方面。 例如,在宏观层面,Alfred J. Lotka(1945)认为,物种的演变最重要的是选择反馈能量流动以捕获越来越多的能源系统的能量。<ref name=Lotka1945/>在人类层面,Richard D. Alexander(1989)提出,人类群体之间和群体内部的社会竞争会影响智力的选择,从而时不时地会产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子<ref name=Crespi2004/>。通过与军备竞赛进行类比,给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/><br />
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[[File:Phanerozoic Biodiversity.svg|300px|right|thumb|显生宙[[生物多样性]]呈现稳定而非单调的增长,从接近于零一直增长到有几千个属。|链接=Special:FilePath/Phanerozoic_Biodiversity.svg]]<br />
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研究表明,在<font color="#32CD32"> 显生宙 ''',生物多样性的变化与双曲模型(广泛用于人口学和宏观社会学)的相关性要比指数模型和逻辑斯特模型(传统上用于人口生物学,并广泛用于生物多样性化石)的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈(更多的祖先,更多的后代)和资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为,生物多样性和人口曲线之间的相似性可能来自这样一个事实,即两者都是由双曲趋势(由正反馈产生)与周期性和随机性的动态干扰而产生的。<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref><br />
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==== 免疫系统====<br />
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细胞因子风暴,或称高细胞因子血症,是一种潜在的致命性免疫反应,表现为各种细胞因子水平高度升高,这是由细胞因子和免疫细胞之间的正反馈环组成。[36]在正常的免疫功能中,可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后,就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合,当B细胞的抗体与C3结合后,就会加快该B细胞分泌更多的抗体和更多的C3蛋白,从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
<br />
====细胞凋亡====<br />
<br />
<br />
细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程,其目的是清除长寿或受损的细胞。这一过程的失效与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活,它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时,无论效应子胱天蛋白酶的中间激活步骤数量有多少,这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/> 当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时,该过程呈现双稳态,从而模拟细胞的存活和死亡状态。<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref><br />
<br />
<br />
<br />
=== 心理学===<br />
<br />
<br />
Winner(1996)将有天赋的孩子描述为受到正反馈循环的驱动,这些反馈循环体现在他们自己的课程学习上,通过反馈自己的满意程度,从而进一步将他们的学习目标提高到更高水平等。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a,2009b)提出,神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释,工作记忆中的思维/表现输出被反馈到小脑,在那里被精简,然后再反馈到工作记忆中,从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/> <br />
<br />
=== 经济学===<br />
<br />
<br />
<br />
<br />
====市场上的社会影响====<br />
<br />
<br />
事实证明,产品推荐和消费者先前的购买信息对消费者的选择影响很大,无论是音乐、电影、书籍、电子产品还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象(马太效应),即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
<br />
====市场动向====<br />
<br />
<br />
根据George Soros提出的反射性理论,价格变化是由一个正反馈过程驱动的,即投资者的预期受到价格变动的影响,因此他们的行为会强化这个方向的价格变动,直到价格的变化变得不可持续,于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
<br />
==== 系统风险====<br />
<br />
<br />
系统性风险是指放大效应或杠杆或正反馈过程给系统带来的风险。这通常是未知的,在某些条件下,这个过程会成倍放大,并迅速导致破坏性或混乱的行为。 庞氏骗局就是正反馈系统的一个很好的例子:来自新投资者的资金被用来支付异常高的回报,反过来又吸引了更多的新投资者,导致快速增长进而走向崩溃。W. Brian Arthur 也对经济中的正反馈进行了研究和著述(如W. Brian Arthur,1990)。Hyman Minsky提出了一个理论,认为某些信用扩张行为会使市场经济变成一个 "偏差放大系统",从而可能会突然崩溃,这有时被称为 "明斯基时刻"。<br />
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输入和输出明确分开的简单系统不容易发生系统性风险。 随着系统复杂性的增加,这种风险更容易发生,因为即使在详细的压力测试条件下,也更难看到或分析系统中所有可能的变量组合。 一个复杂系统的效率越高,就越容易发生系统性风险,因为只需要很小的偏差就可以破坏系统。 因此,设计良好的复杂系统一般都会有一些内在的功能来避免这种情况的发生,比如在系统内有少量的摩擦力,或阻力,或惯性,或时间延迟来使输出与输入脱钩。这些因素造成了低效率,但它们是避免不稳定的必要条件。<br />
<br />
<br />
2010年的闪崩事件被归咎于高频交易(HFT)的做法,不过HFT是否真的会增加系统性风险仍然存在争议。<br />
<br />
<br />
====人口与环境危机====<br />
<br />
可以认为农业和人口之间处于一种正反馈模式,这意味着双方越来越强烈地推动彼此。有人认为,这种正反馈系统终将在某一时刻以灾难结束,因为现代农业正在耗尽所有容易获得的磷酸盐,并且进行高效的单一栽培,使得现代农业更容易受到系统性风险影响。<br />
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技术创新和人类人口也可以有类似的考虑,这也是过去人类人口明显的双曲线增长,而不是简单的指数增长的一个解释。<br />
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有人提出,由于人口和技术之间的二阶正反馈,增长速度正在加快。技术增长增加了土地对人的承载能力,从而导致人口增长,而这反过来又推动了技术的进一步增长。<br />
<br />
==== 偏见、社会制度与贫困====<br />
<br />
Gunnar Myrdal描述了一个不平等和贫困加剧的恶性循环,这就是所谓的”循环累积诱因”。<br />
<br />
===气象学===<br />
<br />
干旱通过正反馈效应加剧。缺雨会降低土壤湿度,从而杀死植物,使它们通过蒸腾作用释放更少的水分。这两个因素都限制了水蒸气从地表加到大气中的过程,并使吸收水分的干燥灰尘进入大气。水汽少了,既意味着露点温度低,白天的供暖效率也高,减少了大气中湿度导致云的形成的机会。最后,没有云,就不会有雨,这个正反馈循环就形成了。<br />
<br />
=== 气候学===<br />
<br />
气候中的"诱因 "可能会将气候系统推向变暖或变冷的方向,例如,大气中温室气体浓度的增加会导致地表变暖。诱因是气候系统的外部因素,而反馈是系统的内部过程。一些反馈机制与气候系统的其他部分相对孤立地发挥作用,而另一些则是紧密耦合的。气候系统的作用力、反馈和动态决定了气候变化的程度和速度。全球变暖中的主要正反馈是变暖使大气中的水汽量增加,进而导致进一步变暖。主要的负反馈来自Stefan-Boltzmann定律,从地球辐射到空间的热量与地球表面和大气温度的四次方成正比。<br />
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气候学中正反馈子系统的其他例子包括:<br />
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大气变暖会使冰融化,从而改变反照率,从而使大气进一步变暖。<br />
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甲烷水合物可能是不稳定的,所以海洋变暖可能会释放更多的温室气体之一的甲烷。<br />
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<br />
泥炭,天然存在于泥炭沼泽中,含有碳。当泥炭干燥时,它会分解,并可能额外燃烧。泥炭还会释放一氧化二氮。<br />
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<br />
全球变暖会影响云的分布。高空的云层会增强温室效应,而低空的云层则主要反射太阳光,对温度产生相反的影响。<br />
<br />
政府间气候变化专门委员会(气专委)第四次评估报告指出,"人类活动的变暖可能导致一些突然或不可逆转的影响,这取决于气候变化的速度和程度"。<br />
<br />
=== 社会学===<br />
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<br />
自我应验预言是信念和行为之间的一个社会正反馈循环: 如果有足够多的人相信某件事是真的,他们的行为就能让它变成真的,而对他们行为的观察又可能反过来增加信念。一个典型的例子是银行挤兑。<br />
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正反馈的另一个社会学例子是网络效应。当更多的人被鼓励加入一个网络时,这就增加了网络的覆盖面,因此网络扩张得越来越快。病毒视频就是网络效应的一个例子,在这个例子中,一个热门视频的链接被分享和再传播,确保更多的人看到这个视频,然后重新发布链接。这是许多社会现象的基础,包括庞氏骗局和连锁信。在许多情况下,人口量是反馈效应的限制因素。<br />
<br />
=== 化学===<br />
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<br />
如果化学反应引起热量的释放,而反应本身在较高的温度下发生得更快,那么就很有可能出现正反馈。如果产生的热量没有足够快地从反应物中排除,就会发生热失控,并很快导致化学爆炸。<br />
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=== 自然保护===<br />
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许多野生动物被猎杀的原因是它们身体的某些部位可能相当有价值。目标物种越是接近灭绝,其身体部位的价格就越高。这就是正反馈的一个例子。<br />
<br />
==参见==<br />
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* Chain reaction – Sequence of reactions 链式反应 -- -- 反应的顺序<br />
* Donella Meadows' twelve leverage points to intervene in a system Donella Meadows干预系统的十二个杠杆点<br />
* Hyperbolic growth 双曲增长<br />
* Reflexivity (social theory)反射性(社会理论)<br />
* Stability criterion稳定性标准<br />
* Strategic complements战略补充<br />
* System dynamics 系统动力学<br />
* Technological singularity – Hypothetical point in time at which technological growth becomes uncontrollable and irreversible 技术奇点 -- -- 假设技术增长变得不可控制和不可逆转的时间点<br />
* Thermal runaway 热失控<br />
* Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop. 恶性/恶性循环:在社会和金融系统中,是通过反馈循环自我强化的事件综合体。<br />
* Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour. 正强化:在操作性条件下,结果会增加行为的频率。<br />
* Praise of performance: a term often applied in the context of performance appraisal,although this usage is disputed 绩效表扬:这个词经常被应用于绩效评估中,尽管这种用法有争议。<br />
* Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage 自我强化反馈:系统动力学中使用的术语,以避免与 "表扬 "的用法相混淆。<br />
* Matthew effect – Effect originally observed by Robert K. Merton 马太效应 -- -- 罗伯特-K-默顿最初观察到的效应。<br />
* Self-fulfilling prophecy – Prediction that causes itself to become true 自证预言 -- -- 导致自己成为现实的预言<br />
* Virtuous circle and vicious circle 良性循环和恶性循环<br />
* Autocatalysis 自催化<br />
* Meander – Sinuous bend in a series in the channel of a river 蜿蜒曲折 -- -- 河道中一系列蜿蜒曲折的弯道。<br />
<br />
<br />
==参考文献==<br />
1. ^ a b c Ben Zuckerman & David Jefferson (1996). Human Population and the Environmental Crisis. Jones & Bartlett Learning. p. 42. ISBN 9780867209662. Archived from the original on 2018-01-06.<br />
<br />
2. ^ Keesing, R.M. (1981). Cultural anthropology: A contemporary perspective (2nd ed.) p.149. Sydney: Holt, Rinehard & Winston, Inc.<br />
<br />
3. ^ a b c d e Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems. Academic Press. p. 55. ISBN 9780127784557. Archived from the original on 2017-01-03. “A positive feedback loop is one with an even number of negative influences [around the loop].”<br />
<br />
4. ^ S W Amos; R W Amos (2002). Newnes Dictionary of Electronics (4th ed.). Newnes. p. 247. ISBN 9780750656429. Archived from the original on 2017-03-29.<br />
<br />
5. ^ Rudolf F. Graf (1999). Modern Dictionary of Electronics (7th ed.). Newnes. p. 276. ISBN 9780750698665. Archived from the original on 2017-03-29.<br />
<br />
6. ^ "Positive feedback". Oxford English Dictionary. Oxford University Press. Archived from the original on 2 March 2014. Retrieved 15 April 2014.<br />
<br />
7. ^ "Feedback". Glossary. Metadesigners Network. Archived from the original on 16 April 2014. Retrieved 15 April 2014.<br />
<br />
8. ^ Electronics circuits and devices second edition. Ralph J. Smith<br />
<br />
9. ^ a b Lopez-Caamal, Fernando; Middleton, Richard H.; Huber, Heinrich (February 2014). "Equilibria and stability of a class of positive feedback loops". Journal of Mathematical Biology. 68 (3): 609–645. doi:10.1007/s00285-013-0644-z. PMID 23358701.<br />
<br />
10. ^ Donella Meadows, Leverage Points: Places to Intervene in a System Archived 2013-10-08 at the Wayback Machine, 1999<br />
<br />
11. ^ a b Mindell, David A. (2002). Between Human and Machine : Feedback, Control, and Computing before Cybernetics.Baltimore, MD: Johns Hopkins University Press. ISBN 9780801868955. Archived from the original on 2018-01-06.<br />
<br />
12. ^ Friis, H. T.; Jensen, A. G. (April 1924), "High Frequency Amplifiers", Bell System Technical Journal, 3 (2): 181–205, doi:10.1002/j.1538-7305.1924.tb01354.x<br />
<br />
13. ^ Black, H. S. (January 1934), "Stabilized feed-back amplifiers", Electrical Engineering, 53: 114–120, doi:10.1109/ee.1934.6540374<br />
<br />
14. ^ US 1113149, Armstrong, E. H., "Wireless receiving system"<br />
<br />
15. ^ Kitchin, Charles. "A Short Wave Regenerative Receiver Project". Archived from the original on 10 July 2010. Retrieved 23 September 2010.<br />
<br />
16. ^ "Sinewave oscillators". EDUCYPEDIA - electronics. Archived from the original on 27 September 2010. Retrieved 23 September 2010.<br />
<br />
17. ^ Self, Douglas (2009). Audio Power Amplifier Design Handbook. Focal Press. pp. 254–255. ISBN 978-0-240-52162-6. Archived from the original on 2014-01-29.<br />
<br />
18. ^ "CMOS Schmitt Trigger—A Uniquely Versatile Design Component" (PDF). Fairchild Semiconductor Application Note 140. Fairchild Semiconductors. 1975. Archived (PDF) from the original on 22 November 2010. Retrieved 29 September 2010.<br />
<br />
19. ^ Strandh, Robert. "Latches and flip-flops". Laboratoire Bordelais de Recherche en Informatique. Archived from the original on 16 July 2011. Retrieved 4 November 2010.<br />
<br />
20. ^ Wayne, Storr. "Sequential Logic Basics: SR Flip-Flop". Electronics-Tutorials.ws. Archived from the original on 16 September 2010. Retrieved 29 September 2010.<br />
<br />
21. ^ Sharma, Bijay Kumar (2009). "Analog Electronics Lecture 4 Part C RC coupled Amplifier Design Procedure". Retrieved 29 September 2010.<br />
<br />
22. ^ Sheff, David (2000). All We Are Saying. New York, New York: St. Martin's Press. p. 173. ISBN 978-0-312-25464-3.<br />
<br />
23. ^ Shadwick, Keith (2003). Jimi Hendrix, Musician. Backbeat Books. p. 92. ISBN 978-0-87930-764-6.<br />
<br />
24. ^ May, Brian. "Burns Brian May Tri-Sonic Pickups". House Music & Duck Productions. Archived from the original on 20 November 2010. Retrieved 2 February 2011.<br />
<br />
25. ^ "Positive Feedback and Bistable Systems" (PDF). University of Washington. Archived (PDF) from the original on 2015-04-13. “* Non-Hysteretic Switches, Memoryless Switches: These systems have no memory, that is, once the input signal is removed, the system returns to its original state. * Hysteretic Switches, Bistability: Bistable systems, in contrast, have memory. That is, when switched to one state or another, these systems remain in that state unless forced to change back. The light switch is a common example of a bistable system from everyday life. All bistable systems are based around some form of positive feedback loop.”<br />
<br />
26. ^ a b c d e f Guyton, Arthur C. (1991) Textbook of Medical Physiology. (8th ed). Philadelphia: W.B. Saunders. ISBN 0-7216-3994-1<br />
<br />
27. ^ Hasty, J.; McMillen, D.; Collins, J. J. (2002). "Engineered gene circuits". Nature. 420 (6912): 224–230. Bibcode:2002Natur.420..224H. doi:10.1038/nature01257. PMID 12432407.<br />
<br />
28. ^ Veening, J.; Smits, W. K.; Kuipers, O. P. (2008). "Bistability, Epigenetics, and Bet-Hedging in Bacteria" (PDF). Annual Review of Microbiology. 62 (1): 193–210. doi:10.1146/annurev.micro.62.081307.163002. hdl:11370/59bec46a-4434-4eaa-aaae-03461dd02bbb. PMID 18537474.<br />
<br />
29. ^ Bagowski, C. P.; Ferrell, J. E. (2001). "Bistability in the JNK cascade". Current Biology. 11 (15): 1176–1182. doi:10.1016/S0960-9822(01)00330-X. PMID 11516948.<br />
<br />
30. ^ Lotka, A (1945). "The law of evolution as a maximal principle". Human Biology. 17: 168–194.<br />
<br />
31. ^ Alexander, R. (1989). Evolution of the human psyche. In P. Millar & C. Stringer (Eds.), The human revolution: Behavioral and biological perspectives on the origins of modern humans (pp. 455-513). Princeton: Princeton University Press.<br />
<br />
32. ^ Crespi, B. J. (2004). "Vicious circles: positive feedback in major evolutionary and ecological transitions". Trends in Ecology and Evolution. 19 (12): 627–633. doi:10.1016/j.tree.2004.10.001. PMID 16701324.<br />
<br />
33. ^ Dawkins, R. 1991. The Blind Watchmaker London: Penguin. Note: W.W. Norton also published this book, and some citations may refer to that publication. However, the text is identical, so it depends on which book is at hand<br />
<br />
34. ^ Markov A., Korotayev A. "Phanerozoic marine biodiversity follows a hyperbolic trend." Palaeoworld. Volume 16, Issue 4, December 2007, Pages 311-318<br />
<br />
35. ^ Markov, A.; Korotayev, A. (2008). "Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution". Journal of General Biology. 69 (3): 175–194. PMID 18677962. Archived from the original on 2009-12-25.<br />
<br />
36. ^ Osterholm, Michael T. (2005-05-05). "Preparing for the Next Pandemic". The New England Journal of Medicine. 352 (18): 1839–1842. CiteSeerX 10.1.1.608.6200. doi:10.1056/NEJMp058068. PMID 15872196.<br />
<br />
37. ^ Paul, William E. (September 1993). "Infectious Diseases and the Immune System". Scientific American. 269 (3): 93. Bibcode:1993SciAm.269c..90P. doi:10.1038/scientificamerican0993-90. PMID 8211095.<br />
<br />
38. ^ Eissing, Thomas (2014). "Bistability analyses of a caspase activation model for receptor-induced apoptosis". Journal of Biological Chemistry. 279 (35): 36892–36897. doi:10.1074/jbc.M404893200. PMID 15208304.<br />
<br />
39. ^ Winner, E. (1996). Gifted children: Myths and Realities. New York: Basic Books. ISBN 978-0465017607.<br />
<br />
40. ^ Vandervert, L. (2009a). Working memory, the cognitive functions of the cerebellum and the child prodigy. In L.V. Shavinina (Ed.), International handbook on giftedness (pp. 295-316). The Netherlands: Springer Science.<br />
<br />
41. ^ Vandervert, L. (2009b). "The emergence of the child prodigy 10,000 years ago: An evolutionary and developmental explanation". Journal of Mind and Behavior. 30 (1–2): 15–32.<br />
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42. ^ Altszyler, E; Berbeglia, F.; Berbeglia, G.; Van Hentenryck, P. (2017). "Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality". PLOS ONE. 12 (7): e0180040. Bibcode:2017PLoSO..1280040A. doi:10.1371/journal.pone.0180040. PMC 5528888. PMID 28746334.<br />
<br />
43. ^ Azzopardi, Paul V. (2010), Behavioural Technical Analysis, Harriman House Limited, p. 116, ISBN 9780857190680, archived from the original on 2017-03-29<br />
<br />
44. ^ Arthur, W. Brian (1990). "Positive Feedbacks in the Economy". Scientific American. 262 (2): 80. Bibcode:1990SciAm.262b..92A. doi:10.1038/scientificamerican0290-92.<br />
<br />
45. ^ The Financial Instability Hypothesis Archived 2009-10-09 at the Wayback Machine by Hyman P. Minsky, Working Paper No. 74, May 1992, pp. 6–8<br />
<br />
46. ^ "Findings Regarding the Market Events of May 6, 2010" (PDF). 2010-09-30. Archived (PDF) from the original on August 15, 2017.<br />
<br />
47. ^ Brown, A. Duncan (2003), Feed or Feedback: Agriculture, Population Dynamics and the State of the Planet, Utrecht: International Books, ISBN 978-90-5727-048-2<br />
<br />
48. ^ Dolgonosov, B.M. (2010). "On the reasons of hyperbolic growth in the biological and human world systems". Ecological Modelling. 221 (13–14): 1702–1709. doi:10.1016/j.ecolmodel.2010.03.028.<br />
<br />
49. ^ a b Korotayev A. Compact Mathematical Models of World System Development, and How they can Help us to Clarify our Understanding of Globalization Processes Archived 2018-01-06 at the Wayback Machine. Globalization as Evolutionary Process: Modeling Global Change. Edited by George Modelski, Tessaleno Devezas, and William R. Thompson. London: Routledge, 2007. P. 133-160.<br />
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50. ^ Korotayev, A. V., & Malkov, A. S. A Compact Mathematical Model of the World System Economic and Demographic Growth, 1 CE–1973 CE // INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES Volume 10, 2016. P. 200-209 Archived 2018-01-06 at the Wayback Machine.<br />
<br />
51. ^ Berger, Sebastian. "Circular Cumulative Causation (CCC) à la Myrdal and Kapp — Political Institutionalism for Minimizing Social Costs" (PDF). Archived (PDF) from the original on 26 April 2012. Retrieved 26 November 2011.<br />
<br />
52. ^ S.-Y. Simon Wang; Jin-Ho Yoon; Christopher C. Funk; Robert R. Gillies, eds. (2017). Climate Extremes: Patterns and Mechanisms. Wiley. pp. 81–82. ISBN 9781119068037.<br />
<br />
53. ^ US NRC (2012), Climate Change: Evidence, Impacts, and Choices, US National Research Council (US NRC), archived from the original on 2016-05-03, p.9. Also available as PDF Archived 2013-02-20 at the Wayback Machine<br />
<br />
54. ^ Understanding Climate Change Feedbacks, U.S. National Academy of Sciences Archived 2012-02-10 at the Wayback Machine<br />
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55. ^ "8.6.3.1 Water Vapour and Lapse Rate - AR4 WGI Chapter 8: Climate Models and their Evaluation". Archived from the original on 2010-04-09. Retrieved 2010-04-23.<br />
<br />
56. ^ IPCC. "Climate Change 2007: Synthesis Report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Pg 53" (PDF). Archived (PDF) from the original on 2010-02-09.<br />
<br />
57. ^ Holden, Matthew H.; McDonald-Madden, Eve (2017). "High prices for rare species can drive large populations extinct: The anthropogenic Allee effect revisited". Journal of Theoretical Biology. 429: 170–180. arXiv:1703.06736. Bibcode:2017arXiv170306736H. doi:10.1016/j.jtbi.2017.06.019. PMID 28669883.<br />
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58. ^ Positive feedback occurs when one is told he has done something well or correctly. Tom Coens and Mary Jenkins, "Abolishing Performance Appraisals", p116.<br />
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==拓展阅读==<br />
* Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.<br />
* Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.<br />
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本中文词条由[[用户:Solitude|Solitude]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%AD%A3%E5%8F%8D%E9%A6%88&diff=29623正反馈2022-03-26T08:44:06Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=自相似性,共形对称,膨胀<br />
|description=在物理学、数学和统计学中,标度不变性是物体或者物理定律的一种特征,如果长度、能量或者其他变量的标度与一个公因子相乘,而不发生改变,因此也就代表某种普遍性。<br />
}}<br />
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[[File:Wiener process animated.gif|thumb|right|500px|<br />
维纳过程具有标度不变性。|链接=Special:FilePath/Wiener_process_animated.gif]]<br />
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{{short description|Destabilising process that occurs in a feedback loop}}<br />
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[[File:Herdwick Stampede.jpg|thumb|right|【图1:有时,警报或恐慌会通过正反馈在一群动物之间传播,从而引起踩踏事件。】.|链接=Special:FilePath/Herdwick_Stampede.jpg]]<br />
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[[File:Stampede loop.png|thumb|【图2:Causal loop diagram that depicts the causes of a stampede as a positive feedback loop. 在因果环路图中,踩踏事件的发生是一个正反馈循环。】|链接=Special:FilePath/Stampede_loop.png]]<br />
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[[File:Birmingham Northern Rock bank run 2007.jpg|thumb|right|【图3:In sociology a network effect can quickly create the positive feedback of a bank run. The above photo is of the UK Northern Rock 2007 bank run. 在社会学中,网络效应可以迅速产生银行挤兑的正反馈效应。上图是2007年英国北岩银行挤兑事件的照片。】|链接=Special:FilePath/Birmingham_Northern_Rock_bank_run_2007.jpg]]<br />
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'''Positive feedback''' ('''exacerbating feedback''', '''self-reinforcing feedback''') is a process that occurs in a [[feedback loop]] which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation.Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback.<ref name="theorymodelling" /> Both concepts play an important role in science and engineering, including biology, chemistry, and [[cybernetics]] .<br />
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正反馈(加剧反馈,自我强化反馈) 是一种在反馈循环中加剧微小扰动影响的过程。也就是说,一个扰动对系统的影响包括它自身扰动幅度的增大。或者说,A会产生更多的B,而B又会产生更多的A,与之相反的是,[[负反馈]]指的是一个系统中,变化的结果会减少或抵消它自己的影响。<ref name="theorymodelling" />这两个概念在科学和工程等领域中发挥着重要作用,包括生物学、化学和控制论。<br />
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在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。<ref name="zuckerman" /><ref>Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". ''Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems''. Academic Press. p. 55. ISBN <bdi>9780127784557</bdi>. Archived from the original on 2017-01-03. <q>A positive feedback loop is one with an even number of negative influences [around the loop].</q></ref><ref name="zuckerman" /> 从结果到始发过程的反馈可以是直接的,也可以通过其他状态变量<ref name="theorymodelling" />。这样的系统可以给出丰富的定性行为,但反馈的瞬时信号是正向还是负向,对结果有极其重要的影响。<ref name="theorymodelling" /> 正反馈强化原过程,而负反馈调节原过程。在这个含义下,''正''和''负''指的是大于或小于零的循环收益,并不代表着最终结果或效果的正负性。<ref name=":0">{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>因此,正反馈的一个重要特点是小扰动变大。当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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===基础===<br />
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[[File:Ideal feedback model.svg|thumb|【图4:A basic feedback system can be represented by this block diagram. In the diagram the + symbol is an adder and A and B are arbitrary causal functions. 一个基本的反馈系统可以用这个框图来表示。在图中,+号是加法器,A和B是任意因果函数。】|链接=Special:FilePath/Ideal_feedback_model.svg]]<br />
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图中显示了一个简单的反馈回路。 如果环增益AB为正值,则存在'正'或'再生'反馈的条件。<br />
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如果函数A和B是线性的,且AB小于1,那么系统从输入到输出的整体增益是有限的,但当AB接近1时,系统的增益可以非常大。<ref name="smith"> Electronics circuits and devices second edition. Ralph J. Smith</ref> 在这种情况下,可以表明从输入到输出的整体或 "闭环 "增益为:<br />
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:<math>G_c = A/(1-AB)</math><br />
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当AB>1时,系统是不稳定的,因此不具有明确的增益;增益可称为无限。<br />
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所以系统状态的变化根据反馈可以是收敛的,也可以是发散的。 而正反馈的结果是增强变化,因此小的扰动就可能导致大的变化。<br />
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对于一个当前处于平衡状态的系统,如果其状态的任何变化都发生了正反馈,从而造成了状态的不稳定,那么这个系统就是一个不稳定平衡的系统。使这种系统远离其平衡状态的力的大小是状态与平衡状态之间的距离的递增函数。<br />
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正反馈并不一定意味着平衡的不稳定性,例如,在正反馈结构中可能存在稳定的开关状态<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>。<br />
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=== 迟滞 ===<br />
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[[File:Hysteresis sharp curve.svg|thumb|【图5 Hysteresis causes the output value to depend on the history of the input 迟滞现象会导致输出值取决于输入的历史记录。】|链接=Special:FilePath/Hysteresis_sharp_curve.svg]]<br />
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[[File:Op-Amp Schmitt Trigger.svg|thumb|【图6 In a Schmitt trigger circuit, feedback to the non-inverting input of an amplifier pushes the output directly away from the applied voltage towards the maximum or minimum voltage the amplifier can generate. 在施密特触发器电路中,利用放大器的非反相输入端口产生的反馈,可以直接将电路的输出从原本的外加电压值推向到放大器所能产生的极值电压。】|链接=Special:FilePath/Op-Amp_Schmitt_Trigger.svg]]<br />
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在现实世界中,正反馈循环通常不会引起不断增长,而是通过某种限制效应来改变。根据Donella Meadows的说法:<br />
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正反馈回路是系统增长、爆炸、腐蚀和崩溃的根源。一个系统如果有一个不受控制的正反馈,最终将会自我毁灭。这就是为什么正反馈如此稀少的原因。通常情况下,负反馈迟早会发生。<ref>Donella Meadows, ''[http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf Leverage Points: Places to Intervene in a System]''2013-10-08 at the Wayback Machine, 1999</ref><br />
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[[迟滞]],即起点影响系统的终点的现象,可以通过正反馈产生。当反馈循环的增益高于1时,那么输出就会远离输入:如果大于输入,则向最近的正极限移动,而如果小于输入,则向最近的负极限移动。<br />
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一旦达到极限,它就会稳定下来。但是,如果输入超过极限,那么反馈将改变符号,输出将向相反的方向移动,直到达到相反的极限。因此,该系统表现出'''双稳态行为bistable behavior'''。<br />
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== 术语的由来==<br />
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正反馈和负反馈这两个名词最早应用于反馈是在二战前。正反馈的概念随着再生电路的问世,在20世纪20年代已经出现。<br />
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Friis 和 Jensen在1924年描述了一种在电子放大器中发生的"回馈 "是正的情况,这一情况与他们顺便提到的负回馈作用相反。到了1934年,Harold Stephen Black在他的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法:<br />
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正反馈会增加放大器的增益,负反馈会降低增益<br />
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据Mindell(2002年)说,术语上的混乱是在这之后不久产生的:<br />
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“ ... ... Friis 和 Jensen 对 Black 在对"正反馈 "和 "负反馈 "的区分方法是一样的,都不是基于反馈本身的符号,而是基于它对放大器增益的影响。与之相反的是,当Nyquist和Bode基于Black的工作基础时,将负反馈称为符号相反的反馈。Black难以说服其他人相信他的发明的实用性,有一部分原因是在基本的定义问题上存在混乱。"<br />
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==实例与应用==<br />
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=== 电子电路===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|【图7 A vintage style regenerative radio receiver. Due to the controlled use of positive feedback, sufficient amplification can be derived from a single [[vacuum tube]] or valve (centre). 一个老式的再生无线电接收器。由于使用正反馈的控制,真空管或阀门(中心)就可以产生足够的放大效果。】|链接=Special:FilePath/Regenerartive_Receiver-S7300056.JPG]]<br />
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'''再生电路Regenerative circuit'''于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>,用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈,可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此,一个信号可以在一个阶段被放大20000甚至100000倍,而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定,开始振荡。无线电操作员必须不断地调整反馈量,以获得良好的接收效果。而现代无线电接收机采用超异构设计,多了许多放大级,去掉了正反馈并使其工作更稳定。<br />
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在再生无线电电路中产生的振荡还可以被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英),经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计,包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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许多电子电路,特别是放大器,都采用了负反馈。这降低了放大器的信号增益,但改善了它的线性度、输入阻抗、输出阻抗和带宽,并稳定了包括闭环增益等参数。同时,这些参数也变得不那么依赖于放大器件本身的细节,而更多地依赖于反馈元件,因为反馈元件一般不随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位:如果信号反馈失相,则反馈为负,如果相位一致,则反馈为正。对于需要使用负反馈放大器的设计者来说,引入负反馈放大器的问题是,电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°,那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波来做到这一点)。如果任何频率下的环增益(放大器增益与正反馈程度的乘积)大于1,那么放大器将在该频率下发生振荡(巴克豪森稳定性准则)。这种振荡有时被称为寄生振荡:在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化,前板(用户界面)的变化,甚至是由于人或其他导电物品的接近。<br />
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放大器可能会以示波器很难检测到的方式轻轻振荡,有时的振荡也可能非常大,只有非常扭曲或根本没有真正的信号,甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似,因此低频寄生振荡也被称为 "汽艇"。<br />
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【图8 The effect of using a Schmitt trigger (B) instead of a comparator (A) 使用施密特触发器(b)代替比较器(a)的效果】<br />
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许多常见的数字电路都采用正反馈。一般简单的布尔逻辑门通常只是依靠增益将数字信号电压从中间值推到代表布尔值0和1的值上,但许多更复杂的门都采用了反馈。当输入的模拟电压发生变化,但后期数字处理需要尖锐阈值时,施密特触发电路通过正反馈机制确保当输入电压轻微超过阈值时,输出电压可以巧妙而迅速地从一个逻辑状态转移到另一个逻辑状态。施密特触发器使用正反馈的一个必然结果是,如果输入电压再次缓慢下降,超过了相同的阈值,由于正反馈的机制,输出电压将保持在相同的逻辑状态而不改变。这种效应被称为滞后: 输入电压必须降到一个不同的、较低的阈值,才能“解锁”输出,并将其重置为原始数字。通过减小正反馈的程度,可以减小滞后宽度,但宽度不能被完全消除。施密特触发器在某种程度上是一个闭锁电路。<br />
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【图9 Positive feedback is a mechanism by which an output is enhanced, such as protein levels. However, in order to avoid any fluctuation in the protein level, the mechanism is inhibited stochastically (I), therefore when the concentration of the activated protein (A) is past the threshold ([I]), the loop mechanism is activated and the concentration of A increases exponentially if d[A]=k [A] 正反馈是一种增强输出的机制,如蛋白质水平。但为了避免蛋白质水平的波动,该机制是随机抑制的(I),因此只有当激活的蛋白质(A)浓度超过阈值([I])时,循环机制被激活,如果d[A]=k[A],A的浓度就会成倍增加。】<br />
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【图10 Illustration of an R-S ('reset-set') flip-flop made from two digital nor gates with positive feedback. Red and black mean logical '1' and '0', respectively. R-S("复位-设置")触发器的说明,由两个带正反馈的数字诺尔门组成。红色和黑色分别表示逻辑上的 "1 "和 "0"。】<br />
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电子触发器,或“锁存器” ,或“双稳态多谐振荡器” ,是一种由于高正反馈而不稳定于平衡或中间状态的电路。这样的双稳态电路是一位电子存储器的基础。 触发器使用一对放大器、晶体管或逻辑门相互连接,正反馈机制使得输入信号被去除后,电路可以维持在两种非平衡稳定状态中的一种,直到一个合适的替代信号重新作为输入,以改变电路状态。计算机随机存取存储器(RAM)可以用这种方式运作,每位存储器有一个锁存电路。<br />
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电子系统中发生'''热失控Thermal runaway'''的原因是,当电路的某些方面变得更热时,它被允许通过更多的电流,然后它越热,通过的电流就越多,这就使它更热一些,因此它又通过更多的电流。这种现象对有关器件来说通常是灾难性的。如果器件不得不在接近其最大功率处理能力的情况下工作,那么某些条件下就可能出现热失控,这通常可以通过精心设计来改进。<br />
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[[File:Technics SL-1210MK2.jpg|thumb|left|【图11 A phonograph turntable is prone to acoustic feedback. 留声机转盘容易受到声反馈的影响。】|链接=Special:FilePath/Technics_SL-1210MK2.jpg]]<br />
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音频和视频系统可以表现出正反馈。如果麦克风录入了同一电路中扬声器的放大声音输出,那么就会听到音频反馈的嚎叫和尖叫声(在放大器的最大功率容量下),因为随机噪声被音频系统和房间的特性所过滤后,通过正反馈重新放大。<br />
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===音频和现场音乐领域===<br />
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音频反馈(也称为声反馈,简称反馈,或拉森效应)是一种特殊的正反馈,当音频输入(例如,麦克风或吉他拾音器)和音频输出(例如,大声放大的扬声器)之间存在声音回路时,就会出现这种反馈。在这个例子中,麦克风接收到的信号被放大并从扬声器传出。然后,来自扬声器的声音可以再次被麦克风接收,进一步放大,然后再次通过扬声器传递出去。 所产生的声音的频率由传声器、放大器和扬声器的共振频率、房间的声学特性、传声器和扬声器的定向拾音和发射模式以及它们之间的距离决定。对于小型的扩声系统来说,这种声音很容易的体现的响亮的吱吱声或尖叫声。<br />
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在歌手或公众演讲者使用扩声系统或扩音系统的活动中,麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来,音频工程师使用各种电子设备,如均衡器或者自动反馈检测设备,来防止这些不受欢迎的尖叫声或尖叫声,这些声音影响了观众对活动的享受。另一方面,自20世纪60年代以来,摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果,有意制造吉他中的正反馈,以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈,但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中,他说,“我敢说任何人都找不到这样的唱片,除非是1922年这张用这种方式录制的老蓝调唱片。”<br />
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音频反馈的原理是由丹麦科学家Søren Absalon Larsen首先发现的。麦克风并不是唯一受此影响的传感器。录音板拾音器也会产生正反馈,通常是在100赫兹以下的低频范围内表现出低沉的轰鸣声。Jimi Hendrix是一个创新者,在他的吉他独奏中有意使用吉他正反馈来创造独特的声音效果。他帮助发展了电吉他演奏中音频反馈的可控性和音乐性,后来Brian May也是这种技术的著名支持者。<br />
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[[File:Adam Savage HOPE.jpg|thumb|right|220px|[[Video feedback]]【图12 视频反馈】.|链接=Special:FilePath/Adam_Savage_HOPE.jpg]]<br />
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===视频===<br />
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同样,如果一台摄像机对准一个正在显示摄像机自身信号的监控屏幕,那么通过正反馈就可以在屏幕上形成重复的图案。这种视频反馈效果在电视剧《神秘博士》前十季的开场白中就被使用了。<br />
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===开关===<br />
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In [[electrical switch]]es, including [[bimetallic strip]] based thermostats, the switch usually has hysteresis in the switching action. In these cases hysteresis is mechanically achieved via positive feedback within a tipping point mechanism. The positive feedback action minimises the length of time arcing occurs for during the switching and also holds the contacts in an open or closed state.<br />
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在电气开关中,包括双金属条型恒温器,开关通常在开关动作中具有滞后性。在这些情况下,滞后是通过一个临界点机构内的正反馈来实现的。正反馈作用可最大限度地减少开关过程中发生电弧的时间,并使触点保持在断开或闭合状态。<br />
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=== 生物学===<br />
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[[File:Positive Feedback- Childbirth (1).svg|thumb|生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。|链接=Special:FilePath/Positive_Feedback-_Childbirth_(1).svg]]<br />
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生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做'''催产素oxytocin'''的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。<br />
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==== 生理学====<br />
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在生理学中可以找到一些正反馈系统的例子。<br />
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* <br />
其中一个例子是分娩时宫缩的发生,称为弗格森反射。当宫缩发生时,激素催产素会引起神经刺激,刺激下丘脑产生更多的催产素,从而增加子宫收缩。这就导致宫缩的幅度和频率增加。<br />
<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders. {{ISBN|0-7216-3994-1}}</ref><br />
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另一个例子是血液凝固的过程。当受伤的组织释放出信号化学物质,激活血液中的血小板时,这个循环就启动了。被激活的血小板释放化学物质,激活更多的血小板,引起快速的级联反应,形成血栓。<ref name=Guyton1991/><br />
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哺乳也涉及正反馈,当婴儿吸吮乳头时,会有神经反应进入脊髓,并上传到大脑的下丘脑,然后刺激垂体产生更多的催乳素以产生更多的乳汁<ref name=Guyton1991/>。<br />
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在月经周期的卵泡期期间,雌激素的飙升会导致排卵<ref name=Guyton1991/>。<br />
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神经信号的产生是另一个例子,神经纤维的膜使钠离子通过钠通道轻微渗漏,导致膜电位的变化,进而引起更多通道的开放(Hodgkin循环)。所以,最初的轻微渗漏会导致钠渗漏的爆发,从而产生神经动作电位<ref name=Guyton1991/>。<br />
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在心脏的兴奋收缩耦合中,肌浆网膜中的兰尼碱受体检测到心肌细胞内钙离子的增加,该受体以正反馈生理反应将钙运出到细胞质中。<br />
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在大多数情况下,这种反馈循环最终会释放出反信号,从而抑制或破坏循环。分娩宫缩在宝宝离开母体时停止。化学物质分解血凝块。当婴儿不再需要被哺乳时,泌乳停止<ref name=Guyton1991/>。<br />
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====基因调控====<br />
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正反馈是基因调控中研究较好的一种现象,其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时,就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络,以证明双稳态的概念。<ref name=Hasty2002/><br />
正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用,因此,基因调控中的正反馈可以产生显著的生理结果。分子动力学中的随机运动加上正反馈可以引发有趣的效应,例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/> 这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中,如酶动力学或代谢途径。<ref name=Christoph2001/><br />
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==== 进化生物学 ====<br />
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在进化生物学中正反馈循环被用来描述生物进化中变化动态的各个方面。 例如,在宏观层面,Alfred J. Lotka(1945)认为,物种的演变最重要的是选择反馈能量流动以捕获越来越多的能源系统的能量。<ref name=Lotka1945/>在人类层面,Richard D. Alexander(1989)提出,人类群体之间和群体内部的社会竞争会影响智力的选择,从而时不时地会产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子<ref name=Crespi2004/>。通过与军备竞赛进行类比,给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/><br />
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[[File:Phanerozoic Biodiversity.svg|300px|right|thumb|显生宙[[生物多样性]]呈现稳定而非单调的增长,从接近于零一直增长到有几千个属。|链接=Special:FilePath/Phanerozoic_Biodiversity.svg]]<br />
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研究表明,在<font color="#32CD32"> 显生宙 ''',生物多样性的变化与双曲模型(广泛用于人口学和宏观社会学)的相关性要比指数模型和逻辑斯特模型(传统上用于人口生物学,并广泛用于生物多样性化石)的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈(更多的祖先,更多的后代)和资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为,生物多样性和人口曲线之间的相似性可能来自这样一个事实,即两者都是由双曲趋势(由正反馈产生)与周期性和随机性的动态干扰而产生的。<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref><br />
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==== 免疫系统====<br />
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细胞因子风暴,或称高细胞因子血症,是一种潜在的致命性免疫反应,表现为各种细胞因子水平高度升高,这是由细胞因子和免疫细胞之间的正反馈环组成。[36]在正常的免疫功能中,可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后,就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合,当B细胞的抗体与C3结合后,就会加快该B细胞分泌更多的抗体和更多的C3蛋白,从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
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====细胞凋亡====<br />
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细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程,其目的是清除长寿或受损的细胞。这一过程的失效与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活,它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时,无论效应子胱天蛋白酶的中间激活步骤数量有多少,这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/> 当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时,该过程呈现双稳态,从而模拟细胞的存活和死亡状态。<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref><br />
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=== 心理学===<br />
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Winner(1996)将有天赋的孩子描述为受到正反馈循环的驱动,这些反馈循环体现在他们自己的课程学习上,通过反馈自己的满意程度,从而进一步将他们的学习目标提高到更高水平等。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a,2009b)提出,神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释,工作记忆中的思维/表现输出被反馈到小脑,在那里被精简,然后再反馈到工作记忆中,从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/> <br />
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=== 经济学===<br />
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====市场上的社会影响====<br />
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事实证明,产品推荐和消费者先前的购买信息对消费者的选择影响很大,无论是音乐、电影、书籍、电子产品还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象(马太效应),即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
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====市场动向====<br />
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根据George Soros提出的反射性理论,价格变化是由一个正反馈过程驱动的,即投资者的预期受到价格变动的影响,因此他们的行为会强化这个方向的价格变动,直到价格的变化变得不可持续,于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
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==== 系统风险====<br />
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系统性风险是指放大效应或杠杆或正反馈过程给系统带来的风险。这通常是未知的,在某些条件下,这个过程会成倍放大,并迅速导致破坏性或混乱的行为。 庞氏骗局就是正反馈系统的一个很好的例子:来自新投资者的资金被用来支付异常高的回报,反过来又吸引了更多的新投资者,导致快速增长进而走向崩溃。W. Brian Arthur 也对经济中的正反馈进行了研究和著述(如W. Brian Arthur,1990)。Hyman Minsky提出了一个理论,认为某些信用扩张行为会使市场经济变成一个 "偏差放大系统",从而可能会突然崩溃,这有时被称为 "明斯基时刻"。<br />
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输入和输出明确分开的简单系统不容易发生系统性风险。 随着系统复杂性的增加,这种风险更容易发生,因为即使在详细的压力测试条件下,也更难看到或分析系统中所有可能的变量组合。 一个复杂系统的效率越高,就越容易发生系统性风险,因为只需要很小的偏差就可以破坏系统。 因此,设计良好的复杂系统一般都会有一些内在的功能来避免这种情况的发生,比如在系统内有少量的摩擦力,或阻力,或惯性,或时间延迟来使输出与输入脱钩。这些因素造成了低效率,但它们是避免不稳定的必要条件。<br />
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2010年的闪崩事件被归咎于高频交易(HFT)的做法,不过HFT是否真的会增加系统性风险仍然存在争议。<br />
<br />
<br />
====人口与环境危机====<br />
<br />
可以认为农业和人口之间处于一种正反馈模式,这意味着双方越来越强烈地推动彼此。有人认为,这种正反馈系统终将在某一时刻以灾难结束,因为现代农业正在耗尽所有容易获得的磷酸盐,并且进行高效的单一栽培,使得现代农业更容易受到系统性风险影响。<br />
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<br />
技术创新和人类人口也可以有类似的考虑,这也是过去人类人口明显的双曲线增长,而不是简单的指数增长的一个解释。<br />
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<br />
有人提出,由于人口和技术之间的二阶正反馈,增长速度正在加快。技术增长增加了土地对人的承载能力,从而导致人口增长,而这反过来又推动了技术的进一步增长。<br />
<br />
==== 偏见、社会制度与贫困====<br />
<br />
Gunnar Myrdal描述了一个不平等和贫困加剧的恶性循环,这就是所谓的”循环累积诱因”。<br />
<br />
==== 气象学====<br />
<br />
干旱通过正反馈效应加剧。缺雨会降低土壤湿度,从而杀死植物,使它们通过蒸腾作用释放更少的水分。这两个因素都限制了水蒸气从地表加到大气中的过程,并使吸收水分的干燥灰尘进入大气。水汽少了,既意味着露点温度低,白天的供暖效率也高,减少了大气中湿度导致云的形成的机会。最后,没有云,就不会有雨,这个正反馈循环就形成了。<br />
<br />
==== 气候学====<br />
<br />
气候中的"诱因 "可能会将气候系统推向变暖或变冷的方向,例如,大气中温室气体浓度的增加会导致地表变暖。诱因是气候系统的外部因素,而反馈是系统的内部过程。一些反馈机制与气候系统的其他部分相对孤立地发挥作用,而另一些则是紧密耦合的。气候系统的作用力、反馈和动态决定了气候变化的程度和速度。全球变暖中的主要正反馈是变暖使大气中的水汽量增加,进而导致进一步变暖。主要的负反馈来自Stefan-Boltzmann定律,从地球辐射到空间的热量与地球表面和大气温度的四次方成正比。<br />
<br />
<br />
气候学中正反馈子系统的其他例子包括:<br />
<br />
大气变暖会使冰融化,从而改变反照率,从而使大气进一步变暖。<br />
<br />
<br />
甲烷水合物可能是不稳定的,所以海洋变暖可能会释放更多的温室气体之一的甲烷。<br />
<br />
<br />
泥炭,天然存在于泥炭沼泽中,含有碳。当泥炭干燥时,它会分解,并可能额外燃烧。泥炭还会释放一氧化二氮。<br />
<br />
<br />
全球变暖会影响云的分布。高空的云层会增强温室效应,而低空的云层则主要反射太阳光,对温度产生相反的影响。<br />
<br />
政府间气候变化专门委员会(气专委)第四次评估报告指出,"人类活动的变暖可能导致一些突然或不可逆转的影响,这取决于气候变化的速度和程度"。<br />
<br />
==== 社会学====<br />
<br />
<br />
自我应验预言是信念和行为之间的一个社会正反馈循环: 如果有足够多的人相信某件事是真的,他们的行为就能让它变成真的,而对他们行为的观察又可能反过来增加信念。一个典型的例子是银行挤兑。<br />
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<br />
正反馈的另一个社会学例子是网络效应。当更多的人被鼓励加入一个网络时,这就增加了网络的覆盖面,因此网络扩张得越来越快。病毒视频就是网络效应的一个例子,在这个例子中,一个热门视频的链接被分享和再传播,确保更多的人看到这个视频,然后重新发布链接。这是许多社会现象的基础,包括庞氏骗局和连锁信。在许多情况下,人口量是反馈效应的限制因素。<br />
<br />
==== 化学====<br />
<br />
<br />
如果化学反应引起热量的释放,而反应本身在较高的温度下发生得更快,那么就很有可能出现正反馈。如果产生的热量没有足够快地从反应物中排除,就会发生热失控,并很快导致化学爆炸。<br />
<br />
==== 自然保护====<br />
<br />
<br />
<br />
许多野生动物被猎杀的原因是它们身体的某些部位可能相当有价值。目标物种越是接近灭绝,其部位的价格就越高。这就是一个正反馈的例子。<br />
<br />
==参见==<br />
<br />
* Chain reaction – Sequence of reactions 链式反应 -- -- 反应的顺序<br />
* Donella Meadows' twelve leverage points to intervene in a system Donella Meadows干预系统的十二个杠杆点<br />
* Hyperbolic growth 双曲增长<br />
* Reflexivity (social theory)反射性(社会理论)<br />
* Stability criterion稳定性标准<br />
* Strategic complements战略补充<br />
* System dynamics 系统动力学<br />
* Technological singularity – Hypothetical point in time at which technological growth becomes uncontrollable and irreversible 技术奇点 -- -- 假设技术增长变得不可控制和不可逆转的时间点<br />
* Thermal runaway 热失控<br />
* Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop. 恶性/恶性循环:在社会和金融系统中,是通过反馈循环自我强化的事件综合体。<br />
* Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour. 正强化:在操作性条件下,结果会增加行为的频率。<br />
* Praise of performance: a term often applied in the context of performance appraisal,although this usage is disputed 绩效表扬:这个词经常被应用于绩效评估中,尽管这种用法有争议。<br />
* Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage 自我强化反馈:系统动力学中使用的术语,以避免与 "表扬 "的用法相混淆。<br />
* Matthew effect – Effect originally observed by Robert K. Merton 马太效应 -- -- 罗伯特-K-默顿最初观察到的效应。<br />
* Self-fulfilling prophecy – Prediction that causes itself to become true 自证预言 -- -- 导致自己成为现实的预言<br />
* Virtuous circle and vicious circle 良性循环和恶性循环<br />
* Autocatalysis 自催化<br />
* Meander – Sinuous bend in a series in the channel of a river 蜿蜒曲折 -- -- 河道中一系列蜿蜒曲折的弯道。<br />
<br />
<br />
==参考文献==<br />
1. ^ a b c Ben Zuckerman & David Jefferson (1996). Human Population and the Environmental Crisis. Jones & Bartlett Learning. p. 42. ISBN 9780867209662. Archived from the original on 2018-01-06.<br />
<br />
2. ^ Keesing, R.M. (1981). Cultural anthropology: A contemporary perspective (2nd ed.) p.149. Sydney: Holt, Rinehard & Winston, Inc.<br />
<br />
3. ^ a b c d e Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems. Academic Press. p. 55. ISBN 9780127784557. Archived from the original on 2017-01-03. “A positive feedback loop is one with an even number of negative influences [around the loop].”<br />
<br />
4. ^ S W Amos; R W Amos (2002). Newnes Dictionary of Electronics (4th ed.). Newnes. p. 247. ISBN 9780750656429. Archived from the original on 2017-03-29.<br />
<br />
5. ^ Rudolf F. Graf (1999). Modern Dictionary of Electronics (7th ed.). Newnes. p. 276. ISBN 9780750698665. Archived from the original on 2017-03-29.<br />
<br />
6. ^ "Positive feedback". Oxford English Dictionary. Oxford University Press. Archived from the original on 2 March 2014. Retrieved 15 April 2014.<br />
<br />
7. ^ "Feedback". Glossary. Metadesigners Network. Archived from the original on 16 April 2014. Retrieved 15 April 2014.<br />
<br />
8. ^ Electronics circuits and devices second edition. Ralph J. Smith<br />
<br />
9. ^ a b Lopez-Caamal, Fernando; Middleton, Richard H.; Huber, Heinrich (February 2014). "Equilibria and stability of a class of positive feedback loops". Journal of Mathematical Biology. 68 (3): 609–645. doi:10.1007/s00285-013-0644-z. PMID 23358701.<br />
<br />
10. ^ Donella Meadows, Leverage Points: Places to Intervene in a System Archived 2013-10-08 at the Wayback Machine, 1999<br />
<br />
11. ^ a b Mindell, David A. (2002). Between Human and Machine : Feedback, Control, and Computing before Cybernetics.Baltimore, MD: Johns Hopkins University Press. ISBN 9780801868955. Archived from the original on 2018-01-06.<br />
<br />
12. ^ Friis, H. T.; Jensen, A. G. (April 1924), "High Frequency Amplifiers", Bell System Technical Journal, 3 (2): 181–205, doi:10.1002/j.1538-7305.1924.tb01354.x<br />
<br />
13. ^ Black, H. S. (January 1934), "Stabilized feed-back amplifiers", Electrical Engineering, 53: 114–120, doi:10.1109/ee.1934.6540374<br />
<br />
14. ^ US 1113149, Armstrong, E. H., "Wireless receiving system"<br />
<br />
15. ^ Kitchin, Charles. "A Short Wave Regenerative Receiver Project". Archived from the original on 10 July 2010. Retrieved 23 September 2010.<br />
<br />
16. ^ "Sinewave oscillators". EDUCYPEDIA - electronics. Archived from the original on 27 September 2010. Retrieved 23 September 2010.<br />
<br />
17. ^ Self, Douglas (2009). Audio Power Amplifier Design Handbook. Focal Press. pp. 254–255. ISBN 978-0-240-52162-6. Archived from the original on 2014-01-29.<br />
<br />
18. ^ "CMOS Schmitt Trigger—A Uniquely Versatile Design Component" (PDF). Fairchild Semiconductor Application Note 140. Fairchild Semiconductors. 1975. Archived (PDF) from the original on 22 November 2010. Retrieved 29 September 2010.<br />
<br />
19. ^ Strandh, Robert. "Latches and flip-flops". Laboratoire Bordelais de Recherche en Informatique. Archived from the original on 16 July 2011. Retrieved 4 November 2010.<br />
<br />
20. ^ Wayne, Storr. "Sequential Logic Basics: SR Flip-Flop". Electronics-Tutorials.ws. Archived from the original on 16 September 2010. Retrieved 29 September 2010.<br />
<br />
21. ^ Sharma, Bijay Kumar (2009). "Analog Electronics Lecture 4 Part C RC coupled Amplifier Design Procedure". Retrieved 29 September 2010.<br />
<br />
22. ^ Sheff, David (2000). All We Are Saying. New York, New York: St. Martin's Press. p. 173. ISBN 978-0-312-25464-3.<br />
<br />
23. ^ Shadwick, Keith (2003). Jimi Hendrix, Musician. Backbeat Books. p. 92. ISBN 978-0-87930-764-6.<br />
<br />
24. ^ May, Brian. "Burns Brian May Tri-Sonic Pickups". House Music & Duck Productions. Archived from the original on 20 November 2010. Retrieved 2 February 2011.<br />
<br />
25. ^ "Positive Feedback and Bistable Systems" (PDF). University of Washington. Archived (PDF) from the original on 2015-04-13. “* Non-Hysteretic Switches, Memoryless Switches: These systems have no memory, that is, once the input signal is removed, the system returns to its original state. * Hysteretic Switches, Bistability: Bistable systems, in contrast, have memory. That is, when switched to one state or another, these systems remain in that state unless forced to change back. The light switch is a common example of a bistable system from everyday life. All bistable systems are based around some form of positive feedback loop.”<br />
<br />
26. ^ a b c d e f Guyton, Arthur C. (1991) Textbook of Medical Physiology. (8th ed). Philadelphia: W.B. Saunders. ISBN 0-7216-3994-1<br />
<br />
27. ^ Hasty, J.; McMillen, D.; Collins, J. J. (2002). "Engineered gene circuits". Nature. 420 (6912): 224–230. Bibcode:2002Natur.420..224H. doi:10.1038/nature01257. PMID 12432407.<br />
<br />
28. ^ Veening, J.; Smits, W. K.; Kuipers, O. P. (2008). "Bistability, Epigenetics, and Bet-Hedging in Bacteria" (PDF). Annual Review of Microbiology. 62 (1): 193–210. doi:10.1146/annurev.micro.62.081307.163002. hdl:11370/59bec46a-4434-4eaa-aaae-03461dd02bbb. PMID 18537474.<br />
<br />
29. ^ Bagowski, C. P.; Ferrell, J. E. (2001). "Bistability in the JNK cascade". Current Biology. 11 (15): 1176–1182. doi:10.1016/S0960-9822(01)00330-X. PMID 11516948.<br />
<br />
30. ^ Lotka, A (1945). "The law of evolution as a maximal principle". Human Biology. 17: 168–194.<br />
<br />
31. ^ Alexander, R. (1989). Evolution of the human psyche. In P. Millar & C. Stringer (Eds.), The human revolution: Behavioral and biological perspectives on the origins of modern humans (pp. 455-513). Princeton: Princeton University Press.<br />
<br />
32. ^ Crespi, B. J. (2004). "Vicious circles: positive feedback in major evolutionary and ecological transitions". Trends in Ecology and Evolution. 19 (12): 627–633. doi:10.1016/j.tree.2004.10.001. PMID 16701324.<br />
<br />
33. ^ Dawkins, R. 1991. The Blind Watchmaker London: Penguin. Note: W.W. Norton also published this book, and some citations may refer to that publication. However, the text is identical, so it depends on which book is at hand<br />
<br />
34. ^ Markov A., Korotayev A. "Phanerozoic marine biodiversity follows a hyperbolic trend." Palaeoworld. Volume 16, Issue 4, December 2007, Pages 311-318<br />
<br />
35. ^ Markov, A.; Korotayev, A. (2008). "Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution". Journal of General Biology. 69 (3): 175–194. PMID 18677962. Archived from the original on 2009-12-25.<br />
<br />
36. ^ Osterholm, Michael T. (2005-05-05). "Preparing for the Next Pandemic". The New England Journal of Medicine. 352 (18): 1839–1842. CiteSeerX 10.1.1.608.6200. doi:10.1056/NEJMp058068. PMID 15872196.<br />
<br />
37. ^ Paul, William E. (September 1993). "Infectious Diseases and the Immune System". Scientific American. 269 (3): 93. Bibcode:1993SciAm.269c..90P. doi:10.1038/scientificamerican0993-90. PMID 8211095.<br />
<br />
38. ^ Eissing, Thomas (2014). "Bistability analyses of a caspase activation model for receptor-induced apoptosis". Journal of Biological Chemistry. 279 (35): 36892–36897. doi:10.1074/jbc.M404893200. PMID 15208304.<br />
<br />
39. ^ Winner, E. (1996). Gifted children: Myths and Realities. New York: Basic Books. ISBN 978-0465017607.<br />
<br />
40. ^ Vandervert, L. (2009a). Working memory, the cognitive functions of the cerebellum and the child prodigy. In L.V. Shavinina (Ed.), International handbook on giftedness (pp. 295-316). The Netherlands: Springer Science.<br />
<br />
41. ^ Vandervert, L. (2009b). "The emergence of the child prodigy 10,000 years ago: An evolutionary and developmental explanation". Journal of Mind and Behavior. 30 (1–2): 15–32.<br />
<br />
42. ^ Altszyler, E; Berbeglia, F.; Berbeglia, G.; Van Hentenryck, P. (2017). "Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality". PLOS ONE. 12 (7): e0180040. Bibcode:2017PLoSO..1280040A. doi:10.1371/journal.pone.0180040. PMC 5528888. PMID 28746334.<br />
<br />
43. ^ Azzopardi, Paul V. (2010), Behavioural Technical Analysis, Harriman House Limited, p. 116, ISBN 9780857190680, archived from the original on 2017-03-29<br />
<br />
44. ^ Arthur, W. Brian (1990). "Positive Feedbacks in the Economy". Scientific American. 262 (2): 80. Bibcode:1990SciAm.262b..92A. doi:10.1038/scientificamerican0290-92.<br />
<br />
45. ^ The Financial Instability Hypothesis Archived 2009-10-09 at the Wayback Machine by Hyman P. Minsky, Working Paper No. 74, May 1992, pp. 6–8<br />
<br />
46. ^ "Findings Regarding the Market Events of May 6, 2010" (PDF). 2010-09-30. Archived (PDF) from the original on August 15, 2017.<br />
<br />
47. ^ Brown, A. Duncan (2003), Feed or Feedback: Agriculture, Population Dynamics and the State of the Planet, Utrecht: International Books, ISBN 978-90-5727-048-2<br />
<br />
48. ^ Dolgonosov, B.M. (2010). "On the reasons of hyperbolic growth in the biological and human world systems". Ecological Modelling. 221 (13–14): 1702–1709. doi:10.1016/j.ecolmodel.2010.03.028.<br />
<br />
49. ^ a b Korotayev A. Compact Mathematical Models of World System Development, and How they can Help us to Clarify our Understanding of Globalization Processes Archived 2018-01-06 at the Wayback Machine. Globalization as Evolutionary Process: Modeling Global Change. Edited by George Modelski, Tessaleno Devezas, and William R. Thompson. London: Routledge, 2007. P. 133-160.<br />
<br />
50. ^ Korotayev, A. V., & Malkov, A. S. A Compact Mathematical Model of the World System Economic and Demographic Growth, 1 CE–1973 CE // INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES Volume 10, 2016. P. 200-209 Archived 2018-01-06 at the Wayback Machine.<br />
<br />
51. ^ Berger, Sebastian. "Circular Cumulative Causation (CCC) à la Myrdal and Kapp — Political Institutionalism for Minimizing Social Costs" (PDF). Archived (PDF) from the original on 26 April 2012. Retrieved 26 November 2011.<br />
<br />
52. ^ S.-Y. Simon Wang; Jin-Ho Yoon; Christopher C. Funk; Robert R. Gillies, eds. (2017). Climate Extremes: Patterns and Mechanisms. Wiley. pp. 81–82. ISBN 9781119068037.<br />
<br />
53. ^ US NRC (2012), Climate Change: Evidence, Impacts, and Choices, US National Research Council (US NRC), archived from the original on 2016-05-03, p.9. Also available as PDF Archived 2013-02-20 at the Wayback Machine<br />
<br />
54. ^ Understanding Climate Change Feedbacks, U.S. National Academy of Sciences Archived 2012-02-10 at the Wayback Machine<br />
<br />
55. ^ "8.6.3.1 Water Vapour and Lapse Rate - AR4 WGI Chapter 8: Climate Models and their Evaluation". Archived from the original on 2010-04-09. Retrieved 2010-04-23.<br />
<br />
56. ^ IPCC. "Climate Change 2007: Synthesis Report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Pg 53" (PDF). Archived (PDF) from the original on 2010-02-09.<br />
<br />
57. ^ Holden, Matthew H.; McDonald-Madden, Eve (2017). "High prices for rare species can drive large populations extinct: The anthropogenic Allee effect revisited". Journal of Theoretical Biology. 429: 170–180. arXiv:1703.06736. Bibcode:2017arXiv170306736H. doi:10.1016/j.jtbi.2017.06.019. PMID 28669883.<br />
<br />
58. ^ Positive feedback occurs when one is told he has done something well or correctly. Tom Coens and Mary Jenkins, "Abolishing Performance Appraisals", p116.<br />
<br />
==拓展阅读==<br />
* Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.<br />
* Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.<br />
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本中文词条由[[用户:Solitude|Solitude]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%AD%A3%E5%8F%8D%E9%A6%88&diff=29622正反馈2022-03-26T08:39:51Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=自相似性,共形对称,膨胀<br />
|description=在物理学、数学和统计学中,标度不变性是物体或者物理定律的一种特征,如果长度、能量或者其他变量的标度与一个公因子相乘,而不发生改变,因此也就代表某种普遍性。<br />
}}<br />
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[[File:Wiener process animated.gif|thumb|right|500px|<br />
维纳过程具有标度不变性。|链接=Special:FilePath/Wiener_process_animated.gif]]<br />
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{{short description|Destabilising process that occurs in a feedback loop}}<br />
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[[File:Herdwick Stampede.jpg|thumb|right|【图1:Alarm or panic can sometimes be spread by positive feedback among a herd of animals to cause a [[stampede.]] 有时,警报或恐慌会通过正反馈在一群动物之间传播,从而引起踩踏事件。】.|链接=Special:FilePath/Herdwick_Stampede.jpg]]<br />
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[[File:Stampede loop.png|thumb|【图2:Causal loop diagram that depicts the causes of a stampede as a positive feedback loop. 在因果环路图中,踩踏事件的发生是一个正反馈循环。】|链接=Special:FilePath/Stampede_loop.png]]<br />
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[[File:Birmingham Northern Rock bank run 2007.jpg|thumb|right|【图3:In sociology a network effect can quickly create the positive feedback of a bank run. The above photo is of the UK Northern Rock 2007 bank run. 在社会学中,网络效应可以迅速产生银行挤兑的正反馈效应。上图是2007年英国北岩银行挤兑事件的照片。】|链接=Special:FilePath/Birmingham_Northern_Rock_bank_run_2007.jpg]]<br />
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'''Positive feedback''' ('''exacerbating feedback''', '''self-reinforcing feedback''') is a process that occurs in a [[feedback loop]] which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation.Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback.<ref name="theorymodelling" /> Both concepts play an important role in science and engineering, including biology, chemistry, and [[cybernetics]] .<br />
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正反馈(加剧反馈,自我强化反馈) 是一种在反馈循环中加剧微小扰动影响的过程。也就是说,一个扰动对系统的影响包括它自身扰动幅度的增大。或者说,A会产生更多的B,而B又会产生更多的A,与之相反的是,[[负反馈]]指的是一个系统中,变化的结果会减少或抵消它自己的影响。<ref name="theorymodelling" />这两个概念在科学和工程等领域中发挥着重要作用,包括生物学、化学和控制论。<br />
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在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。<ref name="zuckerman" /><ref>Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". ''Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems''. Academic Press. p. 55. ISBN <bdi>9780127784557</bdi>. Archived from the original on 2017-01-03. <q>A positive feedback loop is one with an even number of negative influences [around the loop].</q></ref><ref name="zuckerman" /> 从结果到始发过程的反馈可以是直接的,也可以通过其他状态变量<ref name="theorymodelling" />。这样的系统可以给出丰富的定性行为,但反馈的瞬时信号是正向还是负向,对结果有极其重要的影响。<ref name="theorymodelling" /> 正反馈强化原过程,而负反馈调节原过程。在这个含义下,''正''和''负''指的是大于或小于零的循环收益,并不代表着最终结果或效果的正负性。<ref name=":0">{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref>因此,正反馈的一个重要特点是小扰动变大。当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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===基础===<br />
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[[File:Ideal feedback model.svg|thumb|【图4:A basic feedback system can be represented by this block diagram. In the diagram the + symbol is an adder and A and B are arbitrary causal functions. 一个基本的反馈系统可以用这个框图来表示。在图中,+号是加法器,A和B是任意因果函数。】|链接=Special:FilePath/Ideal_feedback_model.svg]]<br />
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图中显示了一个简单的反馈回路。 如果环增益AB为正值,则存在'正'或'再生'反馈的条件。<br />
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如果函数A和B是线性的,且AB小于1,那么系统从输入到输出的整体增益是有限的,但当AB接近1时,系统的增益可以非常大。<ref name="smith"> Electronics circuits and devices second edition. Ralph J. Smith</ref> 在这种情况下,可以表明从输入到输出的整体或 "闭环 "增益为:<br />
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:<math>G_c = A/(1-AB)</math><br />
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当AB>1时,系统是不稳定的,因此不具有明确的增益;增益可称为无限。<br />
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所以系统状态的变化根据反馈可以是收敛的,也可以是发散的。 而正反馈的结果是增强变化,因此小的扰动就可能导致大的变化。<br />
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对于一个当前处于平衡状态的系统,如果其状态的任何变化都发生了正反馈,从而造成了状态的不稳定,那么这个系统就是一个不稳定平衡的系统。使这种系统远离其平衡状态的力的大小是状态与平衡状态之间的距离的递增函数。<br />
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正反馈并不一定意味着平衡的不稳定性,例如,在正反馈结构中可能存在稳定的开关状态<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref>。<br />
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=== 迟滞 ===<br />
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[[File:Hysteresis sharp curve.svg|thumb|【图5 Hysteresis causes the output value to depend on the history of the input 迟滞现象会导致输出值取决于输入的历史记录。】|链接=Special:FilePath/Hysteresis_sharp_curve.svg]]<br />
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[[File:Op-Amp Schmitt Trigger.svg|thumb|【图6 In a Schmitt trigger circuit, feedback to the non-inverting input of an amplifier pushes the output directly away from the applied voltage towards the maximum or minimum voltage the amplifier can generate. 在施密特触发器电路中,利用放大器的非反相输入端口产生的反馈,可以直接将电路的输出从原本的外加电压值推向到放大器所能产生的极值电压。】|链接=Special:FilePath/Op-Amp_Schmitt_Trigger.svg]]<br />
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在现实世界中,正反馈循环通常不会引起不断增长,而是通过某种限制效应来改变。根据Donella Meadows的说法:<br />
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正反馈回路是系统增长、爆炸、腐蚀和崩溃的根源。一个系统如果有一个不受控制的正反馈,最终将会自我毁灭。这就是为什么正反馈如此稀少的原因。通常情况下,负反馈迟早会发生。<ref>Donella Meadows, ''[http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf Leverage Points: Places to Intervene in a System]''2013-10-08 at the Wayback Machine, 1999</ref><br />
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[[迟滞]],即起点影响系统的终点的现象,可以通过正反馈产生。当反馈循环的增益高于1时,那么输出就会远离输入:如果大于输入,则向最近的正极限移动,而如果小于输入,则向最近的负极限移动。<br />
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一旦达到极限,它就会稳定下来。但是,如果输入超过极限,那么反馈将改变符号,输出将向相反的方向移动,直到达到相反的极限。因此,该系统表现出<font color="#ff8000"> 双稳态行为bistable behavior</font>。<br />
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== 术语的由来==<br />
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正反馈和负反馈这两个名词最早应用于反馈是在二战前。正反馈的概念随着再生电路的问世,在20世纪20年代已经出现。<br />
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Friis 和 Jensen在1924年描述了一种在电子放大器中发生的"回馈 "是正的情况,这一情况与他们顺便提到的负回馈作用相反。到了1934年,Harold Stephen Black在他的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法:<br />
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正反馈会增加放大器的增益,负反馈会降低增益<br />
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据Mindell(2002年)说,术语上的混乱是在这之后不久产生的:<br />
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“ ... ... Friis 和 Jensen 对 Black 在对"正反馈 "和 "负反馈 "的区分方法是一样的,都不是基于反馈本身的符号,而是基于它对放大器增益的影响。与之相反的是,当Nyquist和Bode基于Black的工作基础时,将负反馈称为符号相反的反馈。Black难以说服其他人相信他的发明的实用性,有一部分原因是在基本的定义问题上存在混乱。"<br />
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==实例与应用==<br />
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=== 电子电路===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|【图7 A vintage style regenerative radio receiver. Due to the controlled use of positive feedback, sufficient amplification can be derived from a single [[vacuum tube]] or valve (centre). 一个老式的再生无线电接收器。由于使用正反馈的控制,真空管或阀门(中心)就可以产生足够的放大效果。】|链接=Special:FilePath/Regenerartive_Receiver-S7300056.JPG]]<br />
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<font color="#ff8000"> 再生电路Regenerative circuit</font>于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>,用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈,可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此,一个信号可以在一个阶段被放大20000甚至100000倍,而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定,开始振荡。无线电操作员必须不断地调整反馈量,以获得良好的接收效果。而现代无线电接收机采用超异构设计,多了许多放大级,去掉了正反馈并使其工作更稳定。<br />
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在再生无线电电路中产生的振荡还可以被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英),经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计,包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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许多电子电路,特别是放大器,都采用了负反馈。这降低了放大器的信号增益,但改善了它的线性度、输入阻抗、输出阻抗和带宽,并稳定了包括闭环增益等参数。同时,这些参数也变得不那么依赖于放大器件本身的细节,而更多地依赖于反馈元件,因为反馈元件一般不随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位:如果信号反馈失相,则反馈为负,如果相位一致,则反馈为正。对于需要使用负反馈放大器的设计者来说,引入负反馈放大器的问题是,电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°,那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波来做到这一点)。如果任何频率下的环增益(放大器增益与正反馈程度的乘积)大于1,那么放大器将在该频率下发生振荡(巴克豪森稳定性准则)。这种振荡有时被称为寄生振荡:在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化,前板(用户界面)的变化,甚至是由于人或其他导电物品的接近。<br />
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放大器可能会以示波器很难检测到的方式轻轻振荡,有时的振荡也可能非常大,只有非常扭曲或根本没有真正的信号,甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似,因此低频寄生振荡也被称为 "汽艇"。<br />
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【图8 The effect of using a Schmitt trigger (B) instead of a comparator (A) 使用施密特触发器(b)代替比较器(a)的效果】<br />
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许多常见的数字电路都采用正反馈。一般简单的布尔逻辑门通常只是依靠增益将数字信号电压从中间值推到代表布尔值0和1的值上,但许多更复杂的门都采用了反馈。当输入的模拟电压发生变化,但后期数字处理需要尖锐阈值时,施密特触发电路通过正反馈机制确保当输入电压轻微超过阈值时,输出电压可以巧妙而迅速地从一个逻辑状态转移到另一个逻辑状态。施密特触发器使用正反馈的一个必然结果是,如果输入电压再次缓慢下降,超过了相同的阈值,由于正反馈的机制,输出电压将保持在相同的逻辑状态而不改变。这种效应被称为滞后: 输入电压必须降到一个不同的、较低的阈值,才能“解锁”输出,并将其重置为原始数字。通过减小正反馈的程度,可以减小滞后宽度,但宽度不能被完全消除。施密特触发器在某种程度上是一个闭锁电路。<br />
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【图9 Positive feedback is a mechanism by which an output is enhanced, such as protein levels. However, in order to avoid any fluctuation in the protein level, the mechanism is inhibited stochastically (I), therefore when the concentration of the activated protein (A) is past the threshold ([I]), the loop mechanism is activated and the concentration of A increases exponentially if d[A]=k [A] 正反馈是一种增强输出的机制,如蛋白质水平。但为了避免蛋白质水平的波动,该机制是随机抑制的(I),因此只有当激活的蛋白质(A)浓度超过阈值([I])时,循环机制被激活,如果d[A]=k[A],A的浓度就会成倍增加。】<br />
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【图10 Illustration of an R-S ('reset-set') flip-flop made from two digital nor gates with positive feedback. Red and black mean logical '1' and '0', respectively. R-S("复位-设置")触发器的说明,由两个带正反馈的数字诺尔门组成。红色和黑色分别表示逻辑上的 "1 "和 "0"。】<br />
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电子触发器,或“锁存器” ,或“双稳态多谐振荡器” ,是一种由于高正反馈而不稳定于平衡或中间状态的电路。这样的双稳态电路是一位电子存储器的基础。 触发器使用一对放大器、晶体管或逻辑门相互连接,正反馈机制使得输入信号被去除后,电路可以维持在两种非平衡稳定状态中的一种,直到一个合适的替代信号重新作为输入,以改变电路状态。计算机随机存取存储器(RAM)可以用这种方式运作,每位存储器有一个锁存电路。<br />
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电子系统中发生<font color="#ff8000"> 热失控Thermal runaway</font>的原因是,当电路的某些方面变得更热时,它被允许通过更多的电流,然后它越热,通过的电流就越多,这就使它更热一些,因此它又通过更多的电流。这种现象对有关器件来说通常是灾难性的。如果器件不得不在接近其最大功率处理能力的情况下工作,那么某些条件下就可能出现热失控,这通常可以通过精心设计来改进。<br />
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[[File:Technics SL-1210MK2.jpg|thumb|left|【图11 A phonograph turntable is prone to acoustic feedback. 留声机转盘容易受到声反馈的影响。】|链接=Special:FilePath/Technics_SL-1210MK2.jpg]]<br />
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音频和视频系统可以表现出正反馈。如果麦克风录入了同一电路中扬声器的放大声音输出,那么就会听到音频反馈的嚎叫和尖叫声(在放大器的最大功率容量下),因为随机噪声被音频系统和房间的特性所过滤后,通过正反馈重新放大。<br />
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===音频和现场音乐领域===<br />
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音频反馈(也称为声反馈,简称反馈,或拉森效应)是一种特殊的正反馈,当音频输入(例如,麦克风或吉他拾音器)和音频输出(例如,大声放大的扬声器)之间存在声音回路时,就会出现这种反馈。在这个例子中,麦克风接收到的信号被放大并从扬声器传出。然后,来自扬声器的声音可以再次被麦克风接收,进一步放大,然后再次通过扬声器传递出去。 所产生的声音的频率由传声器、放大器和扬声器的共振频率、房间的声学特性、传声器和扬声器的定向拾音和发射模式以及它们之间的距离决定。对于小型的扩声系统来说,这种声音很容易的体现的响亮的吱吱声或尖叫声。<br />
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在歌手或公众演讲者使用扩声系统或扩音系统的活动中,麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来,音频工程师使用各种电子设备,如均衡器或者自动反馈检测设备,来防止这些不受欢迎的尖叫声或尖叫声,这些声音影响了观众对活动的享受。另一方面,自20世纪60年代以来,摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果,有意制造吉他中的正反馈,以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈,但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中,他说,“我敢说任何人都找不到这样的唱片,除非是1922年这张用这种方式录制的老蓝调唱片。”<br />
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音频反馈的原理是由丹麦科学家Søren Absalon Larsen首先发现的。麦克风并不是唯一受此影响的传感器。录音板拾音器也会产生正反馈,通常是在100赫兹以下的低频范围内表现出低沉的轰鸣声。Jimi Hendrix是一个创新者,在他的吉他独奏中有意使用吉他正反馈来创造独特的声音效果。他帮助发展了电吉他演奏中音频反馈的可控性和音乐性,后来Brian May也是这种技术的著名支持者。<br />
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[[File:Adam Savage HOPE.jpg|thumb|right|220px|[[Video feedback]]【图12 视频反馈】.|链接=Special:FilePath/Adam_Savage_HOPE.jpg]]<br />
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===视频===<br />
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同样,如果一台摄像机对准一个正在显示摄像机自身信号的监控屏幕,那么通过正反馈就可以在屏幕上形成重复的图案。这种视频反馈效果在电视剧《神秘博士》前十季的开场白中就被使用了。<br />
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===开关===<br />
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In [[electrical switch]]es, including [[bimetallic strip]] based thermostats, the switch usually has hysteresis in the switching action. In these cases hysteresis is mechanically achieved via positive feedback within a tipping point mechanism. The positive feedback action minimises the length of time arcing occurs for during the switching and also holds the contacts in an open or closed state.<br />
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在电气开关中,包括双金属条型恒温器,开关通常在开关动作中具有滞后性。在这些情况下,滞后是通过一个临界点机构内的正反馈来实现的。正反馈作用可最大限度地减少开关过程中发生电弧的时间,并使触点保持在断开或闭合状态。<br />
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=== 生物学===<br />
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[[File:Positive Feedback- Childbirth (1).svg|thumb|生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做<font color="#ff8000"> 催产素oxytocin</font>的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。|链接=Special:FilePath/Positive_Feedback-_Childbirth_(1).svg]]<br />
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生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做<font color="#ff8000"> 催产素oxytocin</font>的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。<br />
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==== 生理学====<br />
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在生理学中可以找到一些正反馈系统的例子。<br />
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其中一个例子是分娩时宫缩的发生,称为弗格森反射。当宫缩发生时,激素催产素会引起神经刺激,刺激下丘脑产生更多的催产素,从而增加子宫收缩。这就导致宫缩的幅度和频率增加。<br />
<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders. {{ISBN|0-7216-3994-1}}</ref><br />
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另一个例子是血液凝固的过程。当受伤的组织释放出信号化学物质,激活血液中的血小板时,这个循环就启动了。被激活的血小板释放化学物质,激活更多的血小板,引起快速的级联反应,形成血栓。<ref name=Guyton1991/><br />
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哺乳也涉及正反馈,当婴儿吸吮乳头时,会有神经反应进入脊髓,并上传到大脑的下丘脑,然后刺激垂体产生更多的催乳素以产生更多的乳汁<ref name=Guyton1991/>。<br />
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在月经周期的卵泡期期间,雌激素的飙升会导致排卵<ref name=Guyton1991/>。<br />
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神经信号的产生是另一个例子,神经纤维的膜使钠离子通过钠通道轻微渗漏,导致膜电位的变化,进而引起更多通道的开放(Hodgkin循环)。所以,最初的轻微渗漏会导致钠渗漏的爆发,从而产生神经动作电位<ref name=Guyton1991/>。<br />
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在心脏的兴奋收缩耦合中,肌浆网膜中的兰尼碱受体检测到心肌细胞内钙离子的增加,该受体以正反馈生理反应将钙运出到细胞质中。<br />
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在大多数情况下,这种反馈循环最终会释放出反信号,从而抑制或破坏循环。分娩宫缩在宝宝离开母体时停止。化学物质分解血凝块。当婴儿不再需要被哺乳时,泌乳停止<ref name=Guyton1991/>。<br />
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====基因调控====<br />
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正反馈是基因调控中研究较好的一种现象,其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时,就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络,以证明双稳态的概念。<ref name=Hasty2002/><br />
正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用,因此,基因调控中的正反馈可以产生显著的生理结果。分子动力学中的随机运动加上正反馈可以引发有趣的效应,例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/> 这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中,如酶动力学或代谢途径。<ref name=Christoph2001/><br />
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==== 进化生物学 ====<br />
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在进化生物学中正反馈循环被用来描述生物进化中变化动态的各个方面。 例如,在宏观层面,Alfred J. Lotka(1945)认为,物种的演变最重要的是选择反馈能量流动以捕获越来越多的能源系统的能量。<ref name=Lotka1945/>在人类层面,Richard D. Alexander(1989)提出,人类群体之间和群体内部的社会竞争会影响智力的选择,从而时不时地会产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子<ref name=Crespi2004/>。通过与军备竞赛进行类比,给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/><br />
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[[File:Phanerozoic Biodiversity.svg|300px|right|thumb|显生宙[[生物多样性]]呈现稳定而非单调的增长,从接近于零一直增长到有几千个属。|链接=Special:FilePath/Phanerozoic_Biodiversity.svg]]<br />
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研究表明,在<font color="#32CD32"> 显生宙 </font>,生物多样性的变化与双曲模型(广泛用于人口学和宏观社会学)的相关性要比指数模型和逻辑斯特模型(传统上用于人口生物学,并广泛用于生物多样性化石)的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈(更多的祖先,更多的后代)和资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为,生物多样性和人口曲线之间的相似性可能来自这样一个事实,即两者都是由双曲趋势(由正反馈产生)与周期性和随机性的动态干扰而产生的。<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref><br />
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==== 免疫系统====<br />
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细胞因子风暴,或称高细胞因子血症,是一种潜在的致命性免疫反应,表现为各种细胞因子水平高度升高,这是由细胞因子和免疫细胞之间的正反馈环组成。[36]在正常的免疫功能中,可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后,就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合,当B细胞的抗体与C3结合后,就会加快该B细胞分泌更多的抗体和更多的C3蛋白,从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
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====细胞凋亡====<br />
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细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程,其目的是清除长寿或受损的细胞。这一过程的失效与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活,它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时,无论效应子胱天蛋白酶的中间激活步骤数量有多少,这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/> 当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时,该过程呈现双稳态,从而模拟细胞的存活和死亡状态。<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref><br />
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=== 心理学===<br />
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Winner(1996)将有天赋的孩子描述为受到正反馈循环的驱动,这些反馈循环体现在他们自己的课程学习上,通过反馈自己的满意程度,从而进一步将他们的学习目标提高到更高水平等。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a,2009b)提出,神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释,工作记忆中的思维/表现输出被反馈到小脑,在那里被精简,然后再反馈到工作记忆中,从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/> <br />
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=== 经济学===<br />
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====市场上的社会影响====<br />
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事实证明,产品推荐和消费者先前的购买信息对消费者的选择影响很大,无论是音乐、电影、书籍、电子产品还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象(马太效应),即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
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====市场动向====<br />
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根据George Soros提出的反射性理论,价格变化是由一个正反馈过程驱动的,即投资者的预期受到价格变动的影响,因此他们的行为会强化这个方向的价格变动,直到价格的变化变得不可持续,于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
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==== 系统风险====<br />
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系统性风险是指放大效应或杠杆或正反馈过程给系统带来的风险。这通常是未知的,在某些条件下,这个过程会成倍放大,并迅速导致破坏性或混乱的行为。 庞氏骗局就是正反馈系统的一个很好的例子:来自新投资者的资金被用来支付异常高的回报,反过来又吸引了更多的新投资者,导致快速增长进而走向崩溃。W. Brian Arthur 也对经济中的正反馈进行了研究和著述(如W. Brian Arthur,1990)。Hyman Minsky提出了一个理论,认为某些信用扩张行为会使市场经济变成一个 "偏差放大系统",从而可能会突然崩溃,这有时被称为 "明斯基时刻"。<br />
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输入和输出明确分开的简单系统不容易发生系统性风险。 随着系统复杂性的增加,这种风险更容易发生,因为即使在详细的压力测试条件下,也更难看到或分析系统中所有可能的变量组合。 一个复杂系统的效率越高,就越容易发生系统性风险,因为只需要很小的偏差就可以破坏系统。 因此,设计良好的复杂系统一般都会有一些内在的功能来避免这种情况的发生,比如在系统内有少量的摩擦力,或阻力,或惯性,或时间延迟来使输出与输入脱钩。这些因素造成了低效率,但它们是避免不稳定的必要条件。<br />
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2010年的闪崩事件被归咎于高频交易(HFT)的做法,不过HFT是否真的会增加系统性风险仍然存在争议。<br />
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====人口与环境危机====<br />
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可以认为农业和人口之间处于一种正反馈模式,这意味着双方越来越强烈地推动彼此。有人认为,这种正反馈系统终将在某一时刻以灾难结束,因为现代农业正在耗尽所有容易获得的磷酸盐,并且进行高效的单一栽培,使得现代农业更容易受到系统性风险影响。<br />
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技术创新和人类人口也可以有类似的考虑,这也是过去人类人口明显的双曲线增长,而不是简单的指数增长的一个解释。<br />
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有人提出,由于人口和技术之间的二阶正反馈,增长速度正在加快。技术增长增加了土地对人的承载能力,从而导致人口增长,而这反过来又推动了技术的进一步增长。<br />
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==== 偏见、社会制度与贫困====<br />
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Gunnar Myrdal描述了一个不平等和贫困加剧的恶性循环,这就是所谓的”循环累积诱因”。<br />
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==== 气象学====<br />
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干旱通过正反馈效应加剧。缺雨会降低土壤湿度,从而杀死植物,使它们通过蒸腾作用释放更少的水分。这两个因素都限制了水蒸气从地表加到大气中的过程,并使吸收水分的干燥灰尘进入大气。水汽少了,既意味着露点温度低,白天的供暖效率也高,减少了大气中湿度导致云的形成的机会。最后,没有云,就不会有雨,这个正反馈循环就形成了。<br />
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==== 气候学====<br />
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气候中的"诱因 "可能会将气候系统推向变暖或变冷的方向,例如,大气中温室气体浓度的增加会导致地表变暖。诱因是气候系统的外部因素,而反馈是系统的内部过程。一些反馈机制与气候系统的其他部分相对孤立地发挥作用,而另一些则是紧密耦合的。气候系统的作用力、反馈和动态决定了气候变化的程度和速度。全球变暖中的主要正反馈是变暖使大气中的水汽量增加,进而导致进一步变暖。主要的负反馈来自Stefan-Boltzmann定律,从地球辐射到空间的热量与地球表面和大气温度的四次方成正比。<br />
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气候学中正反馈子系统的其他例子包括:<br />
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大气变暖会使冰融化,从而改变反照率,从而使大气进一步变暖。<br />
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甲烷水合物可能是不稳定的,所以海洋变暖可能会释放更多的温室气体之一的甲烷。<br />
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泥炭,天然存在于泥炭沼泽中,含有碳。当泥炭干燥时,它会分解,并可能额外燃烧。泥炭还会释放一氧化二氮。<br />
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全球变暖会影响云的分布。高空的云层会增强温室效应,而低空的云层则主要反射太阳光,对温度产生相反的影响。<br />
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政府间气候变化专门委员会(气专委)第四次评估报告指出,"人类活动的变暖可能导致一些突然或不可逆转的影响,这取决于气候变化的速度和程度"。<br />
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==== 社会学====<br />
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自我应验预言是信念和行为之间的一个社会正反馈循环: 如果有足够多的人相信某件事是真的,他们的行为就能让它变成真的,而对他们行为的观察又可能反过来增加信念。一个典型的例子是银行挤兑。<br />
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正反馈的另一个社会学例子是网络效应。当更多的人被鼓励加入一个网络时,这就增加了网络的覆盖面,因此网络扩张得越来越快。病毒视频就是网络效应的一个例子,在这个例子中,一个热门视频的链接被分享和再传播,确保更多的人看到这个视频,然后重新发布链接。这是许多社会现象的基础,包括庞氏骗局和连锁信。在许多情况下,人口量是反馈效应的限制因素。<br />
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==== 化学====<br />
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如果化学反应引起热量的释放,而反应本身在较高的温度下发生得更快,那么就很有可能出现正反馈。如果产生的热量没有足够快地从反应物中排除,就会发生热失控,并很快导致化学爆炸。<br />
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==== 自然保护====<br />
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许多野生动物被猎杀的原因是它们身体的某些部位可能相当有价值。目标物种越是接近灭绝,其部位的价格就越高。这就是一个正反馈的例子。<br />
<br />
==参见==<br />
<br />
* Chain reaction – Sequence of reactions 链式反应 -- -- 反应的顺序<br />
* Donella Meadows' twelve leverage points to intervene in a system Donella Meadows干预系统的十二个杠杆点<br />
* Hyperbolic growth 双曲增长<br />
* Reflexivity (social theory)反射性(社会理论)<br />
* Stability criterion稳定性标准<br />
* Strategic complements战略补充<br />
* System dynamics 系统动力学<br />
* Technological singularity – Hypothetical point in time at which technological growth becomes uncontrollable and irreversible 技术奇点 -- -- 假设技术增长变得不可控制和不可逆转的时间点<br />
* Thermal runaway 热失控<br />
* Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop. 恶性/恶性循环:在社会和金融系统中,是通过反馈循环自我强化的事件综合体。<br />
* Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour. 正强化:在操作性条件下,结果会增加行为的频率。<br />
* Praise of performance: a term often applied in the context of performance appraisal,although this usage is disputed 绩效表扬:这个词经常被应用于绩效评估中,尽管这种用法有争议。<br />
* Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage 自我强化反馈:系统动力学中使用的术语,以避免与 "表扬 "的用法相混淆。<br />
* Matthew effect – Effect originally observed by Robert K. Merton 马太效应 -- -- 罗伯特-K-默顿最初观察到的效应。<br />
* Self-fulfilling prophecy – Prediction that causes itself to become true 自证预言 -- -- 导致自己成为现实的预言<br />
* Virtuous circle and vicious circle 良性循环和恶性循环<br />
* Autocatalysis 自催化<br />
* Meander – Sinuous bend in a series in the channel of a river 蜿蜒曲折 -- -- 河道中一系列蜿蜒曲折的弯道。<br />
<br />
<br />
==参考文献==<br />
1. ^ a b c Ben Zuckerman & David Jefferson (1996). Human Population and the Environmental Crisis. Jones & Bartlett Learning. p. 42. ISBN 9780867209662. Archived from the original on 2018-01-06.<br />
<br />
2. ^ Keesing, R.M. (1981). Cultural anthropology: A contemporary perspective (2nd ed.) p.149. Sydney: Holt, Rinehard & Winston, Inc.<br />
<br />
3. ^ a b c d e Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems. Academic Press. p. 55. ISBN 9780127784557. Archived from the original on 2017-01-03. “A positive feedback loop is one with an even number of negative influences [around the loop].”<br />
<br />
4. ^ S W Amos; R W Amos (2002). Newnes Dictionary of Electronics (4th ed.). Newnes. p. 247. ISBN 9780750656429. Archived from the original on 2017-03-29.<br />
<br />
5. ^ Rudolf F. Graf (1999). Modern Dictionary of Electronics (7th ed.). Newnes. p. 276. ISBN 9780750698665. Archived from the original on 2017-03-29.<br />
<br />
6. ^ "Positive feedback". Oxford English Dictionary. Oxford University Press. Archived from the original on 2 March 2014. Retrieved 15 April 2014.<br />
<br />
7. ^ "Feedback". Glossary. Metadesigners Network. Archived from the original on 16 April 2014. Retrieved 15 April 2014.<br />
<br />
8. ^ Electronics circuits and devices second edition. Ralph J. Smith<br />
<br />
9. ^ a b Lopez-Caamal, Fernando; Middleton, Richard H.; Huber, Heinrich (February 2014). "Equilibria and stability of a class of positive feedback loops". Journal of Mathematical Biology. 68 (3): 609–645. doi:10.1007/s00285-013-0644-z. PMID 23358701.<br />
<br />
10. ^ Donella Meadows, Leverage Points: Places to Intervene in a System Archived 2013-10-08 at the Wayback Machine, 1999<br />
<br />
11. ^ a b Mindell, David A. (2002). Between Human and Machine : Feedback, Control, and Computing before Cybernetics.Baltimore, MD: Johns Hopkins University Press. ISBN 9780801868955. Archived from the original on 2018-01-06.<br />
<br />
12. ^ Friis, H. T.; Jensen, A. G. (April 1924), "High Frequency Amplifiers", Bell System Technical Journal, 3 (2): 181–205, doi:10.1002/j.1538-7305.1924.tb01354.x<br />
<br />
13. ^ Black, H. S. (January 1934), "Stabilized feed-back amplifiers", Electrical Engineering, 53: 114–120, doi:10.1109/ee.1934.6540374<br />
<br />
14. ^ US 1113149, Armstrong, E. H., "Wireless receiving system"<br />
<br />
15. ^ Kitchin, Charles. "A Short Wave Regenerative Receiver Project". Archived from the original on 10 July 2010. Retrieved 23 September 2010.<br />
<br />
16. ^ "Sinewave oscillators". EDUCYPEDIA - electronics. Archived from the original on 27 September 2010. Retrieved 23 September 2010.<br />
<br />
17. ^ Self, Douglas (2009). Audio Power Amplifier Design Handbook. Focal Press. pp. 254–255. ISBN 978-0-240-52162-6. Archived from the original on 2014-01-29.<br />
<br />
18. ^ "CMOS Schmitt Trigger—A Uniquely Versatile Design Component" (PDF). Fairchild Semiconductor Application Note 140. Fairchild Semiconductors. 1975. Archived (PDF) from the original on 22 November 2010. Retrieved 29 September 2010.<br />
<br />
19. ^ Strandh, Robert. "Latches and flip-flops". Laboratoire Bordelais de Recherche en Informatique. Archived from the original on 16 July 2011. Retrieved 4 November 2010.<br />
<br />
20. ^ Wayne, Storr. "Sequential Logic Basics: SR Flip-Flop". Electronics-Tutorials.ws. Archived from the original on 16 September 2010. Retrieved 29 September 2010.<br />
<br />
21. ^ Sharma, Bijay Kumar (2009). "Analog Electronics Lecture 4 Part C RC coupled Amplifier Design Procedure". Retrieved 29 September 2010.<br />
<br />
22. ^ Sheff, David (2000). All We Are Saying. New York, New York: St. Martin's Press. p. 173. ISBN 978-0-312-25464-3.<br />
<br />
23. ^ Shadwick, Keith (2003). Jimi Hendrix, Musician. Backbeat Books. p. 92. ISBN 978-0-87930-764-6.<br />
<br />
24. ^ May, Brian. "Burns Brian May Tri-Sonic Pickups". House Music & Duck Productions. Archived from the original on 20 November 2010. Retrieved 2 February 2011.<br />
<br />
25. ^ "Positive Feedback and Bistable Systems" (PDF). University of Washington. Archived (PDF) from the original on 2015-04-13. “* Non-Hysteretic Switches, Memoryless Switches: These systems have no memory, that is, once the input signal is removed, the system returns to its original state. * Hysteretic Switches, Bistability: Bistable systems, in contrast, have memory. That is, when switched to one state or another, these systems remain in that state unless forced to change back. The light switch is a common example of a bistable system from everyday life. All bistable systems are based around some form of positive feedback loop.”<br />
<br />
26. ^ a b c d e f Guyton, Arthur C. (1991) Textbook of Medical Physiology. (8th ed). Philadelphia: W.B. Saunders. ISBN 0-7216-3994-1<br />
<br />
27. ^ Hasty, J.; McMillen, D.; Collins, J. J. (2002). "Engineered gene circuits". Nature. 420 (6912): 224–230. Bibcode:2002Natur.420..224H. doi:10.1038/nature01257. PMID 12432407.<br />
<br />
28. ^ Veening, J.; Smits, W. K.; Kuipers, O. P. (2008). "Bistability, Epigenetics, and Bet-Hedging in Bacteria" (PDF). Annual Review of Microbiology. 62 (1): 193–210. doi:10.1146/annurev.micro.62.081307.163002. hdl:11370/59bec46a-4434-4eaa-aaae-03461dd02bbb. PMID 18537474.<br />
<br />
29. ^ Bagowski, C. P.; Ferrell, J. E. (2001). "Bistability in the JNK cascade". Current Biology. 11 (15): 1176–1182. doi:10.1016/S0960-9822(01)00330-X. PMID 11516948.<br />
<br />
30. ^ Lotka, A (1945). "The law of evolution as a maximal principle". Human Biology. 17: 168–194.<br />
<br />
31. ^ Alexander, R. (1989). Evolution of the human psyche. In P. Millar & C. Stringer (Eds.), The human revolution: Behavioral and biological perspectives on the origins of modern humans (pp. 455-513). Princeton: Princeton University Press.<br />
<br />
32. ^ Crespi, B. J. (2004). "Vicious circles: positive feedback in major evolutionary and ecological transitions". Trends in Ecology and Evolution. 19 (12): 627–633. doi:10.1016/j.tree.2004.10.001. PMID 16701324.<br />
<br />
33. ^ Dawkins, R. 1991. The Blind Watchmaker London: Penguin. Note: W.W. Norton also published this book, and some citations may refer to that publication. However, the text is identical, so it depends on which book is at hand<br />
<br />
34. ^ Markov A., Korotayev A. "Phanerozoic marine biodiversity follows a hyperbolic trend." Palaeoworld. Volume 16, Issue 4, December 2007, Pages 311-318<br />
<br />
35. ^ Markov, A.; Korotayev, A. (2008). "Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution". Journal of General Biology. 69 (3): 175–194. PMID 18677962. Archived from the original on 2009-12-25.<br />
<br />
36. ^ Osterholm, Michael T. (2005-05-05). "Preparing for the Next Pandemic". The New England Journal of Medicine. 352 (18): 1839–1842. CiteSeerX 10.1.1.608.6200. doi:10.1056/NEJMp058068. PMID 15872196.<br />
<br />
37. ^ Paul, William E. (September 1993). "Infectious Diseases and the Immune System". Scientific American. 269 (3): 93. Bibcode:1993SciAm.269c..90P. doi:10.1038/scientificamerican0993-90. PMID 8211095.<br />
<br />
38. ^ Eissing, Thomas (2014). "Bistability analyses of a caspase activation model for receptor-induced apoptosis". Journal of Biological Chemistry. 279 (35): 36892–36897. doi:10.1074/jbc.M404893200. PMID 15208304.<br />
<br />
39. ^ Winner, E. (1996). Gifted children: Myths and Realities. New York: Basic Books. ISBN 978-0465017607.<br />
<br />
40. ^ Vandervert, L. (2009a). Working memory, the cognitive functions of the cerebellum and the child prodigy. In L.V. Shavinina (Ed.), International handbook on giftedness (pp. 295-316). The Netherlands: Springer Science.<br />
<br />
41. ^ Vandervert, L. (2009b). "The emergence of the child prodigy 10,000 years ago: An evolutionary and developmental explanation". Journal of Mind and Behavior. 30 (1–2): 15–32.<br />
<br />
42. ^ Altszyler, E; Berbeglia, F.; Berbeglia, G.; Van Hentenryck, P. (2017). "Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality". PLOS ONE. 12 (7): e0180040. Bibcode:2017PLoSO..1280040A. doi:10.1371/journal.pone.0180040. PMC 5528888. PMID 28746334.<br />
<br />
43. ^ Azzopardi, Paul V. (2010), Behavioural Technical Analysis, Harriman House Limited, p. 116, ISBN 9780857190680, archived from the original on 2017-03-29<br />
<br />
44. ^ Arthur, W. Brian (1990). "Positive Feedbacks in the Economy". Scientific American. 262 (2): 80. Bibcode:1990SciAm.262b..92A. doi:10.1038/scientificamerican0290-92.<br />
<br />
45. ^ The Financial Instability Hypothesis Archived 2009-10-09 at the Wayback Machine by Hyman P. Minsky, Working Paper No. 74, May 1992, pp. 6–8<br />
<br />
46. ^ "Findings Regarding the Market Events of May 6, 2010" (PDF). 2010-09-30. Archived (PDF) from the original on August 15, 2017.<br />
<br />
47. ^ Brown, A. Duncan (2003), Feed or Feedback: Agriculture, Population Dynamics and the State of the Planet, Utrecht: International Books, ISBN 978-90-5727-048-2<br />
<br />
48. ^ Dolgonosov, B.M. (2010). "On the reasons of hyperbolic growth in the biological and human world systems". Ecological Modelling. 221 (13–14): 1702–1709. doi:10.1016/j.ecolmodel.2010.03.028.<br />
<br />
49. ^ a b Korotayev A. Compact Mathematical Models of World System Development, and How they can Help us to Clarify our Understanding of Globalization Processes Archived 2018-01-06 at the Wayback Machine. Globalization as Evolutionary Process: Modeling Global Change. Edited by George Modelski, Tessaleno Devezas, and William R. Thompson. London: Routledge, 2007. P. 133-160.<br />
<br />
50. ^ Korotayev, A. V., & Malkov, A. S. A Compact Mathematical Model of the World System Economic and Demographic Growth, 1 CE–1973 CE // INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES Volume 10, 2016. P. 200-209 Archived 2018-01-06 at the Wayback Machine.<br />
<br />
51. ^ Berger, Sebastian. "Circular Cumulative Causation (CCC) à la Myrdal and Kapp — Political Institutionalism for Minimizing Social Costs" (PDF). Archived (PDF) from the original on 26 April 2012. Retrieved 26 November 2011.<br />
<br />
52. ^ S.-Y. Simon Wang; Jin-Ho Yoon; Christopher C. Funk; Robert R. Gillies, eds. (2017). Climate Extremes: Patterns and Mechanisms. Wiley. pp. 81–82. ISBN 9781119068037.<br />
<br />
53. ^ US NRC (2012), Climate Change: Evidence, Impacts, and Choices, US National Research Council (US NRC), archived from the original on 2016-05-03, p.9. Also available as PDF Archived 2013-02-20 at the Wayback Machine<br />
<br />
54. ^ Understanding Climate Change Feedbacks, U.S. National Academy of Sciences Archived 2012-02-10 at the Wayback Machine<br />
<br />
55. ^ "8.6.3.1 Water Vapour and Lapse Rate - AR4 WGI Chapter 8: Climate Models and their Evaluation". Archived from the original on 2010-04-09. Retrieved 2010-04-23.<br />
<br />
56. ^ IPCC. "Climate Change 2007: Synthesis Report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Pg 53" (PDF). Archived (PDF) from the original on 2010-02-09.<br />
<br />
57. ^ Holden, Matthew H.; McDonald-Madden, Eve (2017). "High prices for rare species can drive large populations extinct: The anthropogenic Allee effect revisited". Journal of Theoretical Biology. 429: 170–180. arXiv:1703.06736. Bibcode:2017arXiv170306736H. doi:10.1016/j.jtbi.2017.06.019. PMID 28669883.<br />
<br />
58. ^ Positive feedback occurs when one is told he has done something well or correctly. Tom Coens and Mary Jenkins, "Abolishing Performance Appraisals", p116.<br />
<br />
==拓展阅读==<br />
* Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.<br />
* Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.<br />
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本中文词条由[[用户:Solitude|Solitude]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%AD%A3%E5%8F%8D%E9%A6%88&diff=29621正反馈2022-03-26T08:17:05Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=自相似性,共形对称,膨胀<br />
|description=在物理学、数学和统计学中,标度不变性是物体或者物理定律的一种特征,如果长度、能量或者其他变量的标度与一个公因子相乘,而不发生改变,因此也就代表某种普遍性。<br />
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[[File:Wiener process animated.gif|thumb|right|500px|<br />
维纳过程具有标度不变性。|链接=Special:FilePath/Wiener_process_animated.gif]]<br />
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{{short description|Destabilising process that occurs in a feedback loop}}<br />
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[[File:Herdwick Stampede.jpg|thumb|right|【图1:Alarm or panic can sometimes be spread by positive feedback among a herd of animals to cause a [[stampede.]] 有时,警报或恐慌会通过正反馈在一群动物之间传播,从而引起踩踏事件。】.|链接=Special:FilePath/Herdwick_Stampede.jpg]]<br />
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[[File:Stampede loop.png|thumb|【图2:Causal loop diagram that depicts the causes of a stampede as a positive feedback loop. 在因果环路图中,踩踏事件的发生是一个正反馈循环。】|链接=Special:FilePath/Stampede_loop.png]]<br />
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[[File:Birmingham Northern Rock bank run 2007.jpg|thumb|right|【图3:In sociology a network effect can quickly create the positive feedback of a bank run. The above photo is of the UK Northern Rock 2007 bank run. 在社会学中,网络效应可以迅速产生银行挤兑的正反馈效应。上图是2007年英国北岩银行挤兑事件的照片。】|链接=Special:FilePath/Birmingham_Northern_Rock_bank_run_2007.jpg]]<br />
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'''Positive feedback''' ('''exacerbating feedback''', '''self-reinforcing feedback''') is a process that occurs in a [[feedback loop]] which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation.Positive feedback (exacerbating feedback, self-reinforcing feedback) is a process that occurs in a feedback loop which exacerbates the effects of a small disturbance. That is, the effects of a perturbation on a system include an increase in the magnitude of the perturbation. That is, A produces more of B which in turn produces more of A. In contrast, a system in which the results of a change act to reduce or counteract it has negative feedback.<ref name="theorymodelling" /> Both concepts play an important role in science and engineering, including biology, chemistry, and [[cybernetics]] .<br />
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正反馈(加剧反馈,自我强化反馈) 是一种在反馈循环中加剧微小扰动影响的过程。也就是说,一个扰动对系统的影响包括它自身扰动幅度的增大。或者说,A会产生更多的B,而B又会产生更多的A,与之相反的是,[[负反馈]]指的是一个系统中,变化的结果会减少或抵消它自己的影响。<ref name="theorymodelling" />这两个概念在科学和工程等领域中发挥着重要作用,包括生物学、化学和控制论。<br />
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Mathematically, positive feedback is defined as a positive [[loop gain]] around a closed loop of cause and effect.<ref name="zuckerman" /><ref name="theorymodelling"><br />
[[wikipedia:Positive_feedback#cite_note-zuckerman-1|Ben Zuckerman & David Jefferson (1996). ''Human Population and the Environmental Crisis''. Jones & Bartlett Learning. p. 42. ISBN <bdi>9780867209662</bdi>. Archived from the original on 2018-01-06.]]<br />
</ref><ref name="zuckerman" /> The feedback from the outcome to the originating process can be direct, or it can be via other state variables.<ref name="theorymodelling" /> Such systems can give rich qualitative behaviors, but whether the feedback is instantaneously positive or negative in sign has an extremely important influence on the results.<br />
<nowiki></ref></nowiki> <ref name="theorymodelling" /> Positive feedback reinforces and negative feedback moderates the original process. ''Positive'' and ''negative'' in this sense refer to loop gains greater than or less than zero, and do not imply any [[value judgement]]s as to the desirability of the outcomes or effects.<ref name=":0">{{cite web|title=Feedback|url=http://metadesigners.org/Feedback-Glossary|work=Glossary|publisher=Metadesigners Network|accessdate=15 April 2014|url-status=live|archiveurl=https://web.archive.org/web/20140416183720/http://metadesigners.org/Feedback-Glossary|archivedate=16 April 2014}}</ref> A key feature of positive feedback is thus that small disturbances get bigger. When a change occurs in a system, positive feedback causes further change, in the same direction.<br />
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在数学上,正反馈被定义为一个环绕在闭合因果循环下的正循环增益。<ref name="zuckerman" /><ref>Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". ''Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems''. Academic Press. p. 55. ISBN <bdi>9780127784557</bdi>. Archived from the original on 2017-01-03. <q>A positive feedback loop is one with an even number of negative influences [around the loop].</q></ref><ref name="theorymodelling" /><ref name="zuckerman" /> 从结果到始发过程的反馈可以是直接的,也可以通过其他状态变量。这样的系统可以给出丰富的定性行为,但反馈的瞬时信号是正向还是负向,对结果有极其重要的影响。<ref name="theorymodelling" /> 正反馈强化原过程,而负反馈调节原过程。在这个含义下,''正''和''负''指的是大于或小于零的循环收益,并不代表着最终结果或效果的正负性。<ref name=":0" />因此,正反馈的一个重要特点是小扰动变大。当系统发生变化时,正反馈会引起进一步的同方向变化。<br />
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=== Basic 基础===<br />
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[[File:Ideal feedback model.svg|thumb|【图4:A basic feedback system can be represented by this block diagram. In the diagram the + symbol is an adder and A and B are arbitrary causal functions. 一个基本的反馈系统可以用这个框图来表示。在图中,+号是加法器,A和B是任意因果函数。】|链接=Special:FilePath/Ideal_feedback_model.svg]]<br />
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A simple feedback loop is shown in the diagram. If the loop gain AB is positive, then a condition of ''positive'' or ''regenerative'' feedback exists.<br />
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图中显示了一个简单的反馈回路。 如果环增益AB为正值,则存在'正'或'再生'反馈的条件。<br />
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If the functions A and B are linear and AB is smaller than unity, then the overall system gain from the input to output is finite, but can be very large as AB approaches unity.<ref name=smith> Electronics circuits and devices second edition. Ralph J. Smith</ref> In that case, it can be shown that the overall or "closed loop" gain from input to output is:<br />
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如果函数A和B是线性的,且AB小于1,那么系统从输入到输出的整体增益是有限的,但当AB接近1时,系统的增益可以非常大。<ref name="smith"> Electronics circuits and devices second edition. Ralph J. Smith</ref> 在这种情况下,可以表明从输入到输出的整体或 "闭环 "增益为:<br />
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:<math>G_c = A/(1-AB)</math><br />
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When AB > 1, the system is unstable, so does not have a well-defined gain; the gain may be called infinite.<br />
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当AB>1时,系统是不稳定的,因此不具有明确的增益;增益可称为无限。<br />
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Thus depending on the feedback, state changes can be convergent, or divergent. The result of positive feedback is to augment changes, so that small perturbations may result in big changes.<br />
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所以系统状态的变化根据反馈可以是收敛的,也可以是发散的。 而正反馈的结果是增强变化,因此小的扰动就可能导致大的变化。<br />
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A system in equilibrium in which there is positive feedback to any change from its current state may be unstable, in which case the system is said to be in an unstable equilibrium. The magnitude of the forces that act to move such a system away from its equilibrium are an increasing function of the "distance" of the state from the equilibrium.<br />
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对于一个当前处于平衡状态的系统,如果其状态的任何变化都发生了正反馈,从而造成了状态的不稳定,那么这个系统就是一个不稳定平衡的系统。使这种系统远离其平衡状态的力的大小是状态与平衡状态之间的距离的递增函数。<br />
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Positive feedback does not necessarily imply instability of an equilibrium, for example stable ''on'' and ''off'' states may exist in positive-feedback architectures.<ref name="ReferenceA">{{cite journal|last1=Lopez-Caamal|first1=Fernando|last2=Middleton|first2=Richard H.|last3=Huber|first3=Heinrich|title=Equilibria and stability of a class of positive feedback loops|journal=Journal of Mathematical Biology|date=February 2014|pages=609–645|doi = 10.1007/s00285-013-0644-z|pmid=23358701|volume=68|issue=3}}</ref><br />
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正反馈并不一定意味着平衡的不稳定性,例如,在正反馈结构中可能存在稳定的开关状态。<ref name="ReferenceA" /><br />
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=== Hysteresis迟滞 ===<br />
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{{main|Hysteresis}}<br />
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[[File:Hysteresis sharp curve.svg|thumb|【图5 Hysteresis causes the output value to depend on the history of the input 迟滞现象会导致输出值取决于输入的历史记录。】|链接=Special:FilePath/Hysteresis_sharp_curve.svg]]<br />
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[[File:Op-Amp Schmitt Trigger.svg|thumb|【图6 In a Schmitt trigger circuit, feedback to the non-inverting input of an amplifier pushes the output directly away from the applied voltage towards the maximum or minimum voltage the amplifier can generate. 在施密特触发器电路中,利用放大器的非反相输入端口产生的反馈,可以直接将电路的输出从原本的外加电压值推向到放大器所能产生的极值电压。】|链接=Special:FilePath/Op-Amp_Schmitt_Trigger.svg]]<br />
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In the real world, positive feedback loops typically do not cause ever-increasing growth, but are modified by limiting effects of some sort. According to [[Donella Meadows]]:<br />
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在现实世界中,正反馈循环通常不会引起不断增长,而是通过某种限制效应来改变。根据Donella Meadows的说法:<br />
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"Positive feedback loops are sources of growth, explosion, erosion, and collapse in systems. A system with an unchecked positive loop ultimately will destroy itself. That’s why there are so few of them. Usually a negative loop will kick in sooner or later."<br />
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正反馈回路是系统增长、爆炸、腐蚀和崩溃的根源。一个系统如果有一个不受控制的正反馈,最终将会自我毁灭。这就是为什么正反馈如此稀少的原因。通常情况下,负反馈迟早会发生。<ref>Donella Meadows, ''[http://www.sustainabilityinstitute.org/pubs/Leverage_Points.pdf Leverage Points: Places to Intervene in a System]''2013-10-08 at the Wayback Machine, 1999</ref><br />
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Hysteresis, in which the starting point affects where the system ends up, can be generated by positive feedback. When the gain of the feedback loop is above 1, then the output moves away from the input: if it is above the input, then it moves towards the nearest positive limit, while if it is below the input then it moves towards the nearest negative limit.<br />
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[[迟滞]],即起点影响系统的终点的现象,可以通过正反馈产生。当反馈循环的增益高于1时,那么输出就会远离输入:如果大于输入,则向最近的正极限移动,而如果小于输入,则向最近的负极限移动。<br />
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Once it reaches the limit, it will be stable. However, if the input goes past the limit,{{clarify|date=June 2012}} then the feedback will change sign{{dubious|date=June 2012}} and the output will move in the opposite direction until it hits the opposite limit. The system therefore shows [[bistability|bistable]] behavior.<br />
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一旦达到极限,它就会稳定下来。但是,如果输入超过极限,那么反馈将改变符号,输出将向相反的方向移动,直到达到相反的极限。因此,该系统表现出<font color="#ff8000"> 双稳态行为bistable behavior</font>。<br />
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== Terminology 术语的由来==<br />
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The terms positive and negative were first applied to feedback before World War II. The idea of positive feedback was already current in the 1920s with the introduction of the regenerative circuit.<br />
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正反馈和负反馈这两个名词最早应用于反馈是在二战前。正反馈的概念随着再生电路的问世,在20世纪20年代已经出现。<br />
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Friis & Jensen (1924) described regeneration in a set of electronic amplifiers as a case where the "feed-back" action is positive in contrast to negative feed-back action, which they mention only in passing. Harold Stephen Black's classic 1934 paper first details the use of negative feedback in electronic amplifiers. According to Black:<br />
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Friis 和 Jensen在1924年描述了一种在电子放大器中发生的"回馈 "是正的情况,这一情况与他们顺便提到的负回馈作用相反。到了1934年,Harold Stephen Black在他的经典论文中首次详细介绍了负反馈在电子放大器中的应用。根据Black的说法:<br />
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"Positive feed-back increases the gain of the amplifier, negative feed-back reduces it."<br />
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正反馈会增加放大器的增益,负反馈会降低增益<br />
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According to Mindell (2002) confusion in the terms arose shortly after this:<br />
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据Mindell(2002年)说,术语上的混乱是在这之后不久产生的:<br />
"...Friis and Jensen had made the same distinction Black used between 'positive feed-back' and 'negative feed-back', based not on the sign of the feedback itself but rather on its effect on the amplifier’s gain. In contrast, Nyquist and Bode, when they built on Black’s work, referred to negative feedback as that with the sign reversed. Black had trouble convincing others of the utility of his invention in part because confusion existed over basic matters of definition."<br />
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“ ... ... Friis 和 Jensen 对 Black 在对"正反馈 "和 "负反馈 "的区分方法是一样的,都不是基于反馈本身的符号,而是基于它对放大器增益的影响。与之相反的是,当Nyquist和Bode基于Black的工作基础时,将负反馈称为符号相反的反馈。Black难以说服其他人相信他的发明的实用性,有一部分原因是在基本的定义问题上存在混乱。"<br />
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== Examples and applications 实例与应用==<br />
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=== In electronics 在电子领域===<br />
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[[File:Regenerartive Receiver-S7300056.JPG|thumb|right|【图7 A vintage style regenerative radio receiver. Due to the controlled use of positive feedback, sufficient amplification can be derived from a single [[vacuum tube]] or valve (centre). 一个老式的再生无线电接收器。由于使用正反馈的控制,真空管或阀门(中心)就可以产生足够的放大效果。】|链接=Special:FilePath/Regenerartive_Receiver-S7300056.JPG]]<br />
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[[Regenerative circuit]]s were invented and patented in 1914<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref> for the amplification and reception of very weak radio signals. Carefully controlled positive feedback around a single [[transistor]] amplifier can multiply its [[Gain (electronics)|gain]] by 1,000 or more.<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> Therefore, a signal can be amplified 20,000 or even 100,000 times in one stage, that would normally have a gain of only 20 to 50. The problem with regenerative amplifiers working at these very high gains is that they easily become unstable and start to oscillate. The radio operator has to be prepared to tweak the amount of feedback fairly continuously for good reception. Modern radio receivers use the [[superheterodyne]] design, with many more amplification stages, but much more stable operation and no positive feedback.<br />
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Regenerative circuits were invented and patented in 1914 for the amplification and reception of very weak radio signals. Carefully controlled positive feedback around a single transistor amplifier can multiply its gain by 1,000 or more. Therefore, a signal can be amplified 20,000 or even 100,000 times in one stage, that would normally have a gain of only 20 to 50. The problem with regenerative amplifiers working at these very high gains is that they easily become unstable and start to oscillate. The radio operator has to be prepared to tweak the amount of feedback fairly continuously for good reception. Modern radio receivers use the superheterodyne design, with many more amplification stages, but much more stable operation and no positive feedback.<br />
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<font color="#ff8000"> 再生电路Regenerative circuit</font>于1914年被发明并获得专利<ref>{{cite patent |inventor-last=Armstrong |inventor-first=E. H. |country-code=US |patent-number=1113149 |title=Wireless receiving system |date=1914}}</ref>,用于放大和接收非常微弱的无线电信号。通过仔细控制单晶体管放大器周围的正反馈,可以使其增益增加1000倍或更多<ref>{{cite web|last=Kitchin|first=Charles|title=A Short Wave Regenerative Receiver Project|url=http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|accessdate=23 September 2010|url-status=live|archiveurl=https://web.archive.org/web/20100710100031/http://www.electronics-tutorials.com/receivers/regen-radio-receiver.htm|archivedate=10 July 2010}}</ref> 。因此,一个信号可以在一个阶段被放大20000甚至100000倍,而在通常只有20到50的增益。在如此高的增益下工作带来的问题则是信号很容易变得不稳定,开始振荡。无线电操作员必须不断地调整反馈量,以获得良好的接收效果。而现代无线电接收机采用超异构设计,多了许多放大级,去掉了正反馈并使其工作更稳定。<br />
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The oscillation that can break out in a regenerative radio circuit is used in [[electronic oscillator]]s. By the use of [[tuned circuit]]s or a [[piezoelectricity|piezoelectric]] [[crystal]] (commonly [[quartz]]), the signal that is amplified by the positive feedback remains linear and [[Sine wave|sinusoidal]]. There are several designs for such [[harmonic oscillator]]s, including the [[Armstrong oscillator]], [[Hartley oscillator]], [[Colpitts oscillator]], and the [[Wien bridge oscillator]]. They all use positive feedback to create oscillations.<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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The oscillation that can break out in a regenerative radio circuit is used in electronic oscillators. By the use of tuned circuits or a piezoelectric crystal (commonly quartz), the signal that is amplified by the positive feedback remains linear and sinusoidal. There are several designs for such harmonic oscillators, including the Armstrong oscillator, Hartley oscillator, Colpitts oscillator, and the Wien bridge oscillator. They all use positive feedback to create oscillations.<br />
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在再生无线电电路中产生的振荡还可以被用于电子振荡器中。通过使用调谐电路或压电晶体(常见的是石英),经正反馈放大后的信号仍然是线性的、正弦的。这种谐波振荡器有几种设计,包括阿姆斯特朗振荡器、哈特利振荡器、科尔皮茨振荡器和维恩桥振荡器。它们都是利用正反馈来产生振荡。<ref>{{cite web|title=Sinewave oscillators|url=http://www.educypedia.be/electronics/analogosciltypes.htm|work=EDUCYPEDIA - electronics|accessdate=23 September 2010|url-status=dead|archiveurl=https://web.archive.org/web/20100927094330/http://www.educypedia.be/electronics/analogosciltypes.htm|archivedate=27 September 2010}}</ref><br />
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Many electronic circuits, especially amplifiers, incorporate negative feedback. This reduces their gain, but improves their linearity, input impedance, output impedance, and bandwidth, and stabilises all of these parameters, including the closed-loop gain. These parameters also become less dependent on the details of the amplifying device itself, and more dependent on the feedback components, which are less likely to vary with manufacturing tolerance, age and temperature. The difference between positive and negative feedback for AC signals is one of phase: if the signal is fed back out of phase, the feedback is negative and if it is in phase the feedback is positive. One problem for amplifier designers who use negative feedback is that some of the components of the circuit will introduce phase shift in the feedback path. If there is a frequency (usually a high frequency) where the phase shift reaches 180°, then the designer must ensure that the amplifier gain at that frequency is very low (usually by low-pass filtering). If the loop gain (the product of the amplifier gain and the extent of the positive feedback) at any frequency is greater than one, then the amplifier will oscillate at that frequency (Barkhausen stability criterion). Such oscillations are sometimes called parasitic oscillations. An amplifier that is stable in one set of conditions can break into parasitic oscillation in another. This may be due to changes in temperature, supply voltage, adjustment of front-panel controls, or even the proximity of a person or other conductive item.<br />
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许多电子电路,特别是放大器,都采用了负反馈。这降低了放大器的信号增益,但改善了它的线性度、输入阻抗、输出阻抗和带宽,并稳定了包括闭环增益等参数。同时,这些参数也变得不那么依赖于放大器件本身的细节,而更多地依赖于反馈元件,因为反馈元件一般不随着制造公差、使用年限和温度而变化。交流信号的正反馈和负反馈的区别在于相位:如果信号反馈失相,则反馈为负,如果相位一致,则反馈为正。对于需要使用负反馈放大器的设计者来说,引入负反馈放大器的问题是,电路中的一些元件会在反馈路径中引入相移。如果有一个频率(通常是高频)的相移达到180°,那么设计者必须确保该频率的放大器增益非常低(通常通过低通滤波来做到这一点)。如果任何频率下的环增益(放大器增益与正反馈程度的乘积)大于1,那么放大器将在该频率下发生振荡(巴克豪森稳定性准则)。这种振荡有时被称为寄生振荡:在一组条件下稳定的放大器在另一组条件下可能会发生寄生振荡。这可能是由于温度、电源电压的变化,前板(用户界面)的变化,甚至是由于人或其他导电物品的接近。<br />
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Amplifiers may oscillate gently in ways that are hard to detect without an oscilloscope, or the oscillations may be so extensive that only a very distorted or no required signal at all gets through, or that damage occurs. Low frequency parasitic oscillations have been called 'motorboating' due to the similarity to the sound of a low-revving exhaust note.<br />
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放大器可能会以示波器很难检测到的方式轻轻振荡,有时的振荡也可能非常大,只有非常扭曲或根本没有真正的信号,甚至振荡也会引起损坏发生。由于低频寄生振荡与低转速排气音符的声音相似,因此低频寄生振荡也被称为 "汽艇"。<br />
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【图8 The effect of using a Schmitt trigger (B) instead of a comparator (A) 使用施密特触发器(b)代替比较器(a)的效果】<br />
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Many common digital electronic circuits employ positive feedback. While normal simple boolean logic gates usually rely simply on gain to push digital signal voltages away from intermediate values to the values that are meant to represent boolean '0' and '1', but many more complex gates use feedback. When an input voltage is expected to vary in an analogue way, but sharp thresholds are required for later digital processing, the Schmitt trigger circuit uses positive feedback to ensure that if the input voltage creeps gently above the threshold, the output is forced smartly and rapidly from one logic state to the other. One of the corollaries of the Schmitt trigger's use of positive feedback is that, should the input voltage move gently down again past the same threshold, the positive feedback will hold the output in the same state with no change. This effect is called hysteresis: the input voltage has to drop past a different, lower threshold to 'un-latch' the output and reset it to its original digital value. By reducing the extent of the positive feedback, the hysteresis-width can be reduced, but it can not entirely be eradicated. The Schmitt trigger is, to some extent, a latching circuit.<br />
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许多常见的数字电路都采用正反馈。一般简单的布尔逻辑门通常只是依靠增益将数字信号电压从中间值推到代表布尔值0和1的值上,但许多更复杂的门都采用了反馈。当输入的模拟电压发生变化,但后期数字处理需要尖锐阈值时,施密特触发电路通过正反馈机制确保当输入电压轻微超过阈值时,输出电压可以巧妙而迅速地从一个逻辑状态转移到另一个逻辑状态。施密特触发器使用正反馈的一个必然结果是,如果输入电压再次缓慢下降,超过了相同的阈值,由于正反馈的机制,输出电压将保持在相同的逻辑状态而不改变。这种效应被称为滞后: 输入电压必须降到一个不同的、较低的阈值,才能“解锁”输出,并将其重置为原始数字。通过减小正反馈的程度,可以减小滞后宽度,但宽度不能被完全消除。施密特触发器在某种程度上是一个闭锁电路。<br />
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【图9 Positive feedback is a mechanism by which an output is enhanced, such as protein levels. However, in order to avoid any fluctuation in the protein level, the mechanism is inhibited stochastically (I), therefore when the concentration of the activated protein (A) is past the threshold ([I]), the loop mechanism is activated and the concentration of A increases exponentially if d[A]=k [A] 正反馈是一种增强输出的机制,如蛋白质水平。但为了避免蛋白质水平的波动,该机制是随机抑制的(I),因此只有当激活的蛋白质(A)浓度超过阈值([I])时,循环机制被激活,如果d[A]=k[A],A的浓度就会成倍增加。】<br />
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【图10 Illustration of an R-S ('reset-set') flip-flop made from two digital nor gates with positive feedback. Red and black mean logical '1' and '0', respectively. R-S("复位-设置")触发器的说明,由两个带正反馈的数字诺尔门组成。红色和黑色分别表示逻辑上的 "1 "和 "0"。】<br />
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An electronic flip-flop, or "latch", or "bistable multivibrator", is a circuit that due to high positive feedback is not stable in a balanced or intermediate state. Such a bistable circuit is the basis of one bit of electronic memory. The flip-flop uses a pair of amplifiers, transistors, or logic gates connected to each other so that positive feedback maintains the state of the circuit in one of two unbalanced stable states after the input signal has been removed, until a suitable alternative signal is applied to change the state. Computer random access memory (RAM) can be made in this way, with one latching circuit for each bit of memory.<br />
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电子触发器,或“锁存器” ,或“双稳态多谐振荡器” ,是一种由于高正反馈而不稳定于平衡或中间状态的电路。这样的双稳态电路是一位电子存储器的基础。 触发器使用一对放大器、晶体管或逻辑门相互连接,正反馈机制使得输入信号被去除后,电路可以维持在两种非平衡稳定状态中的一种,直到一个合适的替代信号重新作为输入,以改变电路状态。计算机随机存取存储器(RAM)可以用这种方式运作,每位存储器有一个锁存电路。<br />
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Thermal runaway occurs in electronic systems because some aspect of a circuit is allowed to pass more current when it gets hotter, then the hotter it gets, the more current it passes, which heats it some more and so it passes yet more current. The effects are usually catastrophic for the device in question. If devices have to be used near to their maximum power-handling capacity, and thermal runaway is possible or likely under certain conditions, improvements can usually be achieved by careful design.<br />
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电子系统中发生<font color="#ff8000"> 热失控Thermal runaway</font>的原因是,当电路的某些方面变得更热时,它被允许通过更多的电流,然后它越热,通过的电流就越多,这就使它更热一些,因此它又通过更多的电流。这种现象对有关器件来说通常是灾难性的。如果器件不得不在接近其最大功率处理能力的情况下工作,那么某些条件下就可能出现热失控,这通常可以通过精心设计来改进。<br />
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[[File:Technics SL-1210MK2.jpg|thumb|left|【图11 A phonograph turntable is prone to acoustic feedback. 留声机转盘容易受到声反馈的影响。】|链接=Special:FilePath/Technics_SL-1210MK2.jpg]]<br />
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Audio and video systems can demonstrate positive feedback. If a microphone picks up the amplified sound output of loudspeakers in the same circuit, then howling and screeching sounds of audio feedback (at up to the maximum power capacity of the amplifier) will be heard, as random noise is re-amplified by positive feedback and filtered by the characteristics of the audio system and the room.<br />
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音频和视频系统可以表现出正反馈。如果麦克风录入了同一电路中扬声器的放大声音输出,那么就会听到音频反馈的嚎叫和尖叫声(在放大器的最大功率容量下),因为随机噪声被音频系统和房间的特性所过滤后,通过正反馈重新放大。<br />
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===Audio and live music音频和现场音乐===<br />
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Audio feedback (also known as acoustic feedback, simply as feedback, or the Larsen effect) is a special kind of positive feedback which occurs when a sound loop exists between an audio input (for example, a microphone or guitar pickup) and an audio output (for example, a loudly-amplified loudspeaker). In this example, a signal received by the microphone is amplified and passed out of the loudspeaker. The sound from the loudspeaker can then be received by the microphone again, amplified further, and then passed out through the loudspeaker again. The frequency of the resulting sound is determined by resonance frequencies in the microphone, amplifier, and loudspeaker, the acoustics of the room, the directional pick-up and emission patterns of the microphone and loudspeaker, and the distance between them. For small PA systems the sound is readily recognized as a loud squeal or screech.<br />
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音频反馈(也称为声反馈,简称反馈,或拉森效应)是一种特殊的正反馈,当音频输入(例如,麦克风或吉他拾音器)和音频输出(例如,大声放大的扬声器)之间存在声音回路时,就会出现这种反馈。在这个例子中,麦克风接收到的信号被放大并从扬声器传出。然后,来自扬声器的声音可以再次被麦克风接收,进一步放大,然后再次通过扬声器传递出去。 所产生的声音的频率由传声器、放大器和扬声器的共振频率、房间的声学特性、传声器和扬声器的定向拾音和发射模式以及它们之间的距离决定。对于小型的扩声系统来说,这种声音很容易的体现的响亮的吱吱声或尖叫声。<br />
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Feedback is almost always considered undesirable when it occurs with a singer's or public speaker's microphone at an event using a sound reinforcement system or PA system. Audio engineers use various electronic devices, such as equalizers and, since the 1990s, automatic feedback detection devices to prevent these unwanted squeals or screeching sounds, which detract from the audience's enjoyment of the event. On the other hand, since the 1960s, electric guitar players in rock music bands using loud guitar amplifiers and distortion effects have intentionally created guitar feedback to create a desirable musical effect. "I Feel Fine" by the Beatles marks one of the earliest examples of the use of feedback as a recording effect in popular music. It starts with a single, percussive feedback note produced by plucking the A string on Lennon's guitar. Artists such as the Kinks and the Who had already used feedback live, but Lennon remained proud of the fact that the Beatles were perhaps the first group to deliberately put it on vinyl. In one of his last interviews, he said, "I defy anybody to find a record—unless it's some old blues record in 1922—that uses feedback that way."<br />
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在歌手或公众演讲者使用扩声系统或扩音系统的活动中,麦克风发生的正反馈几乎总是被认为是不受欢迎的。自20世纪90年代以来,音频工程师使用各种电子设备,如均衡器或者自动反馈检测设备,来防止这些不受欢迎的尖叫声或尖叫声,这些声音影响了观众对活动的享受。另一方面,自20世纪60年代以来,摇滚乐队中的电吉他手使用大音量的吉他放大器和失真效果,有意制造吉他中的正反馈,以创造理想的音乐效果。 披头士乐队的 "I Feel Fine "是流行音乐中最早使用反馈作为录音效果的例子之一。它的开头是由Lennon拨动吉他上的A弦产生的一个单一的、有冲击力的反馈音。虽然像 Kinks 和 Who 等艺术家已经在表演中使用了正反馈,但是Lennon仍然为披头士乐队可能是第一个特意把它放在黑胶唱片上的乐队而感到骄傲。在他最后的一次采访中,他说,“我敢说任何人都找不到这样的唱片,除非是1922年这张用这种方式录制的老蓝调唱片。”<br />
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The principles of audio feedback were first discovered by Danish scientist Søren Absalon Larsen. Microphones are not the only transducers subject to this effect. Record deck pickup cartridges can do the same, usually in the low frequency range below about 100&nbsp;Hz, manifesting as a low rumble. Jimi Hendrix was an innovator in the intentional use of guitar feedback in his guitar solos to create unique sound effects. He helped develop the controlled and musical use of audio feedback in electric guitar playing, and later Brian May was a famous proponent of the technique.<br />
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音频反馈的原理是由丹麦科学家Søren Absalon Larsen首先发现的。麦克风并不是唯一受此影响的传感器。录音板拾音器也会产生正反馈,通常是在100赫兹以下的低频范围内表现出低沉的轰鸣声。Jimi Hendrix是一个创新者,在他的吉他独奏中有意使用吉他正反馈来创造独特的声音效果。他帮助发展了电吉他演奏中音频反馈的可控性和音乐性,后来Brian May也是这种技术的著名支持者。<br />
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[[File:Adam Savage HOPE.jpg|thumb|right|220px|[[Video feedback]]【图12 视频反馈】.|链接=Special:FilePath/Adam_Savage_HOPE.jpg]]<br />
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===Video视频===<br />
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Similarly, if a [[video camera]] is pointed at a [[Video monitor|monitor]] screen that is displaying the camera's own signal, then repeating patterns can be formed on the screen by positive feedback. This video feedback effect was used in the opening sequences to the [[Doctor Who (season 1)|first]] [[Doctor Who (season 10)|ten]] series of the television program ''[[Doctor Who]]''.<br />
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Similarly, if a video camera is pointed at a monitor screen that is displaying the camera's own signal, then repeating patterns can be formed on the screen by positive feedback. This video feedback effect was used in the opening sequences to the first ten series of the television program Doctor Who.<br />
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同样,如果一台摄像机对准一个正在显示摄像机自身信号的监控屏幕,那么通过正反馈就可以在屏幕上形成重复的图案。这种视频反馈效果在电视剧《神秘博士》前十季的开场白中就被使用了。<br />
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=== Switches 开关===<br />
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In [[electrical switch]]es, including [[bimetallic strip]] based thermostats, the switch usually has hysteresis in the switching action. In these cases hysteresis is mechanically achieved via positive feedback within a tipping point mechanism. The positive feedback action minimises the length of time arcing occurs for during the switching and also holds the contacts in an open or closed state.<br />
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在电气开关中,包括双金属条型恒温器,开关通常在开关动作中具有滞后性。在这些情况下,滞后是通过一个临界点机构内的正反馈来实现的。正反馈作用可最大限度地减少开关过程中发生电弧的时间,并使触点保持在断开或闭合状态。<br />
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=== In biology在生物学中===<br />
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[[File:Positive Feedback- Childbirth (1).svg|thumb|Positive feedback is the amplification of a body's response to a stimulus. For example, in childbirth, when the head of the fetus pushes up against the cervix (1) it stimulates a nerve impulse from the cervix to the brain (2). When the brain is notified, it signals the pituitary gland to release a hormone called [[oxytocin]](3). Oxytocin is then carried via the bloodstream to the [[uterus]] (4) causing contractions, pushing the fetus towards the cervix eventually inducing childbirth.生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做<font color="#ff8000"> 催产素oxytocin</font>的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。|链接=Special:FilePath/Positive_Feedback-_Childbirth_(1).svg]]<br />
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Positive feedback is the amplification of a body's response to a stimulus. For example, in childbirth, when the head of the fetus pushes up against the cervix (1) it stimulates a nerve impulse from the cervix to the brain (2). When the brain is notified, it signals the pituitary gland to release a hormone called oxytocin(3). Oxytocin is then carried via the bloodstream to the uterus(4) causing contractions, pushing the fetus towards the cervix eventually inducing childbirth.<br />
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生物学中的正反馈是指身体对刺激的反应的放大。例如,在分娩过程中,当胎儿的头顶到子宫颈时(1),会刺激神经冲动从子宫颈到大脑(2)。大脑接到通知后,会向脑垂体发出信号,释放一种叫做<font color="#ff8000"> 催产素oxytocin</font>的激素(3)。催产素随后通过血液流向子宫(4),引起宫缩,将胎儿推向子宫颈,最终促使分娩。<br />
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==== In physiology在生理学中 ====<br />
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A number of examples of positive feedback systems may be found in [[physiology]].<br />
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在生理学中可以找到一些正反馈系统的例子。<br />
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* One example is the onset of [[Contraction (childbirth)|contractions]] in [[childbirth]], known as the [[Ferguson reflex]]. When a contraction occurs, the hormone [[oxytocin]] causes a nerve stimulus, which stimulates the [[hypothalamus]] to produce more oxytocin, which increases uterine contractions. This results in contractions increasing in [[amplitude]] and [[frequency]].<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders. {{ISBN|0-7216-3994-1}}</ref>{{rp|pages=924–925}}<br />
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其中一个例子是分娩时宫缩的发生,称为弗格森反射。当宫缩发生时,激素催产素会引起神经刺激,刺激下丘脑产生更多的催产素,从而增加子宫收缩。这就导致宫缩的幅度和频率增加。<br />
<ref name=Guyton1991>Guyton, Arthur C. (1991) ''Textbook of Medical Physiology''. (8th ed). Philadelphia: W.B. Saunders. {{ISBN|0-7216-3994-1}}</ref>{{rp|pages=924–925}}<br />
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* Another example is the process of [[Coagulation|blood clotting]]. The loop is initiated when injured tissue releases signal chemicals that activate platelets in the blood. An activated platelet releases chemicals to activate more platelets, causing a rapid cascade and the formation of a blood clot.<ref name=Guyton1991/>{{rp|pages=392–394}}<br />
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另一个例子是血液凝固的过程。当受伤的组织释放出信号化学物质,激活血液中的血小板时,这个循环就启动了。被激活的血小板释放化学物质,激活更多的血小板,引起快速的级联反应,形成血栓。<br />
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* [[Lactation]] also involves positive feedback in that as the baby suckles on the nipple there is a nerve response into the spinal cord and up into the hypothalamus of the brain, which then stimulates the [[pituitary]] gland to produce more [[prolactin]] to produce more milk.<ref name=Guyton1991/>{{rp|page=926}}<br />
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哺乳也涉及正反馈,当婴儿吸吮乳头时,会有神经反应进入脊髓,并上传到大脑的下丘脑,然后刺激垂体产生更多的催乳素以产生更多的乳汁。<br />
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* A spike in [[estrogen]] during the [[follicular phase]] of the menstrual cycle causes [[ovulation]].<ref name=Guyton1991/>{{rp|page=907}}<br />
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在月经周期的卵泡期期间,雌激素的飙升会导致排卵。<br />
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* The generation of [[nerve signal]]s is another example, in which the membrane of a nerve fibre causes slight leakage of sodium ions through sodium channels, resulting in a change in the membrane potential, which in turn causes more opening of channels, and so on ([[Hodgkin cycle]]). So a slight initial leakage results in an explosion of sodium leakage which creates the nerve [[action potential]].<ref name=Guyton1991/>{{rp|page=59}}<br />
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神经信号的产生是另一个例子,神经纤维的膜使钠离子通过钠通道轻微渗漏,导致膜电位的变化,进而引起更多通道的开放(Hodgkin循环)。所以,最初的轻微渗漏会导致钠渗漏的爆发,从而产生神经动作电位。<br />
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* In [[excitation–contraction coupling]] of the heart, an increase in intracellular calcium ions to the cardiac myocyte is detected by ryanodine receptors in the membrane of the sarcoplasmic reticulum which transport calcium out into the cytosol in a positive feedback physiological response.<br />
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在心脏的兴奋收缩耦合中,肌浆网膜中的兰尼碱受体检测到心肌细胞内钙离子的增加,该受体以正反馈生理反应将钙运出到细胞质中。<br />
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In most cases, such feedback loops culminate in counter-signals being released that suppress or break the loop. Childbirth contractions stop when the baby is out of the mother's body. Chemicals break down the blood clot. Lactation stops when the baby no longer nurses.<ref name=Guyton1991/><br />
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在大多数情况下,这种反馈循环最终会释放出反信号,从而抑制或破坏循环。分娩宫缩在宝宝离开母体时停止。化学物质分解血凝块。当婴儿不再需要被哺乳时,泌乳停止。<br />
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==== In gene regulation 基因调控====<br />
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Positive feedback is a well studied phenomenon in gene regulation, where it is most often associated with [[bistability]]. Positive feedback occurs when a gene activates itself directly or indirectly via a double negative feedback loop. Genetic engineers have constructed and tested simple positive feedback networks in bacteria to demonstrate the concept of bistability.<ref name=Hasty2002/> A classic example of positive feedback is the [[lac operon]] in ''E. coli''. Positive feedback plays an integral role in cellular differentiation, development, and cancer progression, and therefore, positive feedback in gene regulation can have significant physiological consequences. Random motions in [[molecular dynamics]] coupled with positive feedback can trigger interesting effects, such as create population of phenotypically different cells from the same parent cell.<ref name=Veening2008/> This happens because noise can become amplified by positive feedback. Positive feedback can also occur in other forms of [[cell signaling]], such as enzyme kinetics or metabolic pathways.<ref name=Christoph2001/><br />
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正反馈是基因调控中研究较好的一种现象,其中最常见的是与双稳态有关。当一个基因通过双负反馈循环直接或间接激活自身时,就会出现正反馈。遗传工程师已经在细菌中构建并测试了简单的正反馈网络,以证明双稳态的概念。<ref name=Hasty2002/><br />
正反馈的一个典型例子是大肠杆菌中的乳糖操纵子。正反馈在细胞分化、发育和癌症进展中起着不可或缺的作用,因此,基因调控中的正反馈可以产生显著的生理结果。分子动力学中的随机运动加上正反馈可以引发有趣的效应,例如从同一母细胞中产生表型不同的细胞群。<ref name=Veening2008/> 这种情况的发生是因为噪声会被正反馈放大。正反馈也可以发生在细胞信号的其他形式中,如酶动力学或代谢途径。<ref name=Christoph2001/><br />
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==== In evolutionary biology在进化生物学中 ====<br />
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Positive feedback loops have been used to describe aspects of the dynamics of change in biological [[evolution]]. For example, beginning at the macro level, [[Alfred J. Lotka]] (1945) argued that the evolution of the species was most essentially a matter of selection that fed back energy flows to capture more and more energy for use by living systems.<ref name=Lotka1945/> At the human level, [[Richard D. Alexander]] (1989) proposed that social competition between and within human groups fed back to the selection of intelligence thus constantly producing more and more refined human intelligence. <ref name=Alexander1989/> [[Bernard Crespi|Crespi]] (2004) discussed several other examples of positive feedback loops in evolution.<ref name=Crespi2004/> The analogy of [[Evolutionary arms race]]s provide further examples of positive feedback in biological systems.<ref name=Blindwatchmaker/><br />
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在进化生物学中正反馈循环被用来描述生物进化中变化动态的各个方面。 例如,在宏观层面,Alfred J. Lotka(1945)认为,物种的演变最重要的是选择反馈能量流动以捕获越来越多的能源系统的能量。<ref name=Lotka1945/>在人类层面,Richard D. Alexander(1989)提出,人类群体之间和群体内部的社会竞争会影响智力的选择,从而时不时地会产生更多、更完善的人类智力。 <ref name=Alexander1989/> Bernard Crespi(2004)讨论了进化中正反馈循环的其他几个例子。通过与军备竞赛进行类比,给生物系统中的正反馈提供了进一步的例子。<ref name=Blindwatchmaker/><br />
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[[File:Phanerozoic Biodiversity.svg|300px|right|thumb|During the Phanerozoic the [[biodiversity]] shows a steady but not monotonic increase from near zero to several thousands of genera.显生宙[[生物多样性]]呈现稳定而非单调的增长,从接近于零一直增长到有几千个属。|链接=Special:FilePath/Phanerozoic_Biodiversity.svg]]<br />
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It has been shown that changes in [[biodiversity]] through the [[Phanerozoic]] correlate much better with hyperbolic model (widely used in [[demography]] and [[macrosociology]]) than with [[Exponential growth|exponential]] and [[Logistic function|logistic]] models (traditionally used in [[population biology]] and extensively applied to [[fossil]] [[biodiversity]] as well). The latter models imply that changes in diversity are guided by a first-order positive feedback (more ancestors, more descendants) and/or a [[negative feedback]] arising from resource limitation. Hyperbolic model implies a second-order positive feedback. The hyperbolic pattern of the [[world population growth]] has been demonstrated (see below) to arise from a second-order positive feedback between the population size and the rate of [[technological growth]]. The hyperbolic character of biodiversity growth can be similarly accounted for by a positive feedback between the diversity and community structure complexity. It has been suggested that the similarity between the curves of [[biodiversity]] and human population probably comes from the fact that both are derived from the interference of the hyperbolic trend (produced by the positive feedback) with cyclical and stochastic dynamics.<ref>Markov A., [[Andrey Korotayev|Korotayev A.]] [https://archive.today/20120630063924/http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B83WC-4N0HJMK-2&_user=10&_rdoc=1&_fmt=&_orig=search&_sort=d&_docanchor=&view=c&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=74a80d7c55ff987c9fc8d9c7963feab9 "Phanerozoic marine biodiversity follows a hyperbolic trend." [[Palaeoworld]]. Volume 16, Issue 4, December 2007, Pages 311-318]</ref><ref>{{cite journal | last1 = Markov | first1 = A. | last2 = Korotayev | first2 = A. | year = 2008 | title = Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution | url = http://elementy.ru/genbio/abstracts?artid=177 | journal = Journal of General Biology | volume = 69 | issue = 3 | pages = 175–194 | pmid = 18677962 | url-status = live | archiveurl = https://web.archive.org/web/20091225000305/http://elementy.ru/genbio/abstracts?artid=177 | archivedate = 2009-12-25 }}</ref><br />
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研究表明,在<font color="#32CD32"> 显生宙 </font>,生物多样性的变化与双曲模型(广泛用于人口学和宏观社会学)的相关性要比指数模型和逻辑斯特模型(传统上用于人口生物学,并广泛用于生物多样性化石)的相关性好得多。后者的模型意味着多样性的变化是由一阶正反馈(更多的祖先,更多的后代)和资源限制产生的负反馈所引导的。双曲模型意味着二阶正反馈。世界人口增长的双曲线模式已被证明源于人口数量与技术增长速度之间的二阶正反馈。生物多样性增长的双曲特征同样可以由多样性与群落结构复杂性之间的正反馈来解释。有人认为,生物多样性和人口曲线之间的相似性可能来自这样一个事实,即两者都是由双曲趋势(由正反馈产生)与周期性和随机性的动态干扰而产生的。<br />
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==== Immune system 免疫系统====<br />
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A [[cytokine storm]], or '''hypercytokinemia''' is a potentially fatal immune reaction consisting of a positive feedback loop between [[cytokine]]s and [[immune cell]]s, with highly elevated levels of various cytokines.<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref> In normal immune function, positive feedback loops can be utilized to enhance the action of B lymphocytes. When a B cell binds its antibodies to an antigen and becomes activated, it begins releasing antibodies and secreting a complement protein called C3. Both C3 and a B cell's antibodies can bind to a pathogen, and when a B cell has its antibodies bind to a pathogen with C3, it speeds up that B cell's secretion of more antibodies and more C3, thus creating a positive feedback loop.<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
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细胞因子风暴,或称高细胞因子血症,是一种潜在的致命性免疫反应,表现为各种细胞因子水平高度升高,这是由细胞因子和免疫细胞之间的正反馈环组成。[36]在正常的免疫功能中,可以利用正反馈环来增强B淋巴细胞的作用。<ref name="osterholm">{{cite journal | last = Osterholm | first = Michael T. | author-link = Michael Osterholm |title = Preparing for the Next Pandemic | journal = The New England Journal of Medicine | volume = 352 | issue = 18 | pages = 1839–1842 | date = 2005-05-05 | url = | doi = 10.1056/NEJMp058068 | pmid = 15872196 | citeseerx = 10.1.1.608.6200 }}</ref>当B细胞将其抗体与抗原结合并被激活后,就开始释放抗体并分泌一种称为C3的补体蛋白。C3和B细胞的抗体都可以与病原体结合,当B细胞的抗体与C3结合后,就会加快该B细胞分泌更多的抗体和更多的C3蛋白,从而形成一个正反馈循环。<ref>{{cite journal|last=Paul|first=William E.|title=Infectious Diseases and the Immune System|journal=Scientific American|volume=269|issue=3|date=September 1993|page=93|bibcode=1993SciAm.269c..90P|doi=10.1038/scientificamerican0993-90|pmid=8211095}}</ref><br />
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==== Cell death 细胞凋亡====<br />
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[[Apoptosis]] is a [[caspase]]-mediated process of cellular death, whose aim is the removal of long-lived or damaged cells. A failure of this process has been implicated in prominent conditions such as [[cancer]] or [[Parkinson's disease]]. The very core of the apoptotic process is the auto-activation of caspases, which may be modeled via a positive-feedback loop. This positive feedback exerts an auto-activation of the [[effector caspase]] by means of intermediate caspases. When isolated from the rest of apoptotic pathway, this positive-feedback presents only one stable steady state, regardless of the number of intermediate activation steps of the effector caspase.<ref name="ReferenceA"/> When this core process is complemented with inhibitors and enhancers of caspases effects, this process presents bistability, thereby modeling the alive and dying states of a cell.<ref>{{cite journal|last=Eissing|first=Thomas |doi=10.1074/jbc.M404893200 |title=Bistability analyses of a caspase activation model for receptor-induced apoptosis|journal=Journal of Biological Chemistry|volume=279 |issue=35 |date=2014|pages=36892–36897|pmid=15208304 |doi-access=free}}</ref><br />
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细胞凋亡是一种由酪蛋白酶介导的细胞死亡过程,其目的是清除长寿或受损的细胞。这一过程的失效与癌症或帕金森氏病等著名疾病有关。细胞凋亡过程的核心是半胱氨酸蛋白酶的自动激活,它可以通过一个正反馈循环来建模。这种正反馈通过中间胱天蛋白酶使效应子胱天蛋白酶自动活化。当从凋亡途径的其他部分分离出来时,无论效应子胱天蛋白酶的中间激活步骤数量有多少,这种正反馈仅呈现一种稳定的稳态。<ref name="ReferenceA"/> 当该核心过程与胱天蛋白酶作用的抑制剂和增强剂相辅相成时,该过程呈现双稳态,从而模拟细胞的存活和死亡状态。<br />
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=== In psychology 在心理学上===<br />
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Winner (1996) described gifted children as driven by positive feedback loops involving setting their own learning course, this feeding back satisfaction, thus further setting their learning goals to higher levels and so on.<ref name=Winner1996/> Winner termed this positive feedback loop as a "rage to master." Vandervert (2009a, 2009b) proposed that the [[child prodigy]] can be explained in terms of a positive feedback loop between the output of thinking/performing in [[working memory]], which then is fed to the [[cerebellum]] where it is streamlined, and then fed back to working memory thus steadily increasing the quantitative and qualitative output of working memory.<ref name=Vandervert2009a/><ref name=Vandervert2009b/> Vandervert also argued that this working memory/cerebellar positive feedback loop was responsible for [[language]] evolution in working memory.<br />
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Winner(1996)将有天赋的孩子描述为受到正反馈循环的驱动,这些反馈循环体现在他们自己的课程学习上,通过反馈自己的满意程度,从而进一步将他们的学习目标提高到更高水平等。<ref name=Winner1996/>Winner将这种正反馈循环称为 "狂热的掌握"。 Vandervert(2009a,2009b)提出,神童可以用工作记忆中的思维/表现输出之间的正反馈回路来解释,工作记忆中的思维/表现输出被反馈到小脑,在那里被精简,然后再反馈到工作记忆中,从而稳定地增加工作记忆的数量和质量输出。<ref name=Vandervert2009a/><ref name=Vandervert2009b/> <br />
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=== In economics在经济学中 ===<br />
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====Markets with social influence 具有社会影响力的市场====<br />
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Product recommendations and information about past purchases have been shown to influence consumers choices significantly whether it is for music, movie, book, technological, and other type of products. Social influence often induces a rich-get-richer phenomenon ([[Matthew effect]]) where popular products tend to become even more popular.<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
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事实证明,产品推荐和消费者先前的购买信息对消费者的选择影响很大,无论是音乐、电影、书籍、电子产品还是其他类型的产品。社会影响往往会诱发一种 "富者越富 "的现象(马太效应),即热门产品往往会变得更加受欢迎。<ref name="altszyler2017">{{cite journal | title= Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality. | author1= Altszyler, E | author2= Berbeglia, F. | author3= Berbeglia, G. | author4= Van Hentenryck, P. | journal= PLOS ONE | year= 2017 | volume= 12 | issue= 7 | df= | doi=10.1371/journal.pone.0180040 |pmid = 28746334| pmc= 5528888 | page=e0180040| bibcode= 2017PLoSO..1280040A }}</ref><br />
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====Market dynamics市场动态====<br />
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According to the theory of [[reflexivity (social theory)|reflexivity]] advanced by [[George Soros]], price changes are driven by a positive feedback process whereby investors' expectations are influenced by price movements so their behaviour acts to reinforce movement in that direction until it becomes unsustainable, whereupon the feedback drives prices in the opposite direction.<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
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根据George Soros提出的反射性理论,价格变化是由一个正反馈过程驱动的,即投资者的预期受到价格变动的影响,因此他们的行为会强化这个方向的价格变动,直到价格的变化变得不可持续,于是反馈推动价格向相反的方向发展。<ref>{{citation |title=Behavioural Technical Analysis |first=Paul V. |last=Azzopardi |publisher=Harriman House Limited |year=2010 |page=116 |isbn=9780857190680 |url=https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116 |url-status=live |archiveurl=https://web.archive.org/web/20170329103058/https://books.google.com/books?id=04Ay8qviuwgC&pg=PA116&lpg=PA116&source=bl&hl=en&sa=X&f=false |archivedate=2017-03-29 }}</ref><br />
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==== Systemic risk 系统性风险====<br />
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Systemic risk is the risk that an amplification or leverage or positive feedback process presents to a system. This is usually unknown, and under certain conditions this process can amplify exponentially and rapidly lead to destructive or chaotic behavior. A Ponzi scheme is a good example of a positive-feedback system: funds from new investors are used to pay out unusually high returns, which in turn attract more new investors, causing rapid growth toward collapse. W. Brian Arthur has also studied and written on positive feedback in the economy (e.g. W. Brian Arthur, 1990). Hyman Minsky proposed a theory that certain credit expansion practices could make a market economy into "a deviation amplifying system" that could suddenly collapse, sometimes called a "Minsky moment".<br />
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系统性风险是指放大效应或杠杆或正反馈过程给系统带来的风险。这通常是未知的,在某些条件下,这个过程会成倍放大,并迅速导致破坏性或混乱的行为。 庞氏骗局就是正反馈系统的一个很好的例子:来自新投资者的资金被用来支付异常高的回报,反过来又吸引了更多的新投资者,导致快速增长进而走向崩溃。W. Brian Arthur 也对经济中的正反馈进行了研究和著述(如W. Brian Arthur,1990)。Hyman Minsky提出了一个理论,认为某些信用扩张行为会使市场经济变成一个 "偏差放大系统",从而可能会突然崩溃,这有时被称为 "明斯基时刻"。<br />
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Simple systems that clearly separate the inputs from the outputs are not prone to systemic risk. This risk is more likely as the complexity of the system increases, because it becomes more difficult to see or analyze all the possible combinations of variables in the system even under careful stress testing conditions. The more efficient a complex system is, the more likely it is to be prone to systemic risks, because it takes only a small amount of deviation to disrupt the system. Therefore, well-designed complex systems generally have built-in features to avoid this condition, such as a small amount of friction, or resistance, or inertia, or time delay to decouple the outputs from the inputs within the system. These factors amount to an inefficiency, but they are necessary to avoid instabilities.<br />
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输入和输出明确分开的简单系统不容易发生系统性风险。 随着系统复杂性的增加,这种风险更容易发生,因为即使在详细的压力测试条件下,也更难看到或分析系统中所有可能的变量组合。 一个复杂系统的效率越高,就越容易发生系统性风险,因为只需要很小的偏差就可以破坏系统。 因此,设计良好的复杂系统一般都会有一些内在的功能来避免这种情况的发生,比如在系统内有少量的摩擦力,或阻力,或惯性,或时间延迟来使输出与输入脱钩。这些因素造成了低效率,但它们是避免不稳定的必要条件。<br />
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The 2010 Flash Crash incident was blamed on the practice of high-frequency trading (HFT), although whether HFT really increases systemic risk remains controversial.<br />
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2010年的闪崩事件被归咎于高频交易(HFT)的做法,不过HFT是否真的会增加系统性风险仍然存在争议。<br />
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|title= Human Population and the Environmental Crisis<br />
人口与环境危机<br />
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Agriculture and human population can be considered to be in a positive feedback mode, which means that one drives the other with increasing intensity. It is suggested that this positive feedback system will end sometime with a catastrophe, as modern agriculture is using up all of the easily available phosphate and is resorting to highly efficient monocultures which are more susceptible to systemic risk.<br />
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可以认为农业和人口处于一种正反馈模式,这意味着双方越来越强烈地推动彼此。有人认为,这种正反馈系统终将在某一时刻以灾难结束,因为现代农业正在耗尽所有容易获得的磷酸盐,并且进行高效的单一栽培,使得现代农业更容易受到系统性风险影响。<br />
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Technological innovation and human population can be similarly considered, and this has been offered as an explanation for the apparent hyperbolic growth of the human population in the past, instead of a simpler exponential growth.<br />
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技术创新和人类人口也可以有类似的考虑,这也是过去人类人口明显的双曲线增长,而不是简单的指数增长的一个解释。<br />
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It is proposed that the growth rate is accelerating because of second-order positive feedback between population and technology. Technological growth increases the carrying capacity of land for people, which leads to a growing population, and this in turn drives further technological growth.<br />
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有人提出,由于人口和技术之间的二阶正反馈,增长速度正在加快。技术增长增加了土地对人的承载能力,从而导致人口增长,而这反过来又推动了技术的进一步增长。<br />
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==== Prejudice, social institutions and poverty 偏见、社会制度与贫困====<br />
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Gunnar Myrdal described a vicious circle of increasing inequalities, and poverty, which is known as "circular cumulative causation".<br />
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Gunnar Myrdal描述了一个不平等和贫困加剧的恶性循环,这就是所谓的”循环累积因果关系”。<br />
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==== In meteorology 在气象学中====<br />
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Drought intensifies through positive feedback. A lack of rain decreases soil moisture, which kills plants and/or causes them to release less water through transpiration. Both factors limit evapotranspiration, the process by which water vapor is added to the atmosphere from the surface, and add dry dust to the atmosphere, which absorbs water. Less water vapor means both low dew point temperatures and more efficient daytime heating, decreasing the chances of humidity in the atmosphere leading to cloud formation. Lastly, without clouds, there cannot be rain, and the loop is complete.<br />
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干旱通过正反馈效应加剧。缺雨会降低土壤湿度,从而杀死植物,使它们通过蒸腾作用释放更少的水分。这两个因素都限制了水蒸气从地表加到大气中的过程,并使吸收水分的干燥灰尘进入大气。水汽少了,既意味着露点温度低,白天的供暖效率也高,减少了大气中湿度导致云的形成的机会。最后,没有云,就不会有雨,这个正反馈循环就形成了。<br />
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==== In climatology 在气候学中====<br />
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Climate "forcings" may push a climate system in the direction of warming or cooling, for example, increased atmospheric concentrations of greenhouse gases cause warming at the surface. Forcings are external to the climate system and feedbacks are internal processes of the system. Some feedback mechanisms act in relative isolation to the rest of the climate system while others are tightly coupled. Forcings, feedbacks and the dynamics of the climate system determine how much and how fast the climate changes. The main positive feedback in global warming is the tendency of warming to increase the amount of water vapor in the atmosphere, which in turn leads to further warming. The main negative feedback comes from the Stefan–Boltzmann law, the amount of heat radiated from the Earth into space is proportional to the fourth power of the temperature of Earth's surface and atmosphere.<br />
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气候 中的"诱因 "可能会将气候系统推向变暖或变冷的方向,例如,大气中温室气体浓度的增加会导致地表变暖。诱因是气候系统的外部因素,而反馈是系统的内部过程。一些反馈机制与气候系统的其他部分相对孤立地发挥作用,而另一些则是紧密耦合的。气候系统的作用力、反馈和动态决定了气候变化的程度和速度。全球变暖中的主要正反馈是变暖使大气中的水汽量增加,进而导致进一步变暖。主要的负反馈来自Stefan-Boltzmann定律,从地球辐射到空间的热量与地球表面和大气温度的四次方成正比。<br />
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Other examples of positive feedback subsystems in climatology include:<br />
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气候学中正反馈子系统的其他例子包括:<br />
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A warmer atmosphere will melt ice and this changes the albedo which further warms the atmosphere.<br />
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大气变暖会使冰融化,从而改变反照率,从而使大气进一步变暖。<br />
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Methane hydrates can be unstable so that a warming ocean could release more methane, which is also a greenhouse gas.<br />
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甲烷水合物可能是不稳定的,所以海洋变暖可能会释放更多的温室气体之一的甲烷。<br />
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Peat, occurring naturally in peat bogs, contains carbon. When peat dries it decomposes, and may additionally burn. Peat also releases nitrous oxide.<br />
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泥炭,天然存在于泥炭沼泽中,含有碳。当泥炭干燥时,它会分解,并可能额外燃烧。泥炭还会释放一氧化二氮。<br />
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Global warming affects the cloud distribution. Clouds at higher altitudes enhance the greenhouse effects, while low clouds mainly reflect back sunlight, having opposite effects on temperature.<br />
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全球变暖会影响云的分布。高空的云层会增强温室效应,而低空的云层则主要反射太阳光,对温度产生相反的影响。<br />
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The Intergovernmental Panel on Climate Change (IPCC) Fourth Assessment Report states that "Anthropogenic warming could lead to some effects that are abrupt or irreversible, depending upon the rate and magnitude of the climate change."<br />
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政府间气候变化专门委员会(气专委)第四次评估报告指出,"人类活动的变暖可能导致一些突然或不可逆转的影响,这取决于气候变化的速度和程度"。<br />
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==== In sociology 在社会学中====<br />
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A self-fulfilling prophecy is a social positive feedback loop between beliefs and behavior: if enough people believe that something is true, their behavior can make it true, and observations of their behavior may in turn increase belief. A classic example is a bank run.<br />
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自我应验预言是信念和行为之间的一个社会正反馈循环: 如果有足够多的人相信某件事是真的,他们的行为就能让它变成真的,而对他们行为的观察又可能反过来增加信念。一个典型的例子是银行挤兑。<br />
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Another sociological example of positive feedback is the network effect. When more people are encouraged to join a network this increases the reach of the network therefore the network expands ever more quickly. A viral video is an example of the network effect in which links to a popular video are shared and redistributed, ensuring that more people see the video and then re-publish the links. This is the basis for many social phenomena, including Ponzi schemes and chain letters. In many cases population size is the limiting factor to the feedback effect.<br />
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正反馈的另一个社会学例子是网络效应。当更多的人被鼓励加入一个网络时,这就增加了网络的覆盖面,因此网络扩张得越来越快。病毒视频就是网络效应的一个例子,在这个例子中,一个热门视频的链接被分享和再传播,确保更多的人看到这个视频,然后重新发布链接。这是许多社会现象的基础,包括庞氏骗局和连锁信。在许多情况下,人口量是反馈效应的限制因素。<br />
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==== In chemistry 在化学中====<br />
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If a chemical reaction causes the release of heat, and the reaction itself happens faster at higher temperatures, then there is a high likelihood of positive feedback. If the heat produced is not removed from the reactants fast enough, thermal runaway can occur and very quickly lead to a chemical explosion.<br />
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如果化学反应引起热量的释放,而反应本身在较高的温度下发生得更快,那么就很有可能出现正反馈。如果产生的热量没有足够快地从反应物中排除,就会发生热失控,并很快导致化学爆炸。<br />
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==== In conservation 在自然保护中====<br />
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Many wildlife are hunted for their parts which can be quite valuable. The closer to extinction that targeted species become, the higher the price there is on their parts. This is an example of positive feedback.<br />
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许多野生动物被猎杀的原因是它们身体的某些部位可能相当有价值。目标物种越是接近灭绝,其部位的价格就越高。这就是一个正反馈的例子。<br />
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====See also另请参阅====<br />
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* Chain reaction – Sequence of reactions 链式反应 -- -- 反应的顺序<br />
* Donella Meadows' twelve leverage points to intervene in a system Donella Meadows干预系统的十二个杠杆点<br />
* Hyperbolic growth 双曲增长<br />
* Reflexivity (social theory)反射性(社会理论)<br />
* Stability criterion稳定性标准<br />
* Strategic complements战略补充<br />
* System dynamics 系统动力学<br />
* Technological singularity – Hypothetical point in time at which technological growth becomes uncontrollable and irreversible 技术奇点 -- -- 假设技术增长变得不可控制和不可逆转的时间点<br />
* Thermal runaway 热失控<br />
* Vicious/virtuous circle: in social and financial systems, a complex of events that reinforces itself through a feedback loop. 恶性/恶性循环:在社会和金融系统中,是通过反馈循环自我强化的事件综合体。<br />
* Positive reinforcement: a situation in operant conditioning where a consequence increases the frequency of a behaviour. 正强化:在操作性条件下,结果会增加行为的频率。<br />
* Praise of performance: a term often applied in the context of performance appraisal,although this usage is disputed 绩效表扬:这个词经常被应用于绩效评估中,尽管这种用法有争议。<br />
* Self-reinforcing feedback: a term used in systems dynamics to avoid confusion with the "praise" usage 自我强化反馈:系统动力学中使用的术语,以避免与 "表扬 "的用法相混淆。<br />
* Matthew effect – Effect originally observed by Robert K. Merton 马太效应 -- -- 罗伯特-K-默顿最初观察到的效应。<br />
* Self-fulfilling prophecy – Prediction that causes itself to become true 自证预言 -- -- 导致自己成为现实的预言<br />
* Virtuous circle and vicious circle 良性循环和恶性循环<br />
* Autocatalysis 自催化<br />
* Meander – Sinuous bend in a series in the channel of a river 蜿蜒曲折 -- -- 河道中一系列蜿蜒曲折的弯道。<br />
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====References 参考资料====<br />
1. ^ a b c Ben Zuckerman & David Jefferson (1996). Human Population and the Environmental Crisis. Jones & Bartlett Learning. p. 42. ISBN 9780867209662. Archived from the original on 2018-01-06.<br />
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2. ^ Keesing, R.M. (1981). Cultural anthropology: A contemporary perspective (2nd ed.) p.149. Sydney: Holt, Rinehard & Winston, Inc.<br />
<br />
3. ^ a b c d e Bernard P. Zeigler; Herbert Praehofer; Tag Gon Kim Section (2000). "3.3.2 Feedback in continuous systems". Theory of Modeling and Simulation: Integrating Discrete Event and Continuous Complex Dynamic Systems. Academic Press. p. 55. ISBN 9780127784557. Archived from the original on 2017-01-03. “A positive feedback loop is one with an even number of negative influences [around the loop].”<br />
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4. ^ S W Amos; R W Amos (2002). Newnes Dictionary of Electronics (4th ed.). Newnes. p. 247. ISBN 9780750656429. Archived from the original on 2017-03-29.<br />
<br />
5. ^ Rudolf F. Graf (1999). Modern Dictionary of Electronics (7th ed.). Newnes. p. 276. ISBN 9780750698665. Archived from the original on 2017-03-29.<br />
<br />
6. ^ "Positive feedback". Oxford English Dictionary. Oxford University Press. Archived from the original on 2 March 2014. Retrieved 15 April 2014.<br />
<br />
7. ^ "Feedback". Glossary. Metadesigners Network. Archived from the original on 16 April 2014. Retrieved 15 April 2014.<br />
<br />
8. ^ Electronics circuits and devices second edition. Ralph J. Smith<br />
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9. ^ a b Lopez-Caamal, Fernando; Middleton, Richard H.; Huber, Heinrich (February 2014). "Equilibria and stability of a class of positive feedback loops". Journal of Mathematical Biology. 68 (3): 609–645. doi:10.1007/s00285-013-0644-z. PMID 23358701.<br />
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10. ^ Donella Meadows, Leverage Points: Places to Intervene in a System Archived 2013-10-08 at the Wayback Machine, 1999<br />
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11. ^ a b Mindell, David A. (2002). Between Human and Machine : Feedback, Control, and Computing before Cybernetics.Baltimore, MD: Johns Hopkins University Press. ISBN 9780801868955. Archived from the original on 2018-01-06.<br />
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12. ^ Friis, H. T.; Jensen, A. G. (April 1924), "High Frequency Amplifiers", Bell System Technical Journal, 3 (2): 181–205, doi:10.1002/j.1538-7305.1924.tb01354.x<br />
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13. ^ Black, H. S. (January 1934), "Stabilized feed-back amplifiers", Electrical Engineering, 53: 114–120, doi:10.1109/ee.1934.6540374<br />
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14. ^ US 1113149, Armstrong, E. H., "Wireless receiving system"<br />
<br />
15. ^ Kitchin, Charles. "A Short Wave Regenerative Receiver Project". Archived from the original on 10 July 2010. Retrieved 23 September 2010.<br />
<br />
16. ^ "Sinewave oscillators". EDUCYPEDIA - electronics. Archived from the original on 27 September 2010. Retrieved 23 September 2010.<br />
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17. ^ Self, Douglas (2009). Audio Power Amplifier Design Handbook. Focal Press. pp. 254–255. ISBN 978-0-240-52162-6. Archived from the original on 2014-01-29.<br />
<br />
18. ^ "CMOS Schmitt Trigger—A Uniquely Versatile Design Component" (PDF). Fairchild Semiconductor Application Note 140. Fairchild Semiconductors. 1975. Archived (PDF) from the original on 22 November 2010. Retrieved 29 September 2010.<br />
<br />
19. ^ Strandh, Robert. "Latches and flip-flops". Laboratoire Bordelais de Recherche en Informatique. Archived from the original on 16 July 2011. Retrieved 4 November 2010.<br />
<br />
20. ^ Wayne, Storr. "Sequential Logic Basics: SR Flip-Flop". Electronics-Tutorials.ws. Archived from the original on 16 September 2010. Retrieved 29 September 2010.<br />
<br />
21. ^ Sharma, Bijay Kumar (2009). "Analog Electronics Lecture 4 Part C RC coupled Amplifier Design Procedure". Retrieved 29 September 2010.<br />
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22. ^ Sheff, David (2000). All We Are Saying. New York, New York: St. Martin's Press. p. 173. ISBN 978-0-312-25464-3.<br />
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23. ^ Shadwick, Keith (2003). Jimi Hendrix, Musician. Backbeat Books. p. 92. ISBN 978-0-87930-764-6.<br />
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24. ^ May, Brian. "Burns Brian May Tri-Sonic Pickups". House Music & Duck Productions. Archived from the original on 20 November 2010. Retrieved 2 February 2011.<br />
<br />
25. ^ "Positive Feedback and Bistable Systems" (PDF). University of Washington. Archived (PDF) from the original on 2015-04-13. “* Non-Hysteretic Switches, Memoryless Switches: These systems have no memory, that is, once the input signal is removed, the system returns to its original state. * Hysteretic Switches, Bistability: Bistable systems, in contrast, have memory. That is, when switched to one state or another, these systems remain in that state unless forced to change back. The light switch is a common example of a bistable system from everyday life. All bistable systems are based around some form of positive feedback loop.”<br />
<br />
26. ^ a b c d e f Guyton, Arthur C. (1991) Textbook of Medical Physiology. (8th ed). Philadelphia: W.B. Saunders. ISBN 0-7216-3994-1<br />
<br />
27. ^ Hasty, J.; McMillen, D.; Collins, J. J. (2002). "Engineered gene circuits". Nature. 420 (6912): 224–230. Bibcode:2002Natur.420..224H. doi:10.1038/nature01257. PMID 12432407.<br />
<br />
28. ^ Veening, J.; Smits, W. K.; Kuipers, O. P. (2008). "Bistability, Epigenetics, and Bet-Hedging in Bacteria" (PDF). Annual Review of Microbiology. 62 (1): 193–210. doi:10.1146/annurev.micro.62.081307.163002. hdl:11370/59bec46a-4434-4eaa-aaae-03461dd02bbb. PMID 18537474.<br />
<br />
29. ^ Bagowski, C. P.; Ferrell, J. E. (2001). "Bistability in the JNK cascade". Current Biology. 11 (15): 1176–1182. doi:10.1016/S0960-9822(01)00330-X. PMID 11516948.<br />
<br />
30. ^ Lotka, A (1945). "The law of evolution as a maximal principle". Human Biology. 17: 168–194.<br />
<br />
31. ^ Alexander, R. (1989). Evolution of the human psyche. In P. Millar & C. Stringer (Eds.), The human revolution: Behavioral and biological perspectives on the origins of modern humans (pp. 455-513). Princeton: Princeton University Press.<br />
<br />
32. ^ Crespi, B. J. (2004). "Vicious circles: positive feedback in major evolutionary and ecological transitions". Trends in Ecology and Evolution. 19 (12): 627–633. doi:10.1016/j.tree.2004.10.001. PMID 16701324.<br />
<br />
33. ^ Dawkins, R. 1991. The Blind Watchmaker London: Penguin. Note: W.W. Norton also published this book, and some citations may refer to that publication. However, the text is identical, so it depends on which book is at hand<br />
<br />
34. ^ Markov A., Korotayev A. "Phanerozoic marine biodiversity follows a hyperbolic trend." Palaeoworld. Volume 16, Issue 4, December 2007, Pages 311-318<br />
<br />
35. ^ Markov, A.; Korotayev, A. (2008). "Hyperbolic growth of marine and continental biodiversity through the Phanerozoic and community evolution". Journal of General Biology. 69 (3): 175–194. PMID 18677962. Archived from the original on 2009-12-25.<br />
<br />
36. ^ Osterholm, Michael T. (2005-05-05). "Preparing for the Next Pandemic". The New England Journal of Medicine. 352 (18): 1839–1842. CiteSeerX 10.1.1.608.6200. doi:10.1056/NEJMp058068. PMID 15872196.<br />
<br />
37. ^ Paul, William E. (September 1993). "Infectious Diseases and the Immune System". Scientific American. 269 (3): 93. Bibcode:1993SciAm.269c..90P. doi:10.1038/scientificamerican0993-90. PMID 8211095.<br />
<br />
38. ^ Eissing, Thomas (2014). "Bistability analyses of a caspase activation model for receptor-induced apoptosis". Journal of Biological Chemistry. 279 (35): 36892–36897. doi:10.1074/jbc.M404893200. PMID 15208304.<br />
<br />
39. ^ Winner, E. (1996). Gifted children: Myths and Realities. New York: Basic Books. ISBN 978-0465017607.<br />
<br />
40. ^ Vandervert, L. (2009a). Working memory, the cognitive functions of the cerebellum and the child prodigy. In L.V. Shavinina (Ed.), International handbook on giftedness (pp. 295-316). The Netherlands: Springer Science.<br />
<br />
41. ^ Vandervert, L. (2009b). "The emergence of the child prodigy 10,000 years ago: An evolutionary and developmental explanation". Journal of Mind and Behavior. 30 (1–2): 15–32.<br />
<br />
42. ^ Altszyler, E; Berbeglia, F.; Berbeglia, G.; Van Hentenryck, P. (2017). "Transient dynamics in trial-offer markets with social influence: Trade-offs between appeal and quality". PLOS ONE. 12 (7): e0180040. Bibcode:2017PLoSO..1280040A. doi:10.1371/journal.pone.0180040. PMC 5528888. PMID 28746334.<br />
<br />
43. ^ Azzopardi, Paul V. (2010), Behavioural Technical Analysis, Harriman House Limited, p. 116, ISBN 9780857190680, archived from the original on 2017-03-29<br />
<br />
44. ^ Arthur, W. Brian (1990). "Positive Feedbacks in the Economy". Scientific American. 262 (2): 80. Bibcode:1990SciAm.262b..92A. doi:10.1038/scientificamerican0290-92.<br />
<br />
45. ^ The Financial Instability Hypothesis Archived 2009-10-09 at the Wayback Machine by Hyman P. Minsky, Working Paper No. 74, May 1992, pp. 6–8<br />
<br />
46. ^ "Findings Regarding the Market Events of May 6, 2010" (PDF). 2010-09-30. Archived (PDF) from the original on August 15, 2017.<br />
<br />
47. ^ Brown, A. Duncan (2003), Feed or Feedback: Agriculture, Population Dynamics and the State of the Planet, Utrecht: International Books, ISBN 978-90-5727-048-2<br />
<br />
48. ^ Dolgonosov, B.M. (2010). "On the reasons of hyperbolic growth in the biological and human world systems". Ecological Modelling. 221 (13–14): 1702–1709. doi:10.1016/j.ecolmodel.2010.03.028.<br />
<br />
49. ^ a b Korotayev A. Compact Mathematical Models of World System Development, and How they can Help us to Clarify our Understanding of Globalization Processes Archived 2018-01-06 at the Wayback Machine. Globalization as Evolutionary Process: Modeling Global Change. Edited by George Modelski, Tessaleno Devezas, and William R. Thompson. London: Routledge, 2007. P. 133-160.<br />
<br />
50. ^ Korotayev, A. V., & Malkov, A. S. A Compact Mathematical Model of the World System Economic and Demographic Growth, 1 CE–1973 CE // INTERNATIONAL JOURNAL OF MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES Volume 10, 2016. P. 200-209 Archived 2018-01-06 at the Wayback Machine.<br />
<br />
51. ^ Berger, Sebastian. "Circular Cumulative Causation (CCC) à la Myrdal and Kapp — Political Institutionalism for Minimizing Social Costs" (PDF). Archived (PDF) from the original on 26 April 2012. Retrieved 26 November 2011.<br />
<br />
52. ^ S.-Y. Simon Wang; Jin-Ho Yoon; Christopher C. Funk; Robert R. Gillies, eds. (2017). Climate Extremes: Patterns and Mechanisms. Wiley. pp. 81–82. ISBN 9781119068037.<br />
<br />
53. ^ US NRC (2012), Climate Change: Evidence, Impacts, and Choices, US National Research Council (US NRC), archived from the original on 2016-05-03, p.9. Also available as PDF Archived 2013-02-20 at the Wayback Machine<br />
<br />
54. ^ Understanding Climate Change Feedbacks, U.S. National Academy of Sciences Archived 2012-02-10 at the Wayback Machine<br />
<br />
55. ^ "8.6.3.1 Water Vapour and Lapse Rate - AR4 WGI Chapter 8: Climate Models and their Evaluation". Archived from the original on 2010-04-09. Retrieved 2010-04-23.<br />
<br />
56. ^ IPCC. "Climate Change 2007: Synthesis Report. Contribution of Working Groups I, II and III to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change. Pg 53" (PDF). Archived (PDF) from the original on 2010-02-09.<br />
<br />
57. ^ Holden, Matthew H.; McDonald-Madden, Eve (2017). "High prices for rare species can drive large populations extinct: The anthropogenic Allee effect revisited". Journal of Theoretical Biology. 429: 170–180. arXiv:1703.06736. Bibcode:2017arXiv170306736H. doi:10.1016/j.jtbi.2017.06.019. PMID 28669883.<br />
<br />
58. ^ Positive feedback occurs when one is told he has done something well or correctly. Tom Coens and Mary Jenkins, "Abolishing Performance Appraisals", p116.<br />
<br />
====拓展阅读 ====<br />
* Norbert Wiener (1948), Cybernetics or Control and Communication in the Animal and the Machine, Paris, Hermann et Cie - MIT Press, Cambridge, MA.<br />
* Katie Salen and Eric Zimmerman. Rules of Play. MIT Press. 2004. ISBN 0-262-24045-9. Chapter 18: Games as Cybernetic Systems.<br />
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本中文词条由[[用户:Solitude|Solitude]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E7%A8%B3%E5%AE%9A%E6%80%A7%E7%90%86%E8%AE%BA&diff=29590稳定性理论2022-03-25T08:23:26Z<p>唐糖糖:</p>
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|keywords=微分方程,动力系统,线性自治系统<br />
|description=稳定性理论 Stability theory被用于研究微分方程解的稳定性和动力系统在初始条件的微小扰动下轨迹的稳定性问题。<br />
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{{short description|Part of mathematics that addresses the stability of solutions}}<br />
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在数学上,'''稳定性理论 Stability theory'''被用于研究'''微分方程Differential equation'''解的稳定性和'''动力系统 Dynamical system'''在初始条件的微小扰动下轨迹的稳定性问题。例如,'''热传导方程 Heat equation'''是一个稳定的偏微分方程,因为'''极大值原理 Maximum principle'''的存在,初始数据的微小扰动会导致温度随之产生微小的变化。在偏微分方程中,人们可以使用 <math>Lp</math> 范数或 <math>sup</math> 范数来度量函数之间的距离,而在微分几何中,人们可以使用Gromov–Hausdorff距离来度量空间之间的距离<ref> Duplij S . Gromov–Hausdorff Distance[M]. 2003.</ref>。<br />
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在动力系统中,如果一条'''轨道 Orbit'''上任意点的前向轨道都处于一个足够小的邻域内,或者这条轨道整体停留在一个邻域(一般是较小的邻域,也有可能是较大的邻域)内,则称该轨道的状态为'''李雅普诺夫稳定 Lyapunov stable'''。有各种标准来证明轨道的稳定性或不稳定性。在适当的条件下,这个问题可以简化为一个涉及矩阵'''特征值 Eigenvalue'''的问题,关于这类矩阵特征值的问题已被大量研究并且该领域已经比较成熟。一种更一般的方法涉及'''李雅普诺夫函数 Lyapunov function'''。在实践中,很多'''稳定性判据 Stability criterion'''都可以使用,我们可以使用其中的任何一个作为判断系统稳定性的准则。<br />
[[File:Stability_Diagram.png|thumb|550px|稳定性图将'''庞加莱映射 Poincaré map''' 根据其特征划分为稳定或不稳定区间。<br/>如图可见,图中下半部分区域中系统的稳定性增加。<ref>[http://www.egwald.ca/linearalgebra/lineardifferentialequationsstabilityanalysis.php Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis] Accessed 10 October 2019.</ref>|链接=Special:FilePath/Stability_Diagram.png]]<br />
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常微分方程在经历了长期的求精确解的努力后逐渐停滞,庞加莱在分析的基础上引入几何方法,开创了常微分方程定性理论,同时在分析中引入几何方法,搭建起分析与几何之间的沟通桥梁,带来了微分方程研究的新突破。李雅普诺夫则在庞加莱定性分析的基础上 ,转而进入了新的稳定性研究。如今 ,李雅普诺夫稳定性理论被普遍认为是微分方程定性理论的基本成就之一。不仅有精确的定义 ,更有严格的分析证明 ,将微分方程及稳定性理论的研究推向了新的高度。庞加莱被公认是19世纪后四分之一和二十世纪初的领袖数学家,是对于数学和它的应用具有全面知识的最后一个人,他在数学方面的杰出工作对20世纪和当今的数学造成极其深远的影响。'''庞加莱映射 Poincaré map'''是由相空间中轨道运动定义的一种映射,是当轨道反复穿越同一截面时,反映后继点对先行点依赖关系的映射<ref>Perko. Differential equations and dynamical systems[M]. Springer, 2001.</ref>。一个连续非线性动力系统的求解是非常困难的,庞加莱给出了相图分析法。在相图中虽然不能定量地知道物理量随时间的变化,但可以定性地得到轨线的形态类型及其拓扑结构,从而了解动力系统运动的全局图像。为了更清楚了解高维相空间运动的形态,在连续运动的轨线上用一个截面(称庞加莱截面)将其横截,轨线在截面上穿过的情况就可以简捷地判断运动的形态。对于庞加莱映射是稳定的还是不稳定的判断则取决于其特征,如图所示,在相空间区间中向下的方向上稳定性增加。<br />
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==动力系统概述==<br />
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微分方程和动力系统定性理论的许多部分关心系统或者方程解的渐近性质及其轨迹,这也意味着系统经过很长时间后会发生什么 <ref>Palis J , Melo W D . Geometric theory of dynamical systems[J]. Springer-Verlag, 1982, 10.1007/978-1-4612-5703-5.</ref>。系统最简单的行为表现为'''平衡点 Equilibrium points'''或不动点,以及'''周期轨道 Periodic orbit'''。如果我们已经很好地理解了一个特定的轨道,那么很自然地就会问下一个问题:初始条件的一个微小变化对于系统来说是否仍会保持类似的行为。稳定性理论解决了以下问题:附近的轨道是否会无限靠近给定的轨道?已知的轨道会收敛到给定的轨道吗?在前一种情况下,轨道被称为是'''稳定 Stable'''的;在后一种情况下,轨道是'''渐近稳定 Asymptotically stable '''的,并且收敛到给定的轨道称为'''吸引子 Attractor'''<ref>Zaslavsky G M . The simplest case of a strange attractor[J]. Physics Letters A, 1978, 69(3):145-147.</ref>。<br />
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对于一个一阶常微分方程自治系统的平衡解<math>f_e</math>:<br />
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*如果对于任意(小的)<math>\epsilon > 0</math>,存在<math>\delta > 0 </math>,使得只要初始条件与平衡点的距离在<math> \delta </math>范围内,例如<math> \| f(t_0) - f_e \| < \delta</math>,就有,对任何<math> t \ge t_0 </math>满足解 <math>f(t) </math> 与平衡点的距离在 <math> \epsilon </math> 范围内,例如<math>\| f(t) - f_e \| < \epsilon</math>,那么该平衡点称为稳定的。<br />
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*如果该平衡点是稳定的,并且存在 <math>\delta_0 > 0</math>,使得对于任何<math>\| f(t_0) - f_e \| < \delta_0 </math>,当<math>t \rightarrow \infty </math>时都有<math>f(t) \rightarrow f_e </math>,那么该平衡点是渐近稳定的。<br />
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稳定性意味着在微小的扰动下轨迹不会发生太大的变化。相反的情况中,微小的扰动会使得轨迹发生较大变化,即附近的轨道与给定的轨道互相排斥,这也是一种有趣的现象。一般来说,在某些方向对初始状态的扰动使得轨道渐近地接近给定轨道,而在其他方向的扰动则使得轨道远离给定轨道。也可能存在对初始状态在某些方向的扰动使得轨道行为变得比较复杂(比如既不会收敛也不会完全逃逸),从而稳定性理论不能对于这样的动力学状态给予充分的预测信息。<br />
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稳定性理论的关键思想之一是用轨道附近系统的线性化,来分析轨道在扰动下的定性行为。特别地,在 n 维'''相空间 Phase space'''的光滑动力系统的每个平衡点上,都存在一个 n×n 的矩阵 A,其特征值刻画了邻近点的动力学行为'''(Hartman-Grobman 定理 Hartman–Grobman theorem)'''。更确切地说,如果矩阵所有的特征值都是负实数或实部为负的复数,那么这个平衡点就是一个稳定的吸引子,并且附近的点以指数速率收敛到它,参考'''李雅普诺夫稳定性 Lyapunov stability'''和'''指数稳定性 Exponential stability'''。如果所有的特征值都不是纯虚数(或零) ,那么吸引方向和排斥方向都与矩阵 A 的特征空间有关,其特征值的实部分别为负和正。对于更复杂的轨道上的扰动情形,也有类似的表述。<br />
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==不动点稳定性==<br />
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最简单的一种轨道就是一个不动点,称为平衡态,或者叫做平衡点。如果一个力学系统处于稳定的平衡状态,那么只需要一个很小的推力就会导致局部运动的发生,例如,类似钟摆那样的小规模的振动。在有阻尼的系统中,稳定的平衡态是渐近稳定的<ref> Hui Y , Michel A N , Ling H . Stability theory for hybrid dynamical systems[C]// IEEE Conference on Decision & Control. IEEE, 2002.</ref>。另一方面,对于一个不稳定的平衡,例如一个球停留在山顶的最高顶点上,一个极其微小的推力就会导致一个大幅度的运动,这个运动可能会也可能不会收敛到原始状态。<br />
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对于线性系统而言,存在许多行之有效的测试方法来检验线性系统的稳定性。非线性系统的稳定性通常可以首先考虑其线性化的系统,并从其线性化系统的稳定性中推断出原非线性系统的稳定性。<br />
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===映射===<br />
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设 {{Math|''f'': '''R''' → '''R'''}}是一个连续可微函数,且存在一个不动点{{Math|''a''}},使得 {{Math|1=''f''(''a'') = ''a''}}。<br />
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考虑一个通过迭代函数得到的动力系统:<br />
:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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当函数 {{Math|''f''}} 在 {{Math|''a''}} 点的导数的绝对值严格小于1时,不动点是稳定的;当在 {{Math|''a''}} 点的导数严格大于1时是不稳定的。这是因为在这个点附近,函数的斜率具有的线性近似值为:<br />
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:<math> f(x) \approx f(a)+f'(a)(x-a). </math><br />
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因此<br />
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:<math>x_{n+1}-x_{n} = f(x_n)-x_n \simeq f(a) + f'(a)(x_n-a)-x_n = a + f'(a)(x_n-a)-x_n = (f'(a)-1)(x_n-a) \to \frac{x_{n+1}-x_{n}}{x_n-a}=f'(a)-1</math><br />
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这意味着导数测量的是函数连续迭代接近或偏离不动点 {{Math|''a''}} 的速率。如果不动点 {{Math|''a''}} 处的导数恰好是1或-1,那么就需要更多的信息才能判断系统的稳定性。<br />
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对于具有一个不动点 {{Math|''a''}} 的连续可微映射 {{Math|''f'': '''R'''<sup>''n''</sup> → '''R'''<sup>''n''</sup>}},存在一个类似的判据,由 {{Math|''a''}} 的雅可比矩阵 {{Math|''J''<sub>''a''</sub>(''f'')}} 表示。<br />
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如果 {{Math|''J''}} 的所有特征值都是绝对值严格小于1的实数或复数,则该点是稳定不动点;<br />
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如果{{Math|''J''}} 的所有特征值中至少有一个的绝对值严格大于1,则它是不稳定的。<br />
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对于{{Math|''J''}} 的最大特征值的绝对值等于1的情况,需要进一步研究。仅仅使用雅可比矩阵检验是无法确定稳定性类型的。同样的准则对光滑流形的微分同胚情况也有着广泛的适用性。<br />
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===线性自治系统===<br />
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如我们所知,线性系统是一类数学模型,指的是由线性运算子组成的系统,也就是说,这类系统首先满足线性的特性<ref>Luenberger D G . Observing the State of a Linear System[J]. IEEE Transactions on Military Electronics, 2007, 8(2):74-80.</ref>。相较于非线性系统,线性系统的特性比较简单。<br />
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根据系统矩阵A是否随时间变化,引入'''自治系统 autonomous system'''的概念后,可以把线性系统分为自治的和非自治的,对于线性系统一般也可以称为定常的和时变的,也就是说:<br />
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(1)自治的线性系统就是定常线性系统。<br />
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(2)而非自治的线性系统就是时变线性系统。<br />
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对于非线性系统,就可以分为非线性自治系统和非线性非自治系统。<br />
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这里我们首先考察线性自治系统,利用常系数一阶线性微分方程组对应系数矩阵的特征值,便可以分析其不动点的稳定性。<br />
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对于一个如下的'''自治系统 autonomous system'''<br />
:<math>x' = Ax,</math><br />
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当 {{Math|''x''(''t'') ∈ '''R'''<sup>''n''</sup>}} 且 {{Math|''A''}} 是一个 {{Math|''n''×''n''}} 的实矩阵时,它具有常数解<br />
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:<math>x(t)=0.</math><br />
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:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
<br />
<br />
可以这样描述:最初的原点({{Math|0 ∈ '''R'''<sup>''n''</sup>}} ) 是该动力系统的平衡点。当且仅当对于{{Math|''A''}}的所有特征值 {{Math|''λ''}} 有 {{Math|Re(''λ'') < 0}} 时,这个解是随着{{Math|''t'' → ∞}}是渐近稳定的(未来趋势)。类似地,当且仅当对于 {{Math|''A''}} 的所有特征值 {{Math|''λ''}} 有{{Math|Re(''λ'') > 0}} 时,系统随着{{Math|''t'' → -∞}}是渐近稳定的(负号表示方向指向过去趋势)。如果存在一个{{Math|''A''}}的特征值 {{Math|''λ''}} 使得 {{Math|Re(''λ'') > 0}},则该解在{{Math|''t'' → ∞}}时是不稳定的。<br />
<br />
<br />
为了判定线性系统原点的稳定性,可以使用劳斯-赫尔维茨稳定性判据'''Routh–Hurwitz stability criterion''',来将这一结果应用在实践中。矩阵的特征值是其特征多项式的根。如果所有根的实部都是严格负的,那么一个具有实系数的单变量多项式称为赫尔维茨多项式 '''Hurwitz polynomial''' 。劳斯-赫尔维茨定理 '''Routh–Hurwitz theorem'''通过一种避免计算根的算法来描述赫尔维茨多项式的特征。<br />
<br />
<br />
===非线性自治系统===<br />
<br />
前面我们介绍了线性自治系统的稳定性判断,这里我们来考察非线性自治系统的情况。非线性系统不动点的渐近稳定性通常可以用 Hartman-Grobman 定理来判断。<br />
<br />
<br />
假设{{Math|''v''}}是{{Math|'''R'''<sup>''n''</sup>}}上的一个{{Math|''C''<sup>1</sup>}}-向量场,并且下降至某一点{{Math|''p''}}有{{Math|1=''v''(''p'') = 0}}。那么相应的自治系统<br />
:<math>x'=v(x)</math><br />
<br />
有一个常数解<br />
:<math> x(t)=p.</math><br />
<br />
<br />
设{{Math|''J''<sub>''p''</sub>(''v'')}}为向量场 {{Math|''v''}}在点{{Math|''p''}}的{{Math|''n''×''n''}}'''雅可比矩阵 Jacobian matrix'''。如果 {{Math|''J''}} 的所有特征值都具有严格负的实部,则系统的解是渐近稳定的。这个条件可以用劳斯-赫尔维茨判据'''Routh–Hurwitz stability criterion'''来检验。<br />
<br />
<br />
==一般动力系统的李雅普诺夫函数==<br />
<br />
'''李雅普诺夫函数 Lyapunov functions'''在稳定性分析和控制理论中都起着重要的作用,它的应用使得许多领域中的一系列问题的解决变得相对容易,尤其是在一些应用型的分析领域中。在常微分方程理论中,可用它来证明常微分方程平衡点的稳定性<ref>Branicky, M. S . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL AC, 1998, 43(4):475-482.</ref>。所以我们建立动力系统的李雅普诺夫稳定性或渐近稳定的一般方法即是利用李亚普诺夫函数来分析。<br />
<br />
<br />
==拓展阅读==<br />
<br />
*渐近稳定性 Asymptotic stability <br />
<br />
*超稳定性 Hyperstability <br />
<br />
*线性稳定性 Linear stability <br />
<br />
*轨道稳定性 Orbital stability <br />
<br />
*稳定性判据 Stability criterion <br />
<br />
*稳定半径 Stability radius <br />
<br />
*[[结构稳定性]] Structural stability <br />
<br />
*冯诺依曼稳定性分析 Von Neumann stability analysis<br />
<br />
<br />
==参考文献==<br />
<br />
{{Reflist}}<br />
<br />
<br />
==外部链接==<br />
<br />
*[http://demonstrations.wolfram.com/StableEquilibria/ Stable Equilibria] 源于Michael Schreiber,Wolfram示范项目。<br />
<br />
<br />
==编者推荐==<br />
===集智课程===<br />
[https://campus.swarma.org/course/1641 动力系统分析]<br />
[[file:7bbbe372ca1517de5c9b70a8f75560c1.jpeg|right|thumb|350px|]]<br />
<br />
本课程北京师范大学系统科学学院教授王大辉讲授,主要讲授连续和离散动力系统的定态、极限环及其稳定性分析、动力学系统的结构稳定性和常见的分支类型以及分析方法,混沌概念等。<br />
<br />
本课程是系统科学专业的学位基础课,是系统科学博士研究生培养的基础课程。主要培养硕士、博士研究生从动力学演化角度观察世界的能力,并可以分析具体的动力学系统,能够分析研究对象中随时间变化的状态变量以及变量之间的关系,建立动力学方程并进行定性和定量的分析,是非线性系统控制、控制理论、复杂系统建模与分析以及系统生物学等专业课的理论基础,应用领域涉及国防、科技、经济、工业和农业的各个方面。<br />
<br />
<br />
[https://campus.swarma.org/course/1691 结构稳定性与中心流形]<br />
<br />
本课程中,讨论了在非双曲平衡点,如何利用中心流形定理对系统的结构稳定性进行分析。时长为35min。<br />
<br />
<br />
[https://campus.swarma.org/course/1684 动力系统稳定性初步]<br />
<br />
本课程中,介绍判断动力系统稳定性的两种思路,轨道稳定性与状态稳定性,及具体的判断方法。时长为1h57min。<br />
<br />
===集智文章===<br />
[https://swarma.org/?p=31718 PRL前沿:热力学稳定性意味着因果关系]<br />
[[file:wxsync-2022-01-38fa575df272b3657923b6d64b20c376.jpeg|right|thumb|350px|]]<br />
<br />
相对论流体力学理论的稳定性条件可以直接从平衡态时熵应最大化这一要求推导出来。1月6日发表在PRL上的一项最新研究用一个简单的几何论证证明,如果流体力学理论根据这个熵判据是稳定的,那么对平衡态的局部扰动不能传播到它们的未来光锥外。也就是说,在相对论流体力学中,非因果理论在热力学上必须是不稳定的,至少在接近平衡态如此。研究表明,稳定性和因果关系之间这种深层联系的物理根源在于熵和信息之间的关系。<br />
<br />
<br />
[https://swarma.org/?p=26366 货币的层级结构与金融不稳定性假说 | 复杂经济学读书会]<br />
<br />
复杂经济学读书会第15期,我们邀请到钟华(北京师范大学系统科学学院2019级博士生)和王势与谋(北京师范大学系统科学学院研究助理)做客集智俱乐部直播间,来分享两个经典话题,一是讨论货币的内在层次结构,二是分析金融不稳定性假说。<br />
<br />
Perry Mehrling 认为一些固有的思维定势会影响到思考,这些思维定势可能来源于以前日常生活中,或者是以往的经济学课程中形成的。<br />
<br />
但这些思维方式存在着一定的局限性,我们需要用一种不同的方式来思考货币体系,也就是要提出的层级体系的概念。在文中,他区分了货币的层级结构、金融机构的层级结构、货币体系的层级结构以及做市商的层级结构等。<br />
<br />
通过层级分析,他认为已有的各种理论都只是捕捉到了货币体系整体的一部分,并不是货币体系的完整真相,并以此从一个全新的视角解读了经济危机以及中央银行“最后贷款人”的作用。<br />
<br />
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本中文词条由[[用户:Bnustv|Bnustv]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
<br />
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|2022.03.21-2022.03.28<br />
|[[自催化]]<br />
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|稳定性理论<br />
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|}</div>唐糖糖https://wiki.swarma.org/index.php?title=%E7%A8%B3%E5%AE%9A%E6%80%A7%E7%90%86%E8%AE%BA&diff=29443稳定性理论2022-03-22T15:05:49Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=微分方程,动力系统,线性自治系统<br />
|description=稳定性理论被用于研究微分方程解的稳定性和动力系统在初始条件的微小扰动下轨迹的稳定性问题。<br />
}}<br />
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{{short description|Part of mathematics that addresses the stability of solutions}}<br />
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在数学上,'''稳定性理论 Stability theory'''被用于研究'''微分方程Differential equation'''解的稳定性和'''动力系统 Dynamical system'''在初始条件的微小扰动下轨迹的稳定性问题。例如,'''热传导方程 Heat equation'''是一个稳定的偏微分方程,因为'''极大值原理 Maximum principle'''的存在,初始数据的微小扰动会导致温度随之产生微小的变化。在偏微分方程中,人们可以使用 <math>Lp</math> 范数或 <math>sup</math> 范数来度量函数之间的距离,而在微分几何中,人们可以使用Gromov–Hausdorff距离来度量空间之间的距离<ref> Duplij S . Gromov–Hausdorff Distance[M]. 2003.</ref>。<br />
<br />
<br />
在动力系统中,如果一条'''轨道 Orbit'''上任意点的前向轨道都处于一个足够小的邻域内,或者这条轨道整体停留在一个邻域(一般是较小的邻域,也有可能是较大的邻域)内,则称该轨道的状态为'''李雅普诺夫稳定 Lyapunov stable'''。有各种标准来证明轨道的稳定性或不稳定性。在适当的条件下,这个问题可以简化为一个涉及矩阵'''特征值 Eigenvalue'''的问题,关于这类矩阵特征值的问题已被大量研究并且该领域已经比较成熟。一种更一般的方法涉及'''李雅普诺夫函数 Lyapunov function'''。在实践中,很多'''稳定性判据 Stability criterion'''都可以使用,我们可以使用其中的任何一个作为判断系统稳定性的准则。<br />
[[File:Stability_Diagram.png|thumb|550px|稳定性图将'''庞加莱映射 Poincaré map''' 根据其特征划分为稳定或不稳定区间。<br/>如图可见,图中下半部分区域中系统的稳定性增加。<ref>[http://www.egwald.ca/linearalgebra/lineardifferentialequationsstabilityanalysis.php Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis] Accessed 10 October 2019.</ref>|链接=Special:FilePath/Stability_Diagram.png]]<br />
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常微分方程在经历了长期的求精确解的努力后逐渐停滞,庞加莱在分析的基础上引入几何方法,开创了常微分方程定性理论,同时在分析中引入几何方法,搭建起分析与几何之间的沟通桥梁,带来了微分方程研究的新突破。李雅普诺夫则在庞加莱定性分析的基础上 ,转而进入了新的稳定性研究。如今 ,李雅普诺夫稳定性理论被普遍认为是微分方程定性理论的基本成就之一。不仅有精确的定义 ,更有严格的分析证明 ,将微分方程及稳定性理论的研究推向了新的高度。庞加莱被公认是19世纪后四分之一和二十世纪初的领袖数学家,是对于数学和它的应用具有全面知识的最后一个人,他在数学方面的杰出工作对20世纪和当今的数学造成极其深远的影响。'''庞加莱映射 Poincaré map'''是由相空间中轨道运动定义的一种映射,是当轨道反复穿越同一截面时,反映后继点对先行点依赖关系的映射<ref>Perko. Differential equations and dynamical systems[M]. Springer, 2001.</ref>。一个连续非线性动力系统的求解是非常困难的,庞加莱给出了相图分析法。在相图中虽然不能定量地知道物理量随时间的变化,但可以定性地得到轨线的形态类型及其拓扑结构,从而了解动力系统运动的全局图像。为了更清楚了解高维相空间运动的形态,在连续运动的轨线上用一个截面(称庞加莱截面)将其横截,轨线在截面上穿过的情况就可以简捷地判断运动的形态。对于庞加莱映射是稳定的还是不稳定的判断则取决于其特征,如图所示,在相空间区间中向下的方向上稳定性增加。<br />
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==动力系统概述==<br />
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微分方程和动力系统定性理论的许多部分关心系统或者方程解的渐近性质及其轨迹,这也意味着系统经过很长时间后会发生什么 <ref>Palis J , Melo W D . Geometric theory of dynamical systems[J]. Springer-Verlag, 1982, 10.1007/978-1-4612-5703-5.</ref>。系统最简单的行为表现为'''平衡点 Equilibrium points'''或不动点,以及'''周期轨道 Periodic orbit'''。如果我们已经很好地理解了一个特定的轨道,那么很自然地就会问下一个问题:初始条件的一个微小变化对于系统来说是否仍会保持类似的行为。稳定性理论解决了以下问题:附近的轨道是否会无限靠近给定的轨道?已知的轨道会收敛到给定的轨道吗?在前一种情况下,轨道被称为是'''稳定 Stable'''的;在后一种情况下,轨道是'''渐近稳定 Asymptotically stable '''的,并且收敛到给定的轨道称为'''吸引子 Attractor'''<ref>Zaslavsky G M . The simplest case of a strange attractor[J]. Physics Letters A, 1978, 69(3):145-147.</ref>。<br />
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对于一个一阶常微分方程自治系统的平衡解<math>f_e</math>:<br />
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*如果对于任意(小的)<math>\epsilon > 0</math>,存在<math>\delta > 0 </math>,使得只要初始条件与平衡点的距离在<math> \delta </math>范围内,例如<math> \| f(t_0) - f_e \| < \delta</math>,就有,对任何<math> t \ge t_0 </math>满足解 <math>f(t) </math> 与平衡点的距离在 <math> \epsilon </math> 范围内,例如<math>\| f(t) - f_e \| < \epsilon</math>,那么该平衡点称为稳定的。<br />
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*如果该平衡点是稳定的,并且存在 <math>\delta_0 > 0</math>,使得对于任何<math>\| f(t_0) - f_e \| < \delta_0 </math>,当<math>t \rightarrow \infty </math>时都有<math>f(t) \rightarrow f_e </math>,那么该平衡点是渐近稳定的。<br />
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稳定性意味着在微小的扰动下轨迹不会发生太大的变化。相反的情况中,微小的扰动会使得轨迹发生较大变化,即附近的轨道与给定的轨道互相排斥,这也是一种有趣的现象。一般来说,在某些方向对初始状态的扰动使得轨道渐近地接近给定轨道,而在其他方向的扰动则使得轨道远离给定轨道。也可能存在对初始状态在某些方向的扰动使得轨道行为变得比较复杂(比如既不会收敛也不会完全逃逸),从而稳定性理论不能对于这样的动力学状态给予充分的预测信息。<br />
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稳定性理论的关键思想之一是用轨道附近系统的线性化,来分析轨道在扰动下的定性行为。特别地,在 n 维'''相空间 Phase space'''的光滑动力系统的每个平衡点上,都存在一个 n×n 的矩阵 A,其特征值刻画了邻近点的动力学行为'''(Hartman-Grobman 定理 Hartman–Grobman theorem)'''。更确切地说,如果矩阵所有的特征值都是负实数或实部为负的复数,那么这个平衡点就是一个稳定的吸引子,并且附近的点以指数速率收敛到它,参考'''李雅普诺夫稳定性 Lyapunov stability'''和'''指数稳定性 Exponential stability'''。如果所有的特征值都不是纯虚数(或零) ,那么吸引方向和排斥方向都与矩阵 A 的特征空间有关,其特征值的实部分别为负和正。对于更复杂的轨道上的扰动情形,也有类似的表述。<br />
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==不动点稳定性==<br />
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最简单的一种轨道就是一个不动点,称为平衡态,或者叫做平衡点。如果一个力学系统处于稳定的平衡状态,那么只需要一个很小的推力就会导致局部运动的发生,例如,类似钟摆那样的小规模的振动。在有阻尼的系统中,稳定的平衡态是渐近稳定的<ref> Hui Y , Michel A N , Ling H . Stability theory for hybrid dynamical systems[C]// IEEE Conference on Decision & Control. IEEE, 2002.</ref>。另一方面,对于一个不稳定的平衡,例如一个球停留在山顶的最高顶点上,一个极其微小的推力就会导致一个大幅度的运动,这个运动可能会也可能不会收敛到原始状态。<br />
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对于线性系统而言,存在许多行之有效的测试方法来检验线性系统的稳定性。非线性系统的稳定性通常可以首先考虑其线性化的系统,并从其线性化系统的稳定性中推断出原非线性系统的稳定性。<br />
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===映射===<br />
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设 {{Math|''f'': '''R''' → '''R'''}}是一个连续可微函数,且存在一个不动点{{Math|''a''}},使得 {{Math|1=''f''(''a'') = ''a''}}。<br />
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考虑一个通过迭代函数得到的动力系统:<br />
:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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当函数 {{Math|''f''}} 在 {{Math|''a''}} 点的导数的绝对值严格小于1时,不动点是稳定的;当在 {{Math|''a''}} 点的导数严格大于1时是不稳定的。这是因为在这个点附近,函数的斜率具有的线性近似值为:<br />
<br />
:<math> f(x) \approx f(a)+f'(a)(x-a). </math><br />
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因此<br />
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:<math>x_{n+1}-x_{n} = f(x_n)-x_n \simeq f(a) + f'(a)(x_n-a)-x_n = a + f'(a)(x_n-a)-x_n = (f'(a)-1)(x_n-a) \to \frac{x_{n+1}-x_{n}}{x_n-a}=f'(a)-1</math><br />
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这意味着导数测量的是函数连续迭代接近或偏离不动点 {{Math|''a''}} 的速率。如果不动点 {{Math|''a''}} 处的导数恰好是1或-1,那么就需要更多的信息才能判断系统的稳定性。<br />
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对于具有一个不动点 {{Math|''a''}} 的连续可微映射 {{Math|''f'': '''R'''<sup>''n''</sup> → '''R'''<sup>''n''</sup>}},存在一个类似的判据,由 {{Math|''a''}} 的雅可比矩阵 {{Math|''J''<sub>''a''</sub>(''f'')}} 表示。<br />
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如果 {{Math|''J''}} 的所有特征值都是绝对值严格小于1的实数或复数,则该点是稳定不动点;<br />
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如果{{Math|''J''}} 的所有特征值中至少有一个的绝对值严格大于1,则它是不稳定的。<br />
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对于{{Math|''J''}} 的最大特征值的绝对值等于1的情况,需要进一步研究。仅仅使用雅可比矩阵检验是无法确定稳定性类型的。同样的准则对光滑流形的微分同胚情况也有着广泛的适用性。<br />
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===线性自治系统===<br />
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如我们所知,线性系统是一类数学模型,指的是由线性运算子组成的系统,也就是说,这类系统首先满足线性的特性<ref>Luenberger D G . Observing the State of a Linear System[J]. IEEE Transactions on Military Electronics, 2007, 8(2):74-80.</ref>。相较于非线性系统,线性系统的特性比较简单。<br />
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根据系统矩阵A是否随时间变化,引入'''自治系统 autonomous system'''的概念后,可以把线性系统分为自治的和非自治的,对于线性系统一般也可以称为定常的和时变的,也就是说:<br />
<br />
(1)自治的线性系统就是定常线性系统。<br />
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(2)而非自治的线性系统就是时变线性系统。<br />
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对于非线性系统,就可以分为非线性自治系统和非线性非自治系统。<br />
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这里我们首先考察线性自治系统,利用常系数一阶线性微分方程组对应系数矩阵的特征值,便可以分析其不动点的稳定性。<br />
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对于一个如下的'''自治系统 autonomous system'''<br />
:<math>x' = Ax,</math><br />
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当 {{Math|''x''(''t'') ∈ '''R'''<sup>''n''</sup>}} 且 {{Math|''A''}} 是一个 {{Math|''n''×''n''}} 的实矩阵时,它具有常数解<br />
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:<math>x(t)=0.</math><br />
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:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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可以这样描述:最初的原点({{Math|0 ∈ '''R'''<sup>''n''</sup>}} ) 是该动力系统的平衡点。当且仅当对于{{Math|''A''}}的所有特征值 {{Math|''λ''}} 有 {{Math|Re(''λ'') < 0}} 时,这个解是随着{{Math|''t'' → ∞}}是渐近稳定的(未来趋势)。类似地,当且仅当对于 {{Math|''A''}} 的所有特征值 {{Math|''λ''}} 有{{Math|Re(''λ'') > 0}} 时,系统随着{{Math|''t'' → -∞}}是渐近稳定的(负号表示方向指向过去趋势)。如果存在一个{{Math|''A''}}的特征值 {{Math|''λ''}} 使得 {{Math|Re(''λ'') > 0}},则该解在{{Math|''t'' → ∞}}时是不稳定的。<br />
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为了判定线性系统原点的稳定性,可以使用劳斯-赫尔维茨稳定性判据'''Routh–Hurwitz stability criterion''',来将这一结果应用在实践中。矩阵的特征值是其特征多项式的根。如果所有根的实部都是严格负的,那么一个具有实系数的单变量多项式称为赫尔维茨多项式 '''Hurwitz polynomial''' 。劳斯-赫尔维茨定理 '''Routh–Hurwitz theorem'''通过一种避免计算根的算法来描述赫尔维茨多项式的特征。<br />
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===非线性自治系统===<br />
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前面我们介绍了线性自治系统的稳定性判断,这里我们来考察非线性自治系统的情况。非线性系统不动点的渐近稳定性通常可以用 Hartman-Grobman 定理来判断。<br />
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假设{{Math|''v''}}是{{Math|'''R'''<sup>''n''</sup>}}上的一个{{Math|''C''<sup>1</sup>}}-向量场,并且下降至某一点{{Math|''p''}}有{{Math|1=''v''(''p'') = 0}}。那么相应的自治系统<br />
:<math>x'=v(x)</math><br />
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有一个常数解<br />
:<math> x(t)=p.</math><br />
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设{{Math|''J''<sub>''p''</sub>(''v'')}}为向量场 {{Math|''v''}}在点{{Math|''p''}}的{{Math|''n''×''n''}}'''雅可比矩阵 Jacobian matrix'''。如果 {{Math|''J''}} 的所有特征值都具有严格负的实部,则系统的解是渐近稳定的。这个条件可以用劳斯-赫尔维茨判据'''Routh–Hurwitz stability criterion'''来检验。<br />
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==一般动力系统的李雅普诺夫函数==<br />
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'''李雅普诺夫函数 Lyapunov functions'''在稳定性分析和控制理论中都起着重要的作用,它的应用使得许多领域中的一系列问题的解决变得相对容易,尤其是在一些应用型的分析领域中。在常微分方程理论中,可用它来证明常微分方程平衡点的稳定性<ref>Branicky, M. S . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL AC, 1998, 43(4):475-482.</ref>。所以我们建立动力系统的李雅普诺夫稳定性或渐近稳定的一般方法即是利用李亚普诺夫函数来分析。<br />
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==拓展阅读==<br />
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*渐近稳定性 Asymptotic stability <br />
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*超稳定性 Hyperstability <br />
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*线性稳定性 Linear stability <br />
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*轨道稳定性 Orbital stability <br />
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*稳定性判据 Stability criterion <br />
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*稳定半径 Stability radius <br />
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*[[结构稳定性]] Structural stability <br />
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*冯诺依曼稳定性分析 Von Neumann stability analysis<br />
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==参考文献==<br />
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{{Reflist}}<br />
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==外部链接==<br />
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*[http://demonstrations.wolfram.com/StableEquilibria/ Stable Equilibria] 源于Michael Schreiber,Wolfram示范项目。<br />
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==编者推荐==<br />
===集智课程===<br />
[https://campus.swarma.org/course/1641 动力系统分析]<br />
[[file:7bbbe372ca1517de5c9b70a8f75560c1.jpeg|right|thumb|350px|]]<br />
<br />
本课程北京师范大学系统科学学院教授王大辉讲授,主要讲授连续和离散动力系统的定态、极限环及其稳定性分析、动力学系统的结构稳定性和常见的分支类型以及分析方法,混沌概念等。<br />
<br />
本课程是系统科学专业的学位基础课,是系统科学博士研究生培养的基础课程。主要培养硕士、博士研究生从动力学演化角度观察世界的能力,并可以分析具体的动力学系统,能够分析研究对象中随时间变化的状态变量以及变量之间的关系,建立动力学方程并进行定性和定量的分析,是非线性系统控制、控制理论、复杂系统建模与分析以及系统生物学等专业课的理论基础,应用领域涉及国防、科技、经济、工业和农业的各个方面。<br />
<br />
<br />
[https://campus.swarma.org/course/1691 结构稳定性与中心流形]<br />
<br />
本课程中,讨论了在非双曲平衡点,如何利用中心流形定理对系统的结构稳定性进行分析。时长为35min。<br />
<br />
<br />
[https://campus.swarma.org/course/1684 动力系统稳定性初步]<br />
<br />
本课程中,介绍判断动力系统稳定性的两种思路,轨道稳定性与状态稳定性,及具体的判断方法。时长为1h57min。<br />
<br />
===集智文章===<br />
[https://swarma.org/?p=31718 PRL前沿:热力学稳定性意味着因果关系]<br />
[[file:wxsync-2022-01-38fa575df272b3657923b6d64b20c376.jpeg|right|thumb|350px|]]<br />
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相对论流体力学理论的稳定性条件可以直接从平衡态时熵应最大化这一要求推导出来。1月6日发表在PRL上的一项最新研究用一个简单的几何论证证明,如果流体力学理论根据这个熵判据是稳定的,那么对平衡态的局部扰动不能传播到它们的未来光锥外。也就是说,在相对论流体力学中,非因果理论在热力学上必须是不稳定的,至少在接近平衡态如此。研究表明,稳定性和因果关系之间这种深层联系的物理根源在于熵和信息之间的关系。<br />
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[https://swarma.org/?p=26366 货币的层级结构与金融不稳定性假说 | 复杂经济学读书会]<br />
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复杂经济学读书会第15期,我们邀请到钟华(北京师范大学系统科学学院2019级博士生)和王势与谋(北京师范大学系统科学学院研究助理)做客集智俱乐部直播间,来分享两个经典话题,一是讨论货币的内在层次结构,二是分析金融不稳定性假说。<br />
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Perry Mehrling 认为一些固有的思维定势会影响到思考,这些思维定势可能来源于以前日常生活中,或者是以往的经济学课程中形成的。<br />
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但这些思维方式存在着一定的局限性,我们需要用一种不同的方式来思考货币体系,也就是要提出的层级体系的概念。在文中,他区分了货币的层级结构、金融机构的层级结构、货币体系的层级结构以及做市商的层级结构等。<br />
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通过层级分析,他认为已有的各种理论都只是捕捉到了货币体系整体的一部分,并不是货币体系的完整真相,并以此从一个全新的视角解读了经济危机以及中央银行“最后贷款人”的作用。<br />
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本中文词条由[[用户:Bnustv|Bnustv]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%96%87%E4%BB%B6:7bbbe372ca1517de5c9b70a8f75560c1.jpeg&diff=29442文件:7bbbe372ca1517de5c9b70a8f75560c1.jpeg2022-03-22T15:04:40Z<p>唐糖糖:</p>
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<div></div>唐糖糖https://wiki.swarma.org/index.php?title=%E7%A8%B3%E5%AE%9A%E6%80%A7%E7%90%86%E8%AE%BA&diff=29441稳定性理论2022-03-22T15:04:04Z<p>唐糖糖:/* 集智课程 */</p>
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|keywords=微分方程,动力系统,线性自治系统<br />
|description=稳定性理论被用于研究微分方程解的稳定性和动力系统在初始条件的微小扰动下轨迹的稳定性问题。<br />
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{{short description|Part of mathematics that addresses the stability of solutions}}<br />
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在数学上,'''稳定性理论 Stability theory'''被用于研究'''微分方程Differential equation'''解的稳定性和'''动力系统 Dynamical system'''在初始条件的微小扰动下轨迹的稳定性问题。例如,'''热传导方程 Heat equation'''是一个稳定的偏微分方程,因为'''极大值原理 Maximum principle'''的存在,初始数据的微小扰动会导致温度随之产生微小的变化。在偏微分方程中,人们可以使用 <math>Lp</math> 范数或 <math>sup</math> 范数来度量函数之间的距离,而在微分几何中,人们可以使用Gromov–Hausdorff距离来度量空间之间的距离<ref> Duplij S . Gromov–Hausdorff Distance[M]. 2003.</ref>。<br />
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在动力系统中,如果一条'''轨道 Orbit'''上任意点的前向轨道都处于一个足够小的邻域内,或者这条轨道整体停留在一个邻域(一般是较小的邻域,也有可能是较大的邻域)内,则称该轨道的状态为'''李雅普诺夫稳定 Lyapunov stable'''。有各种标准来证明轨道的稳定性或不稳定性。在适当的条件下,这个问题可以简化为一个涉及矩阵'''特征值 Eigenvalue'''的问题,关于这类矩阵特征值的问题已被大量研究并且该领域已经比较成熟。一种更一般的方法涉及'''李雅普诺夫函数 Lyapunov function'''。在实践中,很多'''稳定性判据 Stability criterion'''都可以使用,我们可以使用其中的任何一个作为判断系统稳定性的准则。<br />
[[File:Stability_Diagram.png|thumb|550px|稳定性图将'''庞加莱映射 Poincaré map''' 根据其特征划分为稳定或不稳定区间。<br/>如图可见,图中下半部分区域中系统的稳定性增加。<ref>[http://www.egwald.ca/linearalgebra/lineardifferentialequationsstabilityanalysis.php Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis] Accessed 10 October 2019.</ref>|链接=Special:FilePath/Stability_Diagram.png]]<br />
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常微分方程在经历了长期的求精确解的努力后逐渐停滞,庞加莱在分析的基础上引入几何方法,开创了常微分方程定性理论,同时在分析中引入几何方法,搭建起分析与几何之间的沟通桥梁,带来了微分方程研究的新突破。李雅普诺夫则在庞加莱定性分析的基础上 ,转而进入了新的稳定性研究。如今 ,李雅普诺夫稳定性理论被普遍认为是微分方程定性理论的基本成就之一。不仅有精确的定义 ,更有严格的分析证明 ,将微分方程及稳定性理论的研究推向了新的高度。庞加莱被公认是19世纪后四分之一和二十世纪初的领袖数学家,是对于数学和它的应用具有全面知识的最后一个人,他在数学方面的杰出工作对20世纪和当今的数学造成极其深远的影响。'''庞加莱映射 Poincaré map'''是由相空间中轨道运动定义的一种映射,是当轨道反复穿越同一截面时,反映后继点对先行点依赖关系的映射<ref>Perko. Differential equations and dynamical systems[M]. Springer, 2001.</ref>。一个连续非线性动力系统的求解是非常困难的,庞加莱给出了相图分析法。在相图中虽然不能定量地知道物理量随时间的变化,但可以定性地得到轨线的形态类型及其拓扑结构,从而了解动力系统运动的全局图像。为了更清楚了解高维相空间运动的形态,在连续运动的轨线上用一个截面(称庞加莱截面)将其横截,轨线在截面上穿过的情况就可以简捷地判断运动的形态。对于庞加莱映射是稳定的还是不稳定的判断则取决于其特征,如图所示,在相空间区间中向下的方向上稳定性增加。<br />
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==动力系统概述==<br />
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微分方程和动力系统定性理论的许多部分关心系统或者方程解的渐近性质及其轨迹,这也意味着系统经过很长时间后会发生什么 <ref>Palis J , Melo W D . Geometric theory of dynamical systems[J]. Springer-Verlag, 1982, 10.1007/978-1-4612-5703-5.</ref>。系统最简单的行为表现为'''平衡点 Equilibrium points'''或不动点,以及'''周期轨道 Periodic orbit'''。如果我们已经很好地理解了一个特定的轨道,那么很自然地就会问下一个问题:初始条件的一个微小变化对于系统来说是否仍会保持类似的行为。稳定性理论解决了以下问题:附近的轨道是否会无限靠近给定的轨道?已知的轨道会收敛到给定的轨道吗?在前一种情况下,轨道被称为是'''稳定 Stable'''的;在后一种情况下,轨道是'''渐近稳定 Asymptotically stable '''的,并且收敛到给定的轨道称为'''吸引子 Attractor'''<ref>Zaslavsky G M . The simplest case of a strange attractor[J]. Physics Letters A, 1978, 69(3):145-147.</ref>。<br />
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对于一个一阶常微分方程自治系统的平衡解<math>f_e</math>:<br />
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*如果对于任意(小的)<math>\epsilon > 0</math>,存在<math>\delta > 0 </math>,使得只要初始条件与平衡点的距离在<math> \delta </math>范围内,例如<math> \| f(t_0) - f_e \| < \delta</math>,就有,对任何<math> t \ge t_0 </math>满足解 <math>f(t) </math> 与平衡点的距离在 <math> \epsilon </math> 范围内,例如<math>\| f(t) - f_e \| < \epsilon</math>,那么该平衡点称为稳定的。<br />
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*如果该平衡点是稳定的,并且存在 <math>\delta_0 > 0</math>,使得对于任何<math>\| f(t_0) - f_e \| < \delta_0 </math>,当<math>t \rightarrow \infty </math>时都有<math>f(t) \rightarrow f_e </math>,那么该平衡点是渐近稳定的。<br />
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稳定性意味着在微小的扰动下轨迹不会发生太大的变化。相反的情况中,微小的扰动会使得轨迹发生较大变化,即附近的轨道与给定的轨道互相排斥,这也是一种有趣的现象。一般来说,在某些方向对初始状态的扰动使得轨道渐近地接近给定轨道,而在其他方向的扰动则使得轨道远离给定轨道。也可能存在对初始状态在某些方向的扰动使得轨道行为变得比较复杂(比如既不会收敛也不会完全逃逸),从而稳定性理论不能对于这样的动力学状态给予充分的预测信息。<br />
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稳定性理论的关键思想之一是用轨道附近系统的线性化,来分析轨道在扰动下的定性行为。特别地,在 n 维'''相空间 Phase space'''的光滑动力系统的每个平衡点上,都存在一个 n×n 的矩阵 A,其特征值刻画了邻近点的动力学行为'''(Hartman-Grobman 定理 Hartman–Grobman theorem)'''。更确切地说,如果矩阵所有的特征值都是负实数或实部为负的复数,那么这个平衡点就是一个稳定的吸引子,并且附近的点以指数速率收敛到它,参考'''李雅普诺夫稳定性 Lyapunov stability'''和'''指数稳定性 Exponential stability'''。如果所有的特征值都不是纯虚数(或零) ,那么吸引方向和排斥方向都与矩阵 A 的特征空间有关,其特征值的实部分别为负和正。对于更复杂的轨道上的扰动情形,也有类似的表述。<br />
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==不动点稳定性==<br />
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最简单的一种轨道就是一个不动点,称为平衡态,或者叫做平衡点。如果一个力学系统处于稳定的平衡状态,那么只需要一个很小的推力就会导致局部运动的发生,例如,类似钟摆那样的小规模的振动。在有阻尼的系统中,稳定的平衡态是渐近稳定的<ref> Hui Y , Michel A N , Ling H . Stability theory for hybrid dynamical systems[C]// IEEE Conference on Decision & Control. IEEE, 2002.</ref>。另一方面,对于一个不稳定的平衡,例如一个球停留在山顶的最高顶点上,一个极其微小的推力就会导致一个大幅度的运动,这个运动可能会也可能不会收敛到原始状态。<br />
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对于线性系统而言,存在许多行之有效的测试方法来检验线性系统的稳定性。非线性系统的稳定性通常可以首先考虑其线性化的系统,并从其线性化系统的稳定性中推断出原非线性系统的稳定性。<br />
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===映射===<br />
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设 {{Math|''f'': '''R''' → '''R'''}}是一个连续可微函数,且存在一个不动点{{Math|''a''}},使得 {{Math|1=''f''(''a'') = ''a''}}。<br />
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考虑一个通过迭代函数得到的动力系统:<br />
:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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当函数 {{Math|''f''}} 在 {{Math|''a''}} 点的导数的绝对值严格小于1时,不动点是稳定的;当在 {{Math|''a''}} 点的导数严格大于1时是不稳定的。这是因为在这个点附近,函数的斜率具有的线性近似值为:<br />
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:<math> f(x) \approx f(a)+f'(a)(x-a). </math><br />
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因此<br />
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:<math>x_{n+1}-x_{n} = f(x_n)-x_n \simeq f(a) + f'(a)(x_n-a)-x_n = a + f'(a)(x_n-a)-x_n = (f'(a)-1)(x_n-a) \to \frac{x_{n+1}-x_{n}}{x_n-a}=f'(a)-1</math><br />
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这意味着导数测量的是函数连续迭代接近或偏离不动点 {{Math|''a''}} 的速率。如果不动点 {{Math|''a''}} 处的导数恰好是1或-1,那么就需要更多的信息才能判断系统的稳定性。<br />
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对于具有一个不动点 {{Math|''a''}} 的连续可微映射 {{Math|''f'': '''R'''<sup>''n''</sup> → '''R'''<sup>''n''</sup>}},存在一个类似的判据,由 {{Math|''a''}} 的雅可比矩阵 {{Math|''J''<sub>''a''</sub>(''f'')}} 表示。<br />
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如果 {{Math|''J''}} 的所有特征值都是绝对值严格小于1的实数或复数,则该点是稳定不动点;<br />
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如果{{Math|''J''}} 的所有特征值中至少有一个的绝对值严格大于1,则它是不稳定的。<br />
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对于{{Math|''J''}} 的最大特征值的绝对值等于1的情况,需要进一步研究。仅仅使用雅可比矩阵检验是无法确定稳定性类型的。同样的准则对光滑流形的微分同胚情况也有着广泛的适用性。<br />
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===线性自治系统===<br />
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如我们所知,线性系统是一类数学模型,指的是由线性运算子组成的系统,也就是说,这类系统首先满足线性的特性<ref>Luenberger D G . Observing the State of a Linear System[J]. IEEE Transactions on Military Electronics, 2007, 8(2):74-80.</ref>。相较于非线性系统,线性系统的特性比较简单。<br />
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根据系统矩阵A是否随时间变化,引入'''自治系统 autonomous system'''的概念后,可以把线性系统分为自治的和非自治的,对于线性系统一般也可以称为定常的和时变的,也就是说:<br />
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(1)自治的线性系统就是定常线性系统。<br />
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(2)而非自治的线性系统就是时变线性系统。<br />
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对于非线性系统,就可以分为非线性自治系统和非线性非自治系统。<br />
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这里我们首先考察线性自治系统,利用常系数一阶线性微分方程组对应系数矩阵的特征值,便可以分析其不动点的稳定性。<br />
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对于一个如下的'''自治系统 autonomous system'''<br />
:<math>x' = Ax,</math><br />
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当 {{Math|''x''(''t'') ∈ '''R'''<sup>''n''</sup>}} 且 {{Math|''A''}} 是一个 {{Math|''n''×''n''}} 的实矩阵时,它具有常数解<br />
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:<math>x(t)=0.</math><br />
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:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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可以这样描述:最初的原点({{Math|0 ∈ '''R'''<sup>''n''</sup>}} ) 是该动力系统的平衡点。当且仅当对于{{Math|''A''}}的所有特征值 {{Math|''λ''}} 有 {{Math|Re(''λ'') < 0}} 时,这个解是随着{{Math|''t'' → ∞}}是渐近稳定的(未来趋势)。类似地,当且仅当对于 {{Math|''A''}} 的所有特征值 {{Math|''λ''}} 有{{Math|Re(''λ'') > 0}} 时,系统随着{{Math|''t'' → -∞}}是渐近稳定的(负号表示方向指向过去趋势)。如果存在一个{{Math|''A''}}的特征值 {{Math|''λ''}} 使得 {{Math|Re(''λ'') > 0}},则该解在{{Math|''t'' → ∞}}时是不稳定的。<br />
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为了判定线性系统原点的稳定性,可以使用劳斯-赫尔维茨稳定性判据'''Routh–Hurwitz stability criterion''',来将这一结果应用在实践中。矩阵的特征值是其特征多项式的根。如果所有根的实部都是严格负的,那么一个具有实系数的单变量多项式称为赫尔维茨多项式 '''Hurwitz polynomial''' 。劳斯-赫尔维茨定理 '''Routh–Hurwitz theorem'''通过一种避免计算根的算法来描述赫尔维茨多项式的特征。<br />
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===非线性自治系统===<br />
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前面我们介绍了线性自治系统的稳定性判断,这里我们来考察非线性自治系统的情况。非线性系统不动点的渐近稳定性通常可以用 Hartman-Grobman 定理来判断。<br />
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假设{{Math|''v''}}是{{Math|'''R'''<sup>''n''</sup>}}上的一个{{Math|''C''<sup>1</sup>}}-向量场,并且下降至某一点{{Math|''p''}}有{{Math|1=''v''(''p'') = 0}}。那么相应的自治系统<br />
:<math>x'=v(x)</math><br />
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有一个常数解<br />
:<math> x(t)=p.</math><br />
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设{{Math|''J''<sub>''p''</sub>(''v'')}}为向量场 {{Math|''v''}}在点{{Math|''p''}}的{{Math|''n''×''n''}}'''雅可比矩阵 Jacobian matrix'''。如果 {{Math|''J''}} 的所有特征值都具有严格负的实部,则系统的解是渐近稳定的。这个条件可以用劳斯-赫尔维茨判据'''Routh–Hurwitz stability criterion'''来检验。<br />
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==一般动力系统的李雅普诺夫函数==<br />
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'''李雅普诺夫函数 Lyapunov functions'''在稳定性分析和控制理论中都起着重要的作用,它的应用使得许多领域中的一系列问题的解决变得相对容易,尤其是在一些应用型的分析领域中。在常微分方程理论中,可用它来证明常微分方程平衡点的稳定性<ref>Branicky, M. S . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL AC, 1998, 43(4):475-482.</ref>。所以我们建立动力系统的李雅普诺夫稳定性或渐近稳定的一般方法即是利用李亚普诺夫函数来分析。<br />
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==拓展阅读==<br />
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*渐近稳定性 Asymptotic stability <br />
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*超稳定性 Hyperstability <br />
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*线性稳定性 Linear stability <br />
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*轨道稳定性 Orbital stability <br />
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*稳定性判据 Stability criterion <br />
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*稳定半径 Stability radius <br />
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*[[结构稳定性]] Structural stability <br />
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*冯诺依曼稳定性分析 Von Neumann stability analysis<br />
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==参考文献==<br />
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{{Reflist}}<br />
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==外部链接==<br />
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*[http://demonstrations.wolfram.com/StableEquilibria/ Stable Equilibria] 源于Michael Schreiber,Wolfram示范项目。<br />
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===编者推荐===<br />
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==编者推荐==<br />
===集智课程===<br />
[https://campus.swarma.org/course/1641 动力系统分析]<br />
[[file:7bbbe372ca1517de5c9b70a8f75560c1.jpeg|right|thumb|350px|]]<br />
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本课程北京师范大学系统科学学院教授王大辉讲授,主要讲授连续和离散动力系统的定态、极限环及其稳定性分析、动力学系统的结构稳定性和常见的分支类型以及分析方法,混沌概念等。<br />
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本课程是系统科学专业的学位基础课,是系统科学博士研究生培养的基础课程。主要培养硕士、博士研究生从动力学演化角度观察世界的能力,并可以分析具体的动力学系统,能够分析研究对象中随时间变化的状态变量以及变量之间的关系,建立动力学方程并进行定性和定量的分析,是非线性系统控制、控制理论、复杂系统建模与分析以及系统生物学等专业课的理论基础,应用领域涉及国防、科技、经济、工业和农业的各个方面。<br />
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[https://campus.swarma.org/course/1691 结构稳定性与中心流形]<br />
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本课程中,讨论了在非双曲平衡点,如何利用中心流形定理对系统的结构稳定性进行分析。时长为35min。<br />
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[https://campus.swarma.org/course/1684 动力系统稳定性初步]<br />
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本课程中,介绍判断动力系统稳定性的两种思路,轨道稳定性与状态稳定性,及具体的判断方法。时长为1h57min。<br />
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===集智文章===<br />
[https://swarma.org/?p=31718 PRL前沿:热力学稳定性意味着因果关系]<br />
[[file:wxsync-2022-01-38fa575df272b3657923b6d64b20c376.jpeg|right|thumb|350px|]]<br />
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相对论流体力学理论的稳定性条件可以直接从平衡态时熵应最大化这一要求推导出来。1月6日发表在PRL上的一项最新研究用一个简单的几何论证证明,如果流体力学理论根据这个熵判据是稳定的,那么对平衡态的局部扰动不能传播到它们的未来光锥外。也就是说,在相对论流体力学中,非因果理论在热力学上必须是不稳定的,至少在接近平衡态如此。研究表明,稳定性和因果关系之间这种深层联系的物理根源在于熵和信息之间的关系。<br />
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[https://swarma.org/?p=26366 货币的层级结构与金融不稳定性假说 | 复杂经济学读书会]<br />
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复杂经济学读书会第15期,我们邀请到钟华(北京师范大学系统科学学院2019级博士生)和王势与谋(北京师范大学系统科学学院研究助理)做客集智俱乐部直播间,来分享两个经典话题,一是讨论货币的内在层次结构,二是分析金融不稳定性假说。<br />
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Perry Mehrling 认为一些固有的思维定势会影响到思考,这些思维定势可能来源于以前日常生活中,或者是以往的经济学课程中形成的。<br />
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但这些思维方式存在着一定的局限性,我们需要用一种不同的方式来思考货币体系,也就是要提出的层级体系的概念。在文中,他区分了货币的层级结构、金融机构的层级结构、货币体系的层级结构以及做市商的层级结构等。<br />
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通过层级分析,他认为已有的各种理论都只是捕捉到了货币体系整体的一部分,并不是货币体系的完整真相,并以此从一个全新的视角解读了经济危机以及中央银行“最后贷款人”的作用。<br />
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本中文词条由[[用户:Bnustv|Bnustv]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E6%96%87%E4%BB%B6:Wxsync-2022-01-38fa575df272b3657923b6d64b20c376.jpeg&diff=29440文件:Wxsync-2022-01-38fa575df272b3657923b6d64b20c376.jpeg2022-03-22T15:01:52Z<p>唐糖糖:</p>
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<div></div>唐糖糖https://wiki.swarma.org/index.php?title=%E7%A8%B3%E5%AE%9A%E6%80%A7%E7%90%86%E8%AE%BA&diff=29439稳定性理论2022-03-22T15:01:16Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=微分方程,动力系统,线性自治系统<br />
|description=稳定性理论被用于研究微分方程解的稳定性和动力系统在初始条件的微小扰动下轨迹的稳定性问题。<br />
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{{short description|Part of mathematics that addresses the stability of solutions}}<br />
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在数学上,'''稳定性理论 Stability theory'''被用于研究'''微分方程Differential equation'''解的稳定性和'''动力系统 Dynamical system'''在初始条件的微小扰动下轨迹的稳定性问题。例如,'''热传导方程 Heat equation'''是一个稳定的偏微分方程,因为'''极大值原理 Maximum principle'''的存在,初始数据的微小扰动会导致温度随之产生微小的变化。在偏微分方程中,人们可以使用 <math>Lp</math> 范数或 <math>sup</math> 范数来度量函数之间的距离,而在微分几何中,人们可以使用Gromov–Hausdorff距离来度量空间之间的距离<ref> Duplij S . Gromov–Hausdorff Distance[M]. 2003.</ref>。<br />
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在动力系统中,如果一条'''轨道 Orbit'''上任意点的前向轨道都处于一个足够小的邻域内,或者这条轨道整体停留在一个邻域(一般是较小的邻域,也有可能是较大的邻域)内,则称该轨道的状态为'''李雅普诺夫稳定 Lyapunov stable'''。有各种标准来证明轨道的稳定性或不稳定性。在适当的条件下,这个问题可以简化为一个涉及矩阵'''特征值 Eigenvalue'''的问题,关于这类矩阵特征值的问题已被大量研究并且该领域已经比较成熟。一种更一般的方法涉及'''李雅普诺夫函数 Lyapunov function'''。在实践中,很多'''稳定性判据 Stability criterion'''都可以使用,我们可以使用其中的任何一个作为判断系统稳定性的准则。<br />
[[File:Stability_Diagram.png|thumb|550px|稳定性图将'''庞加莱映射 Poincaré map''' 根据其特征划分为稳定或不稳定区间。<br/>如图可见,图中下半部分区域中系统的稳定性增加。<ref>[http://www.egwald.ca/linearalgebra/lineardifferentialequationsstabilityanalysis.php Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis] Accessed 10 October 2019.</ref>|链接=Special:FilePath/Stability_Diagram.png]]<br />
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常微分方程在经历了长期的求精确解的努力后逐渐停滞,庞加莱在分析的基础上引入几何方法,开创了常微分方程定性理论,同时在分析中引入几何方法,搭建起分析与几何之间的沟通桥梁,带来了微分方程研究的新突破。李雅普诺夫则在庞加莱定性分析的基础上 ,转而进入了新的稳定性研究。如今 ,李雅普诺夫稳定性理论被普遍认为是微分方程定性理论的基本成就之一。不仅有精确的定义 ,更有严格的分析证明 ,将微分方程及稳定性理论的研究推向了新的高度。庞加莱被公认是19世纪后四分之一和二十世纪初的领袖数学家,是对于数学和它的应用具有全面知识的最后一个人,他在数学方面的杰出工作对20世纪和当今的数学造成极其深远的影响。'''庞加莱映射 Poincaré map'''是由相空间中轨道运动定义的一种映射,是当轨道反复穿越同一截面时,反映后继点对先行点依赖关系的映射<ref>Perko. Differential equations and dynamical systems[M]. Springer, 2001.</ref>。一个连续非线性动力系统的求解是非常困难的,庞加莱给出了相图分析法。在相图中虽然不能定量地知道物理量随时间的变化,但可以定性地得到轨线的形态类型及其拓扑结构,从而了解动力系统运动的全局图像。为了更清楚了解高维相空间运动的形态,在连续运动的轨线上用一个截面(称庞加莱截面)将其横截,轨线在截面上穿过的情况就可以简捷地判断运动的形态。对于庞加莱映射是稳定的还是不稳定的判断则取决于其特征,如图所示,在相空间区间中向下的方向上稳定性增加。<br />
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==动力系统概述==<br />
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微分方程和动力系统定性理论的许多部分关心系统或者方程解的渐近性质及其轨迹,这也意味着系统经过很长时间后会发生什么 <ref>Palis J , Melo W D . Geometric theory of dynamical systems[J]. Springer-Verlag, 1982, 10.1007/978-1-4612-5703-5.</ref>。系统最简单的行为表现为'''平衡点 Equilibrium points'''或不动点,以及'''周期轨道 Periodic orbit'''。如果我们已经很好地理解了一个特定的轨道,那么很自然地就会问下一个问题:初始条件的一个微小变化对于系统来说是否仍会保持类似的行为。稳定性理论解决了以下问题:附近的轨道是否会无限靠近给定的轨道?已知的轨道会收敛到给定的轨道吗?在前一种情况下,轨道被称为是'''稳定 Stable'''的;在后一种情况下,轨道是'''渐近稳定 Asymptotically stable '''的,并且收敛到给定的轨道称为'''吸引子 Attractor'''<ref>Zaslavsky G M . The simplest case of a strange attractor[J]. Physics Letters A, 1978, 69(3):145-147.</ref>。<br />
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对于一个一阶常微分方程自治系统的平衡解<math>f_e</math>:<br />
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*如果对于任意(小的)<math>\epsilon > 0</math>,存在<math>\delta > 0 </math>,使得只要初始条件与平衡点的距离在<math> \delta </math>范围内,例如<math> \| f(t_0) - f_e \| < \delta</math>,就有,对任何<math> t \ge t_0 </math>满足解 <math>f(t) </math> 与平衡点的距离在 <math> \epsilon </math> 范围内,例如<math>\| f(t) - f_e \| < \epsilon</math>,那么该平衡点称为稳定的。<br />
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*如果该平衡点是稳定的,并且存在 <math>\delta_0 > 0</math>,使得对于任何<math>\| f(t_0) - f_e \| < \delta_0 </math>,当<math>t \rightarrow \infty </math>时都有<math>f(t) \rightarrow f_e </math>,那么该平衡点是渐近稳定的。<br />
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稳定性意味着在微小的扰动下轨迹不会发生太大的变化。相反的情况中,微小的扰动会使得轨迹发生较大变化,即附近的轨道与给定的轨道互相排斥,这也是一种有趣的现象。一般来说,在某些方向对初始状态的扰动使得轨道渐近地接近给定轨道,而在其他方向的扰动则使得轨道远离给定轨道。也可能存在对初始状态在某些方向的扰动使得轨道行为变得比较复杂(比如既不会收敛也不会完全逃逸),从而稳定性理论不能对于这样的动力学状态给予充分的预测信息。<br />
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稳定性理论的关键思想之一是用轨道附近系统的线性化,来分析轨道在扰动下的定性行为。特别地,在 n 维'''相空间 Phase space'''的光滑动力系统的每个平衡点上,都存在一个 n×n 的矩阵 A,其特征值刻画了邻近点的动力学行为'''(Hartman-Grobman 定理 Hartman–Grobman theorem)'''。更确切地说,如果矩阵所有的特征值都是负实数或实部为负的复数,那么这个平衡点就是一个稳定的吸引子,并且附近的点以指数速率收敛到它,参考'''李雅普诺夫稳定性 Lyapunov stability'''和'''指数稳定性 Exponential stability'''。如果所有的特征值都不是纯虚数(或零) ,那么吸引方向和排斥方向都与矩阵 A 的特征空间有关,其特征值的实部分别为负和正。对于更复杂的轨道上的扰动情形,也有类似的表述。<br />
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==不动点稳定性==<br />
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最简单的一种轨道就是一个不动点,称为平衡态,或者叫做平衡点。如果一个力学系统处于稳定的平衡状态,那么只需要一个很小的推力就会导致局部运动的发生,例如,类似钟摆那样的小规模的振动。在有阻尼的系统中,稳定的平衡态是渐近稳定的<ref> Hui Y , Michel A N , Ling H . Stability theory for hybrid dynamical systems[C]// IEEE Conference on Decision & Control. IEEE, 2002.</ref>。另一方面,对于一个不稳定的平衡,例如一个球停留在山顶的最高顶点上,一个极其微小的推力就会导致一个大幅度的运动,这个运动可能会也可能不会收敛到原始状态。<br />
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对于线性系统而言,存在许多行之有效的测试方法来检验线性系统的稳定性。非线性系统的稳定性通常可以首先考虑其线性化的系统,并从其线性化系统的稳定性中推断出原非线性系统的稳定性。<br />
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===映射===<br />
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设 {{Math|''f'': '''R''' → '''R'''}}是一个连续可微函数,且存在一个不动点{{Math|''a''}},使得 {{Math|1=''f''(''a'') = ''a''}}。<br />
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考虑一个通过迭代函数得到的动力系统:<br />
:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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当函数 {{Math|''f''}} 在 {{Math|''a''}} 点的导数的绝对值严格小于1时,不动点是稳定的;当在 {{Math|''a''}} 点的导数严格大于1时是不稳定的。这是因为在这个点附近,函数的斜率具有的线性近似值为:<br />
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:<math> f(x) \approx f(a)+f'(a)(x-a). </math><br />
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因此<br />
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:<math>x_{n+1}-x_{n} = f(x_n)-x_n \simeq f(a) + f'(a)(x_n-a)-x_n = a + f'(a)(x_n-a)-x_n = (f'(a)-1)(x_n-a) \to \frac{x_{n+1}-x_{n}}{x_n-a}=f'(a)-1</math><br />
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这意味着导数测量的是函数连续迭代接近或偏离不动点 {{Math|''a''}} 的速率。如果不动点 {{Math|''a''}} 处的导数恰好是1或-1,那么就需要更多的信息才能判断系统的稳定性。<br />
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对于具有一个不动点 {{Math|''a''}} 的连续可微映射 {{Math|''f'': '''R'''<sup>''n''</sup> → '''R'''<sup>''n''</sup>}},存在一个类似的判据,由 {{Math|''a''}} 的雅可比矩阵 {{Math|''J''<sub>''a''</sub>(''f'')}} 表示。<br />
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如果 {{Math|''J''}} 的所有特征值都是绝对值严格小于1的实数或复数,则该点是稳定不动点;<br />
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如果{{Math|''J''}} 的所有特征值中至少有一个的绝对值严格大于1,则它是不稳定的。<br />
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对于{{Math|''J''}} 的最大特征值的绝对值等于1的情况,需要进一步研究。仅仅使用雅可比矩阵检验是无法确定稳定性类型的。同样的准则对光滑流形的微分同胚情况也有着广泛的适用性。<br />
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===线性自治系统===<br />
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如我们所知,线性系统是一类数学模型,指的是由线性运算子组成的系统,也就是说,这类系统首先满足线性的特性<ref>Luenberger D G . Observing the State of a Linear System[J]. IEEE Transactions on Military Electronics, 2007, 8(2):74-80.</ref>。相较于非线性系统,线性系统的特性比较简单。<br />
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根据系统矩阵A是否随时间变化,引入'''自治系统 autonomous system'''的概念后,可以把线性系统分为自治的和非自治的,对于线性系统一般也可以称为定常的和时变的,也就是说:<br />
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(1)自治的线性系统就是定常线性系统。<br />
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(2)而非自治的线性系统就是时变线性系统。<br />
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对于非线性系统,就可以分为非线性自治系统和非线性非自治系统。<br />
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这里我们首先考察线性自治系统,利用常系数一阶线性微分方程组对应系数矩阵的特征值,便可以分析其不动点的稳定性。<br />
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对于一个如下的'''自治系统 autonomous system'''<br />
:<math>x' = Ax,</math><br />
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当 {{Math|''x''(''t'') ∈ '''R'''<sup>''n''</sup>}} 且 {{Math|''A''}} 是一个 {{Math|''n''×''n''}} 的实矩阵时,它具有常数解<br />
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:<math>x(t)=0.</math><br />
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:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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可以这样描述:最初的原点({{Math|0 ∈ '''R'''<sup>''n''</sup>}} ) 是该动力系统的平衡点。当且仅当对于{{Math|''A''}}的所有特征值 {{Math|''λ''}} 有 {{Math|Re(''λ'') < 0}} 时,这个解是随着{{Math|''t'' → ∞}}是渐近稳定的(未来趋势)。类似地,当且仅当对于 {{Math|''A''}} 的所有特征值 {{Math|''λ''}} 有{{Math|Re(''λ'') > 0}} 时,系统随着{{Math|''t'' → -∞}}是渐近稳定的(负号表示方向指向过去趋势)。如果存在一个{{Math|''A''}}的特征值 {{Math|''λ''}} 使得 {{Math|Re(''λ'') > 0}},则该解在{{Math|''t'' → ∞}}时是不稳定的。<br />
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为了判定线性系统原点的稳定性,可以使用劳斯-赫尔维茨稳定性判据'''Routh–Hurwitz stability criterion''',来将这一结果应用在实践中。矩阵的特征值是其特征多项式的根。如果所有根的实部都是严格负的,那么一个具有实系数的单变量多项式称为赫尔维茨多项式 '''Hurwitz polynomial''' 。劳斯-赫尔维茨定理 '''Routh–Hurwitz theorem'''通过一种避免计算根的算法来描述赫尔维茨多项式的特征。<br />
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===非线性自治系统===<br />
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前面我们介绍了线性自治系统的稳定性判断,这里我们来考察非线性自治系统的情况。非线性系统不动点的渐近稳定性通常可以用 Hartman-Grobman 定理来判断。<br />
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假设{{Math|''v''}}是{{Math|'''R'''<sup>''n''</sup>}}上的一个{{Math|''C''<sup>1</sup>}}-向量场,并且下降至某一点{{Math|''p''}}有{{Math|1=''v''(''p'') = 0}}。那么相应的自治系统<br />
:<math>x'=v(x)</math><br />
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有一个常数解<br />
:<math> x(t)=p.</math><br />
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设{{Math|''J''<sub>''p''</sub>(''v'')}}为向量场 {{Math|''v''}}在点{{Math|''p''}}的{{Math|''n''×''n''}}'''雅可比矩阵 Jacobian matrix'''。如果 {{Math|''J''}} 的所有特征值都具有严格负的实部,则系统的解是渐近稳定的。这个条件可以用劳斯-赫尔维茨判据'''Routh–Hurwitz stability criterion'''来检验。<br />
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<br />
==一般动力系统的李雅普诺夫函数==<br />
<br />
'''李雅普诺夫函数 Lyapunov functions'''在稳定性分析和控制理论中都起着重要的作用,它的应用使得许多领域中的一系列问题的解决变得相对容易,尤其是在一些应用型的分析领域中。在常微分方程理论中,可用它来证明常微分方程平衡点的稳定性<ref>Branicky, M. S . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL AC, 1998, 43(4):475-482.</ref>。所以我们建立动力系统的李雅普诺夫稳定性或渐近稳定的一般方法即是利用李亚普诺夫函数来分析。<br />
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<br />
==拓展阅读==<br />
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*渐近稳定性 Asymptotic stability <br />
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*超稳定性 Hyperstability <br />
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*线性稳定性 Linear stability <br />
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*轨道稳定性 Orbital stability <br />
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*稳定性判据 Stability criterion <br />
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*稳定半径 Stability radius <br />
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*[[结构稳定性]] Structural stability <br />
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*冯诺依曼稳定性分析 Von Neumann stability analysis<br />
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<br />
==参考文献==<br />
<br />
{{Reflist}}<br />
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<br />
==外部链接==<br />
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*[http://demonstrations.wolfram.com/StableEquilibria/ Stable Equilibria] 源于Michael Schreiber,Wolfram示范项目。<br />
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===编者推荐===<br />
<br />
==编者推荐==<br />
===集智课程===<br />
[https://campus.swarma.org/course/1641 动力系统分析]<br />
[[file:7bbbe372ca1517de5c9b70a8f75560c1.png|right|thumb|350px|]]<br />
<br />
本课程北京师范大学系统科学学院教授王大辉讲授,主要讲授连续和离散动力系统的定态、极限环及其稳定性分析、动力学系统的结构稳定性和常见的分支类型以及分析方法,混沌概念等。<br />
<br />
本课程是系统科学专业的学位基础课,是系统科学博士研究生培养的基础课程。主要培养硕士、博士研究生从动力学演化角度观察世界的能力,并可以分析具体的动力学系统,能够分析研究对象中随时间变化的状态变量以及变量之间的关系,建立动力学方程并进行定性和定量的分析,是非线性系统控制、控制理论、复杂系统建模与分析以及系统生物学等专业课的理论基础,应用领域涉及国防、科技、经济、工业和农业的各个方面。<br />
<br />
<br />
[https://campus.swarma.org/course/1691 结构稳定性与中心流形]<br />
<br />
本课程中,讨论了在非双曲平衡点,如何利用中心流形定理对系统的结构稳定性进行分析。时长为35min。<br />
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[https://campus.swarma.org/course/1684 动力系统稳定性初步]<br />
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本课程中,介绍判断动力系统稳定性的两种思路,轨道稳定性与状态稳定性,及具体的判断方法。时长为1h57min。<br />
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===集智文章===<br />
[https://swarma.org/?p=31718 PRL前沿:热力学稳定性意味着因果关系]<br />
[[file:wxsync-2022-01-38fa575df272b3657923b6d64b20c376.jpeg|right|thumb|350px|]]<br />
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相对论流体力学理论的稳定性条件可以直接从平衡态时熵应最大化这一要求推导出来。1月6日发表在PRL上的一项最新研究用一个简单的几何论证证明,如果流体力学理论根据这个熵判据是稳定的,那么对平衡态的局部扰动不能传播到它们的未来光锥外。也就是说,在相对论流体力学中,非因果理论在热力学上必须是不稳定的,至少在接近平衡态如此。研究表明,稳定性和因果关系之间这种深层联系的物理根源在于熵和信息之间的关系。<br />
<br />
<br />
[https://swarma.org/?p=26366 货币的层级结构与金融不稳定性假说 | 复杂经济学读书会]<br />
<br />
复杂经济学读书会第15期,我们邀请到钟华(北京师范大学系统科学学院2019级博士生)和王势与谋(北京师范大学系统科学学院研究助理)做客集智俱乐部直播间,来分享两个经典话题,一是讨论货币的内在层次结构,二是分析金融不稳定性假说。<br />
<br />
Perry Mehrling 认为一些固有的思维定势会影响到思考,这些思维定势可能来源于以前日常生活中,或者是以往的经济学课程中形成的。<br />
<br />
但这些思维方式存在着一定的局限性,我们需要用一种不同的方式来思考货币体系,也就是要提出的层级体系的概念。在文中,他区分了货币的层级结构、金融机构的层级结构、货币体系的层级结构以及做市商的层级结构等。<br />
<br />
通过层级分析,他认为已有的各种理论都只是捕捉到了货币体系整体的一部分,并不是货币体系的完整真相,并以此从一个全新的视角解读了经济危机以及中央银行“最后贷款人”的作用。<br />
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本中文词条由[[用户:Bnustv|Bnustv]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E7%A8%B3%E5%AE%9A%E6%80%A7%E7%90%86%E8%AE%BA&diff=29438稳定性理论2022-03-22T14:37:32Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=微分方程,动力系统,线性自治系统<br />
|description=稳定性理论被用于研究微分方程解的稳定性和动力系统在初始条件的微小扰动下轨迹的稳定性问题。<br />
}}<br />
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{{short description|Part of mathematics that addresses the stability of solutions}}<br />
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在数学上,'''稳定性理论 Stability theory'''被用于研究'''微分方程Differential equation'''解的稳定性和'''动力系统 Dynamical system'''在初始条件的微小扰动下轨迹的稳定性问题。例如,'''热传导方程 Heat equation'''是一个稳定的偏微分方程,因为'''极大值原理 Maximum principle'''的存在,初始数据的微小扰动会导致温度随之产生微小的变化。在偏微分方程中,人们可以使用 <math>Lp</math> 范数或 <math>sup</math> 范数来度量函数之间的距离,而在微分几何中,人们可以使用Gromov–Hausdorff距离来度量空间之间的距离<ref> Duplij S . Gromov–Hausdorff Distance[M]. 2003.</ref>。<br />
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在动力系统中,如果一条'''轨道 Orbit'''上任意点的前向轨道都处于一个足够小的邻域内,或者这条轨道整体停留在一个邻域(一般是较小的邻域,也有可能是较大的邻域)内,则称该轨道的状态为'''李雅普诺夫稳定 Lyapunov stable'''。有各种标准来证明轨道的稳定性或不稳定性。在适当的条件下,这个问题可以简化为一个涉及矩阵'''特征值 Eigenvalue'''的问题,关于这类矩阵特征值的问题已被大量研究并且该领域已经比较成熟。一种更一般的方法涉及'''李雅普诺夫函数 Lyapunov function'''。在实践中,很多'''稳定性判据 Stability criterion'''都可以使用,我们可以使用其中的任何一个作为判断系统稳定性的准则。<br />
[[File:Stability_Diagram.png|thumb|550px|稳定性图将'''庞加莱映射 Poincaré map''' 根据其特征划分为稳定或不稳定区间。<br/>如图可见,图中下半部分区域中系统的稳定性增加。<ref>[http://www.egwald.ca/linearalgebra/lineardifferentialequationsstabilityanalysis.php Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis] Accessed 10 October 2019.</ref>|链接=Special:FilePath/Stability_Diagram.png]]<br />
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常微分方程在经历了长期的求精确解的努力后逐渐停滞,庞加莱在分析的基础上引入几何方法,开创了常微分方程定性理论,同时在分析中引入几何方法,搭建起分析与几何之间的沟通桥梁,带来了微分方程研究的新突破。李雅普诺夫则在庞加莱定性分析的基础上 ,转而进入了新的稳定性研究。如今 ,李雅普诺夫稳定性理论被普遍认为是微分方程定性理论的基本成就之一。不仅有精确的定义 ,更有严格的分析证明 ,将微分方程及稳定性理论的研究推向了新的高度。庞加莱被公认是19世纪后四分之一和二十世纪初的领袖数学家,是对于数学和它的应用具有全面知识的最后一个人,他在数学方面的杰出工作对20世纪和当今的数学造成极其深远的影响。'''庞加莱映射 Poincaré map'''是由相空间中轨道运动定义的一种映射,是当轨道反复穿越同一截面时,反映后继点对先行点依赖关系的映射<ref>Perko. Differential equations and dynamical systems[M]. Springer, 2001.</ref>。一个连续非线性动力系统的求解是非常困难的,庞加莱给出了相图分析法。在相图中虽然不能定量地知道物理量随时间的变化,但可以定性地得到轨线的形态类型及其拓扑结构,从而了解动力系统运动的全局图像。为了更清楚了解高维相空间运动的形态,在连续运动的轨线上用一个截面(称庞加莱截面)将其横截,轨线在截面上穿过的情况就可以简捷地判断运动的形态。对于庞加莱映射是稳定的还是不稳定的判断则取决于其特征,如图所示,在相空间区间中向下的方向上稳定性增加。<br />
<br />
<br />
==动力系统概述==<br />
<br />
微分方程和动力系统定性理论的许多部分关心系统或者方程解的渐近性质及其轨迹,这也意味着系统经过很长时间后会发生什么 <ref>Palis J , Melo W D . Geometric theory of dynamical systems[J]. Springer-Verlag, 1982, 10.1007/978-1-4612-5703-5.</ref>。系统最简单的行为表现为'''平衡点 Equilibrium points'''或不动点,以及'''周期轨道 Periodic orbit'''。如果我们已经很好地理解了一个特定的轨道,那么很自然地就会问下一个问题:初始条件的一个微小变化对于系统来说是否仍会保持类似的行为。稳定性理论解决了以下问题:附近的轨道是否会无限靠近给定的轨道?已知的轨道会收敛到给定的轨道吗?在前一种情况下,轨道被称为是'''稳定 Stable'''的;在后一种情况下,轨道是'''渐近稳定 Asymptotically stable '''的,并且收敛到给定的轨道称为'''吸引子 Attractor'''<ref>Zaslavsky G M . The simplest case of a strange attractor[J]. Physics Letters A, 1978, 69(3):145-147.</ref>。<br />
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对于一个一阶常微分方程自治系统的平衡解<math>f_e</math>:<br />
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*如果对于任意(小的)<math>\epsilon > 0</math>,存在<math>\delta > 0 </math>,使得只要初始条件与平衡点的距离在<math> \delta </math>范围内,例如<math> \| f(t_0) - f_e \| < \delta</math>,就有,对任何<math> t \ge t_0 </math>满足解 <math>f(t) </math> 与平衡点的距离在 <math> \epsilon </math> 范围内,例如<math>\| f(t) - f_e \| < \epsilon</math>,那么该平衡点称为稳定的。<br />
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*如果该平衡点是稳定的,并且存在 <math>\delta_0 > 0</math>,使得对于任何<math>\| f(t_0) - f_e \| < \delta_0 </math>,当<math>t \rightarrow \infty </math>时都有<math>f(t) \rightarrow f_e </math>,那么该平衡点是渐近稳定的。<br />
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稳定性意味着在微小的扰动下轨迹不会发生太大的变化。相反的情况中,微小的扰动会使得轨迹发生较大变化,即附近的轨道与给定的轨道互相排斥,这也是一种有趣的现象。一般来说,在某些方向对初始状态的扰动使得轨道渐近地接近给定轨道,而在其他方向的扰动则使得轨道远离给定轨道。也可能存在对初始状态在某些方向的扰动使得轨道行为变得比较复杂(比如既不会收敛也不会完全逃逸),从而稳定性理论不能对于这样的动力学状态给予充分的预测信息。<br />
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稳定性理论的关键思想之一是用轨道附近系统的线性化,来分析轨道在扰动下的定性行为。特别地,在 n 维'''相空间 Phase space'''的光滑动力系统的每个平衡点上,都存在一个 n×n 的矩阵 A,其特征值刻画了邻近点的动力学行为'''(Hartman-Grobman 定理 Hartman–Grobman theorem)'''。更确切地说,如果矩阵所有的特征值都是负实数或实部为负的复数,那么这个平衡点就是一个稳定的吸引子,并且附近的点以指数速率收敛到它,参考'''李雅普诺夫稳定性 Lyapunov stability'''和'''指数稳定性 Exponential stability'''。如果所有的特征值都不是纯虚数(或零) ,那么吸引方向和排斥方向都与矩阵 A 的特征空间有关,其特征值的实部分别为负和正。对于更复杂的轨道上的扰动情形,也有类似的表述。<br />
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==不动点稳定性==<br />
<br />
最简单的一种轨道就是一个不动点,称为平衡态,或者叫做平衡点。如果一个力学系统处于稳定的平衡状态,那么只需要一个很小的推力就会导致局部运动的发生,例如,类似钟摆那样的小规模的振动。在有阻尼的系统中,稳定的平衡态是渐近稳定的<ref> Hui Y , Michel A N , Ling H . Stability theory for hybrid dynamical systems[C]// IEEE Conference on Decision & Control. IEEE, 2002.</ref>。另一方面,对于一个不稳定的平衡,例如一个球停留在山顶的最高顶点上,一个极其微小的推力就会导致一个大幅度的运动,这个运动可能会也可能不会收敛到原始状态。<br />
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对于线性系统而言,存在许多行之有效的测试方法来检验线性系统的稳定性。非线性系统的稳定性通常可以首先考虑其线性化的系统,并从其线性化系统的稳定性中推断出原非线性系统的稳定性。<br />
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===映射===<br />
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设 {{Math|''f'': '''R''' → '''R'''}}是一个连续可微函数,且存在一个不动点{{Math|''a''}},使得 {{Math|1=''f''(''a'') = ''a''}}。<br />
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考虑一个通过迭代函数得到的动力系统:<br />
:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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当函数 {{Math|''f''}} 在 {{Math|''a''}} 点的导数的绝对值严格小于1时,不动点是稳定的;当在 {{Math|''a''}} 点的导数严格大于1时是不稳定的。这是因为在这个点附近,函数的斜率具有的线性近似值为:<br />
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:<math> f(x) \approx f(a)+f'(a)(x-a). </math><br />
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因此<br />
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:<math>x_{n+1}-x_{n} = f(x_n)-x_n \simeq f(a) + f'(a)(x_n-a)-x_n = a + f'(a)(x_n-a)-x_n = (f'(a)-1)(x_n-a) \to \frac{x_{n+1}-x_{n}}{x_n-a}=f'(a)-1</math><br />
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这意味着导数测量的是函数连续迭代接近或偏离不动点 {{Math|''a''}} 的速率。如果不动点 {{Math|''a''}} 处的导数恰好是1或-1,那么就需要更多的信息才能判断系统的稳定性。<br />
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对于具有一个不动点 {{Math|''a''}} 的连续可微映射 {{Math|''f'': '''R'''<sup>''n''</sup> → '''R'''<sup>''n''</sup>}},存在一个类似的判据,由 {{Math|''a''}} 的雅可比矩阵 {{Math|''J''<sub>''a''</sub>(''f'')}} 表示。<br />
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如果 {{Math|''J''}} 的所有特征值都是绝对值严格小于1的实数或复数,则该点是稳定不动点;<br />
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如果{{Math|''J''}} 的所有特征值中至少有一个的绝对值严格大于1,则它是不稳定的。<br />
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对于{{Math|''J''}} 的最大特征值的绝对值等于1的情况,需要进一步研究。仅仅使用雅可比矩阵检验是无法确定稳定性类型的。同样的准则对光滑流形的微分同胚情况也有着广泛的适用性。<br />
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===线性自治系统===<br />
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如我们所知,线性系统是一类数学模型,指的是由线性运算子组成的系统,也就是说,这类系统首先满足线性的特性<ref>Luenberger D G . Observing the State of a Linear System[J]. IEEE Transactions on Military Electronics, 2007, 8(2):74-80.</ref>。相较于非线性系统,线性系统的特性比较简单。<br />
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根据系统矩阵A是否随时间变化,引入'''自治系统 autonomous system'''的概念后,可以把线性系统分为自治的和非自治的,对于线性系统一般也可以称为定常的和时变的,也就是说:<br />
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(1)自治的线性系统就是定常线性系统。<br />
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(2)而非自治的线性系统就是时变线性系统。<br />
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对于非线性系统,就可以分为非线性自治系统和非线性非自治系统。<br />
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这里我们首先考察线性自治系统,利用常系数一阶线性微分方程组对应系数矩阵的特征值,便可以分析其不动点的稳定性。<br />
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对于一个如下的'''自治系统 autonomous system'''<br />
:<math>x' = Ax,</math><br />
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当 {{Math|''x''(''t'') ∈ '''R'''<sup>''n''</sup>}} 且 {{Math|''A''}} 是一个 {{Math|''n''×''n''}} 的实矩阵时,它具有常数解<br />
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:<math>x(t)=0.</math><br />
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:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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<br />
可以这样描述:最初的原点({{Math|0 ∈ '''R'''<sup>''n''</sup>}} ) 是该动力系统的平衡点。当且仅当对于{{Math|''A''}}的所有特征值 {{Math|''λ''}} 有 {{Math|Re(''λ'') < 0}} 时,这个解是随着{{Math|''t'' → ∞}}是渐近稳定的(未来趋势)。类似地,当且仅当对于 {{Math|''A''}} 的所有特征值 {{Math|''λ''}} 有{{Math|Re(''λ'') > 0}} 时,系统随着{{Math|''t'' → -∞}}是渐近稳定的(负号表示方向指向过去趋势)。如果存在一个{{Math|''A''}}的特征值 {{Math|''λ''}} 使得 {{Math|Re(''λ'') > 0}},则该解在{{Math|''t'' → ∞}}时是不稳定的。<br />
<br />
<br />
为了判定线性系统原点的稳定性,可以使用劳斯-赫尔维茨稳定性判据'''Routh–Hurwitz stability criterion''',来将这一结果应用在实践中。矩阵的特征值是其特征多项式的根。如果所有根的实部都是严格负的,那么一个具有实系数的单变量多项式称为赫尔维茨多项式 '''Hurwitz polynomial''' 。劳斯-赫尔维茨定理 '''Routh–Hurwitz theorem'''通过一种避免计算根的算法来描述赫尔维茨多项式的特征。<br />
<br />
<br />
===非线性自治系统===<br />
<br />
前面我们介绍了线性自治系统的稳定性判断,这里我们来考察非线性自治系统的情况。非线性系统不动点的渐近稳定性通常可以用 Hartman-Grobman 定理来判断。<br />
<br />
<br />
假设{{Math|''v''}}是{{Math|'''R'''<sup>''n''</sup>}}上的一个{{Math|''C''<sup>1</sup>}}-向量场,并且下降至某一点{{Math|''p''}}有{{Math|1=''v''(''p'') = 0}}。那么相应的自治系统<br />
:<math>x'=v(x)</math><br />
<br />
有一个常数解<br />
:<math> x(t)=p.</math><br />
<br />
<br />
设{{Math|''J''<sub>''p''</sub>(''v'')}}为向量场 {{Math|''v''}}在点{{Math|''p''}}的{{Math|''n''×''n''}}'''雅可比矩阵 Jacobian matrix'''。如果 {{Math|''J''}} 的所有特征值都具有严格负的实部,则系统的解是渐近稳定的。这个条件可以用劳斯-赫尔维茨判据'''Routh–Hurwitz stability criterion'''来检验。<br />
<br />
<br />
==一般动力系统的李雅普诺夫函数==<br />
<br />
李雅普诺夫函数 Lyapunov functions在稳定性分析和控制理论中都起着重要的作用,它的应用使得许多领域中的一系列问题的解决变得相对容易,尤其是在一些应用型的分析领域中。在常微分方程理论中,可用它来证明常微分方程平衡点的稳定性<ref>Branicky, M. S . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL AC, 1998, 43(4):475-482.</ref>。所以我们建立动力系统的李雅普诺夫稳定性或渐近稳定的一般方法即是利用李亚普诺夫函数来分析。<br />
<br />
<br />
==拓展阅读==<br />
<br />
*渐近稳定性 Asymptotic stability <br />
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*超稳定性 Hyperstability <br />
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*线性稳定性 Linear stability <br />
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*轨道稳定性 Orbital stability <br />
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*稳定性判据 Stability criterion <br />
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*稳定半径 Stability radius <br />
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*[[结构稳定性]] Structural stability <br />
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*冯诺依曼稳定性分析 Von Neumann stability analysis<br />
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<br />
==参考文献==<br />
<br />
{{Reflist}}<br />
<br />
<br />
==外部链接==<br />
<br />
*[http://demonstrations.wolfram.com/StableEquilibria/ Stable Equilibria] 源于Michael Schreiber,Wolfram示范项目。<br />
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===编者推荐===<br />
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<br/><br />
----<br />
本中文词条由[[用户:Bnustv|Bnustv]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E7%A8%B3%E5%AE%9A%E6%80%A7%E7%90%86%E8%AE%BA&diff=29437稳定性理论2022-03-22T14:37:01Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=微分方程,动力系统,线性自治系统<br />
|description=稳定性理论被用于研究微分方程解的稳定性和动力系统在初始条件的微小扰动下轨迹的稳定性问题。<br />
}}<br />
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{{short description|Part of mathematics that addresses the stability of solutions}}<br />
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在数学上,'''稳定性理论 Stability theory'''被用于研究'''微分方程Differential equation'''解的稳定性和'''动力系统 Dynamical system'''在初始条件的微小扰动下轨迹的稳定性问题。例如,'''热传导方程 Heat equation'''是一个稳定的偏微分方程,因为'''极大值原理 Maximum principle'''的存在,初始数据的微小扰动会导致温度随之产生微小的变化。在偏微分方程中,人们可以使用 <math>Lp</math> 范数或 <math>sup</math> 范数来度量函数之间的距离,而在微分几何中,人们可以使用Gromov–Hausdorff距离来度量空间之间的距离<ref> Duplij S . Gromov–Hausdorff Distance[M]. 2003.</ref>。<br />
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在动力系统中,如果一条'''轨道 Orbit'''上任意点的前向轨道都处于一个足够小的邻域内,或者这条轨道整体停留在一个邻域(一般是较小的邻域,也有可能是较大的邻域)内,则称该轨道的状态为'''李雅普诺夫稳定 Lyapunov stable'''。有各种标准来证明轨道的稳定性或不稳定性。在适当的条件下,这个问题可以简化为一个涉及矩阵'''特征值 Eigenvalue'''的问题,关于这类矩阵特征值的问题已被大量研究并且该领域已经比较成熟。一种更一般的方法涉及'''李雅普诺夫函数 Lyapunov function'''。在实践中,很多'''稳定性判据 Stability criterion'''都可以使用,我们可以使用其中的任何一个作为判断系统稳定性的准则。<br />
[[File:Stability_Diagram.png|thumb|550px|稳定性图将'''庞加莱映射 Poincaré map''' 根据其特征划分为稳定或不稳定区间。如图可见,图中下半部分区域中系统的稳定性增加。<ref>[http://www.egwald.ca/linearalgebra/lineardifferentialequationsstabilityanalysis.php Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis] Accessed 10 October 2019.</ref>|链接=Special:FilePath/Stability_Diagram.png]]<br />
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<br />
常微分方程在经历了长期的求精确解的努力后逐渐停滞,庞加莱在分析的基础上引入几何方法,开创了常微分方程定性理论,同时在分析中引入几何方法,搭建起分析与几何之间的沟通桥梁,带来了微分方程研究的新突破。李雅普诺夫则在庞加莱定性分析的基础上 ,转而进入了新的稳定性研究。如今 ,李雅普诺夫稳定性理论被普遍认为是微分方程定性理论的基本成就之一。不仅有精确的定义 ,更有严格的分析证明 ,将微分方程及稳定性理论的研究推向了新的高度。庞加莱被公认是19世纪后四分之一和二十世纪初的领袖数学家,是对于数学和它的应用具有全面知识的最后一个人,他在数学方面的杰出工作对20世纪和当今的数学造成极其深远的影响。'''庞加莱映射 Poincaré map'''是由相空间中轨道运动定义的一种映射,是当轨道反复穿越同一截面时,反映后继点对先行点依赖关系的映射<ref>Perko. Differential equations and dynamical systems[M]. Springer, 2001.</ref>。一个连续非线性动力系统的求解是非常困难的,庞加莱给出了相图分析法。在相图中虽然不能定量地知道物理量随时间的变化,但可以定性地得到轨线的形态类型及其拓扑结构,从而了解动力系统运动的全局图像。为了更清楚了解高维相空间运动的形态,在连续运动的轨线上用一个截面(称庞加莱截面)将其横截,轨线在截面上穿过的情况就可以简捷地判断运动的形态。对于庞加莱映射是稳定的还是不稳定的判断则取决于其特征,如图所示,在相空间区间中向下的方向上稳定性增加。<br />
<br />
<br />
==动力系统概述==<br />
<br />
微分方程和动力系统定性理论的许多部分关心系统或者方程解的渐近性质及其轨迹,这也意味着系统经过很长时间后会发生什么 <ref>Palis J , Melo W D . Geometric theory of dynamical systems[J]. Springer-Verlag, 1982, 10.1007/978-1-4612-5703-5.</ref>。系统最简单的行为表现为'''平衡点 Equilibrium points'''或不动点,以及'''周期轨道 Periodic orbit'''。如果我们已经很好地理解了一个特定的轨道,那么很自然地就会问下一个问题:初始条件的一个微小变化对于系统来说是否仍会保持类似的行为。稳定性理论解决了以下问题:附近的轨道是否会无限靠近给定的轨道?已知的轨道会收敛到给定的轨道吗?在前一种情况下,轨道被称为是'''稳定 Stable'''的;在后一种情况下,轨道是'''渐近稳定 Asymptotically stable '''的,并且收敛到给定的轨道称为'''吸引子 Attractor'''<ref>Zaslavsky G M . The simplest case of a strange attractor[J]. Physics Letters A, 1978, 69(3):145-147.</ref>。<br />
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<br />
对于一个一阶常微分方程自治系统的平衡解<math>f_e</math>:<br />
<br />
<br />
*如果对于任意(小的)<math>\epsilon > 0</math>,存在<math>\delta > 0 </math>,使得只要初始条件与平衡点的距离在<math> \delta </math>范围内,例如<math> \| f(t_0) - f_e \| < \delta</math>,就有,对任何<math> t \ge t_0 </math>满足解 <math>f(t) </math> 与平衡点的距离在 <math> \epsilon </math> 范围内,例如<math>\| f(t) - f_e \| < \epsilon</math>,那么该平衡点称为稳定的。<br />
<br />
<br />
*如果该平衡点是稳定的,并且存在 <math>\delta_0 > 0</math>,使得对于任何<math>\| f(t_0) - f_e \| < \delta_0 </math>,当<math>t \rightarrow \infty </math>时都有<math>f(t) \rightarrow f_e </math>,那么该平衡点是渐近稳定的。<br />
<br />
<br />
稳定性意味着在微小的扰动下轨迹不会发生太大的变化。相反的情况中,微小的扰动会使得轨迹发生较大变化,即附近的轨道与给定的轨道互相排斥,这也是一种有趣的现象。一般来说,在某些方向对初始状态的扰动使得轨道渐近地接近给定轨道,而在其他方向的扰动则使得轨道远离给定轨道。也可能存在对初始状态在某些方向的扰动使得轨道行为变得比较复杂(比如既不会收敛也不会完全逃逸),从而稳定性理论不能对于这样的动力学状态给予充分的预测信息。<br />
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<br />
稳定性理论的关键思想之一是用轨道附近系统的线性化,来分析轨道在扰动下的定性行为。特别地,在 n 维'''相空间 Phase space'''的光滑动力系统的每个平衡点上,都存在一个 n×n 的矩阵 A,其特征值刻画了邻近点的动力学行为'''(Hartman-Grobman 定理 Hartman–Grobman theorem)'''。更确切地说,如果矩阵所有的特征值都是负实数或实部为负的复数,那么这个平衡点就是一个稳定的吸引子,并且附近的点以指数速率收敛到它,参考'''李雅普诺夫稳定性 Lyapunov stability'''和'''指数稳定性 Exponential stability'''。如果所有的特征值都不是纯虚数(或零) ,那么吸引方向和排斥方向都与矩阵 A 的特征空间有关,其特征值的实部分别为负和正。对于更复杂的轨道上的扰动情形,也有类似的表述。<br />
<br />
<br />
==不动点稳定性==<br />
<br />
最简单的一种轨道就是一个不动点,称为平衡态,或者叫做平衡点。如果一个力学系统处于稳定的平衡状态,那么只需要一个很小的推力就会导致局部运动的发生,例如,类似钟摆那样的小规模的振动。在有阻尼的系统中,稳定的平衡态是渐近稳定的<ref> Hui Y , Michel A N , Ling H . Stability theory for hybrid dynamical systems[C]// IEEE Conference on Decision & Control. IEEE, 2002.</ref>。另一方面,对于一个不稳定的平衡,例如一个球停留在山顶的最高顶点上,一个极其微小的推力就会导致一个大幅度的运动,这个运动可能会也可能不会收敛到原始状态。<br />
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对于线性系统而言,存在许多行之有效的测试方法来检验线性系统的稳定性。非线性系统的稳定性通常可以首先考虑其线性化的系统,并从其线性化系统的稳定性中推断出原非线性系统的稳定性。<br />
<br />
<br />
===映射===<br />
<br />
设 {{Math|''f'': '''R''' → '''R'''}}是一个连续可微函数,且存在一个不动点{{Math|''a''}},使得 {{Math|1=''f''(''a'') = ''a''}}。<br />
<br />
<br />
考虑一个通过迭代函数得到的动力系统:<br />
:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
<br />
<br />
当函数 {{Math|''f''}} 在 {{Math|''a''}} 点的导数的绝对值严格小于1时,不动点是稳定的;当在 {{Math|''a''}} 点的导数严格大于1时是不稳定的。这是因为在这个点附近,函数的斜率具有的线性近似值为:<br />
<br />
:<math> f(x) \approx f(a)+f'(a)(x-a). </math><br />
<br />
<br />
因此<br />
<br />
:<math>x_{n+1}-x_{n} = f(x_n)-x_n \simeq f(a) + f'(a)(x_n-a)-x_n = a + f'(a)(x_n-a)-x_n = (f'(a)-1)(x_n-a) \to \frac{x_{n+1}-x_{n}}{x_n-a}=f'(a)-1</math><br />
<br />
<br />
这意味着导数测量的是函数连续迭代接近或偏离不动点 {{Math|''a''}} 的速率。如果不动点 {{Math|''a''}} 处的导数恰好是1或-1,那么就需要更多的信息才能判断系统的稳定性。<br />
<br />
<br />
对于具有一个不动点 {{Math|''a''}} 的连续可微映射 {{Math|''f'': '''R'''<sup>''n''</sup> → '''R'''<sup>''n''</sup>}},存在一个类似的判据,由 {{Math|''a''}} 的雅可比矩阵 {{Math|''J''<sub>''a''</sub>(''f'')}} 表示。<br />
<br />
<br />
如果 {{Math|''J''}} 的所有特征值都是绝对值严格小于1的实数或复数,则该点是稳定不动点;<br />
<br />
如果{{Math|''J''}} 的所有特征值中至少有一个的绝对值严格大于1,则它是不稳定的。<br />
<br />
<br />
对于{{Math|''J''}} 的最大特征值的绝对值等于1的情况,需要进一步研究。仅仅使用雅可比矩阵检验是无法确定稳定性类型的。同样的准则对光滑流形的微分同胚情况也有着广泛的适用性。<br />
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===线性自治系统===<br />
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如我们所知,线性系统是一类数学模型,指的是由线性运算子组成的系统,也就是说,这类系统首先满足线性的特性<ref>Luenberger D G . Observing the State of a Linear System[J]. IEEE Transactions on Military Electronics, 2007, 8(2):74-80.</ref>。相较于非线性系统,线性系统的特性比较简单。<br />
<br />
<br />
根据系统矩阵A是否随时间变化,引入'''自治系统 autonomous system'''的概念后,可以把线性系统分为自治的和非自治的,对于线性系统一般也可以称为定常的和时变的,也就是说:<br />
<br />
(1)自治的线性系统就是定常线性系统。<br />
<br />
(2)而非自治的线性系统就是时变线性系统。<br />
<br />
<br />
对于非线性系统,就可以分为非线性自治系统和非线性非自治系统。<br />
<br />
这里我们首先考察线性自治系统,利用常系数一阶线性微分方程组对应系数矩阵的特征值,便可以分析其不动点的稳定性。<br />
<br />
<br />
对于一个如下的'''自治系统 autonomous system'''<br />
:<math>x' = Ax,</math><br />
<br />
当 {{Math|''x''(''t'') ∈ '''R'''<sup>''n''</sup>}} 且 {{Math|''A''}} 是一个 {{Math|''n''×''n''}} 的实矩阵时,它具有常数解<br />
<br />
:<math>x(t)=0.</math><br />
<br />
:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
<br />
<br />
可以这样描述:最初的原点({{Math|0 ∈ '''R'''<sup>''n''</sup>}} ) 是该动力系统的平衡点。当且仅当对于{{Math|''A''}}的所有特征值 {{Math|''λ''}} 有 {{Math|Re(''λ'') < 0}} 时,这个解是随着{{Math|''t'' → ∞}}是渐近稳定的(未来趋势)。类似地,当且仅当对于 {{Math|''A''}} 的所有特征值 {{Math|''λ''}} 有{{Math|Re(''λ'') > 0}} 时,系统随着{{Math|''t'' → -∞}}是渐近稳定的(负号表示方向指向过去趋势)。如果存在一个{{Math|''A''}}的特征值 {{Math|''λ''}} 使得 {{Math|Re(''λ'') > 0}},则该解在{{Math|''t'' → ∞}}时是不稳定的。<br />
<br />
<br />
为了判定线性系统原点的稳定性,可以使用劳斯-赫尔维茨稳定性判据'''Routh–Hurwitz stability criterion''',来将这一结果应用在实践中。矩阵的特征值是其特征多项式的根。如果所有根的实部都是严格负的,那么一个具有实系数的单变量多项式称为赫尔维茨多项式 '''Hurwitz polynomial''' 。劳斯-赫尔维茨定理 '''Routh–Hurwitz theorem'''通过一种避免计算根的算法来描述赫尔维茨多项式的特征。<br />
<br />
<br />
===非线性自治系统===<br />
<br />
前面我们介绍了线性自治系统的稳定性判断,这里我们来考察非线性自治系统的情况。非线性系统不动点的渐近稳定性通常可以用 Hartman-Grobman 定理来判断。<br />
<br />
<br />
假设{{Math|''v''}}是{{Math|'''R'''<sup>''n''</sup>}}上的一个{{Math|''C''<sup>1</sup>}}-向量场,并且下降至某一点{{Math|''p''}}有{{Math|1=''v''(''p'') = 0}}。那么相应的自治系统<br />
:<math>x'=v(x)</math><br />
<br />
有一个常数解<br />
:<math> x(t)=p.</math><br />
<br />
<br />
设{{Math|''J''<sub>''p''</sub>(''v'')}}为向量场 {{Math|''v''}}在点{{Math|''p''}}的{{Math|''n''×''n''}}'''雅可比矩阵 Jacobian matrix'''。如果 {{Math|''J''}} 的所有特征值都具有严格负的实部,则系统的解是渐近稳定的。这个条件可以用劳斯-赫尔维茨判据'''Routh–Hurwitz stability criterion'''来检验。<br />
<br />
<br />
==一般动力系统的李雅普诺夫函数==<br />
<br />
李雅普诺夫函数 Lyapunov functions在稳定性分析和控制理论中都起着重要的作用,它的应用使得许多领域中的一系列问题的解决变得相对容易,尤其是在一些应用型的分析领域中。在常微分方程理论中,可用它来证明常微分方程平衡点的稳定性<ref>Branicky, M. S . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL AC, 1998, 43(4):475-482.</ref>。所以我们建立动力系统的李雅普诺夫稳定性或渐近稳定的一般方法即是利用李亚普诺夫函数来分析。<br />
<br />
<br />
==拓展阅读==<br />
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*渐近稳定性 Asymptotic stability <br />
<br />
*超稳定性 Hyperstability <br />
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*线性稳定性 Linear stability <br />
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*轨道稳定性 Orbital stability <br />
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*稳定性判据 Stability criterion <br />
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*稳定半径 Stability radius <br />
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*[[结构稳定性]] Structural stability <br />
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*冯诺依曼稳定性分析 Von Neumann stability analysis<br />
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<br />
==参考文献==<br />
<br />
{{Reflist}}<br />
<br />
<br />
==外部链接==<br />
<br />
*[http://demonstrations.wolfram.com/StableEquilibria/ Stable Equilibria] 源于Michael Schreiber,Wolfram示范项目。<br />
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===编者推荐===<br />
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<br />
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<br/><br />
----<br />
本中文词条由[[用户:Bnustv|Bnustv]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E7%A8%B3%E5%AE%9A%E6%80%A7%E7%90%86%E8%AE%BA&diff=29436稳定性理论2022-03-22T14:33:36Z<p>唐糖糖:</p>
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<div>{{#seo:<br />
|keywords=微分方程,动力系统,线性自治系统<br />
|description=稳定性理论被用于研究微分方程解的稳定性和动力系统在初始条件的微小扰动下轨迹的稳定性问题。<br />
}}<br />
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{{short description|Part of mathematics that addresses the stability of solutions}}<br />
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在数学上,'''稳定性理论 Stability theory'''被用于研究'''微分方程Differential equation'''解的稳定性和'''动力系统 Dynamical system'''在初始条件的微小扰动下轨迹的稳定性问题。例如,'''热传导方程 Heat equation'''是一个稳定的偏微分方程,因为'''极大值原理 Maximum principle'''的存在,初始数据的微小扰动会导致温度随之产生微小的变化。在偏微分方程中,人们可以使用 <math>Lp</math> 范数或 <math>sup</math> 范数来度量函数之间的距离,而在微分几何中,人们可以使用Gromov–Hausdorff距离来度量空间之间的距离<ref> Duplij S . Gromov–Hausdorff Distance[M]. 2003.</ref>。<br />
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在动力系统中,如果一条'''轨道 Orbit'''上任意点的前向轨道都处于一个足够小的邻域内,或者这条轨道整体停留在一个邻域(一般是较小的邻域,也有可能是较大的邻域)内,则称该轨道的状态为'''李雅普诺夫稳定 Lyapunov stable'''。有各种标准来证明轨道的稳定性或不稳定性。在适当的条件下,这个问题可以简化为一个涉及矩阵'''特征值 Eigenvalue'''的问题,关于这类矩阵特征值的问题已被大量研究并且该领域已经比较成熟。一种更一般的方法涉及'''李雅普诺夫函数 Lyapunov function'''。在实践中,很多'''稳定性判据 Stability criterion'''都可以使用,我们可以使用其中的任何一个作为判断系统稳定性的准则。<br />
[[File:Stability_Diagram.png|thumb|550px|稳定性图将'''庞加莱映射 Poincaré map''' 根据其特征划分为稳定或不稳定区间。如图可见,图中下半部分区域中系统的稳定性增加。<ref>[http://www.egwald.ca/linearalgebra/lineardifferentialequationsstabilityanalysis.php Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis] Accessed 10 October 2019.</ref>|链接=Special:FilePath/Stability_Diagram.png]]<br />
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常微分方程在经历了长期的求精确解的努力后逐渐停滞,庞加莱在分析的基础上引入几何方法,开创了常微分方程定性理论,同时在分析中引入几何方法,搭建起分析与几何之间的沟通桥梁,带来了微分方程研究的新突破。李雅普诺夫则在庞加莱定性分析的基础上 ,转而进入了新的稳定性研究。如今 ,李雅普诺夫稳定性理论被普遍认为是微分方程定性理论的基本成就之一。不仅有精确的定义 ,更有严格的分析证明 ,将微分方程及稳定性理论的研究推向了新的高度。庞加莱被公认是19世纪后四分之一和二十世纪初的领袖数学家,是对于数学和它的应用具有全面知识的最后一个人,他在数学方面的杰出工作对20世纪和当今的数学造成极其深远的影响。'''庞加莱映射 Poincaré map'''是由相空间中轨道运动定义的一种映射,是当轨道反复穿越同一截面时,反映后继点对先行点依赖关系的映射<ref>Perko. Differential equations and dynamical systems[M]. Springer, 2001.</ref>。一个连续非线性动力系统的求解是非常困难的,庞加莱给出了相图分析法。在相图中虽然不能定量地知道物理量随时间的变化,但可以定性地得到轨线的形态类型及其拓扑结构,从而了解动力系统运动的全局图像。为了更清楚了解高维相空间运动的形态,在连续运动的轨线上用一个截面(称庞加莱截面)将其横截,轨线在截面上穿过的情况就可以简捷地判断运动的形态。对于庞加莱映射是稳定的还是不稳定的判断则取决于其特征,如图所示,在相空间区间中向下的方向上稳定性增加。<br />
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==动力系统概述==<br />
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微分方程和动力系统定性理论的许多部分关心系统或者方程解的渐近性质及其轨迹,这也意味着系统经过很长时间后会发生什么 <ref>Palis J , Melo W D . Geometric theory of dynamical systems[J]. Springer-Verlag, 1982, 10.1007/978-1-4612-5703-5.</ref>。系统最简单的行为表现为'''平衡点 Equilibrium points'''或不动点,以及'''周期轨道 Periodic orbit'''。如果我们已经很好地理解了一个特定的轨道,那么很自然地就会问下一个问题:初始条件的一个微小变化对于系统来说是否仍会保持类似的行为。稳定性理论解决了以下问题:附近的轨道是否会无限靠近给定的轨道?已知的轨道会收敛到给定的轨道吗?在前一种情况下,轨道被称为是'''稳定 Stable'''的;在后一种情况下,轨道是'''渐近稳定 Asymptotically stable '''的,并且收敛到给定的轨道称为'''吸引子 Attractor'''<ref>Zaslavsky G M . The simplest case of a strange attractor[J]. Physics Letters A, 1978, 69(3):145-147.</ref>。<br />
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对于一个一阶常微分方程自治系统的平衡解<math>f_e</math>:<br />
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*如果对于任意(小的)<math>\epsilon > 0</math>,存在<math>\delta > 0 </math>,使得只要初始条件与平衡点的距离在<math> \delta </math>范围内,例如<math> \| f(t_0) - f_e \| < \delta</math>,就有,对任何<math> t \ge t_0 </math>满足解 <math>f(t) </math> 与平衡点的距离在 <math> \epsilon </math> 范围内,例如<math>\| f(t) - f_e \| < \epsilon</math>,那么该平衡点称为稳定的。<br />
<br />
*如果该平衡点是稳定的,并且存在 <math>\delta_0 > 0</math>,使得对于任何<math>\| f(t_0) - f_e \| < \delta_0 </math>,当<math>t \rightarrow \infty </math>时都有<math>f(t) \rightarrow f_e </math>,那么该平衡点是渐近稳定的。<br />
<br />
稳定性意味着在微小的扰动下轨迹不会发生太大的变化。相反的情况中,微小的扰动会使得轨迹发生较大变化,即附近的轨道与给定的轨道互相排斥,这也是一种有趣的现象。一般来说,在某些方向对初始状态的扰动使得轨道渐近地接近给定轨道,而在其他方向的扰动则使得轨道远离给定轨道。也可能存在对初始状态在某些方向的扰动使得轨道行为变得比较复杂(比如既不会收敛也不会完全逃逸),从而稳定性理论不能对于这样的动力学状态给予充分的预测信息。<br />
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稳定性理论的关键思想之一是用轨道附近系统的线性化,来分析轨道在扰动下的定性行为。特别地,在 n 维'''相空间 Phase space'''的光滑动力系统的每个平衡点上,都存在一个 n×n 的矩阵 A,其特征值刻画了邻近点的动力学行为'''(Hartman-Grobman 定理 Hartman–Grobman theorem)'''。更确切地说,如果矩阵所有的特征值都是负实数或实部为负的复数,那么这个平衡点就是一个稳定的吸引子,并且附近的点以指数速率收敛到它,参考'''李雅普诺夫稳定性 Lyapunov stability'''和'''指数稳定性 Exponential stability'''。如果所有的特征值都不是纯虚数(或零) ,那么吸引方向和排斥方向都与矩阵 A 的特征空间有关,其特征值的实部分别为负和正。对于更复杂的轨道上的扰动情形,也有类似的表述。<br />
<br />
==不动点稳定性==<br />
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最简单的一种轨道就是一个不动点,称为平衡态,或者叫做平衡点。如果一个力学系统处于稳定的平衡状态,那么只需要一个很小的推力就会导致局部运动的发生,例如,类似钟摆那样的小规模的振动。在有阻尼的系统中,稳定的平衡态是渐近稳定的<ref> Hui Y , Michel A N , Ling H . Stability theory for hybrid dynamical systems[C]// IEEE Conference on Decision & Control. IEEE, 2002.</ref>。另一方面,对于一个不稳定的平衡,例如一个球停留在山顶的最高顶点上,一个极其微小的推力就会导致一个大幅度的运动,这个运动可能会也可能不会收敛到原始状态。<br />
<br />
对于线性系统而言,存在许多行之有效的测试方法来检验线性系统的稳定性。非线性系统的稳定性通常可以首先考虑其线性化的系统,并从其线性化系统的稳定性中推断出原非线性系统的稳定性。<br />
<br />
===映射===<br />
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设 {{Math|''f'': '''R''' → '''R'''}}是一个连续可微函数,且存在一个不动点{{Math|''a''}},使得 {{Math|1=''f''(''a'') = ''a''}}。<br />
<br />
考虑一个通过迭代函数得到的动力系统:<br />
:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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当函数 {{Math|''f''}} 在 {{Math|''a''}} 点的导数的绝对值严格小于1时,不动点是稳定的;当在 {{Math|''a''}} 点的导数严格大于1时是不稳定的。这是因为在这个点附近,函数的斜率具有的线性近似值为:<br />
<br />
:<math> f(x) \approx f(a)+f'(a)(x-a). </math><br />
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因此<br />
<br />
:<math>x_{n+1}-x_{n} = f(x_n)-x_n \simeq f(a) + f'(a)(x_n-a)-x_n = a + f'(a)(x_n-a)-x_n = (f'(a)-1)(x_n-a) \to \frac{x_{n+1}-x_{n}}{x_n-a}=f'(a)-1</math><br />
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这意味着导数测量的是函数连续迭代接近或偏离不动点 {{Math|''a''}} 的速率。如果不动点 {{Math|''a''}} 处的导数恰好是1或-1,那么就需要更多的信息才能判断系统的稳定性。<br />
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对于具有一个不动点 {{Math|''a''}} 的连续可微映射 {{Math|''f'': '''R'''<sup>''n''</sup> → '''R'''<sup>''n''</sup>}},存在一个类似的判据,由 {{Math|''a''}} 的雅可比矩阵 {{Math|''J''<sub>''a''</sub>(''f'')}} 表示。<br />
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如果 {{Math|''J''}} 的所有特征值都是绝对值严格小于1的实数或复数,则该点是稳定不动点;<br />
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如果{{Math|''J''}} 的所有特征值中至少有一个的绝对值严格大于1,则它是不稳定的。<br />
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对于{{Math|''J''}} 的最大特征值的绝对值等于1的情况,需要进一步研究。仅仅使用雅可比矩阵检验是无法确定稳定性类型的。同样的准则对光滑流形的微分同胚情况也有着广泛的适用性。<br />
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===线性自治系统===<br />
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如我们所知,线性系统是一类数学模型,指的是由线性运算子组成的系统,也就是说,这类系统首先满足线性的特性<ref>Luenberger D G . Observing the State of a Linear System[J]. IEEE Transactions on Military Electronics, 2007, 8(2):74-80.</ref>。相较于非线性系统,线性系统的特性比较简单。<br />
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根据系统矩阵A是否随时间变化,引入'''自治系统 autonomous system'''的概念后,可以把线性系统分为自治的和非自治的,对于线性系统一般也可以称为定常的和时变的,也就是说:<br />
<br />
(1)自治的线性系统就是定常线性系统。<br />
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(2)而非自治的线性系统就是时变线性系统。<br />
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对于非线性系统,就可以分为非线性自治系统和非线性非自治系统。<br />
<br />
这里我们首先考察线性自治系统,利用常系数一阶线性微分方程组对应系数矩阵的特征值,便可以分析其不动点的稳定性。<br />
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对于一个如下的'''自治系统 autonomous system'''<br />
:<math>x' = Ax,</math><br />
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当 {{Math|''x''(''t'') ∈ '''R'''<sup>''n''</sup>}} 且 {{Math|''A''}} 是一个 {{Math|''n''×''n''}} 的实矩阵时,它具有常数解<br />
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:<math>x(t)=0.</math><br />
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:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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可以这样描述:最初的原点({{Math|0 ∈ '''R'''<sup>''n''</sup>}} ) 是该动力系统的平衡点。当且仅当对于{{Math|''A''}}的所有特征值 {{Math|''λ''}} 有 {{Math|Re(''λ'') < 0}} 时,这个解是随着{{Math|''t'' → ∞}}是渐近稳定的(未来趋势)。类似地,当且仅当对于 {{Math|''A''}} 的所有特征值 {{Math|''λ''}} 有{{Math|Re(''λ'') > 0}} 时,系统随着{{Math|''t'' → -∞}}是渐近稳定的(负号表示方向指向过去趋势)。如果存在一个{{Math|''A''}}的特征值 {{Math|''λ''}} 使得 {{Math|Re(''λ'') > 0}},则该解在{{Math|''t'' → ∞}}时是不稳定的。<br />
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为了判定线性系统原点的稳定性,可以使用劳斯-赫尔维茨稳定性判据'''Routh–Hurwitz stability criterion''',来将这一结果应用在实践中。矩阵的特征值是其特征多项式的根。如果所有根的实部都是严格负的,那么一个具有实系数的单变量多项式称为赫尔维茨多项式 '''Hurwitz polynomial''' 。劳斯-赫尔维茨定理 '''Routh–Hurwitz theorem'''通过一种避免计算根的算法来描述赫尔维茨多项式的特征。<br />
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===非线性自治系统===<br />
<br />
前面我们介绍了线性自治系统的稳定性判断,这里我们来考察非线性自治系统的情况。非线性系统不动点的渐近稳定性通常可以用 Hartman-Grobman 定理来判断。<br />
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假设{{Math|''v''}}是{{Math|'''R'''<sup>''n''</sup>}}上的一个{{Math|''C''<sup>1</sup>}}-向量场,并且下降至某一点{{Math|''p''}}有{{Math|1=''v''(''p'') = 0}}。那么相应的自治系统<br />
:<math>x'=v(x)</math><br />
<br />
有一个常数解<br />
:<math> x(t)=p.</math><br />
<br />
<br />
设{{Math|''J''<sub>''p''</sub>(''v'')}}为向量场 {{Math|''v''}}在点{{Math|''p''}}的{{Math|''n''×''n''}}'''雅可比矩阵 Jacobian matrix'''。如果 {{Math|''J''}} 的所有特征值都具有严格负的实部,则系统的解是渐近稳定的。这个条件可以用劳斯-赫尔维茨判据'''Routh–Hurwitz stability criterion'''来检验。<br />
<br />
==一般动力系统的李雅普诺夫函数==<br />
<br />
李雅普诺夫函数 Lyapunov functions在稳定性分析和控制理论中都起着重要的作用,它的应用使得许多领域中的一系列问题的解决变得相对容易,尤其是在一些应用型的分析领域中。在常微分方程理论中,可用它来证明常微分方程平衡点的稳定性<ref>Branicky, M. S . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL AC, 1998, 43(4):475-482.</ref>。所以我们建立动力系统的李雅普诺夫稳定性或渐近稳定的一般方法即是利用李亚普诺夫函数来分析。<br />
<br />
==拓展阅读==<br />
<br />
*渐近稳定性 Asymptotic stability <br />
<br />
*超稳定性 Hyperstability <br />
<br />
*线性稳定性 Linear stability <br />
<br />
*轨道稳定性 Orbital stability <br />
<br />
*稳定性判据 Stability criterion <br />
<br />
*稳定半径 Stability radius <br />
<br />
*[[结构稳定性]] Structural stability <br />
<br />
*冯诺依曼稳定性分析 Von Neumann stability analysis<br />
<br />
==参考文献==<br />
<br />
{{Reflist}}<br />
<br />
==外部链接==<br />
<br />
*[http://demonstrations.wolfram.com/StableEquilibria/ Stable Equilibria] 源于Michael Schreiber,Wolfram示范项目。<br />
<br />
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===编者推荐===<br />
<br />
<br />
<br />
<br />
<br/><br />
----<br />
本中文词条由[[用户:Bnustv|Bnustv]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
<br />
<br />
'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E7%A8%B3%E5%AE%9A%E6%80%A7%E7%90%86%E8%AE%BA&diff=29435稳定性理论2022-03-22T14:31:16Z<p>唐糖糖:/* 拓展阅读 */</p>
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<div>{{#seo:<br />
|keywords=布莱恩大脑,元胞自动机<br />
|description=布莱恩的大脑(Brain's brain)是由加拿大计算机科学家布莱恩·西尔弗曼 Brian Silverman设计的元胞自动机。其特点在于,规则模拟了大脑神经元之间的信息传递规则。<br />
}}<br />
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此词条由整理和审校<br />
{{short description|Part of mathematics that addresses the stability of solutions}}<br />
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在数学上,'''稳定性理论 Stability theory'''被用于研究'''微分方程Differential equation'''解的稳定性和'''动力系统 Dynamical system'''在初始条件的微小扰动下轨迹的稳定性问题。例如,'''热传导方程 Heat equation'''是一个稳定的偏微分方程,因为'''极大值原理 Maximum principle'''的存在,初始数据的微小扰动会导致温度随之产生微小的变化。在偏微分方程中,人们可以使用 <math>Lp</math> 范数或 <math>sup</math> 范数来度量函数之间的距离,而在微分几何中,人们可以使用Gromov–Hausdorff距离来度量空间之间的距离<ref> Duplij S . Gromov–Hausdorff Distance[M]. 2003.</ref>。<br />
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在动力系统中,如果一条'''轨道 Orbit'''上任意点的前向轨道都处于一个足够小的邻域内,或者这条轨道整体停留在一个邻域(一般是较小的邻域,也有可能是较大的邻域)内,则称该轨道的状态为'''李雅普诺夫稳定 Lyapunov stable'''。有各种标准来证明轨道的稳定性或不稳定性。在适当的条件下,这个问题可以简化为一个涉及矩阵'''特征值 Eigenvalue'''的问题,关于这类矩阵特征值的问题已被大量研究并且该领域已经比较成熟。一种更一般的方法涉及'''李雅普诺夫函数 Lyapunov function'''。在实践中,很多'''稳定性判据 Stability criterion'''都可以使用,我们可以使用其中的任何一个作为判断系统稳定性的准则。<br />
[[File:Stability_Diagram.png|thumb|550px|稳定性图将'''庞加莱映射 Poincaré map''' 根据其特征划分为稳定或不稳定区间。如图可见,图中下半部分区域中系统的稳定性增加。<ref>[http://www.egwald.ca/linearalgebra/lineardifferentialequationsstabilityanalysis.php Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis] Accessed 10 October 2019.</ref>|链接=Special:FilePath/Stability_Diagram.png]]<br />
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常微分方程在经历了长期的求精确解的努力后逐渐停滞,庞加莱在分析的基础上引入几何方法,开创了常微分方程定性理论,同时在分析中引入几何方法,搭建起分析与几何之间的沟通桥梁,带来了微分方程研究的新突破。李雅普诺夫则在庞加莱定性分析的基础上 ,转而进入了新的稳定性研究。如今 ,李雅普诺夫稳定性理论被普遍认为是微分方程定性理论的基本成就之一。不仅有精确的定义 ,更有严格的分析证明 ,将微分方程及稳定性理论的研究推向了新的高度。庞加莱被公认是19世纪后四分之一和二十世纪初的领袖数学家,是对于数学和它的应用具有全面知识的最后一个人,他在数学方面的杰出工作对20世纪和当今的数学造成极其深远的影响。'''庞加莱映射 Poincaré map'''是由相空间中轨道运动定义的一种映射,是当轨道反复穿越同一截面时,反映后继点对先行点依赖关系的映射<ref>Perko. Differential equations and dynamical systems[M]. Springer, 2001.</ref>。一个连续非线性动力系统的求解是非常困难的,庞加莱给出了相图分析法。在相图中虽然不能定量地知道物理量随时间的变化,但可以定性地得到轨线的形态类型及其拓扑结构,从而了解动力系统运动的全局图像。为了更清楚了解高维相空间运动的形态,在连续运动的轨线上用一个截面(称庞加莱截面)将其横截,轨线在截面上穿过的情况就可以简捷地判断运动的形态。对于庞加莱映射是稳定的还是不稳定的判断则取决于其特征,如图所示,在相空间区间中向下的方向上稳定性增加。<br />
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==动力系统概述==<br />
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微分方程和动力系统定性理论的许多部分关心系统或者方程解的渐近性质及其轨迹,这也意味着系统经过很长时间后会发生什么 <ref>Palis J , Melo W D . Geometric theory of dynamical systems[J]. Springer-Verlag, 1982, 10.1007/978-1-4612-5703-5.</ref>。系统最简单的行为表现为'''平衡点 Equilibrium points'''或不动点,以及'''周期轨道 Periodic orbit'''。如果我们已经很好地理解了一个特定的轨道,那么很自然地就会问下一个问题:初始条件的一个微小变化对于系统来说是否仍会保持类似的行为。稳定性理论解决了以下问题:附近的轨道是否会无限靠近给定的轨道?已知的轨道会收敛到给定的轨道吗?在前一种情况下,轨道被称为是'''稳定 Stable'''的;在后一种情况下,轨道是'''渐近稳定 Asymptotically stable '''的,并且收敛到给定的轨道称为'''吸引子 Attractor'''<ref>Zaslavsky G M . The simplest case of a strange attractor[J]. Physics Letters A, 1978, 69(3):145-147.</ref>。<br />
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对于一个一阶常微分方程自治系统的平衡解<math>f_e</math>:<br />
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*如果对于任意(小的)<math>\epsilon > 0</math>,存在<math>\delta > 0 </math>,使得只要初始条件与平衡点的距离在<math> \delta </math>范围内,例如<math> \| f(t_0) - f_e \| < \delta</math>,就有,对任何<math> t \ge t_0 </math>满足解 <math>f(t) </math> 与平衡点的距离在 <math> \epsilon </math> 范围内,例如<math>\| f(t) - f_e \| < \epsilon</math>,那么该平衡点称为稳定的。<br />
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*如果该平衡点是稳定的,并且存在 <math>\delta_0 > 0</math>,使得对于任何<math>\| f(t_0) - f_e \| < \delta_0 </math>,当<math>t \rightarrow \infty </math>时都有<math>f(t) \rightarrow f_e </math>,那么该平衡点是渐近稳定的。<br />
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稳定性意味着在微小的扰动下轨迹不会发生太大的变化。相反的情况中,微小的扰动会使得轨迹发生较大变化,即附近的轨道与给定的轨道互相排斥,这也是一种有趣的现象。一般来说,在某些方向对初始状态的扰动使得轨道渐近地接近给定轨道,而在其他方向的扰动则使得轨道远离给定轨道。也可能存在对初始状态在某些方向的扰动使得轨道行为变得比较复杂(比如既不会收敛也不会完全逃逸),从而稳定性理论不能对于这样的动力学状态给予充分的预测信息。<br />
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稳定性理论的关键思想之一是用轨道附近系统的线性化,来分析轨道在扰动下的定性行为。特别地,在 n 维'''相空间 Phase space'''的光滑动力系统的每个平衡点上,都存在一个 n×n 的矩阵 A,其特征值刻画了邻近点的动力学行为'''(Hartman-Grobman 定理 Hartman–Grobman theorem)'''。更确切地说,如果矩阵所有的特征值都是负实数或实部为负的复数,那么这个平衡点就是一个稳定的吸引子,并且附近的点以指数速率收敛到它,参考'''李雅普诺夫稳定性 Lyapunov stability'''和'''指数稳定性 Exponential stability'''。如果所有的特征值都不是纯虚数(或零) ,那么吸引方向和排斥方向都与矩阵 A 的特征空间有关,其特征值的实部分别为负和正。对于更复杂的轨道上的扰动情形,也有类似的表述。<br />
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==不动点稳定性==<br />
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最简单的一种轨道就是一个不动点,称为平衡态,或者叫做平衡点。如果一个力学系统处于稳定的平衡状态,那么只需要一个很小的推力就会导致局部运动的发生,例如,类似钟摆那样的小规模的振动。在有阻尼的系统中,稳定的平衡态是渐近稳定的<ref> Hui Y , Michel A N , Ling H . Stability theory for hybrid dynamical systems[C]// IEEE Conference on Decision & Control. IEEE, 2002.</ref>。另一方面,对于一个不稳定的平衡,例如一个球停留在山顶的最高顶点上,一个极其微小的推力就会导致一个大幅度的运动,这个运动可能会也可能不会收敛到原始状态。<br />
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对于线性系统而言,存在许多行之有效的测试方法来检验线性系统的稳定性。非线性系统的稳定性通常可以首先考虑其线性化的系统,并从其线性化系统的稳定性中推断出原非线性系统的稳定性。<br />
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===映射===<br />
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设 {{Math|''f'': '''R''' → '''R'''}}是一个连续可微函数,且存在一个不动点{{Math|''a''}},使得 {{Math|1=''f''(''a'') = ''a''}}。<br />
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考虑一个通过迭代函数得到的动力系统:<br />
:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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当函数 {{Math|''f''}} 在 {{Math|''a''}} 点的导数的绝对值严格小于1时,不动点是稳定的;当在 {{Math|''a''}} 点的导数严格大于1时是不稳定的。这是因为在这个点附近,函数的斜率具有的线性近似值为:<br />
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:<math> f(x) \approx f(a)+f'(a)(x-a). </math><br />
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因此<br />
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:<math>x_{n+1}-x_{n} = f(x_n)-x_n \simeq f(a) + f'(a)(x_n-a)-x_n = a + f'(a)(x_n-a)-x_n = (f'(a)-1)(x_n-a) \to \frac{x_{n+1}-x_{n}}{x_n-a}=f'(a)-1</math><br />
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这意味着导数测量的是函数连续迭代接近或偏离不动点 {{Math|''a''}} 的速率。如果不动点 {{Math|''a''}} 处的导数恰好是1或-1,那么就需要更多的信息才能判断系统的稳定性。<br />
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对于具有一个不动点 {{Math|''a''}} 的连续可微映射 {{Math|''f'': '''R'''<sup>''n''</sup> → '''R'''<sup>''n''</sup>}},存在一个类似的判据,由 {{Math|''a''}} 的雅可比矩阵 {{Math|''J''<sub>''a''</sub>(''f'')}} 表示。<br />
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如果 {{Math|''J''}} 的所有特征值都是绝对值严格小于1的实数或复数,则该点是稳定不动点;<br />
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如果{{Math|''J''}} 的所有特征值中至少有一个的绝对值严格大于1,则它是不稳定的。<br />
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对于{{Math|''J''}} 的最大特征值的绝对值等于1的情况,需要进一步研究。仅仅使用雅可比矩阵检验是无法确定稳定性类型的。同样的准则对光滑流形的微分同胚情况也有着广泛的适用性。<br />
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===线性自治系统===<br />
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如我们所知,线性系统是一类数学模型,指的是由线性运算子组成的系统,也就是说,这类系统首先满足线性的特性<ref>Luenberger D G . Observing the State of a Linear System[J]. IEEE Transactions on Military Electronics, 2007, 8(2):74-80.</ref>。相较于非线性系统,线性系统的特性比较简单。<br />
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根据系统矩阵A是否随时间变化,引入'''自治系统 autonomous system'''的概念后,可以把线性系统分为自治的和非自治的,对于线性系统一般也可以称为定常的和时变的,也就是说:<br />
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(1)自治的线性系统就是定常线性系统。<br />
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(2)而非自治的线性系统就是时变线性系统。<br />
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对于非线性系统,就可以分为非线性自治系统和非线性非自治系统。<br />
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这里我们首先考察线性自治系统,利用常系数一阶线性微分方程组对应系数矩阵的特征值,便可以分析其不动点的稳定性。<br />
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对于一个如下的'''自治系统 autonomous system'''<br />
:<math>x' = Ax,</math><br />
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当 {{Math|''x''(''t'') ∈ '''R'''<sup>''n''</sup>}} 且 {{Math|''A''}} 是一个 {{Math|''n''×''n''}} 的实矩阵时,它具有常数解<br />
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:<math>x(t)=0.</math><br />
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:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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可以这样描述:最初的原点({{Math|0 ∈ '''R'''<sup>''n''</sup>}} ) 是该动力系统的平衡点。当且仅当对于{{Math|''A''}}的所有特征值 {{Math|''λ''}} 有 {{Math|Re(''λ'') < 0}} 时,这个解是随着{{Math|''t'' → ∞}}是渐近稳定的(未来趋势)。类似地,当且仅当对于 {{Math|''A''}} 的所有特征值 {{Math|''λ''}} 有{{Math|Re(''λ'') > 0}} 时,系统随着{{Math|''t'' → -∞}}是渐近稳定的(负号表示方向指向过去趋势)。如果存在一个{{Math|''A''}}的特征值 {{Math|''λ''}} 使得 {{Math|Re(''λ'') > 0}},则该解在{{Math|''t'' → ∞}}时是不稳定的。<br />
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为了判定线性系统原点的稳定性,可以使用劳斯-赫尔维茨稳定性判据'''Routh–Hurwitz stability criterion''',来将这一结果应用在实践中。矩阵的特征值是其特征多项式的根。如果所有根的实部都是严格负的,那么一个具有实系数的单变量多项式称为赫尔维茨多项式 '''Hurwitz polynomial''' 。劳斯-赫尔维茨定理 '''Routh–Hurwitz theorem'''通过一种避免计算根的算法来描述赫尔维茨多项式的特征。<br />
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===非线性自治系统===<br />
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前面我们介绍了线性自治系统的稳定性判断,这里我们来考察非线性自治系统的情况。非线性系统不动点的渐近稳定性通常可以用 Hartman-Grobman 定理来判断。<br />
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假设{{Math|''v''}}是{{Math|'''R'''<sup>''n''</sup>}}上的一个{{Math|''C''<sup>1</sup>}}-向量场,并且下降至某一点{{Math|''p''}}有{{Math|1=''v''(''p'') = 0}}。那么相应的自治系统<br />
:<math>x'=v(x)</math><br />
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有一个常数解<br />
:<math> x(t)=p.</math><br />
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设{{Math|''J''<sub>''p''</sub>(''v'')}}为向量场 {{Math|''v''}}在点{{Math|''p''}}的{{Math|''n''×''n''}}'''雅可比矩阵 Jacobian matrix'''。如果 {{Math|''J''}} 的所有特征值都具有严格负的实部,则系统的解是渐近稳定的。这个条件可以用劳斯-赫尔维茨判据'''Routh–Hurwitz stability criterion'''来检验。<br />
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==一般动力系统的李雅普诺夫函数==<br />
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李雅普诺夫函数 Lyapunov functions在稳定性分析和控制理论中都起着重要的作用,它的应用使得许多领域中的一系列问题的解决变得相对容易,尤其是在一些应用型的分析领域中。在常微分方程理论中,可用它来证明常微分方程平衡点的稳定性<ref>Branicky, M. S . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL AC, 1998, 43(4):475-482.</ref>。所以我们建立动力系统的李雅普诺夫稳定性或渐近稳定的一般方法即是利用李亚普诺夫函数来分析。<br />
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==拓展阅读==<br />
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*渐近稳定性 Asymptotic stability <br />
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*超稳定性 Hyperstability <br />
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*线性稳定性 Linear stability <br />
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*轨道稳定性 Orbital stability <br />
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*稳定性判据 Stability criterion <br />
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*稳定半径 Stability radius <br />
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*[[结构稳定性]] Structural stability <br />
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*冯诺依曼稳定性分析 Von Neumann stability analysis<br />
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==参考文献==<br />
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{{Reflist}}<br />
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==外部链接==<br />
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*[http://demonstrations.wolfram.com/StableEquilibria/ Stable Equilibria] 源于Michael Schreiber,Wolfram示范项目。<br />
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本中文词条由[[用户:Bnustv|Bnustv]]整理和审校,[[用户:唐糖糖|糖糖]]编辑,如有问题,欢迎在讨论页面留言。<br />
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'''本词条内容源自wikipedia及公开资料,遵守 CC3.0协议。'''</div>唐糖糖https://wiki.swarma.org/index.php?title=%E7%A8%B3%E5%AE%9A%E6%80%A7%E7%90%86%E8%AE%BA&diff=29434稳定性理论2022-03-22T14:26:39Z<p>唐糖糖:</p>
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{{short description|Part of mathematics that addresses the stability of solutions}}<br />
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在数学上,'''稳定性理论 Stability theory'''被用于研究'''微分方程Differential equation'''解的稳定性和'''动力系统 Dynamical system'''在初始条件的微小扰动下轨迹的稳定性问题。例如,'''热传导方程 Heat equation'''是一个稳定的偏微分方程,因为'''极大值原理 Maximum principle'''的存在,初始数据的微小扰动会导致温度随之产生微小的变化。在偏微分方程中,人们可以使用 <math>Lp</math> 范数或 <math>sup</math> 范数来度量函数之间的距离,而在微分几何中,人们可以使用Gromov–Hausdorff距离来度量空间之间的距离<ref> Duplij S . Gromov–Hausdorff Distance[M]. 2003.</ref>。<br />
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在动力系统中,如果一条'''轨道 Orbit'''上任意点的前向轨道都处于一个足够小的邻域内,或者这条轨道整体停留在一个邻域(一般是较小的邻域,也有可能是较大的邻域)内,则称该轨道的状态为'''李雅普诺夫稳定 Lyapunov stable'''。有各种标准来证明轨道的稳定性或不稳定性。在适当的条件下,这个问题可以简化为一个涉及矩阵'''特征值 Eigenvalue'''的问题,关于这类矩阵特征值的问题已被大量研究并且该领域已经比较成熟。一种更一般的方法涉及'''李雅普诺夫函数 Lyapunov function'''。在实践中,很多'''稳定性判据 Stability criterion'''都可以使用,我们可以使用其中的任何一个作为判断系统稳定性的准则。<br />
[[File:Stability_Diagram.png|thumb|550px|稳定性图将'''庞加莱映射 Poincaré map''' 根据其特征划分为稳定或不稳定区间。如图可见,图中下半部分区域中系统的稳定性增加。<ref>[http://www.egwald.ca/linearalgebra/lineardifferentialequationsstabilityanalysis.php Egwald Mathematics - Linear Algebra: Systems of Linear Differential Equations: Linear Stability Analysis] Accessed 10 October 2019.</ref>|链接=Special:FilePath/Stability_Diagram.png]]<br />
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常微分方程在经历了长期的求精确解的努力后逐渐停滞,庞加莱在分析的基础上引入几何方法,开创了常微分方程定性理论,同时在分析中引入几何方法,搭建起分析与几何之间的沟通桥梁,带来了微分方程研究的新突破。李雅普诺夫则在庞加莱定性分析的基础上 ,转而进入了新的稳定性研究。如今 ,李雅普诺夫稳定性理论被普遍认为是微分方程定性理论的基本成就之一。不仅有精确的定义 ,更有严格的分析证明 ,将微分方程及稳定性理论的研究推向了新的高度。庞加莱被公认是19世纪后四分之一和二十世纪初的领袖数学家,是对于数学和它的应用具有全面知识的最后一个人,他在数学方面的杰出工作对20世纪和当今的数学造成极其深远的影响。'''庞加莱映射 Poincaré map'''是由相空间中轨道运动定义的一种映射,是当轨道反复穿越同一截面时,反映后继点对先行点依赖关系的映射<ref>Perko. Differential equations and dynamical systems[M]. Springer, 2001.</ref>。一个连续非线性动力系统的求解是非常困难的,庞加莱给出了相图分析法。在相图中虽然不能定量地知道物理量随时间的变化,但可以定性地得到轨线的形态类型及其拓扑结构,从而了解动力系统运动的全局图像。为了更清楚了解高维相空间运动的形态,在连续运动的轨线上用一个截面(称庞加莱截面)将其横截,轨线在截面上穿过的情况就可以简捷地判断运动的形态。对于庞加莱映射是稳定的还是不稳定的判断则取决于其特征,如图所示,在相空间区间中向下的方向上稳定性增加。<br />
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==动力系统概述==<br />
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微分方程和动力系统定性理论的许多部分关心系统或者方程解的渐近性质及其轨迹,这也意味着系统经过很长时间后会发生什么 <ref>Palis J , Melo W D . Geometric theory of dynamical systems[J]. Springer-Verlag, 1982, 10.1007/978-1-4612-5703-5.</ref>。系统最简单的行为表现为'''平衡点 Equilibrium points'''或不动点,以及'''周期轨道 Periodic orbit'''。如果我们已经很好地理解了一个特定的轨道,那么很自然地就会问下一个问题:初始条件的一个微小变化对于系统来说是否仍会保持类似的行为。稳定性理论解决了以下问题:附近的轨道是否会无限靠近给定的轨道?已知的轨道会收敛到给定的轨道吗?在前一种情况下,轨道被称为是'''稳定 Stable'''的;在后一种情况下,轨道是'''渐近稳定 Asymptotically stable '''的,并且收敛到给定的轨道称为'''吸引子 Attractor'''<ref>Zaslavsky G M . The simplest case of a strange attractor[J]. Physics Letters A, 1978, 69(3):145-147.</ref>。<br />
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对于一个一阶常微分方程自治系统的平衡解<math>f_e</math>:<br />
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*如果对于任意(小的)<math>\epsilon > 0</math>,存在<math>\delta > 0 </math>,使得只要初始条件与平衡点的距离在<math> \delta </math>范围内,例如<math> \| f(t_0) - f_e \| < \delta</math>,就有,对任何<math> t \ge t_0 </math>满足解 <math>f(t) </math> 与平衡点的距离在 <math> \epsilon </math> 范围内,例如<math>\| f(t) - f_e \| < \epsilon</math>,那么该平衡点称为稳定的。<br />
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*如果该平衡点是稳定的,并且存在 <math>\delta_0 > 0</math>,使得对于任何<math>\| f(t_0) - f_e \| < \delta_0 </math>,当<math>t \rightarrow \infty </math>时都有<math>f(t) \rightarrow f_e </math>,那么该平衡点是渐近稳定的。<br />
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稳定性意味着在微小的扰动下轨迹不会发生太大的变化。相反的情况中,微小的扰动会使得轨迹发生较大变化,即附近的轨道与给定的轨道互相排斥,这也是一种有趣的现象。一般来说,在某些方向对初始状态的扰动使得轨道渐近地接近给定轨道,而在其他方向的扰动则使得轨道远离给定轨道。也可能存在对初始状态在某些方向的扰动使得轨道行为变得比较复杂(比如既不会收敛也不会完全逃逸),从而稳定性理论不能对于这样的动力学状态给予充分的预测信息。<br />
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稳定性理论的关键思想之一是用轨道附近系统的线性化,来分析轨道在扰动下的定性行为。特别地,在 n 维'''相空间 Phase space'''的光滑动力系统的每个平衡点上,都存在一个 n×n 的矩阵 A,其特征值刻画了邻近点的动力学行为'''(Hartman-Grobman 定理 Hartman–Grobman theorem)'''。更确切地说,如果矩阵所有的特征值都是负实数或实部为负的复数,那么这个平衡点就是一个稳定的吸引子,并且附近的点以指数速率收敛到它,参考'''李雅普诺夫稳定性 Lyapunov stability'''和'''指数稳定性 Exponential stability'''。如果所有的特征值都不是纯虚数(或零) ,那么吸引方向和排斥方向都与矩阵 A 的特征空间有关,其特征值的实部分别为负和正。对于更复杂的轨道上的扰动情形,也有类似的表述。<br />
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==不动点稳定性==<br />
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最简单的一种轨道就是一个不动点,称为平衡态,或者叫做平衡点。如果一个力学系统处于稳定的平衡状态,那么只需要一个很小的推力就会导致局部运动的发生,例如,类似钟摆那样的小规模的振动。在有阻尼的系统中,稳定的平衡态是渐近稳定的<ref> Hui Y , Michel A N , Ling H . Stability theory for hybrid dynamical systems[C]// IEEE Conference on Decision & Control. IEEE, 2002.</ref>。另一方面,对于一个不稳定的平衡,例如一个球停留在山顶的最高顶点上,一个极其微小的推力就会导致一个大幅度的运动,这个运动可能会也可能不会收敛到原始状态。<br />
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对于线性系统而言,存在许多行之有效的测试方法来检验线性系统的稳定性。非线性系统的稳定性通常可以首先考虑其线性化的系统,并从其线性化系统的稳定性中推断出原非线性系统的稳定性。<br />
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===映射===<br />
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设 {{Math|''f'': '''R''' → '''R'''}}是一个连续可微函数,且存在一个不动点{{Math|''a''}},使得 {{Math|1=''f''(''a'') = ''a''}}。<br />
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考虑一个通过迭代函数得到的动力系统:<br />
:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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当函数 {{Math|''f''}} 在 {{Math|''a''}} 点的导数的绝对值严格小于1时,不动点是稳定的;当在 {{Math|''a''}} 点的导数严格大于1时是不稳定的。这是因为在这个点附近,函数的斜率具有的线性近似值为:<br />
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:<math> f(x) \approx f(a)+f'(a)(x-a). </math><br />
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因此<br />
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:<math>x_{n+1}-x_{n} = f(x_n)-x_n \simeq f(a) + f'(a)(x_n-a)-x_n = a + f'(a)(x_n-a)-x_n = (f'(a)-1)(x_n-a) \to \frac{x_{n+1}-x_{n}}{x_n-a}=f'(a)-1</math><br />
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这意味着导数测量的是函数连续迭代接近或偏离不动点 {{Math|''a''}} 的速率。如果不动点 {{Math|''a''}} 处的导数恰好是1或-1,那么就需要更多的信息才能判断系统的稳定性。<br />
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对于具有一个不动点 {{Math|''a''}} 的连续可微映射 {{Math|''f'': '''R'''<sup>''n''</sup> → '''R'''<sup>''n''</sup>}},存在一个类似的判据,由 {{Math|''a''}} 的雅可比矩阵 {{Math|''J''<sub>''a''</sub>(''f'')}} 表示。<br />
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如果 {{Math|''J''}} 的所有特征值都是绝对值严格小于1的实数或复数,则该点是稳定不动点;<br />
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如果{{Math|''J''}} 的所有特征值中至少有一个的绝对值严格大于1,则它是不稳定的。<br />
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对于{{Math|''J''}} 的最大特征值的绝对值等于1的情况,需要进一步研究。仅仅使用雅可比矩阵检验是无法确定稳定性类型的。同样的准则对光滑流形的微分同胚情况也有着广泛的适用性。<br />
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===线性自治系统===<br />
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如我们所知,线性系统是一类数学模型,指的是由线性运算子组成的系统,也就是说,这类系统首先满足线性的特性<ref>Luenberger D G . Observing the State of a Linear System[J]. IEEE Transactions on Military Electronics, 2007, 8(2):74-80.</ref>。相较于非线性系统,线性系统的特性比较简单。<br />
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根据系统矩阵A是否随时间变化,引入'''自治系统 autonomous system'''的概念后,可以把线性系统分为自治的和非自治的,对于线性系统一般也可以称为定常的和时变的,也就是说:<br />
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(1)自治的线性系统就是定常线性系统。<br />
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(2)而非自治的线性系统就是时变线性系统。<br />
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对于非线性系统,就可以分为非线性自治系统和非线性非自治系统。<br />
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这里我们首先考察线性自治系统,利用常系数一阶线性微分方程组对应系数矩阵的特征值,便可以分析其不动点的稳定性。<br />
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对于一个如下的'''自治系统 autonomous system'''<br />
:<math>x' = Ax,</math><br />
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当 {{Math|''x''(''t'') ∈ '''R'''<sup>''n''</sup>}} 且 {{Math|''A''}} 是一个 {{Math|''n''×''n''}} 的实矩阵时,它具有常数解<br />
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:<math>x(t)=0.</math><br />
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:<math> x_{n+1}=f(x_n), \quad n=0,1,2,\ldots.</math><br />
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可以这样描述:最初的原点({{Math|0 ∈ '''R'''<sup>''n''</sup>}} ) 是该动力系统的平衡点。当且仅当对于{{Math|''A''}}的所有特征值 {{Math|''λ''}} 有 {{Math|Re(''λ'') < 0}} 时,这个解是随着{{Math|''t'' → ∞}}是渐近稳定的(未来趋势)。类似地,当且仅当对于 {{Math|''A''}} 的所有特征值 {{Math|''λ''}} 有{{Math|Re(''λ'') > 0}} 时,系统随着{{Math|''t'' → -∞}}是渐近稳定的(负号表示方向指向过去趋势)。如果存在一个{{Math|''A''}}的特征值 {{Math|''λ''}} 使得 {{Math|Re(''λ'') > 0}},则该解在{{Math|''t'' → ∞}}时是不稳定的。<br />
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为了判定线性系统原点的稳定性,可以使用劳斯-赫尔维茨稳定性判据'''Routh–Hurwitz stability criterion''',来将这一结果应用在实践中。矩阵的特征值是其特征多项式的根。如果所有根的实部都是严格负的,那么一个具有实系数的单变量多项式称为赫尔维茨多项式 '''Hurwitz polynomial''' 。劳斯-赫尔维茨定理 '''Routh–Hurwitz theorem'''通过一种避免计算根的算法来描述赫尔维茨多项式的特征。<br />
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===非线性自治系统===<br />
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前面我们介绍了线性自治系统的稳定性判断,这里我们来考察非线性自治系统的情况。非线性系统不动点的渐近稳定性通常可以用 Hartman-Grobman 定理来判断。<br />
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假设{{Math|''v''}}是{{Math|'''R'''<sup>''n''</sup>}}上的一个{{Math|''C''<sup>1</sup>}}-向量场,并且下降至某一点{{Math|''p''}}有{{Math|1=''v''(''p'') = 0}}。那么相应的自治系统<br />
:<math>x'=v(x)</math><br />
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有一个常数解<br />
:<math> x(t)=p.</math><br />
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设{{Math|''J''<sub>''p''</sub>(''v'')}}为向量场 {{Math|''v''}}在点{{Math|''p''}}的{{Math|''n''×''n''}}'''雅可比矩阵 Jacobian matrix'''。如果 {{Math|''J''}} 的所有特征值都具有严格负的实部,则系统的解是渐近稳定的。这个条件可以用劳斯-赫尔维茨判据'''Routh–Hurwitz stability criterion'''来检验。<br />
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==一般动力系统的李雅普诺夫函数==<br />
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李雅普诺夫函数 Lyapunov functions在稳定性分析和控制理论中都起着重要的作用,它的应用使得许多领域中的一系列问题的解决变得相对容易,尤其是在一些应用型的分析领域中。在常微分方程理论中,可用它来证明常微分方程平衡点的稳定性<ref>Branicky, M. S . Multiple Lyapunov functions and other analysis tools for switched and hybrid systems[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL AC, 1998, 43(4):475-482.</ref>。所以我们建立动力系统的李雅普诺夫稳定性或渐近稳定的一般方法即是利用李亚普诺夫函数来分析。<br />
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==拓展阅读==<br />
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*[[Asymptotic stability 渐近稳定性]]<br />
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*[[Hyperstability 超稳定性]]<br />
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*[[Linear stability 线性稳定性]]<br />
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*[[Orbital stability 轨道稳定性]]<br />
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*[[Stability criterion 稳定性判据]]<br />
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*[[Stability radius 稳定半径]]<br />
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*[[Structural stability 结构稳定性]]<br />
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*[[von Neumann stability analysis 冯诺依曼稳定性分析]]<br />
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==参考文献==<br />
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{{Reflist}}<br />
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==外部链接==<br />
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*[http://demonstrations.wolfram.com/StableEquilibria/ Stable Equilibria] 源于Michael Schreiber,Wolfram示范项目。<br />
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