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'''Emergence.'''  Interactions between components in integrated systems often generate phenomena, functions, or effects that cannot be trivially reduced to properties of the components alone.  Instead these functions emerge as a result of structured interactions and are properties of the system as a whole.  In many cases, even a detailed and complete examination of the individual components will fail to predict the range of emergent processes that these components are capable of if allowed to interact as part of a system.  In turn, dissection of an integrated system into components and interactions generally results in a loss of the emergent process.  
 
'''Emergence.'''  Interactions between components in integrated systems often generate phenomena, functions, or effects that cannot be trivially reduced to properties of the components alone.  Instead these functions emerge as a result of structured interactions and are properties of the system as a whole.  In many cases, even a detailed and complete examination of the individual components will fail to predict the range of emergent processes that these components are capable of if allowed to interact as part of a system.  In turn, dissection of an integrated system into components and interactions generally results in a loss of the emergent process.  
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'''涌现''' 系统中组件之间的相互作用往往产生不能被简单地归结为组件特性的现象、功能或效应。相反,这些功能是结构化交互的结果,是系统作为一个整体的属性。在许多情况下,即使对单个组件进行详细而全面的检查,也无法预测这些组件作为系统的一部分进行交互时能够发生的突发过程的范围。反过来,将一个集成的系统拆解成组件和相互作用通常会导致涌现过程的丢失。
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In summary, systems with numerous components capable of structured interactions that generate emergent phenomena may be called complex.  The observation of complex systems poses many challenges, as an observer needs simultaneously to record states and state transitions of many components and interactions.  Such observations require that choices be made concerning the definition of states, state space and time resolution.  How states are defined and measured can impact other derived measures such as those of system complexity.
 
In summary, systems with numerous components capable of structured interactions that generate emergent phenomena may be called complex.  The observation of complex systems poses many challenges, as an observer needs simultaneously to record states and state transitions of many components and interactions.  Such observations require that choices be made concerning the definition of states, state space and time resolution.  How states are defined and measured can impact other derived measures such as those of system complexity.
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总之,具有大量组件的、能够产生涌现现象的、结构化交互的系统可以称为'''复杂系统'''。对复杂系统得观察提出了许多挑战,因为观察者需要同时记录许多组件和交互的状态和状态转换。这种观测要求对状态的定义、状态空间和时间分辨率作出选择。怎样定义和度量系统的状态会影响到其他派生出来的度量方法,比如系统复杂性度量方法。
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[[Image:complexity_figure1.jpg|thumb|300px|left|F1|Complexity as a mixture of order and disorder. Drawn after Huberman and Hogg (1986).]]
 
[[Image:complexity_figure1.jpg|thumb|300px|left|F1|Complexity as a mixture of order and disorder. Drawn after Huberman and Hogg (1986).]]
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==复杂性的度量==
 
==复杂性的度量==
    
Measures of complexity allow different systems to be compared to each other by applying a common metric.  This is especially meaningful for systems that are structurally or functionally related.  Differences in complexity among such related systems may reveal features of their organization that promote complexity.
 
Measures of complexity allow different systems to be compared to each other by applying a common metric.  This is especially meaningful for systems that are structurally or functionally related.  Differences in complexity among such related systems may reveal features of their organization that promote complexity.
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通过应用一个共同的度量标准,复杂性度量使得不同的系统可以相互比较。这对于结构上或功能上相关的系统尤其有意义。这些相关系统之间复杂性的差异可能揭示其组织的特征,从而促进我们对复杂性的理解。
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Some measures of complexity are algorithmic in nature and attempt to identify a minimal description length.  For these measures complexity applies to a description, not the system or process per se.  Other measures of complexity take into account the time evolution of a system and often build on the theoretical foundations of statistical information theory.
 
Some measures of complexity are algorithmic in nature and attempt to identify a minimal description length.  For these measures complexity applies to a description, not the system or process per se.  Other measures of complexity take into account the time evolution of a system and often build on the theoretical foundations of statistical information theory.
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一些复杂性度量是算法性质的,并试图确定最小描述长度。对于这些度量,复杂性仅适用于描述,而不适用于系统或流程本身。其他衡量复杂性的方法考虑到一个系统的时间演变,并且往往建立在统计信息理论的理论基础之上。
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Most extant complexity measures can be grouped into two main categories.  Members of the first category (algorithmic information content and logical depth) all capture the randomness, information content or description length of a system or process, with random processes possessing the highest complexity since they most resist compression.  The second category (including statistical complexity, physical complexity and neural complexity) conceptualizes complexity as distinct from randomness.  Here, complex systems are those that possess a high amount of structure or information, often across multiple temporal and spatial scales.  Within this category of measures, highly complex systems are positioned somewhere between systems that are highly ordered (regular) or highly disordered (random). <figref>Complexity_figure1.jpg</figref> shows a schematic diagram of the shape of such measures, however, it should be emphasized again that a generally accepted quantitative expression linking complexity and disorder does not currently exist.
 
Most extant complexity measures can be grouped into two main categories.  Members of the first category (algorithmic information content and logical depth) all capture the randomness, information content or description length of a system or process, with random processes possessing the highest complexity since they most resist compression.  The second category (including statistical complexity, physical complexity and neural complexity) conceptualizes complexity as distinct from randomness.  Here, complex systems are those that possess a high amount of structure or information, often across multiple temporal and spatial scales.  Within this category of measures, highly complex systems are positioned somewhere between systems that are highly ordered (regular) or highly disordered (random). <figref>Complexity_figure1.jpg</figref> shows a schematic diagram of the shape of such measures, however, it should be emphasized again that a generally accepted quantitative expression linking complexity and disorder does not currently exist.
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