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层次

2021-02-07T04:09:17Z

Miyasaki：

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{{Redirect|Subordinate|other uses|Subordination (disambiguation){{!}}Subordination}}

{{short description|System of elements that are subordinated to each other}}

A '''hierarchy''' (from the [[Ancient Greek|Greek]] ἱεραρχία ''hierarkhia'', "rule of a high priest", from ''[[ordinary (officer)|hierarkhes]]'', "president of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as [[philosophy]], [[mathematics]], [[computer science]], [[organizational theory]], [[systems theory]], and the [[social sciences]] (especially [[political philosophy]]).

A hierarchy (from the Greek ἱεραρχία hierarkhia, "rule of a high priest", from hierarkhes, "president of sacred rites") is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being "above", "below", or "at the same level as" one another. Hierarchy is an important concept in a wide variety of fields, such as philosophy, mathematics, computer science, organizational theory, systems theory, and the social sciences (especially political philosophy).

'''“层次 hierarchy”'''（从古希腊语 ἱεραρχία hierarkhia“大祭司的统治”和hierarkhes“神圣仪式的主持者”而来）是一组相互之间被表示成具有“之上”“之下”或“同级”关系的元素（对象、名称、值、类别等）。在哲学、数学、计算机科学、系统论和社会科学（尤其是政治哲学）中，层次都是很重要的概念。

A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates, although a system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a [[path (graph theory)|path]]. All parts of the hierarchy that are not linked vertically to one another nevertheless can be "horizontally" linked through a path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two [[co-worker]]s or [[Comrade|colleague]]s; each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy. [[Heterarchy]] is one such form.

A hierarchy can link entities either directly or indirectly, and either vertically or diagonally. The only direct links in a hierarchy, insofar as they are hierarchical, are to one's immediate superior or to one of one's subordinates, although a system that is largely hierarchical can also incorporate alternative hierarchies. Hierarchical links can extend "vertically" upwards or downwards via multiple links in the same direction, following a path. All parts of the hierarchy that are not linked vertically to one another nevertheless can be "horizontally" linked through a path by traveling up the hierarchy to find a common direct or indirect superior, and then down again. This is akin to two co-workers or colleagues; each reports to a common superior, but they have the same relative amount of authority. Organizational forms exist that are both alternative and complementary to hierarchy. Heterarchy is one such form.

一个层次结构可直接或间接地、竖向或对角地将实体联系起来。尽管一个大体上呈层次结构的系统也可以吸收另外的层次结构，一个层次结构中的直接联系——前提是，它们是等级制的——只有与其直接上级或直接下级的联系。层次联系可通过同向的多个联系汇成的路径“垂直”向上或向下发展。层次结构中所有没有垂直相连的部分都可以通过水平路径（向上找到共同直接或间接上级再向下）相连。就像两个同事、同僚各自向共同上级汇报，但他们各自都有同等的相对权限。组织形式的存在对层次结构既是替代也是补充。异质结构也是这样一种形式。

==名称 Nomenclature==

{{see also| Glossary of graph theory| Taxonomy (general)| Structure}}

Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see [[#Visualization|below]]).

Hierarchies have their own special vocabulary. These terms are easiest to understand when a hierarchy is diagrammed (see below).

层次结构有其特殊词汇，这些术语在层次图解（见下）中较易理解。

In an organizational context, the following terms are often used related to hierarchies:<ref name="Dawkins"/><ref name="Architecture"/>

In an organizational context, the following terms are often used related to hierarchies:

在组织的语境下，以下术语的使用经常与层次结构相关:<ref name="Dawkins"/><ref name="Architecture"/>

* '''[[Non-physical entity|Object]]''': one entity (e.g., a person, department or [[concept]] or element of arrangement or member of a set)
*'''对象 Object'''：一个实体（例如一个人，一个部门或概念或配置集中的一个元素或一组中的成员）

* '''[[System]]''': the entire set of objects that are being arranged hierarchically (e.g., an administration)
*'''系统 System'''：层次性地组织起来的一整组对象（例如管理体系）

* '''[[Dimension]]''': another word for "system" from on-line analytical processing (e.g. cubes)
*'''维度 Dimension'''：联机分析处理（例如立方体）中“系统”的另一种说法

* '''[[Element (mathematics)|Member]]''': an (element or object) at any (level or rank) in a (class-system, taxonomy or dimension)
*'''成员 Member'''：处于（分类系统、分类学或维度）中任一（等级或阶层）的一个（元素或对象）

*'''位置相关的术语 Terms about Positioning'''

**'''[[Ranking|Rank]]''': the relative [[value (ethics)|value]], worth, [[complexity]], [[Power (philosophy)|power]], importance, [[authority]], level etc. of an object
**'''阶层 Rank'''：一个对象的相对值、价值、复杂度、力量、重要度、权威性、等级等

**'''[[wikt:level#Noun|Level]] or Tier''': a set of objects with the same rank OR importance
**'''等级 Level'''：阶层或重要度相同的一组对象

**'''[[Order of precedence|Ordering]]''': the arrangement of the (ranks or levels)
**'''排序 Ordering'''：等级或阶层的配置

**'''Hierarchy''': the arrangement of a particular set of members into (ranks or levels). Multiple hierarchies are possible per (dimension taxonomy or Classification-system), in which selected levels of the dimension are omitted to flatten the structure
**'''层次 Hierarchy'''：将特定的一组成员按等级或阶层配置起来的组织。通过忽视所选等级以扁平化结构，一个维度、分类学或体系分类的多层次是可能的

*'''位置相关的术语Terms about Placement'''

**'''[[wikt:hierarch|Hierarch]]''', the apex of the hierarchy, consisting of one single orphan (object or member) in the top level of a dimension. The root of an inverted-tree structure
**'''顶 Hierarch'''：层次的顶，由位于维度中顶层的一个独立个体（对象或成员）组成。倒树形结构的根源

**'''[[wikt:member|Member]]''', a (member or node) in any level of a hierarchy in a dimension to which (superior and subordinate) members are attached
**'''成员 Member'''：维系（上级或下级）成员的维度中层次结构里任一层的一个成员或节点

**'''[[wikt:orphan|Orphan]]''', a member in any level of a dimension without a parent member. Often the apex of a disconnected branch. Orphans can be grafted back into the hierarchy by creating a relationship (interaction) with a parent in the immediately superior level
**'''孤体 Orphan'''：一个维度中某等级中的一没有父级的成员。通常是孤立分支的顶。孤体可通过创建与直接上层中的一个父级的关系而重新嫁接到层次中。

**'''[[wikt:leaf|Leaf]]''', a member in any level of a dimension without subordinates in the hierarchy
**'''叶 Leaf'''：维度中任一层里没有下级的成员

**'''[[wikt:neighbour|Neighbour]]''': a member adjacent to another member in the same (level or rank). Always a peer.
**'''近邻 Neighbour'''：同一等级或阶层中相邻与另一成员的成员，通常是同级。

**'''[[Superior (hierarchy)|Superior]]''': a higher level or an object ranked at a higher level (A parent or an ancestor)
**'''上级 Superior'''：更高等级或更高等级中的对象（父级或祖先级）

**'''[[wikt:subordinate|Subordinate]]''': a lower level or an object ranked at a lower level (A child or a descendant)
**'''下级 Subordinate'''：更低等级或更低等级中的对象（子级或后裔级）

** '''[[Family of sets|Collection]]''': all of the objects at one level (i.e. Peers)
**'''群 Collection'''：一等级中的所有对象（例如同级成员）

** '''[[wikt:peer|Peer]]''': an object with the same rank (and therefore at the same level)
**'''同级 Peer'''：同一阶层（即同一等级）的对象

** '''[[Interpersonal relationship|Interaction]]''': the relationship between an object and its direct superior or subordinate (i.e. a superior/inferior pair)
**'''交互 Interaction'''：对象与其直接上级或下级的关系（例如一对上下级）

*** a '''direct''' interaction occurs when one object is on a level exactly one higher or one lower than the other (i.e., on a [[tree (graph theory)|tree]], the two objects have a line between them)
***，一个对象比另一个刚好高一等级或低一等级时（例如在树形图中两个对象间有连线）发生'''直接 Direct'''交互

** '''[[Distance (graph theory)|Distance]]''': the minimum number of connections between two objects, i.e., one less than the number of objects that need to be "crossed" to trace a [[path (graph theory)|path]] from one object to another
**'''距离 Distance'''：两个对象间的最小连接数，例如若连接数比对象数少1则需要一个对象到另一个对象的路径交叉

** '''[[wikt:Span|Span]]''': a [[qualitative data|qualitative]] description of the width of a level when diagrammed, i.e., the number of subordinates an object has
**'''跨度 Span'''：层级宽度图表化的量化表述，例如一个对象所拥有的下级的数量。

*'''与自然相关的术语 Terms about Nature'''

** '''[[wikt:attribute|Attribute]]''': a heritable characteristic of (members and their subordinates) in a level (e.g. ''hair-colour'')
**'''属性 Attribute'''：等级中（成员或其下级）的遗传特征（例如''发色''）

** '''[[wikt:attribute-value|Attribute-value]]''': the specific value of a heritable characteristic (e.g. ''Auburn'')
**'''属性值 Attribute-value'''：遗传特征的具体值（例如''棕发''）

In a mathematical context (in [[graph theory]]), the [[Glossary of graph theory|general terminology]] used is different.

In a mathematical context (in graph theory), the general terminology used is different.

在数学语境下（图论）所用的一般术语则不同。

Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with [[data structure]]s, objects are known as [[node (computer science)|nodes]], superiors are called [[parent node|parents]] and subordinates are called [[child node|children]]. In a business setting, a superior is a [[supervisor|supervisor/boss]] and a peer is a [[Comrade|colleague]].

Most hierarchies use a more specific vocabulary pertaining to their subject, but the idea behind them is the same. For example, with data structures, objects are known as nodes, superiors are called parents and subordinates are called children. In a business setting, a superior is a supervisor/boss and a peer is a colleague.

大多数层次结构按其主题不同而使用更具体的词汇，但其背后的理念是相同的。例如，在数据结构中，对象称为节点，上级称为父级，下级称为子级。在商业环境中，上级是主管/老板，同级即同事。

===支化度 Degree of branching ===

[[Degree (graph theory)|Degree]] of [[Bifurcation theory|branching]] refers to the number of direct [[#Terminology|subordinates]] or children an object has (in graph theory, equivalent to the number of other [[vertex (graph theory)|vertices]] connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in the system as a whole. Categorization in this way yields two broad classes: ''linear'' and ''branching''.

Degree of branching refers to the number of direct subordinates or children an object has (in graph theory, equivalent to the number of other vertices connected to via outgoing arcs, in a directed graph) a node has. Hierarchies can be categorized based on the "maximum degree", the highest degree present in the system as a whole. Categorization in this way yields two broad classes: linear and branching.

支化度是指对象所有直接下级或子项的数量（在图论中，即有向图通过外向弧所连接的顶点数）。层次可按其“最大度”分类，即系统整体中存在的支化度的最高值，这种分类方式产生了两个广类：线性和支化。

In a '''linear hierarchy''', the maximum degree is 1.<ref name="Dawkins"/> In other words, all of the objects can be visualized in a line-up, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. Note that this is referring to the ''objects'' and not the ''levels''; every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects. An example of a linear hierarchy is the [[hierarchy of life]].

In a linear hierarchy, the maximum degree is 1. In other words, all of the objects can be visualized in a line-up, and each object (excluding the top and bottom ones) has exactly one direct subordinate and one direct superior. Note that this is referring to the objects and not the levels; every hierarchy has this property with respect to levels, but normally each level can have an infinite number of objects. An example of a linear hierarchy is the hierarchy of life.

'''线性层次结构'''的最大度是1。即所有对象都可呈现在一个列表中，每个对象(顶部和底部的除外)只有一个直接下级和一个直接上级。注意，这里说的是对象而不是级别；就级别而言每个层次结构都有这种属性，但每个级别通常可以有无限个对象。生命层次结构就是线性层次的一个例子。

In a '''branching hierarchy''', one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher).<ref name="Dawkins"/> For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy.<ref name="Dawkins"/> Branching hierarchies are present within numerous systems, including [[organization]]s and [[classification scheme]]s. The broad category of branching hierarchies can be further subdivided based on the degree.

In a branching hierarchy, one or more objects has a degree of 2 or more (and therefore the minimum degree is 2 or higher). For many people, the word "hierarchy" automatically evokes an image of a branching hierarchy. Branching hierarchies are present within numerous systems, including organizations and classification schemes. The broad category of branching hierarchies can be further subdivided based on the degree.

在'''分支层次结构'''中，至少有一个对象的支化度在2或以上（即支化度下限是2或更高）。<ref name="Dawkins"/> 对许多人来说，提到“层次”这个词就会想起支化层次结构。<ref name="Dawkins"/> 支化层次存在于很多系统中，包括组织、分类法。广义上的分支层次可据其分支度进一步细分。

A '''flat hierarchy''' is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span.<ref name="Architecture">{{cite journal|last=Simon|first=Herbert A.|title=The Architecture of Complexity|journal=[[Proc. Am. Philos. Soc.]]|volume=106|issue=6|date=12 December 1962|pages=467–482|publisher=[[American Philosophical Society]]|issn=0003-049X|location=Philadelphia, Pennsylvania |jstor=985254 |citeseerx=10.1.1.110.961}}{{registration required}}</ref> Most often, systems intuitively regarded as hierarchical have at most a moderate span. Therefore, a flat hierarchy is often not viewed as a hierarchy at all. For example, [[diamond]]s and [[graphite]] are flat hierarchies of numerous [[carbon]] atoms that can be further decomposed into subatomic particles.

A flat hierarchy is a branching hierarchy in which the maximum degree approaches infinity, i.e., that has a wide span. Most often, systems intuitively regarded as hierarchical have at most a moderate span. Therefore, a flat hierarchy is often not viewed as a hierarchy at all. For example, diamonds and graphite are flat hierarchies of numerous carbon atoms that can be further decomposed into subatomic particles.

'''扁平层次结构'''是指最大度接近无穷的支化层次结构，例如跨度很大的层次结构。<ref name="Architecture">{{cite journal|last=Simon|first=Herbert A.|title=The Architecture of Complexity|journal=[[Proc. Am. Philos. Soc.]]|volume=106|issue=6|date=12 December 1962|pages=467–482|publisher=[[American Philosophical Society]]|issn=0003-049X|location=Philadelphia, Pennsylvania |jstor=985254 |citeseerx=10.1.1.110.961}}{{registration required}}</ref>分层系统一般最多只有中等的跨度，故扁平层次结构通常根本不被视为层次结构。例如钻石和石墨是由许多碳原子组成的扁平层次结构，而这些碳原子可进一步分解为亚原子粒子。

An '''overlapping hierarchy''' is a branching hierarchy in which at least one object has two parent objects.<ref name="Dawkins"/> For example, a [[graduate student]] can have two [[research supervisor|co-supervisors]] to whom the student reports directly and equally, and who have the same level of authority within the [[university]] hierarchy (i.e., they have the same [[list of academic ranks|position]] or [[tenure]] status).

An overlapping hierarchy is a branching hierarchy in which at least one object has two parent objects. For example, a graduate student can have two co-supervisors to whom the student reports directly and equally, and who have the same level of authority within the university hierarchy (i.e., they have the same position or tenure status).

'''重叠层次结构'''是指至少有一个对象具有两个父级对象的分支层次结构。<ref name="Dawkins"/>例如，一个研究生可以有两个联合主管，学生可同等地直接向他们汇报，且二人在大学层级制度中具有同等的权力水平(例如他们都拥有相同的职位或任期)。

==术语历史 History of the term==

Possibly the first use of the English word "hierarchy" cited by the ''[[Oxford English Dictionary]]'' was in 1881, when it was used in reference to the three orders of three angels as depicted by [[Pseudo-Dionysius the Areopagite]] (5th–6th centuries). Pseudo-Dionysius used the related [[Ancient Greek|Greek]] word (ἱεραρχία ''hierarchia'') both in reference to the [[De Coelesti Hierarchia|celestial hierarchy]] and the [[ecclesiastical hierarchy]].<ref>[http://www.newadvent.org/cathen/07322c.htm CATHOLIC ENCYCLOPEDIA: Hierarchy]</ref> The Greek term ἱεραρχία means "rule of a high priest"<ref>[https://www.etymonline.com/word/hierarchy "hierarchy"]. [[Online Etymology Dictionary]].</ref> (from ἱεράρχης ''hierarches'', meaning "president of sacred rites, high-priest"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28era%2Frxhs ἱεράρχης],
Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref>and that from ἱερεύς ''hiereus'', "priest"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28ereu%2Fs ἱερεύς], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref> and ἀρχή ''arche'', amongst others "first place or power, rule"<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Da%29rxh%2F ἀρχή], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref>),and Dionysius is credited with first use of it as an abstract noun. Since hierarchical churches, such as the [[Roman Catholicism|Roman Catholic]] (see [[Catholic Church hierarchy]]) and [[Eastern Orthodoxy|Eastern Orthodox]] churches, had tables of organization that were "hierarchical" in the modern sense of the word (traditionally with [[God in Christianity|God]] as the pinnacle or head of the hierarchy), the term came to refer to similar organizational methods in [[secular]] settings.

Possibly the first use of the English word "hierarchy" cited by the Oxford English Dictionary was in 1881, when it was used in reference to the three orders of three angels as depicted by Pseudo-Dionysius the Areopagite (5th–6th centuries). Pseudo-Dionysius used the related Greek word (ἱεραρχία hierarchia) both in reference to the celestial hierarchy and the ecclesiastical hierarchy. The Greek term ἱεραρχία means "rule of a high priest" (from ἱεράρχης hierarches, meaning "president of sacred rites, high-priest" and that from ἱερεύς ''hiereus'', "priest"and ἀρχή ''arche'', amongst others "first place or power, rule"), and Dionysius is credited with first use of it as an abstract noun. Since hierarchical churches, such as the Roman Catholic (see Catholic Church hierarchy) and Eastern Orthodox churches, had tables of organization that were "hierarchical" in the modern sense of the word (traditionally with God as the pinnacle or head of the hierarchy), the term came to refer to similar organizational methods in secular settings.

“层次”这一英语单词的首次被牛津英语词典引用的使用可能是在1881年，被用来指伪狄奥尼修斯 Pseudo-Dionysius the Areopagite（5-6世纪）所描述的3个天使的3个阶层。伪狄奥尼修斯使用相关的希腊单词(ἱεραρχία hierarchia) 来指代天界阶层和教会阶层。<ref>[http://www.newadvent.org/cathen/07322c.htm CATHOLIC ENCYCLOPEDIA: Hierarchy]</ref> 希腊语 ἱεραρχία表示大祭司的统治<ref>[https://www.etymonline.com/word/hierarchy "hierarchy"]. [[Online Etymology Dictionary]].</ref>（源自ἱεράρχης hierarches，“神圣仪式的主持，高阶祭司”，自ἱερεύς hiereus, “祭司”<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Di%28ereu%2Fs ἱερεύς], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref>，及 ἀρχή arche等“最初的地方或力量，统治”<ref>[http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.04.0057%3Aentry%3Da%29rxh%2F ἀρχή], Henry George Liddell, Robert Scott, ''A Greek-English Lexicon'', on Perseus Digital Library</ref>）
伪狄奥尼修斯首次将其用作抽象名词概念，自阶层式教会，如罗马天主教和东正教，拥有现代语义上的层次性结构（按照传统层次结构的顶部或头部表示神）以来，该术语开始指称世俗语境下类似的组织方式。

==层次的视觉呈现 Visually representing hierarchies==

= = = 视觉表现层次结构 = = = < ! -- 如果你更改这个部分的标题，请也更改文章中链接到它的 wikileink！-->

[[File:Maslow's hierarchy of needs.png|thumb|right|200px|[[Maslow's hierarchy of needs|Maslow's hierarchy of human needs]]. This is an example of a hierarchy visualized with a triangle diagram.]]

Maslow's hierarchy of human needs. This is an example of a hierarchy visualized with a triangle diagram.]]

'''马斯洛的人类需求层次理论 Maslow's hierarchy of human needs'''这是用三角图表呈现层次结构的一个实例。

A hierarchy is typically depicted as a [[pyramid (geometry)|pyramid]], where the height of a level represents that level's status and width of a level represents the quantity of items at that level relative to the whole.<ref>{{cite book | title=Regions of War and Peace | publisher=University of Cambridge | author=Douglas Lemke | year=2002 | location=Cambridge | pages=49}}</ref> For example, the few [[Board of Directors|Directors]] of a company could be at the [[apex (geometry)|apex]], and the [[Base (geometry)|base]] could be thousands of people who have no subordinates.

A hierarchy is typically depicted as a pyramid, where the height of a level represents that level's status and width of a level represents the quantity of items at that level relative to the whole. For example, the few Directors of a company could be at the apex, and the base could be thousands of people who have no subordinates.

层次结构通常被描述为金字塔形，其中高度代表层次状态而宽度代表该层的元素多寡。例如，一个公司的几个董事处于顶峰，而基层可能是成千上万没有下级的人。

These pyramids are typically diagrammed with a [[tree structure|tree]] or [[triangle]] [[diagram]] (but note that not all triangle/pyramid diagrams are hierarchical; for example, the 1992 [[History of USDA nutrition guides#Food Guide Pyramid|USDA food guide pyramid]]), both of which serve to emphasize the size differences between the levels. An example of a triangle diagram appears to the right. An [[organizational chart]] is the diagram of a hierarchy within an [[organization]], and is depicted in tree form in {{section link|#Organizations}}, below.

These pyramids are typically diagrammed with a tree or triangle diagram (but note that not all triangle/pyramid diagrams are hierarchical; for example, the 1992 USDA food guide pyramid), both of which serve to emphasize the size differences between the levels. An example of a triangle diagram appears to the right. An organizational chart is the diagram of a hierarchy within an organization, and is depicted in tree form in , below.

这样的金字塔通常用树形或三角形图表绘制（注意，并非所有的三角形/金字塔形图表都是层次性的；例如1992年美国农业部膳食指南金字塔），两种图表都表现了各层次的大小差异。右侧是一个三角形图表的例子。组织结构图是组织内部层次结构的图表，在下面的树形图中有所描述。

More recently, as computers have allowed the storage and navigation of ever larger data sets, various methods have been developed to represent hierarchies in a manner that makes more efficient use of the available space on a computer's screen. Examples include [[fractal]] maps, [[treemapping|TreeMaps]] and [[Radial tree|Radial Trees]].

More recently, as computers have allowed the storage and navigation of ever larger data sets, various methods have been developed to represent hierarchies in a manner that makes more efficient use of the available space on a computer's screen. Examples include fractal maps, TreeMaps and Radial Trees.

最近，随着计算机的发展使存储和索引更大的数据集成为可能，人们开发出各种能更有效地利用计算机屏幕空间的方法来表示层次结构。例如分形图、树形图和辐射状树图。

==视觉层次 Visual hierarchy==

In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on the rules of [[visual hierarchy]]. Visual hierarchy is also important for proper organization of files on computers.

In the design field, mainly graphic design, successful layouts and formatting of the content on documents are heavily dependent on the rules of visual hierarchy. Visual hierarchy is also important for proper organization of files on computers.

在设计领域，主要是平面设计，文件内容排版和格式的成功很大程度上取决于视觉层次的规则。视觉层次对于像样的电脑文件的安配也至关重要。

An example of visually representing hierarchy is through the Nested clusters. The Nested clusters represents hierarchical relationships by using layers of information. The child element is within the parent element, such as in a [[Venn diagram]]. This structure of representing hierarchy is most effective in representing simple relationships. For example, when directing someone to open a file on a computer desktop, one may first direct them towards the main folder, then the subfolders within the main folder. They will keep opening files within the folders until the designated file is located.

An example of visually representing hierarchy is through the Nested clusters. The Nested clusters represents hierarchical relationships by using layers of information. The child element is within the parent element, such as in a Venn diagram. This structure of representing hierarchy is most effective in representing simple relationships. For example, when directing someone to open a file on a computer desktop, one may first direct them towards the main folder, then the subfolders within the main folder. They will keep opening files within the folders until the designated file is located.

嵌套集群是层次结构的一个可视化示例。嵌套集群用信息层来表示层次关系。子元素位于父元素之内，例如'''维恩图 Venn diagram'''。这种结构可有效表示简单层次关系。例如，当需要打开一个电脑桌面的文件时，可能要先让操作者打开主文件夹，然后是主文件夹中的子文件夹，不断打开直到找到指定文件。

For more complicated hierarchies, the stair structure represents hierarchical relationships through the use of visual stacking. Visually imagine the top of a downward staircase beginning at the left and descending on the right. The child elements are towards the bottom of the stairs and the parent elements are at the top. This structure is effective when representing more complicated hierarchies where steps are not placed in obvious sequences. Further steps are concealed unless all of the steps are revealed in sequence. In the computer desktop example, a file that is being sought after can only be found once another file is opened. The link for the desired file is within another document. All the steps must be completed until the final destination is reached.

For more complicated hierarchies, the stair structure represents hierarchical relationships through the use of visual stacking. Visually imagine the top of a downward staircase beginning at the left and descending on the right. The child elements are towards the bottom of the stairs and the parent elements are at the top. This structure is effective when representing more complicated hierarchies where steps are not placed in obvious sequences. Further steps are concealed unless all of the steps are revealed in sequence. In the computer desktop example, a file that is being sought after can only be found once another file is opened. The link for the desired file is within another document. All the steps must be completed until the final destination is reached.

对于更复杂的层次结构，楼梯结构用堆叠效果表示层次关系。请从视觉上想象一下从左到右下楼楼梯的顶部，子元素位于楼梯底部而父元素位于顶部。当表示更复杂的层次结构时，这种结构非常有效，尤其当台阶没有位于明显的序列中时。下一台阶必须基于所有台阶都顺序显示后才会出现。在计算机桌面的例子中，只有先打开别的文件才能找到目标文件，因为通向目标文件的链接位于另一个文件内。所有步骤都必须完成才能到达最终目标。

==通俗表达 Informal representation==

In plain English, a hierarchy can be thought of as a [[Set (mathematics)|set]] in which:<ref name="Dawkins">{{cite conference|last=Dawkins|first=Richard|authorlink=Richard Dawkins|title=Hierarchical organization: a candidate principle for ethology|conference=Growing points in ethology: based on a conference sponsored by St. John's College and King's College, Cambridge|editor1=Bateson, Paul Patrick Gordon |editor2=Hinde, Robert A.|year=1976|publisher=Cambridge University Press|location=Cambridge, England|isbn=0-521-29086-4|pages=7–54}}</ref>

In plain English, a hierarchy can be thought of as a set in which:

在日常英语中，层次可以被看作是一个集合，其中:

# No element is superior to itself, and

# 任何元素都不高于自身，且

# One element, the ''hierarch'', is superior to all of the other elements in the set.

# 其中有一个''教主''元素，高于集合中的所有其他元素。

The first requirement is also interpreted to mean that a hierarchy can have no [[Cycle (graph theory)|circular relationships]]; the association between two objects is always [[Transitive relation|transitive]].

The first requirement is also interpreted to mean that a hierarchy can have no circular relationships; the association between two objects is always transitive.

第一个前提也可理解为层次结构不能有循环关系; 两个对象之间的关联总是可传递的。

The second requirement asserts that a hierarchy must have a leader or [[root node|root]] that is common to all of the objects.

The second requirement asserts that a hierarchy must have a leader or root that is common to all of the objects.

第二个要求则确定了层次结构必须有一个所有元素都共有的代表或根源。

==数学表达 Mathematical representation==

{{Main|层次（数学） Hierarchy (mathematics)}}

Mathematically, in its most general form, a hierarchy is a [[partially ordered set]] or ''poset''.<ref name="Lehmann">{{cite conference|last=Lehmann|first=Fritz|title=Big Posets of Participatings and Thematic Roles|pages=50–74|conference=Conceptual structures: knowledge representation as interlingua—4th International Conference on Conceptual Structures, ICCS '96, Sydney, Australia, August 19–22, 1996—proceedings|isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref> The [[#Terminology|system]] in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting [[#Terminology|levels]] is referred to as a [[class (set theory)|class]].

|isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref> The system in this case is the entire poset, which is constituted of elements. Within this system, each element shares a particular unambiguous property. Objects with the same property value are grouped together, and each of those resulting levels is referred to as a class.

"Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. 

"Hierarchy" is particularly used to refer to a poset in which the classes are organized in terms of increasing complexity. 

Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parenthesis is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example:

Operations such as addition, subtraction, multiplication and division are often performed in a certain sequence or order. Usually, addition and subtraction are performed after multiplication and division has already been applied to a problem. The use of parenthesis is also a representation of hierarchy, for they show which operation is to be done prior to the following ones. For example:

(2 + 5) × (7 - 4).

(2 + 5) × (7 - 4).

(2 + 5) × (7 - 4).

In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations.

In this problem, typically one would multiply 5 by 7 first, based on the rules of mathematical hierarchy. But when the parentheses are placed, one will know to do the operations within the parentheses first before continuing on with the problem. These rules are largely dominant in algebraic problems, ones that include several steps to solve. The use of hierarchy in mathematics is beneficial to quickly and efficiently solve a problem without having to go through the process of slowly dissecting the problem. Most of these rules are now known as the proper way into solving certain equations.

数学上，层次结构最一般的形式是'''偏序集 Partially Ordered Set或Poset'''。<ref name="Lehmann">{{cite conference|last=Lehmann|first=Fritz|title=Big Posets of Participatings and Thematic Roles|pages=50–74|conference=Conceptual structures: knowledge representation as interlingua—4th International Conference on Conceptual Structures, ICCS '96, Sydney, Australia, August 19–22, 1996—proceedings|isbn=3-540-61534-2|year=1996|publisher=Springer|editor-last=Eklund|editor-first=Peter G.|editor2-last=Ellis|editor2-first=Gerard|editor3-last=Mann|editor3-first=Graham|series=Lecture Notes in Artificial Intelligence 115|location=Germany}}</ref>元素所组成的系统即整个偏序集。系统内每个元素都共享一些具体无歧义的属性。相同属性的元素可集结成群，最终形成类别层次。

“层次”专用作指称随复杂度增加而组织的偏序集。例如加法、减法、乘法和除法通常按特定序列实施。一般乘除先于加减，括号也是层次的一种表示，表达了哪些运算优先。例如在(2 + 5) × (7 - 4)中，按数学的层次规则本应先作5乘以7，但加入了括号，则表示了应当先对括号内作运算。在需要多步求解的代数问题上这些规则占主导地位。在数学中使用层次结构有利于快速高效地解决问题，而不必经历漫长的剖析过程。现在认为大多数这类规则是求解特定方程的适当方法。

==亚型 Subtypes==

===嵌套层次 Nested hierarchy===

= = = 嵌套层次结构 = = = = < ! -- 如果您更改此标题，请更改链接到该标题的文章中的 wiki 链接! -- >

[[File:Russian-Matroshka no bg.jpg|200px|right|thumb|[[Matryoshka doll]]s, also known as ''nesting dolls'' or ''Russian dolls''. Each doll is encompassed inside another until the smallest one is reached. This is the concept of ''nesting''. When the concept is applied to [[set (mathematics)|sets]], the resulting ordering is a ''nested hierarchy''.]]

[[Matryoshka dolls, also known as nesting dolls or Russian dolls. Each doll is encompassed inside another until the smallest one is reached. This is the concept of nesting. When the concept is applied to sets, the resulting ordering is a nested hierarchy.]]

'''玛特罗什卡套娃 Matryoshka Doll'''，又称嵌套娃娃或俄罗斯套娃。每个洋娃娃都被包裹在另一个洋娃娃里面，直到最小的洋娃娃。这就是嵌套的概念。当这个概念应用于集合时，其结果排序是一个嵌套的层次结构。

A nested hierarchy or ''inclusion hierarchy'' is a hierarchical ordering of [[nested set]]s.<ref name="natsocsci-ch4">{{cite encyclopedia|title=Hierarchy, Complexity, Society|last=Lane|first=David|pages=81–120|encyclopedia=Hierarchy in Natural and Social Sciences|editor=Pumain, Denise|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}</ref> The concept of nesting is exemplified in Russian [[matryoshka doll]]s. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example:

A nested hierarchy or inclusion hierarchy is a hierarchical ordering of nested sets.<ref name="natsocsci-ch4">{{cite encyclopedia|title=Hierarchy, Complexity, Society|last=Lane|first=David|pages=81–120|encyclopedia=Hierarchy in Natural and Social Sciences|editor=Pumain, Denise|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}</ref> The concept of nesting is exemplified in Russian matryoshka dolls. Each doll is encompassed by another doll, all the way to the outer doll. The outer doll holds all of the inner dolls, the next outer doll holds all the remaining inner dolls, and so on. Matryoshkas represent a nested hierarchy where each level contains only one object, i.e., there is only one of each size of doll; a generalized nested hierarchy allows for multiple objects within levels but with each object having only one parent at each level. The general concept is both demonstrated and mathematically formulated in the following example:

嵌套层次结构或包含层次结构，是指嵌套集的层次结构排序。嵌套的概念在俄罗斯套娃中得到体现。每个玩偶都被另一个玩偶包裹着，一直到最外层的。外部的套娃包含所有其内部的玩偶，往外一层的玩偶也包含所有其内部剩余的玩偶，如此反复。套娃结构是一个每层都只有一个对象的嵌套层次结构，例如在套娃中同样大小的玩偶只有一个；广义的嵌套层次可以每层都有多个对象，但每层里的对象都只有一个父级对象。嵌套层次一般概念的论证及数学表达如下：

: <math> \text{square} \subset \text{quadrilateral} \subset \text{polygon} \subset \text{shape} \, </math>

<math> \text{square} \subset \text{quadrilateral} \subset \text{polygon} \subset \text{shape} \, </math>

A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can ''only'' be a quadrilateral; it can never be a [[triangle]], [[hexagon]], etc.

A square can always also be referred to as a quadrilateral, polygon or shape. In this way, it is a hierarchy. However, consider the set of polygons using this classification. A square can only be a quadrilateral; it can never be a triangle, hexagon, etc.

正方形总是可以被称为四边形、多边形或形状。这样看来是层次性的。然而若多边形集采用这种分类法，则正方形只能是四边形，而不会是三角形、六边形等。

Nested hierarchies are the organizational schemes behind [[Taxonomy (general)|taxonomies]] and systematic classifications. For example, using the original [[Linnaean taxonomy]] (the version he laid out in the 10th edition of ''[[Systema Naturae]]''), a human can be formulated as:<ref>{{cite book|title=Systema naturae per regna tria naturae :secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis|last=Linnaei|first=Carl von|authorlink=Carl Linnaeus|year=1959|edition=10th|language=Latin|url=https://www.biodiversitylibrary.org/bibliography/542#|location=[[Stockholm]]|publisher=Impensis Direct|isbn=0-665-53008-0|accessdate=2011-09-24}}</ref>

Nested hierarchies are the organizational schemes behind taxonomies and systematic classifications. For example, using the original Linnaean taxonomy (the version he laid out in the 10th edition of Systema Naturae), a human can be formulated as:

嵌套层次结构是'''分类学 Taxonomies''' 和'''系统分类 Systematic Classifications'''背后的组织性方案。例如，在最初的'''林奈分类法 Linnaean Taxonomy'''（他在《自然系统》第10版中所列）中，人类可被归为：ref>{{cite book|title=Systema naturae per regna tria naturae :secundum classes, ordines, genera, species, cum characteribus, differentiis, synonymis, locis|last=Linnaei|first=Carl von|authorlink=Carl Linnaeus|year=1959|edition=10th|language=Latin|url=https://www.biodiversitylibrary.org/bibliography/542#|location=[[Stockholm]]|publisher=Impensis Direct|isbn=0-665-53008-0|accessdate=2011-09-24}}</ref>

: <math>\text{H. sapiens} \subset \text{Homo} \subset \text{Primates} \subset \text{Mammalia} \subset \text{Animalia}</math>

Taxonomies may change frequently (as seen in [[biological classification|biological taxonomy]]), but the underlying concept of nested hierarchies is always the same.

Taxonomies may change frequently (as seen in biological taxonomy), but the underlying concept of nested hierarchies is always the same.

'''分类法 Taxonomies'''可能会频繁改变（如在生物分类法中所见），但嵌套层次结构这一基本理念始终不变。

In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of [[self-similarity]] and [[recursion]]. Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic.<ref name=Corballis>{{cite book |first=Michael |last=Corballis |title=The Recursive Mind |publisher=Princeton University Press |year=2011 |isbn=978-0691145471}}</ref>

In many programming taxonomies and syntax models (as well as fractals in mathematics), nested hierarchies, including Russian dolls, are also used to illustrate the properties of self-similarity and recursion. Recursion itself is included as a subset of hierarchical programming, and recursive thinking can be synonymous with a form of hierarchical thinking and logic.

在许多编程分类法和句法模型（以及数学中的分形）中，嵌套的层次结构，包括俄罗斯套娃，也用作自相似和递归性质的呈现。递归本身是层次性编程的一个子集，递归思维可用作层次思维和逻辑的同义词。<ref name="natsocsci-ch4">{{cite encyclopedia|title=Hierarchy, Complexity, Society|last=Lane|first=David|pages=81–120|encyclopedia=Hierarchy in Natural and Social Sciences|editor=Pumain, Denise|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}</ref>

===包容层次 Containment hierarchy===

A containment hierarchy is a direct extrapolation of the [[#Nested hierarchy|nested hierarchy]] concept. All of the ordered sets are still nested, but every set must be "[[strict subset|strict]]"—no two sets can be identical. The shapes example above can be modified to demonstrate this:

A containment hierarchy is a direct extrapolation of the nested hierarchy concept. All of the ordered sets are still nested, but every set must be "strict"—no two sets can be identical. The shapes example above can be modified to demonstrate this:

包容层次是嵌套层次概念的直接外推。所有的有序集仍然是嵌套的，但是每个集合必须是“严格”的——不存在两个相同的集合。上面的图形示例可稍作改变来对此进行论证:

: <math> \text{square} \subsetneq \text{quadrilateral} \subsetneq \text{polygon} \subsetneq \text{shape} \, </math>

The notation <math> x \subsetneq y \, </math> means ''x'' is a subset of ''y'' but is not equal to ''y''.

The notation <math> x \subsetneq y \, </math> means x is a subset of y but is not equal to y.

符号 < math > x subsetneq y，</math > 表示x是y的子集，但不等于y。

A general example of a containment hierarchy is demonstrated in [[inheritance (computer science)|class inheritance]] in [[object-oriented programming]].

A general example of a containment hierarchy is demonstrated in class inheritance in object-oriented programming.

'''面向对象编程 Object-oriented Programming'''的'''类继承 Class Inheritance'''是包容层次的一个例证。

Two types of containment hierarchies are the ''subsumptive'' containment hierarchy and the ''compositional'' containment hierarchy. A subsumptive hierarchy "[[wikt:subsume|subsumes]]" its children, and a compositional hierarchy is "[[wikt:composed|composed]]" of its children. A hierarchy can also be both subsumptive ''and'' compositional{{example needed|date=August 2018}}.<ref name="AI industrial">{{cite encyclopedia|title=Industrial and Engineering Applications of Artificial Intelligence and Expert Systems|last=Kopisch|first=Manfred|last2=Günther|first2=Andreas|doi=10.1007/BFb0024994|editor-last=Belli|editor-first=Fevzi|encyclopedia=Industrial and engineering applications of artificial intelligence and expert systems: 5th international conference, IEA/AIE-92, Paderborn, Germany, June 9–12, 1992 : proceedings|year=1992|publisher=[[Springer Science+Business Media|Springer]]|pages=424–427|isbn=3-540-55601-X|series=Lecture Notes in Computer Science Series|volume=602|issn=0302-9743|editor6-last=Radermacher|editor8-first=Franz-Josef|chapter=Configuration of a passenger aircraft cabin based on conceptual hierarchy, constraints and flexible control}}</ref>

Two types of containment hierarchies are the subsumptive containment hierarchy and the compositional containment hierarchy. A subsumptive hierarchy "subsumes" its children, and a compositional hierarchy is "composed" of its children. A hierarchy can also be both subsumptive and compositional.

包容层次有包含包容层次和组合包容层次两种。包含包容层次“包含”其子级，而组合包容层次“组合”其子级。层次结构也可能同时是包含的和组合的。<ref name="AI industrial">{{cite encyclopedia|title=Industrial and Engineering Applications of Artificial Intelligence and Expert Systems|last=Kopisch|first=Manfred|last2=Günther|first2=Andreas|doi=10.1007/BFb0024994|editor-last=Belli|editor-first=Fevzi|encyclopedia=Industrial and engineering applications of artificial intelligence and expert systems: 5th international conference, IEA/AIE-92, Paderborn, Germany, June 9–12, 1992 : proceedings|year=1992|publisher=[[Springer Science+Business Media|Springer]]|pages=424–427|isbn=3-540-55601-X|series=Lecture Notes in Computer Science Series|volume=602|issn=0302-9743|editor6-last=Radermacher|editor8-first=Franz-Josef|chapter=Configuration of a passenger aircraft cabin based on conceptual hierarchy, constraints and flexible control}}</ref>

=====包容层次结构 Subsumptive containment hierarchy=====

A ''[[Category theory|subsumptive]]'' containment hierarchy is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and "[[is-a|IS-A]] hierarchy".<ref name="Lehmann"/><ref name="ibm">{{cite web|url=http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|archive-url=https://archive.today/20130103052727/http://publib.boulder.ibm.com/infocenter/wtxdoc/v8r2m0/index.jsp?topic=/com.ibm.websphere.dtx.md.doc/concepts/c_map_design_Compositional_Hierarchy.htm|url-status=dead|archive-date=3 January 2013|title=Compositional hierarchy|work=WebSphere Transformation Extender Design Studio|accessdate=9 October 2009}}</ref><ref name="sys model">{{cite book|chapter=An advanced modeling environment based on a hybrid AI-OR approach|chapterurl=https://books.google.com/books?id=ds2eIQ6XZy0C&pg=PA366|pages=366–75|last=Funke|first=Birger|last2=Sebastian|first2=Hans-Jürgen|title=Systems modelling and optimization: proceedings of the 18th IFIP TC7 conference|volume=396|series=Research notes in mathematics series|editor1-last=Polis|editor1-first=Michael P.|editor2-last=Dontchev|editor2-first=Asen L.|editor3-last=Kall|editor3-first=Peter|editor4-last=Lascieka|editor4-first=Irena|editor5-last=Olbrot|editor5-first=Andrzej W.|publisher=[[CRC Press]]|year=1999|isbn=978-0-8493-0607-5}}</ref> The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that is part of the level ''Mammalia'' "is a" member of the level ''Animalia''; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of "[[concept]]s".<ref name="sys model"/> For example, with the Linnaean hierarchy outlined above, an entity name like ''Animalia'' is a way to group all the species that fit the [[wikt:conceptualization|conceptualization]] of an animal.

A subsumptive containment hierarchy is a classification of object classes from the general to the specific. Other names for this type of hierarchy are "taxonomic hierarchy" and "IS-A hierarchy". The last term describes the relationship between each level—a lower-level object "is a" member of the higher class. The taxonomical structure outlined above is a subsumptive containment hierarchy. Using again the example of Linnaean taxonomy, it can be seen that an object that is part of the level Mammalia "is a" member of the level Animalia; more specifically, a human "is a" primate, a primate "is a" mammal, and so on. A subsumptive hierarchy can also be defined abstractly as a hierarchy of "concepts". For example, with the Linnaean hierarchy outlined above, an entity name like Animalia is a way to group all the species that fit the conceptualization of an animal.

包容层次结构 subsumptive containment hierarchy是对象类从一般到特定的分类。这类层次结构的其他名称是“分类层次结构”和“ IS-A 层次结构”。最后一个术语描述了每个级别之间的关系——较低级别的对象“是”较高级别类的成员。上面概述的分类结构是一个包容性的层次结构。再次使用林奈分类系统的例子，可以看到，属于哺乳动物 Mammalia 等级的物体“是”动物等级的成员；更具体地说，人类“是”灵长类动物，灵长类动物“是”哺乳动物等等。也可以抽象地将包含的层次结构定义为“概念”的层次结构。例如，根据上述的林奈分类系统，像动物这样的实体名称是对所有符合动物概念的物种进行分类的一种方法。

=====构成性包容层次结构 Compositional containment hierarchy=====

A ''compositional'' containment hierarchy is an ordering of the parts that make up a system—the system is "composed" of these parts.<ref name="Parsons">{{cite book|last=Parsons|first=David|title=Object Oriented Programming in C++|publisher=Cengage Learning|year=2002|pages=110–185|isbn=0-8264-5428-3}}</ref> Most engineered structures, whether natural or artificial, can be broken down in this manner.

A compositional containment hierarchy is an ordering of the parts that make up a system—the system is "composed" of these parts. Most engineered structures, whether natural or artificial, can be broken down in this manner.

构成性包容层次结构 Compositional containment hierarchy是构成系统的各个部分的顺序——系统是由这些部分“构成”的。大多数工程结构，无论是自然的还是人工的，都可以用这种方式分解。

The compositional hierarchy that every person encounters at every moment is the [[hierarchy of life]]. Every person can be reduced to [[organ system]]s, which are composed of [[organ (anatomy)|organs]], which are composed of [[tissue (biology)|tissues]], which are composed of [[cells (biology)|cells]], which are composed of [[molecule]]s, which are composed of [[atom]]s. In fact, the last two levels apply to all [[matter]], at least at the [[macroscopic scale]]. Moreover, each of these levels inherit all the properties of their [[#Terminology|children]].

The compositional hierarchy that every person encounters at every moment is the hierarchy of life. Every person can be reduced to organ systems, which are composed of organs, which are composed of tissues, which are composed of cells, which are composed of molecules, which are composed of atoms. In fact, the last two levels apply to all matter, at least at the macroscopic scale. Moreover, each of these levels inherit all the properties of their children.

每个人每时每刻都会遇到的构成性层次就是生命的层次结构 hierarchy of life。每个人都可以被分解为器官系统 organ system，器官系统是由器官构成的，器官又是由组织构成的，组织是由细胞构成的，分子是由原子构成的。事实上，至少在宏观层面上，最后两个层次适用于所有物质。此外，每个级别都继承了它们子级别的所有属性。

In this particular example, there are also ''[[emergent properties]]''—functions that are not seen at the lower level (e.g., [[cognition]] is not a property of [[neuron]]s but is of the [[Human brain|brain]])—and a scalar quality (molecules are bigger than atoms, cells are bigger than molecules, etc.). Both of these concepts commonly exist in compositional hierarchies, but they are not a required general property. These ''level hierarchies'' are characterized by bi-directional [[Causality|causation]].<ref name="natsocsci-ch4"/> ''Upward causation'' involves lower-level entities causing some property of a higher level entity; children entities may interact to yield parent entities, and parents are composed at least partly by their children. ''[[Downward causation]]'' refers to the effect that the incorporation of entity ''x'' into a higher-level entity can have on ''x'''s properties and interactions. Furthermore, the entities found at each level are ''[[autonomous]]''.

In this particular example, there are also emergent properties—functions that are not seen at the lower level (e.g., cognition is not a property of neurons but is of the brain)—and a scalar quality (molecules are bigger than atoms, cells are bigger than molecules, etc.). Both of these concepts commonly exist in compositional hierarchies, but they are not a required general property. These level hierarchies are characterized by bi-directional causation. Upward causation involves lower-level entities causing some property of a higher level entity; children entities may interact to yield parent entities, and parents are composed at least partly by their children. Downward causation refers to the effect that the incorporation of entity x into a higher-level entity can have on xs properties and interactions. Furthermore, the entities found at each level are autonomous.

在这个特定的例子中，还有一些涌现特性 emergent properties——在较低层次上看不到的功能（例如认知 cognition不是神经元的特性，而是大脑的特性）——以及标度特性（分子比原子大，细胞比分子大等等）。这两个概念通常都存在于组合层次结构中，但它们不是必要的一般属性。这些层次结构是拥有属性的双向因果关系。涉及较低层次实体的上向因果关系 Upward causation导致较高层次实体的某些属性；子实体可以相互作用产生父实体，并且父实体至少部分由他们的子实体组成。下向因果关系 Downward causation是指将实体 x 并入更高级别的实体可能对 x 的属性和相互作用产生的影响。此外，每个级别上的实体都是自治的 autonomous。

==Contexts and applications 语境和应用==

= = 上下文和应用 = = < ! ——如果你更改了这个部分的标题，请也更改文章中链接到它的 wikileink！-->

According to Kulish, V. V. (2002), almost every system of organization applied to the world is arranged hierarchically.<ref name="electrodynamics">{{cite book|title=Hierarchical Methods: Hierarchy and hierarchical asymptotic methods in electrodynamics|last=Kulish|first=V. V.|isbn=1-4020-0757-4|year=2002|volume=1|publisher=[[Springer Science+Business Media|Springer]]|pages=xvii–xx; 49–71}}</ref> By their common definitions, every [[nation]] has a government and every government is hierarchical.<ref>{{Cite book|contribution=government|title=Compact Oxford English Dictionary|contribution-url=http://www.askoxford.com/concise_oed/government?view=uk|isbn=978-0-19-861022-9|year=1991|title-link=Oxford English Dictionary|last1=Soanes|first1=Catherine|last2=Hawker|first2=Sara}}</ref><ref>{{Cite book|contribution=nation|title=Compact Oxford English Dictionary|contribution-url=http://www.askoxford.com/concise_oed/nation?view=uk|isbn=978-0-19-861022-9|year=1991|title-link=Oxford English Dictionary|last1=Soanes|first1=Catherine|last2=Hawker|first2=Sara}}</ref> Socioeconomic systems are stratified into a social hierarchy (the [[social stratification]] of societies), and all [[systematic name|systematic classification schemes]] ([[Taxonomy (general)|taxonomies]]) are hierarchical. Most [[organized religion]]s, regardless of their internal governance structures, operate as a hierarchy under [[God]]. Many [[Christian denomination]]s have an [[autocephalous]] [[ecclesiastical hierarchy]] of leadership. Families are viewed as a hierarchical structure in terms of [[cousinship]] (e.g., first cousin once removed, second cousin, etc.), [[ancestry]] (as depicted in a [[family tree]]) and [[inheritance]] ([[order of succession|succession]] and [[heir]]ship). All the requisites of a well-rounded life and [[lifestyle (sociology)|lifestyle]] can be organized using [[Maslow's hierarchy of needs|Maslow's hierarchy of human needs]]. [[Learning]] must often follow a hierarchical scheme—to learn [[differential equation]]s one must first learn [[calculus]]; to learn calculus one must first learn [[elementary algebra]]; and so on. Even [[nature]] itself has its own hierarchies, as numerous schemes such as [[Linnaean taxonomy]], the [[biological organisation|organization of life]], and [[biomass pyramid]]s attempt to document. Hierarchies are so infused into daily life that they are viewed as trivial.<ref name="Dawkins"/><ref name="electrodynamics"/>

According to Kulish, V. V. (2002), almost every system of organization applied to the world is arranged hierarchically. By their common definitions, every nation has a government and every government is hierarchical. Socioeconomic systems are stratified into a social hierarchy (the social stratification of societies), and all systematic classification schemes (taxonomies) are hierarchical. Most organized religions, regardless of their internal governance structures, operate as a hierarchy under God. Many Christian denominations have an autocephalous ecclesiastical hierarchy of leadership. Families are viewed as a hierarchical structure in terms of cousinship (e.g., first cousin once removed, second cousin, etc.), ancestry (as depicted in a family tree) and inheritance (succession and heirship). All the requisites of a well-rounded life and lifestyle can be organized using Maslow's hierarchy of human needs. Learning must often follow a hierarchical scheme—to learn differential equations one must first learn calculus; to learn calculus one must first learn elementary algebra; and so on. Even nature itself has its own hierarchies, as numerous schemes such as Linnaean taxonomy, the organization of life, and biomass pyramids attempt to document. Hierarchies are so infused into daily life that they are viewed as trivial.

根据 Kulish v. v. (2002) 的研究，几乎世界上所有的组织系统都是等级制度的。<ref name="electrodynamics">{{cite book|title=Hierarchical Methods: Hierarchy and hierarchical asymptotic methods in electrodynamics|last=Kulish|first=V. V.|isbn=1-4020-0757-4|year=2002|volume=1|publisher=[[Springer Science+Business Media|Springer]]|pages=xvii–xx; 49–71}}</ref>按照他们的共同定义，每个国家 nation都有一个政府，每个政府都是层级制度的。<ref>{{Cite book|contribution=government|title=Compact Oxford English Dictionary|contribution-url=http://www.askoxford.com/concise_oed/government?view=uk|isbn=978-0-19-861022-9|year=1991|title-link=Oxford English Dictionary|last1=Soanes|first1=Catherine|last2=Hawker|first2=Sara}}</ref><ref>{{Cite book|contribution=nation|title=Compact Oxford English Dictionary|contribution-url=http://www.askoxford.com/concise_oed/nation?view=uk|isbn=978-0-19-861022-9|year=1991|title-link=Oxford English Dictionary|last1=Soanes|first1=Catherine|last2=Hawker|first2=Sara}}</ref> 社会经济系统被分为一个社会等级制（社会的社会分层 social stratification），所有的系统分类方案(分类法)都是分等级的。大多数有组织的宗教，不管它们的内部管理结构如何，都在上帝之下按照层级运作。许多基督教教派 Christian denominations都有一个独立的教会领导层次。从表亲关系（例如，第一代表兄弟，第二代表兄弟等等）、祖先(由家谱 family tree描述)和继承(继承和继承权)的角度来看，家庭可以看作是一种等级结构。一个全面的生活和生活方式的所有必需品都可以用马斯洛人类需求层次 Maslow's hierarchy of human needs来组织。学习通常必须遵循一个层次框架——学习微分方程必须先学习微积分；学习微积分必须先学习初等代数等等。甚至自然本身也有它自己的层级，许多方案试图记录下来，例如林奈分类学、生命的组织和生物量金字塔。层级制度是如此地深入到日常生活中，以至于人们认为它们微不足道。<ref name="Dawkins"/><ref name="electrodynamics"/>

While the above examples are often clearly depicted in a hierarchical form and are classic examples, hierarchies exist in numerous systems where this branching structure is not immediately apparent. For example, most [[postal code]] systems are hierarchical. Using the [[Postal codes in Canada|Canadian postal code system]] as an example, the top level's binding concept is the "[[forward sortation area|postal district]]", and consists of 18 objects (letters). The next level down is the "zone", where the objects are the digits 0–9. This is an example of an [[#Degree_of_branching|overlapping hierarchy]], because each of these 10 objects has 18 parents. The hierarchy continues downward to generate, in theory, 7,200,000 unique codes of the format ''A0A 0A0'' (the second and third letter position allow 20 objects each). Most [[library classification]] systems are also hierarchical. The [[Dewey Decimal Classification|Dewey Decimal System]] is regarded as infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point.<ref name="Dewey">{{cite journal|title=Tracking Nuclear Sources|date=May–June 2009|last=Walker|first=Randy|publisher=wellservicingmagazine.com|pages=28–30|url=http://wellservicingmagazine.com/sites/default/files/pdfmag/WSM_MAYJUN09.PDF}}{{dead link|date=November 2017 |bot=InternetArchiveBot |fix-attempted=yes}} See also [[Dewey Decimal Classification|Wikipedia article]].</ref>

While the above examples are often clearly depicted in a hierarchical form and are classic examples, hierarchies exist in numerous systems where this branching structure is not immediately apparent. For example, most postal code systems are hierarchical. Using the Canadian postal code system as an example, the top level's binding concept is the "postal district", and consists of 18 objects (letters). The next level down is the "zone", where the objects are the digits 0–9. This is an example of an overlapping hierarchy, because each of these 10 objects has 18 parents. The hierarchy continues downward to generate, in theory, 7,200,000 unique codes of the format A0A 0A0 (the second and third letter position allow 20 objects each). Most library classification systems are also hierarchical. The Dewey Decimal System is regarded as infinitely hierarchical because there is no finite bound on the number of digits can be used after the decimal point.

虽然上面的例子通常以层次形式清楚地描述并且很经典，但是层次结构也存在于许多分支结构并不是很明显的系统中。例如，大多数邮政编码 postal code系统是分层的。以加拿大邮政编码系统为例，顶层的概念是“邮区 postal district”，由18个对象(字母)组成。下一层是“地区 zone”，其中的对象是数字0-9。这是重叠层次结构的一个例子，因为这10个对象中的每一个都有18个父对象。层次继续向下生成，理论上存在720万个 A0A 0A0 (第二个和第三个字母的位置每个允许20个对象)格式的唯一代码。大多数图书分类法系统也是分层级的。杜威十进制图书分类法 Dewey Decimal System被认为是无限层次的，因为在小数点之后可以使用的数字数量是没有限制的。

[[File:Organizational chart.svg|thumb|200px|A simple [[hierarchical organization|organizational hierarchy]] depicted in the form of a [[tree structure|tree]]. Diagrams like this are called [[organizational chart]]s.]]

organizational hierarchy depicted in the form of a tree. Diagrams like this are called organizational charts.]]

以树的形式描述的组织层次结构。这样的图被称为组织结构图 organizational charts。

===Organizations 组织===

{{Main|Organizational structure|Hierarchical organization}}

[[Organization]]s can be structured as a [[dominance hierarchy]]. In an organizational hierarchy, there is a single person or group with the most [[power (philosophy)|power]] and [[authority]], and each subsequent level represents a lesser authority. Most organizations are structured in this manner, including [[Forms of government|governments]], [[Company|companies]], [[militia]] and [[organized religion]]s. The units or persons within an organization are depicted hierarchically in an [[organizational chart]].

Organizations can be structured as a dominance hierarchy. In an organizational hierarchy, there is a single person or group with the most power and authority, and each subsequent level represents a lesser authority. Most organizations are structured in this manner, including governments, companies, militia and organized religions. The units or persons within an organization are depicted hierarchically in an organizational chart.

组织 Organizations可以被构建成一个支配等级 dominance hierarchy。在一个组织的层次结构中，有一个人或一个群体拥有最大的权力和权威，每个后续的层次代表一个较小的权威。大多数组织都是这样构建的，包括政府、公司、民兵和有组织的宗教。组织中的单位或人员在组织结构图中按等级进行描述。

In a [[reverse hierarchy]], the conceptual [[pyramid (geometry)|pyramid]] of authority is turned upside-down, so that the apex is at the bottom and the base is at the top. This mode represents the idea that members of the higher rankings are responsible for the members of the lower rankings.

In a reverse hierarchy, the conceptual pyramid of authority is turned upside-down, so that the apex is at the bottom and the base is at the top. This mode represents the idea that members of the higher rankings are responsible for the members of the lower rankings.

在反向层次结构 reverse hierarchy中，权威的概念金字塔是颠倒的，因此顶点在底部，底部在顶部。这种模式代表了等级较高的成员对等级较低的成员负责的思想。

=== Life 生命===

{{Main|Biological organisation#Fundamentals}}

Empirically, we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure. On theoretical grounds we could expect complex systems to be hierarchies in a world in which complexity had to evolve from simplicity. [[Systems theory|System]] hierarchies analysis performed in the 1950s,<ref>{{harvnb|Evans|1951}}</ref><ref>{{harvnb|Evans|1956}}</ref> laid the empirical foundations for a [[Branches of science|field]] that would be, from the 1980s, '''hierarchical ecology'''.<ref>{{harvnb|Margalef|1975}}</ref><ref>{{harvnb|O'Neill|1986}}</ref><ref>{{harvnb|Wicken|Ulanowicz|1988}}</ref><ref>{{harvnb|Pumain|2006}}</ref><ref>{{harvnb|Jordan|Jørgensen|2012}}</ref>

Empirically, we observe in nature a large proportion of the (complex) biological systems, they exhibit hierarchic structure. On theoretical grounds we could expect complex systems to be hierarchies in a world in which complexity had to evolve from simplicity. System hierarchies analysis performed in the 1950s, laid the empirical foundations for a field that would be, from the 1980s, hierarchical ecology.

在实践中，我们观察到自然界中很大一部分(复杂的)生物系统呈现出层次结构。从理论上讲，在一个复杂性必须从简单性演化而来的世界中，我们可以预期复杂系统具有层次结构。20世纪50年代进行的系统层次分析，<ref>{{harvnb|Evans|1951}}</ref><ref>{{harvnb|Evans|1956}}</ref>为从20世纪80年代开始的层次生态学领域奠定了经验基础。<ref>{{harvnb|Margalef|1975}}</ref><ref>{{harvnb|O'Neill|1986}}</ref><ref>{{harvnb|Wicken|Ulanowicz|1988}}</ref><ref>{{harvnb|Pumain|2006}}</ref><ref>{{harvnb|Jordan|Jørgensen|2012}}</ref>

The theoretical foundations are summarized by Thermodynamics. When [[biological systems]] are modeled as [[physical system]]s, in its most general abstraction, they are [[Thermodynamic system#Open system|thermodynamic open systems]] that exhibit [[self-organisation|self-organised]] behavior, and the [[Set theory|set/subset]] relations between [[dissipative structures]] can be characterized in a hierarchy.

The theoretical foundations are summarized by Thermodynamics. When biological systems are modeled as physical systems, in its most general abstraction, they are thermodynamic open systems that exhibit self-organised behavior, and the set/subset relations between dissipative structures can be characterized in a hierarchy.

这些理论基础由热力学的方法来总结。当生物系统被模拟为物理系统时，在其最一般的抽象中，它们是表现出自组织行为的热力学开放系统，耗散结构 dissipative structures之间的集合/子集关系可以用层次结构来刻画。

===Computer graphic imaging 计算机图形成像===

{{Main|3D modeling}}

[[Computer-generated imagery|CGI]] and [[computer animation]] [[computer program|programs]] mostly use hierarchies for models. On a [[3D computer graphics|3D]] [[3d modeling|model]] of a [[human]] for example, the [[chest]] is a [[parent]] of the upper left arm, which is a parent of the lower left arm, which is a parent of the [[hand]]. This is used in [[3D modeling|modeling]] and [[animation]] for almost everything built as a 3D [[Digital data|digital]] model.

CGI and computer animation programs mostly use hierarchies for models. On a 3D model of a human for example, the chest is a parent of the upper left arm, which is a parent of the lower left arm, which is a parent of the hand. This is used in modeling and animation for almost everything built as a 3D digital model.

CGI 和计算机动画程序 computer animation programs大多使用层次结构建模。例如在一个人体的三维模型中，胸部是左上臂的母体，而左上臂是左下臂的母体。层次结构用于几乎所有三维数字模型的建模和动画。

===Linguistics 语言学===

Many grammatical theories, such as [[phrase-structure grammar]], involve hierarchy.

Many grammatical theories, such as phrase-structure grammar, involve hierarchy.

许多语法理论都包括层次结构，例如短语结构语法。

[[Direct–inverse language]]s such as [[Cree language|Cree]] and [[Mapudungun language|Mapudungun]] distinguish subject and object on [[verb]]s not by different subject and object markers, but via a hierarchy of persons.

Direct–inverse languages such as Cree and Mapudungun distinguish subject and object on verbs not by different subject and object markers, but via a hierarchy of persons.

克里语(Cree)和马普敦根语(Mapudungun)等正动-反动语言 Direct–inverse languages不是通过不同的主语和宾语标记来区分动词的主语和宾语，而是通过人的层级来区分。

In this system, the three (or four with [[Algonquian languages]]) persons are placed in a hierarchy of [[salience (language)|salience]]. To distinguish which is subject and which object, ''inverse markers'' are used if the object outranks the subject.

In this system, the three (or four with Algonquian languages) persons are placed in a hierarchy of salience. To distinguish which is subject and which object, inverse markers are used if the object outranks the subject.

在这个系统中，三个人(或者阿尔冈昆诸语言中四个人)被放在显著的等级中。为了区分哪个是主语，哪个是宾语，如果宾语的级别高于主语，则使用反向标记。

On the other hand, languages include a variety of phenomena that are not hierarchical. For example, the relationship between a pronoun and a prior noun phrase to which it refers, commonly crosses grammatical boundaries in non-hierarchical ways.

On the other hand, languages include a variety of phenomena that are not hierarchical. For example, the relationship between a pronoun and a prior noun phrase to which it refers, commonly crosses grammatical boundaries in non-hierarchical ways.

另一方面，语言包括多种非等级性的现象。例如，代词和它所指的名词短语之间的关系，通常以非等级的方式跨越语法界限。

===Music 音乐===

The structure of a musical composition is often understood hierarchically (for example by [[Heinrich Schenker]] (1768–1835, see [[Schenkerian analysis]]), and in the (1985) [[Generative theory of tonal music|Generative Theory of Tonal Music]], by composer [[Fred Lerdahl]] and linguist Ray [[Jackendoff]]). The sum of all notes in a piece is understood to be an all-inclusive surface, which can be reduced to successively more sparse and more fundamental types of motion. The levels of structure that operate in Schenker's theory are the foreground, which is seen in all the details of the musical score; the middle ground, which is roughly a summary of an essential contrapuntal progression and voice-leading; and the background or [[Ursatz]], which is one of only a few basic "long-range counterpoint" structures that are shared in the gamut of tonal music literature.

The structure of a musical composition is often understood hierarchically (for example by Heinrich Schenker (1768–1835, see Schenkerian analysis), and in the (1985) Generative Theory of Tonal Music, by composer Fred Lerdahl and linguist Ray Jackendoff). The sum of all notes in a piece is understood to be an all-inclusive surface, which can be reduced to successively more sparse and more fundamental types of motion. The levels of structure that operate in Schenker's theory are the foreground, which is seen in all the details of the musical score; the middle ground, which is roughly a summary of an essential contrapuntal progression and voice-leading; and the background or Ursatz, which is one of only a few basic "long-range counterpoint" structures that are shared in the gamut of tonal music literature.

音乐作品的结构通常是按层次来理解的（例如 Heinrich Schenker （1768-1835，见 Schenkerian 分析），以及 Fred Lerdahl 和语言学家 Ray Jackendoff 1985年的《调性音乐的生成理论 Generative Theory of Tonal Music》）。一段乐曲中所有音符的总和被理解为一个包含所有音符的曲面，它可以简化为更加稀疏和更加基本的运动类型。在Schenker的理论中运作的结构层次包括前景层次，这在音乐乐谱的所有细节中都可以看到；中间层次，大致上是对位进行和主音的总结; 背景层次，即 Ursatz，这是调性音乐著作中仅有的几个共享的基本“远距离对位”结构之一。

The [[pitch (music)|pitches]] and [[Musical form|form]] of [[Tonality|tonal]] music are organized hierarchically, all pitches deriving their importance from their relationship to a [[Tonic (music)|tonic]] [[Key signature|key]], and secondary themes in other keys are brought back to the tonic in a recapitulation of the primary theme. [[Susan McClary]] connects this specifically in the [[sonata-allegro form]] to the feminist hierarchy of gender (see above) in her book ''Feminine Endings'', even pointing out that primary themes were often previously called "masculine" and secondary themes "feminine."

The pitches and form of tonal music are organized hierarchically, all pitches deriving their importance from their relationship to a tonic key, and secondary themes in other keys are brought back to the tonic in a recapitulation of the primary theme. Susan McClary connects this specifically in the sonata-allegro form to the feminist hierarchy of gender (see above) in her book Feminine Endings, even pointing out that primary themes were often previously called "masculine" and secondary themes "feminine."

调性音乐 tonal music的音高 pitches和形式是按等级组织的，所有音高的重要性来自于它们与主调 tonic key的关系，其他调中的次要主题在主要主题的再现中被带回主调。苏珊·麦克拉里（Susan McClary）在她的《女性结局（(Feminine Endings）一书中将这一点在奏鸣曲式中具体地与女性主义的性别层次结构(见上文)联系起来，甚至指出，主要的主题通常以前被称为“阳性” ，而次要主题被称为“阴性”。

==Criticisms of views, concerning distinctions of type and categories well as distinguishability 关于类型和范畴的区别以及区别性的观点的批判==

In the work of diverse theorists such as [[William James]] (1842–1910), [[Michel Foucault]] (1926–1984) and [[Hayden White]], important critiques of hierarchical [[epistemology]] are advanced. James famously asserts in his work "Radical Empiricism" that clear distinctions of type and category are a constant but unwritten goal of scientific reasoning, so that when they are discovered, success is declared. But if aspects of the world are organized differently, involving inherent and intractable ambiguities, then scientific questions are often considered unresolved.

In the work of diverse theorists such as William James (1842–1910), Michel Foucault (1926–1984) and Hayden White, important critiques of hierarchical epistemology are advanced. James famously asserts in his work "Radical Empiricism" that clear distinctions of type and category are a constant but unwritten goal of scientific reasoning, so that when they are discovered, success is declared. But if aspects of the world are organized differently, involving inherent and intractable ambiguities, then scientific questions are often considered unresolved.

在William James(1842-1910)、Michel Foucault (1926-1984)和Hayden White等不同理论家的著作中，提出了对等级认识论的重要批判。詹姆斯在他的著作“彻底经验主义 Radical Empiricism”中断言，明确类型和范畴的区分是科学推理的一个恒定但不成文的目标，因此当此目标实现时，就是宣告成功之时。但是，如果世界的各个方面以不同的方式组织起来，涉及到固有的和难以解决的模糊性，那么科学问题通常被认为是没有解决的。

Hierarchy in ethics emerged in Western Europe, West Asia and North Africa around the 1600s. In this aspect, the term hierarchy refers to how distinguishable they are from real to unreal. [[Feminists]], [[Marxists]], [[anarchists]], [[communists]], [[critical theorists]] and others, all of whom have multiple interpretations, criticize the hierarchies commonly found within human society, especially in social relationships. Hierarchies are present in all parts of society: in businesses, schools, families, etc. These relationships are often viewed as necessary. Entities that stand in hierarchical arrangements are animals, humans, plants, etc.

Hierarchy in ethics emerged in Western Europe, West Asia and North Africa around the 1600s. In this aspect, the term hierarchy refers to how distinguishable they are from real to unreal. Feminists, Marxists, anarchists, communists, critical theorists and others, all of whom have multiple interpretations, criticize the hierarchies commonly found within human society, especially in social relationships. Hierarchies are present in all parts of society: in businesses, schools, families, etc. These relationships are often viewed as necessary. Entities that stand in hierarchical arrangements are animals, humans, plants, etc.

17世纪左右，伦理学中的等级制度在西欧、西亚和北非出现。在这方面，术语层次是指它们从真实到非真实是如何区分的。女权主义者 Feminists、马克思主义者 Marxists、无政府主义者 anarchists、共产主义者 communists、批判理论家 critical theorists以及其他人，他们对人类社会中普遍存在的等级制度，尤其是社会关系中的等级制度，都有不同的解释与批判。等级制度存在于社会的各个部分：企业、学校、家庭等等。这些关系通常被认为是必要的。存在于等级结构中的实体可以是动物、人类、植物等等。

===Ethics, behavioral psychology, philosophies of identity 伦理，行为心理学，同一哲学 philosophies of identity ===

[[File:Hierarchy Of Purposes.jpg|thumb|right|alt=|Career-oriented purposes can be diagrammed using a hierarchy describing how less important actions support a larger goal.]]

Career-oriented purposes can be diagrammed using a hierarchy describing how less important actions support a larger goal.

职业目标可以用一个描述次要行动如何支持一个更大的目标的层次结构来图示。

In [[ethics]], various [[virtues]] are enumerated and sometimes organized hierarchically according to certain brands of [[virtue theory]].

In ethics, various virtues are enumerated and sometimes organized hierarchically according to certain brands of virtue theory.

伦理学 ethics中会列举各种美德 virtues，并有时将其根据特定美德理论有层次地组织起来。

In some of these random examples, there is an asymmetry of 'compositional' significance between levels of structure, so that small parts of the whole hierarchical array depend, for their meaning, on their membership in larger parts. There is a hierarchy of activities in human life: productive activity serves or is guided by the moral life; the moral life is guided by practical reason; practical reason (used in moral and political life) serves contemplative reason (whereby we contemplate God). Practical reason sets aside time and resources for contemplative reason.

In some of these random examples, there is an asymmetry of 'compositional' significance between levels of structure, so that small parts of the whole hierarchical array depend, for their meaning, on their membership in larger parts. There is a hierarchy of activities in human life: productive activity serves or is guided by the moral life; the moral life is guided by practical reason; practical reason (used in moral and political life) serves contemplative reason (whereby we contemplate God). Practical reason sets aside time and resources for contemplative reason.

在一些随机的例子中，结构层次之间的“构成的”重要性是不对称的，因此整个层次组的小部分的意义依赖于它们在更大部分中的隶属关系。人类生活中的活动有一种层次：生产活动服务于或被道德生活所指导；道德生活被实践理性所指导；实践理性(用于道德和政治生活)服务于冥想理性(我们借以思考上帝)。实用理性为深思的理由留出时间和资源。

==Examples of other applications 其他应用的例子==





<！-- 本节仅供直接举例说明等级制度，仅供上文未概述的例子参考。方法学属于下面的适当部分。相关概念列在“请参阅”部分。如果您不确定链接属于哪个位置，请将其放在“请参阅”部分。提示: 如果你不能很容易地说出它是什么的层次结构，它就不属于这里(但这并不意味着只要你能说出它是什么的层次结构，它就属于这里)。-->

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====Information-based====

====Information-based 基于信息====

= = = = = 信息为基础 = = = = < ! -- 是的，连字符是正确的，即使按照 wp: hyphen ー这个类别的逻辑标题是“信息为基础的层次结构” -- >

* [[Library classification 图书馆分类法]]

** [[Dewey Decimal Classification 杜威十进制分类法]]

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====City planning-based====

====City planning-based 基于城市规划====

= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

* [[Hierarchy of roads|Roads 道路]]

** [[Street hierarchy|Streets 街道]]

* [[Settlement hierarchy 聚落等级]]

** [[Settlement hierarchy#Example of a settlement hierarchy|As of 2010 截至2010年]]

** [[Ekistic units|As of 2100 (estimate according to Doxiadis, 1968) 截至2010年（根据Doxiadis 1968年的估计）]]

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====Linguistics-based====

====Linguistics-based 基于语言学====

= = = 基于语言学的 = = = = = < ! -- 是的，连字符是正确的，即使按 wp: hyphen ー这个类别的逻辑标题是“基于语言学的层次” -- >

* [[Tree model|Language family tree 语言家谱]]

* [[Levels of adequacy|Levels of adequacy for evaluating grammars 评价语法的充分性等级]]

* [[Direct–inverse languages 正对-反对语言]]

* [[Structural linguistics 结构语言学]]

** [[Parse tree 分析树]]

** [[Formal grammars 形式语法]]

** [[Abstract syntax tree 抽象语法树]]

* [[Color terms#Basic color terms|Evolution of basic color terminology in languages 语言中基本颜色术语的演变]]

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====Power- or authority-based====

====Power- or authority-based 基于权利或权威====

= = = 权力-或基于权威 = = = = = < ! -- 是的，连字符是正确的，即使按照 wp: hyphen ー这个类别的逻辑标题是“权力-或基于权威的层次结构” -- >

* [[Noble ranks|Aristocratic hierarchies 贵族等级]]

** In [[Royal and noble ranks#General chart of "translations" between languages|Europe 欧洲]]

** In [[Chinese nobility#Princehood and peerage|China 中国]]

* [[Ecclesiastical hierarchy|Ecclesiastical hierarchies 教会等级]]

** [[Catholic Church hierarchy 天主教会圣统制]]

** [[Priesthood (LDS Church)|LDS Church hierarchy 摩门教教堂层次结构]]

** [[Kimbanguism#Hierarchy|Kimbanguist Church hierarchy Kimbanguist教堂层次结构]]

** [[Raëlism#Member hierarchy|Raëlism Church hierarchy Raëlism教堂层次结构]]

** see also [[autocephaly]] 另见[[自治 autocephaly]]

* Administrative branch of government geographical hierarchies

** [[Administrative divisions of China (disambiguation)|Administrative divisions of China]] 

** [[Administrative divisions of India]]

** [[Administrative divisions of the United States]]

** [[Administrative divisions of Russia]]

* Political party hierarchies 政党的层次结构

** [[Ranks and insignia of the Nazi Party|Nazi Party 纳粹党]]

*** [[SS Ranks#Final SS ranks 1934–1945|SS]]

*** [[Glossary of Nazi Germany#G|Hierarchy of subdivisions within the Gau Gau内部的细分层次结构]]

** [[Communist Party of the Soviet Union#Structure|Communist Party of the Soviet Union 苏联共产党]]

** [[Communist Party of China 中国共产党]]

* [[Command hierarchy|Chain of command 指挥系统]]

** [[List of comparative military ranks|Military ranks 军衔]]

** [[Military organization#Hierarchy of modern armies|Military units 部队]]

** [[Unified Combatant Command|U.S. Military Combatant Commands 美国军事战斗司令部]]

* [[Dominance hierarchy|Intraspecial dominance 种内优势]]

** [[Pecking order 啄食顺序]]

* [[Social stratification|Social classes 社会阶级]]

** [[Caste system in India 印度种姓制度]]

** [[Hierarchical structure of Feudal Japan 封建日本的等级结构]]

** [[Master race#White racist hierarchy|White racist hierarchy 白人种族主义的层次结构]]

** [[Hierarchy of Exclusion 层次结构的排斥]] (Ender's Game 安德的游戏)

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====Value-based====

====Value-based 基于价值====

= = = = = 基于价值的价值 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =

* [[Hierarchy of genres|Hierarchy of genres in art 艺术流派的等级]]

* [[Hierarchy of evidence|Evidence 证据]]

* [[Maslow's hierarchy of needs|Human needs 人类需求]]

* [[Hierarchy of precious substances|Precious substances 贵重物品]]

* [[Hierarchy of values|Judicial hierarchy of social values 社会价值的司法等级]]

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====Perception-based====

====Perception-based 基于感知====

= = = 基于感知的感知 = = = = = < ! -- 是的，连字符是正确的，即使按照 wp: hyphen ー这个类别的逻辑标题是“基于感知的层级” -- >

* [[Color wheel 色环]]

** [[Primary colors 三原色]]

*** [[Secondary colors 二次色]]

**** [[Tertiary colors 三次色]]

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====History-based====

====History-based 基于历史====

= = = 历史为基础 = = = = < ! -- 是的，连字符是正确的，即使按 wp: hyphen ー这个类别的逻辑标题是“基于历史的层级” -- >

* [[Three-age system 史前三时代分类系统]]

* [[Comparative history|Cyclic theory of civilization 文明的循环说]]

** [[Spengler's civilization model|Oswald Spengler 奥斯瓦尔德·斯宾格勒]]

** [[A Study of History#List of civilizations|Arnold J. Toynbee]]

* [[Spiral dynamics 螺旋动力学]]

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====Science-based 基于科学====





< ! -- wp: hyphen ー这个类别的逻辑标题是"科学层次">

* [[Earth's location in the universe#Earth in the universe|Hierarchy of organization within the Universe 宇宙中的组织层次]]

* [[Hierarchical ternary star system|Star systems 恒星系统]]

* [[Biological classification 生物分类]]

* [[Biological organization 生物组织]]

* [[Phylogenetic tree 进化树]]

* [[Timeline of evolution|Evolutionary development 进化发展]]

* [[Ecological land classification#Hierarchy of classification levels in ecology compared to other fields|Hierarchy of ecological georegions 生态地理等级]]

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====Technology-based 基于技术====

* [[Memory hierarchy 存储层次结构]]

** [[Cache hierarchy 缓存层次]]

* [[Hierarchical clustering|Clusters 聚类]]

* [[Hierarchy (object-oriented programming)|Class constructs 类构造]]

* [[Hierarchical database model|Data organization 数据组织]]

** [[Hierarchical query 层次查询]]

* [[Hierarchical Data Format|Data storage 数据存储]]

** [[Hierarchical File System|Computer files (Macintosh) 计算机文件(Macintosh)]]

* [[Hierarchical control system|Devices 设备]]

* [[Classless inter-domain routing|IP addresses IP地址]]

* [[Memory hierarchy|Memory 内存]]

** [[Hierarchical page tables|Virtual memory allocation 虚拟内存分配]]

* [[Hierarchical internetworking model|Networks 网络]]

* [[Hierarchical cell structure|Radio cells 无线电单元]]

* [[Hierarchical state machine|States (configurations) 状态（配置）]]

* [[Hierarchical name space|Web addresses 网页地址]]

* [[Structure 结构]]

** [[Data Structure 数据结构]]

* [[Inheritance (object-oriented programming) 继承（面向对象编程）]]

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====Religion-based====

====Religion-based 基于宗教====

= = = = 基于宗教的 = = = = = = = = = = 是的，连字符是正确的，即使按照 wp: hyphen ー这个类别的逻辑标题是“基于宗教和神话的等级制度” -- >

* Levels of consciousness 意识层次

** [[Chakra#The seven major chakras|Chakras 轮穴]]

** [[Great chain of being 存在之链]]

** [[Ray of Creation|G.I. Gurdjieff]]

** [[Eight Circuit Model of Consciousness#The eight circuits|Timothy Leary 蒂莫西·利里]]

* Levels of spiritual development 精神发展层次

** In [[Four stages of enlightenment|Theravada Buddhism 南传上座部佛教]]

** In [[Bhumi (Buddhism)|Mahayana Buddhism 大乘佛教]]

** In [[Initiation (Theosophy)|Theosophy 神智学]]

* Ages in the evolution of society 社会发展的时代

** In [[Astrological age#Past ages|Astrology 占星术]]

** In [[Ages of Man|Hellenism (the Ancient Greek Religion) 希腊文化(古希腊的宗教)]]

** [[Dispensation (period)#Protestant dispensations|Dispensations in Protestantism 新教的豁免]]

** [[Dispensation (period)#Latter Day Saint dispensations|Dispensations in Mormonism 摩门教特许]]

* [[Hierarchical communion|Degrees of communion between various Christian churches 不同基督教会之间的交流程度]]

* [[UFO religions UFO宗教]]

** [[Master Jesus#Airborne Division of the Brotherhood of Light|Command hierarchy of the ''Ashtar Galactic Command'' flying saucer fleet 阿斯塔银河司令部”飞碟舰队的指挥等级]]

* Deities 神灵

** In [[Japanese Buddhist pantheon#Hierarchical structure of the Buddhist pantheon|Japanese Buddhism 日本佛教]]

** In [[Spiritual Hierarchy#Levels of the spiritual hierarchy|Theosophy 神智学]]

* Angels 天使

** In [[Christian angelic hierarchy|Christianity 基督教]]

** In [[Islamic view of angels#Angel hierarchy|Islam 伊斯兰教]]

** In [[Jewish angelic hierarchy|Judaism 犹太教]]

*** [[Kabbalistic angelic hierarchy|Kabbalistic 卡巴拉教派]]

** In [[Yazata|Zoroastrianism 琐罗亚斯德教]]

* Devils and Demons 撒旦与恶魔

** [[Hierarchy of devils|Devils]]

** [[Hierarchy of demons|Demons]]

* [[Hells 地狱]]

** In [[Inferno (Dante)|Catholicism (Nine Levels of Hell) 天主教(九层地狱)]]

** In [[Naraka (Buddhism)|Buddhism (Sixteen Levels of Hell) 佛教(十六层地狱)]]

* [[Religious stratification|Religions in society 社会上的宗教]]

* (organizational hierarchies are listed under 组织和层次列举于{{nowrap|"[[#Power- or authority-based|Power- or authority-based]]"}})

===Methods using hierarchy===

===Methods using hierarchy 使用层次结构的方法===

= = = = 使用层次结构的方法 = = = < ! -- 参见“ further applications” -- >

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* [[Analytic Hierarchy Process 层次分析法]]

** [[Hierarchical Decision Process 层次决策过程]]

* [[HOOD method|Hierarchic Object-Oriented Design 分层的面向对象设计]]

* [[Hierarchical Bayes model 贝叶斯层次模型]]

* [[Hierarchical clustering 层次聚类]]

** [[Hierarchical clustering of networks 网络层次聚类]]

* [[Hierarchical constraint satisfaction 层次约束满足]]

* [[Hierarchical linear modeling 多层阶线性模型]]

* [[Hierarchical modulation 分层调制]]

* [[Hierarchical proportion 分层比例]]

* [[Hierarchical RBF|Hierarchical radial basis function 层次径向基函数]]

* [[Hierarchical storage management 分级存储管理]]

* [[Hierarchical task network 分层任务网络]]

* [[Hierarchical temporal memory 皮质学习算法]]
--[[用户:Jxzhou|Jxzhou]]（[[用户讨论:Jxzhou|讨论]]）根据上下文感觉应该是计算机方面的术语，memory是内存，但是维基百科这个词条对应的连接也是神经生物学相关的HTM算法

* [[Hierarchical Token Bucket|Hierarchical token bucket 分层令牌桶]]

* [[Hierarchical visitor pattern 分层访问者模式]]

* [[Presentation-abstraction-control 表示-抽象-控制]]

** [[Hierarchical-Model-View-Controller 层次-模型-视图-控制器]]

}}

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==See also==

==See also 参见==

= = 也见 = = < ! -- 参见“ further applications” -- >

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* [[Anarchy 无政府状态]]

* [[Class browser 类浏览器]]

* [[Forms of government 政体]]

* [[Graph theory 图论]]

* [[Heterarchy 差异化结构]]

* [[Hierarchical classifier 层次化分类器]]

* [[Hierarchical epistemology 分层认识论]]

* [[Hierarchical hidden Markov model 分层隐马尔科夫模型]]

* [[Hierarchical INTegration 阶层统整]]

* [[Hierarchical Music Specification Language 分级音乐规范语言]]

* [[Hierarchy Open Service Interface Definition 层次结构开放服务接口定义]]

* [[Hierarchy problem 等级问题]]

* {{section link|Holarchy#Different meanings 合弄结构#不同意义}}

* [[Instrumental value 工具价值]]

* [[Layer (disambiguation) 层（消歧）]]

* [[Multilevel model 多层模型]]

* [[Multitree 多树]]

* [[Ordinary (officer) 牧师]]

** {{section link|Characters of Halo#High Prophets}}

** [[List of Coptic Orthodox Popes of Alexandria 亚历山大科普特东正教教皇名单]]

* [[Peter Principle 彼得原理]]

* [[Ring (computer security) 环（计算机安全）]]

* [[Social dominance theory 社会支配论]]

}}

}}

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===Strucure-related concepts 结构相关概念===

''(For example, in {{section link|#Subtype}})''

(For example, in )

(例如，在

* [[Is-a]]

** [[Hypernymy 上位关系]] (and [[supertype 超类型]])

** [[Hyponymy 下义关系]] (and [[subtype 亚类型]])

* [[Has-a]]

** [[Holonymy 整体-部分]]

** [[Meronymy 部分-整体]]

==Footnotes==

{{Reflist}}

==Further reading==

* {{cite book|first=Valerie|last=Ahl|first2=Timothy F. H.|last2=Allen|authorlink2=Timothy F. H. Allen|year=1996|title=Hierarchy Theory|location=New York|publisher=Columbia University Press|isbn=0-231-08481-1}}

* {{cite conference|last=Akl |first=Selim G. |authorlink=Selim Akl |last2=Taylor |first2=Peter D. |title=Cryptographic solution to a multilevel security problem |conference=Advances in Cryptology: Proceedings of [[CRYPTO]] '82 |pages=237–249 |publisher=[[Plenum Publishing Corporation]] |year=1983 |location=New York |url=http://dsns.csie.nctu.edu.tw/research/crypto/HTML/PDF/C82/237.PDF |archive-url=https://web.archive.org/web/20021229212150/http://dsns.csie.nctu.edu.tw/research/crypto/HTML/PDF/C82/237.PDF |url-status=dead |archive-date=2002-12-29 |isbn=0-306-41366-3}}

* {{cite journal | last1 = Carbone | first1 = June | last2 = Cahn | first2 = Naomi |title= Is marriage for rich men? |journal = [[Nevada Law Journal]]| volume = 13 | issue = 2 | page = 6 | publisher = [[William S. Boyd School of Law]] | url = http://scholars.law.unlv.edu/nlj/vol13/iss2/6 | date = 2013}}

* {{cite journal|title=Regulatory hierarchies in auxin signal transduction and vascular tissue development|last=Ckurshumova|first=Wenzislava|isbn=978-0-494-27682-2|year=2007|journal=Dissertation Abstracts International|volume=68|issue=5|page=section B|place=University of Toronto|publication-place=|postscript=. Ph.D. dissertation.}}

* {{Cite book|last1=Galindo|first1=Cipriano|last2=Fernández-Madrigal|first2=Juan-Antonio|title=Multiple Abstraction Hierarchies for Mobile Robot Operation in Large Environments|series=Studies in Computational Intelligence|editor-last=Kacprzyk|editor-first=Janusz|year=2007|publisher=Springer Berlin Heidelberg|location=Berlin|isbn=978-3-540-72688-3}}

* {{cite journal|first=Julie|last=Nelson|authorlink=Julie Nelson (economist)|year=1992|title=Gender, Metaphor and the Definition of Economics|journal=Economics and Philosophy|volume=8|issue=1|pages=103–25|doi=10.1017/S026626710000050X}}

* {{cite book|last=Pumain|first=Denise|title=Hierarchy in Natural and Social Sciences|publisher=[[Springer-Verlag]]|location=New York, New York|year=2006|isbn=978-1-4020-4126-6}}

* {{cite book|first=A.|last=Rosenbaum|authorlink=Alexis Rosenbaum|year=2000|title=Les représentations hiérarchiques en philosophie|language=French|location=Paris|publisher=Desclee de Brouwer}}

* {{cite journal|title=Improving classification models when a class hierarchy is available|last=Shahbaba|first=Babak|isbn=978-0-494-28076-8|journal=Dissertation Abstracts International|volume=68|issue=6|page=section B|place=University of Toronto|publication-place=|postscript=. Ph.D. dissertation.|year=2007}}

** Also includes full copies of:

** {{cite journal|title=Improving Classification When a Class Hierarchy is Available Using a Hierarchy-Based Prior|last=Shahbaba|first=Babak|last2=Neal|first2=Radford M.|journal=Bayesian Analysis|volume=2|issue=1|pages=221–228|year=2007|issn=1936-0975|publisher=[[International Society for Bayesian Analysis]]|location=[[Carnegie Mellon University]], Pittsburgh, Pennsylvania|url=http://ba.stat.cmu.edu/journal/2007/vol02/issue01/shahbaba.pdf|bibcode=2005math.....10449S|arxiv=math/0510449|doi=10.1214/07-ba209|url-status=dead|archiveurl=https://web.archive.org/web/20150903231224/http://ba.stat.cmu.edu/journal/2007/vol02/issue01/shahbaba.pdf|archivedate=2015-09-03}}

** {{cite journal|last=Shahbaba|first=Babak|last2=Neal|first2=Radford M.|title=Gene function classification using Bayesian models with hierarchy-based priors|journal=[[BMC Bioinformatics]]|publisher=[[BioMed Central]]|location=London, England|year=2006|volume=7|page=448|doi=10.1186/1471-2105-7-448|pmc=1618412|pmid=17038174|issn=1471-2105|bibcode=2006q.bio.....5015S|arxiv=q-bio/0605015}}

==External links==

{{wikiquote}}

* {{commons category-inline}}

* [https://web.archive.org/web/20020207202512/http://isss.org/hierarchy.htm Principles and annotated bibliography of hierarchy theory]

* [https://web.archive.org/web/20060721201540/http://www.nbi.dk/%7Enatphil/salthe/Summary_of_the_Principles_o.pdf Summary of the Principles of Hierarchy Theory] — S.N. Salthe

{{Authority control}}

[[Category:Hierarchy| ]]

[[Category:Patterns]]

Category:Patterns

分类: 模式

[[Category:Structure]]

Category:Structure

类别: 结构

[[Category:Political culture]]

Category:Political culture

类别: 政治文化

<noinclude>

This page was moved from [[wikipedia:en:Hierarchy]]. Its edit history can be viewed at [[层次/edithistory]]</noinclude>

[[Category:待整理页面]]

临界点

2020-12-05T08:32:20Z

Miyasaki：

此词条暂由Henry翻译

此词条暂由Miyasaki审校

{{Other uses|Critical point (disambiguation){{!}}Critical point}}

[[Image:CriticalPointMeasurementEthane.jpg|thumb|right|upright=1.5|

[[Image:CriticalPointMeasurementEthane.jpg|thumb|right|upright=1.5|

[图片: 临界点测量乙烷 jpg | thumb | right | upright = 1.5 |

{{ordered list

{{ordered list

{有序列表

|Subcritical [[ethane]], liquid and gas phase coexist.

|Subcritical ethane, liquid and gas phase coexist.

亚临界乙烷，液态和气态共存。

|Critical point (32.17 °C, 48.72 bar), opalescence.

|Critical point (32.17 °C, 48.72 bar), opalescence.

临界点(32.17 °C，48.72 bar) ，乳白色。

|Supercritical [[ethane]], [[fluid]].<ref>{{cite thesis |first=Sven |last=Horstmann |title=Theoretische und experimentelle Untersuchungen zum Hochdruckphasengleichgewichtsverhalten fluider Stoffgemische für die Erweiterung der PSRK-Gruppenbeitragszustandsgleichung |language=de |trans-title=Theoretical and experimental investigations of the high-pressure phase equilibrium behavior of fluid mixtures for the expansion of the [[PSRK]] group contribution equation of state |type=Ph.D. |location=Oldenburg, Germany |publisher=[[University of Oldenburg|Carl-von-Ossietzky Universität Oldenburg]] |year=2000 |isbn=3-8265-7829-5|oclc=76176158}}</ref>

|Supercritical ethane, fluid.

超临界乙烷，流体。<ref>{{cite thesis |first=Sven |last=Horstmann |title=Theoretische und experimentelle Untersuchungen zum Hochdruckphasengleichgewichtsverhalten fluider Stoffgemische für die Erweiterung der PSRK-Gruppenbeitragszustandsgleichung |language=de |trans-title=Theoretical and experimental investigations of the high-pressure phase equilibrium behavior of fluid mixtures for the expansion of the [[PSRK]] group contribution equation of state |type=Ph.D. |location=Oldenburg, Germany |publisher=[[University of Oldenburg|Carl-von-Ossietzky Universität Oldenburg]] |year=2000 |isbn=3-8265-7829-5|oclc=76176158}}</ref>

}}]]

}}]]

}}]]

In [[thermodynamics]], a '''critical point''' (or '''critical state''') is the end point of a phase [[Equilibrium (thermodynamics)|equilibrium]] curve. The most prominent example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a [[liquid]] and its [[vapor]] can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone. At the critical point, defined by a ''critical temperature'' ''T''c and a ''critical pressure'' ''p''c, [[phase (matter)|phase]] boundaries vanish. Other examples include the liquid–liquid critical points in mixtures.

In thermodynamics, a critical point (or critical state) is the end point of a phase equilibrium curve. The most prominent example is the liquid–vapor critical point, the end point of the pressure–temperature curve that designates conditions under which a liquid and its vapor can coexist. At higher temperatures, the gas cannot be liquefied by pressure alone. At the critical point, defined by a critical temperature Tc and a critical pressure pc, phase boundaries vanish. Other examples include the liquid–liquid critical points in mixtures.

在热力学中，一个 临界点Critical point （或临界状态）就是相平衡曲线的终点。最突出的例子是液-汽临界点，即压力-温度曲线的终点，它指明了液体和其蒸汽可以共存的条件。温度再高，气体就不能单靠压力液化。在由临界温度Tc和临界压力pc定义的临界点，相边界消失。其他例子包括混合物中的液-液临界点。

== Liquid–vapor critical point液-汽临界点 ==

=== Overview 总览===

[[Image:phase-diag2.svg|thumb|upright=1.5|In a typical phase diagram, the boundary between gas and liquid runs from the triple point to the critical point.|The liquid–vapor critical point in a pressure–temperature [[phase diagram]] is at the high-temperature extreme of the liquid–gas phase boundary. The dotted green line shows the anomalous behavior of water.]]

The liquid–vapor critical point in a pressure–temperature [[phase diagram is at the high-temperature extreme of the liquid–gas phase boundary. The dotted green line shows the anomalous behavior of water.]]

在压力-温度[[相图]中，液-汽临界点位于液-气相界面的高温极端处。绿色虚线显示了水的反常行为。]

For simplicity and clarity, the generic notion of ''critical point'' is best introduced by discussing a specific example, the liquid–vapor critical point. This was the first critical point to be discovered, and it is still the best known and most studied one.

For simplicity and clarity, the generic notion of critical point is best introduced by discussing a specific example, the liquid–vapor critical point. This was the first critical point to be discovered, and it is still the best known and most studied one.

为使表述简单明晰，临界点的一般概念最好通过讨论一个具体的例子，液体-蒸汽临界点，来介绍。这是第一个被发现的临界点，也仍然是最著名和被研究最多的一个。

The figure to the right shows the schematic [[PT diagram]] of a ''pure substance'' (as opposed to mixtures, which have additional state variables and richer phase diagrams, discussed below). The commonly known [[phase (matter)|phases]] ''solid'', ''liquid'' and ''vapor'' are separated by phase boundaries, i.e. pressure–temperature combinations where two phases can coexist. At the [[triple point]], all three phases can coexist. However, the liquid–vapor boundary terminates in an endpoint at some ''critical temperature'' ''T''c and ''critical pressure'' ''p''c. This is the ''critical point''.

The figure to the right shows the schematic PT diagram of a pure substance (as opposed to mixtures, which have additional state variables and richer phase diagrams, discussed below). The commonly known phases solid, liquid and vapor are separated by phase boundaries, i.e. pressure–temperature combinations where two phases can coexist. At the triple point, all three phases can coexist. However, the liquid–vapor boundary terminates in an endpoint at some critical temperature Tc and critical pressure pc. This is the critical point.

右图显示了纯物质的PT示意图（与混合物相反，混合物具有额外的状态变量和更丰富的相图，如下所述）。众所周知的固相、液相和汽相通过相边界分离，即两相可以共存的压力-温度组合。在三相点，所有三个相可以共存。然而，在临界温度Tc和临界压力 pc时，液-汽边界终止于一个端点。这便是临界点。

In water, the critical point occurs at {{convert|647.096|K|C F}} and {{convert|22.064|MPa|psi atm}}.<ref name=IAPWS95>{{cite journal |last1=Wagner |first1=W. |last2=Pruß |first2=A. |title=The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use |journal=Journal of Physical and Chemical Reference Data |date=June 2002 |volume=31 |issue=2 |page=398 |doi=10.1063/1.1461829}}</ref>

In water, the critical point occurs at and .

在水中，临界点发生在647.096K 和22.064MPa下。<ref name=IAPWS95>{{cite journal |last1=Wagner |first1=W. |last2=Pruß |first2=A. |title=The IAPWS Formulation 1995 for the Thermodynamic Properties of Ordinary Water Substance for General and Scientific Use |journal=Journal of Physical and Chemical Reference Data |date=June 2002 |volume=31 |issue=2 |page=398 |doi=10.1063/1.1461829}}</ref>

In the ''vicinity'' of the critical point, the physical properties of the liquid and the vapor change dramatically, with both phases becoming ever more similar. For instance, liquid water under normal conditions is nearly incompressible, has a low thermal expansion coefficient, has a high [[dielectric constant]], and is an excellent solvent for electrolytes. Near the critical point, all these properties change into the exact opposite: water becomes compressible, expandable, a poor [[dielectric]], a bad solvent for electrolytes, and prefers to mix with nonpolar gases and organic molecules.<ref>Anisimov, Sengers, [[Anneke Levelt Sengers|Levelt Sengers]] (2004):Near-critical behavior of aqueous systems.
水体系的近临界行为
Chapter 2 inAqueous System at Elevated Temperatures and Pressures
高温高压下的水体系
Palmer et al., eds.

<math>\left(\frac{\partial p}{\partial V}\right)_T = 0,</math>

左(frac { partial p }{ partial v } right) _ t = 0,

Elsevier.</ref>

In the vicinity of the critical point, the physical properties of the liquid and the vapor change dramatically, with both phases becoming ever more similar. For instance, liquid water under normal conditions is nearly incompressible, has a low thermal expansion coefficient, has a high dielectric constant, and is an excellent solvent for electrolytes. Near the critical point, all these properties change into the exact opposite: water becomes compressible, expandable, a poor dielectric, a bad solvent for electrolytes, and prefers to mix with nonpolar gases and organic molecules.

在临界点附近，液体和蒸汽的物理性质发生了巨大的变化，两个相变得越来越相似。例如，因为液态水在正常条件下几乎不可压缩，热膨胀系数低，介电常数高，所以它是电解液的优良溶剂。在临界点附近，所有这些性质都会发生完全相反的变化：水变得可压缩、可膨胀、介电性差、电解质溶剂性差，更容易与非极性气体和有机分子混合。

''At'' the critical point, only one phase exists. The [[heat of vaporization]] is zero. There is a [[stationary point|stationary]] [[inflection point]] in the constant-temperature line (''critical isotherm'') on a [[PV diagram]]. This means that at the critical point:<ref name=Atkins>P. Atkins and J. de Paula, Physical Chemistry, 8th ed. (W. H. Freeman 2006), p. 21.</ref><ref>K. J. Laidler and J. H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p. 27.</ref><ref>P. A. Rock, Chemical Thermodynamics (MacMillan 1969), p. 123.</ref>

At the critical point, only one phase exists. The heat of vaporization is zero. There is a stationary inflection point in the constant-temperature line (critical isotherm) on a PV diagram. This means that at the critical point:

在临界点，只有一个相存在。汽化热为零。在PV图上的恒温线（ 临界等温线Critical isotherm）中有一个固定的拐点。这意味着在临界点：<ref name=Atkins>P. Atkins and J. de Paula, Physical Chemistry, 8th ed. (W. H. Freeman 2006), p. 21.</ref><ref>K. J. Laidler and J. H. Meiser, Physical Chemistry (Benjamin/Cummings 1982), p. 27.</ref><ref>P. A. Rock, Chemical Thermodynamics (MacMillan 1969), p. 123.</ref>

The critical isotherm with the critical point K

临界点 k 的临界等温线

: <math>\left(\frac{\partial p}{\partial V}\right)_T = 0,</math>

''Above'' the critical point there exists a state of matter that is continuously connected with (can be transformed without phase transition into) both the liquid and the gaseous state. It is called [[supercritical fluid]]. The common textbook knowledge that all distinction between liquid and vapor disappears beyond the critical point has been challenged by [[Michael Fisher|Fisher]] and [[Benjamin Widom|Widom]],<ref>Fisher, Widom: ''Decay of Correlations in Linear Systems'', J. Chem. Phys. 50, 3756 (1969).</ref> who identified a ''p''–''T'' line that separates states with different asymptotic statistical properties ([[Fisher–Widom line]]).

Above the critical point there exists a state of matter that is continuously connected with (can be transformed without phase transition into) both the liquid and the gaseous state. It is called supercritical fluid. The common textbook knowledge that all distinction between liquid and vapor disappears beyond the critical point has been challenged by Fisher and Widom, who identified a p–T line that separates states with different asymptotic statistical properties (Fisher–Widom line).

在临界点以上存在一种物质状态，它与液态和气态连续相连（无相变即可转化）。它被称为超临界流体。关于液体和蒸汽之间的所有区别都在临界点之外消失的共同教科书知识受到了费舍尔和威登的质疑，他们确定了一条p-T线，它分开了具有不同渐近统计性质的状态（Fisher-Widom线）。

: <math>\left(\frac{\partial^2p}{\partial V^2}\right)_T = 0.</math>

Some times the critical point does not manifest in most thermodynamic or mechanical properties, but is hidden and reveals itself in the onset of inhomogeneities in elastic moduli, marked changes in the appearance and local properties of non-affine droplets and a sudden enhancement in defect pair concentration. In those cases we have a hidden critical point, otherwise we have an exposed critical point.

有时，临界点并不表现在大多数热力学或机械性质上，而是隐藏在弹性模量的不均匀性开始、非仿射液滴的外观和局部特性的显著变化以及缺陷对浓度的突然增强中。在这些情况下，我们会有一个隐藏的临界点，否则我们就有一个暴露的临界点。
[[Image:Real Gas Isotherms.svg|thumb|upright=1.5|The ''critical isotherm'' with the critical point K]]

Some times the critical point does not manifest in most thermodynamic or mechanical properties, but is ''hidden'' and reveals itself in the onset of inhomogeneities in elastic moduli, marked changes in the appearance and local properties of non-affine droplets and a sudden enhancement in defect pair concentration. In those cases we have a [[hidden critical point]], otherwise we have an [[exposed critical point]].<ref>{{cite journal |last1=Das |first1=Tamoghna |last2=Ganguly |first2=Saswati |last3=Sengupta |first3=Surajit |last4=Rao |first4=Madan |title=Pre-Yield Non-Affine Fluctuations and A Hidden Critical Point in Strained Crystals |journal=Scientific Reports |date=3 June 2015 |volume=5 |issue=1 |pages=10644 |doi=10.1038/srep10644 |pmid=26039380 |pmc=4454149 |bibcode=2015NatSR...510644D |doi-access=free }}</ref>

=== History历史 ===

Critical [[carbon dioxide exuding fog while cooling from supercritical to critical temperature.]]

在从超临界温度冷却到临界温度时，临界二氧化碳释放出雾。

[[Image:Critical carbon dioxide.jpg|thumb|Critical [[carbon dioxide]] exuding [[fog]] while cooling from supercritical to critical temperature.]]

Solving the above condition <math>(\partial p / \partial V)_T = 0</math> for the van der Waals equation, one can compute the critical point as

解决上述条件(∂p/∂V)T=0，对于范德华方程，可以计算临界点为

The existence of a critical point was first discovered by [[Charles Cagniard de la Tour]] in 1822<ref>{{cite journal |author=Charles Cagniard de la Tour |date=1822 |url=https://books.google.com/books?id=rzNCAAAAcAAJ&q=Cagniard&pg=PA127 |title=Exposé de quelques résultats obtenu par l'action combinée de la chaleur et de la compression sur certains liquides, tels que l'eau, l'alcool, l'éther sulfurique et l'essence de pétrole rectifiée |trans-title=Presentation of some results obtained by the combined action of heat and compression on certain liquids, such as water, alcohol, sulfuric ether (i.e., diethyl ether), and distilled petroleum spirit |journal=Annales de Chimie et de Physique |volume=21 |pages=127–132 |language=fr}}</ref><ref>Berche, B., Henkel, M., Kenna, R (2009) Critical phenomena: 150 years since Cagniard de la Tour. Journal of Physical Studies 13 (3), pp. 3001-1–3001-4.</ref> and named by [[Dmitri Mendeleev]] in 1860<ref>Mendeleev called the critical point the "absolute temperature of boiling" ({{lang-ru|абсолютная температура кипения}}; {{lang-de|absolute Siedetemperatur}}).

<math>T_\text{c} = \frac{8a}{27Rb},

8 a }{27Rb } ,

* {{cite journal |last1=Менделеев |first1=Д. |title=О расширении жидкостей от нагревания выше температуры кипения |journal=Горный Журнал [Mining Journal] |date=1861 |volume=4 |pages=141–152 |trans-title=On the expansion of liquids from heating above the temperature of boiling |language=ru}} The "absolute temperature of boiling" is defined on p. 151. Available at [https://upload.wikimedia.org/wikipedia/commons/e/e6/%D0%93%D0%BE%D1%80%D0%BD%D1%8B%D0%B9_%D0%B6%D1%83%D1%80%D0%BD%D0%B0%D0%BB%2C_1861%2C_%E2%84%9604_%28%D0%B0%D0%BF%D1%80%D0%B5%D0%BB%D1%8C%29.pdf Wikimedia]

\quad V_\text{c} = 3nb,

3nb,

* German translation: {{cite journal |last1=Mendelejeff |first1=D. |title=Ueber die Ausdehnung der Flüssigkeiten beim Erwärmen über ihren Siedepunkt |journal=Annalen der Chemie und Pharmacie |date=1861 |volume=119 |pages=1–11 |url=https://babel.hathitrust.org/cgi/pt?id=uc1.c036497486;view=1up;seq=13 |trans-title=On the expansion of fluids during heating above their boiling point |language=de |doi=10.1002/jlac.18611190102 }} The "absolute temperature of boiling" is defined on p. 11: "{{lang|de|2=Als absolute Siedetemperatur müssen wir den Punkt betrachten, bei welchem 1) die Cohäsion der Flüssigkeit = 0° ist und a2 = 0, bei welcher 2) die latente Verdamfungswärme auch = 0 ist und bei welcher sich 3) die Flüssigkeit in Dampf verwandelt, unabhängig von Druck und Volum."}} (As the "absolute temperature of boiling" we must regard the point at which (1) the cohesion of the liquid equals 0° and ''a''2 = 0 [where ''a''2 is the coefficient of capillarity, p. 6], at which (2) the latent heat of vaporization also equals zero, and at which (3) the liquid is transformed into vapor, independently of the pressure and the volume.)

\quad p_\text{c} = \frac{a}{27b^2}.</math>

27b ^ 2} . </math >

* In 1870, Mendeleev asserted, against Thomas Andrews, his priority regarding the definition of the critical point: {{cite journal |last1=Mendelejeff |first1=D. |title=Bemerkungen zu den Untersuchungen von Andrews über die Compressibilität der Kohlensäure |journal=Annalen der Physik |date=1870 |volume=141 |pages=618–626 |url=https://babel.hathitrust.org/cgi/pt?id=wu.89048352249;view=1up;seq=648 |series=2nd series |trans-title=Comments on Andrews' investigations into the compressibility of carbon dioxide |language=de}}</ref><ref>Landau, Lifshitz, Theoretical Physics, Vol. V: Statistical Physics, Ch. 83 [German edition 1984].</ref> and [[Thomas Andrews (scientist)|Thomas Andrews]] in 1869.<ref>{{cite journal |author=Andrews, Thomas |date=1869 |url=http://rstl.royalsocietypublishing.org/content/159/575.full.pdf+html |title=The Bakerian lecture: On the continuity of the gaseous and liquid states of matter |journal=Philosophical Transactions of the Royal Society |location=London |volume=159 |pages=575–590 |doi=10.1098/rstl.1869.0021 |doi-access=free }} The term "critical point" appears on page 588.</ref> Cagniard showed that CO2 could be liquefied at 31 °C at a pressure of 73 atm, but not at a slightly higher temperature, even under pressures as high as 3000 atm.

The existence of a critical point was first discovered by Charles Cagniard de la Tour in 1822 and named by Dmitri Mendeleev in 1860 and Thomas Andrews in 1869. Cagniard showed that CO2 could be liquefied at 31 °C at a pressure of 73 atm, but not at a slightly higher temperature, even under pressures as high as 3000 atm.

临界点的存在于1822年<ref>{{cite journal |author=Charles Cagniard de la Tour |date=1822 |url=https://books.google.com/books?id=rzNCAAAAcAAJ&q=Cagniard&pg=PA127 |title=Exposé de quelques résultats obtenu par l'action combinée de la chaleur et de la compression sur certains liquides, tels que l'eau, l'alcool, l'éther sulfurique et l'essence de pétrole rectifiée |trans-title=Presentation of some results obtained by the combined action of heat and compression on certain liquids, such as water, alcohol, sulfuric ether (i.e., diethyl ether), and distilled petroleum spirit |journal=Annales de Chimie et de Physique |volume=21 |pages=127–132 |language=fr}}</ref><ref>Berche, B., Henkel, M., Kenna, R (2009) Critical phenomena: 150 years since Cagniard de la Tour. Journal of Physical Studies 13 (3), pp. 3001-1–3001-4.</ref> 由Charles Cagniard de la Tour首次发现，1860年<ref>Mendeleev called the critical point the "absolute temperature of boiling" ({{lang-ru|абсолютная температура кипения}}; {{lang-de|absolute Siedetemperatur}}).

<math>T_\text{c} = \frac{8a}{27Rb},

8 a }{27Rb } ,

* {{cite journal |last1=Менделеев |first1=Д. |title=О расширении жидкостей от нагревания выше температуры кипения |journal=Горный Журнал [Mining Journal] |date=1861 |volume=4 |pages=141–152 |trans-title=On the expansion of liquids from heating above the temperature of boiling |language=ru}} The "absolute temperature of boiling" is defined on p. 151. Available at [https://upload.wikimedia.org/wikipedia/commons/e/e6/%D0%93%D0%BE%D1%80%D0%BD%D1%8B%D0%B9_%D0%B6%D1%83%D1%80%D0%BD%D0%B0%D0%BB%2C_1861%2C_%E2%84%9604_%28%D0%B0%D0%BF%D1%80%D0%B5%D0%BB%D1%8C%29.pdf Wikimedia]

\quad V_\text{c} = 3nb,

3nb,

* German translation: {{cite journal |last1=Mendelejeff |first1=D. |title=Ueber die Ausdehnung der Flüssigkeiten beim Erwärmen über ihren Siedepunkt |journal=Annalen der Chemie und Pharmacie |date=1861 |volume=119 |pages=1–11 |url=https://babel.hathitrust.org/cgi/pt?id=uc1.c036497486;view=1up;seq=13 |trans-title=On the expansion of fluids during heating above their boiling point |language=de |doi=10.1002/jlac.18611190102 }} The "absolute temperature of boiling" is defined on p. 11: "{{lang|de|2=Als absolute Siedetemperatur müssen wir den Punkt betrachten, bei welchem 1) die Cohäsion der Flüssigkeit = 0° ist und a2 = 0, bei welcher 2) die latente Verdamfungswärme auch = 0 ist und bei welcher sich 3) die Flüssigkeit in Dampf verwandelt, unabhängig von Druck und Volum."}} (As the "absolute temperature of boiling" we must regard the point at which (1) the cohesion of the liquid equals 0° and ''a''2 = 0 [where ''a''2 is the coefficient of capillarity, p. 6], at which (2) the latent heat of vaporization also equals zero, and at which (3) the liquid is transformed into vapor, independently of the pressure and the volume.)

\quad p_\text{c} = \frac{a}{27b^2}.</math>

27b ^ 2} . </math >

* In 1870, Mendeleev asserted, against Thomas Andrews, his priority regarding the definition of the critical point: {{cite journal |last1=Mendelejeff |first1=D. |title=Bemerkungen zu den Untersuchungen von Andrews über die Compressibilität der Kohlensäure |journal=Annalen der Physik |date=1870 |volume=141 |pages=618–626 |url=https://babel.hathitrust.org/cgi/pt?id=wu.89048352249;view=1up;seq=648 |series=2nd series |trans-title=Comments on Andrews' investigations into the compressibility of carbon dioxide |language=de}}</ref><ref>Landau, Lifshitz, Theoretical Physics, Vol. V: Statistical Physics, Ch. 83 [German edition 1984].</ref> Dmitri mendelev和Thomas Andrews于1869年<ref>{{cite journal |author=Andrews, Thomas |date=1869 |url=http://rstl.royalsocietypublishing.org/content/159/575.full.pdf+html |title=The Bakerian lecture: On the continuity of the gaseous and liquid states of matter |journal=Philosophical Transactions of the Royal Society |location=London |volume=159 |pages=575–590 |doi=10.1098/rstl.1869.0021 |doi-access=free }} The term "critical point" appears on page 588.</ref> 分别命名。Cagniard表明， CO2在31°C的压力下可以液化，但在更高一点的温度下，即使在高达3000 atm的压力下也不能液化。

However, the van der Waals equation, based on a mean-field theory, does not hold near the critical point. In particular, it predicts wrong scaling laws.

然而，基于平均场理论的van der Waals方程在临界点附近并不成立。尤其是，它预测了错误的标度定律

=== Theory理论 ===

To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties

为了分析临界点附近的流体性质，有时需要定义相对于临界性质的简化状态变量

Solving the above condition <math>(\partial p / \partial V)_T = 0</math> for the [[van der Waals equation]], one can compute the critical point as

解对于van der Waals方程的上述条件<math>(\partial p / \partial V)_T = 0</math>，就能将临界点计算为

<math>T_\text{r} = \frac{T}{T_\text{c}},

如果你想知道更多的信息，请访问我的网站,

: <math>T_\text{c} = \frac{8a}{27Rb},

\quad p_\text{r} = \frac{p}{p_\text{c}},

4.1.1.1.2.2.2.2.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3.3

\quad V_\text{c} = 3nb,

\quad V_\text{r} = \frac{V}{RT_\text{c} / p_\text{c}}.</math>

4 v _ text { r } = frac { v }{ RT _ text { c }/p _ text { c } . </math >

\quad p_\text{c} = \frac{a}{27b^2}.</math>

--[[用户:Miyasaki|Miyasaki]]（[[用户讨论:Miyasaki|讨论]]）这里内容有待整理

However, the van der Waals equation, based on a [[mean-field theory]], does not hold near the critical point. In particular, it predicts wrong [[scaling law]]s.

但是，基于一个平均场理论的van der Waals方程，不能在近临界点成立。尤其是，它会得出错误的标度律。

The principle of corresponding states indicates that substances at equal reduced pressures and temperatures have equal reduced volumes. This relationship is approximately true for many substances, but becomes increasingly inaccurate for large values of pr.

对应态原理表明，在相同的减压和温度下，物质具有相等的还原体积。这种关系对于许多物质来说几乎是正确的，但是对于pr的大值，这种关系变得越来越不准确。

To analyse properties of fluids near the critical point, reduced state variables are sometimes defined relative to the critical properties<ref>{{Cite book | last1 = Cengel | first1 = Yunus A. | last2 = Boles | first2 = Michael A. | title = Thermodynamics: an engineering approach | year = 2002 | publisher = McGraw-Hill | location = Boston | isbn = 978-0-07-121688-3 | pages = 91–93}}</ref>

为分析接近临界点的液体的性质，还原态变量有时会被相对于临界性质定义。<ref>{{Cite book | last1 = Cengel | first1 = Yunus A. | last2 = Boles | first2 = Michael A. | title = Thermodynamics: an engineering approach | year = 2002 | publisher = McGraw-Hill | location = Boston | isbn = 978-0-07-121688-3 | pages = 91–93}}</ref>

For some gases, there is an additional correction factor, called ''Newton's correction'', added to the critical temperature and critical pressure calculated in this manner. These are empirically derived values and vary with the pressure range of interest.<ref>{{cite journal |title= Compressibility Chart for Hydrogen and Inert Gases |first1= Frank D. |last1= Maslan |first2= Theodore M. |last2= Littman |journal= Ind. Eng. Chem. |year= 1953 |volume= 45 |issue= 7 |pages= 1566–1568 |doi= 10.1021/ie50523a054 }}</ref>

For some gases, there is an additional correction factor, called Newton's correction, added to the critical temperature and critical pressure calculated in this manner. These are empirically derived values and vary with the pressure range of interest.

对于某些气体，在以这种方式计算的临界温度和临界压力上，还有一个额外的修正系数，叫做牛顿修正。这些是根据经验得出的值，并随感兴趣的压力范围而变化。<ref>{{cite journal |title= Compressibility Chart for Hydrogen and Inert Gases |first1= Frank D. |last1= Maslan |first2= Theodore M. |last2= Littman |journal= Ind. Eng. Chem. |year= 1953 |volume= 45 |issue= 7 |pages= 1566–1568 |doi= 10.1021/ie50523a054 }}</ref>

: <math>T_\text{r} = \frac{T}{T_\text{c}},

\quad p_\text{r} = \frac{p}{p_\text{c}},

\quad V_\text{r} = \frac{V}{RT_\text{c} / p_\text{c}}.</math>

<center>

< 中心 >

{| class="wikitable sortable" style="text-align: center;"

{ | class = “ wikitable sortable” style = “ text-align: center; ”

The [[theorem of corresponding states|principle of corresponding states]] indicates that substances at equal reduced pressures and temperatures have equal reduced volumes. This relationship is approximately true for many substances, but becomes increasingly inaccurate for large values of ''p''r.

|-

|-

! Substance

!物质

! Critical temperature

!临界温度

! Critical pressure (absolute)

!临界压力(绝对值)

=== Table of liquid–vapor critical temperature and pressure for selected substances ===

|-

|-

{{see also|Critical points of the elements (data page)}}

| Argon

| 氩气

<center>

| }}

| }}

{| class="wikitable sortable" style="text-align: center;"

| }}

| }}

|-

|-

|-

! Substance<ref>{{cite book |last= Emsley |first= John |title= The Elements |edition= Second |publisher= [[Oxford University Press]] |year= 1991 |isbn= 978-0-19-855818-7 }}</ref><ref>{{cite book |first1= Yunus A. |last1= Cengel |first2= Michael A. |last2= Boles |title= Thermodynamics: An Engineering Approach |pages= [https://archive.org/details/thermodynamicsen00ceng_0/page/824 824] |edition= Fourth |publisher= [[McGraw-Hill]] |year= 2002 |isbn= 978-0-07-238332-4 |url-access= registration |url= https://archive.org/details/thermodynamicsen00ceng_0/page/824 }}</ref>

| Ammonia (NH3)

| 氨(NH 3 )

! Critical temperature

| }}

| }}

! Critical pressure (absolute)

| }}

| }}

|-

|-

|-

| [[Argon]]

| {{sort|0150.8|{{convert|-122.4|C|K}}}}

| R-134a

| R-134a

| {{sort|0048.1|{{convert|48.1|atm|kPa|abbr=on}}}}

| }}

| }}

|-

| }}

| }}

| [[Ammonia]] (NH3)<ref>{{Cite web|url=http://www.engineeringtoolbox.com/ammonia-d_971.html|title=Ammonia - NH3 - Thermodynamic Properties|website=www.engineeringtoolbox.com|access-date=2017-04-07}}</ref>

|-

|-

| {{sort|0405.6|{{convert|132.4|C|K}}}}

| {{sort|0111.3|{{convert|111.3|atm|kPa|abbr=on}}}}

| R-410A

| R-410A

|-

| }}

| }}

| }}

| }}

| [[R-134a]]

|-

|-

| {{sort|0374|{{convert|101.06|C|K}}}}

| {{sort|0040|{{convert|40.06|atm|kPa|abbr=on}}}}

| Bromine

| 溴

|-

| }}

| }}

| }}

| }}

| [[R-410A]]

|-

|-

| {{sort|0346|{{convert|72.8|C|K}}}}

| Caesium

铯

| {{sort|0047|{{convert|47.08|atm|kPa|abbr=on}}}}

| }}

| }}

|-

| }}

| }}

|-

|-

| [[Bromine]]

| Chlorine

| 氯气

| {{sort|0584.0|{{convert|310.8|C|K}}}}

| }}

| }}

| {{sort|0102|{{convert|102|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Caesium]]

| Ethanol (C2H5OH)

| 乙醇(c 2 h 5 OH)

| {{sort|1938.00|{{convert|1664.85|C|K}}}}

| }}

| }}

| {{sort|0094|{{convert|94|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Chlorine]]

| Fluorine

| 氟

| {{sort|0417.0|{{convert|143.8|C|K}}}}

| }}

| }}

| {{sort|0076.0|{{convert|76.0|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Ethanol]] (C2H5OH)

| Helium

| 氦气

| {{sort|0514.0|{{convert|241|C|K}}}}

| }}

| }}

| {{sort|0062.2|{{convert|62.18|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Fluorine]]

| Hydrogen

| 氢气

| {{sort|0144.30|{{convert|-128.85|C|K}}}}

| }}

| }}

| {{sort|0051.5|{{convert|51.5|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Helium]]

| Krypton

氪星

| {{sort|0005.19|{{convert|-267.96|C|K}}}}

| }}

| }}

| {{sort|0002.24|{{convert|2.24|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Hydrogen]]

| Methane (CH4)

| 甲烷(CH 4 )

| {{sort|0033.20|{{convert|-239.95|C|K}}}}

| }}

| }}

| {{sort|0012.8|{{convert|12.8|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Krypton]]

| Neon

霓虹灯

| {{sort|0209.4|{{convert|-63.8|C|K}}}}

| }}

| }}

| {{sort|0054.3|{{convert|54.3|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Methane]] (CH4)

| Nitrogen

| 氮气

| {{sort|0190.8|{{convert|-82.3|C|K}}}}

| }}

| }}

| {{sort|0045.79|{{convert|45.79|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Neon]]

| Oxygen (O2)

| 氧气(o 2 )

| {{sort|0044.40|{{convert|-228.75|C|K}}}}

| }}

| }}

| {{sort|0027.2|{{convert|27.2|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Nitrogen]]

| Carbon dioxide (CO2)

| 二氧化碳(CO 2 )

| {{sort|0126.3|{{convert|-146.9|C|K}}}}

| }}

| }}

| {{sort|0033.5|{{convert|33.5|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Oxygen]] (O2)

| Nitrous oxide (N2O)

| 氧化亚氮(n 2 o)

| {{sort|0154.6|{{convert|-118.6|C|K}}}}

| }}

| }}

| {{sort|0049.8|{{convert|49.8|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Carbon dioxide]] (CO2)

| Sulfuric acid (H2SO4)

| 硫酸(h 2 SO 4 )

| {{sort|0304.19|{{convert|31.04|C|K}}}}

| }}

| }}

| {{sort|0072.8|{{convert|72.8|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Nitrous oxide]] (N2O)

| Xenon

| 氙气

| {{sort|0304.19|{{convert|36.4|C|K}}}}

| }}

| }}

| {{sort|0072.8|{{convert|71.5|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Sulfuric acid]] (H2SO4)

| Lithium

| Lithium

| {{sort|0927|{{convert|654|C|K}}}}

| }}

| }}

| {{sort|0045.4|{{convert|45.4|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Xenon]]

| Mercury

水星

| {{sort|0289.8|{{convert|16.6|C|K}}}}

| }}

| }}

| {{sort|0057.6|{{convert|57.6|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Lithium]]

| Sulfur

硫磺

| {{sort|3223|{{convert|2950|C|K}}}}

| }}

| }}

| {{sort|0652|{{convert|652|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Mercury (element)|Mercury]]

| Iron

铁

| {{sort|1750.1|{{convert|1476.9|C|K}}}}

| }}

| }}

| {{sort|1720|{{convert|1720|atm|kPa|abbr=on}}}}

|

|

|-

|-

|-

| [[Sulfur]]

| Gold

| 黄金

| {{sort|1314.00|{{convert|1040.85|C|K}}}}

| }}

| }}

| {{sort|0207|{{convert|207|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Iron]]

| Aluminium

| 铝

| {{sort|8500|{{convert|8227|C|K}}}}

| }}

| }}

|

|

|

|-

|-

|-

| [[Gold]]

| Water (H2O)

| 水(h 2 o)

| {{sort|7250|{{convert|6977|C|K}}}}

| }}

| }}

| {{sort|5000|{{convert|5000|atm|kPa|abbr=on}}}}

| }}

| }}

|-

|-

|-

| [[Aluminium]]

|}

|}

| {{sort|7850|{{convert|7577|C|K}}}}

</center>

</center >

|

|-

| [[Water]] (H2O)<ref name=IAPWS95/><ref>{{cite web | title = Critical Temperature and Pressure | publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-19 }}</ref>

| {{sort|0647.096|{{convert|373.946|C|K}}}}

A plot of typical polymer solution phase behavior including two critical points: a [[LCST and an UCST]]

典型的聚合物溶液相行为图，包括两个临界点: a [ LCST 和 UCST ]

| {{sort|0217.7|{{convert|217.7|atm|kPa|abbr=on}}}}

The liquid–liquid critical point of a solution, which occurs at the critical solution temperature, occurs at the limit of the two-phase region of the phase diagram. In other words, it is the point at which an infinitesimal change in some thermodynamic variable (such as temperature or pressure) leads to separation of the mixture into two distinct liquid phases, as shown in the polymer–solvent phase diagram to the right. Two types of liquid–liquid critical points are the upper critical solution temperature (UCST), which is the hottest point at which cooling induces phase separation, and the lower critical solution temperature (LCST), which is the coldest point at which heating induces phase separation.

溶液的液-液临界点出现在临界溶液温度下，出现在相图两相区的极限处。换言之，它是某个热力学变量（如温度或压力）的微小变化导致混合物分离为两个不同的液相的点，如右侧的聚合物-溶剂相图所示。两种类型的液-液临界点是上临界溶液温度（UCST），这是冷却导致相分离的最热点，而下临界溶液温度（LCST）是加热导致相分离的最冷点。

|-

|}

</center>

From a theoretical standpoint, the liquid–liquid critical point represents the temperature–concentration extremum of the spinodal curve (as can be seen in the figure to the right). Thus, the liquid–liquid critical point in a two-component system must satisfy two conditions: the condition of the spinodal curve (the second derivative of the free energy with respect to concentration must equal zero), and the extremum condition (the third derivative of the free energy with respect to concentration must also equal zero or the derivative of the spinodal temperature with respect to concentration must equal zero).

从理论上讲，液-液临界点代表旋节曲线的温度-浓度极值（如右图所示）。因此，双组分体系的液-液临界点必须满足两个条件：旋节曲线的条件（自由能对浓度的二阶导数必须等于零），以及极值条件（自由能对浓度的三阶导数也必须等于零，或者旋节温度对浓度的导数必须等于零）
==Mixtures: liquid–liquid critical point混合物：液体-液体临界点 ==

[[Image:LCST-UCST plot.svg|thumb|upright=1.5|A plot of typical polymer solution phase behavior including two critical points: a [[LCST]] and an [[Upper critical solution temperature|UCST]]]]

The [[liquid–liquid critical point]] of a solution, which occurs at the ''critical solution temperature'', occurs at the limit of the two-phase region of the phase diagram. In other words, it is the point at which an infinitesimal change in some thermodynamic variable (such as temperature or pressure) leads to separation of the mixture into two distinct liquid phases, as shown in the polymer–solvent phase diagram to the right. Two types of liquid–liquid critical points are the [[upper critical solution temperature]] (UCST), which is the hottest point at which cooling induces phase separation, and the [[lower critical solution temperature]] (LCST), which is the coldest point at which heating induces phase separation.
在“临界溶液温度”下，溶液的[[液-液临界点]]出现在相图两相区的极限处。换言之，它是某个热力学变量（如温度或压力）的微小变化导致混合物分离为两个不同的液相的点，如右侧的聚合物-溶剂相图所示。两种类型的液-液临界点是[[上临界溶液温度]]（UCST），这是冷却导致相分离的最热点，和[[下临界溶液温度]]（LCST），这是加热导致相分离的最冷点。

===Mathematical definition数学定义===

From a theoretical standpoint, the liquid–liquid critical point represents the temperature–concentration extremum of the [[spinodal]] curve (as can be seen in the figure to the right). Thus, the liquid–liquid critical point in a two-component system must satisfy two conditions: the condition of the spinodal curve (the ''second'' derivative of the [[Gibbs free energy|free energy]] with respect to concentration must equal zero), and the extremum condition (the ''third'' derivative of the free energy with respect to concentration must also equal zero or the derivative of the spinodal temperature with respect to concentration must equal zero).
从理论上看，从液体的临界点（从理论上看，是指液体的临界温度）。因此，双组分体系中的液-液临界点必须满足两个条件：旋节曲线的条件（[[Gibbs自由能|自由能]]相对于浓度的“二阶”导数必须等于零）和极值条件（自由能相对于浓度的“第三”导数）也必须等于零，或者旋节温度对浓度的导数必须等于零）。

==See also参见==

{{colbegin}}

* [[Conformal field theory]]
共形场论
* [[Critical exponents]]
临界指数
* [[Critical phenomena]] (more advanced article)
临界现象
* [[Critical points of the elements (data page)]]
要素临界点
* [[Curie point]]
居里点
* [[Joback method]], [[Klincewicz method]], [[Lydersen method]] (estimation of critical temperature, pressure, and volume from molecular structure)
Joback 方法 Klingewicz方法 Lydersen 方法（从分子结构估算临界温度、压力和体积）
* [[Liquid–liquid critical point]]
液体-液体临界点
* [[Lower critical solution temperature]]
较低临界溶液温度
* [[Néel point]]
Néel点
* [[Percolation thresholds]]
过滤阈值
* [[Phase transition]]
相变
* [[Rushbrooke inequality]]
Rushbrooke不等式
* [[Scale invariance]]
比例不变性
* [[Self-organized criticality]]
自组织临界性
* [[Supercritical fluid]], [[Supercritical drying]], [[Supercritical water oxidation]], [[Supercritical fluid extraction]]
超临界流体超临界干燥超临界水氧化超临界流体萃取
* [[Tricritical point]]
三临界点
* [[Triple point]]
三重点
* [[Upper critical solution temperature]]
上临界溶液温度
* [[Widom scaling]]
Widom缩放
{{colend}}

== Footnotes脚注 ==

{{Reflist|38em}}

| publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-03 }}

| publisher = 普渡大学 | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-03}

== References参考 ==

*{{cite web | title = Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam | publisher = International Association for the Properties of Water and Steam | date = August 2007 | url = http://www.iapws.org/relguide/IF97-Rev.pdf | accessdate = 2009-06-09 }}

Category:Condensed matter physics

类别: 凝聚态物理学

==External links外部链接==

Category:Conformal field theory

类别: 共形场论

* {{cite web |title=Critical points for some common solvents |url=http://www.proscitech.com.au/catalogue/notes/cpd.htm |archiveurl=https://web.archive.org/web/20080131081956/http://www.proscitech.com.au/catalogue/notes/cpd.htm |publisher=ProSciTech |archivedate=2008-01-31}}

Category:Critical phenomena

范畴: 关键现象

*{{cite web | title = Critical Temperature and Pressure | work = Department of Chemistry

Category:Phase transitions

类别: 阶段转变

| publisher = Purdue University | url = http://www.chem.purdue.edu/gchelp/liquids/critical.html | accessdate = 2006-12-03 }}

Category:Renormalization group

类别: 重整化群

Category:Threshold temperatures

类别: 临界温度

{{Phase_of_matter}}

Category:Gases

分类: 气体

<noinclude>

This page was moved from [[wikipedia:en:Critical point (thermodynamics)]]. Its edit history can be viewed at [[临界点（热力学）/edithistory]]</noinclude>

[[Category:待整理页面]]

用户:Miyasaki

2020-11-24T09:58:09Z

Miyasaki：建立内容为“姓名：邵佳蕊集智用户名：Miyasaki 联系：miyasaki_akiya 专业：历史（日新书院）院校：清华大学方向：历史学、社会学…”的新页面

姓名：邵佳蕊

集智用户名：Miyasaki

联系：miyasaki_akiya

专业：历史（日新书院）

院校：清华大学

方向：历史学、社会学、外国语言文学、语言学、英语

其他：对好几门二外都浅尝即止，是个没什么恒心的人；因为专业方向的原因不得不老老实实学拉丁语，结果还在挣扎着背各种变格和语法规则；目前的梦想是能发现satyricon失传的部分。

零和博弈

2020-11-21T08:32:33Z

Miyasaki：

此词条暂由水流心不竞初译，翻译字数共1421，带来阅读不便，请见谅。

此词条暂由Miyasaki审校
--[[用户:Miyasaki|Miyasaki]]（[[用户讨论:Miyasaki|讨论]]）此词条存在重复部分，有些重复段落不能确切定位，暂搁置。

{{short description|Mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants}}

{{distinguish|Empty sum|Zero game}}

{{other uses|Zero sum (disambiguation)}}

In [[game theory]] and [[economic theory]], a '''zero-sum game''' is a [[Mathematical model|mathematical representation]] of a situation in which each participant's gain or loss of [[utility]] is exactly balanced by the losses or gains of the utility of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero. Thus, [[Fair cake-cutting|cutting a cake]], where taking a larger piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if all participants value each unit of cake equally (see [[marginal utility]]).

In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero. Thus, cutting a cake, where taking a larger piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if all participants value each unit of cake equally (see marginal utility).

在博弈论和经济理论中，''' 零和博弈Zero-sum game'''是对某种情形的一种数学描述，在这种情形中每个参与者的效用增减与其他参与者的效用的增减互相平衡。如果将参与者的总收益加起来，再减去总损失，则它们之和为零。因此，如果公认蛋糕每一部分都具有同等价值，那么切蛋糕就是一个零和游戏，切一块蛋糕会减少给其他人的蛋糕量，同时也会增加给那个接受者的蛋糕量。

In contrast, '''non-zero-sum''' describes a situation in which the interacting parties' aggregate gains and losses can be less than or more than zero. A zero-sum game is also called a ''strictly competitive'' game while non-zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the [[minimax theorem]] which is closely related to [[LP duality|linear programming duality]],<ref name="Binmore2007"/> or with [[Nash equilibrium]].

In contrast, non-zero-sum describes a situation in which the interacting parties' aggregate gains and losses can be less than or more than zero. A zero-sum game is also called a strictly competitive game while non-zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality,

相比之下，非零和描述了另一种情形，在这种情形中，相互作用的各方的总计收益和损失可能小于或大于零。零和博弈也称为严格竞争博弈，而非零和博弈可以是竞争博弈，也可以是非竞争博弈。零和博弈通常是用极大极小定理来解决的，这个定理与线性规划二元性密切相关。

Many people have a [[cognitive bias]] towards seeing situations as zero-sum, known as [[zero-sum bias]].

许多人对将情况视为零和有[[认知偏差]]，称为[[零和偏差]]。

Zero-sum games are a specific example of constant sum games where the sum of each outcome is always zero. Such games are distributive, not integrative; the pie cannot be enlarged by good negotiation.

零和博弈是常数和博弈的一个具体例子，其中每个结果的和总是为零。这种游戏是分配性的，而不是综合性的; 良好的谈判无法扩大这块蛋糕。

== Definition 定义==

Situations where participants can all gain or suffer together are referred to as non-zero-sum. Thus, a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the transaction, is in a non-zero-sum situation. Other non-zero-sum games are games in which the sum of gains and losses by the players are sometimes more or less than what they began with.

参与者可以共同获益或共同受苦的情况称为''' 非零和Non-zero-sum'''。因此，如果一个香蕉过剩的国家与另一个国家进行交易以换取其过剩的苹果，这两个国家都从交易中受益，那么这个国家就处于一种非零和情况。其他''' 非零和博弈'''是这样一种博弈，在这种博弈中，参与者的得与失之和有时大于或小于开始时的水平。

{{Payoff matrix | Name = Generic zero-sum game

The idea of Pareto optimal payoff in a zero-sum game gives rise to a generalized relative selfish rationality standard, the punishing-the-opponent standard, where both players always seek to minimize the opponent's payoff at a favorable cost to himself rather to prefer more than less. The punishing-the-opponent standard can be used in both zero-sum games (e.g. warfare game, chess) and non-zero-sum games (e.g. pooling selection games).

在零和博弈中，帕累托最优收益的概念引出了一个广义的相对自私的理性标准，即惩罚对手的标准，在这个标准中，双方总是以对自己较有利的代价来寻求最小化对手的收益，而不是偏好多于少。惩罚对手标准可以同时用在零和博弈（例如战争游戏，国际象棋)和非零和博弈(例如:集合选择游戏)。

| 2L = Choice 1 | 2R = Choice 2 |

1U =Choice 1 | UL = −A, A | UR = B, −B |

1D = Choice 2 | DL = C, −C | DR = −D, D }}

For two-player finite zero-sum games, the different [[game theory|game theoretic]] [[solution concept]]s of [[Nash equilibrium]], [[minimax]], and [[maximin (decision theory)|maximin]] all give the same solution. If the players are allowed to play a [[mixed strategy]], the game always has an equilibrium.

For two-player finite zero-sum games, the different game theoretic solution concepts of Nash equilibrium, minimax, and maximin all give the same solution. If the players are allowed to play a mixed strategy, the game always has an equilibrium.

对于双人有限零和博弈来说，''' 纳什均衡点Nash equilibrium'''、极大极小和极大的不同对策理论解概念都给出了相同的解。如果允许参与者采用混合策略，博弈中总是存在平衡。

The zero-sum property (if one gains, another loses) means that any result of a zero-sum situation is [[Pareto optimal]]. Generally, any game where all strategies are Pareto optimal is called a conflict game.<ref>{{cite book |first=Samuel |last=Bowles |title=Microeconomics: Behavior, Institutions, and Evolution |url=https://archive.org/details/microeconomicsbe00bowl |url-access=limited |location= |publisher=[[Princeton University Press]] |pages=[https://archive.org/details/microeconomicsbe00bowl/page/n47 33]–36 |year=2004 |isbn=0-691-09163-3 }}</ref>

零和属性（如果一个获得，另一个失败）意味着零和情况的任何结果都是[[帕累托最优]]。一般来说，所有策略都是帕累托最优的博弈称为冲突博弈.<ref>{{cite book |first=Samuel |last=Bowles |title=Microeconomics: Behavior, Institutions, and Evolution |url=https://archive.org/details/microeconomicsbe00bowl |url-access=limited |location= |publisher=[[Princeton University Press]] |pages=[https://archive.org/details/microeconomicsbe00bowl/page/n47 33]–36 |year=2004 |isbn=0-691-09163-3 }}</ref>。

{| class="wikitable" style="float:right; margin-left:1em;"

{ | class = “ wikable” style = “ float: right; margin-left: 1em; ”

Situations where participants can all gain or suffer together are referred to as non-zero-sum. Thus, a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the transaction, is in a non-zero-sum situation. Other non-zero-sum games are games in which the sum of gains and losses by the players are sometimes more or less than what they began with.

|+ align=bottom |A zero-sum game

| + align = bottom | 零和博弈

! |}}

!|}}

The idea of Pareto optimal payoff in a zero-sum game gives rise to a generalized relative selfish rationality standard, the punishing-the-opponent standard, where both players always seek to minimize the opponent's payoff at a favorable cost to himself rather to prefer more than less. The punishing-the-opponent standard can be used in both zero-sum games (e.g. warfare game, chess) and non-zero-sum games (e.g. pooling selection games).<ref>Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. {{ISBN|978-1507658246}}. Chapter 1 and Chapter 4.</ref>

零和博弈中帕累托最优收益的思想产生了一种广义的相对自私理性标准，即惩罚对手标准，在这种标准中，双方总是以对自己有利的成本来寻求最小化对手的回报，而不是偏好多而少。惩罚对手标准可用于零和博弈（如战争博弈、国际象棋）和非零和博弈（如池选博弈）<ref>Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. {{ISBN|978-1507658246}}. Chapter 1 and Chapter 4.</ref>。

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== Solution 方案==

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For two-player finite zero-sum games, the different [[game theory|game theoretic]] [[solution concept]]s of [[Nash equilibrium]], [[minimax]], and [[maximin (decision theory)|maximin]] all give the same solution. If the players are allowed to play a [[mixed strategy]], the game always has an equilibrium.

对于两人有限零和对策，[[Nash均衡]], [[最小最大]]和[[最大最小（决策理论）| 最大最小]]的不同的[[博弈论|博弈论]][[解概念]]都给出了相同的解。如果允许玩家玩一个[[混合策略]]，游戏总是有一个平衡点。

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会发生什么

=== Example 举例===

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会发生什么

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会发生什么

{| class="wikitable" style="float:right; margin-left:1em;"

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|+ align=bottom |''A zero-sum game''“一个零和博弈”

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! {{diagonal split header|{{red|Red}}|{{blue|Blue}}}}

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会发生什么

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会发生什么

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会发生什么

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! {{red|''1''}}

A game's payoff matrix is a convenient representation. Consider for example the two-player zero-sum game pictured at right or above.

一场博弈的收益矩阵是一种方便的表示形式。让我们以图中右上方的两人零和博弈为例来考虑一下。

| {{diagonal split header|{{red|30}}|{{blue|−30}}|white}}

| {{diagonal split header|{{red|−10}}|{{blue|10}}|white}}

The order of play proceeds as follows: The first player (red) chooses in secret one of the two actions 1 or 2; the second player (blue), unaware of the first player's choice, chooses in secret one of the three actions A, B or C. Then, the choices are revealed and each player's points total is affected according to the payoff for those choices.

进行的顺序如下: 第一个玩家(红色)秘密地在两个动作1或2中选择一个; 第二个玩家(蓝色)不知道第一个玩家的选择，秘密地在三个动作 a、 b 或 c 中选择一个，然后，选择公布，每个玩家的总分受到这些选择的收益的影响。

| {{diagonal split header|{{red|20}}|{{blue|−20}}|white}}

|-

Example: Red chooses action 2 and Blue chooses action B. When the payoff is allocated, Red gains 20 points and Blue loses 20 points.

例如: 玩家红选择操作2，玩家蓝选择操作B。当回报被分配时，红色获得20点，蓝色失去20点。

! {{red|''2''}}

| {{diagonal split header|{{red|−10}}|{{blue|10}}|white}}

In this example game, both players know the payoff matrix and attempt to maximize the number of their points. Red could reason as follows: "With action 2, I could lose up to 20 points and can win only 20, and with action 1 I can lose only 10 but can win up to 30, so action 1 looks a lot better." With similar reasoning, Blue would choose action C. If both players take these actions, Red will win 20 points. If Blue anticipates Red's reasoning and choice of action 1, Blue may choose action B, so as to win 10 points. If Red, in turn, anticipates this trick and goes for action 2, this wins Red 20 points.

在这个例子中，两个玩家都知道收益矩阵，并试图最大化他们的分数。红队的理由如下: “在第二场比赛中，我可能输掉20分，只能赢20分，而在第一场比赛中，我只能输掉10分，但可以赢得30分，所以第一场比赛看起来要好得多。”根据类似的推理，蓝方会选择动作 c。如果两个玩家都采取这些动作，红方会赢得20分。如果蓝色预料到红色的推理和行动1的选择，蓝色可能会选择行动 b，从而赢得10点。如果红色，反过来，预测到这个计策，并选择行动2，这将为红色赢得20点。

| {{diagonal split header|{{red|20}}|{{blue|−20}}|white}}

| {{diagonal split header|{{red|−20}}|{{blue|20}}|white}}

[[Émile Borel]] and [[John von Neumann]] had the fundamental insight that [[probability]] provides a way out of this conundrum. Instead of deciding on a definite action to take, the two players assign probabilities to their respective actions, and then use a random device which, according to these probabilities, chooses an action for them. Each player computes the probabilities so as to minimize the maximum [[expected value|expected]] point-loss independent of the opponent's strategy. This leads to a [[linear programming]] problem with the optimal strategies for each player. This [[minimax]] method can compute probably optimal strategies for all two-player zero-sum games.

[[Émile Borel]]和[[John von Neumann]]的基本见解是[[概率]]提供了一种解决这个难题的方法。这两个玩家没有决定要采取的明确行动，而是给他们各自的行动分配概率，然后使用一个随机装置，根据这些概率，为他们选择一个行动。每个玩家计算概率，以使最大[[期望值|预期]]点损失最小化，与对手的策略无关。这就导致了一个[[线性规划]]问题，每个参与者的最优策略。这种[[极大极小]]方法可以计算所有两人零和博弈的可能最优策略。
|}

For the example given above, it turns out that Red should choose action 1 with probability and action 2 with probability , and Blue should assign the probabilities 0, and to the three actions A, B, and C. Red will then win points on average per game.

对于上面给出的例子，结果表明，红色应该选择行动1的概率和行动2的概率，和蓝色应该将概率0，分配给三个行动A，B，C。红色将赢得平均每场比赛的分数。

--[[用户:Miyasaki|Miyasaki]]（[[用户讨论:Miyasaki|讨论]]）这里原文应该有缺漏。

The order of play proceeds as follows: The first player (red) chooses in secret one of the two actions 1 or 2; the second player (blue), unaware of the first player's choice, chooses in secret one of the three actions A, B or C. Then, the choices are revealed and each player's points total is affected according to the payoff for those choices.

进行的顺序如下：第一个玩家（红色）秘密选择两个动作1或2中的一个；第二个玩家（蓝色）不知道第一个玩家的选择，秘密地选择A、B或C三个动作中的一个。然后，这些选择被揭示出来，并且每个玩家的积分总和会根据这些选择的回报而受到影响。

The Nash equilibrium for a two-player, zero-sum game can be found by solving a linear programming problem. Suppose a zero-sum game has a payoff matrix where element }} is the payoff obtained when the minimizing player chooses pure strategy and the maximizing player chooses pure strategy (i.e. the player trying to minimize the payoff chooses the row and the player trying to maximize the payoff chooses the column). Assume every element of is positive. The game will have at least one Nash equilibrium. The Nash equilibrium can be found (Raghavan 1994, p. 740) by solving the following linear program to find a vector :

一个双人零和游戏的纳什均衡点可以通过解决一个线性规划问题来找到。假设一个零和对策有一个支付矩阵，其中元素}是最小化对策者选择纯策略而最大化对策者选择纯策略(即最小化对策者选择纯策略)所获得的支付。试图最小化回报的参与人选择行，而试图最大化回报的参与人选择列)。假设元素的每个元素都是正的。这个游戏至少有一个纳什均衡点。可以通过解决下面的线性程序找到一个向量来找到纳什均衡点:

''Example: Red chooses action 2 and Blue chooses action B. When the payoff is allocated, Red gains 20 points and Blue loses 20 points.''

例如：红色选择动作2，蓝色选择动作B。分配收益时，红色获得20点，蓝色失去20点。

The first constraint says each element of the vector must be nonnegative, and the second constraint says each element of the vector must be at least 1. For the resulting vector, the inverse of the sum of its elements is the value of the game. Multiplying by that value gives a probability vector, giving the probability that the maximizing player will choose each of the possible pure strategies.

第一个约束表示向量的每个元素必须是非负的，第二个约束表示向量的每个元素必须至少是1。对于得到的向量，其元素和的倒数是游戏的值。乘以这个值得到一个概率向量，给出了最大化的玩家选择每个可能的纯策略的概率。

=== Solving 解答===

If the game matrix does not have all positive elements, simply add a constant to every element that is large enough to make them all positive. That will increase the value of the game by that constant, and will have no effect on the equilibrium mixed strategies for the equilibrium.

如果游戏矩阵不具备所有的正元素，只要在每个元素上加一个足够大的常数，使得它们都是正的。这个常数会增加游戏的价值，对均衡的混合策略没有影响。

The [[Nash equilibrium]] for a two-player, zero-sum game can be found by solving a [[linear programming]] problem. Suppose a zero-sum game has a payoff matrix {{mvar|M}} where element {{math|''M''{{sub|''i'',''j''}}}} is the payoff obtained when the minimizing player chooses pure strategy {{mvar|i}} and the maximizing player chooses pure strategy {{mvar|j}} (i.e. the player trying to minimize the payoff chooses the row and the player trying to maximize the payoff chooses the column). Assume every element of {{mvar|M}} is positive. The game will have at least one Nash equilibrium. The Nash equilibrium can be found (Raghavan 1994, p. 740) by solving the following linear program to find a vector {{mvar|u}}:

一个两人零和博弈的[[纳什均衡]]可以通过求解一个[[线性规划]]问题得到。假设一个零和博弈有一个支付矩阵{{mvar|M}}，其中元素{{math|''M''{{sub|''i'',''j''}}}}是当最小化的玩家选择纯策略 {{mvar|i}}而最大化的玩家选择纯策略 {{mvar|j}} 时获得的收益（即，试图最小化收益的玩家选择行，而试图最大化收益的玩家选择列）。假设 {{mvar|M}}的每个元素都是正的。博弈至少有一个纳什均衡。纳什均衡可以通过求解以下线性规划找到向量 {{mvar|u}}来找到（Raghavan 1994，p.740）：

The equilibrium mixed strategy for the minimizing player can be found by solving the dual of the given linear program. Or, it can be found by using the above procedure to solve a modified payoff matrix which is the transpose and negation of (adding a constant so it's positive), then solving the resulting game.

通过求解给定线性规划的对偶问题，可以找到最小化问题的均衡混合策略。或者，可以用上述方法求解一个修正后的收益矩阵，它是(加一个常数使其为正)的转置和否定，然后求解结果博弈。

: Minimize:
: 最小化：
::: <math>\sum_{i} u_i</math>

If all the solutions to the linear program are found, they will constitute all the Nash equilibria for the game. Conversely, any linear program can be converted into a two-player, zero-sum game by using a change of variables that puts it in the form of the above equations. So such games are equivalent to linear programs, in general.

如果找到线性规划的所有解，它们就构成了博弈的所有纳什均衡。相反，任何线性规划可以转换成一个两人，零和博弈使用变量的变化，使其成为上述方程的形式。所以这样的博弈一般等价于线性规划。

: Subject to the constraints:
：受限于以下约束：

:: {{math|''u'' ≥ 0}}

:: {{math|''M u'' ≥ 1}}.

If avoiding a zero-sum game is an action choice with some probability for players, avoiding is always an equilibrium strategy for at least one player at a zero-sum game. For any two players zero-sum game where a zero-zero draw is impossible or non-credible after the play is started, such as poker, there is no Nash equilibrium strategy other than avoiding the play. Even if there is a credible zero-zero draw after a zero-sum game is started, it is not better than the avoiding strategy. In this sense, it's interesting to find reward-as-you-go in optimal choice computation shall prevail over all two players zero-sum games with regard to starting the game or not.

如果回避零和博弈是一个具有一定概率的行动选择，那么在零和博弈中，至少一个参与者的回避总是一个均衡策略。对于任何一个零和游戏的玩家来说，在游戏开始后零和游戏是不可能的或者不可信的，比如说扑克，除了回避游戏之外没有其他的纳什均衡点策略。即使在零和博弈开始后出现了可信的零比零平局，这也不比回避策略好。从这个意义上说，有趣的是，在最优选择计算中找到随走随奖在开始与否的问题上将比所有所有双人零和游戏。

The first constraint says each element of the {{mvar|u}} vector must be nonnegative, and the second constraint says each element of the {{mvar|M u}} vector must be at least 1. For the resulting {{mvar|u}} vector, the inverse of the sum of its elements is the value of the game. Multiplying {{mvar|u}} by that value gives a probability vector, giving the probability that the maximizing player will choose each of the possible pure strategies.

第一个约束说明{{mvar|u}}向量的每个元素都必须是非负的，第二个约束要求{{mvar|M u}}向量的每个元素必须至少为1。对于得到的{{mvar|u}} 向量，其元素和的倒数就是博弈的值。将 {{mvar|u}}乘以这个值就得到了一个概率向量，给出了最大化的玩家选择每个可能的纯策略的概率。

If the game matrix does not have all positive elements, simply add a constant to every element that is large enough to make them all positive. That will increase the value of the game by that constant, and will have no effect on the equilibrium mixed strategies for the equilibrium.

如果博弈矩阵没有所有的正元素，只需在每个元素上添加一个常量，该元素足够大，足以使它们都是正的。这将使博弈值增加该常数，并且不会对均衡的均衡混合策略产生影响。

The equilibrium mixed strategy for the minimizing player can be found by solving the dual of the given linear program. Or, it can be found by using the above procedure to solve a modified payoff matrix which is the transpose and negation of {{mvar|M}} (adding a constant so it's positive), then solving the resulting game.

通过求解给定线性规划的对偶问题，可以找到最小化博弈者的均衡混合策略。或者，也可以通过使用上述过程来求解修正的支付矩阵，即 {{mvar|M}}的转置和否定（添加一个常数使其为正），然后求解结果博弈。

If all the solutions to the linear program are found, they will constitute all the Nash equilibria for the game. Conversely, any linear program can be converted into a two-player, zero-sum game by using a change of variables that puts it in the form of the above equations. So such games are equivalent to linear programs, in general. {{citation needed|date=October 2010}}

如果找到线性规划的所有解，它们将构成博弈的所有''' 纳什均衡'''。相反，任何线性程序都可以通过使用变量上述方程形式的变化，将其转换为两人零和博弈。所以，一般来说，这种游戏相当于线性程序。{{citation needed|date=October 2010}}

=== Universal solution通解 ===

It has been theorized by Robert Wright in his book Nonzero: The Logic of Human Destiny, that society becomes increasingly non-zero-sum as it becomes more complex, specialized, and interdependent.

Robert Wright在他的《非零: 人类命运的逻辑》一书中提出了这样的理论: 当社会变得越来越复杂、专门化和相互依存时，它就会变得越来越非零和。

If avoiding a zero-sum game is an action choice with some probability for players, avoiding is always an equilibrium strategy for at least one player at a zero-sum game. For any two players zero-sum game where a zero-zero draw is impossible or non-credible after the play is started, such as poker, there is no Nash equilibrium strategy other than avoiding the play. Even if there is a credible zero-zero draw after a zero-sum game is started, it is not better than the avoiding strategy. In this sense, it's interesting to find reward-as-you-go in optimal choice computation shall prevail over all two players zero-sum games with regard to starting the game or not.<ref>Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. {{ISBN|978-1507658246}}. Chapter 4.</ref>

如果避免零和博弈对玩家来说是一种有一定概率的行为选择，那么在零和博弈中，回避总是至少一个参与者的均衡策略。对于任何两个玩家的零和游戏，在游戏开始后零-零平局是不可能或不可信的，例如扑克，没有纳什均衡策略，除非不做游戏。即使在零和博弈开始后出现了可信的零-零平局，也不比回避策略好。从这个意义上说，有趣的是，在最优选择计算中，在开始游戏或不开始游戏时，最佳选择计算应优先于所有两个玩家的零和博弈<ref>Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. {{ISBN|978-1507658246}}. Chapter 4.</ref>。

In 1944, John von Neumann and Oskar Morgenstern proved that any non-zero-sum game for n players is equivalent to a zero-sum game with n + 1 players; the (n + 1)th player representing the global profit or loss.

1944年，John von Neumann和Oskar Morgenstern证明了 n 个玩家的任何非零和博弈等价于 n + 1个玩家的零和博弈，第(n + 1)个玩家代表全球的盈亏。

The most common or simple example from the subfield of [[social psychology]] is the concept of "[[social trap]]s". In some cases pursuing individual personal interest can enhance the collective well-being of the group, but in other situations all parties pursuing personal interest results in mutually destructive behavior.

[[社会心理学]]子领域中最常见或最简单的例子是“[[社会陷阱]]”的概念。在某些情况下，追求个人利益可以增进群体的集体福祉，但在其他情况下，追求个人利益的各方都会导致相互破坏的行为。

=== Complexity 复杂性===

It has been theorized by [[Robert Wright (journalist)|Robert Wright]] in his book ''[[Nonzero: The Logic of Human Destiny]]'', that society becomes increasingly non-zero-sum as it becomes more complex, specialized, and interdependent.

[[Robert Wright（记者）|Robert Wright]]在他的著作“[[非零：人类命运的逻辑]]”中提出，随着社会变得更加复杂、专业化和相互依存，社会变得越来越非零和。

== Extensions 扩展==

In psychology, zero-sum thinking refers to the perception that a situation is like a zero-sum game, where one person's gain is another's loss.

在心理学中，零和思维指的是这样一种感觉，即某种情况就像一个零和游戏，一个人的得到就是另一个人的损失。

In 1944, [[John von Neumann]] and [[Oskar Morgenstern]] proved that any non-zero-sum game for ''n'' players is equivalent to a zero-sum game with ''n'' + 1 players; the (''n'' + 1)th player representing the global profit or loss.<ref>{{cite book|url=https://press.princeton.edu/titles/7802.html |title=Theory of Games and Economic Behavior |publisher=Princeton University Press (1953) |date=June 25, 2005|accessdate=2018-02-25|isbn=9780691130613 }}</ref>

1944年，[[John von Neumann]]和[[Oskar Morgenstern]]证明了“n”玩家的任何非零和游戏都等价于一个“n”玩家+1玩家的零和游戏，即第(''n'' + 1)th 个玩家代表全球盈亏。

== Misunderstandings 争议问题==

Zero-sum games and particularly their solutions are commonly misunderstood by critics of [[game theory]], usually with respect to the independence and [[Rational choice theory|rationality]] of the players, as well as to the interpretation of utility functions. Furthermore, the word "game" does not imply the model is valid only for recreational [[game]]s.<ref name="Binmore2007">{{cite book|author=Ken Binmore|title=Playing for real: a text on game theory|url=https://books.google.com/?id=eY0YhSk9ujsC|year=2007|publisher=Oxford University Press US|isbn=978-0-19-530057-4|authorlink=Ken Binmore}}, chapters 1 & 7</ref>

零和博弈，尤其是它们的解决方案经常被[[博弈论]]的批评者误解，通常是关于参与者的独立性和[[理性选择理论|理性]]，以及对效用函数的解释。此外，“游戏”一词并不意味着该模型仅对娱乐[[游戏]]有效<ref name="Binmore2007">{{cite book|author=Ken Binmore|title=Playing for real: a text on game theory|url=https://books.google.com/?id=eY0YhSk9ujsC|year=2007|publisher=Oxford University Press US|isbn=978-0-19-530057-4|authorlink=Ken Binmore}}, chapters 1 & 7</ref>。

Politics is sometimes called zero sum.<ref>{{cite news|last=Rubin |first=Jennifer |url=https://www.washingtonpost.com/blogs/right-turn/wp/2013/10/04/the-flaw-in-zero-sum-politics/ |title=The flaw in zero sum politics |newspaper=The Washington Post |date=2013-10-04 |accessdate=2017-03-08}}</ref><ref>{{cite news|url=https://www.economist.com/news/united-states/21595973-voters-think-both-parties-are-telling-truth-about-how-awful-other-lot-are-zero-sum |title=Lexington: Zero-sum politics |newspaper=The Economist |date=2014-02-08 |accessdate=2017-03-08}}</ref><ref>{{cite dictionary|url=http://www.dictionary.com/browse/zero-sum-game |title=Zero-sum game | Define Zero-sum game at |dictionary=Dictionary.com |accessdate=2017-03-08}}</ref>

政治有时被称为零和。<ref>{{cite news|last=Rubin |first=Jennifer |url=https://www.washingtonpost.com/blogs/right-turn/wp/2013/10/04/the-flaw-in-zero-sum-politics/ |title=The flaw in zero sum politics |newspaper=The Washington Post |date=2013-10-04 |accessdate=2017-03-08}}</ref><ref>{{cite news|url=https://www.economist.com/news/united-states/21595973-voters-think-both-parties-are-telling-truth-about-how-awful-other-lot-are-zero-sum |title=Lexington: Zero-sum politics |newspaper=The Economist |date=2014-02-08 |accessdate=2017-03-08}}</ref><ref>{{cite dictionary|url=http://www.dictionary.com/browse/zero-sum-game |title=Zero-sum game | Define Zero-sum game at |dictionary=Dictionary.com |accessdate=2017-03-08}}</ref>

== Zero-sum thinking 零和思维==

In psychology, [[zero-sum thinking]] refers to the perception that a situation is like a zero-sum game, where one person's gain is another's loss.

在心理学中，[[零和思维]]指的是一种感觉，即感觉某情形就像一场零和博弈，一个人的收益就是另一个人的损失。

== See also又及 ==

{{col div|colwidth=30em}}

* [[Bimatrix game]]
*[[双矩阵游戏]]
* [[Comparative advantage]]
*[[比较优势]]
* [[Dutch disease]]
* [[荷兰病]]
* [[Gains from trade]]
*[[贸易收益]]
* [[Lump of labour fallacy]]
*[[劳动谬误]]
* [[Positive-sum game]]
*[[正和博弈]]
{{colend}}

== References ==

{{reflist}}

== Further reading 拓展阅读==

* ''Misstating the Concept of Zero-Sum Games within the Context of Professional Sports Trading Strategies'', series ''Pardon the Interruption'' (2010-09-23) [[ESPN]], created by [[Tony Kornheiser]] and [[Michael Wilbon]], performance by [[Bill Simmons]]

*“在职业体育交易策略的背景下错误陈述零和游戏的概念”，系列“原谅中断”（2010-09-23）[[ESPN]]，由[[Tony Kornheiser]]和[[Michael Wilbon]]创建，由[[Bill Simmons]]表演

* ''Handbook of Game Theory – volume 2'', chapter ''Zero-sum two-person games'', (1994) [[Elsevier]] Amsterdam, by Raghavan, T. E. S., Edited by Aumann and Hart, pp. 735–759, {{ISBN|0-444-89427-6}}

*“博弈论手册-第2卷”，章节“零和二人游戏”，（1994）[[Elsevier]]阿姆斯特丹，Raghavan，T.E.S.著，Aumann和Hart编辑，第735–759页，{{ISBN | 0-444-89427-6}}

Category:Non-cooperative games

类别: 非合作性游戏

* ''Power: Its Forms, Bases and Uses'' (1997) Transaction Publishers, by [[Dennis Wrong]]{{ISBN?}}

*《权力：它的形式、基础和用途》（1997年）交易出版商，作者[[Dennis Error]]{ISBN？}}

Category:International relations theory

类别: 国际关系理论

Category:Game theory game classes

类别: 博弈论游戏类

<noinclude>

This page was moved from [[wikipedia:en:Zero-sum game]]. Its edit history can be viewed at [[零和博弈/edithistory]]</noinclude>

此页摘自[[维基百科：英语：零和博弈]]。其编辑历史可在[[零和博弈编辑历史记录]]查看</noinclude>

[[Category:待整理页面]]

零和博弈

2020-11-21T08:28:49Z

Miyasaki：

此词条暂由水流心不竞初译，翻译字数共1421，带来阅读不便，请见谅。

此词条暂由Miyasaki审校
--[[用户:Miyasaki|Miyasaki]]（[[用户讨论:Miyasaki|讨论]]）此词条存在重复部分，有些重复段落不能确切定位，暂搁置。

{{short description|Mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants}}

{{distinguish|Empty sum|Zero game}}

{{other uses|Zero sum (disambiguation)}}

In [[game theory]] and [[economic theory]], a '''zero-sum game''' is a [[Mathematical model|mathematical representation]] of a situation in which each participant's gain or loss of [[utility]] is exactly balanced by the losses or gains of the utility of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero. Thus, [[Fair cake-cutting|cutting a cake]], where taking a larger piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if all participants value each unit of cake equally (see [[marginal utility]]).

In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. If the total gains of the participants are added up and the total losses are subtracted, they will sum to zero. Thus, cutting a cake, where taking a larger piece reduces the amount of cake available for others as much as it increases the amount available for that taker, is a zero-sum game if all participants value each unit of cake equally (see marginal utility).

在博弈论和经济理论中，''' 零和博弈Zero-sum game'''是对某种情形的一种数学描述，在这种情形中每个参与者的效用增减与其他参与者的效用的增减互相平衡。如果将参与者的总收益加起来，再减去总损失，则它们之和为零。因此，如果公认蛋糕每一部分都具有同等价值，那么切蛋糕就是一个零和游戏，切一块蛋糕会减少给其他人的蛋糕量，同时也会增加给那个接受者的蛋糕量。

In contrast, '''non-zero-sum''' describes a situation in which the interacting parties' aggregate gains and losses can be less than or more than zero. A zero-sum game is also called a ''strictly competitive'' game while non-zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the [[minimax theorem]] which is closely related to [[LP duality|linear programming duality]],<ref name="Binmore2007"/> or with [[Nash equilibrium]].

In contrast, non-zero-sum describes a situation in which the interacting parties' aggregate gains and losses can be less than or more than zero. A zero-sum game is also called a strictly competitive game while non-zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality,

相比之下，非零和描述了另一种情形，在这种情形中，相互作用的各方的总计收益和损失可能小于或大于零。零和博弈也称为严格竞争博弈，而非零和博弈可以是竞争博弈，也可以是非竞争博弈。零和博弈通常是用极大极小定理来解决的，这个定理与线性规划二元性密切相关。

Many people have a [[cognitive bias]] towards seeing situations as zero-sum, known as [[zero-sum bias]].

许多人对将情况视为零和有[[认知偏差]]，称为[[零和偏差]]。

Zero-sum games are a specific example of constant sum games where the sum of each outcome is always zero. Such games are distributive, not integrative; the pie cannot be enlarged by good negotiation.

零和博弈是常数和博弈的一个具体例子，其中每个结果的和总是为零。这种游戏是分配性的，而不是综合性的; 良好的谈判无法扩大这块蛋糕。

== Definition 定义==

Situations where participants can all gain or suffer together are referred to as non-zero-sum. Thus, a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the transaction, is in a non-zero-sum situation. Other non-zero-sum games are games in which the sum of gains and losses by the players are sometimes more or less than what they began with.

参与者可以共同获益或共同受苦的情况称为''' 非零和Non-zero-sum'''。因此，如果一个香蕉过剩的国家与另一个国家进行交易以换取其过剩的苹果，这两个国家都从交易中受益，那么这个国家就处于一种非零和情况。其他''' 非零和博弈'''是这样一种博弈，在这种博弈中，参与者的得与失之和有时大于或小于开始时的水平。

{{Payoff matrix | Name = Generic zero-sum game

The idea of Pareto optimal payoff in a zero-sum game gives rise to a generalized relative selfish rationality standard, the punishing-the-opponent standard, where both players always seek to minimize the opponent's payoff at a favorable cost to himself rather to prefer more than less. The punishing-the-opponent standard can be used in both zero-sum games (e.g. warfare game, chess) and non-zero-sum games (e.g. pooling selection games).

在零和博弈中，帕累托最优收益的概念引出了一个广义的相对自私的理性标准，即惩罚对手的标准，在这个标准中，双方总是以对自己较有利的代价来寻求最小化对手的收益，而不是偏好多于少。惩罚对手标准可以同时用在零和游戏（例如战争游戏，国际象棋)和非零和游戏(例如:集合选择游戏)。

| 2L = Choice 1 | 2R = Choice 2 |

1U =Choice 1 | UL = −A, A | UR = B, −B |

1D = Choice 2 | DL = C, −C | DR = −D, D }}

For two-player finite zero-sum games, the different [[game theory|game theoretic]] [[solution concept]]s of [[Nash equilibrium]], [[minimax]], and [[maximin (decision theory)|maximin]] all give the same solution. If the players are allowed to play a [[mixed strategy]], the game always has an equilibrium.

For two-player finite zero-sum games, the different game theoretic solution concepts of Nash equilibrium, minimax, and maximin all give the same solution. If the players are allowed to play a mixed strategy, the game always has an equilibrium.

对于双人有限零和游戏来说，''' 纳什均衡点Nash equilibrium'''、极大极小和极大的不同对策理论解概念都给出了相同的解。如果允许参与者采用混合策略，游戏中总是存在平衡。

The zero-sum property (if one gains, another loses) means that any result of a zero-sum situation is [[Pareto optimal]]. Generally, any game where all strategies are Pareto optimal is called a conflict game.<ref>{{cite book |first=Samuel |last=Bowles |title=Microeconomics: Behavior, Institutions, and Evolution |url=https://archive.org/details/microeconomicsbe00bowl |url-access=limited |location= |publisher=[[Princeton University Press]] |pages=[https://archive.org/details/microeconomicsbe00bowl/page/n47 33]–36 |year=2004 |isbn=0-691-09163-3 }}</ref>

零和属性（如果一个获得，另一个失败）意味着零和情况的任何结果都是[[帕累托最优]]。一般来说，所有策略都是帕累托最优的博弈称为冲突博弈.<ref>{{cite book |first=Samuel |last=Bowles |title=Microeconomics: Behavior, Institutions, and Evolution |url=https://archive.org/details/microeconomicsbe00bowl |url-access=limited |location= |publisher=[[Princeton University Press]] |pages=[https://archive.org/details/microeconomicsbe00bowl/page/n47 33]–36 |year=2004 |isbn=0-691-09163-3 }}</ref>。

{| class="wikitable" style="float:right; margin-left:1em;"

{ | class = “ wikable” style = “ float: right; margin-left: 1em; ”

Situations where participants can all gain or suffer together are referred to as non-zero-sum. Thus, a country with an excess of bananas trading with another country for their excess of apples, where both benefit from the transaction, is in a non-zero-sum situation. Other non-zero-sum games are games in which the sum of gains and losses by the players are sometimes more or less than what they began with.

|+ align=bottom |A zero-sum game

| + align = bottom | 零和游戏

! |}}

!|}}

The idea of Pareto optimal payoff in a zero-sum game gives rise to a generalized relative selfish rationality standard, the punishing-the-opponent standard, where both players always seek to minimize the opponent's payoff at a favorable cost to himself rather to prefer more than less. The punishing-the-opponent standard can be used in both zero-sum games (e.g. warfare game, chess) and non-zero-sum games (e.g. pooling selection games).<ref>Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. {{ISBN|978-1507658246}}. Chapter 1 and Chapter 4.</ref>

零和博弈中帕累托最优收益的思想产生了一种广义的相对自私理性标准，即惩罚对手标准，在这种标准中，双方总是以对自己有利的成本来寻求最小化对手的回报，而不是偏好多而少。惩罚对手标准可用于零和博弈（如战争博弈、国际象棋）和非零和博弈（如池选博弈）<ref>Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. {{ISBN|978-1507658246}}. Chapter 1 and Chapter 4.</ref>。

!

!

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== Solution 方案==

!

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|-

For two-player finite zero-sum games, the different [[game theory|game theoretic]] [[solution concept]]s of [[Nash equilibrium]], [[minimax]], and [[maximin (decision theory)|maximin]] all give the same solution. If the players are allowed to play a [[mixed strategy]], the game always has an equilibrium.

对于两人有限零和对策，[[Nash均衡]], [[最小最大]]和[[最大最小（决策理论）| 最大最小]]的不同的[[博弈论|博弈论]][[解概念]]都给出了相同的解。如果允许玩家玩一个[[混合策略]]，游戏总是有一个平衡点。

!

!

| ||white}}

会发生什么

=== Example 举例===

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会发生什么

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会发生什么

{| class="wikitable" style="float:right; margin-left:1em;"

|-

|-

|+ align=bottom |''A zero-sum game''“一个零和博弈”

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! {{diagonal split header|{{red|Red}}|{{blue|Blue}}}}

| ||white}}

会发生什么

! {{blue|''A''}}

| ||white}}

会发生什么

! {{blue|''B''}}

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会发生什么

! {{blue|''C''}}

|}

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! {{red|''1''}}

A game's payoff matrix is a convenient representation. Consider for example the two-player zero-sum game pictured at right or above.

一场游戏的收益矩阵是一种方便的表示形式。让我们以图中右上方的两人零和游戏为例来考虑一下。

| {{diagonal split header|{{red|30}}|{{blue|−30}}|white}}

| {{diagonal split header|{{red|−10}}|{{blue|10}}|white}}

The order of play proceeds as follows: The first player (red) chooses in secret one of the two actions 1 or 2; the second player (blue), unaware of the first player's choice, chooses in secret one of the three actions A, B or C. Then, the choices are revealed and each player's points total is affected according to the payoff for those choices.

游戏的顺序如下: 第一个玩家(红色)秘密地在两个动作1或2中选择一个; 第二个玩家(蓝色)不知道第一个玩家的选择，秘密地在三个动作 a、 b 或 c 中选择一个，然后，选择公布，每个玩家的总分受到这些选择的收益的影响。

| {{diagonal split header|{{red|20}}|{{blue|−20}}|white}}

|-

Example: Red chooses action 2 and Blue chooses action B. When the payoff is allocated, Red gains 20 points and Blue loses 20 points.

例如: 玩家红选择操作2，玩家蓝选择操作B。当回报被分配时，红色获得20点，蓝色失去20点。

! {{red|''2''}}

| {{diagonal split header|{{red|−10}}|{{blue|10}}|white}}

In this example game, both players know the payoff matrix and attempt to maximize the number of their points. Red could reason as follows: "With action 2, I could lose up to 20 points and can win only 20, and with action 1 I can lose only 10 but can win up to 30, so action 1 looks a lot better." With similar reasoning, Blue would choose action C. If both players take these actions, Red will win 20 points. If Blue anticipates Red's reasoning and choice of action 1, Blue may choose action B, so as to win 10 points. If Red, in turn, anticipates this trick and goes for action 2, this wins Red 20 points.

在这个例子中，两个玩家都知道收益矩阵，并试图最大化他们的分数。红队的理由如下: “在第二场比赛中，我可能输掉20分，只能赢20分，而在第一场比赛中，我只能输掉10分，但可以赢得30分，所以第一场比赛看起来要好得多。”根据类似的推理，蓝方会选择动作 c。如果两个玩家都采取这些动作，红方会赢得20分。如果蓝色预料到红色的推理和行动1的选择，蓝色可能会选择行动 b，从而赢得10点。如果红色，反过来，预测到这个计策，并选择行动2，这将为红色赢得20点。

| {{diagonal split header|{{red|20}}|{{blue|−20}}|white}}

| {{diagonal split header|{{red|−20}}|{{blue|20}}|white}}

[[Émile Borel]] and [[John von Neumann]] had the fundamental insight that [[probability]] provides a way out of this conundrum. Instead of deciding on a definite action to take, the two players assign probabilities to their respective actions, and then use a random device which, according to these probabilities, chooses an action for them. Each player computes the probabilities so as to minimize the maximum [[expected value|expected]] point-loss independent of the opponent's strategy. This leads to a [[linear programming]] problem with the optimal strategies for each player. This [[minimax]] method can compute probably optimal strategies for all two-player zero-sum games.

[[Émile Borel]]和[[John von Neumann]]的基本见解是[[概率]]提供了一种解决这个难题的方法。这两个玩家没有决定要采取的明确行动，而是给他们各自的行动分配概率，然后使用一个随机装置，根据这些概率，为他们选择一个行动。每个玩家计算概率，以使最大[[期望值|预期]]点损失最小化，与对手的策略无关。这就导致了一个[[线性规划]]问题，每个参与者的最优策略。这种[[极大极小]]方法可以计算所有两人零和博弈的可能最优策略。
|}

For the example given above, it turns out that Red should choose action 1 with probability and action 2 with probability , and Blue should assign the probabilities 0, and to the three actions A, B, and C. Red will then win points on average per game.

对于上面给出的例子，结果表明，红色应该选择行动1的概率和行动2的概率，和蓝色应该将概率0，分配给三个行动A，B，C。红色将赢得平均每场比赛的分数。

--[[用户:Miyasaki|Miyasaki]]（[[用户讨论:Miyasaki|讨论]]）这里原文应该有缺漏。

The order of play proceeds as follows: The first player (red) chooses in secret one of the two actions 1 or 2; the second player (blue), unaware of the first player's choice, chooses in secret one of the three actions A, B or C. Then, the choices are revealed and each player's points total is affected according to the payoff for those choices.

游戏顺序如下：第一个玩家（红色）秘密选择两个动作1或2中的一个；第二个玩家（蓝色）不知道第一个玩家的选择，秘密地选择A、B或C三个动作中的一个。然后，这些选择被揭示出来，并且每个玩家的积分总和会根据这些选择的回报而受到影响。

The Nash equilibrium for a two-player, zero-sum game can be found by solving a linear programming problem. Suppose a zero-sum game has a payoff matrix where element }} is the payoff obtained when the minimizing player chooses pure strategy and the maximizing player chooses pure strategy (i.e. the player trying to minimize the payoff chooses the row and the player trying to maximize the payoff chooses the column). Assume every element of is positive. The game will have at least one Nash equilibrium. The Nash equilibrium can be found (Raghavan 1994, p. 740) by solving the following linear program to find a vector :

一个双人零和游戏的纳什均衡点可以通过解决一个线性规划问题来找到。假设一个零和对策有一个支付矩阵，其中元素}是最小化对策者选择纯策略而最大化对策者选择纯策略(即最小化对策者选择纯策略)所获得的支付。试图最小化回报的参与人选择行，而试图最大化回报的参与人选择列)。假设元素的每个元素都是正的。这个游戏至少有一个纳什均衡点。可以通过解决下面的线性程序找到一个向量来找到纳什均衡点:

''Example: Red chooses action 2 and Blue chooses action B. When the payoff is allocated, Red gains 20 points and Blue loses 20 points.''

例如：红色选择动作2，蓝色选择动作B。分配收益时，红色获得20点，蓝色失去20点。

The first constraint says each element of the vector must be nonnegative, and the second constraint says each element of the vector must be at least 1. For the resulting vector, the inverse of the sum of its elements is the value of the game. Multiplying by that value gives a probability vector, giving the probability that the maximizing player will choose each of the possible pure strategies.

第一个约束表示向量的每个元素必须是非负的，第二个约束表示向量的每个元素必须至少是1。对于得到的向量，其元素和的倒数是游戏的值。乘以这个值得到一个概率向量，给出了最大化的玩家选择每个可能的纯策略的概率。

=== Solving 解答===

If the game matrix does not have all positive elements, simply add a constant to every element that is large enough to make them all positive. That will increase the value of the game by that constant, and will have no effect on the equilibrium mixed strategies for the equilibrium.

如果游戏矩阵不具备所有的正元素，只要在每个元素上加一个足够大的常数，使得它们都是正的。这个常数会增加游戏的价值，对均衡的混合策略没有影响。

The [[Nash equilibrium]] for a two-player, zero-sum game can be found by solving a [[linear programming]] problem. Suppose a zero-sum game has a payoff matrix {{mvar|M}} where element {{math|''M''{{sub|''i'',''j''}}}} is the payoff obtained when the minimizing player chooses pure strategy {{mvar|i}} and the maximizing player chooses pure strategy {{mvar|j}} (i.e. the player trying to minimize the payoff chooses the row and the player trying to maximize the payoff chooses the column). Assume every element of {{mvar|M}} is positive. The game will have at least one Nash equilibrium. The Nash equilibrium can be found (Raghavan 1994, p. 740) by solving the following linear program to find a vector {{mvar|u}}:

一个两人零和博弈的[[纳什均衡]]可以通过求解一个[[线性规划]]问题得到。假设一个零和博弈有一个支付矩阵{{mvar|M}}，其中元素{{math|''M''{{sub|''i'',''j''}}}}是当最小化的玩家选择纯策略 {{mvar|i}}而最大化的玩家选择纯策略 {{mvar|j}} 时获得的收益（即，试图最小化收益的玩家选择行，而试图最大化收益的玩家选择列）。假设 {{mvar|M}}的每个元素都是正的。博弈至少有一个纳什均衡。纳什均衡可以通过求解以下线性规划找到向量 {{mvar|u}}来找到（Raghavan 1994，p.740）：

The equilibrium mixed strategy for the minimizing player can be found by solving the dual of the given linear program. Or, it can be found by using the above procedure to solve a modified payoff matrix which is the transpose and negation of (adding a constant so it's positive), then solving the resulting game.

通过求解给定线性规划的对偶问题，可以找到最小化问题的均衡混合策略。或者，可以用上述方法求解一个修正后的收益矩阵，它是(加一个常数使其为正)的转置和否定，然后求解结果博弈。

: Minimize:
: 最小化：
::: <math>\sum_{i} u_i</math>

If all the solutions to the linear program are found, they will constitute all the Nash equilibria for the game. Conversely, any linear program can be converted into a two-player, zero-sum game by using a change of variables that puts it in the form of the above equations. So such games are equivalent to linear programs, in general.

如果找到线性规划的所有解，它们就构成了博弈的所有纳什均衡。相反，任何线性规划可以转换成一个两人，零和博弈使用变量的变化，使其成为上述方程的形式。所以这样的博弈一般等价于线性规划。

: Subject to the constraints:
：受限于以下约束：

:: {{math|''u'' ≥ 0}}

:: {{math|''M u'' ≥ 1}}.

If avoiding a zero-sum game is an action choice with some probability for players, avoiding is always an equilibrium strategy for at least one player at a zero-sum game. For any two players zero-sum game where a zero-zero draw is impossible or non-credible after the play is started, such as poker, there is no Nash equilibrium strategy other than avoiding the play. Even if there is a credible zero-zero draw after a zero-sum game is started, it is not better than the avoiding strategy. In this sense, it's interesting to find reward-as-you-go in optimal choice computation shall prevail over all two players zero-sum games with regard to starting the game or not.

如果回避零和博弈是一个具有一定概率的行动选择，那么在零和博弈中，至少一个参与者的回避总是一个均衡策略。对于任何一个零和游戏的玩家来说，在游戏开始后零和游戏是不可能的或者不可信的，比如说扑克，除了回避游戏之外没有其他的纳什均衡点策略。即使在零和博弈开始后出现了可信的零比零平局，这也不比回避策略好。从这个意义上说，有趣的是，在最优选择计算中找到随走随奖在开始与否的问题上将比所有所有双人零和游戏。

The first constraint says each element of the {{mvar|u}} vector must be nonnegative, and the second constraint says each element of the {{mvar|M u}} vector must be at least 1. For the resulting {{mvar|u}} vector, the inverse of the sum of its elements is the value of the game. Multiplying {{mvar|u}} by that value gives a probability vector, giving the probability that the maximizing player will choose each of the possible pure strategies.

第一个约束说明{{mvar|u}}向量的每个元素都必须是非负的，第二个约束要求{{mvar|M u}}向量的每个元素必须至少为1。对于得到的{{mvar|u}} 向量，其元素和的倒数就是博弈的值。将 {{mvar|u}}乘以这个值就得到了一个概率向量，给出了最大化的玩家选择每个可能的纯策略的概率。

If the game matrix does not have all positive elements, simply add a constant to every element that is large enough to make them all positive. That will increase the value of the game by that constant, and will have no effect on the equilibrium mixed strategies for the equilibrium.

如果博弈矩阵没有所有的正元素，只需在每个元素上添加一个常量，该元素足够大，足以使它们都是正的。这将使博弈值增加该常数，并且不会对均衡的均衡混合策略产生影响。

The equilibrium mixed strategy for the minimizing player can be found by solving the dual of the given linear program. Or, it can be found by using the above procedure to solve a modified payoff matrix which is the transpose and negation of {{mvar|M}} (adding a constant so it's positive), then solving the resulting game.

通过求解给定线性规划的对偶问题，可以找到最小化博弈者的均衡混合策略。或者，也可以通过使用上述过程来求解修正的支付矩阵，即 {{mvar|M}}的转置和否定（添加一个常数使其为正），然后求解结果博弈。

If all the solutions to the linear program are found, they will constitute all the Nash equilibria for the game. Conversely, any linear program can be converted into a two-player, zero-sum game by using a change of variables that puts it in the form of the above equations. So such games are equivalent to linear programs, in general. {{citation needed|date=October 2010}}

如果找到线性规划的所有解，它们将构成博弈的所有''' 纳什均衡'''。相反，任何线性程序都可以通过使用变量上述方程形式的变化，将其转换为两人零和博弈。所以，一般来说，这种游戏相当于线性程序。{{citation needed|date=October 2010}}

=== Universal solution通解 ===

It has been theorized by Robert Wright in his book Nonzero: The Logic of Human Destiny, that society becomes increasingly non-zero-sum as it becomes more complex, specialized, and interdependent.

Robert Wright在他的《非零: 人类命运的逻辑》一书中提出了这样的理论: 当社会变得越来越复杂、专门化和相互依存时，它就会变得越来越非零和。

If avoiding a zero-sum game is an action choice with some probability for players, avoiding is always an equilibrium strategy for at least one player at a zero-sum game. For any two players zero-sum game where a zero-zero draw is impossible or non-credible after the play is started, such as poker, there is no Nash equilibrium strategy other than avoiding the play. Even if there is a credible zero-zero draw after a zero-sum game is started, it is not better than the avoiding strategy. In this sense, it's interesting to find reward-as-you-go in optimal choice computation shall prevail over all two players zero-sum games with regard to starting the game or not.<ref>Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. {{ISBN|978-1507658246}}. Chapter 4.</ref>

如果避免零和博弈对玩家来说是一种有一定概率的行为选择，那么在零和博弈中，回避总是至少一个参与者的均衡策略。对于任何两个玩家的零和游戏，在游戏开始后零-零平局是不可能或不可信的，例如扑克，没有纳什均衡策略，除非不做游戏。即使在零和博弈开始后出现了可信的零-零平局，也不比回避策略好。从这个意义上说，有趣的是，在最优选择计算中，在开始游戏或不开始游戏时，最佳选择计算应优先于所有两个玩家的零和游戏<ref>Wenliang Wang (2015). Pooling Game Theory and Public Pension Plan. {{ISBN|978-1507658246}}. Chapter 4.</ref>。

In 1944, John von Neumann and Oskar Morgenstern proved that any non-zero-sum game for n players is equivalent to a zero-sum game with n + 1 players; the (n + 1)th player representing the global profit or loss.

1944年，John von Neumann和Oskar Morgenstern证明了 n 个玩家的任何非零和博弈等价于 n + 1个玩家的零和博弈，第(n + 1)个玩家代表全球的盈亏。

The most common or simple example from the subfield of [[social psychology]] is the concept of "[[social trap]]s". In some cases pursuing individual personal interest can enhance the collective well-being of the group, but in other situations all parties pursuing personal interest results in mutually destructive behavior.

[[社会心理学]]子领域中最常见或最简单的例子是“[[社会陷阱]]”的概念。在某些情况下，追求个人利益可以增进群体的集体福祉，但在其他情况下，追求个人利益的各方都会导致相互破坏的行为。

=== Complexity 复杂性===

It has been theorized by [[Robert Wright (journalist)|Robert Wright]] in his book ''[[Nonzero: The Logic of Human Destiny]]'', that society becomes increasingly non-zero-sum as it becomes more complex, specialized, and interdependent.

[[Robert Wright（记者）|Robert Wright]]在他的著作“[[非零：人类命运的逻辑]]”中提出，随着社会变得更加复杂、专业化和相互依存，社会变得越来越非零和。

== Extensions 扩展==

In psychology, zero-sum thinking refers to the perception that a situation is like a zero-sum game, where one person's gain is another's loss.

在心理学中，零和思维指的是这样一种感觉，即某种情况就像一个零和游戏，一个人的得到就是另一个人的损失。

In 1944, [[John von Neumann]] and [[Oskar Morgenstern]] proved that any non-zero-sum game for ''n'' players is equivalent to a zero-sum game with ''n'' + 1 players; the (''n'' + 1)th player representing the global profit or loss.<ref>{{cite book|url=https://press.princeton.edu/titles/7802.html |title=Theory of Games and Economic Behavior |publisher=Princeton University Press (1953) |date=June 25, 2005|accessdate=2018-02-25|isbn=9780691130613 }}</ref>

1944年，[[John von Neumann]]和[[Oskar Morgenstern]]证明了“n”玩家的任何非零和游戏都等价于一个“n”玩家+1玩家的零和游戏，即第(''n'' + 1)th 个玩家代表全球盈亏。

== Misunderstandings 争议问题==

Zero-sum games and particularly their solutions are commonly misunderstood by critics of [[game theory]], usually with respect to the independence and [[Rational choice theory|rationality]] of the players, as well as to the interpretation of utility functions. Furthermore, the word "game" does not imply the model is valid only for recreational [[game]]s.<ref name="Binmore2007">{{cite book|author=Ken Binmore|title=Playing for real: a text on game theory|url=https://books.google.com/?id=eY0YhSk9ujsC|year=2007|publisher=Oxford University Press US|isbn=978-0-19-530057-4|authorlink=Ken Binmore}}, chapters 1 & 7</ref>

零和博弈，尤其是它们的解决方案经常被[[博弈论]]的批评者误解，通常是关于参与者的独立性和[[理性选择理论|理性]]，以及对效用函数的解释。此外，“游戏”一词并不意味着该模型仅对娱乐[[游戏]]有效<ref name="Binmore2007">{{cite book|author=Ken Binmore|title=Playing for real: a text on game theory|url=https://books.google.com/?id=eY0YhSk9ujsC|year=2007|publisher=Oxford University Press US|isbn=978-0-19-530057-4|authorlink=Ken Binmore}}, chapters 1 & 7</ref>。

Politics is sometimes called zero sum.<ref>{{cite news|last=Rubin |first=Jennifer |url=https://www.washingtonpost.com/blogs/right-turn/wp/2013/10/04/the-flaw-in-zero-sum-politics/ |title=The flaw in zero sum politics |newspaper=The Washington Post |date=2013-10-04 |accessdate=2017-03-08}}</ref><ref>{{cite news|url=https://www.economist.com/news/united-states/21595973-voters-think-both-parties-are-telling-truth-about-how-awful-other-lot-are-zero-sum |title=Lexington: Zero-sum politics |newspaper=The Economist |date=2014-02-08 |accessdate=2017-03-08}}</ref><ref>{{cite dictionary|url=http://www.dictionary.com/browse/zero-sum-game |title=Zero-sum game | Define Zero-sum game at |dictionary=Dictionary.com |accessdate=2017-03-08}}</ref>

政治有时被称为零和。<ref>{{cite news|last=Rubin |first=Jennifer |url=https://www.washingtonpost.com/blogs/right-turn/wp/2013/10/04/the-flaw-in-zero-sum-politics/ |title=The flaw in zero sum politics |newspaper=The Washington Post |date=2013-10-04 |accessdate=2017-03-08}}</ref><ref>{{cite news|url=https://www.economist.com/news/united-states/21595973-voters-think-both-parties-are-telling-truth-about-how-awful-other-lot-are-zero-sum |title=Lexington: Zero-sum politics |newspaper=The Economist |date=2014-02-08 |accessdate=2017-03-08}}</ref><ref>{{cite dictionary|url=http://www.dictionary.com/browse/zero-sum-game |title=Zero-sum game | Define Zero-sum game at |dictionary=Dictionary.com |accessdate=2017-03-08}}</ref>

== Zero-sum thinking 零和思维==

In psychology, [[zero-sum thinking]] refers to the perception that a situation is like a zero-sum game, where one person's gain is another's loss.

在心理学中，[[零和思维]]指的是一种感觉，即感觉某情形就像一场零和游戏，一个人的收益就是另一个人的损失。

== See also又及 ==

{{col div|colwidth=30em}}

* [[Bimatrix game]]
*[[双矩阵游戏]]
* [[Comparative advantage]]
*[[比较优势]]
* [[Dutch disease]]
* [[荷兰病]]
* [[Gains from trade]]
*[[贸易收益]]
* [[Lump of labour fallacy]]
*[[劳动谬误]]
* [[Positive-sum game]]
*[[正和博弈]]
{{colend}}

== References ==

{{reflist}}

== Further reading 拓展阅读==

* ''Misstating the Concept of Zero-Sum Games within the Context of Professional Sports Trading Strategies'', series ''Pardon the Interruption'' (2010-09-23) [[ESPN]], created by [[Tony Kornheiser]] and [[Michael Wilbon]], performance by [[Bill Simmons]]

*“在职业体育交易策略的背景下错误陈述零和游戏的概念”，系列“原谅中断”（2010-09-23）[[ESPN]]，由[[Tony Kornheiser]]和[[Michael Wilbon]]创建，由[[Bill Simmons]]表演

* ''Handbook of Game Theory – volume 2'', chapter ''Zero-sum two-person games'', (1994) [[Elsevier]] Amsterdam, by Raghavan, T. E. S., Edited by Aumann and Hart, pp. 735–759, {{ISBN|0-444-89427-6}}

*“博弈论手册-第2卷”，章节“零和二人游戏”，（1994）[[Elsevier]]阿姆斯特丹，Raghavan，T.E.S.著，Aumann和Hart编辑，第735–759页，{{ISBN | 0-444-89427-6}}

Category:Non-cooperative games

类别: 非合作性游戏

* ''Power: Its Forms, Bases and Uses'' (1997) Transaction Publishers, by [[Dennis Wrong]]{{ISBN?}}

*《权力：它的形式、基础和用途》（1997年）交易出版商，作者[[Dennis Error]]{ISBN？}}

Category:International relations theory

类别: 国际关系理论

Category:Game theory game classes

类别: 博弈论游戏类

<noinclude>

This page was moved from [[wikipedia:en:Zero-sum game]]. Its edit history can be viewed at [[零和博弈/edithistory]]</noinclude>

此页摘自[[维基百科：英语：零和游戏]]。其编辑历史可在[[零和博弈编辑历史记录]]查看</noinclude>

[[Category:待整理页面]]

自适应系统

2020-11-15T09:37:00Z

Miyasaki：

此词条暂由Henry翻译。{{Refimprove|date=November 2008}}
此词条由Miyasaki审校

An '''adaptive system''' is a set of interacting or interdependent entities, real or abstract, forming an integrated whole that together are able to respond to environmental changes or changes in the interacting parts, in a way analogous to either continuous physiological [[homeostasis]] or evolutionary [[adaptation]] in [[biology]]. [[Feedback loops]] represent a key feature of adaptive systems, such as [[ecosystems]] and individual [[organisms]]; or in the human world, [[communities]], [[organizations]], and [[families]].

An adaptive system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole that together are able to respond to environmental changes or changes in the interacting parts, in a way analogous to either continuous physiological homeostasis or evolutionary adaptation in biology. Feedback loops represent a key feature of adaptive systems, such as ecosystems and individual organisms; or in the human world, communities, organizations, and families.

 适应系统adaptive system是一组相互作用或相互依存的实体，它们或真实或抽象，形成一个能够共同响应环境的变化或相互作用部分的变化的综合整体，类似于生物学中持续的生理稳态或进化适应。反馈循环代表了适应系统的一个关键特征，例如生态系统和个体有机体; 或者在人类世界中的社区、组织和家庭。

Artificial adaptive systems include [[robots]] with [[control system]]s that utilize [[negative feedback]] to maintain desired states.

Artificial adaptive systems include robots with control systems that utilize negative feedback to maintain desired states.

人工自适应系统包括具有控制系统的机器人，这些机器人利用负反馈来维持想要的状态。

==The law of adaptation==

==The law of adaptation==

适应法则

The law of adaptation can be stated informally as:

The law of adaptation can be stated informally as:

适应法则可以非正式地被阐释为:

{{quote|Every adaptive system converges to a state in which all kind of stimulation ceases.<ref>José Antonio Martín H., Javier de Lope and Darío Maravall: "Adaptation, Anticipation and Rationality in Natural and Artificial Systems: Computational Paradigms Mimicking Nature" Natural Computing, December, 2009. Vol. 8(4), pp. 757-775. [https://dx.doi.org/10.1007/s11047-008-9096-6 doi]</ref>}}

Formally, the law can be defined as follows:

Formally, the law can be defined as follows:

正式地，该法则可以定义如下:

Given a system <math>S</math>, we say that a physical event <math>E</math> is a stimulus for the system <math>S</math> if and only if the probability <math>P(S \rightarrow S'|E)</math> that the system suffers a change or be perturbed (in its elements or in its processes) when the event <math>E</math> occurs is strictly greater than the prior probability that <math>S</math> suffers a change independently of <math>E</math>:

Given a system <math>S</math>, we say that a physical event <math>E</math> is a stimulus for the system <math>S</math> if and only if the probability <math>P(S \rightarrow S'|E)</math> that the system suffers a change or be perturbed (in its elements or in its processes) when the event <math>E</math> occurs is strictly greater than the prior probability that <math>S</math> suffers a change independently of <math>E</math>:

给定一个系统<math>S</math>，我们说物理事件 <math>E</math>是<math>S</math>的刺激物，当且仅当数学<math>P(S \rightarrow S'|E)</math>，即当事件<math>E</math>发生时系统发生变化或（其组成元素或过程）被干扰的概率严格大于<math>S</math>独立于<math>E</math>而发生改变的概率。

:<math>P(S \rightarrow S'|E)>P(S \rightarrow S') </math>

<math>P(S \rightarrow S'|E)>P(S \rightarrow S') </math>

''Let <math>S</math> be an arbitrary system subject to changes in time <math>t</math> and let <math>E</math> be an arbitrary event that is a stimulus for the system <math>S</math>: we say that <math>S</math> is an adaptive system if and only if when t tends to infinity <math>(t\rightarrow \infty)</math> the probability that the system <math>S</math> change its behavior <math>(S\rightarrow S')</math> in a time step <math>t_0</math> given the event <math>E</math> is equal to the probability that the system change its behavior independently of the occurrence of the event <math>E</math>. In mathematical terms:''

Let <math>S</math> be an arbitrary system subject to changes in time <math>t</math> and let <math>E</math> be an arbitrary event that is a stimulus for the system <math>S</math>: we say that <math>S</math> is an adaptive system if and only if when t tends to infinity <math>(t\rightarrow \infty)</math> the probability that the system <math>S</math> change its behavior <math>(S\rightarrow S')</math> in a time step <math>t_0</math> given the event <math>E</math> is equal to the probability that the system change its behavior independently of the occurrence of the event <math>E</math>. In mathematical terms:

假设<math>S</math>是一个随时间变化的任意系统，<math>t</math>是一个随时间变化的系统，<math>e</math>是一个随时间变化的事件，是系统<math>s</math>的一个刺激: 我们说<math>S</math>是一个适应性系统，当且仅当 t 趋向于无穷时(t→∞)，给定事件E的系统<math>S</math>在时间步长t0改变其行为（S→S′）的概率等于系统改变其行为独立于事件的发生的概率，用数学术语来表达如下：

#- <math> P_{t_0}(S\rightarrow S'|E) > P_{t_0}(S\rightarrow S') > 0 </math>

- <math> P_{t_0}(S\rightarrow S'|E) > P_{t_0}(S\rightarrow S') > 0 </math>

#- <math> \lim_{t\rightarrow \infty} P_t(S\rightarrow S' | E) = P_t(S\rightarrow S')</math>

- <math> \lim_{t\rightarrow \infty} P_t(S\rightarrow S' | E) = P_t(S\rightarrow S')</math>

Thus, for each instant <math>t</math> will exist a temporal interval <math>h</math> such that:

Thus, for each instant <math>t</math> will exist a temporal interval <math>h</math> such that:

因此，对于每一个即时<math>t</math>，都会存在一个时间间隔<math>h</math>，这样:

:<math> P_{t+h}(S\rightarrow S' | E) - P_{t+h}(S\rightarrow S') < P_t(S\rightarrow S' | E) - P_t(S\rightarrow S')</math>

<math> P_{t+h}(S\rightarrow S' | E) - P_{t+h}(S\rightarrow S') < P_t(S\rightarrow S' | E) - P_t(S\rightarrow S')</math>

==Benefit of self-adjusting systems==

==Benefit of self-adjusting systems==

自动调节系统的好处

In an adaptive system, a parameter changes slowly and has no preferred value. In a self-adjusting system though, the parameter value “depends on the history of the system dynamics”. One of the most important qualities of ''self-adjusting systems'' is its “[[edge of chaos|adaptation to the edge of chaos]]” or ability to avoid [[chaos theory|chaos]]. Practically speaking, by heading to the [[edge of chaos]] without going further, a leader may act spontaneously yet without disaster. A March/April 2009 Complexity article further explains the self-adjusting systems used and the realistic implications.<ref>Hübler, A. & Wotherspoon, T.: "Self-Adjusting Systems Avoid Chaos". Complexity. 14(4), 8 – 11. 2008</ref> Physicists have shown that [[adaptation]] to the [[edge of chaos]] occurs in almost all systems with [[feedback]].<ref>{{cite journal|last1=Wotherspoon|first1=T.|last2=Hubler|first2=A.|title=Adaptation to the edge of chaos with random-wavelet feedback|journal=J Phys Chem A|volume=113|issue=1|pages=19–22|doi=10.1021/jp804420g|pmid=19072712|year=2009|bibcode=2009JPCA..113...19W}}</ref>

In an adaptive system, a parameter changes slowly and has no preferred value. In a self-adjusting system though, the parameter value “depends on the history of the system dynamics”. One of the most important qualities of self-adjusting systems is its “adaptation to the edge of chaos” or ability to avoid chaos. Practically speaking, by heading to the edge of chaos without going further, a leader may act spontaneously yet without disaster. A March/April 2009 Complexity article further explains the self-adjusting systems used and the realistic implications. Physicists have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.

在自适应系统中，参数变化缓慢，没有优先值。然而，在一个自调整系统中，参数值“取决于系统动力的历史”。自调节系统最重要的特性之一是它能“适应混乱的边缘”或避免混乱的能力。实际上来讲，通过朝着混乱的边缘出发但是不走的太远，领导者就可以在避免灾难的情况下自发地行动。Complexity期刊2009年3/4月一期的一篇文章进一步解释了自我调节系统的使用和现实意义。<ref>Hübler, A. & Wotherspoon, T.: "Self-Adjusting Systems Avoid Chaos". Complexity. 14(4), 8 – 11. 2008</ref>物理学家已经证明，对混沌边缘的适应几乎发生在所有具有反馈的系统中。<ref>{{cite journal|last1=Wotherspoon|first1=T.|last2=Hubler|first2=A.|title=Adaptation to the edge of chaos with random-wavelet feedback|journal=J Phys Chem A|volume=113|issue=1|pages=19–22|doi=10.1021/jp804420g|pmid=19072712|year=2009|bibcode=2009JPCA..113...19W}}</ref>

==Practopoiesis==

==Practopoiesis==

拓扑实践

How do various types of adaptations interact in a living system? ''Practopoiesis,'' a term due to its originator Danko Nikolić, is a reference to a hierarchy of adaptation mechanisms answering this question. The adaptive hierarchy forms a kind of a self-adjusting system in which [[autopoiesis]] of the entire ''organism'' or a ''cell'' occurs through a hierarchy of [[allopoiesis|allopoietic]] interactions among ''components''.<ref name=Nikolic2015>{{cite journal|title=Practopoiesis: Or how life fosters a mind. |author=Danko Nikolić|date=2015|doi=10.1016/j.jtbi.2015.03.003|pmid = 25791287|volume=373|journal=Journal of Theoretical Biology|pages=40–61|arxiv=1402.5332}}</ref> This is possible because the components are organized into a [[poiesis|poietic]] hierarchy: adaptive actions of one component result in creation of another component. The theory proposes that living systems exhibit a hierarchy of a total of four such adaptive poietic operations:

How do various types of adaptations interact in a living system? Practopoiesis, a term due to its originator Danko Nikolić, is a reference to a hierarchy of adaptation mechanisms answering this question. The adaptive hierarchy forms a kind of a self-adjusting system in which autopoiesis of the entire organism or a cell occurs through a hierarchy of allopoietic interactions among components. This is possible because the components are organized into a poietic hierarchy: adaptive actions of one component result in creation of another component. The theory proposes that living systems exhibit a hierarchy of a total of four such adaptive poietic operations:

在一个生命系统中，各种类型的适应性是如何相互作用的？ 拓扑实践Practopoiesis，这个术语源于它的发明者 Danko nikoli，指向了能回答这个问题的一个适应机制层次结构。这种适应性层次结构形成了一种自我调节系统，其中整个生物体或细胞的自创生是通过各组分<ref name=Nikolic2015>{{cite journal|title=Practopoiesis: Or how life fosters a mind. |author=Danko Nikolić|date=2015|doi=10.1016/j.jtbi.2015.03.003|pmid = 25791287|volume=373|journal=Journal of Theoretical Biology|pages=40–61|arxiv=1402.5332}}</ref>之间的异体生成相互作用而发生的。这之所以可能是因为组件被组织成一个极端层次结构: 一个组件的自适应操作导致另一个组件的创建。该理论提出，生命系统展示了一个由四个这样的适应性极化操作组成的层级结构:

''evolution'' (i) → ''gene expression'' (ii) → ''non gene-involving homeostatic mechanisms (anapoiesis)'' (iii) → ''final cell function'' (iv)

evolution (i) → gene expression (ii) → non gene-involving homeostatic mechanisms (anapoiesis) (iii) → final cell function (iv)

进化(i) → 基因表达(ii) → 非基因参与的稳态机制(anapoiesis) (iii) → 最终细胞功能(iv)

As the hierarchy evolves towards higher levels of organization, the speed of adaptation increases. Evolution is the slowest; the final cell function is the fastest. Ultimately, practopoiesis challenges current neuroscience doctrine by asserting that mental operations primarily occur at the homeostatic, anapoietic level (iii) — i.e., that minds and thought emerge from fast homeostatic mechanisms poietically controlling the cell function. This contrasts the widespread belief that thinking is synonymous with neural activity (i.e., with the 'final cell function' at level iv).

As the hierarchy evolves towards higher levels of organization, the speed of adaptation increases. Evolution is the slowest; the final cell function is the fastest. Ultimately, practopoiesis challenges current neuroscience doctrine by asserting that mental operations primarily occur at the homeostatic, anapoietic level (iii) — i.e., that minds and thought emerge from fast homeostatic mechanisms poietically controlling the cell function. This contrasts the widespread belief that thinking is synonymous with neural activity (i.e., with the 'final cell function' at level iv).

随着层级结构向更高级别的组织发展，适应的速度也在加快。进化是最慢的，最后的细胞功能是最快的。最终，实践拓扑学挑战当前的神经科学学说，认为心理活动主要发生在稳态，非生物水平上。也就是说，意识和想法从快速的稳态机制中产生，从而控制了细胞功能。这与人们普遍认为的思考是神经活动的同义词(也就是说，与第四级的“最终细胞功能”)形成了鲜明对比。

Each slower level contains knowledge that is more general than the faster level; for example, genes contain more general knowledge than anapoietic mechanisms, which in turn contain more general knowledge than cell functions. This hierarchy of knowledge enables the anapoietic level to directly activate concepts, which are the most fundamental ingredient for the emergence of the mind.

Each slower level contains knowledge that is more general than the faster level; for example, genes contain more general knowledge than anapoietic mechanisms, which in turn contain more general knowledge than cell functions. This hierarchy of knowledge enables the anapoietic level to directly activate concepts, which are the most fundamental ingredient for the emergence of the mind.

每一个较慢的层次包含的知识比较快的层次包含的知识更一般性; 例如，基因包含的一般知识比无生殖机制多，而无生殖机制又比细胞功能包含更多的一般知识。这种知识的层次结构使得无生命层次能够直接激活概念，而这些概念是意识出现的最基本的原料。

==See also==

==See also==

参见

{{Portal|Evolutionary biology}}

{{div col|colwidth=22em}}

* [[Adaptive immune system]]

适应免疫系统

* [[Artificial neural network]]

人工神经网络

* [[Complex adaptive system]]

复杂适应系统

* [[Diffusion of innovations]]

创新扩散

* [[Ecosystems]]

生态系统

* [[Gaia hypothesis]]

盖亚假说

* [[Gene expression programming]]

基因表达式编程算法

* [[Genetic algorithms]]

基因算法

* [[Learning]]

学习

* [[Neural adaptation]]

神经适应

{{div col end}}

==Notes==

==Notes==

注释

{{Reflist}}

==References==

==References==

参考资料

* {{cite journal

| last = Martin H. | first = Jose Antonio. | authorlink = Jose Antonio Martin H.

| last = Martin H. | first = Jose Antonio. | authorlink = Jose Antonio Martin H.

| author2 = [[Javier de Lope]]; [[Darío Maravall]]

| author2 = Javier de Lope; Darío Maravall

| author2 = Javier de Lope; Darío Maravall

| title = Adaptation, Anticipation and Rationality in Natural and Artificial Systems: Computational Paradigms Mimicking Nature

| title = Adaptation, Anticipation and Rationality in Natural and Artificial Systems: Computational Paradigms Mimicking Nature

自然和人工系统中的适应、预测和理性: 模仿自然的计算模式

| journal = Natural Computing

| journal = Natural Computing

自然计算杂志

| volume = 8 | issue = 4

| volume = 8 | issue = 4

第八卷，第四期

| pages = 757–775

| pages = 757–775

第757-775页

| date = 2009

| date = 2009

2009年

| doi = 10.1007/s11047-008-9096-6

| doi = 10.1007/s11047-008-9096-6

10.1007 / s11047-008-9096-6

}}

}}

}}

==External links==

==External links==

外部链接

{{Wiktionary | anapoiesis}}

{{Wiktionary | practopoiesis}}

* Funny [https://www.youtube.com/watch?v=WIzsz03X8qc animated video] explaining the theory of practopoiesis, made by Mind & Brain.

* Practopoiesis offers solutions to [http://www.danko-nikolic.com/long-standing-problems-solved-by-practopoiesis/ nine long-standing problems] in neuroscience and philosophy of mind

* [https://sapienlabs.co/?s=danko+nikol Blog series on practopoiesis]

[[Category:Control engineering]]

Category:Control engineering

类别: 控制工程

[[Category:Cybernetics]]

Category:Cybernetics

类别: 控制论

[[Category:Systems theory]]

Category:Systems theory

范畴: 系统论

<noinclude>

This page was moved from [[wikipedia:en:Adaptive system]]. Its edit history can be viewed at [[自适应系统/edithistory]]</noinclude>

[[Category:待整理页面]]

自适应系统

2020-11-15T09:28:52Z

Miyasaki：

此词条暂由Henry翻译。{{Refimprove|date=November 2008}}
此词条由Miyasaki审校

An '''adaptive system''' is a set of interacting or interdependent entities, real or abstract, forming an integrated whole that together are able to respond to environmental changes or changes in the interacting parts, in a way analogous to either continuous physiological [[homeostasis]] or evolutionary [[adaptation]] in [[biology]]. [[Feedback loops]] represent a key feature of adaptive systems, such as [[ecosystems]] and individual [[organisms]]; or in the human world, [[communities]], [[organizations]], and [[families]].

An adaptive system is a set of interacting or interdependent entities, real or abstract, forming an integrated whole that together are able to respond to environmental changes or changes in the interacting parts, in a way analogous to either continuous physiological homeostasis or evolutionary adaptation in biology. Feedback loops represent a key feature of adaptive systems, such as ecosystems and individual organisms; or in the human world, communities, organizations, and families.

 适应系统adaptive system是一组相互作用或相互依存的实体，它们或真实或抽象，形成一个能够共同响应环境的变化或相互作用部分的变化的综合整体，类似于生物学中持续的生理稳态或进化适应。反馈循环代表了适应系统的一个关键特征，例如生态系统和个体有机体; 或者在人类世界中的社区、组织和家庭。

Artificial adaptive systems include [[robots]] with [[control system]]s that utilize [[negative feedback]] to maintain desired states.

Artificial adaptive systems include robots with control systems that utilize negative feedback to maintain desired states.

人工自适应系统包括具有控制系统的机器人，这些机器人利用负反馈来维持想要的状态。

==The law of adaptation==

==The law of adaptation==

适应法则

The law of adaptation can be stated informally as:

The law of adaptation can be stated informally as:

适应法则可以非正式地被阐释为:

{{quote|Every adaptive system converges to a state in which all kind of stimulation ceases.<ref>José Antonio Martín H., Javier de Lope and Darío Maravall: "Adaptation, Anticipation and Rationality in Natural and Artificial Systems: Computational Paradigms Mimicking Nature" Natural Computing, December, 2009. Vol. 8(4), pp. 757-775. [https://dx.doi.org/10.1007/s11047-008-9096-6 doi]</ref>}}

Formally, the law can be defined as follows:

Formally, the law can be defined as follows:

正式地，该法则可以定义如下:

Given a system <math>S</math>, we say that a physical event <math>E</math> is a stimulus for the system <math>S</math> if and only if the probability <math>P(S \rightarrow S'|E)</math> that the system suffers a change or be perturbed (in its elements or in its processes) when the event <math>E</math> occurs is strictly greater than the prior probability that <math>S</math> suffers a change independently of <math>E</math>:

Given a system <math>S</math>, we say that a physical event <math>E</math> is a stimulus for the system <math>S</math> if and only if the probability <math>P(S \rightarrow S'|E)</math> that the system suffers a change or be perturbed (in its elements or in its processes) when the event <math>E</math> occurs is strictly greater than the prior probability that <math>S</math> suffers a change independently of <math>E</math>:

给定一个系统<math>S</math>，我们说物理事件 <math>E</math>是<math>S</math>的刺激物，当且仅当数学<math>P(S \rightarrow S'|E)</math>，即当事件<math>E</math>发生时系统发生变化或（其组成元素或过程）被干扰的概率严格大于<math>S</math>独立于<math>E</math>而发生改变的概率。

:<math>P(S \rightarrow S'|E)>P(S \rightarrow S') </math>

<math>P(S \rightarrow S'|E)>P(S \rightarrow S') </math>

''Let <math>S</math> be an arbitrary system subject to changes in time <math>t</math> and let <math>E</math> be an arbitrary event that is a stimulus for the system <math>S</math>: we say that <math>S</math> is an adaptive system if and only if when t tends to infinity <math>(t\rightarrow \infty)</math> the probability that the system <math>S</math> change its behavior <math>(S\rightarrow S')</math> in a time step <math>t_0</math> given the event <math>E</math> is equal to the probability that the system change its behavior independently of the occurrence of the event <math>E</math>. In mathematical terms:''

Let <math>S</math> be an arbitrary system subject to changes in time <math>t</math> and let <math>E</math> be an arbitrary event that is a stimulus for the system <math>S</math>: we say that <math>S</math> is an adaptive system if and only if when t tends to infinity <math>(t\rightarrow \infty)</math> the probability that the system <math>S</math> change its behavior <math>(S\rightarrow S')</math> in a time step <math>t_0</math> given the event <math>E</math> is equal to the probability that the system change its behavior independently of the occurrence of the event <math>E</math>. In mathematical terms:

假设<math>S</math>是一个随时间变化的任意系统，<math>t</math>是一个随时间变化的系统，<math>e</math>是一个随时间变化的事件，是系统<math>s</math>的一个刺激: 我们说<math>S</math>是一个适应性系统，当且仅当 t 趋向于无穷时(t→∞)，给定事件E的系统<math>S</math>在时间步长t0改变其行为（S→S′）的概率等于系统改变其行为独立于事件的发生的概率，用数学术语来表达如下：

#- <math> P_{t_0}(S\rightarrow S'|E) > P_{t_0}(S\rightarrow S') > 0 </math>

- <math> P_{t_0}(S\rightarrow S'|E) > P_{t_0}(S\rightarrow S') > 0 </math>

#- <math> \lim_{t\rightarrow \infty} P_t(S\rightarrow S' | E) = P_t(S\rightarrow S')</math>

- <math> \lim_{t\rightarrow \infty} P_t(S\rightarrow S' | E) = P_t(S\rightarrow S')</math>

Thus, for each instant <math>t</math> will exist a temporal interval <math>h</math> such that:

Thus, for each instant <math>t</math> will exist a temporal interval <math>h</math> such that:

因此，对于每一个即时<math>t</math>，都会存在一个时间间隔<math>h</math>，这样:

:<math> P_{t+h}(S\rightarrow S' | E) - P_{t+h}(S\rightarrow S') < P_t(S\rightarrow S' | E) - P_t(S\rightarrow S')</math>

<math> P_{t+h}(S\rightarrow S' | E) - P_{t+h}(S\rightarrow S') < P_t(S\rightarrow S' | E) - P_t(S\rightarrow S')</math>

==Benefit of self-adjusting systems==

==Benefit of self-adjusting systems==

自动调节系统的好处

In an adaptive system, a parameter changes slowly and has no preferred value. In a self-adjusting system though, the parameter value “depends on the history of the system dynamics”. One of the most important qualities of ''self-adjusting systems'' is its “[[edge of chaos|adaptation to the edge of chaos]]” or ability to avoid [[chaos theory|chaos]]. Practically speaking, by heading to the [[edge of chaos]] without going further, a leader may act spontaneously yet without disaster. A March/April 2009 Complexity article further explains the self-adjusting systems used and the realistic implications.<ref>Hübler, A. & Wotherspoon, T.: "Self-Adjusting Systems Avoid Chaos". Complexity. 14(4), 8 – 11. 2008</ref> Physicists have shown that [[adaptation]] to the [[edge of chaos]] occurs in almost all systems with [[feedback]].<ref>{{cite journal|last1=Wotherspoon|first1=T.|last2=Hubler|first2=A.|title=Adaptation to the edge of chaos with random-wavelet feedback|journal=J Phys Chem A|volume=113|issue=1|pages=19–22|doi=10.1021/jp804420g|pmid=19072712|year=2009|bibcode=2009JPCA..113...19W}}</ref>

In an adaptive system, a parameter changes slowly and has no preferred value. In a self-adjusting system though, the parameter value “depends on the history of the system dynamics”. One of the most important qualities of self-adjusting systems is its “adaptation to the edge of chaos” or ability to avoid chaos. Practically speaking, by heading to the edge of chaos without going further, a leader may act spontaneously yet without disaster. A March/April 2009 Complexity article further explains the self-adjusting systems used and the realistic implications. Physicists have shown that adaptation to the edge of chaos occurs in almost all systems with feedback.

在自适应系统中，参数变化缓慢，没有优先值。然而，在一个自调整系统中，参数值“取决于系统动力的历史”。自调节系统最重要的特性之一是它能“适应混乱的边缘”或避免混乱的能力。实际上来讲，通过朝着混乱的边缘出发但是不走的太远，领导者就可以在避免灾难的情况下自发地行动。Complexity期刊2009年3/4月一期的一篇文章进一步解释了自我调节系统的使用和现实意义。物理学家已经证明，对混沌边缘的适应几乎发生在所有具有反馈的系统中。

==Practopoiesis==

==Practopoiesis==

拓扑实践

How do various types of adaptations interact in a living system? ''Practopoiesis,'' a term due to its originator Danko Nikolić, is a reference to a hierarchy of adaptation mechanisms answering this question. The adaptive hierarchy forms a kind of a self-adjusting system in which [[autopoiesis]] of the entire ''organism'' or a ''cell'' occurs through a hierarchy of [[allopoiesis|allopoietic]] interactions among ''components''.<ref name=Nikolic2015>{{cite journal|title=Practopoiesis: Or how life fosters a mind. |author=Danko Nikolić|date=2015|doi=10.1016/j.jtbi.2015.03.003|pmid = 25791287|volume=373|journal=Journal of Theoretical Biology|pages=40–61|arxiv=1402.5332}}</ref> This is possible because the components are organized into a [[poiesis|poietic]] hierarchy: adaptive actions of one component result in creation of another component. The theory proposes that living systems exhibit a hierarchy of a total of four such adaptive poietic operations:

How do various types of adaptations interact in a living system? Practopoiesis, a term due to its originator Danko Nikolić, is a reference to a hierarchy of adaptation mechanisms answering this question. The adaptive hierarchy forms a kind of a self-adjusting system in which autopoiesis of the entire organism or a cell occurs through a hierarchy of allopoietic interactions among components. This is possible because the components are organized into a poietic hierarchy: adaptive actions of one component result in creation of another component. The theory proposes that living systems exhibit a hierarchy of a total of four such adaptive poietic operations:

在一个生命系统中，各种类型的适应性是如何相互作用的？ 拓扑实践Practopoiesis，这个术语源于它的发明者 Danko nikoli，指向了能回答这个问题的一个适应机制层次结构。这种适应性层次结构形成了一种自我调节系统，其中整个生物体或细胞的自创生是通过各组分之间的异体生成相互作用而发生的。这之所以可能是因为组件被组织成一个极端层次结构: 一个组件的自适应操作导致另一个组件的创建。该理论提出，生命系统展示了一个由四个这样的适应性极化操作组成的层级结构:

''evolution'' (i) → ''gene expression'' (ii) → ''non gene-involving homeostatic mechanisms (anapoiesis)'' (iii) → ''final cell function'' (iv)

evolution (i) → gene expression (ii) → non gene-involving homeostatic mechanisms (anapoiesis) (iii) → final cell function (iv)

进化(i) → 基因表达(ii) → 非基因参与的稳态机制(anapoiesis) (iii) → 最终细胞功能(iv)

As the hierarchy evolves towards higher levels of organization, the speed of adaptation increases. Evolution is the slowest; the final cell function is the fastest. Ultimately, practopoiesis challenges current neuroscience doctrine by asserting that mental operations primarily occur at the homeostatic, anapoietic level (iii) — i.e., that minds and thought emerge from fast homeostatic mechanisms poietically controlling the cell function. This contrasts the widespread belief that thinking is synonymous with neural activity (i.e., with the 'final cell function' at level iv).

As the hierarchy evolves towards higher levels of organization, the speed of adaptation increases. Evolution is the slowest; the final cell function is the fastest. Ultimately, practopoiesis challenges current neuroscience doctrine by asserting that mental operations primarily occur at the homeostatic, anapoietic level (iii) — i.e., that minds and thought emerge from fast homeostatic mechanisms poietically controlling the cell function. This contrasts the widespread belief that thinking is synonymous with neural activity (i.e., with the 'final cell function' at level iv).

随着层级结构向更高级别的组织发展，适应的速度也在加快。进化是最慢的，最后的细胞功能是最快的。最终，实践拓扑学挑战当前的神经科学学说，认为心理活动主要发生在稳态，非生物水平上。也就是说，意识和想法从快速的稳态机制中产生，从而控制了细胞功能。这与人们普遍认为的思考是神经活动的同义词(也就是说，与第四级的“最终细胞功能”)形成了鲜明对比。

Each slower level contains knowledge that is more general than the faster level; for example, genes contain more general knowledge than anapoietic mechanisms, which in turn contain more general knowledge than cell functions. This hierarchy of knowledge enables the anapoietic level to directly activate concepts, which are the most fundamental ingredient for the emergence of the mind.

Each slower level contains knowledge that is more general than the faster level; for example, genes contain more general knowledge than anapoietic mechanisms, which in turn contain more general knowledge than cell functions. This hierarchy of knowledge enables the anapoietic level to directly activate concepts, which are the most fundamental ingredient for the emergence of the mind.

每一个较慢的层次包含的知识比较快的层次包含的知识更一般性; 例如，基因包含的一般知识比无生殖机制多，而无生殖机制又比细胞功能包含更多的一般知识。这种知识的层次结构使得无生命层次能够直接激活概念，而这些概念是意识出现的最基本的原料。

==See also==

==See also==

参见

{{Portal|Evolutionary biology}}

{{div col|colwidth=22em}}

* [[Adaptive immune system]]

适应免疫系统

* [[Artificial neural network]]

人工神经网络

* [[Complex adaptive system]]

复杂适应系统

* [[Diffusion of innovations]]

创新扩散

* [[Ecosystems]]

生态系统

* [[Gaia hypothesis]]

盖亚假说

* [[Gene expression programming]]

基因表达式编程算法

* [[Genetic algorithms]]

基因算法

* [[Learning]]

学习

* [[Neural adaptation]]

神经适应

{{div col end}}

==Notes==

==Notes==

注释

{{Reflist}}

==References==

==References==

参考资料

* {{cite journal

| last = Martin H. | first = Jose Antonio. | authorlink = Jose Antonio Martin H.

| last = Martin H. | first = Jose Antonio. | authorlink = Jose Antonio Martin H.

| author2 = [[Javier de Lope]]; [[Darío Maravall]]

| author2 = Javier de Lope; Darío Maravall

| author2 = Javier de Lope; Darío Maravall

| title = Adaptation, Anticipation and Rationality in Natural and Artificial Systems: Computational Paradigms Mimicking Nature

| title = Adaptation, Anticipation and Rationality in Natural and Artificial Systems: Computational Paradigms Mimicking Nature

自然和人工系统中的适应、预测和理性: 模仿自然的计算模式

| journal = Natural Computing

| journal = Natural Computing

自然计算杂志

| volume = 8 | issue = 4

| volume = 8 | issue = 4

第八卷，第四期

| pages = 757–775

| pages = 757–775

第757-775页

| date = 2009

| date = 2009

2009年

| doi = 10.1007/s11047-008-9096-6

| doi = 10.1007/s11047-008-9096-6

10.1007 / s11047-008-9096-6

}}

}}

}}

==External links==

==External links==

外部链接

{{Wiktionary | anapoiesis}}

{{Wiktionary | practopoiesis}}

* Funny [https://www.youtube.com/watch?v=WIzsz03X8qc animated video] explaining the theory of practopoiesis, made by Mind & Brain.

* Practopoiesis offers solutions to [http://www.danko-nikolic.com/long-standing-problems-solved-by-practopoiesis/ nine long-standing problems] in neuroscience and philosophy of mind

* [https://sapienlabs.co/?s=danko+nikol Blog series on practopoiesis]

[[Category:Control engineering]]

Category:Control engineering

类别: 控制工程

[[Category:Cybernetics]]

Category:Cybernetics

类别: 控制论

[[Category:Systems theory]]

Category:Systems theory

范畴: 系统论

<noinclude>

This page was moved from [[wikipedia:en:Adaptive system]]. Its edit history can be viewed at [[自适应系统/edithistory]]</noinclude>

[[Category:待整理页面]]

阿喀琉斯之踵

2020-10-19T07:57:44Z

Miyasaki：

本词条由Miyasaki审校

本词条由Agnes初步翻译

此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。

{{short description|Critical weakness which can lead to downfall in spite of overall strength}}

{{About|the phrase|the anatomical part|Achilles tendon||Achilles Heel (disambiguation)}}

[[File:Detail of Achilles thniskon.JPG|thumb|260px|Statue of Achilleas Thniskon (''Dying Achilles'') at the [[Corfu]] [[Achilleion (Corfu)|Achilleion]].]]

Statue of Achilleas Thniskon (Dying Achilles) at the [[Corfu Achilleion.]]

【图1：Statue of Achilleas Thniskon (Dying Achilles) at the Corfu Achilleion.希腊科孚岛“垂死的阿喀琉斯”雕像】

==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]Statue of Achilleas Thniskon (Dying Achilles)省译

An '''Achilles' heel''' or '''Achilles heel'''<ref>{{Cite web|url=https://dictionary.cambridge.org/dictionary/english/achilles-heel|title=Achilles heel {{!}} meaning in the Cambridge English Dictionary|website=dictionary.cambridge.org|language=en|access-date=2019-09-29}}</ref><ref>{{Cite web|url=https://www.lexico.com/en/definition/achilles_heel|title=Achilles heel {{!}} Definition of Achilles heel by Lexico|website=Lexico Dictionaries {{!}} English|language=en|access-date=2019-09-29}}</ref> is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.

An Achilles' heel or Achilles heel is a weakness in spite of overall strength, which can lead to downfall. While the mythological origin refers to a physical vulnerability, idiomatic references to other attributes or qualities that can lead to downfall are common.

“阿喀琉斯之踵”是指一种弱点，这个弱点可以导致一个强大整体的毁灭。虽然“阿喀琉斯之踵”一词的神话起源指的是身体的脆弱性，但在习惯表达中也常用于其他能摧毁整体的特征或品质。

==[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]An Achilles' heel or Achilles heel 此处省译，因为通过查询发现两种不同的英文表达在中文中都翻译为阿喀琉斯之踵，故译者认为无需重复赘述。

== Origin ==

起源

In [[Greek mythology]], when [[Achilles]] was a baby, it was foretold that he would die young. To prevent his death, his mother [[Thetis]] took [[Achilles]] to the [[Styx|River Styx]], which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the [[heel]], his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles.

In Greek mythology, when Achilles was a baby, it was foretold that he would die young. To prevent his death, his mother Thetis took Achilles to the River Styx, which was supposed to offer powers of invulnerability, and dipped his body into the water; however, as Thetis held Achilles by the heel, his heel was not washed over by the water of the magical river. Achilles grew up to be a man of war who survived many great battles.

在希腊神话中，当阿喀琉斯还是个婴儿的时候，人们就预言他会英年早逝。为了阻止阿喀琉斯的死亡，他的母亲忒提丝（音译）把他带到冥河，并把他的身体浸入河水中，因为冥河水据说可以提供刀枪不入的能力; 然而，因为忒提丝提着阿喀琉斯的脚后跟，所以他的脚后跟并没有被冥河的水浸泡到。阿喀琉斯长大后成为一个战士，在许多伟大的战役中幸存下来。

[[File:Peter Paul Rubens 181.jpg|thumb|right|Oil painting (c. 1625) by [[Peter Paul Rubens]] of the goddess Thetis dipping her son Achilles in the [[River Styx]], which runs through [[Hades]]. In the background, the ferryman [[Charon (mythology)|Charon]] rows the dead across the river in his boat.]]

【图2：Oil painting (c. 1625) by Peter Paul Rubens of the goddess Thetis dipping her son Achilles in the River Styx, which runs through Hades. In the background, the ferryman Charon rows the dead across the river in his boat.
由彼得·保罗·鲁本斯创作的油画(约1625年)，女神忒提丝在流经地狱的冥河中浸泡她的儿子阿喀琉斯。背景中，摆渡人卡戎撑着船运为死者摆渡。】

Although the death of Achilles is predicted by Hector in [[Homer]]’s ''[[Iliad]]'', it does not actually occur in the ''Iliad'', but is described in later Greek and Roman poetry and drama<ref>E.g. [[Ovid]], ''[[Metamorphoses]]'' 12.580–619.</ref> concerning events after the ''Iliad'', later in the [[Trojan War]]. In the myths surrounding the war, Achilles was said to have died from a wound to his heel,<ref name=":0">{{Cite web|url=https://blog.britishmuseum.org/who-was-achilles/|title=Who was Achilles?|date=2019-10-15|website=The British Museum Blog|language=en-GB|access-date=2019-12-24}}</ref><ref>{{Cite web|url=https://www.history.com/topics/ancient-history|title=Ancient History|website=HISTORY|language=en|access-date=2019-12-24}}</ref> ankle,<ref>http://www.perseus.tufts.edu/hopper/text?doc=Perseus%3Atext%3A1999.01.0022%3Atext%3DEpitome%3Abook%3DE%3Achapter%3D5%3Asection%3D3</ref> or torso,<ref name=":0" /> which was the result of an arrow—possibly poisoned—shot by [[Paris (mythology)|Paris]].<ref>See P. J. Heslin, ''The Transvestite Achilles: Gender and Genre in Statius’'' Achilleid, Cambridge: Cambridge University Press: 2005, 166–169.</ref>

Although the death of Achilles is predicted by Hector in Homer’s Iliad, it does not actually occur in the Iliad, but is described in later Greek and Roman poetry and drama concerning events after the Iliad, later in the Trojan War. In the myths surrounding the war, Achilles was said to have died from a wound to his heel, ankle, or torso,

尽管赫克托在荷马史诗《伊利亚特》中预言了阿喀琉斯的死亡，但阿喀琉斯之死实际上并没有出现在《伊利亚特》中，而是出现在后来的古希腊罗马诗歌和戏剧所描述的《伊利亚特》之后的事件中，后来又出现在特洛伊战争中。在围绕特洛伊战争的神话中，据说阿喀琉斯是死于脚跟、脚踝或躯干的伤口。

Classical myths attribute Achilles’s invulnerability to his mother [[Thetis]] having treated him with [[ambrosia]] and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete.<ref>Apollonius, Argonautica 4.869–872</ref> According to a myth arising later, his mother had dipped the infant Achilles in the river [[Styx (mythology)|Styx]], holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.<ref>Statius, Achilleid 1.122f., 269f., 480f.</ref>

Classical myths attribute Achilles’s invulnerability to his mother Thetis having treated him with ambrosia and burned away his mortality in the hearth fire except on the heel, by which she held him. Peleus, his father, discovered the treatment and was alarmed to see Thetis holding the baby in the flames, which offended her and made her leave the treatment incomplete. According to a myth arising later, his mother had dipped the infant Achilles in the river Styx, holding onto him by his heel, and he became invulnerable where the waters touched him—that is, everywhere except the areas of his heel that were covered by her thumb and forefinger.

古典神话中将阿喀琉斯的刀枪不入归功于他的母亲忒提丝曾经给他吃过珍馐（专供给神的食物），并在炉火中赋予他不死的命运，只留下了手提着的脚后跟。他的父亲珀琉斯发现忒提丝使用这种治疗方法后非常担忧，这不仅激怒了忒提丝，也使她未能完成治疗。而根据后来出现的另一个神话，阿喀琉斯的母亲抓住他的脚后跟，将他在冥河水里蘸了一下，他与河水接触到的地方变得坚不可摧——除了脚后跟被他母亲的拇指和食指覆盖的地方。

--[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]burned away his mortality中mortality一词在牛津英汉双解词典中解释为“the state of being human and not being for ever”，译者反复思考后决定译为“生命的限期”，但是原文仍然不能完全通畅，所以对于morality一词的翻译仍然存疑；

--[[用户:Miyasaki|Miyasaki]]（[[用户讨论:Miyasaki|讨论]]）【审校】mortality可理解为凡人必死之命运，在此处多种直译方式都不通畅，因此对burned away his mortality 做了意译处理。

--[[用户:Agnes|Agnes]]（[[用户讨论:Agnes|讨论]]）[翻译]译者认为，原文中破折号“——”和“that is”所起到的作用相同，都是解释说明，为保证译文通常，此处采用省译，省去了that is 的翻译。

The oldest-known written record of the tendon being named for [[Achilles]] is in 1693 by the Flemish/Dutch anatomist [[Philip Verheyen]]. In his widely used text ''Corporis Humani Anatomia'' he described the tendon's location and said that it was commonly called "the cord of Achilles".<ref>}}|title=Corporis humani anatomia|last1=Veheyen|first1=Philip|authorlink=Philip Verheyen|publisher=Aegidium Denique|place=Leuven|year=1693|quote=Vocatum passim ''chorda Achillis'', & ab Hippocrate ''tendo magnus''. (Appendix, caput XII. ''De musculis pedii et antipedii'', p. 269)
|url=https://archive.org/stream/corporishumanian00verh#page/268/mode/2up|accessdate=12 Mar 2018|page=269
</ref><ref name="Klenerman2007">{{cite journal |last1=Klenerman |first1=L. |title=The early history of tendo Achillis and its rupture |journal=The Journal of Bone and Joint Surgery. British Volume |date=April 2007 |volume=89-B |issue=4 |pages=545–547 |doi=10.1302/0301-620X.89B4.18978|pmid=17463129 }}</ref> As an expression meaning "area of weakness, vulnerable spot," the use of "Achilles heel" dates only to 1840, with implied use in [[Samuel Taylor Coleridge]]'s "Ireland, that vulnerable heel of the British Achilles!" from 1810 (''Oxford English Dictionary'').<ref>{{Cite web|url=https://www.oed.com/start;jsessionid=7F12E25F0F46A5BB16B0EAE3979CBEB6?authRejection=true&url=%2Fview%2FEntry%2F272524%3FredirectedFrom%3DAchilles%2520heel|title=Home : Oxford English Dictionary|website=www.oed.com|language=en|access-date=2019-09-29}}</ref>

The oldest-known written record of the tendon being named for Achilles is in 1693 by the Flemish/Dutch anatomist Philip Verheyen. In his widely used text Corporis Humani Anatomia he described the tendon's location and said that it was commonly called "the cord of Achilles." As an expression meaning "area of weakness, vulnerable spot," the use of "Achilles heel" dates only to 1840, with implied use in Samuel Taylor Coleridge's "Ireland, that vulnerable heel of the British Achilles!" from 1810 (Oxford English Dictionary).

已知最古老的关于以阿喀琉斯命名跟腱的文字记录是由弗兰德/荷兰解剖学家菲利普 · 费尔海因在1693年撰写的。在他的著作《人体解剖学》中，他描述了跟腱的位置，并说它通常被称为“阿喀琉斯腱”。“阿喀琉斯之踵”这种表达，意思是“弱点所在，脆弱的地方”，最早只能追溯到1840年，同时1810年《牛津英语词典》中，塞缪尔·泰勒·柯勒律治隐晦地使用过“爱尔兰，那英国的阿喀琉斯脆弱的脚后跟！”这一表达。

==Anatomy==

解剖学

{{Original research section|date=June 2019|comment=this is mythology!}}

The large and prominent tendon of the [[gastrocnemius]], [[soleus]], and [[plantaris]] muscles of the calf is called the ''tendo achilleus'' or [[Achilles tendon]]. This is commonly associated with the site of Achilles's death wound. Tendons are avascular, so such an injury is unlikely to be fatal; however, the myth has the arrow poisoned with the blood of the [[Lernaean Hydra]].

腓肠肌、比目鱼肌和跖肌的大而突出的肌腱称为小腿腱或跟腱。这个部位通常与阿喀琉斯的致命伤的部位有关。肌腱是无血管的，所以这种损伤不太可能是致命的; 然而，神话中的箭淬上了勒拿九头蛇有毒的血液。

A more likely anatomical basis for Achilles's death, assuming an unpoisoned dart, would have been an injury to his [[posterior tibial artery]] behind the [[medial malleolus]], in between the tendons of the flexor digitorum longus and the posterior tibial vein. This area could also have been included in [[Thetis]]'s grip.

假设箭没有沾上毒液，那么阿喀琉斯之死的解剖学基础更有可能是由位于长屈指肌腱和胫后静脉之间的内踝后侧胫后动脉的损伤导致。这个区域也可能包括在忒提丝手握住的地方里。

==See also==

参见

*{{wiktionary|Achilles heel}}

*{{annotated link|Achilles tendon}}

*{{annotated link|Baldr|Balder}} in [[Norse mythology]]

==编者推荐==
[https://campus.swarma.org/course/651 集智学园课程稳健又脆弱的无标度网络]

Category:Trojan War literature

类别：特洛伊战争文学

*[[Duryodhana#Gandhari's blessing and the fight with Bhima|Duryodhana]] in the [[Mahabharatha]]

Category:Idioms

类别：成语

*{{annotated link|Esfandiyār}} in the [[Shahnameh]]

Category:Achilles

分类：阿喀琉斯

<noinclude>

This page was moved from [[wikipedia:en:Achilles' heel]]. Its edit history can be viewed at [[阿喀琉斯之踵/edithistory]]</noinclude>

[[Category:待整理页面]]

同质性

2020-10-12T07:20:24Z

Miyasaki：

此词条暂由彩云小译翻译，未经人工整理和审校，带来阅读不便，请见谅。
本词条由信白初步翻译 
本词条由Miyasaki初步审校

{{distinguish|Homophile}}

{{Short description|Process by which people befriend similar people}}{{expert needed|sociology|reason=statements about humans are unqualified|date=November 2011}}

{{Network science}}

'''Homophily''' (from [[Ancient Greek]]: ''[[:wiktionary:ὁμοῦ#Ancient Greek|homoû]]'', 'together' + ''philíē'', 'friendship, love') is the tendency of individuals to associate and [[human bonding|bond]] with similar others, as in the [[proverb]] "[[wikt:birds of a feather flock together|birds of a feather flock together]]."<ref>{{cite magazine |magazine=[[Foreign Affairs]] |first=Niall |last=Ferguson |quote=At the same time, birds of a feather flock together. Because of the phenomenon known as “homophily”, or attraction to similarity, social networks tend to form clusters of nodes with similar properties or attitudes. |url=https://www.foreignaffairs.com/articles/2017-08-15/false-prophecy-hyperconnection |title=The False Prophecy of Hyperconnection |date=August 15, 2017 |access-date=October 1, 2017}}</ref> The presence of homophily has been discovered in a vast array of [[social network|network]] studies: over {{nowrap|100 studies}} have observed homophily in some form or another, and they establish that similarity is associated with connection.<ref name=birds>{{cite journal | last1 = McPherson | first1 = M. | last2 = Smith-Lovin | first2 = L. | last3 = Cook | first3 = J. M. | year = 2001 | title = Birds of a Feather: Homophily in Social Networks | journal = Annual Review of Sociology | volume = 27 | issue = | pages = 415–444 | doi=10.1146/annurev.soc.27.1.415}}</ref> The categories on which homophily occurs include [[Age group|age]], [[gender]], [[social class|class]], and organizational role.<ref name=aaron>{{cite news|last=Retica|first=Aaron|title=Homophily|url=https://www.nytimes.com/2006/12/10/magazine/10Section2a.t-4.html|newspaper=New York Times|date=10 December 2006}}</ref>

Homophily (from Ancient Greek: homoû, 'together' + philíē, 'friendship, love') is the tendency of individuals to associate and bond with similar others, as in the proverb "birds of a feather flock together." The presence of homophily has been discovered in a vast array of network studies: over have observed homophily in some form or another, and they establish that similarity is associated with connection. The categories on which homophily occurs include age, gender, class, and organizational role.

'''同质性 Homophily '''（源自古希腊语：homoû，“ together” +philíē，“ friendship，love”）是个体趋向于与其他相似的人交往和发展关系的一种倾向，就像谚语“物以类聚，人以群分”。在大批网络研究中都发现了同质性的存在：过去观察到同质性以各式各样的形式存在，并且他们已证实相似性与人际联系有关。同质性建立在以年龄，性别，阶级和组织角色划分的类别上。

The opposite of homophily is [[heterophily]] or [[intermingling]]. Individuals in homophilic relationships share common characteristics (beliefs, [[values]], education, etc.) that make communication and relationship formation easier. Homophily between [[Breeding pair|mated pairs]] in animals has been extensively studied in the field of [[evolutionary biology]], where it is known as [[assortative mating|''assortative mating'']]. Homophily between mated pairs is common within natural animal mating populations.<ref name="Assortative Mating in Animals">{{cite journal |last1=Jiang |first1=Yuexin |last2=Bolnick |first2=Daniel I. |last3=Kirkpatrick |first3=Mark |title=Assortative Mating in Animals |journal=The American Naturalist |date=June 2013 |volume=181 |issue=6 |pages=E125–38 |doi=10.1086/670160 |pmid=23669548 |jstor=10.1086/670160 |ref=Assortative Mating in Animals|hdl=2152/31270 |hdl-access=free }}</ref>

The opposite of homophily is heterophily or intermingling. Individuals in homophilic relationships share common characteristics (beliefs, values, education, etc.) that make communication and relationship formation easier. Homophily between mated pairs in animals has been extensively studied in the field of evolutionary biology, where it is known as assortative mating. Homophily between mated pairs is common within natural animal mating populations.

同质性的相反是'''异质性 heterophily '''或'''混合 Intermingling '''。处于同质性关系中的个人具有共同的特征（信念，价值观，教育程度等），这使沟通和关系的形成变得更加容易。动物配偶之间的同质性已在进化生物学领域被广泛研究，被称为'''分类交配 Assortative Mating '''。在自然动物的交配种群中，配偶之间的同质性很普遍。

Homophily has a variety of consequences for social and economic outcomes, ranging from facilitating cooperation<ref name=":0" /> to slowing processes of [[Consensus decision-making|consensus-formation]],<ref name=":1">{{Cite journal|last=Golub and Jackson|first=|date=2012z|title=How homophily affects the speed of learning and best-response dynamics|url=http://www.bengolub.net/papers/homophily.pdf|journal=Quarterly Journal of Economics|volume=127(3)|pages=1287–1338|via=}}</ref> among others.

Homophily has a variety of consequences for social and economic outcomes, ranging from facilitating cooperation to slowing processes of consensus-formation, among others.

同质性对社会和经济结果有多种影响，其中包括促进合作、放慢达成共识的过程。

==Types and dimensions==
类型和维度 

==Baseline vs. inbreeding==
基础与近交 

To test the relevance of homophily, researchers have distinguished between two types:<ref name=birds />

To test the relevance of homophily, researchers have distinguished between two types:

为了测试同质性的相关性，研究人员区分了两种类型：

* '''Baseline homophily''': simply the amount of homophily that would be expected by chance given an existing uneven distribution of people with varying characteristics; and
*'''基础同质性 Baseline Homophily '''：即，在现存的不均匀分布的不同特征的人中，偶然形成的同质性的多少；
* '''Inbreeding homophily''': the amount of homophily over and above this expected value, typically due to personal preferences and choices.

*'''近交同质性 Inbreeding Homophily '''：通常是由于个人偏好和选择而产生的，超出预期价值的同质性的多少。
==Status vs. value==
地位与价值 

In their original formulation of homophily, [[Paul Lazarsfeld]] and [[Robert K. Merton]] (1954) distinguished between ''status homophily'' and ''value homophily'', find that individuals with similar [[social status]] characteristics are more likely to associate with each other than by chance:<ref name="lazar">[[Paul Lazarsfeld|Lazarsfeld, Paul F.]], and [[Robert K. Merton|Merton, Robert K.]] 1954. "Friendship as a Social Process: A Substantive and Methodological Analysis." Pp. 18–66 in ''Freedom and Control in Modern Society'', edited by M. Berger, T. Abel, and C. H. Page. New York: [[Van Nostrand Reinhold|Van Nostrand]]. </ref><ref name="birds" />

In their original formulation of homophily, Paul Lazarsfeld and Robert K. Merton (1954) distinguished between status homophily and value homophily, find that individuals with similar social status characteristics are more likely to associate with each other than by chance:

保罗·拉扎斯菲尔德（Paul Lazarsfeld）和罗伯特·K·默顿（Robert K.Merton）（1954）在最初对同质性的表述中，区分了地位同质性和价值同质性，发现具有相似社会地位特征的个体更可能与彼此交往：

* '''Status homophily''': includes both [[ascribed characteristics]] (e.g. race, ethnicity, sex, and age) and [[Acquired characteristic|acquired characteristics]] (e.g., religion and education).
*'''同质状态 Status Homophily '''：既包括先天决定的特征（例如种族，民族，性别和年龄），也包括后天获得的特征（例如宗教和教育）。
* '''Value homophily''': involves association with others who think in similar ways, regardless of differences in status characteristics.
*'''价值同质 Value Homophily '''：包括与相同思维模式的人的联系，而与地位特征的差别无关。

== Dimensions ==
维度 

==Race and ethnicity==
种族和民族

[[Social network]]s in the United States today are strongly divided by [[Race (human categorization)|race]] and [[ethnicity]],<ref>{{Cite journal|last=Moody|first=James|date=November 2001|title=Race, School Integration, and Friendship Segregation in America|journal=American Journal of Sociology|language=en|volume=107|issue=3|pages=679–716|doi=10.1086/338954|issn=0002-9602}}</ref> which account for the greatest proportion of ''inbreeding'' homophily (though classification by these criteria can be problematic in [[sociology]] due to fuzzy boundaries and different definitions of race).

Social networks in the United States today are strongly divided by race and ethnicity, which account for the greatest proportion of inbreeding homophily (though classification by these criteria can be problematic in sociology due to fuzzy boundaries and different definitions of race).

在今天的美国，社会网络在种族和民族之间有很强的区分，这在近交同质性中占最大比例（尽管由于模糊的边界和种族的不同定义，根据这些标准进行分类在社会学上可能会出现问题）。

Smaller groups have lower [[Racial diversity|diversity]] simply due to the number of members. This tends to give racial and ethnic minority groups a higher ''baseline'' homophily. Race and ethnicity also correlates with [[educational attainment]] and occupation, which further increase baseline homophily.<ref name="birds" />

Smaller groups have lower diversity simply due to the number of members. This tends to give racial and ethnic minority groups a higher baseline homophily. Race and ethnicity also correlates with educational attainment and occupation, which further increase baseline homophily.

较小的组仅由于成员数而具有较低的多样性。这容易使少数族裔群体具有更高的基础同质性。种族和民族也与学业成就和职业相互关联，这进一步加强了基础同质性。

==Sex and gender==
性别 

In regard to [[sex]] and [[gender]], ''baseline'' homophily of networks is relatively low compared to race and ethnicity. Men and women frequently live together, and are both large and equally-sized populations. Most sex homophily is of the inbreeding type.<ref name="birds" /> Especially in schools, students tend to have a high gender homophily.<ref>{{Cite journal|last=Shrum|first=Wesley|last2=Cheek|first2=Neil H.|last3=Hunter|first3=Saundra MacD.|date=October 1988|title=Friendship in School: Gender and Racial Homophily|journal=Sociology of Education|volume=61|issue=4|pages=227|doi=10.2307/2112441|issn=0038-0407|jstor=2112441}}</ref>

In regard to sex and gender, baseline homophily of networks is relatively low compared to race and ethnicity. Men and women frequently live together, and are both large and equally-sized populations. Most sex homophily is of the inbreeding type.

关于性别，与种族和民族相比，社会网络的基础同质性相对较低。男女经常生活在一起，且男女人口数量相近，都很庞大。大多数性别同质性是近交类型。

==Age==
年龄

Most age homophily is of the ''baseline'' type. An interesting pattern of inbreeding age homophily for groups of different ages was found by Marsden (1988).<ref>Marsden, P. V. 1988. "Homogeneity in confiding relations." ''[[Social Networks (journal)|Social Networks]]'' 10:57–76.</ref> It indicated a strong relationship between someone's age and the social distance to other people with regard to confiding in someone. For example, the larger age gap someone had, the smaller chances that they were confided by others with lower ages to "discuss important matters."<ref name="birds" />

Most age homophily is of the baseline type. An interesting pattern of inbreeding age homophily for groups of different ages was found by Marsden (1988). It indicated a strong relationship between someone's age and the social distance to other people with regard to confiding in someone. For example, the larger age gap someone had, the smaller chances that they were confided by others with lower ages to "discuss important matters."

大多数年龄同质性属于基础类型。 Marsden发现了不同年龄组的近交年龄同质性的有趣模式（1988）。它表明某人的年龄和与他人的社会距离对于信赖某人有很强的关系。例如，某人与他人的年龄差距越大，他们受较低年龄的其他人信赖，“共商重要问题”的机率就越小。

==Religion==
宗教 

Homophily based on religion is due to both ''baseline'' and ''inbreeding'' homophily.<ref name="birds" />

Homophily based on religion is due to both baseline and inbreeding homophily.

基于宗教的同质性是由基础同质性和近交同质性共同造成的。

==Education, occupation and social class==
教育，职业和社会阶层 

Family of birth accounts for considerable baseline homophily with respect to education, occupation, and [[social class]].<ref name="birds" />

Family of birth accounts for considerable baseline homophily with respect to education, occupation, and social class.

出生家庭在教育，职业和社会阶层方面占相当大的基础同质性。

== Social media ==
社交媒体 

As [[social network]]s are largely divided by race, [[Social networking service|social-networking websites]] like [[Facebook]] also foster homophilic atmospheres.<ref>{{Cite journal|last=Aiello|first=Luca Maria|last2=Barrat|first2=Alain|last3=Schifanella|first3=Rossano|last4=Cattuto|first4=Ciro|last5=Markines|first5=Benjamin|last6=Menczer|first6=Filippo|date=2012-05-01|title=Friendship prediction and homophily in social media|journal=ACM Transactions on the Web|volume=6|issue=2|pages=1–33|doi=10.1145/2180861.2180866|issn=1559-1131}}</ref> When a Facebook user '[[Facebook like button|likes]]' or interacts with an article or post of a certain [[ideology]], Facebook continues to show that user posts of that similar ideology (which Facebook believes they will be drawn to). In a research article, McPherson, Smith-Lovin, and Cook (2003) write that [[Homogeneity and heterogeneity|homogeneous]] [[Personal network|personal networks]] result in limited "social worlds in a way that has powerful implications for the information they receive, the attitudes they form, and the interactions they experience."<ref>{{Cite journal |last=McPherson |first=Miller |last2=Smith-Lovin |first2=Lynn |last3=Cook |first3=James M. |date=2003-11-28 |title=Birds of a Feather: Homophily in Social Networks |journal=Annual Review of Sociology |language=en |volume=27 |issue=1 |pages=415–444 |doi=10.1146/annurev.soc.27.1.415}}</ref> This homophily can foster divides and [[Echo chamber (media)|echo chambers]] on social networking sites, where people of similar ideologies only interact with each other.

As social networks are largely divided by race, social-networking websites like Facebook also foster homophilic atmospheres. When a Facebook user 'likes' or interacts with an article or post of a certain ideology, Facebook continues to show that user posts of that similar ideology (which Facebook believes they will be drawn to). In a research article, McPherson, Smith-Lovin, and Cook (2003) write that homogeneous personal networks result in limited "social worlds in a way that has powerful implications for the information they receive, the attitudes they form, and the interactions they experience." This homophily can foster divides and echo chambers on social networking sites, where people of similar ideologies only interact with each other.

由于社会网络在很大程度上由种族划分，因此诸如Facebook之类的社交网站也营造出了同质性的氛围。当Facebook用户点赞某种特定意识形态的文章或帖子或与之互动时，Facebook会继续显示相似意识形态的帖子（Facebook觉得帖子那些会吸引他们）。 McPherson，Smith-Lovin和Cook（2003）在一篇研究文章中写道，同质的个人网络会导致有限的“社会世界，从而对他们所接收的信息，所形成的态度以及所经历的互动产生强大的影响。” 这种同质性可以在社交网站上促进分歧和回声室，在这里人们只和与自己拥有相似意识形态的人互动

==Causes and effects==
因与果 

== Causes ==
原因 

{{Unreferenced section|date=July 2020}}

'''Geography''': Baseline homophily often arises when the people who are located nearby also have similar characteristics. People are more likely to have contact with those who are geographically closer than those who are distant. Technology such as the telephone, e-mail, and social networks have reduced but not eliminated this effect.

Geography: Baseline homophily often arises when the people who are located nearby also have similar characteristics. People are more likely to have contact with those who are geographically closer than those who are distant. Technology such as the telephone, e-mail, and social networks have reduced but not eliminated this effect.

'''地理环境 Geography '''：当附近的人也具有相似的特征时，通常会产生基础同质性。人们更可能与地理位置较近的人有联系。电话，电子邮件和社交网络等技术已经减少但并未消除这种影响。

'''Family ties''': [[Family relationships]] often produce relatively close, frequent contact among those who are at great geographic distance. These ties tend to decay slowly, but can be dramatically restructured when new marriages occur.

Family ties: Family relationships often produce relatively close, frequent contact among those who are at great geographic distance. These ties tend to decay slowly, but can be dramatically restructured when new marriages occur.

'''家庭关系 Family Ties '''：家庭关系通常会在相距遥远的人之间产生相对紧密的、频繁的联系。这些纽带趋向于缓慢瓦解，但是当新的婚姻出现时，它们可以被大幅重组。

'''Organizations''': School, work, and volunteer activities provide the great majority of non-family ties. Many friendships, confiding relations, and social support ties are formed within voluntary groups. The social homogeneity of most organizations creates a strong baseline homophily in networks that are formed there.

Organizations: School, work, and volunteer activities provide the great majority of non-family ties. Many friendships, confiding relations, and social support ties are formed within voluntary groups. The social homogeneity of most organizations creates a strong baseline homophily in networks that are formed there.

'''组织 Organizations'''：学校，工作和志愿者活动提供了绝大多数的非家庭纽带。志愿团体内部建立了许多友谊，信任关系和社会支持纽带。大多数组织的社会同质性在形成于其中的网络中建立了强大的基础同质性。

'''Isomorphic sources''': The connections between people who occupy equivalent roles will induce homophily in the system of network ties. This is common in three domains: [[workplace]] (e.g., all heads of [[HR department|HR departments]] will tend to associate with other HR heads), family (e.g., mothers tend to associate with other mothers), and informal networks.

Isomorphic sources: The connections between people who occupy equivalent roles will induce homophily in the system of network ties. This is common in three domains: workplace (e.g., all heads of HR departments will tend to associate with other HR heads), family (e.g., mothers tend to associate with other mothers), and informal networks.

'''同构信息源 Isomorphic Sources '''：扮演同等角色的人们之间的联系将导致网络纽带系统中的同质性。这在三个领域很常见：工作场所（例如，人力资源部门的所有负责人都倾向于与其他人力资源负责人联系），家庭（例如，母亲倾向于与其他母亲联系）以及非正式网络。

'''Cognitive processes''': People who have demographic similarity tend to own shared knowledge, and therefore they have a greater ease of communication and share cultural tastes, which can also generate homophily.

Cognitive processes: People who have demographic similarity tend to own shared knowledge, and therefore they have a greater ease of communication and share cultural tastes, which can also generate homophily.

'''认知过程 Cognitive Processes'''：具有人口统计学相似性的人倾向于拥有共同的知识，因此他们更容易交流和分享文化品味，这也可能产生同质性。

==Effects==
后果 

According to one study, [[perception]] of [[Interpersonal attraction|interpersonal]] similarity improves coordination and increase the expected payoff of interactions, above and beyond the effect of merely "liking others."<ref>{{cite journal|last1=Chierchia|first1=Gabriele|last2=Coricelli|first2=Giorgio|title=The impact of perceived similarity on tacit coordination: propensity for matching and aversion to decoupling choices|journal=Frontiers in Behavioral Neuroscience|doi=10.3389/fnbeh.2015.00202|pmid=26283940|pmc=4516978|volume=9|pages=202|year=2015}}</ref> Another study claims that homophily produces [[Social tolerance|tolerance]] and cooperation in [[Social space|social spaces]].<ref name=":0">{{cite journal|last1=Mark|first1=N. P.|title=Culture and competition: Homophily and distancing explanations for cultural niches|journal=American Sociological Review|date=2003|volume=68|issue=3|pages=319–345|jstor=1519727|doi=10.2307/1519727}}</ref> However, homophilic patterns can also restrict access to information or inclusion for minorities.<ref>{{Cite journal|last=Karimi|first=Fariba|last2=Génois|first2=Mathieu|last3=Wagner|first3=Claudia|last4=Singer|first4=Philipp|last5=Strohmaier|first5=Markus|date=2018-07-23|title=Homophily influences ranking of minorities in social networks|journal=Scientific Reports|volume=8|issue=1|pages=11077|doi=10.1038/s41598-018-29405-7|pmid=30038426|bibcode=2018NatSR...811077K|issn=2045-2322|doi-access=free}}</ref>

According to one study, perception of interpersonal similarity improves coordination and increase the expected payoff of interactions, above and beyond the effect of merely "liking others." Another study claims that homophily produces tolerance and cooperation in social spaces. However, homophilic patterns can also restrict access to information or inclusion for minorities.

根据一项研究，感知到人际间的相似性不仅可以产生“喜欢别人”的效果，还可以提高协调能力并增加预期的互动收益。另一项研究声称同质性在社会空间中产生宽容与合作。但是，同质性模式对于少数群体来说，也可能限制信息的获取和接纳性。

The effects of homophily on the diffusion of information and behaviors are also complex. Some studies have claimed that homophily facilitates [[Access to information|access information]],<ref>{{cite arXiv|last1=Choudhury|first1=M. D|title="Birds of a feather": Does user homophily impact information diffusion in social media |date=2010 |eprint=1006.1702|class=cs.CY}}</ref> the diffusion of innovations and behaviors,<ref>{{cite journal|last1=Christakis|first1=N. A|last2=Fowler|first2=J. H.|title=The spread of obesity in a large social network over 32 years|journal=The New England Journal of Medicine|date=2007|volume=357|issue=4|pages=370–379|url=http://media.timesfreepress.com/docs/2010/01/Obesity_studies_0104.pdf|doi=10.1056/nejmsa066082|pmid=17652652|citeseerx=10.1.1.581.4893}}</ref> and the formation of [[Social norm|social norms]].<ref>{{cite journal|last1=Centola|first1=D|last2=R|first2=Willer|last3=M|first3=Macy|title=The emperor's dilemma: A computational model of self-enforcing norms. |journal=American Journal of Sociology|date=2005|volume=110|issue=4|pages=1009–1040|jstor=10.1086/427321|doi=10.1086/427321|url=https://repository.upenn.edu/cgi/viewcontent.cgi?article=1604&context=asc_papers}}</ref> Other studies, however, highlight mechanisms through which homophily can maintain disagreement, exacerbate [[Social polarization|polarization]] of opinions, and slow the formation of an overall [[Consensus decision-making|consensus]].<ref name=":1" /><ref>{{Cite journal|last=Centola D, Gonzalez-Avella JC, Eguiluz VM, San Miguel M.|first=|date=2007|title=Homophily, cultural drift, and the co-evolution of cultural groups|url=|journal=Journal of Conflict Resolution|volume=51(6)|pages=905–29|via=}}</ref>

The effects of homophily on the diffusion of information and behaviors are also complex. Some studies have claimed that homophily facilitates access information, the diffusion of innovations and behaviors, and the formation of social norms. Other studies, however, highlight mechanisms through which homophily can maintain disagreement, exacerbate polarization of opinions, and slow the formation of an overall consensus.

同质性对信息和行为传播的影响也很复杂。一些研究声称，同质性促进了信息的获取，创新和行为的传播以及社会规范的形成。但是，其他研究强调了同质性可以维持分歧，加剧意见极化并减缓整体共识形成的机制。

Homophily is a cause of [[Homogamy (sociology)|homogamy]]—marriage between people with similar characteristics.<ref name="fiore">Fiore, A. T. and Donath, J. S. (2005). [http://smg.media.mit.edu/papers/Fiore/fiore_donath_chi2005_short.pdf "Homophily in Online Dating: When Do You Like Someone Like Yourself?"]. ''MIT Media Lab''.</ref> Homophily is a [[fertility factor (demography)|fertility factor]]; an increased [[fertility]] is seen in people with a tendency to seek acquaintance among those with common characteristics.<ref name="fent2013" /> Governmental family policies have a decreased influence on [[Total fertility rate|fertility rates]] in such populations.<ref name="fent2013">{{cite journal|title=Family policies in the context of low fertility and social structure|url=http://www.demographic-research.org/Volumes/Vol29/37/|journal=Demographic Research|volume=29|issue=37|author1=Thomas Fent |author2=Belinda Aparicio Diaz |author3=Alexia Prskawetz |year=2013}}</ref>

Homophily is a cause of homogamy—marriage between people with similar characteristics. Homophily is a fertility factor; an increased fertility is seen in people with a tendency to seek acquaintance among those with common characteristics.

同质性是门当户对的婚姻——即具有相似特征的人之间的婚姻——产生的一个原因。同质性是一个生育率的要素。在倾向于结识具有相似特征的人中，我们发现生育几率增加了。

==See also==

*[[Groupthink]]

==References==

{{reflist|30em}}

{{World view}}

[[Category:Interpersonal relationships]]

Category:Interpersonal relationships

类别: 人际关系

[[Category:Sociological terminology]]

Category:Sociological terminology

类别: 社会学术语

<noinclude>

This page was moved from [[wikipedia:en:Homophily]]. Its edit history can be viewed at [[同质性/edithistory]]</noinclude>

[[Category:待整理页面]]