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'''Emergence.'''  Interactions between components in integrated systems often generate phenomena, functions, or effects that cannot be trivially reduced to properties of the components alone.  Instead these functions emerge as a result of structured interactions and are properties of the system as a whole.  In many cases, even a detailed and complete examination of the individual components will fail to predict the range of emergent processes that these components are capable of if allowed to interact as part of a system.  In turn, dissection of an integrated system into components and interactions generally results in a loss of the emergent process.  

'''Emergence.'''  Interactions between components in integrated systems often generate phenomena, functions, or effects that cannot be trivially reduced to properties of the components alone.  Instead these functions emerge as a result of structured interactions and are properties of the system as a whole.  In many cases, even a detailed and complete examination of the individual components will fail to predict the range of emergent processes that these components are capable of if allowed to interact as part of a system.  In turn, dissection of an integrated system into components and interactions generally results in a loss of the emergent process.  

In summary, systems with numerous components capable of structured interactions that generate emergent phenomena may be called complex.  The observation of complex systems poses many challenges, as an observer needs simultaneously to record states and state transitions of many components and interactions.  Such observations require that choices be made concerning the definition of states, state space and time resolution.  How states are defined and measured can impact other derived measures such as those of system complexity.

In summary, systems with numerous components capable of structured interactions that generate emergent phenomena may be called complex.  The observation of complex systems poses many challenges, as an observer needs simultaneously to record states and state transitions of many components and interactions.  Such observations require that choices be made concerning the definition of states, state space and time resolution.  How states are defined and measured can impact other derived measures such as those of system complexity.

[[Image:complexity_figure1.jpg|thumb|300px|left|F1|Complexity as a mixture of order and disorder. Drawn after Huberman and Hogg (1986).]]

[[Image:complexity_figure1.jpg|thumb|300px|left|F1|Complexity as a mixture of order and disorder. Drawn after Huberman and Hogg (1986).]]

==复杂性的度量==

==复杂性的度量==

Measures of complexity allow different systems to be compared to each other by applying a common metric.  This is especially meaningful for systems that are structurally or functionally related.  Differences in complexity among such related systems may reveal features of their organization that promote complexity.

Measures of complexity allow different systems to be compared to each other by applying a common metric.  This is especially meaningful for systems that are structurally or functionally related.  Differences in complexity among such related systems may reveal features of their organization that promote complexity.

Some measures of complexity are algorithmic in nature and attempt to identify a minimal description length.  For these measures complexity applies to a description, not the system or process per se.  Other measures of complexity take into account the time evolution of a system and often build on the theoretical foundations of statistical information theory.

Some measures of complexity are algorithmic in nature and attempt to identify a minimal description length.  For these measures complexity applies to a description, not the system or process per se.  Other measures of complexity take into account the time evolution of a system and often build on the theoretical foundations of statistical information theory.

Most extant complexity measures can be grouped into two main categories.  Members of the first category (algorithmic information content and logical depth) all capture the randomness, information content or description length of a system or process, with random processes possessing the highest complexity since they most resist compression.  The second category (including statistical complexity, physical complexity and neural complexity) conceptualizes complexity as distinct from randomness.  Here, complex systems are those that possess a high amount of structure or information, often across multiple temporal and spatial scales.  Within this category of measures, highly complex systems are positioned somewhere between systems that are highly ordered (regular) or highly disordered (random). <figref>Complexity_figure1.jpg</figref> shows a schematic diagram of the shape of such measures, however, it should be emphasized again that a generally accepted quantitative expression linking complexity and disorder does not currently exist.

Most extant complexity measures can be grouped into two main categories.  Members of the first category (algorithmic information content and logical depth) all capture the randomness, information content or description length of a system or process, with random processes possessing the highest complexity since they most resist compression.  The second category (including statistical complexity, physical complexity and neural complexity) conceptualizes complexity as distinct from randomness.  Here, complex systems are those that possess a high amount of structure or information, often across multiple temporal and spatial scales.  Within this category of measures, highly complex systems are positioned somewhere between systems that are highly ordered (regular) or highly disordered (random). <figref>Complexity_figure1.jpg</figref> shows a schematic diagram of the shape of such measures, however, it should be emphasized again that a generally accepted quantitative expression linking complexity and disorder does not currently exist.