Complexity as information

Given an object com[)osed of N interconnected and interacting [)arts, one might at first be te,m[)ted to equate the complexity of an object with its conventional information content, as defined l)y Shannon [.shann49]  

Another drawback to using Shannon information as a measure of complexity is the fact that it is based on an ensemble of all possible states of a system and therefore cannot describe the information content of a single state. Shannon information thus resembles traditional statistical mechanics - which describes the average or aggregate behavior of, say, a gas, rather than the motion of its constituent molecules - more so than it docs a complexity theory that must address the complexity of individual objects. 

Another way of looking at it is that Shannon information is a formal equivalent of thermodynamic entroi)y, or the degree of disorder in a physical system. As such it essentially measures how much information is missing about the individual constituents of a system. In contrast, a measure of complexity ought to (1) refer to individual states and not ensembles, and (2) reflect how mnc h is known about a system vice what is not. One approach that satisfies both of these requirements is algorithmic complexity theory. 

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However the problem of deciding whether or not a compound resembles benzene has become increasingly complex as information multiplies. Evidence from different aspects is often mutually conflicting, and, even when it is relatively consistent, the decision as to whether or not a molecule is aromatic may depend on the disposition of the person drawing the line. 

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See also in sourсe #XX -- [ ]

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