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are not characteristic of the individual agents. Analyses of these systems address fundamental questions about the relationship between information content and function. For example, How much information does it take to encode a function? Are there multiple distinct solutions? How are solutions distributed in configuration space? How much more information does it take to encode a given improvement in function? What environmental factors might influence these relationships?

The function of some emergent systems is obvious: a sequence of letters communicates a specific idea, a computer algorithm performs a specific computation, and an enzyme catalyzes at least one specific reaction. Less obvious are the functions of systems of many interacting inanimate particles, such as molecules, sand grains, or stars, but these systems may also be described quantitatively in terms of function, for example, in terms of their ability to dissipate energy or to maximize entropy production through patterning (e.g., Bertalanffy, 1968; Nicolis and Prigogine, 1977; Swensen and Turvey, 1991; Emanuel, 2006). Living systems, by contrast, typically display multiple essential functions (Allen et al., 1998; Ayala, 1999; McShea, 2000). This consideration of complexity in terms of the function of a system, as opposed to some intrinsic measure of its patterning or structural intricacy, distinguishes our treatment from many previous efforts.

QUANTIFYING COMPLEXITY

Development of a quantitative measure of complexity has proven difficult for at least three reasons, each of which relates to the diversity of systems that may be labeled “complex.”

  1. Systems may be complex in terms of information content, physical structure, and/or behavior. Consider three stages in the life cycle of a multicellular organism: a fertilized egg, a live adult, and a postmortem adult. All three states are complex, but they are complex in different respects. All three states possess the sequence information (a genome) necessary to grow a living organism. Living and dead adult organisms also display complex anatomical structures, but only living organisms possess behavioral complexity. Any universal definition of complexity must thus have the potential to quantify complexity independently in terms of information, structure, or behavior.

  2. It has been difficult to define complexity in terms of a metric that applies to all complex systems. No obvious common thread exists in comparing the complexity of symbolic systems, such as language, with those of physical agents, such as cells. Parameters useful in characterizing symbolic systems (e.g., algorithm- or information-based complexity metrics)



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