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 Chapter Three

Dynamical Complexity

3.0 Recap and Survey

Let’s take a moment to summarize the relative strengths and weaknesses of the various approaches to defining complexity we considered in the last section; it will help us build a satisfactory definition if we have a clear target at which to aim, and clear criteria for what our definition should do. Here’s a brief recap, then.

The mereological size and hierarchical position measures suffered from parallel problems. In particular, it’s difficult to say precisely which parts we ought to be attending to when we’re defining complexity in terms of mereological size or (similarly) which way of structuring the hierarchy of systems is the right way (and why). Both of these approaches, though, did seem to be tracking something interesting: there does seem to be a sense in which a system’s place in a sort of “nested hierarchy” seems to be a reliable guide to its complexity. All other things being equal, a basic physical system (e.g. a free photon traveling through deep space) does indeed seem less complex than a chemical system (e.g. a combination of hydrogen and oxygen atoms to form H$2$O molecules), which in turn seems less complex than a biological system (e.g. an amoeba undergoing asexual reproduction), which seems less complex than a social system (e.g. the global stock market). The problem (again) is that it’s difficult to say why this is the case: the hierarchical and mereological size measures take it as a brute fact that chemical systems are less complex than biological systems, but have trouble explaining that relationship. A satisfactory 78