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 sciences from simple systems sciences, opening the door to more fruitful cross-talk between branches of science that, prior to the ascription of complexity, seemed to have very little in common with one another. I shall argue that such an understanding of complexity emerges very naturally from the account of science given in Chapter One. I’m going to begin by just laying out the concept I have in mind without offering much in the way of argument for why we ought to adopt it. Once we have a clear account of dynamical complexity on the table, then I’ll argue that it satisfies all the criteria given above—I’ll argue, in other words, that it captures what seems right about the mereological, hierarchical, information-theoretic, and fractal accounts of complexity while also avoiding the problems endemic to those views.

Back in Section 1.5, I said, “In a system with a relatively high degree of complexity—very roughly, a system with a relatively high-dimensional configuration space—there will be a very large number of ways of specifying regions such that we won’t be able to identify any interesting patterns in how those regions behave over time,” and issued a promissory note for an explanation to come later. We’re now in a position to examine this claim, and to (finally) cash that promissory check. First, note that the way the definition was phrased in the last chapter isn’t going to quite work: having a very high-dimensional configuration space is surely not a sufficient condition for complexity. After all, a system consisting of a large number of non-interacting particles may have a very high-dimensional phase space indeed: even given featureless particles in a Newtonian system, the dimensionality of the phase space of a system with n particles will be (recall) 6n. Given an arbitrarily large number of particles, the phase space of a system like this will also be of an arbitrarily large dimensionality. Still, it seems clear that simply increasing the number of particles in a system like that doesn’t really increase the 81