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formalism of effective complexity, and a physical interpretation that takes the multiplicity of ways that physical systems can be described into account. It offers a natural way to understand how the abstraction described by Gell-Mann and others relates to the actual practice of scientists. The conceptual machinery underwriting the account of science that we developed in this chapter and the last helps us get an intuitive picture of complexity and its place in science. The formalism of effective complexity provides a formalism that can be used to underwrite this intuitive formulation, making the concepts described more precise.

2.3 Conclusion, Summary, and the Shape of Things to Come

In the previous chapter, we examined several different ways that “complexity” might be defined. We saw that each attempt seemed to capture something interesting about complexity, but each also faced serious problems. After arguing that none of these definitions by itself was sufficient to yield a rigorous understanding of complexity, I introduced a new concept—dynamical complexity. This chapter has consisted in a sustained description of the concept, and an argument for its role as a marker for the kind of complexity we’re after when we’re doing science. The insight at the heart of dynamical complexity is that complexity, at least as it concerns science, is a feature of active, changing, evolving systems. Previous attempts to define complexity have overlooked this fact to one degree or another, and have tried to account for complexity primarily in terms of facts about the static state of a system. Dynamical complexity, on the other hand, tracks facts about how systems change over time, and (moreover) embraces the notion that change over time can be tracked in numerous different ways, even for a single system. If our account of science from Chapter One is right—if science is the business