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 us a theoretical tool to help us think about the difference between systems that seem intuitively "simple" (e.g. a free photon in a vacuum) and systems that seem intuitively "complex" (e.g. the global climate) more clearly, and to begin to get a grasp on important differences between the methods of sciences that study systems with high dynamical complexity and those of sciences that study systems with low dynamical complexity. I then argue that, based on this definition, climate science is a paradigmatic complex-systems science, and that recognition of this fact is essential if we're to bring all our resources to bear on solving the problems posed by climate change.

In Chapter Four, we turn from explicitly foundational issues in the philosophy of science and complexity theory to more concrete methodological questions. I introduce the basics of climate science, and construct a very simple climate model from first principles. This chapter closes with a consideration of the limitations of the methods behind this basic model, and of the general principles that inform it. This paves the way for the discussion of deeper challenges in Chapter Five.

Chapter Five describes some of the specific problems faced by scientists seeking to create detailed models of complex systems. After a general introduction to the language of dynamical systems theory, I focus on two challenges in particular: non-linearity and chaotic dynamics. I discuss how these challenges arise in the context of climatology.

We'll then focus on a more concrete examination of a particular methodological innovation that is characteristic of complex-systems sciences: computer-aided model-building. Because of the nature of complexity (as described in Chapter Three) and the various special difficulties 8