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they appear across disciplines. Articulating this common core in a systematic way is one of the most important foundational contributions that remains to be made, as it will provide a common language in which scientists interested in complexity (but trained in different disciplines) can come together to discuss their work. Doing this ground-clearing work is also a necessary precursor to the more daunting task of defining complexity itself. While I cannot hope to disentangle all the relevant concepts here, I would like to now turn to an examination of two of the most important for our purposes: non-linearity and chaos. Where our discussions of complexity have thus far been principally focused on defining complexity, this section focuses on the practical challenges of actually working with dynamically complex systems. We would do well to keep the distinction between these two lines of discussion clear in our minds, though—while the issues we’ll be discussing in this chapter are characteristic of complex systems, they are not definitive of them. That is, neither non-linearity nor chaos (nor the conjunction of the two) is sufficient for dynamical complexity[1].

5.1.1 Non-Linearity

Before we can tackle what it means to say that a system’s behavior is non-linear, we need to get some basic terminology under our belt. Complex systems theory is built largely on the back of a more general approach to scientific modeling called dynamical systems theory, which deals

  1. Whether or not either of these two features is a necessary feature of dynamically complex systems is a more complicated question. As we shall see, both non-linearity and chaos are best understood as properties of particular models rather than of systems themselves. Dynamically complex systems are (by definition) those which admit of sensible and useful consideration from a large variety of different perspectives; many interesting dynamically complex systems might exhibit chaotic behavior from some perspectives but not others. We should resist the temptation to even consider the question of whether systems like that are “really” chaotic or not in just the same way that we should resist the temptation to generally privilege one set of real patterns describing a system’s time-evolution over the others.