Page:Lawhead columbia 0054D 12326.pdf/112



As usual, let’s begin by briefly reviewing where we are in our overall discussion, with an eye toward how to proceed from here. The last two chapters have focused very heavily on the details of certain aspects of complexity theory, and it might be easy to lose sight of our overall goal. In Chapter Two, I presented a primer on complex systems theory and surveyed various attempts to reduce the notoriously slippery notion of complexity itself to various proxy concepts, including mereological size, chaotic behavior, algorithmic incompressibility, fractal dimension, Shannon entropy, and hierarchical position. I argued (convincingly, I hope) that none of these definitions precisely captures the intuition behind complexity and that moreover, the nature of complexity is such that it is likely that no single unifying definition is forthcoming. Rather, we should aim at a constellation of related notions of complexity, each of which is tailored to the different purposes toward which complexity theory might be used. I proposed the concept of dynamical complexity as best capturing the aspects of the varied proxy concepts we considered that are most relevant to scientists seeking to understand active, dynamical complex systems in the natural world (as opposed to, say, those interested in studying aspects of abstract signals), and argued effective complexity can plausibly be taken as a physical interpretation of the existing mathematical framework of effective complexity. A system’s dynamical complexity, recall, is a fact about the pattern-richness of the system’s location in the configuration space defined by fundamental physics. Equivalently, we can think of it as being a fact about how many predictively useful ways the system can be carved up. Formally, a system’s dynamical complexity is the sum of the 102