Bigger than Chaos: Outline
A town may have thousands of inhabitants, an ecosystem millions, and the complex systems studied by statistical physicists, septillions. In each of these systems the individual parts interact in complicated and unpredictable ways. Yet, for all this chaos, the behavior of gases, ecosystems and societies can be quite orderly. Gases conform to gas laws, ecosystems conform to various laws of population dynamics, and even massed humanity is in some respects quite predictable to the social scientist: consider the robust statistical correlation between socioeconomic status and success. In short, complex systems – in the sense of systems with many, somewhat independent, strongly interacting, parts – often behave in surprisingly simple ways.
Bigger Than Chaos attempts to explain how complex systems, so chaotic in their details, can exhibit simple regularities when viewed from a statistical distance. In so doing, I examine also the limits of statistical science – the point at which the tabulation of numbers concerning present and past behavior ceases to provide any insight into the long term behavior of a system.
The key concept in this project is probability. If the movements of a complex systems' parts can be characterized by independent probability distributions, the statistical behavior of the system will be relatively simple. Thus, I argue, a better understanding of the application of probability to complex systems provides a foundation for understanding complex systems' simple behavior. This better understanding of probability comes not in the form of a traditional metaphysical account of probability, but in the form of an account of what I call the physics of probability, that is, an account of what physical properties give rise to probability-like behaviors and why.
Especially important to the physics of probability, for my purposes, is the question of what physical properties underlie probabilistic independence. It is well-known that independent probabilities can give rise to statistical stability, in virtue of "laws of large numbers". I show that the probabilities governing the movements of parts of complex systems can be probabilistically independent despite the fact that the parts are not causally independent. (This casts some light on a closely related problem in the foundations of statistical mechanics.) Principal among the roots of probabilistic independence is low level chaos itself.