# Bigger than Chaos: Chapter Summary

## Chapter One: The Simple Behavior of Complex Systems

Chapter one introduces the simple behavior of complex systems as a philosophical problem (as described in the outline). Some current approaches to complexity are considered, and rejected, as providing a solution to the problem. I introduce my own approach: the simple behavior of complex systems can be explained if the behavior of complex systems can be given a certain kind of probabilistic description. In order to answer the question whether such a description is possible, it is necessary to inquire into what I call the *physics* of complex probability, the study of the physical foundation of complex probabilistic properties. (Complex probabilistic properties are properties characteristic of probabilities that can be explained as consequences of lower level properties and laws of nature. I take it that the probabilities in most complex systems are complex probabilities.) Two kinds of independence properties, in particular, require some foundation if the probabilistic approach to complex systems is to succeed. The project of providing a physics of probability is contrasted with the traditional project of providing a metaphysics of probability.

## Chapter Two: The Physics of Complex Probability

Chapter two presents the first part of the physics of complex probability. The most important part of the chapter is the development of a notion I call *microconstancy*, which provides a foundation for one of the independence properties designated as an explanatory target in chapter one. Two other themes of this chapter, of some interest independently of the study of complex systems, are: (a) the ways in which complex probabilities generate their characteristic patterns of outcomes, patterns which exhibit short term disorder and long term order (in the form of stable frequencies); and (b) the nature and the consequences of the physical relations that hold between different complex probability distributions. Neither topic has been much discussed in the literature.

## Chapter Three: The Independence of Complex Probabilities

The purpose of this chapter is to develop a theory of the second independence property designated as an explanatory target in chapter one. The chapter proceeds by giving conditions for the probabilistic independence of outcomes generated by pairs of probabilistic trials bearing the following relations to one another:

- Causal independence,
- Causal dependence, due to a short term coupling between the trial mechanisms during the generation of the outcomes, and
- Causal dependence, due to the outcome of one trial determining the initial conditions of the other.

## Chapter Four: The Simple Behavior of Complex Systems Explained

I apply my physics of probability to the kind of complex system described in chapter one, and I show that, in many circumstances, such systems will behave simply. My central example is an ecosystem. The foundations of probabilistic independence in complex systems are examined, drawing on the results of the previous two chapters; the most important such foundation turns out to be the "chaotic" behavior of complex systems at the microlevel. Microlevel chaos gives rise to probabilistic independence, which in turn gives rise to macrolevel simplicity, which is thus bigger than – but also founded in – chaos.

## Chapter Five: Implications for the Philosophy of the Higher Level Sciences

In this chapter, I apply some of my results to other philosophical questions about higher level sciences (that is, sciences above the level of fundamental physics, including biology, economics, sociology, perhaps even statistical physics). Issues discussed are reduction, higher level laws of nature, causal relevance, inductive inference, the applicability of my work to the social sciences, and the ideal mathematical form for a theory of complex systems.