1 - Introduction

Summary

Consider a collection of electrons, or a pile of sand grains, a bucket of fluid, an elastic network of springs, an ecosystem, or the community of stock-market dealers. Each of these systems consists of many components that interact through some kind of exchange of forces or information. In addition to these internal interactions, the system may be driven by some external force: an electric or a magnetic field, gravitation (in the case of sand grains), environmental changes, and so forth. The system will now evolve in time under the influence of the external driving forces and the internal interaction forces, assuming we can break the system up into internal and external components in an unproblematic way. What happens? Is there some simplifying mechanism that produces a typical behavior shared by large classes of systems, or will the behavior always depend crucially on the details of each system?

The paper by Bak, Tang, and Wiesenfeld (1987) contained the hypothesis that, indeed, systems consisting of many interacting constituents may exhibit some general characteristic behavior. The seductive claim was that, under very general conditions, dynamical systems organize themselves into a state with a complex but rather general structure. The systems are complex in the sense that no single characteristic event size exists: there is not just one time and one length scale that controls the temporal evolution of these systems. Although the dynamical response of the systems is complex, the simplifying aspect is that the statistical properties are described by simple power laws. Moreover, some of the exponents may be identical for systems that appear to be different from a microscopic perspective.