COMPLEXITY, CONTINGENCY, AND CRITICALITY

Complexity originates from the tendency of large dynamical systems to organize themselves into a critical state, with avalanches or ''punctu ations'' of all sizes. In the critical state, events which would other wise be uncoupled become correlated. The apparent, historical continge ncy in many sciences, including geology, biology, and economies, finds a natural interpretation as a self-organized critical phenomenon. The se ideas are discussed in the context of simple mathematical models of sandpiles and biological evolution. Insights are gained not only from numerical simulations but also from rigorous mathematical analysis.