Chaos is a phenomenon shown by some dynamical systems, which consists of a curious, infinitely complex pattern of behavior that lies just beyond the edge of total order. A system is chaotic if it is predictable in principle and yet is unpredictable in practice over long periods because its behavior depends very sensitively on initial conditions. Despite this unpredictability, however, there are certain constants, such as Feigenbaum's Constant, and certain structures, such as chaotic attractors, that are fixed and susceptible to analysis. The weather, the movements of a metal pendulum moving over fixed magnets, and the orbits of closely-spaced moons are all examples of chaotic systems. Although the ideas behind modern chaos theory were actively studied at some level throughout most of the twentieth century, the word as a mathematical term dates only from an article in American Mathematical Monthly in 1975 called "Period Three Implies Chaos."
In everyday language chaos has come to mean the exact opposite of order. But the Greek root khaox means "empty space," specifically the primordial emptiness that in Greek cosmogony existed before anything else came into being, and this meaning still persists in archaic usage where it refers to a canyon or abyss. Later this notion of emptiness was superceded and chaos came to refer to an aboriginal state of confusion. In this sense, Paracelsus applied the term to describe air, hence the modern term gas. The evolution of the word to mean disorder before the forces of creation filled the emptiness and established order led to chaos in the mathematical sense, as an unexpected third state: a deterministic system subject to simple rules that nevertheless displays infinitely complex behavior.
1. Gleick, James. Chaos: Making a New Science. New York: Penguin, 1988.