Chaos at fifty

Until the 19th century, the tacit assumption had always been that approximate knowledge of the initial state implies approximate knowledge of the final state. Given their success describing the motion of the planets, comets, and stars and the dynamics of countless other systems, physicists had little reason to assume otherwise. Starting in the 19th century, however, and culminating with a 1963 paper by MIT meteorologist Edward Lorenz, a series of developments revealed that the notion of deterministic predictability although appealingly intuitive, is in practice false for most systems. Small uncertainties in an initial state can indeed become large errors in a final one. Even simple systems for which all forces are known can behave unpredictably. Determinism, surprisingly enough, doesn't preclude chaos. Here, Motter and Campbell provide more details on chaos theory.