MM#1: Lecture #5, 7:30pm, Monday 15 May 2000
Chaos and determinism

Pierre Simon, Marquis de Laplace, 1814

An intelligence which, at a given instant, would know all the forces by which Nature is animated, and the respective situation of all the elements of which it is composed, if furthermore it were vast enough to submit all these data to analysis, would in the same formula encompass the motions of the largest bodies of the universe, and those of the most minute atom: nothing for it would be uncertain, and the future as well as the past would be present to its eyes.

Henri Poincare, 1908

A very small cause, which escapes us, determines a considerable effect which we cannot ignore, and we then say that this effect is due to chance.

Ralph Abraham, 1983

Although the large-scale attractors are aspects of a dynamical system which are fully deterministic in the formal mathematical sense, the behavior of a trajectory attracted to such an attractor is totally unpredictable, in the long run.

Steve Smale, 1998

Chaos is a new science which establishes the omnipresence of unpredictability as a fundamental feature of common experience.