Chaos & Fractals

Laplace's Demon

A scientific revolution began in the seventeenth century with Sir Isaac Newton's development of the calculus and the laws of classical mechanics. Thereafter, scientists viewed nature from a profoundly different perspective. For the first time, Newtonian physics made it possible for scientists to determine the dynamics of bodies by simple equations.

Newton's work in this area was continued in the late eighteenth and early nineteenth centuries by the French physicist Pierre-Simon Laplace. Laplace is credited with the following famous quotation which is often referred to as "Laplace's Demon."

"We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at any given moment knew all of the forces that animate nature and the mutual positions of the beings that compose it, if this intellect were vast enough to submit the data to analysis, could condense into a single formula the movement of the greatest bodies of the universe and that of the lightest atom; for such an intellect nothing could be uncertain and the future just like the past would be present before its eyes."
— Marquis Pierre Simon de Laplace

"Laplace's Demon" concerns the idea of determinism, namely the belief that the past completely determines the future. Clearly, one can see why determinism was so attractive to scientists (and philosophers — determinism has roots that can be traced back to Socrates). Indeed, this passage had a strong influence on setting the course of science for years to come, and by the early 1800's determinism had become very firmly entrenched among many scientists. In Laplace's world everything would be predetermined — no chance, no choice, and no uncertainty.

Nature, however, is much more clever than this. Towards the end of the 1800's, mathematicians and scientists began encountering some very difficult equations to solve — some in fact were completely unsolvable. A particularly troublesome set of mathematical equations were non-linear differential equations. Much in the same vein, there existed the horribly difficult and outstanding problem of three mutually gravitationally attracted bodies — the so called "three-body problem" (or its generalization to "n-bodies").

At first, problems such as these were cast-off as special cases and largely ignored. It would turn out that these so-called "special cases" would bring the birth of a new way of thinking. When these equations were finally studied in detail a fundamental change, which would ultimately overthrow the ideas of determinism, began to occur in mathematics and science. Inklings of the science that would be come to be known as "chaos" began to appear. Niels Bohr said it best:

"Prediction is difficult, especially the future."
— Niels Bohr