The History of Chaos Theory
Introduction
This is not intended as an overview of all of chaos theory, it is instead as a look back to before chaos theory, and an introduction to the subject. First we go back in time...
Before Chaos Theory
During the 17th and 18th centuries, Newton led a scientific revolution that encompassed many new theories and ideas. These new ideas brought about an atmosphere of excitement in the scientific community because they worked - phenomenon such as heat, sound, waves, light, magnetism, electricity and mechanics were all explained. The degree to which they were explained obviously varied, but the overall feeling was one of optimism - that deterministic science held all the answers. This led to the view that the future of the entire universe was in fact predetermined, and therefore, with enough knowledge, could be predicted. This was the view held by Pierre Simon de Laplace, a leading 18th century mathematician, in his "Philosophical Essays on Probabilities":
"An intellect which at any given moment knew all the forces that animate Nature and the mutual positions of the beings that comprise it, if this intellect was vast enough to submit its 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."
The Advent of Chaos
These views were held until very recently, and by some very important and well respected people - for example both Newton and Einstein, see the quote from Einstein on the first page. When examples of chaos were first constructed by mathematicians, they were ignored, on the grounds that the equations were obscure, mathematical curiosities. However, examples of chaos in nature were turning up, and the equations that were seen as obscure constructs turned out to be actually more common than classical deterministic equations. The maths of chaos began to be explored. Now, though the subject is still young and much is still to be learnt, the basics of chaos have been discovered, and agreed upon throughout the world.
The Mathematical Definition of Chaos
chaos ('keios) n. Stochastic behaviour occuring in a deterministic system.
A deterministic system is a system governed by equations which have a definite, determinable outcome. These were the type of systems which Newton and Einstein worked on. Such systems were always thought to have a determinable outcome, ie a specific outcome that could be calculated exactly.
Stochastic behaviour is seemingly unordered, unpredictable, behaviour, ie chaotic behaviour.
So, chaos is the mathematics of seemingly normal, predictable systems exhibiting behaviour that is anything but.
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Will Bolam 2001