In the 17th century, Sir Isaac Newton, a mathematician and scientist, developed three rules of motion which have since formed the basis of our understanding of the world. They are the basis of so-called classical mechanics.
These laws allowed Newton and his contemporaries to explain, they thought, any mechanical system.
This led to a deterministic view of the universe. The scientist Laplace formed the idea of a Vast Intellect - a person who knew the position of, and the forces acting upon, every particle in the universe would be able to predict their behavior for any subsequent point in time.
Newton's laws, for the scientists of the seventeenth and eighteenth centuries, allowed the explanation of all mechanical systems.
However, by the nineteenth century, flaws had begun to appear in this belief. The French mathematician Jules Henri Poincare tried to use these methods to assess the stability of the solar system, but came up with results which did not support the deterministic view advanced by Newton.
For example, Newton's laws could predict what would happen when one object was struck by another object. However, they could not explain what would happen if an object hit two other objects simultaneously.
Examples such as these caused doubt in the minds of physicists and mathematicians - the validity of Laplace's Vast Intellect was beginning to look doubtful.
One of the main problem with the use of Newton's laws was the fact that everything was treated as a linear equation. The usual method was to consider small changes in the system, and then use the results of this to predict the behavior of the system on a wider scale.
This would have worked had the systems involved been linear - however, many were not. For non-linear systems, this method did not work, and so the application of Newton's theories was giving false results.
It was Henri Poincare who first identified the real nature of chaos. He wrote: "It may happen that small differences in the initial conditions produce very great ones in the final phenomena. A small error in the former will produce an enormous error in the latter. Prediction becomes impossible.".
This is what chaos is really about. Minor differences between initial conditions in a system can cause great alterations to the behavior of that system. Laplace's Vast Intellect is not feasible because it is not possible to know precisely the location of, and forces acting upon, a body. There will always be inaccuracies, and these will lead to chaotic behavior.