E-Lectures
The lecture summarized below is available on the web, at commercial rates, from www.boxmind.com
Order and Chaos in Mathematics and Nature
SUMMARY
Anyone with a sense of numerical relationships or a feeling for geometric form can hardly fail to notice that the natural world contains many regularities--- patterns. The stars revolve steadily in the night sky. The moon goes through repeated 'phases'. Snail shells are spiral, flowers are symmetric. The quest for scientific understanding of the world around us has largely been a response to the implicit questions raised by these patterns. It has led to the discovery of remarkable mathematical rules that appear to govern the deep structure of the universe: the 'laws of nature'.
At first, such laws seem to explain why the patterns occur: simple mathematical laws obviously lead to simple mathematical patterns in behaviour. But since the 1960s (with roots that go back quite a bit earlier) mathematicians and scientists have come to appreciate that the relationship between laws and behaviour is not that straightforward. Simple rules can generate patterned behaviour--- but they can also, apparely just as readily, generate highly irregular behaviour: chaos. In this sense, chaos is not another term for 'randomness'. Quite the contrary: chaos is governed by non-random laws. It just looks as though it isn't. The lecture describes the origins of chaos and its implications for the present and the future, contrasting the concept with more conventional views of science.
CONTENTS