Monday, November 13, 2006

Catastrophe Theory

Catastrophe theory was born in 1972, with the publication of a very learned book by René Thom entitled Structural Stability and Morphogenesis. It has also a subtitle: An Essay on the General Theory of Models. Title and subtitle together indicate that here we have a mathematical theory with unusual claims to universality.

Thom is a leading mathematician; his ideas were already known in mathematical circles and spread very quickly to scientists in general and to the public at large. Catastrophe theory became an instant success, treatises and research papers were written, articles and interviews appeared in newspapers and magazines. In fact, so much has already been written about catastrophe theory that it seems quite superfluous to add yet another chapter to this growing list.

Despite so many explanations and commentaries, I still have the feeling that the instant success of catastrophe theory is largely due to a misunderstanding of what a theory is and what catastrophe means.

Let me first say what catastrophe theory is not. It does not announce catastrophes; it cannot tell whether the world will end in nuclear war. Catastrophe theory does not enable us to make precise, quantitative predictions, the way relativity theory does, for instance. Neither can it be proved or disproved by an experiment, and so the question arises whether it is a scientific theory at all.

Actually it is—but it is much closer to biological theories like that of evolution than to physical theories like that of relativity. It fits certain facts together and provides an abstract setting to grasp them all at once. It is a way to make some sense out of the hopeless tangle of natural phenomena, like a listening device which picks some garbled message out of the overpowering background noise. It is a mathematical code to help us decipher the book of nature.

Ivar Ekeland
Mathematics And The Unexpected

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