Speaking Volumes: René Thom's Structural Stability and Morphogenesis

October 10, 1997

Ian Stewart on René Thom's Structural Stability and Morphogenesis.

The most curious thing about the book that changed my life is that it exerted its main effects several years before it was published, and several years after - but not at the actual time of publication. The book was Rene Thom's Structural Stability and Morphogenesis. Until then, Thom had been familiar only to the mathematical community, but overnight he became a household name as the inventor of catastrophe theory - a new and controversial way of understanding sudden changes in nature.

Scientists often assume that sudden effects must have sudden causes. This belief underlies much discussion of the demise of the dinosaurs, for example. Yet in the physical sciences it has long been known that gradually changing causes can have dramatic effects - explosions, fracture of materials, breaking waves. Thom tried to transfer the same insight into biology and other "soft" sciences, by laying down a general mathematical framework for such phenomena.

More than half a century earlier, another Frenchman, Henri Poincare, had first understood the power of visual imagery in dynamics. He introduced the notion of a phase space, representing all possible behaviours of the system as a coherent whole. Thom exploited phase space to classify sudden changes - "catastrophes". Christopher Zeeman became an enthusiastic developer of Thom's ideas, coining the term "catastrophe theory". In 1970, as a PhD student, I attended his first-ever lecture course on catastrophe theory. It embraced everything from rainbows to lemmings, all centred on the most beautiful geometric concept that I had seen. Until then, my research had been purely symbolic: I was an algebraist. Suddenly my eyes were opened to the visual side of mathematics, and to the possibility of putting it to practical use. I did not know it at the time, but I was hooked, In those days Thom's ideas were somewhat mysterious - largely because his book, though rumoured on the grapevine, had not appeared. Its English translation was finally published in 1975 - so by the time I got to read it, I had already imbibed its main message. I was hooked, but nothing was reeling me in.

Then Tim Poston, another Warwick mathematician, suggested that we write a book to make Thom's ideas more accessible. Catastrophe Theory and Its Applications hit the bookstores in late 1977. I was now equipped with the mathematical background to do research in the area, but my output still remained mostly algebraic. What papers I did write on catastrophe theory were just a minor sideline.

I was finally hauled in and netted by an American mathematician, Marty Golubitsky. I had been invited to visit the University of Connecticut to work on algebra. Early in 1978 Golubitsky arrived unannounced at the front door of our campus apartment. He was interested in Thom's work, knew that I was too, and thought it was time we got together. It took until 1983 to arrange for me to spend a year at the University of Houston. By then, the subject had moved on: the name "catastrophe theory" had pretty much disappeared, but the ideas had not. We picked up one idea - periodic behaviour in systems with symmetry - and followed our noses.

Virtually all of my research since - over 50 journal papers - has stemmed from that initial insight. It has had a substantial (positive) effect on my academic career, and it has given me many themes for my books. Together or separately, Marty and I have developed our methods and applied them to fluid flow, chemistry, electronics, quantum physics, celestial mechanics, animal movement, evolution and other things.

Ironically, I now realise how little I understood of what Thom really meant when he first penned his obscure, unorthodox, idiosyncratic masterpiece. His scope was far broader than the message that I received. Structural Stability and Morphogenesis changed my life - but it was a slow burner with a very long fuse.

I have a sneaky feeling that at any moment it may explode into my life again - with equally unpredictable consequences.

Ian Stewart is professor of mathematics, University of Warwick.

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