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Introduction to Catastrophe Theory with Applications to Biology and the Social Sciences

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Catastrophe theory is a method of modelling discovered by Rene Thom in the 1960’s. It is based on deep theorems in mathematics that are hard to prove, but easy to understand geometrically. It is particularly useful for modelling phenomena in which continuous causes can produce discontinuous effects, and which occur throughout science.

This lecture will give an introduction to the method, focusing on applications in the biological and social sciences. The first example to be discussed is a model by F J Seif that helped to explain hyperthyroidism; he was able to fit the data of 400 patients onto a cusp catastrophe, from which he was then able to identify the onset of the disorder and to predict an unexpected and successful cure for those whom the conventional treatment had unfortunately switched into hypothyroidism.

The second model concerns switches of mood, between fight and flight. This can help to explain the behaviour of dogs, the resolution of children’s tantrums, and the strategies used by some animals in the defence of their territories.

Finally, we shall apply the method to certain famous switches of perception in literature.

Bio: Sir Christopher Zeeman is a fellow of the Royal Society, and has held posts at a number of universities, including Cambridge, Oxford, Princeton, the University of Chicago, the University of Warwick, and Hertford College. An expert in topology and dynamical systems, his lectures at the University of Warwick were often fillted to capacity (in a lecture hall of 400 seats).

Sir Christopher has received numerous honours thoughout his career, including the Faraday Medal from the Royal Society in 1988 in recognition of his ability to communicate science to public audiences. He has been invited to speak at dozens of named lectures—a testament to his teaching abiliities.

This talk is part of the Pembroke Papers, Pembroke College series.

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