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Further work on the Power-Law Distribution

RELATED STORIES

Move to Geneva to work with Jean Piaget
Benoît Mandelbrot Mathematician
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Well, after the end of that year in Princeton I came back to Paris and that year was very busy. Aillette and I decided to marry, so I was very occupied outside of science. While this was going on I met a very strange individual, at least strange to me. I was standing in the library of the Institute of Statistics in Paris, when an old-looking man came in and asked me, "Do you know where Mandelbrot is?" I said, "I am Mandelbrot." and he said, "I am Jean Piaget." Now Piaget was a very famous psychologist. I knew of him, a man who had studied children's intelligence, and was surprised that he would bother to come to me. What he wanted was to have me participate in an effort he was starting of putting psychology on a sound scientific basis. He had always had the impression that what he lacked was knowledge of mathematics and physics, and had been asking around: who were the people who might perhaps talk to him and help him, and he was just asking me whether I would do so. Well, very frankly, my reason for accepting his offer - the offer was an assistant professorship at Geneva for one or two years - we felt, Aillette and I, that it was better not to be in Paris after we were married. Geneva was far, but not too far. Besides, the offer seemed to be strange but tempting, and above all I had not yet decided whether I was going to continue in those social sciences where I was successful and well known, or in physics. And so for the next two years I was an assistant professor of mathematics in Geneva and a strong participant in a seminar that Piaget ran. Now Piaget, first of all, turned out to be much younger than he looked. He was man who was always outside, so had a weathered face. Also, judging from his works, I would assume that he was thirty or thirty-five when he wrote his famous books. In fact he was very much younger, early twenties; had married extremely young, had children very young, therefore he had in a way become famous at an unusually young age. He was famous in a very strange sense, because he was very much a local celebrity in Geneva, in Neuchatel, and also in France. He did not speak English, did not travel, and was barely known outside. What he wanted was to try to push this idea, it was of a well-defined logic in children, which was not a symbolic logic; to organise it, to see to what extent it could be made coherent, and in general he wanted to pursue this dream of making psychology mathematical. Now, since again I was so much hesitating between two directions, which became one half of my activities over the next two years. For the other half, I may say immediately, I was pushing the foundations of thermo- dynamics, and in fact that became very interesting. So the division of my thesis, which was so awkward, was actually continuing with very substantial success in both sciences, both sides, but without the any coherence between them at that point. Piaget knew about your thesis about Zipf's law? Piaget knew of my thesis on Zipf's Law, and he said that he believed that of all the mathematicians and physicists, all the people who were reputed for being fast on their feet and willing to take risks, I was the best to bring to Geneva. It was very interesting. Piaget in many ways was a very impressive figure. I would say - if I were to sort of mock, that he had a clear genius but no talent, in the sense that there was a lack of technique, of research and of science organisation in his case. He was certainly very old-fashioned, a naturalist - originally, I think, his thesis was on snails or something - he was a very old-fashioned observational naturalist who had moved that kind of science into psychology, eighteenth century natural history, and he was good at describing, but he just did not have any idea what the theoretical system is.

Benoît Mandelbrot (1924-2010) discovered his ability to think about mathematics in images while working with the French Resistance during the Second World War, and is famous for his work on fractal geometry - the maths of the shapes found in nature.

Listeners: Bernard Sapoval Daniel Zajdenweber

Bernard Sapoval is Research Director at C.N.R.S. Since 1983 his work has focused on the physics of fractals and irregular systems and structures and properties in general. The main themes are the fractal structure of diffusion fronts, the concept of percolation in a gradient, random walks in a probability gradient as a method to calculate the threshold of percolation in two dimensions, the concept of intercalation and invasion noise, observed, for example, in the absorbance of a liquid in a porous substance, prediction of the fractal dimension of certain corrosion figures, the possibility of increasing sharpness in fuzzy images by a numerical analysis using the concept of percolation in a gradient, calculation of the way a fractal model will respond to external stimulus and the correspondence between the electrochemical response of an irregular electrode and the absorbance of a membrane of the same geometry.

Daniel Zajdenweber is a Professor at the College of Economics, University of Paris.

Duration: 4 minutes, 45 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008