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Mathematical disagreements with Uncle


Uncle and Father
Benoît Mandelbrot Mathematician
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Before I continue I would like to stop to say more about my father and my uncle. Let me begin by my uncle perhaps. He was sixteen years younger than my father and one of the features of his personality which struck me always when I was small, and he was in a way the big figure in the family, was how he divided his mind between being a mathematician on weekdays and a painter on weekends. He was perhaps as good a painter as Churchill, or maybe not as good, but anyhow it was certainly a Sunday vocation. He was very much interested in painting and art. But for him there was an absolutely necessary separation between the two. His weekday mathematics had nothing left of geometry. For him geometry was very good for children to get into mathematics, to confirm their interest in mathematics. But to grow, one had to forget about it, because mathematics to his mind had completely gone beyond anything that was visual, sensorial or in the fingers, and had become extremely abstract. Even though his mathematics was mathematical analysis, which was born from very clear physical problems, he was very much in the spirit of 'mathematics without pictures', with not even diagrams because they were not necessary and were in fact, if anything, illusions. Quite clearly in my mind the two have been present very strongly and totally linked. Where my uncle made the separation, I did not want to see any, and this antipathy towards mathematics that had been deprived of its visual and sensorial aspect has been a driving factor in my life over many years. My uncle had led a charming life. He, as I say, came to Paris when he was needed very badly. He fulfilled a very important role. He was an excellent teacher. He helped greater mathematics survive at the time when otherwise it might have been crushed by other investigations. But the influence he tried to exert on me had been quite negative, even though, at one point, he started me on the study of iteration and Julia sets, which later became perhaps the most spectacular part of my own work. Therefore I owe to him this inspiration. My father had had a very hard life. He was nearly the oldest of a very large family. He was a very devoted son and stayed on to help his father and many sisters and brothers when his father, my grandfather, was not quite able to cope with everything. So he started working at a very young age. He was mostly self-taught. He was the kind of man of 1900 who throughout the bad years of the war was going to do self-improvements. Things were terrible but he would take self-improvement books and learn this and that, because he felt that everything he learned would be a good addition to what he knew, and also perhaps it would be additional ammunition if things went very, very bad. For him it was not a matter of mathematics and painting; it was a matter of engineering and painting, and this symbolic fact that he took us to the Louvre and to the other museum was very much emblematic of what he wanted us to understand. I saw the correspondence of my father when he was wooing my mother; he was sending her postcards of paintings he had seen because he was travelling for his business a great deal. My uncle was a very nice man but I would say he was a nice man in environments which were not hostile. My father succeeded in something, which we, that is my mother and my brother and I, felt impossible. He had a small business in Paris manufacturing clothing for children, rather cheap clothing. This was closed in 1939, and in 1945 my mother thought that he perhaps should become an employee somewhere, because he was such a great accountant, he was such a fast person, but he didn't want to start working for just anybody. He was a very independent person, had never worked for any length of time for anybody except when he was very young. He started from scratch and went to travel to these fairs and markets in western France, in the country, to see those people and say, "Well, five years ago I was selling you good stuff at a good price. I am back." Well they worked with him.

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: Daniel Zajdenweber Bernard Sapoval

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

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.

Duration: 5 minutes, 41 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008