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My big fight with my uncle


Ph.D. Thesis
Benoît Mandelbrot Mathematician
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While I was a consultant at Philips, I was also writing my Ph.D. And it was based upon Zipf's distribution for word frequencies which I view as totally devoid of interest, but perfectly fitting my personal search of some esoterica about nature, which I could explain the basis of as esoterica of physics. The latter took the following form: the partition function was not analytic, it had similarity, and the similarity partition - function, by an argument, which was rather straightforward but I could not state it in words gave rise to a result, which was very different from distributions encountered in the theory of gases. Which is why word frequencies follow a law so unusual by the standards of physics. I was very much aware of this thermo dynamical analogy and for many years I was writing articles with titles like Statistical?Macroscopic?Linguistic?' or something, because my, how should I say, beacon was thermodynamics. And I would like perhaps to go back a step for that. Why did I become so enamoured of thermodynamics and why did I acquire the facility to manipulate it? Not because of Leprince-Ringuet at the École Polytechnique, that was a course of rather a dry fashion. But at Caltech, since I was not working on a very specific subject I was taking courses of various kinds, and Richard Tolman, who was then a very old man, was giving actually his swan song, the last course he gave. He met us, rather a large group because he was a famous man. In fact he was one of the very few old professors at Caltech. At Caltech, when I was there, everybody was either very old or very young because of the break of the war. He met us and said, "Gentlemen, this course is not to learn thermodynamics. I'm not going to teach you the formalism. If you don't know it, you don't need to stay. I'm going to explain to you why it works." And then, I had my notes, I maybe even have them - I took notes for two lessons. I stopped. He was saying nothing that could be taken down, but he was, how to say, dismantling the clock and putting together to see how it worked. And also I read Gibbs. His thermodynamics was expressed in a very general abstract fashion. As a matter of fact Boltzmann had criticised Gibbs by saying that he did not need all that stuff. He was interested in gases, and not in an assembly of screwdrivers and sewing machines - or something of this sort, because Gibbs was so general that he could accommodate this assembly. I was overjoyed, because what I had was an assembly of trees, of coding trees which of course have very different properties from gas molecules, and that Gibbs' kind of thinking worked, whereas the Bozeman's kind of thinking would have been totally helpless. From this viewpoint, the fact that in my random studying I had had the experience of having these few remarkable people as models was very important, very, very useful. So, again, I wrote this thesis, of which actually one half was on thermodynamics, in 1952, and the big question was, what was the thesis in? At that time it hardly mattered from a bureaucratic viewpoint because it was a thesis in the sciences. It didn't say mathematical sciences or physical sciences, but still one has to say which category. I was very much in the dark about that, but then I met in the street a very close of friend of my uncle whose name was Alfred Kastler, who later became a very famous physicist, a man of great charm and great wisdom, and I asked him to help me decide whether I could call it mathematics or physics, because everybody who had read it was complaining that one half was a topic that no longer existed, namely thermodynamics, and the other half was a topic that didn't yet exist, namely the statistical study of these crazy esoteric phenomena. Where to put it? And he said, without hesitation, "Mathematics, because in physics you'll come in competition with a huge crop of new people, of Ph.D.s, good or bad, but you'll have plenty of competition. In mathematics you are so far from French mathematics, so despised and detested by them, that it will be perfectly clear you could only do applied mathematics, but there are no applied mathematicians. Therefore when jobs become open, as there will have to be because life moves and that thing cannot go on," - he was very much in a conflicting position with mathematicians - "you'll be the first to get a job." So you see how certain major decisions are taken for reasons that are not very theoretical! But all my life, and I don't like to hide it, events which I knew how to interpret or manipulate sometimes had a very good influence. I never felt I was following the flow of history, the inevitable development of some idea; I felt that I was being hit back and forth by various ideas and accepting or refusing their contribution. Refusing dull subjects? Refusing subjects, which looked dull. So this is the line, still? Yes, yes. Refusing subjects which were, in a certain sense, terminal.

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: 6 minutes, 20 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008