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Turbulence: Kolmogorov, Nabukov, Heisenberg, Weizsäcker and Onsager
Benoît Mandelbrot Mathematician
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One thing I learned then, which was very important for later, was about turbulence. Kolmogorov's work- well it's a co-op between Kolmogorov, Nabukov, Heisenberg, Weizsäcker and Onsager- had done this work during the war, was now becoming known. It was totally disbelieved. Nobody thought it was right, but the quality of those men and the simplicity of the result and the strange nature of the arguments were very, very attractive, and so we had a number of lectures about turbulence which later on were essential to my life, because I both saw what had been done and I saw how difficult it was to verify, to believe it, and how beautiful it was. And let me say a few words about that. In the most extreme form of this argument, which I think is due to Onsager and not to Kolmogorov, the spectrum of turbulence, which is a great monument of human understanding, came out of pure thought; not out of the equation of flow motion, no relation whatsoever; not out of experience with flow motion, no relation whatsoever; just, if the spectrum were K-5/3 so many things would be nice and simple and convenient. It was a totally ridiculous kind of science, but at the same time extremely mystifying and also very attractive. How come that the human mind can, starting with principles so devoid of content, make predictions so full of content which one could try to verify and at that time one could not verify? So, I emphasise, it was very much a limbo, a world in which interesting things were being said but very little belief was attracted to it.

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: 2 minutes, 5 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008