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Critical opalescence, Onsager and work in physics


IBM and the educational system
Benoît Mandelbrot Mathematician
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Well, that leads us to the period where a tool that I was using, the fractal dimension, was increasingly important and increasingly ill-understood. I came to mountains not because of their beauty and because of my attraction, but because I needed a neutral example to show that fractal dimension was something you could look at. But I think it is interesting in terms of the biographical and the sociological aspect of my story - how my life orbit which is so complicated, so involved, reflects upon our educational system. To consider the following- suppose someone would have the idea that certain techniques could apply, mathematical techniques that could be used to represent the structure of mountains. How could a person proceed? Would he write a report to the National Research Council, the CNRS, National Science Foundation, saying, "I would like to receive a hundred thousand dollars, or two or three or four hundred thousand dollars for myself and collaborators to seek formulas to make forgeries of mountains"? Totally ridiculous, and it would be never accepted. There are some tasks that are simply too ridiculous and either represent non-professional attitudes of the applicant, or represent just folly. I was fortunate at IBM that I didn't have to tell anybody what I was going to do. We did that on Sundays, nights, and besides I was being given an enormous amount of leeway in these affairs, and there was a good understanding that when the computer was not used, there was no need, no reason to do bureaucratic things about it. It could be used by anybody for any purpose. Almost all of it went to waste, but if the computer had been under lock and key everything would have gone to waste. So the few things that were very successful were a justification for a liberal availability of tools.

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, 10 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008