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Self-affining variability

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Cartoons
Benoît Mandelbrot Mathematician
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When you assess the properties of these random objects, some of the properties may be very well approximated by properties of these regular shapes like the Sierpinski triangle; you know this is one? Absolutely. I certainly recognised that and in my most recent book on finance, which I will discuss elsewhere in this interview I describe them as being cartoons. A cartoon, a political cartoon, must be resemblant. If you make a cartoon of a statesman or of a figure on stage and people don't immediately recognise some common features, the cartoon is very bad. But one must underline that they have certain restrictions. They are not the same as a whole and complete imitation. I think it's very important to have both cartoons and more realistic structures. The cartoons have the power of representing the essential very often, but have this intrinsic weakness of being in a certain sense predictable. Once you look at the Sierpinski triangle for a very long time you see more consequences of the construction, but they are rather short consequences, they don't require a very long sequence of thinking. In a certain sense, the most surprising, the richest sciences are those in which we start from simple rules and then go on to very, very long trains of consequences and very long trains of consequences, which you are still predicting correctly. Therefore for me this possibility of going very far from the initial deliberate construction, and of predicting phenomena, which were not consciously put in is extremely valuable. And that's why I always play in parallel with cartoons and with the models proper. I'm very aware of it, I do it quite schematically.

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, 16 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008