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Cartoons and forgeries


The importance of the eye
Benoît Mandelbrot Mathematician
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Now, this is a very, very crude sketch of a long description, but I would like to mention very strongly, to link this work even further to what I said before about fractals: the importance of the eye in this context is extraordinarily high. I found that early on, when my work was at the same time popular and very much criticised, a landmark step occurred when some colleagues of mine at Bell Telephone laboratories decided to test it visually. What they did was to create a collection of charts, very much what I had done before for hydrology. They took charts in which they would plot Brownian motion and my model, the first model, the '63 model, for various values of the exponent alpha. They showed it to a friend of theirs who was a broker, a very sophisticated person, and asked him whether he could, just by looking at these charts, say which ones were real, which were unreal. And the broker immediately identified Brownian motion by saying "this is ridiculous, this supposes a degree of regularity, of continuity in the market which everybody who knows anything knows is not present. " He also immediately put aside the charts corresponding to very small values of alpha where the discontinuity is overwhelming, by saying, "Well, those scientists, when they are told that geometry doesn't apply in the world, all they do is to just dress it up: so it didn't work without discontinuity, so add discontinuities. But nobody can add them properly." And then he zeroed in on the value corresponding to alpha equalling one point seven, which happens to be, I hasten to say, a value often encountered in price series, and said, "That is a real price series." No model could catch this extraordinary mixture of continuity and discontinuity, which the market alone in its great strength and power and wisdom produces, well, this (a=1.7 model) was just as artificial as all the others. Now a closer look, a few tests, would have convinced him that it was not quite so good, but I thought and they thought when they put it to me, that this was a very strong element to be added to all the quantitative tests we had been going through.

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: 2 minutes, 47 seconds

Date story recorded: May 1998

Date story went live: 29 September 2010