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Fractals and the importance of proper description (Part 2)

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Fractals and the importance of proper description (Part 1)
Benoît Mandelbrot Mathematician
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The word 'fractal', once introduced, had an extraordinary integrating effect upon myself and upon many people around. Initially again it was simply a word to write a book about, but once a word exists one begins to try to define it, even though initially it was simply something very subjective and indicating my field. Now the main property of all fractals, put in very loose terms, is that each part - they're made of parts- each part is like the whole except it is smaller. After having coined this word I sorted my own research over a very long period of time and I realised that I had been doing almost nothing else in my life. When I was speaking of these errors of transmission, they were different pieces of an error record and each piece, when blown up, was like the whole record. When I was speaking of turbulence I was emphasising the fact that each piece of turbulence, when blown up, was like the whole record. And in general that the idea of replication of the structure of the whole in the parts was the crucial cement that had in a way glued my works together, or, changing the metaphor, the thread that had led me through so many different investigations. Now, is that a concept which is explanatory? Is it descriptive? Is it purely a matter of curve-fitting? Well, that is where a very important distinction resides. Most of statistics consisted in curve-fitting, of presenting phenomena by one of the formulas out of a certain tool box which may be small or big, and curve-fitting them separately. You curve fit each phenomenon separately. Turbulence, for better or worse, is full of such relationships, many of them very important, others less so. The hope of science is to explain everything as much as possible, to reduce as much as possible to a few criteria, to a few rules from which everything else follows as a consequence. For me this goal of explanation has always been essential but not unique. I feel very strongly that many fields of science have been not been helped but slowed by the constant preoccupation with explaining a phenomenon without having got an appropriate description of it. Therefore I have a very strong feeling in my mind of what a proper description is.

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: 3 minutes, 14 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008