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Lewis Fry Richardson and Leonardo da Vinci


A new geometry of nature
Benoît Mandelbrot Mathematician
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So a big part of my work in the '60s consisted in creating mathematical structures that would represent different flavours of 1/f noise in different times - and those flavours are extremely different from each other. It is not as if they are different chapters of the same part in a book; they almost belong to different parts of the book, 'The Great Book Of Science', then their formulas were generalised to tackle turbulence. I mentioned 'The Great Book Of Science' because suddenly I remembered, as I often do, this wonderful quotation of Galileo Galilei that 'The Great Book of Science', or 'The Great Book Of The Universe' is written in mathematical characters which are circles, lines and triangles, and without them one errs for ever in the dark labyrinth. Galileo was right in terms of the language that the book uses, that is, mathematics, but wrong in terms of whose dialect was being used. And as time went on and as I was developing the various formulas and formulations for the various fields, it became increasingly clear once again that Euclid was simply not adequate for it on the one hand, and on the other hand that something else could be constructed. A new geometry of nature, the purpose of which is to represent not everything that the old one had left aside, but a big part of those. And by extraordinary luck, coincidence, or perhaps for reasons very profound that I don't understand, this second batch of geometric phenomena did include as important things as fluctuation of rivers, turbulence, mountains, etc., etc.

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: 1 minute, 51 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008