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A new alphabet
Benoît Mandelbrot Mathematician
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In summary, my work in those hard sciences, and I could add other examples but I think it would be rather tedious, consists in either representing well known phenomena in real space, or representing phenomena in some representational space in which a system is represented by a point in phase space or something like that, in which a great deal of irregularity prevails, in which the alphabet of which Galilei spoke of in 1623, of "straight lines, circles and triangles," is totally inadequate, a new alphabet can be added. Now, do I claim that this alphabet allows us to read the whole book of nature? Of course, not. Only a few more chapters, a few more parts, a few more volumes perhaps, because it pushes away the boundaries of the unknown. But in many cases, like for turbulence, perhaps even for DLA and other such phenomena, we're maybe reaching very hard boundaries where we may find progress is very slow. In other cases we are moving quite rapidly.

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, 20 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008