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The butterfly effect


Background to work in mathematics, physics, economics and finance
Benoît Mandelbrot Mathematician
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Now my work made a very parallel but very different distinction in stochastic behaviour, in random behaviour, unpredictable behaviour, which has no dynamics. Sometimes the behaviour is, how should I say, mild, the randomness is mild, and a fair amount of predictability can be obtained. In other cases the predictability is much less so, the control is much more difficult, and these correspond to what are called wild fluctuations. This parallel division of dynamics between classical and chaotic, and of randomness between mild and wild, with many other states in between on both sides, means that many habits of thought, which go much further than technical procedures, which people were completely trusting, identifying with science, were no longer applicable. These took different forms, my work in mathematics, my work in physics, and my work in economics and finance.

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: 1 minute, 11 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008