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Background to work in mathematics, physics, economics and finance


The twentieth century - predictability
Benoît Mandelbrot Mathematician
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Now in the twentieth century the inverse of what happened in the eighteenth was taken. It became known - and that is the theory of chaos which I will come back to later on for some details - that under certain conditions systems which obey totally well-described, well-understood laws, in which one can predict with certainty the progress of a trajectory once one knows initial conditions, that those systems were so sensitive to initial conditions that in practice they could predict nothing. That is, if you know fifteen decimals of initial conditions you could go on for a certain time and then essentially have no prediction whatsoever. If you knew more decimals for every initial condition you could go on longer but eventually, again, predictability is lost. Therefore, mechanics/dynamics - the same thing - became split into two parts: the nice, well-behaved dynamics which, if you know a few decimals you know pretty well how things behave; and the chaotic dynamics in which you must know an infinite number of decimals to have exact predictions. In theory you could predict everything, but in practice you can predict very, very little.

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, 26 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008