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The twentieth century - predictability


Background to chaos and wild randomness: Galileo, Newton, Laplace
Benoît Mandelbrot Mathematician
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Before I begin to speak of my work in mathematics, in physics and in economics separately, I would like to say a few words of the notions of chaos and wild randomness, which I will come back to repeatedly, but which deserve to be spoken about separately. Now chaos is a word that has acquired an extraordinary popularity in recent decades, sometimes for bad reasons because it is misunderstood, but also for a very good reason. And to understand it very well I think it is very important to go back several centuries to the eighteenth century. After Newton's work became known in France it became a topic of extraordinary passion on the part of the intellectuals. In a way the intellectuals were very much wedded to a scheme of things that went back to Aristotle, which said that on earth everything's a mess, and in the heavens everything is perfect. That is, the stars proceed, the planets proceed along well-defined trajectories, the sun is flawless, the moon is flawless. On earth everything is messy, nothing's predictable, everything is terrible. Now Galileo showed that in fact there was some regularity on earth, and there was also messiness in the sky. But Newton was the one who made this idea go through very deeply. It was very shocking to intellectuals in the eighteenth-century because they really took it for granted that in the sky you could predict everything in advance. But on earth the story was embodied in this little rhyme about "for the sake of a nail the horse was lost, for the sake of a horse a battle was lost, for lack of a battle a war was lost, for lack of a war a kingdom was lost". Very tiny differences initially can lead to totally different behaviour. Two people have to meet; one is late; the first doesn't wait; a beautiful match is off. It's very familiar, and Newton gave this totally shattering notion, which in fact in substantial parts of the world we understand; total predictability prevails. Laplace followed by proclaiming a kind of overwhelming imperialist view that one could predict everything precisely; one could also reconstitute the past by knowing the present very accurately; and he wrote it in a very eloquent fashion that was very influential on science. So science, the hard sciences, predicted, and everything else did not. That was something, which the scientists believed, but I think the common man never believed. Underlying all kinds of acknowledgement of the power of science, I believe there was always strong resistance: 'that wouldn't work'.

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