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Self-organised criticality


Wild randomness and globality
Benoît Mandelbrot Mathematician
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The behaviour of IBM stock ten years ago does not influence its stock today through IBM, but IBM the enormous corporation has changed the environment very strongly. The way its price varied, went up or went up and fluctuated, had discontinuities, had effects upon all kinds of other quantities, and they in turn affect us. And so my argument was always been that each of these causal chains is totally incomprehensible in detail, probably exponentially decaying. There are so many of them that a very strong dependence may be perfectly compatible. Now I would like to mention that this is precisely the reason why infinite dependence exists, for example, in physics. In a magnet- because two parts far away have very minor dependence along any path of actual dependence. There are so many different paths that they all combine to create a global structure. In other words, there is no global structure in one dimension, but there's one in two and three dimensions etc. for magnets -the basis of Onsager's work and the whole theory. And in economics there is nothing comparable to these calculations, but the intuition of what they represent is the same. And that was always my motivation for transforming infinite dependence from being a ridiculous - not only an exotic but a ridiculous idea, into being an idea which is totally inevitable. One must envision this possibility. And so let me observe the following. The difference between mild and wild randomness goes beyond, how do you say, limited technical details. Mild randomness, in a certain sense, is local; it's happening in a certain period, it doesn't go very far. If you take a large number of particles, what's happening at one end doesn't affect anything else. Wild randomness is global and that is why it is not a matter of the degree of difficulty, it's a matter of the kind of difficulty, which is why I think that this notion of states of randomness, more precisely states of variability, applies also to non-random variability and is essential because it embodies a profound dichotomy. That is why I think that the reason why the phenomena which I have been studying most of my life are so much more difficult than the phenomena, the ordinary phenomena, of physics, because ordinary physics doesn't have the global character. That's why many of the attacks on these questions of economics and of physics have been unsuccessful; it is because they were always simplified, approximated to be local, whereas globality is their principle characteristic.

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: 3 minutes, 6 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008