a story lives forever
Sign in
Form submission failed!

Stay signed in

Recover your password?
Form submission failed!

Web of Stories Ltd would like to keep you informed about our products and services.

Please tick here if you would like us to keep you informed about our products and services.

I have read and accepted the Terms & Conditions.

Please note: Your email and any private information provided at registration will not be passed on to other individuals or organisations without your specific approval.

Video URL

You must be registered to use this feature. Sign in or register.


Measuring roughness


Self-organised criticality
Benoît Mandelbrot Mathematician
Comments (0) Please sign in or register to add comments
This has evolved now into what's named self-organised criticality? Well, it is substantially different because criticality goes beyond what I had in mind. In fact, I think perhaps it goes beyond what is necessary. I have not made up my mind on self-organised criticality, because the characteristic of the question of magnets is that there is a parameter like temperature. At a certain critical temperature very special things happen. The characteristic of phenomena like prices or like turbulence, there's no parameter. Therefore to embed a prime without a parameter in one which has a parameter, and then argue that this parameter somehow arranges to take its own value is presupposing something that is beyond reality. I mean there are no non-critical situations. So I have not made up my mind about the power of this metaphor. The idea that dependence can be global, that variance can be infinite, and in fact that everything that has been taken as finite without any question in physics or in statistics can, in fact be divergent or zero which is sometimes equally bad or equally rich in consequences. This idea is something that did not depend upon any broader conjecture about the causes of these phenomena. It comes out of efforts to describe them and has been made unavoidable by those efforts.

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, 44 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008