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Development of work with turbulence and multifractals


Lewis Fry Richardson and Leonardo da Vinci
Benoît Mandelbrot Mathematician
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Now, I would like to say only a few words about one topic which is turbulence - then go to a different chapter of science, in which I became interested later on. Turbulence, again, is a very, very old phenomenon. Many people broke their teeth on it, and in the early '20s a very strange character named Lewis Fry Richardson made a decisive contribution to it. I would like to say perhaps a few words about Lewis Fry Richardson because in my life, as I mentioned and keep mentioning, I encountered either in person or in their writings a certain number of very forceful personalities. Richardson was one. He was an eccentric Englishman, one of the last ones of the kind. He started by being employed by the weather office. When the weather office became part of the Air Ministry he resigned because he was Quaker and had very deep convictions. He would not want to work for any branch of the military. Well, he resigned and had a rough time for a while. He was fortunate whilst still working for the weather office to become Fellow of the Royal Society, and then an opening became vacant at Paisley College, a small school in Glasgow. When Richardson applied they barely read his application, they were so proud to have a Fellow of the Royal Society as their principal. Well, when he came they were somewhat disappointed, as I learned when I participated in the ceremonies for his centenary - because someone from his time was still available. Richardson was not what they expected to have as the principal of a small college. In due time he resigned because he had a small inheritance and occupied himself as he pleased. He left a number of great works and a large amount of unpublished work, but the most significant part of Richardson was to did something that I so deeply admire because it is exactly the kind of thing I love to do when I can. He took as a guide, pictures of turbulence, not measurements of turbulence, pictures of turbulence, more precisely the fountains of Leonardo da Vinci. Now Leonardo da Vinci has been described as being the last and greatest of medieval engineers; as his primary occupation - he was also a painter of course, and a poet - but as an engineer he was in the habit of drawing natural phenomena extremely accurately. Many of the drawings as a matter of fact start with him but were familiar to medieval architects and engineers. One of the most beautiful is a collection of drawings of fountains in which one sees very well the behaviour of water which falls into a pool and being divided into eddies, big eddies, small eddies, middle-sized eddies, etc., etc. For Richardson this was not just a picture. This was not something that had to be replaced instantly by measurements and by theory: it was something that inspired him to have this picture of turbulence as being made of a cascade. He wrote this wonderful parody of some verses by Swift. Swift had written of his contemporaries, the poets: they're big fleas on which smaller fleas feed, and the smaller and smaller and so on. Richardson said, they're big eddies on which smaller eddies feed and smaller yet and so on, to viscosity. Swift said to infinity; Richardson said to viscosity. Small enough eddies are impossible.

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: 4 minutes, 9 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008