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Background to chaos and wild randomness: Galileo, Newton, Laplace


Being entertained by world class musicians
Benoît Mandelbrot Mathematician
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But there was also an extraordinary experience that I'll never forget: the concert. It is the custom if one has a well-endowed meeting to have musical entertainment. Now we are not well-endowed at all; however by coincidence, Sir George Solti was then directing the European Youth Orchestra and so before the meeting opened I could say, "As to musical entertainment, Sir George Solti, conductor of the Chicago Symphony Orchestra, has agreed to invite us to a performance of his orchestra." Well, I had never had an opportunity like that, of having a man of his stature to do it. Then his associate was Claudio Abbado, who also gave us the privilege of showing us his skill as a conductor. It was something quite, quite incredible. The main fact was that at that meeting everything went- that is, mathematicians were so completely amazed that esoterica could be the core of something else that they stayed even at lectures that otherwise they would never have been caught dead attending. Physicists who were totally turned off by esoterica attended lectures that they would have never attended. This meeting remains as a kind of goal, perhaps never to be repeated because at this point mathematicians who come to fractals meetings know more or less what to expect, and so does everybody else. At that time nobody knew what to expect: whether the meeting would be held, whether held together, whether people would stay, whether people would remember it. Well, beginnings are often like that. In this case the beginnings were followed up, and each year the number of fractal meetings. They are much more organised now, they correspond to better-defined fields. When they are miscellaneous the people who come tend to be from less active fields who just now are learning about fractals. I am very pleased that so many meetings are held, that the spirit of total coming together of so many different kinds of people, that spirit cannot be artificially created, it just happens every so often under rare conditions. It happened in Courchevel in 1982. The people received those very poorly made Xerox copies of my master copy of the book. Many of them tell me that they cherish them even though they are very difficult to read and quite faint, because they use the book when they want to read it, but they hold onto this very, messy copy because, again, it represented something that was just being born, and with all the uncertainty, all the hesitation, might not have survived, it might just, well, last for a day or last for a week. Some people are saying, "Well, it's a little fashion." My French chamber girl told me one day, "If anybody tells you it's a fashion, tell them that fashion lasts a week, a month, a year. That if a fashion lasts fifteen years it becomes a style." And that was something that I hope is true.

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, 37 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008