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The printing of Fractal Objects


Origins and publication of Fractal Objects
Benoît Mandelbrot Mathematician
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In 1975 I came to publish a book, which was based on a lecture I made at the Collège de France in very early 1973. IBM gave me a kind of sabbatical; I came to Paris and I think on 16th of January 1973, it was a Saturday, I was asked to give a lecture at the Collège of France in some kind of interdisciplinary seminar. Now my friends advertised the lecture quite widely among different fields and the crowd was gigantic, which means that that very small room at the Collège of France was full. I gave my lecture for one hour, again with pictures showing how by very simple construction you can get fake galaxy maps, fake mountains, fake this and fake that. I also emphasised the simplicity of the tools, the distinction between all these structures and those of ordinary geometry; the fact that one had to go beyond Euclid, because Euclid plus amendments plus replications was becoming totally unwieldy and helpless and one had to just go well beyond. After my lecture a discussion which lasted for a whole hour ensued, and people from a large number of different fields asked me very sharp pointed questions: "What about this?" "What about that?" "What about that?" Apparently I responded concisely and convincingly. This lecture ended up in triumph. It was very different from the lecture at Princeton in '54! In fact, Pierre Masse, who was a very influential man at that time in France, wrote a column about it in Le Figaro, which was not customary for a lecture by an unknown in a interdisciplinary seminar. And that is the time when I realised that my various activities of economics and of physics and of everything had come together and that the unity of my work was being created. In a way, some people think of a piece of science as starting from a seed and expanding in a very gradual fashion, and that's true for many fields of science. I felt that for a long time I was having, in a certain sense - well, like for example, the kingdom of France: a little county here, a little duchy here, obtained by one means or another, by marrying the heiress or by beheading the owner and pursuing this. Then finally linking two of them together, linking three of them together, but they are still isolated pieces in a landscape; and that all my life before had been in a way spent justifying why a person who did that was, not in a certain sense, acknowledging their defeat and failure, but proclaiming a success and victory, which I was. Because what I was doing did not seem at all like being the basis of any well thought up enterprise. At one point these various duchies and counties became connected - with plenty of holes in the middle, of course, and plenty of very, ill-defended outside explorations, and the whole thing deserved to write a book about it. As a matter of fact the book that I wrote about it - well, I started writing a book, and stopped half way through because half way through I had enough material for a book, and I wanted it to be very, very short. It was referring to its own topic very elusively and very badly, and a friend of mine whom I should have mentioned and shall mention perhaps now much more, Marcel Berger read that text and gave me very strong criticism in many ways and very strong praise in many others. He told me that I was entitled to give a name to this material, that I had won the right to name it whatever I pleased, and I had better do it. And the publisher also wanted to have a snappy title for the book.

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: 4 minutes, 32 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008