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Family background and early education


The future for fractals
Benoît Mandelbrot Mathematician
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What about the future? The question is, will fractal geometry continue as a field? Personally, I don't think it will, at least not for a long time because the mixture of interests, which my strange education, which the ups and downs of my life produced, will not be reproduced: the combination of interests in different fields has no reason to be reconstituted. In a way, there are many, how to say, basic intrinsic fields, like mathematics, like physics, like economics, which are not invented around one idea or around a technique. They are just inevitable. It is not at all interesting to imagine that a new field, yet another one, called fractal geometry will become organised besides them, with all these endless questions of turf that would represent: is that part of straight mathematics? Is it part of fractal geometry? Is it part of straight finance or fractal finance? These ideas seem to be almost impossible to envision. Therefore I believe that as a field fractal geometry is unlikely to continue. The extraordinary surprise that my first pictures provoked is unlikely to be continued. Many people saw them fifteen years ago, ten years ago. Now children see it on their computers when the computers do nothing else. The surprise is not there. The shock of novelty is not there. Therefore the unity that the shock of novelty, surprise, provided to all these activities will not continue. People will know about fractals earlier and earlier, more and more progressively. I think that the best future to expect and perhaps also the best future to hope for, is that fractal ideas will remain either as a peripheral or as a central tool in very many fields. I think the story of iteration will continue for a while, then probably will slow down when things get very tough and resume again when new techniques come in, and then fractal ideas will be part of that study. The same way in physics, some fields will grow- slow down because the problems become too difficult, then resume again when new ideas come or when needs arise. In other words, the unity is unlikely to be preserved. I think that the best we can hope is that in those cases where we failed, where we found that we couldn't go very far, others will soon succeed - or maybe not so soon - but others will do it not as fractalists but as mathematicians or as physicists or as economists. The thought that one unifying idea should continue forever is simply not realistic and therefore not to be hoped for, but I think that for quite a number of years still, perhaps if I am lucky to the end of my life, because I would hate to see that stop in my lifetime, those questions will become very active and still somewhat separate, as different branches of learning become accustomed to them. I cannot imagine that this idea would vanish, not because I am so proud of what I've been doing all my life, but because this is not an artificial thought coming from nowhere in no time and vanishing again rapidly in no time. It has in every one of its manifestations profound roots in the history of the various sciences and the various manners of human enterprise and those roots will not be broken. The continuity of these thoughts will continue, and if any substitute comes, if any other name comes, which is possible, the ideas will remain. Therefore from the viewpoint of the future I am both extremely optimistic and in the substance, quite relaxed about the continuation of the field as a separate endeavour. I think the same remarks apply to chaos theory in general.

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: 5 minutes, 23 seconds

Date story recorded: May 1998

Date story went live: 29 September 2010