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The ability of the model to make predictions


Interactive procedure; the Deutschmark-Dollar exchange
Benoît Mandelbrot Mathematician
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My first theory supposed independent price changes. It gave rise to prices which didn't fit at all, because they have large price changes but not their interrelation, not their bunches, not their clustering. And I refined, I tuned the idea of scaling and obtained a more powerful scaling model with fewer constraints, which gave a better fit. I must say other scientists faced with the same difficulties said that prices were not scaling. I think they were wrong. They are not scaling in a primitive fashion, which I had introduced in 1963, but they may very well be scaling in a better fashion two years later. So, in terms of general principles that I followed in all my work, this interactive procedure has proven surprisingly powerful. As a matter of fact, as a kind of icing on the cake, something astonishing happened with two very good students I had last year. We studied in great detail the Deutschmark/Dollar exchange, which has many virtues as a topic of study. It is known every minute, if you wish, for long periods of time, and known every day for very long periods of time. Therefore the range of small and larger time spans is extremely large, even by the standards of quite demanding physics. It does not have a market, which means that complications which may follow from the fact that New York has specialists and other exchanges do not have specialists, by the fact that there are some rules in different markets which are, how to say, imposed by the authority on the basis of legal requirements or tradition, these rules are absent. It is a market that is completely decentralised in the hands of a large number of people who trade all over the world. It is a market in which the daily cycle is diminished because these exchanges trade in New York, London, in Frankfurt and in Tokyo, in gigantic amounts. In between there are stock exchanges in Delhi or elsewhere which fit in. Therefore there is always a price almost any time for twenty-four hours, except for very, very short periods. So various complications that are present in economics in general, which overwhelm some other investigations very early, are there, but they are not overwhelming. They certainly require tuning and adjustment and may be extremely important from the viewpoint of actual trading procedures, because the difference between taking account of them or not may make the difference between loss and gain. But for the overall behaviour, I think that it would be very imprudent policy, both from a viewpoint of, how to say, scientific method and from a viewpoint of actual effectiveness, to put in too much too early. As a matter of fact when I give talks on this work, which I do very often at this time, almost always someone tells me, "Why didn't you put in the following fact about the stock market?" I say, "Because I don't want to put anything beyond what I know early on because perhaps I may not have to put it in. Perhaps what you want to put in deliberately is already a consequence of what has been put before." That is, to put the conjectures one by one, to study the consequences as much as that can be, and then, when they fail, to add. And to add hopefully not quantitative properties but qualitative properties, of the sort which distinguish great inequality from lack of inequality, which are called evenness, and so on and so on. I expect that this model will be much improved. It may look entirely different in a few years, but in terms of my own intellectual development, in terms of the kind of science I have learned myself to practice, I think it is a very striking example. The fact that it came early on, and inspired multifractals, and in due time multifractals inspired it, is a very strong element of unity in this enterprise.

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, 39 seconds

Date story recorded: May 1998

Date story went live: 29 September 2010