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Interaction between work in physics and economics (Part 2)


Interaction between work in physics and economics (Part 1)
Benoît Mandelbrot Mathematician
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Now by the time that events were bringing me back into economics and finance, another phenomenon had occurred, so I would like to come back also to underline the 'back and forth' interaction between my work in physics and my work in economics. At the end of my first paper on multifractals, the purpose of which was to represent the intermittency of turbulence, I had a paragraph saying that this model, this scenario, namely multifractals, involves a kind of variation that is very much reminiscent of economics, and that I hope on a better occasion to explore it. That was in 1972. I didn't explore it again for many, many years, but the seed of the idea was present there in a very strong fashion. And what was the seed? That in turbulence, effects come in gusts. There is no very clear intensity of wind, there are big puffs of wind, of dissipation, then low dissipation, then again big puffs, extremely big puffs. The bulk of dissipation actually does not occur in the big puffs; it occurs in middle-size puffs and it is something very, very important but outside of our concern. However the fact that I had learned with multifractals to deal with phenomena that presented together the two features that I previously studied separately was fundamental. And let me define those features in the vocabulary I used in the context of a river's variation. Instantaneous changes remind me of the Bible, the forty days and forty nights. You would say that was not an instantaneous change, but many of these discontinuities of the economy are not individual changes but bunches of changes, which together to make an enormous difference. I called that the Noah effect. Sequences of very high and very low level cycles are present in the weather, they are present, certainly very strongly, in the levels and discharges of the Nile river - these are called the Joseph effect because of the story of Joseph, son of Jacob, seven fat years, seven lean years - and the two effects were easier to study separately. That is, if I neglected the Joseph effect, the dependence, and looked only at changes, I could get a quite reasonable fit for some data, which were mostly governed by the large changes. I'll call them margin dependent. If I neglect the big margins and looked only at dependence, I could also model very well, by the same methods I had been using for modelling the weather and the River Nile. But the great difficulty represented by the reality of finance is that the two effects are present simultaneously. And again the multifractal which I developed in the late '60s and early '70s provided the key, but I didn't use this key until much, much later, that is in the last few years.

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, 36 seconds

Date story recorded: May 1998

Date story went live: 29 September 2010