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Power-Law Distribution


Work with Philips: spectral analysis and colour televisions
Benoît Mandelbrot Mathematician
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My father again took matters in his hand, and I emphasise the influence of these two men, my father and uncle, who at different times took my affairs in their hands. My father had become worried, about this, not his business, by my not deciding what to do, about my being overly demanding. At that time Philips of Eindhoven were establishing a laboratory in Paris; they were advertising for a person to help them, and I volunteered, I mean I responded to the ad. They hired me, essentially, on the spot. In fact they were quite right to hire me because it was a very interesting time in many ways. I had had substantial experience with spectral analysis, not as mathematical theory, even though my uncle had given me lessons about mathematics, but as a tool to study turbulence. Not a very good tool, but never mind. I know what spectral analysis was. It was not formulas, it was 'stuff '; you divide a signal into its components and looked at the components. It was a very concrete way of looking at it. And what Philips was bothered by then was the coming of colour television. Now, there was this process, which was in a certain sense the best, and the worst of all things the National Television Standards Committee, NTSC standard, which was being proposed by RCA and General Electric. There was a different system proposed by CBS which was just having a filter in front - a gigantic machine, it would have been a disaster to do it - but very simply, the people at Philips did not understand what RCA and GE were on about, and I understood it because I had a feeling about spectral analysis. In fact, my feeling improved, and I would like to say a few words because in some sense it's an amazing piece of engineering. They observed that if you divide the signal into three, green, blue and red, the eye perceives the green signal with great precision, and the red and blue with very low precision. So if you make the three signals equally sharp it's wasteful because the eye does not know that the red and the blue signals are so sharp. So the green signal had to be very sharp, and the others can be less so. Also they looked at the spectrum, at the actual osculation of spectrum by the signal of television; they observed that the green signal had big holes, that is, patches where the level is very low; and that if you took everything out, made it zero, it didn't make much difference to the signal. So this brave mind put the red and blue signal in the holes of the green signal. Now, that was very acrobatic! I was the expert on spectral analysis for a while. When, later on, colour television came to be, I was an absolute skeptic. I said, "I've seen this thing, how it works. It will never work!" We had such pain to make this machine work in the lab, I was absolutely amazed when they started being sold by the million, and then a little bit of tweaking of this NTSC made the TV we had which is - well, not the best but still a miracle of technology. So this was the reason why Philips was interested in me, and I think I performed this particular duty, and for the rest Philips did not know what to do with me. So I decided to look for another Ph.D. subject.

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, 56 seconds

Date story recorded: May 1998

Date story went live: 24 January 2008