New Scientist has a fun article on Benoit Mandelbrot, the Yale professor most famous for discovering fractals. The article covers his discovery of fractals. his early years, his newfound research interest in the financial world, mathematics in general and his current work.
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How did you feel when you discovered it?
Its astounding complication was completely out of proportion with what I was expecting. Here is the curious thing: the first night I saw the set, it was just wild. The second night, I became used to it. After a few nights, I became familiar with it. It was as if somehow I had seen it before. Of course I hadn't. No one had seen it. No one had described it. The fact that a certain aspect of its mathematical nature remains mysterious, despite hundreds of brilliant people working on it, is the icing on the cake to me.
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Your uncle Szolem Mandelbrojt was also a mathematician. How has he influenced your life and work?
In every way imaginable. I was 13 when my uncle became professor at Collège de France in Paris. I learned early on that mathematics is an honourable profession from which you can make a living. My uncle was a pure mathematician on weekdays and a painter and fanatic museum visitor on Sundays. He had a gifted eye. But he felt that beauty and mathematics were completely separate. These two gifts probably existed in the family and I put them together, which made a big difference to my work. I could relate mathematical formulae to pictures.
Is that where the Mandelbrot set came from?
The Mandelbrot set is the modern development of a theory developed independently in 1918 by Gaston Julia and Pierre Fatou. Julia wrote an enormous book - several hundred pages long - and was very hostile to his rival Fatou. That killed the subject for 60 years because nobody had a clue how to go beyond them. My uncle didn't know either, but he said it was the most beautiful problem imaginable and that it was a shame to neglect it. He insisted that it was important to learn Julia's work and he pushed me hard to understand how equations behave when you iterate them rather than solve them. At first, I couldn't find anything to say. But later, I decided a computer could take over where Julia had stopped 60 years previously.
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How did the war affect your thinking about maths?
Until mid-1942, my education was only a little disrupted. After that, until early 1944, it was very disrupted and life was very dangerous. The winter of 1944 was awful and at the same time one of the high points of my life. During that time, it became clear that I had a peculiar gift of being able to almost instantaneously transform into geometry everything that I could handle in my head.
Has this been your prime motivation?
What motivates me now are ideas I developed 10, 20 or 30 years ago, and the feeling that these ideas may be lost if I don't push them a little bit further. Does that matter? Most ideas in science that are abandoned are picked up by someone else later, but not all. I have reflected on this issue a great deal. Perhaps I would like to finish my ideas for aesthetic reasons - a feeling of closure.
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In your book, you challenge Alan Greenspan, chairman of the Federal Reserve, and other financiers to set aside $ 20 million for fundamental research into market dynamics. Why do you feel this is necessary?
There is a problem that is specific to financial markets. In most fields of research, when someone makes an important finding, they publish it. In the case of prices, they set up a firm and sell advice about their discovery. If they can make money from it, they will. So the research into market dynamics is a closed field.
Another reason is that the research carried out so far has proved ineffective because so many fixes and twiddles are added to a theory until it works. That leaves you with a theory that is out of shape. You don't know which is more important - the thing you started with or all the fixes and twiddles. The level of theory in finance has been disappointing.
Do better theories really matter, though?
Financial risks are much underestimated. The effects of wrong business decisions are global. Nobody takes realistic measurements of risk and we should. I think we should take a strongly conservative attitude towards evaluating risks. I have lived all my life skating on thin ice, which does make you conservative. I've met stockbrokers who say that they are perfectly happy that they have judged the financial risks correctly in 95 per cent of their cases. They wonder why they should bother about a few cases that turned out wrong. Well, those are the ones that matter most - such as the Russian market crash of 1998.
I would like scientists, engineers and the whole of society to understand the true meaning of statistics. People have generally been indoctrinated to believe that the world is simpler than it is. I'd like people to understand the difference between what I call mild randomness and wild randomness. Mild randomness is the thing that everyone thinks about where things go up and down a little bit in the financial market. Wild randomness is where one bad event in the stockmarket wipes out a long period of favourable events. "
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The rest of the article is quite good and well worth the read.
ION, I placed my pre-order for Metal Gear Solid 3 today and purchased Ronin for $7.
Kinda sad. Ronin was a great movie with a superior cast and the longest car chase in a feature film. I think it clocks in at 15 minutes or something like that. A steal at twice the price.
As for Metal Gear, the reviews look very promising, but I think it's been eclipsed by GTA:San Andreas, Halo 2, Sims 2, and the upcoming Gran Turismo 4. Much like Ronin, which was eclipsed by Saving Private Ryan, Godzilla, Armageddon, and Rush Hour.
Posted by Jeffrey at November 13, 2004 1:00 AM