A Fractal Life

NSCROW_13.11.04_050 06/11/04 01:06 Page 50 Interview– A fractal life Few people would recognise Benoit Mandelbrot in the street, but the intricate pattern of blobs, swirls and spikes that bears his name – the Mandelbrot set – is an icon of science. It has come to symbolise the geometry of fractals, patterns whose shape stays the same whatever scale you view them on. His life has followed a path as jagged as any fractal. Next week he turns 80. He tells Valerie Jamieson that he still has plenty of work to do What is it like seeing the Mandelbrot set yet baffles everybody, makes it attractive Benoit Mandelbrot emblazoned on T-shirts and posters? to mathematicians. The conjecture was born in I’m delighted. I always felt that science is the mathematical face of the Warsaw in 1924 to as the preserve of people from Mandelbrot set, and the T-shirts a Jewish family. Oxbridge or Ivy League universities – are the popular face. In 1936 he moved and not for the common mortal – to Paris, where his was a very bad idea. Fractals seem to appear all over nature and mathematician in economics. Even the internet is fractal. uncle had a strong Even though most people view it as a What does that say about the underlying influence on his beautiful image and ignore the underlying nature of these phenomena? education. He spent mathematics? Well, it depends on the field. much of the war That’s right. Yet there is nothing more Circles and straight lines also appear hiding in the French to this than a simple iterative formula. everywhere. Does this mean that all countryside. Later It is so simple that most children can those phenomena have something in he discovered fractal program their home computers to common? Of course not. The roughly geometry. He has produce the Mandelbrot set. circular trajectory of a planet around shown how many the sun is due to gravitational complex phenomena How did you feel when you discovered it? interactions. Berries are round because such as coastlines, Its astounding complication was a sphere has a smaller skin. The beauty galaxy clusters and completely out of proportion with of geometry is that it is a language of share prices can be what I was expecting. Here is the extraordinary subtlety that serves described as fractals. curious thing: the first night I saw the many purposes. He is Sterling Professor set, it was just wild. The second night, of Mathematical I became used to it. After a few nights, So fractals don’t point to a single rule Sciences at Yale I became familiar with it. It was as if underlying reality? University, and an somehow I had seen it before. Of course There is no single rule that governs emeritus fellow I hadn’t. No one had seen it. No one the use of geometry. I don’t think that at IBM’s Watson had described it. The fact that a certain one exists. Research Center in aspect of its mathematical nature Yorktown Heights, remains mysterious, despite hundreds Your uncle Szolem Mandelbrojt was also New York of brilliant people working on it, a mathematician. How has he influenced is the icing on the cake to me. your life and work? In every way imaginable. I was 13 when which made a big difference to my What’s the mystery? my uncle became professor at Collège work. I could relate mathematical It relates to a rather subtle de France in Paris. I learned early on formulae to pictures. mathematical property. In simple that mathematics is an honourable terms, there are two ways to define the profession from which you can Is that where the Mandelbrot set came from? Mandelbrot set. It is rather like proving make a living. My uncle was a pure The Mandelbrot set is the modern that 3+1 and 2+2 give the same result. mathematician on weekdays and development of a theory developed I have always thought that the two a painter and fanatic museum visitor independently in 1918 by Gaston Julia definitions were equivalent. But one on Sundays. He had a gifted eye. and Pierre Fatou. Julia wrote an is easy to study whereas the other is But he felt that beauty and enormous book – several hundred extremely difficult. So far, the proof mathematics were completely separate. pages long – and was very hostile to has defeated many people. The fact that These two gifts probably existed in his rival Fatou. That killed the subject my conjecture is so simple to state, the family and I put them together, for 60 years because nobody had a 50 | NewScientist | 13 November 2004 www.newscientist.com.

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