Benoit Mandelbrot Quotes
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Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.
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My life seemed to be a series of events and accidents. Yet when I look back I see a pattern.
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Humanity has known for a long time what fractals are. It is a very strange situation in which an idea which each time I look at all documents have deeper and deeper roots, never (how to say it), jelled.
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Many painters had a clear idea of what fractals are. Take a French classic painter named Poussin. Now, he painted beautiful landscapes, completely artificial ones, imaginary landscapes. And how did he choose them? Well, he had the balance of trees, of lawns, of houses in the distance. He had a balance of small objects, big objects, big trees in front and his balance of objects at every scale is what gives to Poussin a special feeling.
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I had many books and I had dreams of all kinds. Dreams in which were in a certain sense, how to say, easy to make because the near future was always extremely threatening.
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I spent my time very nicely in many ways, but not fully satisfactory. Then I became Professor in France, but realized that I was not - for the job that I should spend my life in.
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I was asking questions which nobody else had asked before, because nobody else had actually looked at certain structures. Therefore, as I will tell, the advent of the computer, not as a computer but as a drawing machine, was for me a major event in my life. That's why I was motivated to participate in the birth of computer graphics, because for me computer graphics was a way of extending my hand, extending it and being able to draw things which my hand by itself, and the hands of nobody else before, would not have been able to represent.
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In fact, I barely missed being number one in France in both schools. In particular I did very well in mathematical problems.
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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.
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A fractal is a way of seeing infinity.
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Unfortunately, the world has not been designed for the convenience of mathematicians.
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There is a saying that every nice piece of work needs the right person in the right place at the right time.
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If one takes the kinds of risks which I took, which are colossal, but taking risks, I was rewarded by being able to contribute in a very substantial fashion to a variety of fields. I was able to reawaken and solve some very old problems.
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When the weather changes and hurricanes hit, nobody believes that the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed. It's the same stock market with the same mechanisms and the same people.
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The most complex object in mathematics, the Mandelbrot Set ... is so complex as to be uncontrollable by mankind and describable as 'chaos'.
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Although computer memory is no longer expensive, there's always a finite size buffer somewhere. When a big piece of news arrives, everybody sends a message to everybody else, and the buffer fills
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I went to the computer and tried to experiment. I introduced a very high level of experiment in very pure mathematics.
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A formula can be very simple, and create a universe of bottomless complexity.
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I didn't feel comfortable at first with pure mathematics, or as a professor of pure mathematics. I wanted to do a little bit of everything and explore the world.
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One couldn't even measure roughness. So, by luck, and by reward for persistence, I did found the theory of roughness, which certainly I didn't expect and expecting to found one would have been pure madness.
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A cauliflower shows how an object can be made of many parts, each of which is like a whole, but smaller. Many plants are like that. A cloud is made of billows upon billows upon billows that look like clouds. As you come closer to a cloud you don't get something smooth but irregularities at a smaller scale.
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Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory.
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Nobody will deny that there is at least some roughness everywhere
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The existence of these patterns [fractals] challenges us to study forms that Euclid leaves aside as being formless, to investigate the morphology of the amorphous. Mathematicians have disdained this challenge, however, and have increasingly chosen to flee from nature by devising theories unrelated to anything we can see or feel.