Asking the right questions is as important as answering them
BENOIT MANDELBROTMy fate has been that what I undertook was fully understood only after the fact.
More Benoit Mandelbrot Quotes
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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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The Mandelbrot set is the most complex mathematical object known to mankind.
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Some mathematicians didn’t even perceive of the possibility of a picture being helpful. To the contrary, I went into an orgy of looking at pictures by the hundreds; the machines became a little bit better.
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It was astonishing when at one point, I got the idea of how to make artifical clouds with a collaborator, we had pictures made which were theoretically completely artificial pictures based upon that one very simple idea. And this picture everybody views as being clouds.
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Both chaos theory and fractal have had contacts in the past when they are both impossible to develop and in a certain sense not ready to be developed.
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Bottomless wonders spring from simple rules, which are repeated without end.
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There are very complex shapes which would be the same from close by and far away.
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The beauty of what I happened by extraordinary chance to put together is that nobody would have believed that this is possible, and certainly I didn’t expect that it was possible. I just moved from step to step to step.
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Think of color, pitch, loudness, heaviness, and hotness. Each is the topic of a branch of physics
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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
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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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Nobody will deny that there is at least some roughness everywhere
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I spent half my life, roughly speaking, doing the study of nature in many aspects and half of my life studying completely artificial shapes. And the two are extraordinarily close; in one way both are fractal.
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The straight line has a property of self-similarity. Each piece of the straight line is the same as the whole line when used to a big or small extent.
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When people ask me what’s my field? I say, on one hand, a fractalist. Perhaps the only one, the only full-time one.
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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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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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I didn’t want to become a pure mathematician, as a matter of fact, my uncle was one, so I knew what the pure mathematician was and I did not want to be a pure – I wanted to do something different.
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If you look at a shape like a straight line, what’s remarkable is that if you look at a straight line from close by, from far away, it is the same; it is a straight line.
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A formula can be very simple, and create a universe of bottomless complexity.
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Everything is roughness, except for the circles. How many circles are there in nature? Very, very few. The straight lines. Very shapes are very, very smooth. But geometry had laid them aside because they were too complicated.
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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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Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree.
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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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I was in an industrial laboratory because academia found me unsuitable
BENOIT MANDELBROT