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.
BENOIT MANDELBROTSome 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.
More Benoit Mandelbrot Quotes
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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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If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
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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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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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My fate has been that what I undertook was fully understood only after the fact.
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For much of my life there was no place where the things I wanted to investigate were of interest to anyone.
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Order doesn’t come by itself.
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A formula can be very simple, and create a universe of bottomless complexity.
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Bottomless wonders spring from simple rules, which are repeated without end.
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The theory of chaos and theory of fractals are separate, but have very strong intersections. That is one part of chaos theory is geometrically expressed by fractal shapes.
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Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.
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My life has been extremely complicated. Not by choice at the beginning at all, but later on, I had become used to complication and went on accepting things that other people would have found too difficult to accept.
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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 had very, very little training in taking an exam to determine a scientist’s life in France.
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Beautiful, damn hard, increasingly useful. That’s fractals.
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I conceived and developed a new geometry of nature and implemented its use in a number of diverse fields. It describes many of the irregular and fragmented patterns around us, and leads to full-fledged theories, by identifying a family of shapes I call fractals.
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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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The rare scholars who are nomads-by-choice are essential to the intellectual welfare of the settled disciplines.
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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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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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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 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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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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An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
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Pictures were completely eliminated from mathematics; in particular when I was young this happened in a very strong fashion.
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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
BENOIT MANDELBROT