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.
BENOIT MANDELBROTIn mathematics and science definition are simple, but bare-bones. Until you get to a problem which you understand it takes hundreds and hundreds of pages and years and years of learning.
More Benoit Mandelbrot Quotes
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There are very complex shapes which would be the same from close by and far away.
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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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Bottomless wonders spring from simple rules, which are repeated without end.
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I don’t seek power and do not run around
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If you assume continuity, you can open the well-stocked mathematical toolkit of continuous functions and differential equations, the saws and hammers of engineering and physics for the past two centuries (and the foreseeable future).
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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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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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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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An extraordinary amount of arrogance is present in any claim of having been the first in inventing something.
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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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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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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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There is a saying that every nice piece of work needs the right person in the right place at the right time.
BENOIT MANDELBROT