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Regular geometry, the geometry of Euclid, is concerned with shapes which are smooth, except perhaps for corners and lines, special lines which are singularities, but some shapes in nature are so complicated that they are equally complicated at the big scale and come closer and closer and they don't become any less complicated.

Benoit Mandelbrot

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Benoit Mandelbrot
Age: 85 †
Born: 1924
Born: November 20
Died: 2010
Died: October 14
Computer Scientist
Economist
Engineer
Mathematician
Professor
Scientist
Writer
Warszawa
Mandelbrot
B. B.‏
Benoît Mandelbrot
Benoit B. Mandelbrot
Come
Concerned
Scale
Perhaps
Closer
Special
Equally
Lines
Scales
Euclid
Less
Corners
Singularity
Bigs
Complicated
Geometry
Nature
Shapes
Smooth
Become
Except
Regular

More quotes by Benoit Mandelbrot

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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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A formula can be very simple, and create a universe of bottomless complexity.
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The extraordinary fact is that the first idea I had which motivated me, that worked, is conjecture, a mathematical idea which may or may not be true. And that idea is still unproven. It is the foundation, what started me and what everybody failed to **** prove has so far defeated the greatest efforts by experts to be proven.
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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.
Benoit Mandelbrot
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A fractal is a way of seeing infinity.
Benoit Mandelbrot
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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.
Benoit Mandelbrot
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Everybody in mathematics had given up for 100 years or 200 years the idea that you could from pictures, from looking at pictures, find new ideas. That was the case long ago in the Middle Ages, in the Renaissance, in later periods, but then mathematicians had become very abstract.
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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.
Benoit Mandelbrot
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Engineering is too important to wait for science.
Benoit Mandelbrot
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Nobody will deny that there is at least some roughness everywhere
Benoit Mandelbrot
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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
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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 Mandelbrot
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Now that I near 80, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years ahead of my time.
Benoit Mandelbrot
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There are very complex shapes which would be the same from close by and far away.
Benoit Mandelbrot
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In 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.
Benoit Mandelbrot
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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.
Benoit Mandelbrot
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I had very, very little training in taking an exam to determine a scientist's life in France.
Benoit Mandelbrot
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There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable
Benoit Mandelbrot
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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.
Benoit Mandelbrot
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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.
Benoit Mandelbrot