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.
BENOIT MANDELBROTA 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.
More Benoit Mandelbrot Quotes
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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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Asking the right questions is as important as answering them
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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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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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A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…
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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.
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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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Beautiful, damn hard, increasingly useful. That’s fractals.
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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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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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Unfortunately, the world has not been designed for the convenience of mathematicians.
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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 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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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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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