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My work is more varied than at any other point in my life. I am still carrying out research in pure mathematics. And I am working on an idea that I h… - Benoit Mandelbrot
" "My work is more varied than at any other point in my life. I am still carrying out research in pure mathematics. And I am working on an idea that I had several years ago on negative dimensions. … Negative dimensions are a way of measuring how empty something is. In mathematics, only one set is called empty. It contains nothing whatsoever. But I argued that some sets are emptier than others in a certain useful way. It is an idea that almost everyone greets with great suspicion, thinking I've gone soft in the brain in my old age. Then I explain it and people realise it is obvious. Now I'm developing the idea fully with a colleague. I have high hopes that once we write it down properly and give a few lectures about it at suitable places that negative dimensions will become standard in mathematics.
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About Benoit Mandelbrot
Benoît B. Mandelbrot (20 November 1924 – 14 October 2010) was a Poland-born French-American mathematician known as the "father of fractal geometry".
Biography information from Wikiquote
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Mandelbrot, B. B.
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Benoît Mandelbrot
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Benoit B. Mandelbrot
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Benoît B. Mandelbrot
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Additional quotes by Benoit Mandelbrot
"Society was not a "social pyramid" with the proportion of rich to poor sloping gently from one class to the next. Instead, it was more of a "social arrow"- very fat at the bottom where the mass of men live, and very thing at the top where sit the wealthy elite. Nor was this effect by chance; the data did not remotely fit a bell curve, as one would expect if wealth were distributed randomly. It is a social law, he wrote: something "in the nature of man.
That something, though expressed in a neat equation, is harsh and Darwinian, in Pareto's view. At the very bottom of the wealth curve, he wrote, men and women starve and children die young. In the broad middle of the curve all is turmoil and motion: people rising and falling, climbing by talent or luck and falling by alcoholism, tuberculosis, or other forms of unfitness. At the very narrow top sit the elite of the elite, who control wealth and power for a time-until they are unseated through revolution or upheaval by a new aristocratic class. There is not progress in human history. Democracy is a fraud. Human nature is primitive, emotional, unyielding. The smarter, abler, stronger, and shrewder take the lion's share. The weak starve, lest society become degenerate: One can, Pareto wrote, "compare the social body to the human body, which will promptly perish if prevented from eliminating toxins." Inflammatory stuff-and it burned Pareto's reputation. At his death in 1923, Italian fascists were beatifying him, republicans demonizing him. British philosopher Karl Popper called him the "Theoretician of totalitarianism."
My efforts over the years had been successful to the extent, to take an example, that fractals made many mathematicians learn a lot about physics, biology, and economics. Unfortunately, most were beginning to feel they had learned enough to last for the rest of their lives. They remained mathematicians, had been changed by considering the new problems I raised, but largely went their own way.
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