Zitate von Benoît Mandelbrot

Benoît Mandelbrot Foto
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Benoît Mandelbrot

Geburtstag: 20. November 1924
Todesdatum: 14. Oktober 2010

Benoît B. Mandelbrot war ein französisch-US-amerikanischer Mathematiker.

Mandelbrot leistete Beiträge zu einem breiten Spektrum mathematischer Probleme, einschließlich der theoretischen Physik, der Finanzmathematik und der Chaosforschung. Am bekanntesten aber wurde er als Vater der fraktalen Geometrie. Er beschrieb die Mandelbrot-Menge und prägte den Begriff „fraktal“. Mandelbrot trug selbst stark zur Popularisierung seiner Arbeiten bei, indem er Bücher schrieb und Vorlesungen hielt, die für die Allgemeinheit bestimmt waren.

Mandelbrot verbrachte die meiste Zeit seiner Karriere an IBMs Thomas J. Watson Research Center, wo er die Position eines IBM Fellows innehatte. Später wurde er Sterling Professor für Mathematik an der Yale University. Er war ferner wissenschaftlicher Mitarbeiter am Pacific Northwest National Laboratory, der Universität Lille I, dem Institute for Advanced Study und dem Centre national de la recherche scientifique. Mandelbrot lebte bis zu seinem Tode in den Vereinigten Staaten.

Zitate Benoît Mandelbrot

„Wolken sind keine Kugeln, Berge keine Kegel, Küstenlinien keine Kreise und Rinde ist nicht glatt, so wie auch der Blitz nicht auf einer Geraden unterwegs ist“

—  Benoît Mandelbrot

Benoit B. Mandelbrot, Richard L. Hudson: Fraktale und Finanzen, Helmut Reuter (Übers.), Piper Verlag, München 2007, ISBN 978-3-492-24861-7, S.180

„Die frühesten und bedeutendsten Werkzeuge der Wissenschaft entstanden, um die Leistungen unserer Sinne zu beobachten, zu messen und zu verbessern.“

—  Benoît Mandelbrot

Benoit B. Mandelbrot, Richard L. Hudson: Fraktale und Finanzen, Helmut Reuter (Übers.), Piper Verlag, München 2007, ISBN 978-3-492-24861-7, S.179

„I think it's very important to have both cartoons and more realistic structures. The cartoons have the power of representing the essential very often, but have this intrinsic weakness of being in a certain sense predictable.“

—  Benoît Mandelbrot

Segment 70
Peoples Archive interview
Kontext: I think it's very important to have both cartoons and more realistic structures. The cartoons have the power of representing the essential very often, but have this intrinsic weakness of being in a certain sense predictable. Once you look at the Sierpinski triangle for a very long time you see more consequences of the construction, but they are rather short consequences, they don't require a very long sequence of thinking. In a certain sense, the most surprising, the richest sciences are those in which we start from simple rules and then go on to very, very long trains of consequences and very long trains of consequences, which you are still predicting correctly.

„I was asking questions which nobody else had asked before, because nobody else had actually looked at certain structures.“

—  Benoît Mandelbrot

Segment 8
Peoples Archive interview
Kontext: I was asking questions which nobody else had asked before, because nobody else had actually looked at certain structures. Therefore, as I will tell, the advent of the computer, not as a computer but as a drawing machine, was for me a major event in my life. That's why I was motivated to participate in the birth of computer graphics, because for me computer graphics was a way of extending my hand, extending it and being able to draw things which my hand by itself, and the hands of nobody else before, would not have been able to represent.

„The extraordinary surprise that my first pictures provoked is unlikely to be continued. Many people saw them fifteen years ago, ten years ago. Now children see it on their computers when the computers do nothing else. The surprise is not there.“

—  Benoît Mandelbrot

Segment 144
Peoples Archive interview
Kontext: The extraordinary surprise that my first pictures provoked is unlikely to be continued. Many people saw them fifteen years ago, ten years ago. Now children see it on their computers when the computers do nothing else. The surprise is not there. The shock of novelty is not there. Therefore the unity that the shock of novelty, surprise, provided to all these activities will not continue. People will know about fractals earlier and earlier, more and more progressively. I think that the best future to expect and perhaps also the best future to hope for, is that fractal ideas will remain either as a peripheral or as a central tool in very many fields.

„He insisted that it was important to learn Julia's work and he pushed me hard to understand how equations behave when you iterate them rather than solve them.“

—  Benoît Mandelbrot

New Scientist interview (2004)
Kontext: The Mandelbrot set is the modern development of a theory developed independently in 1918 by Gaston Julia and Pierre Fatou. Julia wrote an enormous book — several hundred pages long — and was very hostile to his rival Fatou. That killed the subject for 60 years because nobody had a clue how to go beyond them. My uncle didn't know either, but he said it was the most beautiful problem imaginable and that it was a shame to neglect it. He insisted that it was important to learn Julia's work and he pushed me hard to understand how equations behave when you iterate them rather than solve them. At first, I couldn't find anything to say. But later, I decided a computer could take over where Julia had stopped 60 years previously.

„After having coined this word I sorted my own research over a very long period of time and I realised that I had been doing almost nothing else in my life.“

—  Benoît Mandelbrot

Segment 67
Peoples Archive interview
Kontext: The word fractal, once introduced, had an extraordinary integrating effect upon myself and upon many people around. Initially again it was simply a word to write a book about, but once a word exists one begins to try to define it, even though initially it was simply something very subjective and indicating my field. Now the main property of all fractals, put in very loose terms, is that each part — they're made of parts — each part is like the whole except it is smaller. After having coined this word I sorted my own research over a very long period of time and I realised that I had been doing almost nothing else in my life.

„How could it be that the same technique applies to the Internet, the weather and the stock market? Why, without particularly trying, am I touching so many different aspects of many different things?“

—  Benoît Mandelbrot

A Theory of Roughness (2004)
Kontext: How could it be that the same technique applies to the Internet, the weather and the stock market? Why, without particularly trying, am I touching so many different aspects of many different things?
A recent, important turn in my life occurred when I realized that something that I have long been stating in footnotes should be put on the marquee. I have engaged myself, without realizing it, in undertaking a theory of roughness. Think of color, pitch, heaviness, and hotness. Each is the topic of a branch of physics. Chemistry is filled with acids, sugars, and alcohols; all are concepts derived from sensory perceptions. Roughness is just as important as all those other raw sensations, but was not studied for its own sake. … I was not particularly precocious, but I'm particularly long-lived and continue to evolve even today. Above a multitude of specialized considerations, I see the bulk of my work as having been directed towards a single overarching goal: to develop a rigorous analysis for roughness. At long last, this theme has given powerful cohesion to my life … my fate has been that what I undertook was fully understood only after the fact, very late in my life.

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„When you seek some unspecified and hidden property, you don't want extraneous complexity to interfere. In order to achieve homogeneity, I decided to make the motion end where it had started. The resulting motion biting its own tail created a distinctive new shape I call Brownian cluster. … Today, after the fact, the boundary of Brownian motion might be billed as a "natural" concept. But yesterday this concept had not occurred to anyone.“

—  Benoît Mandelbrot

A Theory of Roughness (2004)
Kontext: When you seek some unspecified and hidden property, you don't want extraneous complexity to interfere. In order to achieve homogeneity, I decided to make the motion end where it had started. The resulting motion biting its own tail created a distinctive new shape I call Brownian cluster. … Today, after the fact, the boundary of Brownian motion might be billed as a "natural" concept. But yesterday this concept had not occurred to anyone. And even if it had been reached by pure thought, how could anyone have proceeded to the dimension 4/3? To bring this topic to life it was necessary for the Antaeus of Mathematics to be compelled to touch his Mother Earth, if only for one fleeting moment.

„There is a saying that every nice piece of work needs the right person in the right place at the right time. For much of my life, however, there was no place where the things I wanted to investigate were of interest to anyone.“

—  Benoît Mandelbrot

A Theory of Roughness (2004)
Kontext: There is a saying that every nice piece of work needs the right person in the right place at the right time. For much of my life, however, there was no place where the things I wanted to investigate were of interest to anyone. So I spent much of my life as an outsider, moving from field to field, and back again, according to circumstances. Now that I near 80, write my memoirs, and look back, I realize with wistful pleasure that on many occasions I was 10, 20, 40, even 50 years "ahead of my time.

„Here is the curious thing: the first night I saw the set, it was just wild. The second night, I became used to it. After a few nights, I became familiar with it. It was as if somehow I had seen it before. Of course I hadn't. No one had seen it.“

—  Benoît Mandelbrot

New Scientist interview (2004)
Kontext: There is nothing more to this than a simple iterative formula. It is so simple that most children can program their home computers to produce the Mandelbrot set. … Its astounding complication was completely out of proportion with what I was expecting. Here is the curious thing: the first night I saw the set, it was just wild. The second night, I became used to it. After a few nights, I became familiar with it. It was as if somehow I had seen it before. Of course I hadn't. No one had seen it. No one had described it. The fact that a certain aspect of its mathematical nature remains mysterious, despite hundreds of brilliant people working on it, is the icing on the cake to me.

„So limited is our knowledge that we resort, not to science, but to shamans. We place control of the world's largest economy in the hands of a few elderly men, the central bankers.“

—  Benoît Mandelbrot

Quelle: The (Mis)Behavior of Markets (2004, 2008), Ch. 13, p. 254–255
Kontext: It is beyond belief that we know so little about how people get rich or poor, about how it is they come to dwell in comfort and health or die in penury and disease. Financial markets are the machines in which much of human welfare is decided; yet we know more about how our car engines work than about how our global financial system functions. We lurch from crisis to crisis. In a networked world, mayhem in one market spreads instantaneously to all others—and we have only the vaguest of notions how this happens, or how to regulate it. So limited is our knowledge that we resort, not to science, but to shamans. We place control of the world's largest economy in the hands of a few elderly men, the central bankers.

„So important is this skill that we apply it everywhere, warranted or not.“

—  Benoît Mandelbrot

Quelle: The (Mis)Behavior of Markets (2004, 2008), Ch. 12, p. 245
Kontext: People want to see patterns in the world. It is how we evolved. We descended from those primates who were best at spotting the telltale pattern of a predator in the forest, or of food in the savannah. So important is this skill that we apply it everywhere, warranted or not.

„It is beyond belief that we know so little about how people get rich or poor, about how it is they come to dwell in comfort and health or die in penury and disease.“

—  Benoît Mandelbrot

Quelle: The (Mis)Behavior of Markets (2004, 2008), Ch. 13, p. 254–255
Kontext: It is beyond belief that we know so little about how people get rich or poor, about how it is they come to dwell in comfort and health or die in penury and disease. Financial markets are the machines in which much of human welfare is decided; yet we know more about how our car engines work than about how our global financial system functions. We lurch from crisis to crisis. In a networked world, mayhem in one market spreads instantaneously to all others—and we have only the vaguest of notions how this happens, or how to regulate it. So limited is our knowledge that we resort, not to science, but to shamans. We place control of the world's largest economy in the hands of a few elderly men, the central bankers.

„Contrary to popular opinion, mathematics is about simplifying life, not complicating it.“

—  Benoît Mandelbrot

Quelle: The (Mis)Behavior of Markets (2004, 2008), Ch. 7, p. 125
Kontext: Contrary to popular opinion, mathematics is about simplifying life, not complicating it. A child learns a bag of candies can be shared fairly by counting them out: That is numeracy. She abstracts that notion to dividing a candy bar into equal pieces: arithmetic. Then, she learns how to calculate how much cocoa and sugar she will need to make enough chocolate for fifteen friends: algebra.

„An extraordinary amount of arrogance is present in any claim of having been the first in "inventing" something. It's an arrogance that some enjoy, and others do not. Now I reach beyond arrogance when I proclaim that fractals had been pictured forever but their true role remained unrecognized and waited for me to be uncovered.“

—  Benoît Mandelbrot

A Theory of Roughness (2004)
Kontext: My book, The Fractal Geometry of Nature, reproduced Hokusai's print of the Great Wave, the famous picture with Mt. Fuji in the background, and also mentioned other unrecognized examples of fractality in art and engineering. Initially, I viewed them as amusing but not essential. But I changed my mind as innumerable readers made me aware of something strange. They made me look around and recognize fractals in the works of artists since time immemorial. I now collect such works. An extraordinary amount of arrogance is present in any claim of having been the first in "inventing" something. It's an arrogance that some enjoy, and others do not. Now I reach beyond arrogance when I proclaim that fractals had been pictured forever but their true role remained unrecognized and waited for me to be uncovered.

„A complicated phenomenon need not be fractal, but finding that a phenomenon is "not even fractal" is bad news, because so far nobody has invested anywhere near my effort in identifying and creating new techniques valid beyond fractals.“

—  Benoît Mandelbrot

A Theory of Roughness (2004)
Kontext: Do I claim that everything that is not smooth is fractal? That fractals suffice to solve every problem of science? Not in the least. What I'm asserting very strongly is that, when some real thing is found to be un-smooth, the next mathematical model to try is fractal or multi-fractal. A complicated phenomenon need not be fractal, but finding that a phenomenon is "not even fractal" is bad news, because so far nobody has invested anywhere near my effort in identifying and creating new techniques valid beyond fractals. Since roughness is everywhere, fractals — although they do not apply to everything — are present everywhere. And very often the same techniques apply in areas that, by every other account except geometric structure, are separate.

„The next thing which surprised us very much, is that both for Julia sets and even more so for the Mandelbrot set, the complication was not, how to say, arbitrary, and almost everybody found the impression that these shapes were hauntingly beautiful.“

—  Benoît Mandelbrot

Segment 85
Peoples Archive interview
Kontext: The next thing which surprised us very much, is that both for Julia sets and even more so for the Mandelbrot set, the complication was not, how to say, arbitrary, and almost everybody found the impression that these shapes were hauntingly beautiful. These shapes resulted from the most ridiculous transformation, z2+c, taken seriously, respectfully and visually. And people thought at first that they were totally wild, totally extraterrestrial, but then after a very short time, they came back and said, "You know, I think they remind me of something. I think they're natural. I think they are like perhaps nightmares or dreams, but they're natural." And this combination of being so new, because literally when we saw them nobody had seen them before, and being the next day so familiar, is still to me extraordinarily baffling.

„Lorem ipsum dolor sit amet, consectetuer adipiscing elit. Etiam egestas wisi a erat. Morbi imperdiet, mauris ac auctor dictum.“

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