Zitate von Benoît Mandelbrot

Benoît Mandelbrot Foto
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Benoît Mandelbrot

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

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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.

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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

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„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

„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), Context: 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.

„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
The (Mis)Behavior of Markets (2004, 2008), Context: 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. Ch. 13, p. 254–255

„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
Peoples Archive interview, Context: 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. Segment 144

„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), Context: 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.

„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), Context: 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), Context: 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
Peoples Archive interview, Context: 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. Segment 85

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„The thought that one unifying idea should continue forever is simply not realistic and therefore not to be hoped for“

—  Benoît Mandelbrot
Peoples Archive interview, Context: The thought that one unifying idea should continue forever is simply not realistic and therefore not to be hoped for, but I think that for quite a number of years still, perhaps if I am lucky to the end of my life, because I would hate to see that stop in my lifetime, those questions will become very active and still somewhat separate, as different branches of learning become accustomed to them. I cannot imagine that this idea would vanish, not because I am so proud of what I've been doing all my life, but because this is not an artificial thought coming from nowhere in no time and vanishing again rapidly in no time. It has in every one of its manifestations profound roots in the history of the various sciences and the various manners of human enterprise and those roots will not be broken. The continuity of these thoughts will continue, and if any substitute comes, if any other name comes, which is possible, the ideas will remain. Segment 144

„People want to see patterns in the world. It is how we evolved.“

—  Benoît Mandelbrot
The (Mis)Behavior of Markets (2004, 2008), Context: 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. Ch. 12, p. 245

„For many years I had been hearing the comment that fractals make beautiful pictures, but are pretty useless. I was irritated because important applications always take some time to be revealed.“

—  Benoît Mandelbrot
A Theory of Roughness (2004), Context: For many years I had been hearing the comment that fractals make beautiful pictures, but are pretty useless. I was irritated because important applications always take some time to be revealed. For fractals, it turned out that we didn't have to wait very long. In pure science, fads come and go. To influence basic big-budget industry takes longer, but hopefully also lasts longer.

„The word fractal, once introduced, had an extraordinary integrating effect upon myself and upon many people around.“

—  Benoît Mandelbrot
Peoples Archive interview, Context: 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. Segment 67

„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
Peoples Archive interview, Context: 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. Segment 70

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

—  Benoît Mandelbrot
Peoples Archive interview, Context: 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. Segment 8

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

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