Бенуа Мандельброт цитаты

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„Перенос чужих выводов в терминологически более изящную форму редко расценивается как научное достижение.“

„Большая часть моих трудов — это муки рождения новой научной дисциплины.“

„Самоподобие в приложении к случайным множествам — понятие не столь строгое, … так как здесь части не обязательно должны быть в точности подобны целому. Достаточно того, что части и уменьшенное в масштабе целое имеют одинаковые распределения.“

„Сингулярную составляющую большинство физиков считает абсолютно бесполезной патологией. Последнее мнение является абсолютно безосновательной чепухой.“

„Белый гауссов шум представляет собой маловразумительное гудение.“

„Я готов поспорить, что отсутствие серьёзной мотивировки в модели, которая согласуется с явлением и должным образом работает, гораздо предпочтительнее, нежели недостаток согласованности в модели, которая выглядит хорошо мотивированной; однако учёным подавай и то, и другое.“

„Незрелые идеи, высказанные слишком рано, не заслуживают ничего большего, нежели сострадательное забвение. (Стент Дж.“

„Не дόлжно судить о ценности научного открытия, исходя из причин его совершения.“

“This difficulty — am I a mathematician because my degree says so? Am I an engineer because I'm interested in things? Am I a social scientist because I don't think there's a difference between the turbulence in stock markets in terms of unpredictability? At IBM I wouldn't have to worry about that. The names of departments were totally strange and totally meaningless, so it looked like a promising situation for a short time. As it turned out I was going to spend thirty-five years and twelve days at IBM, almost from the beginning to the day when IBM decided that successful research was no longer going to be carried on in that division.”

“Being a language, mathematics may be used not only to inform but also, among other things, to seduce.”

“A cauliflower shows how an object can be made of many parts, each of which is like a whole, but smaller. Many plants are like that. 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.”

“A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension.”

“A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales…”

“My ambition was not to create a new field, but I would have welcomed a permanent group of people having interests close to mine and therefore breaking the disastrous tendency towards increasingly well-defined fields. Unfortunately, I failed on this essential point, very badly. Order doesn't come by itself.”

“Britain for a long time had a reflection of its class structure which meant that people like, well, J. B. S. Haldane who was the nephew of Lord Haldane, or Bertrand Russell who became Lord Russell, could do what they pleased, and it's interesting to think that Bertrand Russell never had a job, he never had to compete for a job. Haldane had four or five different jobs in his life, totally different. He probably could have — if he had been bothered — have just abandoned his job and went on to live otherwise. … But this no longer exists. IBM no longer exists. I don't see a place now where somebody like myself who combined, let's say, unusual gifts and unusual tastes and, who everybody said has promise, was certainly a misfit of the worst kind could find a position at this point and I think that a tragedy.”

“Georg Cantor claimed the essence of mathematics lies in its freedom. But mathematicians do not pick problems from thin air for the pleasure of solving them. To the contrary, a mark of greatness resides in the ability to identify the most interesting problems in the framework of what is already known.”

“For most of my life, one of the persons most baffled by my own work was myself.”

“I always saw a close kinship between the needs of "pure" mathematics and a certain hero of Greek mythology, Antaeus. The son of Earth, he had to touch the ground every so often in order to reestablish contact with his Mother; otherwise his strength waned. To strangle him, Hercules simply held him off the ground. Back to mathematics. Separation from any down-to-earth input could safely be complete for long periods — but not forever. In particular, the mathematical study of Brownian motion deserved a fresh contact with reality.”

“Smooth shapes are very rare in the wild but extremely important in the ivory tower and the factory, and besides were my love when I was a young man. Cauliflowers exemplify a second area of great simplicity, that of shapes which appear more or less the same as you look at them up close or from far away, as you zoom in and zoom out.
Before my work, those shapes had no use, hence no word was needed to denote them. My work created such a need and I coined "fractals."”

“Engineering is too important to wait for science.”

“There is no single rule that governs the use of geometry. I don't think that one exists.”

“My life seemed to be a series of events and accidents. Yet when I look back I see a pattern.”

“Given the profits he and Pharaoh must have made, one might call Joseph the first international arbitrageur.”

“There is a problem that is specific to financial markets. In most fields of research, when someone makes an important finding, they publish it. In the case of prices, they set up a firm and sell advice about their discovery. If they can make money from it, they will. So the research into market dynamics is a closed field.”

“I conceived, developed and applied in many areas a new geometry of nature, which finds order in chaotic shapes and processes. It grew without a name until 1975, when I coined a new word to denote it, fractal geometry, from the Latin word for irregular and broken up, fractus. Today you might say that, until fractal geometry became organized, my life had followed a fractal orbit.”

“In a different era, I would have called myself a natural philosopher. All my life, I have enjoyed the reputation of being someone who disrupted prevailing ideas. Now that I'm in my 80th year, I can play on my age and provoke people even more.”

“Unfortunately, the world has not been designed for the convenience of mathematicians.”

“I claim that many patterns of Nature are so irregular and fragmented, that, compared with Euclid — a term used in this work to denote all of standard geometry — Nature exhibits not simply a higher degree but an altogether different level of complexity … The existence of these patterns challenges us to study these forms that Euclid leaves aside as being "formless," to investigate the morphology of the "amorphous."”

“When the weather changes and hurricanes hit, nobody believes that the laws of physics have changed. Similarly, I don't believe that when the stock market goes into terrible gyrations its rules have changed. It's the same stock market with the same mechanisms and the same people.”

“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.”

“How Long Is the Coast of Britain?”

“The Mandelbrot set covers a small space yet carries a large number of different implications. Is it a fitting epitaph? Absolutely.”

“A branch of physics that I was working in for many years has lately become much less active. Many problems have been solved and others are so difficult that nobody knows what to do about them. This means that I do much less physics today than 15 years ago. By contrast, fractal tools have plenty to do. There is a joke that your hammer will always find nails to hit. I find that perfectly acceptable. The hammer I crafted is the first effective tool for all kinds of roughness and nobody will deny that there is at last some roughness everywhere.”