Frases de Benoît Mandelbrot

Benoît Mandelbrot Foto

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Benoît Mandelbrot

Fecha de nacimiento: 20. Noviembre 1924
Fecha de muerte: 14. Octubre 2010

Benoît Mandelbrot fue un matemático conocido por sus trabajos sobre los fractales. Es considerado el principal responsable del auge de este campo de las matemáticas desde el inicio de los años setenta, así como de su popularidad al utilizar la herramienta que se estaba popularizando en ésta época - el ordenador - para trazar los más conocidos ejemplos de geometría fractal: el conjunto de Mandelbrot y los conjuntos de Julia descubiertos por Gaston Julia, quien inventó las matemáticas de los fractales, y desarrollados luego por Mandelbrot.

Frases Benoît Mandelbrot

„Las nubes no son esferas, las montañas no son conos, las líneas costeras no son círculos, y la corteza no es suave, ni los rayos viajan en línea recta.“

— Benoît Mandelbrot

Original en inglés: «Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line».
Hablando sobre los fractales y el caos.
Fuente: Frame, Michael; Mandelbrot; Benoit. Fractals, Graphics, and Mathematics Education. Volumen 58 de Mathematical Association of America Notes. Editores Michael Frame, Benoit Mandelbrot, Mathematical Association of America. Colaborador Lynn Arthur Steen. Edición ilustrada. Cambridge University Press, 2002. ISBN 9780883851692, p. 150. 206 páginas https://books.google.es/books?id=Wz7iCaiB2C0C&pg=PA200&dq=9780883851692&hl=es&sa=X&ved=0ahUKEwi-pduiqb_hAhUm3uAKHXlBDgIQ6AEIKDAA#v=snippet&q=Clouds%20are%20not%20spheres%2C%20mountains%20are%20not%20cones%2C&f=false

„Me encontré en la posición de ese niño de un cuento que ve un trozo de cuerda y, por curiosidad, tira de ella para descubrir que era solo la punta de una cuerda muy larga y cada vez más gruesa … y seguí mostrando maravillas más allá del cálculo de cuentas.“

— Benoît Mandelbrot

Original en inglés: «I found myself in the position of that child in a story who noticed a bit of string and - out of curiosity - pulled on it to discover that it was just the tip of a very long and increasingly thick string...and kept bringing out wonders beyond reckoning».
Fuente: Mandelbrot, Benoit. The Fractalist: Memoir of a Scientific Maverick. Página 150. Knopf Doubleday Publishing Group, 2012. ISBN 9780307378606. 352 páginas. https://books.google.es/books?id=o7Vo7sG-6FgC&pg=PA64&dq=9780307378606&hl=es&sa=X&ved=0ahUKEwjFvPe1lcDhAhUGExoKHRkUA8oQ6AEIKDAA#v=onepage&q=I%20found%20myself%20in%20the%20position%20of%20that%20child%20in%20a%20story%20&f=false

„Para una persona que piensa, la enfermedad mental más grave es no estar seguro de quién es.“

— Benoît Mandelbrot

Original en inglés: «For a thinking person, the most serious mental illness is not being sure of who you are».
Fuente: Mandelbrot, Benoit. The Fractalist: Memoir of a Scientific Maverick. Editor Knopf Doubleday Publishing Group, 2012. ISBN 9780307378606. 352 páginas. https://books.google.es/books?id=o7Vo7sG-6FgC&dq=For+a+thinking+person,+the+most+serious+mental+illness+is+not+being+sure+of+who+you+are&hl=es&source=gbs_navlinks_s

De enfermedades

„(*) «La acuñé yo, porque me preocupaba que la misma palabra posea múltiples significados en matemáticas. Distribución, por ejemplo. Se me asocia a menudo con el caos, otro término sobrecargado porque no tiene nada que ver con el descrito en la Biblia. Quería recoger la impresión de una piedra que golpeas, y se fractura. De ese fractus latín surgió el fractal. La terminación se debió a que quería que funcionara en inglés y francés.»“

— Benoît Mandelbrot

Refiriéndose a la palabra 'fractal'
Fuente: Entrevista para El Diario de Mallorca http://www.diariodemallorca.es/secciones/noticia.jsp?pNumEjemplar=1285&pIdSeccion=13&pIdNoticia=208932

„Con demasiada frecuencia, la importancia de un evento no se reconoce hasta que es demasiado tarde para un registro adecuado.“

— Benoît Mandelbrot

Original en inglés: «Too often, an event’s importance is not recognized until it is too late for proper recording».
Fuente: Mandelbrot, Benoit. The Fractalist: Memoir of a Scientific Maverick. Página 4. Knopf Doubleday Publishing Group, 2012. ISBN 9780307378606. 352 páginas. https://books.google.es/books?id=o7Vo7sG-6FgC&pg=PA64&dq=9780307378606&hl=es&sa=X&ved=0ahUKEwjFvPe1lcDhAhUGExoKHRkUA8oQ6AEIKDAA#v=onepage&q=Too%20often%2C%20an%20event%E2%80%99s%20importance%20is%20not%20recognized%20until%20it%20is%20too%20late%20for%20proper%20recording&f=false

„Mi vida parecía ser una serie de sucesos y accidentes. Sin embargo, cuando miro hacia atrás, veo un patrón.“

— Benoît Mandelbrot

Original en inglés: «My life seemed to be a series of events and accidents. Yet when I look back, I see a pattern».
Fuente: New Scientist, volumen 184,números 2472-2480. Editor IPC Magazines, 2004. Página 51.

„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.“

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— Benoît Mandelbrot

Segment 144
Peoples Archive interview
Contexto: 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.“

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— Benoît Mandelbrot

New Scientist interview (2004)
Contexto: 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.

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

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— Benoît Mandelbrot

Fuente: The (Mis)Behavior of Markets (2004, 2008), Ch. 7, p. 125
Contexto: 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.

„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.“

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— Benoît Mandelbrot

Segment 67
Peoples Archive interview
Contexto: 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.

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„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?“

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— Benoît Mandelbrot

A Theory of Roughness (2004)
Contexto: 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.

„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.“

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— Benoît Mandelbrot

A Theory of Roughness (2004)
Contexto: 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.“

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— Benoît Mandelbrot

A Theory of Roughness (2004)
Contexto: 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.“

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— Benoît Mandelbrot

New Scientist interview (2004)
Contexto: 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.

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

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— Benoît Mandelbrot

Fuente: The (Mis)Behavior of Markets (2004, 2008), Ch. 12, p. 245
Contexto: 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.

„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.“

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— Benoît Mandelbrot

A Theory of Roughness (2004)
Contexto: 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.

„Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.“

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— Benoît Mandelbrot, libro The Fractal Geometry of Nature

The Fractal Geometry of Nature (1982)
Contexto: Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line. <!-- ** p. 1

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

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— Benoît Mandelbrot

Segment 144
Peoples Archive interview
Contexto: 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.

„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.“

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— Benoît Mandelbrot

Segment 85
Peoples Archive interview
Contexto: 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.

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

Help us translate this quote

— Benoît Mandelbrot

Fuente: The (Mis)Behavior of Markets (2004, 2008), Ch. 12, p. 245
Contexto: 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.

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

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