Frases de 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

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.

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

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

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

A Theory of Roughness (2004)
Contexto: 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.

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.

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.

The Fractal Geometry of Nature (1982), p. 1

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.

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.

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

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.

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.

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.

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

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.

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.

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.