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Benoît Mandelbrot

Mandelbrot in 2007
Born 20 November 1924 (1924-11-20) (age 85)
Warsaw, Poland
Residence France; United States
Nationality French, US
Fields Mathematician
Institutions Yale University
International Business Machines (IBM)
Pacific Northwest National Laboratory
Alma mater École Polytechnique
California Institute of Technology
University of Paris
Doctoral students F. Kenton Musgrave
Eugene F. Fama
among others
Known for Mandelbrot set
Notable awards Wolf Prize (1993)
Japan Prize (2003)

Benoît B. Mandelbrot[1] (born 20 November 1924) is a French and American mathematician, best known as the father of fractal geometry. He is Sterling Professor of Mathematical Sciences, Emeritus at Yale University; IBM Fellow Emeritus at the Thomas J. Watson Research Center; and Battelle Fellow at the Pacific Northwest National Laboratory. Mandelbrot was born in Poland. His family moved to France when he was a child, and he was educated in France. He is a dual French and American citizen. Mandelbrot now lives and works in the United States.

Contents

Early years

Mandelbrot was born in Warsaw in a Jewish family from Lithuania. Anticipating the threat posed by Nazi Germany, the family fled from Poland to France in 1936 when he was 11. He remained in France through the war to near the end of his college studies. He was born into a family with a strong academic tradition—his mother was a medical doctor and he was introduced to mathematics by two uncles. His uncle, Szolem Mandelbrojt, was a Parisian mathematician. His father, however, made his living trading clothing.[2] Mandelbrot attended the Lycée Rolin in Paris until the start of World War II, when his family moved to Tulle. He was helped by Rabbi David Feuerwerker, the Rabbi of Brive-la-Gaillarde, to continue his studies. In 1944 he returned to Paris. He studied at the Lycée du Parc in Lyon and in 1945-47 attended the École Polytechnique, where he studied under Gaston Julia and Paul Lévy. From 1947 to 1949 he studied at California Institute of Technology where he studied aeronautics. Back in France, he obtained a Ph.D. in Mathematical Sciences at the University of Paris in 1952.[2]

From 1949 to 1957 Mandelbrot was a staff member at the Centre National de la Recherche Scientifique. During this time he spent a year at the Institute for Advanced Study in Princeton, New Jersey where he was sponsored by John von Neumann. In 1955 he married Aliette Kagan and moved to Geneva, Switzerland then Lille, France.[3]

In 1958 the couple moved to the United States where Mandelbrot joined the research staff at the IBM Thomas J. Watson Research Center in Yorktown Heights, New York.[3] He remained at IBM for thirty-two years, becoming an IBM Fellow, and later Fellow Emeritus.[2]

Later years

Mandelbrot speaking at the École Polytechnique in 2006, during the ceremony when he was made an officer of the Legion of Honour.

From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as information theory, economics, and fluid dynamics. He became convinced that two key themes, fat tails and self-similar structure, ran through a multitude of problems encountered in those fields.

Mandelbrot found that price changes in financial markets did not follow a Gaussian distribution, but rather Lévy stable distributions having theoretically infinite variance. He found, for example, that cotton prices followed a Lévy stable distribution with parameter α equal to 1.7 rather than 2 as in a Gaussian distribution. "Stable" distributions have the property that the sum of many instances of a random variable follows the same distribution but with a larger scale parameter.[4]

Mandelbrot also put his ideas to work in cosmology. He offered in 1974 a new explanation of Olbers' Paradox (the "dark night sky" riddle), demonstrating the consequences of fractal theory as a sufficient, but not necessary, resolution of the paradox. He postulated that if the stars in the universe were fractally distributed (for example, like Cantor dust), it would not be necessary to rely on the Big Bang theory to explain the paradox. His model would not rule out a Big Bang, but would allow for a dark sky even if the Big Bang had not occurred.

In 1975, Mandelbrot coined the term fractal to describe these structures, and published his ideas in Les objets fractals, forme, hasard et dimension (1975; an English translation Fractals: Form, Chance and Dimension was published in 1977).[5] Mandelbrot developed here ideas from the article Deux types fondamentaux de distribution statistique[6] (1938; an English translation Two Basic Types of Statistical Distribution) of Czech geographer, demographer and statistician Jaromír Korčák.

The Mandelbrot set and periodicities of orbits.

While on secondment as Visiting Professor of Mathematics at Harvard University in 1979, Mandelbrot began to study fractals called Julia sets that were invariant under certain transformations of the complex plane. Building on previous work by Gaston Julia and Pierre Fatou, Mandelbrot used a computer to plot images of the Julia sets of the formula z² − μ. While investigating how the topology of these Julia sets depended on the complex parameter μ he studied the Mandelbrot set fractal that is now named after him. (Note that the Mandelbrot set is now usually defined in terms of the formula z² + c, so Mandelbrot's early plots in terms of the earlier parameter μ are left–right mirror images of more recent plots in terms of the parameter c.)

In 1982, Mandelbrot expanded and updated his ideas in The Fractal Geometry of Nature.[7] This influential work brought fractals into the mainstream of professional and popular mathematics, as well as silencing critics, who had dismissed fractals as "program artifacts".

Upon his retirement from IBM in 1987, Mandelbrot joined the Yale Department of Mathematics. At the time of his retirement in 2005, he was Sterling Professor of Mathematical Sciences. His awards include the Wolf Prize for Physics in 1993, the Lewis Fry Richardson Prize of the European Geophysical Society in 2000, the Japan Prize in 2003, and the Einstein Lectureship of the American Mathematical Society in 2006. The small asteroid 27500 Mandelbrot was named in his honor. In November 1990, he was made a Knight in the French Legion of Honour. In December 2005, Mandelbrot was appointed to the position of Battelle Fellow at the Pacific Northwest National Laboratory.[8] Mandelbrot was promoted to Officer of the French Legion of Honour in January 2006.[9]

Fractals and regular roughness

Although Mandelbrot coined the term fractal, some of the mathematical objects he presented in The Fractal Geometry of Nature had been described by other mathematicians. Before Mandelbrot, they had been regarded as isolated curiosities with unnatural and non-intuitive properties. Mandelbrot brought these objects together for the first time and turned them into essential tools for the long-stalled effort to extend the scope of science to non-smooth objects in the real world. He highlighted their common properties, such as self-similarity (linear, non-linear, or statistical), scale invariance, and a (usually) non-integer Hausdorff dimension.

He also emphasized the use of fractals as realistic and useful models of many "rough" phenomena in the real world. Natural fractals include the shapes of mountains, coastlines and river basins; the structures of plants, blood vessels and lungs; the clustering of galaxies; and Brownian motion. Fractals are found in human pursuits, such as music, painting, architecture, and stock market prices. Mandelbrot believed that fractals, far from being unnatural, were in many ways more intuitive and natural than the artificially smooth objects of traditional Euclidean geometry:

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.
  —Mandelbrot, in his introduction to The Fractal Geometry of Nature

Fractal geometry is useful to accurately describe the development and resulting shape of many growth processes evident in nature, both organic and inorganic. Mandelbrot's work has changed the way researchers in many fields both perceive and characterize the phenomenon of natural growth.

A limb of a maple tree, illustrating organic fractal branching.
Natural water frost crystal growth on cold glass, showing fractal branching growth in a purely physical system.

Mandelbrot has been called a visionary[10] and a maverick.[11] His informal and passionate style of writing and his emphasis on visual and geometric intuition (supported by the inclusion of numerous illustrations) made The Fractal Geometry of Nature accessible to non-specialists. The book sparked widespread popular interest in fractals and contributed to chaos theory and other fields of science and mathematics.

Mandel zoom 00 mandelbrot set.jpg Mandel zoom 01 head and shoulder.jpg Mandel zoom 02 seehorse valley.jpg Mandel zoom 03 seehorse.jpg Mandel zoom 04 seehorse tail.jpg
Mandel zoom 05 tail part.jpg Mandel zoom 06 double hook.jpg Mandel zoom 07 satellite.jpg Mandel zoom 08 satellite antenna.jpg Mandel zoom 09 satellite head and shoulder.jpg
Mandel zoom 10 satellite seehorse valley.jpg Mandel zoom 11 satellite double spiral.jpg Mandel zoom 12 satellite spirally wheel with julia islands.jpg Mandel zoom 13 satellite seehorse tail with julia island.jpg Mandel zoom 14 satellite julia island.jpg
Views of the Mandelbrot set.

Honors and awards

A partial list of awards received by Mandelbrot:[12]

  • 2004 Best Business Book of the Year Award
  • AMS Einstein Lectureship
  • Barnard Medal
  • Caltech Service
  • Casimir Frank Natural Sciences Award
  • Charles Proteus Steinmetz Medal
  • Franklin Medal
  • Harvey Prize
  • Honda Prize
  • Humboldt Preis
  • IBM Fellowship
  • Japan Prize
  • John Scott Award
  • Lewis Fry Richardson Medal
  • Medaglia della Presidenza della Repubblica Italiana
  • Médaille de Vermeil de la Ville de Paris
  • Nevada Prize
  • Science for Art
  • Sven Berggren-Priset
  • Władysław Orlicz Prize
  • Wolf Foundation Prize for Physics

See also

Notes and references

  1. ^ Benoît is pronounced [bənwa] in French. The English pronunciation of the name "Mandelbrot", which is a Yiddish and German word meaning "almond bread", is given variously in dictionaries. The Oxford English Dictionary gives /ˈmændəlbrɒt/ MAN-dl-brot; Merriam-Webster Collegiate Dictionary and the Longman Pronouncing Dictionary give /ˈmændəlbroʊt/ MAN-dl-broht; the Bollard Pronouncing Dictionary of Proper Names gives the pseudo-French pronunciation /ˈmændəlbrɔː/ MAN-dl-braw; and the American Heritage Dictionary gives /ˈmɑːndəlbrɒt/ MAHN-dl-brot. When speaking in French, Mandelbrot pronounces his name [mɑ̃dɛlbʁot]. (Source: recording of the September 11, 2006, ceremony at which Mandelbrot received the Officer of the Legion of honour insignia.)
  2. ^ a b c Mandelbrot, Benoit (2002), "A maverick's apprenticeship", The Wolf Prizes for Physics, Imperial College Press, http://www.math.yale.edu/mandelbrot/web_pdfs/mavericksApprenticeship.pdf 
  3. ^ a b Barcellos, Anthony (1984), "Interview Of B. B. Mandelbrot", Mathematical People, Birkhaüser, http://www.math.yale.edu/mandelbrot/web_pdfs/inHisOwnWords.pdf 
  4. ^ New Scientist, 19 April 1997
  5. ^ Fractals: Form, Chance and Dimension, by Benoît Mandelbrot; W H Freeman and Co, 1977; ISBN 0716704730
  6. ^ Jaromír Korčák (1938): Deux types fondamentaux de distribution statistique. Prague, Comité d’organisation, Bull. de l'Institute Int'l de Statistique, vol. 3, pp. 295–299.
  7. ^ The Fractal Geometry of Nature, by Benoît Mandelbrot; W H Freeman & Co, 1982; ISBN 0716711869
  8. ^ PNNL press release: Mandelbrot joins Pacific Northwest National Laboratory
  9. ^ Légion d'honneur announcement of promotion of Mandelbrot to officier
  10. ^ Devaney, Robert L. (2004). ""Mandelbrot’s Vision for Mathematics" in Proceedings of Symposia in Pure Mathematics. Volume 72.1". American Mathematical Society. http://www.math.yale.edu/mandelbrot/web_pdfs/jubileeletters.pdf. Retrieved 2007-01-05. 
  11. ^ Jersey, Bill (April 24, 2005). "A Radical Mind". Hunting the Hidden Dimension. NOVA/ PBS. http://www.pbs.org/wgbh/nova/fractals/mandelbrot.html. Retrieved 2009-08-20. 
  12. ^ Mandelbrot, Benoit B. (2 February 2006). "Vita and Awards (Word document)". http://www.math.yale.edu/mandelbrot/web_docs/VitaSeveralPage.doc. Retrieved 2007-01-06. 

Further reading

External links

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Quotes

Up to date as of January 14, 2010

From Wikiquote

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.

Benoît B. Mandelbrot (born 20 November 1924) is a Poland-born French-American mathematician known as the "father of fractal geometry".

Contents

Sourced

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."
  • Being a language, mathematics may be used not only to inform but also, among other things, to seduce.
    • Fractals : Form, chance and dimension (1977)
  • A fractal is a mathematical set or concrete object that is irregular or fragmented at all scales...
    • As quoted in a review of The Fractal Geometry of Nature by J. W. Cannon in The American Mathematical Monthly, Vol. 91, No. 9 (November 1984), p. 594
  • 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."
    • As quoted in a review of The Fractal Geometry of Nature by J. W. Cannon in The American Mathematical Monthly, Vol. 91, No. 9 (November 1984), p. 594
  • 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.
    • As quoted in Encyclopedia of World Biography (1997) edited by Thomson Gale
  • For most of my life, one of the persons most baffled by my own work was myself.
    • Lecture at the University of Maryland (March 2005)
If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
  • If you have a hammer, use it everywhere you can, but I do not claim that everything is fractal.
    • As quoted in "Fractal Finance" by Greg Phelan in Yale Economic Review (Fall 2005)

The Fractal Geometry of Nature (1982)

Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.
  • 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.
  • Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.

New Scientist interview (2004)

Quotations from "A Fractal Life" by Valerie Jamieson in New Scientist (November 2004)
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.
  • I always felt that science as the preserve of people from Oxbridge or Ivy League universities — and not for the common mortal — was a very bad idea.
There is no single rule that governs the use of geometry. I don't think that one exists.
  • 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.
  • There is no single rule that governs the use of geometry. I don't think that one exists.
  • 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.
  • My life seemed to be a series of events and accidents. Yet when I look back I see a pattern.
  • What motivates me now are ideas I developed 10, 20 or 30 years ago, and the feeling that these ideas may be lost if I don't push them a little bit further.
The Mandelbrot set covers a small space yet carries a large number of different implications...
  • The most important thing I have done is to combine something esoteric with a practical issue that affects many people. In this spirit, the stock market is one of the most attractive things imaginable. Stock-market data is abundant so I can check everything. Financial markets are very influential and I want to be part of this field now that it is maturing.
  • 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.
  • 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.
  • 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.
  • The Mandelbrot set covers a small space yet carries a large number of different implications. Is it a fitting epitaph? Absolutely.

A Theory of Roughness (2004)

Interview at The Edge (20 December 2004)
The notion that these conjectures might have been reached by pure thought — with no picture — is simply inconceivable.
  • 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.
  • 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.
  • My efforts over the years had been successful to the extent, to take an example, that fractals made many mathematicians learn a lot about physics, biology, and economics. Unfortunately, most were beginning to feel they had learned enough to last for the rest of their lives. They remained mathematicians, had been changed by considering the new problems I raised, but largely went their own way.
  • 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.
  • One of my conjectures was solved in six months, a second in five years, a third in ten. But the basic conjecture, despite heroic efforts rewarded by two Fields Medals, remains a conjecture, now called MLC: the Mandelbrot Set is locally connected. The notion that these conjectures might have been reached by pure thought — with no picture — is simply inconceivable.
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?
  • 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.
  • 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.
The infinite sea of complexity includes two islands: one of Euclidean simplicity, and also a second of relative simplicity in which roughness is present, but is the same at all scales.
  • 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.
  • To appreciate the nature of fractals, recall Galileo's splendid manifesto that "Philosophy is written in the language of mathematics and its characters are triangles, circles and other geometric figures, without which one wanders about in a dark labyrinth." Observe that circles, ellipses, and parabolas are very smooth shapes and that a triangle has a small number of points of irregularity. Galileo was absolutely right to assert that in science those shapes are necessary. But they have turned out not to be sufficient, "merely" because most of the world is of infinitely great roughness and complexity. However, the infinite sea of complexity includes two islands: one of Euclidean simplicity, and also a second of relative simplicity in which roughness is present, but is the same at all scales.
  • 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.
  • 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."
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.
  • 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.
  • 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.
  • 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.
  • 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.

The (Mis)Behavior of Markets (2004, 2008)

With Richard L. Hudson. Second edition, 2008, ISBN 0465043577
Unfortunately, the world has not been designed for the convenience of mathematicians.
People want to see patterns in the world. It is how we evolved … So important is this skill that we apply it everywhere, warranted or not.
  • Unfortunately, the world has not been designed for the convenience of mathematicians.
    • Ch. 2, p. 41
  • 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.
    • Ch. 7, p. 125
  • Given the profits he and Pharaoh must have made, one might call Joseph the first international arbitrageur.
    • Ch. 10, p. 201 (A reference to Genesis 41:48–49, 54–57.)
  • 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
  • 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

Peoples Arcive interview

Interview at Peoples Archive (Video and transcripts in 144 segments)
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.
The cartoons have the power of representing the essential very often, but have this intrinsic weakness of being in a certain sense predictable.
  • 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
  • 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.
    • Segment 44
  • 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.
    • Segment 45
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.
  • 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. 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
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. 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
  • 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
  • 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

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