Johannes Kepler
INFLUENCED Nassim Nicholas Taleb NOTABLE AWARDS Légion d\'honneur (Chevalier 1990 · Officier 2006) 2003 Japan Prize 1993 Wolf Prize 1989 Harvey Prize 1986 Franklin Medal 1985 Barnard Medal SPOUSE Aliette Kagan married 1955–2010 (his death) BENOIT B. MANDELBROT (20 November 1924 – 14 October 2010) was a Polishborn, French and American mathematician with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness " of physical phenomena and "the uncontrolled element in life." He referred to himself as a "fractalist". He is recognized for his contribution to the field of fractal geometry , which included coining the word "fractal'", as well as developing a theory of "roughness and selfsimilarity " in nature.
In 1936, while he was a child, Mandelbrot's family migrated to
France. After
World War II
Because of his access to IBM's computers, Mandelbrot was one of the first to use computer graphics to create and display fractal geometric images, leading to his discovering the Mandelbrot set in 1979. He showed how visual complexity can be created from simple rules. He said that things typically considered to be "rough", a "mess" or "chaotic", like clouds or shorelines, actually had a "degree of order." His math and geometrycentered research career included contributions to such fields as statistical physics , meteorology , hydrology , geomorphology , anatomy , taxonomy , neurology , linguistics , information technology , computer graphics , economics , geology , medicine , physical cosmology , engineering , chaos theory , econophysics , metallurgy and the social sciences . Toward the end of his career, he was
Sterling Professor
CONTENTS * 1 Early years * 2 Research career * 2.1 States of randomness and financial markets * 2.2 Developing "fractal geometry" and the Mandelbrot set * 2.3 Fractals and the "theory of roughness" * 3 Awards and honors * 4 Death and legacy * 5 Bibliography * 5.1 in English * 5.2 In French * 6 References in popular culture * 7 See also * 8 Notes * 9 References * 10 Bibliography * 11 Further reading * 12 External links EARLY YEARS Mandelbrot was born in
Warsaw
The family emigrated from Poland to France in 1936, when he was 11.
"The fact that my parents, as economic and political refugees, joined
Szolem in France saved our lives," he writes. :17 Mandelbrot attended
the Lycée Rolin in Paris until the start of
World War II
Our constant fear was that a sufficiently determined foe might report us to an authority and we would be sent to our deaths. This happened to a close friend from Paris, Zina Morhange, a physician in a nearby county seat. Simply to eliminate the competition, another physician denounced her ... We escaped this fate. Who knows why? :49 In 1944, Mandelbrot returned to Paris, studied at the Lycée du Parc
in
Lyon
RESEARCH CAREER From 1949 to 1958, 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
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 . STATES OF RANDOMNESS AND FINANCIAL MARKETS Mandelbrot found that price changes in financial markets did not
follow a
Gaussian distribution
DEVELOPING "FRACTAL GEOMETRY" AND THE MANDELBROT SET As a visiting professor at
Harvard University
In 1975, Mandelbrot coined the term fractal to describe these structures and first published his ideas, and later translated, Fractals: Form, Chance and Dimension. According to mathematics scientist Stephen Wolfram , the book was a "breakthrough" for Mandelbrot, who until then would typically "apply fairly straightforward mathematics … to areas that had barely seen the light of serious mathematics before." Wolfram adds that as a result of this new research, he was no longer a "wandering scientist", and later called him "the father of fractals": Mandelbrot ended up doing a great piece of science and identifying a much stronger and more fundamental idea—put simply, that there are some geometric shapes, which he called "fractals", that are equally "rough" at all scales. No matter how close you look, they never get simpler, much as the section of a rocky coastline you can see at your feet looks just as jagged as the stretch you can see from space. Wolfram briefly describes fractals as a form of geometric repetition, "in which smaller and smaller copies of a pattern are successively nested inside each other, so that the same intricate shapes appear no matter how much you zoom in to the whole. Fern leaves and Romanesco broccoli are two examples from nature." He points out an unexpected conclusion: One might have thought that such a simple and fundamental form of regularity would have been studied for hundreds, if not thousands, of years. But it was not. In fact, it rose to prominence only over the past 30 or so years—almost entirely through the efforts of one man, the mathematician Benoit Mandelbrot. Mandelbrot used the term "fractal" as it derived from the Latin word
"fractus", defined as broken or shattered glass. Using the newly
developed
IBM
Mandelbrot, however, never felt he was inventing a new idea. He describes his feelings in a documentary with science writer Arthur C. Clarke: Exploring this set I certainly never had the feeling of invention. I never had the feeling that my imagination was rich enough to invent all those extraordinary things on discovering them. They were there, even though nobody had seen them before. It's marvelous, a very simple formula explains all these very complicated things. So the goal of science is starting with a mess, and explaining it with a simple formula, a kind of dream of science. According to Clarke, "the Mandelbrot set is indeed one of the most astonishing discoveries in the entire history of mathematics. Who could have dreamed that such an incredibly simple equation could have generated images of literally infinite complexity?" Clarke also notes an "odd coincidence:" "the name Mandelbrot, and the word "mandala "—for a religious symbol—which I'm sure is a pure coincidence, but indeed the Mandelbrot set does seem to contain an enormous number of mandalas." Mandelbrot left
IBM
FRACTALS AND THE "THEORY OF ROUGHNESS" Mandelbrot created the firstever "theory of roughness", and he saw "roughness" in the shapes of mountains, coastlines and river basins ; the structures of plants, blood vessels and lungs ; the clustering of galaxies . His personal quest was to create some mathematical formula to measure the overall "roughness" of such objects in nature. :xi He began by asking himself various kinds of questions related to nature: Can geometry deliver what the Greek root of its name seemed to promise—truthful measurement, not only of cultivated fields along the Nile River but also of untamed Earth? :xii In his paper entitled How Long Is the Coast of Britain? Statistical SelfSimilarity and Fractional Dimension published in Science in 1967 Mandelbrot discusses selfsimilar curves that have Hausdorff dimension that are examples of fractals , although Mandelbrot does not use this term in the paper, as he did not coin it until 1975. The paper is one of Mandelbrot's first publications on the topic of fractals. Mandelbrot emphasized the use of fractals as realistic and useful
models for describing many "rough" phenomena in the real world. He
concluded that "real roughness is often fractal and can be measured."
:296 Although Mandelbrot coined the term "fractal ", some of the
mathematical objects he presented in The
Fractal
The form of geometry I increasingly favored is the oldest, most concrete, and most inclusive, specifically empowered by the eye and helped by the hand and, today, also by the computer … bringing an element of unity to the worlds of knowing and feeling … and, unwittingly, as a bonus, for the purpose of creating beauty. :292 Section of a Mandelbrot set Fractals are also 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
Mandelbrot has been called a visionary and a maverick. 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
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. AWARDS AND HONORS Mandelbrot's awards include the
Wolf Prize for Physics in 1993, the
Lewis Fry Richardson Prize of the
European Geophysical Society
The small asteroid
27500 Mandelbrot was named in his honor. In
November 1990, he was made a Knight in the French
Legion of Honour
A partial list of awards received by Mandelbrot: * 2004 Best Business
Book
DEATH AND LEGACY Wikinews has related news: MATHEMATICIAN BENOîT MANDELBROT DIES AGED 85 Mandelbrot died from pancreatic cancer at the age of 85 in a hospice
in
Cambridge, Massachusetts
Chris Anderson , TED conference curator, described Mandelbrot as "an icon who changed how we see the world". Nicolas Sarkozy , President of France at the time of Mandelbrot's death, said Mandelbrot had "a powerful, original mind that never shied away from innovating and shattering preconceived notions is work, developed entirely outside mainstream research, led to modern information theory." Mandelbrot's obituary in The Economist points out his fame as "celebrity beyond the academy" and lauds him as the "father of fractal geometry". Bestselling essayistauthor Nassim Nicholas Taleb , a Mandelbrot protégé and a scientific adviser at Universa Investments , has remarked that Mandelbrot's book The (Mis)Behavior of Markets is in his opinion "The deepest and most realistic finance book ever published". BIBLIOGRAPHY IN ENGLISH * Fractals: Form, Chance and Dimension , 1977
* The
Fractal
IN FRENCH * La forme d\'une vie. Mémoires (19242010) by Benoît Mandelbrot (Author), JohanFrédérik Hel Guedj (Translator) REFERENCES IN POPULAR CULTURE In 2004, the American singersongwriter Jonathan Coulton wrote "The Mandelbrot Set", a song dedicated to Mandelbrot and his famous fractal. In 2007, the author Laura Ruby published a sequel to "The Wall and the Wing" series named "The Chaos King". One of the main characters is named Mandelbrot and his work is referenced in the novel, specifically, the chaos theory . SEE ALSO External video Family background and early education, (4:11) Benoit Mandelbrot interview, Part 1 of 144, Web of Stories * "How Long is the Coast of Britain? "
*
Louis Bachelier
*
ZipfMandelbrot law
*
Seven states of randomness
*
Skewness risk
*
Kurtosis risk
*
Fractal
*
Selfsimilarity
NOTES * ^ A B In his autobiography, Mandelbrot did not add a circumflex to the "i" (i.e. "î") in his first name. He included "B" as a middle initial . The New York Times obituary stated that "he added the middle initial himself, though it does not stand for a middle name". But other sources suggest that he intended his middle initial B. to recursively mean Benoit B. Mandelbrot, thereby including a fractal (his mathematical discovery) in his own name. * ^ Pronounced /ˈmændəlbrɒt/ MANdəlbrot in English. When speaking in French, Mandelbrot pronounced his name . REFERENCES * ^ A B C Hoffman, Jascha (16 October 2010). "Benoît Mandelbrot,
Mathematician, Dies at 85". The New York Times. Retrieved 16 October
2010.
* ^ A B LesmoirGordon, Nigel (17 October 2010). "Benoît
Mandelbrot obituary".
The Guardian
BIBLIOGRAPHY * Hudson, Richard L.; Mandelbrot, Benoît B. (2004). The
(Mis)Behavior of Markets: A
Fractal
FURTHER READING * Mandelbrot, Benoit B. (2010). The Fractalist, Memoir of a
Scientific Maverick. New York: Vintage Books, Division of Random
House. ISBN 9780307389916
* Mandelbrot, Benoît B. (1983). The
Fractal
