Benoit Mandelbrot Benoit Mandelbrot was born in Warsaw, Poland on November 20 th, 1924 to a Lithuanian-Jewish family. Correctly sensing the geo-political turmoil forming, his family moved to France in 1936, when Benoit was 11. His uncle Szolem Mandelbrot, who succeeded Hadamard as Professor of Mathematics at the Coll ” ege de France and a member of the elite “Bourbaki”, took responsibility for Benoit’s education. It was his uncle who in 1945 introduced him to Gaston Maurice Julia’s 1918 masterpiece, “M’emoire sur l’it ” eration des fonctions rationnelles”, a 199 page treatise in which Julia, then 25 years old, described the set J (f) of those z in C for which the nth iterate f (z) stays bounded as n tends to infinity.
Mandelbrot, however, disliked it, and it disregarded the work for some thirty years, until working with his own theories, he found his attention drawn to Julia’s paper again. As a child, Mandelbrot attended the Llc ” ee Rol in in Paris until the start of World War II, when his family moved to Tulle where he received no formal education. Even though he was never taught the alphabet, nor learned multiplication tables past the fives, Mandelbrot has attributed much of his success to his varied and unconventional education. As a bizarre side note, Mandelbrot claims to be unable to use a phonebook, to this day, due to not knowing the alphabet! After World War II, Mandelbrot took the examinations for the Ecole Normale and Ecole Polytechnique, two prestigious French schools with no equivalent in American education. On his entrance exams, Mandelbrot could not do algebra very well, but still managed to receive the highest grade by, as he put it, translating the questions mentally into pictures. He soon entered the more prestigious Ecole Normale.
The Term Paper on Teacher: Early Childhood Education and Family Involvement
Family involvement matters for young children’s cognitive and social development. But what do effective involvement processes look like, and how do they occur? This research brief summarizes the latest evidence base on effective involvement—that is, the research studies that link family involvement in early childhood to outcomes and programs that have been evaluated to show what works. The ...
It was at Normale that Mandelbrot first encountered Bourbaki Mathematics, a standard set by fifty prestigious mathematicians who were working to produce a systematic mathematical method that stressed a separation of mathematics from other sciences; they shunned the use of geometry and shapes. Because of the assertions of this group, Mandelbrot fled Normale, transferring to Ecole Polytechnique within a few days. Mandelbrot received his diploma from Ecole Polytechnique, in 1947, his Master of Science in Aeronautics from the California Institute of Technology in 1948, and his Ph. D. in Mathematical Sciences from the University of Paris in 1952. He worked at the Centre National de la Recherch’e Scientific from 1949 to 1957.
Around the same time he also worked as a professor of mathematics in Geneva between 1955-1957, and at L”Ecole Polytechnique in 1957-1958. However the Mathematics of his uncle’s Bourbaki would eventually drive him away from home to pursue the developments of his gifts on his own terms. In 1958 he moved to the United States and the shelter of IBM’s research center in Yorktown Heights, New York. Working for IBM has proven to be a fruitful arrangement. Benoit has pursued is intellectual interests regardless of how “out of the way” the discipline was. Some of the areas he delved into include; linguistics, game theories, aeronautics, engineering, economics, physiology, geography, astronomy and of course physics.
Eventually he became an expert in processes with unusual statistical properties and their geometric features, which would prove to be the basis for modern fractal geometry. The turning point came with Mandelbrot’s article “How long is the coast of Britain?” published in Science magazine in 1967. In it, he suggested that the Britain’s coastline does not have a determinable length. Instead, he postulated that its longitude is relative to the resolution of measurement or scale. This demonstration gave way to other analogous discussions and explanations regarding other mathematical figures, often referred to as “pathological shapes.” It opened a floodgate of mathematicians trying to understand some natural phenomena as rivers, clouds, plants, mountain ranges, galaxies, population growth, hurricanes, electronic noise and chaotic attractors. All of which share one unifying feature: “their general patterns repeat in different scales within the same object.” (Martinez) The term “Fractal,” from the Latin root Fr actus meaning fractured or broken off, came about in the 197 o’s to help to iterate the culmination of Mandelbrot’s eclectic research: The Mandelbrot Set.
The Essay on Calls for Change in High School Mathematics
Mathematic educators, parents and students are calling for proper changes in approaches to learning mathematics in high schools. The need to improve learning of mathematics in schools is highly recognized and underlined. Thus, the National Council of Teachers of Mathematics published the Curriculum and Evaluation Standards for School Mathematics that offered recommendations for high school ...
z -> z^2 + c It is a simple looking mathematic equation with implications that are as far-reaching and limitless as the nature of the set itself. It starts with a set of randomly generated points in a complex number plane then progressing them through the sequence zn+1 = zn 2 + c. The number either tends towards infinity or ends up trapped within a commonly repeated orbit that is visible when millions of calculations are plotted on a two dimensional plane, such as a computer screen. These patterns are more than mere plotted formulae, they are recognizable formations that border on nature itself.
Their complex base beauty speaks to our very soul. We are able to recognize a repeating notion within them that at first appears random, but upon closer examination shows a much more specific and exact repetition of self-similar iterations. The part resembles the whole, and the closer we examine the occurance, the more similarities we see with the original. At first these sets were simply regarded as a new field of advanced mathematics, but in very short order, Mandelbrot and others began applying the theories to the appear ant imperfections of the real world.
As Mandelbrot said: “Fractal geometry is not just a chapter of mathematics, but one that helps Everyman to see the same world differently.” (fractal wisdom. com) Or as he said in his 1983 book The Fractal Geometry of Nature: “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.” As one of the fathers of modern Chaos Theory, Mandelbrot is on par with Einstein for the advances he has made in the world of science and mathematics. Today he is a Sterling Professor of mathematics at Yale University. He is also the Abraham Robinson Professor of Mathematical Sciences and IBM Fellow Emeritus, at the IBM T. J.
The Essay on Mathematics & Natural Sciences with absolute certainty (TOK)
Write an essay outlining your personal response to this topic. “Mathematicians have the concept of rigorous proof, which leads to knowing something with complete certainty. Consider the extent to which complete certainty might be achievable in mathematics and the natural sciences.” To what extent can man use mathematics and the natural sciences to embrace the concept of achieving absolute ...
Watson Research Center. He also lectured at the Albert Einstein College of Medicine in Physiology, and the University of Paris-Sud in Mathematics, and many others. In 1995, he served as Profess eur de l’Acad ” emi e des Sciences de Ecole Polytechnique. Some of the many awards, prizes and medals he has earned include the “Barnard Medal for Meritorious Service to Science” (1985), the Franklin Medal for Signal and Eminent Service in Science (1986), the Alexander von Humboldt Prize (1988), the Charles Proteus Steinmetz Medal (1988), the “Science for Art” Prize (1988), the Harvey Prize for Science and Technology (1989), the Nevada Prize (1991), the Wolf Prize for Physics (1993), the Honda Prize (1994), the M’edaille de Vermeil (1996), the John Scott Award (1999), the Lewis Fry Richardson Medal (1999), the Meda glia della Prezidenza della Republica Italiana (1999), and the William Procter Prize for Scientific Achievement (2002), among other awards, diplomas, grants, decorations and honorary doctorates. He’s also a member of the American Academy of Arts and Sciences; the USA National Academy of Sciences; the European Academy of Arts, Sciences and Humanities; the IBM Academy of Technology, and the Norwegian Academy of Science and Letters. (Martinez) Works Cited Fractal Wisdom.
“The Story of Benoit B. Mandelbrot and Fractal Chaos ” Fractal Chaos (2003): 27 May. GNU. “Mandelbrot Set” Wikipedia (2003): 27 May.
Exploratorium. “Benoit Mandelbrot ” Complexion (2003): 27 May. Mandelbrot, Benoit. The Fractal Geometry of Nature New York: W. H. Freeman, 1983.
Mandelbrot, Benoit. Fractals: Form, Chance and Dimension New York: W. H. Freeman, 1977. Martinez, Juan Luis. “Benoit Mandelbrot ” Third Apex to Fractovia (2003): 27 May.
New school. edu. “Benoit Mandelbrot ” The History of Economic Thought Website (2003): 27 May. Stetson University.
The Essay on The Nobel Prize And Its First Laureates
Alfred Nobel was a Swedish industrialist, and inventor. In 1866 he invented dynamite, which made him very wealthy, but he left all of his money to establish a fund for the Nobel Prize. The Nobel Prize is awarded annually for achievements during the previous year, in the categories of physics, chemistry, medicine, or physiology, literature, and the promotion of peace. Each winner receives a set ...
“Benoit Mandelbrot ” Periodic Table (2003): 27 May.
