Benoit B. Mandelbrot was a Polish-born and American mathematician and polymath with broad interests in the practical sciences 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" and 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 self-similarity" in nature. In 1936, while he was a child, Mandelbrot's family emigrated to France from Poland. After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and the United States and receiving a master's degree in aeronautics from the California Institute of Technology, he spent most of his career in both the United States and France, having dual French and American citizenship. In 1958, he began a 35-year career at IBM, where he became an IBM Fellow, periodically took leaves of absence to teach at Harvard University.
At Harvard, following the publication of his study of U. S. commodity markets in relation to cotton futures, he applied sciences. 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 discovery of the Mandelbrot set in 1980, he showed. He said that things considered to be "rough", a "mess" or "chaotic", like clouds or shorelines had a "degree of order", his math and geometry-centered research career included contributions to such fields as statistical physics, hydrology, anatomy, neurology, information technology, computer graphics, geology, physical cosmology, chaos theory, econophysics and the social sciences. Toward the end of his career, he was Sterling Professor of Mathematical Sciences at Yale University, where he was the oldest professor in Yale's history to receive tenure. Mandelbrot held positions at the Pacific Northwest National Laboratory, Université Lille Nord de France, Institute for Advanced Study and Centre National de la Recherche Scientifique.
During his career, he received over 15 honorary doctorates and served on many science journals, along with winning numerous awards. His autobiography, The Fractalist: Memoir of a Scientific Maverick, was published posthumously in 2012. Mandelbrot was born in a Jewish family, in Warsaw during the Second Polish Republic, his father made his living trading clothing. During his first two school years, he was tutored by an uncle who despised rote learning: "Most of my time was spent playing chess, reading maps and learning how to open my eyes to everything around me." The family's move to France, the war, his acquaintance with his father's brother, the mathematician Szolem Mandelbrojt who had moved to Paris around 1920, further prevented a standard education. 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. Mandelbrot attended the Lycée Rolin in Paris until the start of World War II, when his family moved to Tulle, France.
He was helped by the Rabbi of Brive-la-Gaillarde, to continue his studies. Much of France was occupied by the Nazis at the time, Mandelbrot recalls this period: 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 a physician in a nearby county seat. To eliminate the competition, another physician denounced her... We escaped this fate. Who knows why? In 1944, Mandelbrot returned to Paris, studied at the Lycée du Parc in Lyon, in 1945 to 1947 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 earned a master's degree in aeronautics. Returning to France, he obtained his PhD degree in Mathematical Sciences at the University of Paris in 1952. 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, where he was sponsored by John von Neumann.
In 1955 he married Aliette Kagan and moved to Geneva, Switzerland and to the Université Lille Nord de France. 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, he remained at IBM for 35 years, becoming an IBM Fellow, Fellow Emeritus. From 1951 onward, Mandelbrot worked on problems and published papers not only in mathematics but in applied fields such as information theory and fluid dynamics. Mandelbrot saw financial markets as an example of "wild randomness", characterized by concentration and long range dependence, he developed several original approaches for modelling financial fluctuations. In his early work, he found that the price changes in financial markets did not follow a Gaussian distribution, but rather Lévy stable distributions having 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. As a visiting profe
Villelaure is a commune in the Vaucluse department in the Provence-Alpes-Côte d'Azur region in southeastern France. The village takes its name from the Roman-era settlement of Villa Laura, at the same location or nearby. Since Roman times, a nucleus of inhabitants lived near the present village. However, like all the southern Luberon and its region were ruined in the second half of the 14th century by the ravages of the Hundred Years War and the Black Death. Villelaure is one of about forty localities, on both sides of the Luberon, in which at least 1,400 families from the alpine valleys of Piedmont and 6,000 people came from the alpine dioceses of Turin and Embrun between 1460 and 1560. In 1512, Antoinette de la Terre, assisted by her husband Jean de Forbin, established Villelaure with 19 families from the neighboring villages and Piedmont. Côtes du Luberon AOC Communes of the Vaucluse department Luberon INSEE
Benjamin Esmond Nicker was a legendary bushman born and raised in Central Australia. In 1923, at 15, Nicker crossed the Tanami Desert solo and, in 1932 and 1933 he guided the expeditions of Michael Terry through the Gibson Desert. Nicker was the son of Elizabeth and Sam Nicker who arrived at the Arltunga goldfields in the Northern Territory in 1903, after a two year journey through the centre, by which time the output of gold had diminished; this disappointed the two and, rather mine Sam purchased a wagon from a "disgruntled quitter" and delivered water to the miners whilst Elizabeth started a market garden and herded feral goats for milk and useful skins. By 1908, when Nicker was born, the family had moved, a little north of Arltunga, to establish what would become The Garden station which would provide produce, on a larger scale the Elizabeth's market garden, to the Arltunga and Winnecke Depot goldfields. In 1914 they uprooted again when Sam purchased the lease on Ryan's Well, near Aileron, where the family operated a cattle station and supplemented their income by operating the well for travelling stock and operating as a post and telegraph office.
It was at Ryan's Well, which the family called Glen Maggie, that Nicker developed a relationship with the passing Afghan Cameleers and one of them, gifted Nicker with an orphaned camel calf and he spent a lot of time training the camel and exploring the station. In 1923 Joe Brown, an explorer and prospector, came through Ryan's Well on his way to cross the Tanami Desert and 15 year old Nicker convinced his parents to let him go with him. Nicker was unable to take his camels, as they didn't get along with Brown's horses and, instead, he took two station horses with him. Brown is described as an argumentative and difficult man and at Halls Creek the two parted company leaving Nicker to travel alone back to Ryan's Well; this was a dangerous journey, in which many had died, at any time but was so in 1923 with the desert in the midst of severe drought and many wells in disuse. In his book The Last Explorer Michael Terry says: "At fifteen, he had come back well, he had safely completed the finest, solo venture in inland history, so I claim."
Following his return from this expedition in 1924 Nicker continued to explore in order to take in points of interest he had heard about and to make his own discoveries. He was helped in his explorations my his language skills as he could fluently speak a number of local languages including Luritja, Pitjantjatjara and Pintupi. In 1928 Nicker met Terry for the first time and "the stage was set for a mutual admiration which would last a life time". Nicker served as Terry's guide, alongside Aboriginal cameleers, on his 1932 and 1933 expeditions which, under his influence, used camels only; these expeditions became the subject of Terry's book Sand. In 1939 Nicker volunteered to enlist into World War II where, after a brief time at the Colchester Barracks 50 km from London, he met a local girl named Jane whom he married by special licence after a month of courtship; the couple were only able to spend six weeks together. Following this he was first sent to the Middle East before being sent to Greece where he died on 19 April 1941