Mandelbrot, Benoît (1924 - 2010 Oct 14)

[makc]

In my family noone knows who the guy was.

[neufer]

In my family no one knows who the guy was.

Reports of his death have been greatly embellished:

"Survivors include an infinite number of smaller versions of himself."

[makc]

wikipedia(ns) say there's no evidence of his death

[bystander]

Benoit Mandelbrot, Mathematician, Dies at 85
New York Times | 16 Oct 2010

“He Gave Us Order Out of Chaos” — R.I.P. Benoît Mandelbrot, 1924-2010
Wired Science | 16 Oct 2010

[neufer]

Journal of Mathematical Analysis and Applications
Volume 132, Issue 2, June 1988, Pages 520-529
Received 27 May 1986.

Functional powers near a fixed point
Lawrence J. Crone and Arthur C. Neuendorffer

The American University, Washington, D.C. 20016, U.S.A.

National Oceanic and Atmospheric Administration/NESDIS, Suitland, Maryland 20233, U.S.A.

Abstract

It is proved that if a function F(z) is analytic in a neighborhood of a fixed point z₀, and if 0 < ¦F′(z₀)¦ < 1, then there exists a family of related functions F(p, z), each defined in a neighborhood of z₀, which act as functional powers of F(z). In particular, F(0, z) = z, F(1, z) = F(z), and F(p, F(q, z)) = F(p + q, z). It is further demonstrated that the family of functions F(p, z) is identical with the set of nonconstant analytic functions with fixed point z₀ which commute with F(z).

"You don't understand. I coulda had class. I coulda been a Mandelbrot.
I coulda been somebody, instead of a bum, which is what I am, let's face it."

[Ann]

I love the Mandelbrot turtles. Those with heads and heart-shaped behinds, that is. I guess this proves that there are turtles all the way down, except after a while the turtles change shapes and turn into bacteria. Well, don't we all know that bacteria rule the world?



Ann

[makc]

I coulda been a Mandelbrot.

What's your Erdos Mandelbrot number?

[neufer]

"You don't understand. I coulda had class. I coulda been a Mandelbrot.
I coulda been somebody, instead of a bum, which is what I am, let's face it."

What's your Erdos Mandelbrot number?

Mandelbrot 'bum-NER' = 0 + 0i

NER : down; in a direction downwards (Swedish adverb)

<<Nucleotide Excision Repair (NER) is a DNA repair mechanism. NER is a particularly important mechanism by which the cell can prevent unwanted mutations by removing the vast majority of UV-induced DNA damage.>>

[mak¢]

by your logic emmmmethod, ner = neufer - unrestricted free agent. Could be said that once you give up your freedom and bow to restrictions, you could become a number, perhaps in some extrnal universe simulation... except you're a bum, who doesn't know he's a number. Doesn't make much sense, but that's how it's always with your posts.

[Ann]

From New York Times (http://www.nytimes.com/2010/10/17/us/17mandelbrot.html?src=ISMR_AP_LO_MST_FB):

Dr. Mandelbrot traced his work on fractals to a question he first encountered as a young researcher: how long is the coast of Britain? The answer, he was surprised to discover, depends on how closely one looks. On a map an island may appear smooth, but zooming in will reveal jagged edges that add up to a longer coast. Zooming in further will reveal even more coastline.

“Here is a question, a staple of grade-school geometry that, if you think about it, is impossible,” Dr. Mandelbrot told The New York Times earlier this year in an interview. “The length of the coastline, in a sense, is infinite.”

The length of the coastline of Britain is infinite? I beg your pardon!! (I've just been watching Disney's Holes with a class.)


I beg your pardon?

The coastline of Britain can't be infinite! There are only so many molecules and atoms, let alone strings, that you can line up along the coastline of Britain!



Infinite oh no no!

But the learned anecdotes that can be sqeezed out of the neurons of our very own Quotidian Quotationist is a fair approximation of Mandelbrotian infinitude.



Mandelbröd = Almond bread = Mandelbrot?

Ann

[makc]

[Ann]

Makc, that's delightful! The "turtle" is Mandelbrot himself, and he goes on and on, like Art said, as infinitely smaller versions of himself.

Ann

[neufer]

The coastline of Britain can't be infinite!
There are only so many molecules and atoms, let alone strings,
that you can line up along the coastline of Britain!

Well... Norway then!

<<Slartibartfast is a Magrathean, and a designer of planets. His favourite part of the job is creating coastlines, the most notable of which are the fjords found on the coast of Norway on planet Earth, for which he wins an award. While trapped on prehistoric Earth, Arthur Dent and Ford Prefect see Slartibartfast's signature deep inside a glacier in ancient Norway. When Earth Mk. II is being made, Slartibartfast is assigned to the continent of Africa. He is unhappy about this because he wants to make more fjords (arguing that they give a continent a baroque feel), and fjords in Africa would be hard for him to explain without natural glacial movement.>>

<<Vikings usually demand a tribute so they can leave or as they called it a Danegeld (for an instance a Viking leader Ragnar invaded Paris with 150 ships. Frances king paid the Vikings 50 million dollars in silver so that they would NEVER come back…. That didn’t last that long). The invaders would split up the money and took it home; for a side note archaeologists have found 30,000 English coins in Sweden- More ever [than] found in England. In 1012 the Vikings demanded 48,000 pounds of silver from the English as well as a ransom from the Archbishop of Canterbury (a Viking captive). When the Vikings didn’t get there extra ransom they pelted the Archbishop to death with bones. Four years later Cnut the Great conquered all of England and collected 82,500 pounds of silver then declared himself king.>>

[emc]

we see whatever is in the capacity of our cortex... but sometimes it requires a little help from outside

[emc]

Mandlebrot problem… if a bird in the hand is worth two in the bush, then how much are two birds in the hand worth?
Ans. Once you pass one there’s infinity. So two birds in the hand are priceless.

[neufer]

<<Benoît Mandelbrot died in a hospice in Cambridge, Massachusetts, on 14 October 2010 from pancreatic cancer, at the age of 85.

In 1974 Mandelbrot offered 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.>>

Felix Hausdorff (November 8, 1868 – January 26, 1942) was a German mathematician who is considered to be one of the founders of modern topology and who contributed significantly to set theory, descriptive set theory, measure theory, function theory, and functional analysis. He introduced the concepts now called Hausdorff measure and Hausdorff dimension, which have been useful in the theory of fractals.

Hausdorff also published philosophical and literary works under the pseudonym "Paul Mongré". "Paul Mongre" published a number of books and articles on the philosopher Friedrich Nietzsche, as well as a number of reviews of contemporary literature and drama. Mongre-Hausdorff also published a satirical play which performed in a dozen German cities. In the course of attempts to refute Nietzsche's doctrine of "the eternal return of the same," Hausdorff was led to Cantor's set theory, which set Hausdorff on the road to his set-theoretical discoveries.

Hausdorff studied at the University of Leipzig, obtaining his Ph.D. in 1891. He taught mathematics in Leipzig until 1910, when he became professor of mathematics at the University of Bonn. When the Nazis came to power, Hausdorff, who was Jewish, felt that as a respected university professor he would be spared from persecution. However, his abstract mathematics was denounced as "Jewish", useless, and "un-German" and he lost his position in 1935. Though he could no longer publish in Germany, Hausdorff continued to be an active research mathematician, publishing in the Polish journal Fundamenta Mathematicae. After Kristallnacht in 1938 as persecution of Jews escalated, Hausdorff became more and more isolated. He wrote to George Polya requesting a research fellowship in the United States, but these efforts came to nothing. Finally, in 1942 when he could no longer avoid being sent to a concentration camp, Hausdorff committed suicide together with his wife, Charlotte Goldschmidt Hausdorff, and sister-in-law, Edith Goldschmidt Pappenheim, on the 26th of January. They are buried in Bonn, Germany.>>

<<Benoit Mandelbrot, a well-known mathematician who was largely responsible for developing the field of fractal geometry and who once worked as an IBM researcher in Yorktown, died Thursday. He was 85 and lived in Cambridge, MA.

Benoît Mandelbrot was born in Warsaw, Poland, on November 20, 1924. His family was Jewish and had originally come from Lithuania. They were well educated; Mandelbrot's father was a clothing manufacturer, and his mother had been a physician. The boy was taught at home for his first years because his mother was afraid of epidemics. He quickly mastered reading and also showed himself to be a strong chess player, winning the championship for his age group.

In 1936, when Mandelbrot was 12 years old and Hitler was beginning to threaten Europe, the family moved to Paris. Mandelbrot's uncle Szolem Mandelbrot taught mathematics as a university professor, and the youngster thus met many mathematicians and heard plenty of mathematical talk. Young Mandelbrot became especially interested in geometry. His uncle, who worked in advanced analysis (calculus), did not approve of this interest. He shared the opinion of many mathematicians of the time that geometry had reached a dead end and was suitable only for beginning students.

In September 1939, Germany started World War II by invading Poland. The next spring, the Germans invaded and quickly occupied much of France, including Paris. The Mandelbrot family moved into the French countryside and had to move again frequently to avoid the Nazi police. It was thus impossible for Mandelbrot to attend any sort of regular school. Mandelbrot was aided in his self-directed study by his memory for shapes and his ability to recognize patterns. When Paris was liberated in 1944, Mandelbrot took the national university entrance examinations. Although he had never formally studied advanced algebra or calculus, Mandelbrot found that his familiarity with geometry and facilities with shapes helped him translate problems in other kinds of mathematics into familiar forms.

In 1945, Mandelbrot's Uncle Szolem returned from the United States, where he had been living during the war. They argued about the young man's future career. Szolem supported a mathematical movement called Bourbaki, which stressed a style of mathematical analysis that was formal, strict, and elegant. Mandelbrot resisted his uncle's suggestions. Perhaps because his youth had been spent in a world of constant change and uncertainty, he instinctively sought a field that would have rough edges and complex texture a world of changing geometric shapes.

Mandelbrot briefly attended the École Normale of Paris but left because they had little interest in geometry. However, at the Polytechnique School of Paris, Mandelbrot found a mathematician who shared this spirit of adventure: Paul Pierre Lévy. Lévy had become an expert in probability theory and had also studied physical phenomena that involved probability, such as the jittery random way in which small particles move in response to heat energy. "Lévy helped Mandelbrot learn to look for mathematical phenomena in nature rather than only in the neat, tidy abstractions favored by many established mathematicians."

Mandelbrot's career took a brief turn toward practicality. He went to the California Institute of Technology in Pasadena and earned master's and professional degrees in aeronautical engineering. Returning to France, he joined the French air force for a year, then returned to academic studies in Paris. In 1952, Mandelbrot received his Ph.D. from the University of Paris. His doctoral thesis, "Mathematical Theories of Games of Communication," brought together ideas from thermodynamics, cybernetics (the science of communication and control pioneered by Norbert Wiener), and the game theory of John von Neumann. "Mandelbrot said later that the thesis was poorly written and badly organized, but it included an idea that would be very important in his later work structures that replicated themselves over and over again on smaller and smaller scales, such as a tree with a trunk, branches, and twigs."

During 1953 and 1954, Mandelbrot continued his mathematical explorations by being sponsored by John von Neumann for a fellowship at the Institute for Advanced Studies at Princeton, the home of many of Europe's "mathematical refugees." "There he first encountered another key idea that would greatly figure in his later work: the so-called Hausdorff-Besicovitch dimension, where a sort of mathematical perspective reveals two-dimensional motion around a one-dimensional line." (The particular example he studied was the tiny but frenetic Brownian motion of molecules in a fluid.) In 1955, Mandelbrot returned to Europe, teaching in Geneva, Switzerland, and Lille, France.

The work that would finally bring together all of Mandelbrot's interests began in 1958, when he accepted an open-ended position in the research department of IBM. "In 1961, IBM asked Mandelbrot to analyze mysterious noise that was causing problems in telephone circuits. IBM thought that the noise might be caused by workmen's tools as they made repairs to the system. " However, Mandelbrot realized that the noise had a peculiar structure similar to the paths of Brownian motion. There were big bursts of noise that when analyzed more closely proved to consist of a clump of smaller bursts. The noise was inherent in the structure of the circuits themselves. Based on Mandelbrot's work, IBM canceled an expensive but futile antinoise project.

The erratic behavior that had showed up in incomes and cotton prices had also appeared in physics in Brownian motion and other forms of behavior of fluids and gases and in Mandelbrot's earlier work with the telephone circuits. "In geometry, it showed up in patterns that were made of tiny clumps that were distributed seemingly randomly. The patterns lacked the neatness of the straight lines and smooth curves of Euclidean geometry, but the patterns were self-similar, that is, if one magnified the pattern, each part looked like a miniature copy of the whole." This could be done indefinitely, moving to a smaller and smaller scale. Mandelbrot used the word fractal (meaning fractured or broken up) to describe these geometric patterns.

In the 1960s, computers had just begun the transition from vacuum tubes to the solid-state world of the transistor. Computer time was still an expensive commodity, and Mandelbrot and his assistants had to spend many weeks calculating fractal patterns that can now be generated in a few seconds on a modern desktop computer. The most intricate and beautiful discovery of Mandelbrot's research was the object that came to be known as the Mandelbrot set. "The first hints had been sketched by hand years earlier, based on the work of two early 20th-century French mathematicians: Gaston Julia and Pierre Fatou. Mandelbrot had read their paper in his college days, when it represented only an obscure mathematical curiosity."

Now the computer made it possible to see the actual realization of the mathematics that described a vast array of "Julia sets." "Mandelbrot's program plotted on a grid similar to the Cartesian coordinates used in high school geometry, except it included complex numbers with their imaginary component. As the first crude version of his program ran, it created a symmetrical array of disks. However, after refining the program to calculate in finer increments, Mandelbrot seemed to see what appeared to be fuzzy clumps of tiny dots. At first he thought that there was a problem with the computer's numeric routines, but when he got some time on a bigger IBM machine, the fuzzy dots, like a distant galaxy in a more powerful telescope, resolved into an intricate array of spiral tendrils.>>

[Ann]

The coastline of Britain can't be infinite!
There are only so many molecules and atoms, let alone strings,
that you can line up along the coastline of Britain!

Well... Norway then!

<<Slartibartfast is a Magrathean, and a designer of planets. His favourite part of the job is creating coastlines, the most notable of which are the fjords found on the coast of Norway on planet Earth, for which he wins an award. While trapped on prehistoric Earth, Arthur Dent and Ford Prefect see Slartibartfast's signature deep inside a glacier in ancient Norway. When Earth Mk. II is being made, Slartibartfast is assigned to the continent of Africa. He is unhappy about this because he wants to make more fjords (arguing that they give a continent a baroque feel), and fjords in Africa would be hard for him to explain without natural glacial movement.>>

Okay then, Art! I guess you may be right. If inifinity exists, it may be the coastline of Norway!



Infinity, yeah!



Ann

[bystander]

Remembering The Father Of Fractals
Inside Science | 22 Oct 2010

Measuring the scale of Benoit Mandelbrot's achievements.

[neufer]

Okay then, Art! I guess you may be right. If infinity exists, it may be the coastline of Norway!

On August 26, 2000, the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) on NASA’s Terra satellite captured this false-color image of Oslofjorden and the nearby city of Oslo. Vegetation is red, urbanized areas are blue-gray, water is navy, and clouds are white. This image has been rotated and north is to the lower left.

<<Fjords—long, skinny inlets where the sea has flooded glacial valleys—fringe the coastline of Norway. The country’s largest fjord, however, is not really a fjord but a rift valley running mostly north-south. Tectonic forces have slowly wrenched apart the planet’s crust in this region, leaving behind Oslofjorden, or Oslofjord. The sea has snaked its way up convoluted valley floor, terminating along the margin of Norway’s capital city of Oslo.

A 2008 study described the complex geologic history of Oslofjorden. Today’s landscape, the authors concluded, results from a prolonged period of faulting and volcanic activity that began during the Late Carboniferous Period, perhaps starting more than 300 million years ago. During the Late Carboniferous, sedimentary rocks—rocks eroded by wind and water and deposited as fine sediments—carpeted much of the region, which might have been partially flooded from time to time. Subsequent lava flows deposited volcanic rocks up to 20 meters (65 feet) thick in some places. As geologic forces pulled the crustal plate apart, new volcanoes formed in parts of the rift. A graben—area of low-lying land bordered by higher-elevation land—formed, bounded by geologic fault lines. The rift development slowly halted some 250 to 245 million years ago, around the beginning of the Mesozoic Era.>>