(1894–1964; b. Columbia, Missouri; d. Stockholm, Sweden) American mathematician. The son of Russian immigrants, Wiener was a child prodigy, obtaining his PhD (in mathematical logic) from Harvard U at the age of eighteen. He developed the mathematics of a Wiener process, which is fundamental to an understanding of Brownian motion. His interests were wide-ranging: he became well known to the general scientific public for his philosophical discussion of cybernetics (a term he coined in 1945). Amongst his sayings is 'A professor is one who can speak on any subject — for precisely fifty minutes', though some might disagree with this observation! A lunar crater is named after him.
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American mathematician (1894–1964)
Born in Columbia, Missouri, Wiener was a child prodigy in mathematics who sustained his early promise to become a mathematician of great originality and creativity. He is probably one of the most outstanding mathematicians to have been born in the United States. Such was Wiener's precocity that he took his degree in mathematics, from Tufts University, at the age of 14 in 1909.
Throughout his life Wiener had many extramathematical interests, especially in biology and philosophy. At Harvard his studies in philosophy led him to an interest in mathematical logic and this was the subject of his doctoral thesis, which he completed at the age of 18. Wiener went from Harvard to Europe to pursue his interest in mathematical logic with Bertrand Russell in Cambridge and with David Hilbert in Göttingen. After he returned from Europe, Wiener's mathematical interests broadened but, surprisingly, he was unable to get a suitable post as a professional mathematician and for a time tried such unlikely occupations as journalism and even writing entries for an encyclopedia. In 1919 Wiener finally obtained a post in the mathematics department of the Massachusetts Institute of Technology, where he remained for the rest of his career.
After his arrival at MIT Wiener began his extremely important work on the theory of stochastic (random) processes and Brownian motion. Among his other very wide mathematical interests at this time was the generalization of Fourier's work on resolving functions into series of periodic functions (this is known as harmonic analysis). He also worked on the theory of Fourier transforms. During World War II Wiener devoted his mathematical talents to working for the military – in particular to the problem of giving a mathematical solution to the problem of aiming a gun at a moving target. In the course of this work Wiener discovered the theory of the prediction of stationary time series and brought essentially statistical methods to bear on the mathematical analysis of control and communication engineering.
From here it was a short step to his important work in the mathematical analysis of mechanical and biological systems, their information flow, and the analogies between them – the subject he named ‘cybernetics’. It allowed full rein to his wide interests in the sciences and philosophy and Wiener spent much time popularizing the subject and explaining its possible social and philosophical applications. Wiener also worked on a wide range of other mathematical topics, particularly important being his work on quantum mechanics.
The American mathematician Norbert Wiener (1894-1964) studied computing and control devices. Out of these studies he created the science of cybernetics.
Norbert Wiener was born on Nov. 26, 1894, at Cambridge, Mass. His father, Leo Wiener, professor of Slavonic languages and literature at Harvard University, determined to train the boy actively and single-mindedly as a scholar. Norbert was driven hard on the way to becoming a prodigy; fortunately he had the intellect and energy to emerge without undue suffering. He graduated with a bachelor's degree from Tufts College at the age of 14 and obtained his doctorate at Harvard four years later.
Wiener was awarded a traveling fellowship which he spent at the two centers where learning, especially in the mathematical and physical sciences, was perhaps the most significant and the most exciting in Europe: the University of Cambridge, England, and the University of Göttingen, Germany. After a varied career during World War I, he joined the Massachusetts Institute of Technology in 1919 as an instructor in the department of mathematics, and he remained on its staff for the whole of his career. There he was introduced to the work of the chemist Josiah Willard Gibbs, whose research on statistical mechanics, published in 1902, was a decisive influence in the development of Wiener's intellectual career.
Wiener had been instructed in the Lebesgue integral by G. H. Hardy at Cambridge, and with this grounding and his recognition of the importance of Gibbs's writings, he attacked the problem of the Brownian motion and produced one of his first major contributions to research. About the same time he began work on harmonic analysis. He brought to bear on this problem the method of Tauberian theorems and by this means refined his theory of harmonic analysis and also produced simple proofs of the prime-number theorem. He also worked on Fourier transforms and wrote Fourier Transforms in a Complex Domain.
At the same time that he pursued these studies into the field of quasi-analytic functions, Wiener was developing his interest in electrical circuits. The knowledge he gained on the problems of feedback control was of use when he became engaged in World War II on fire-control apparatus for antiaircraft guns. His interest in the parallels between feedback control in circuits and mental processes led to the creation of a new discipline which he called cybernetics, the study of control, communication, and organization. In Cybernetics (1948), his most influential work outside the field of pure mathematics, he propounded a new approach to the study of man in his technological environment, a science of man as component of an age of automation. On March 18, 1964, Wiener died in Stockholm.
Further Reading
The best sources of biographical material are Wiener's two volumes of memoirs, Ex Prodigy: My Childhood and Youth (1953) and I Am a Mathematician: The Later Life of a Prodigy (1956). See also Mitchell Wilson, American Science and Invention (1954).
Bibliography
See F. Conway and J. Siegelman, Dark Hero of the Information Age (2004).
See also mind–body problem: philosophical theories.
— Frank George
Quotes:
"The idea that information can be stored in a changing world without an overwhelming depreciation of its value is false. It is scarcely less false than the more plausible claim that after a war we may take our existing weapons, fill their barrels with information."
| Norbert Wiener | |
|---|---|
| Born | November 26, 1894 Columbia, Missouri, U.S. |
| Died | March 18, 1964 (aged 69) Stockholm, Sweden |
| Nationality | American |
| Fields | Mathematics Cybernetics |
| Institutions | Massachusetts Institute of Technology |
| Alma mater | Tufts College BA 1909 Harvard University PhD 1912 |
| Doctoral advisor | Karl Schmidt Josiah Royce |
| Doctoral students | Amar Bose Colin Cherry Shikao Ikehara Norman Levinson |
Norbert Wiener (November 26, 1894, Columbia, Missouri – March 18, 1964, Stockholm, Sweden) was an American mathematician. He was Professor of Mathematics at MIT.
A famous child prodigy, Wiener later became an early researcher in stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.
Wiener is regarded as the originator of cybernetics, a formalization of the notion of feedback, with many implications for engineering, systems control, computer science, biology, philosophy, and the organization of society.
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Wiener was the first child of Leo Wiener and Bertha Kahn, Jews of Polish and German descent, respectively. Norbert Wiener became a famous child prodigy. Leo had educated Norbert at home until 1903, employing teaching methods of his own invention, except for a brief interlude when Norbert was 7 years of age. Earning his living teaching German and Slavic languages, Leo read widely and accumulated a personal library from which the young Norbert benefited greatly. Leo also had ample ability in mathematics, and tutored his son in the subject until he left home.
After graduating from Ayer High School in 1906 at 11 years of age, Wiener entered Tufts College. He was awarded a BA in mathematics in 1909 at the age of 14, whereupon he began graduate studies of zoology at Harvard. In 1910 he transferred to Cornell to study philosophy.
The next year he returned to Harvard, while still continuing his philosophical studies. Back at Harvard, Wiener became influenced by Edward Vermilye Huntington, whose mathematical interests ranged from axiomatic foundations to engineering problems. Harvard awarded Wiener a Ph.D. in 1912, when he was merely 17 years old, for a dissertation on mathematical logic, supervised by Karl Schmidt, the essential results of which were published as Wiener (1914). In that dissertation, he was the first to state publicly that ordered pairs can be defined in terms of elementary set theory. Hence relations can be defined by set theory, thus the theory of relations does not require any axioms or primitive notions distinct from those of set theory. In 1921, Kazimierz Kuratowski proposed a simplification of Wiener's definition of ordered pairs, and that simplification has been in common use ever since.
In 1914, Wiener traveled to Europe, to be taught by Bertrand Russell and G. H. Hardy at Cambridge University, and by David Hilbert and Edmund Landau at the University of Göttingen. During 1915–16, he taught philosophy at Harvard, then worked as an engineer for General Electric and wrote for the Encyclopedia Americana. Wiener worked briefly as a journalist for the Boston Herald, where he wrote a feature story on the poor labor conditions for mill workers in Lawrence, Massachusetts, but he was fired soon afterwards for his reluctance to write favorable articles about a politician the newspaper's owners sought to promote.[1]
Although Wiener eventually became a staunch pacifist, he eagerly contributed to the war effort in World War I. In 1916, with America's entry into the war drawing closer, Wiener attended a training camp for potential military officers, but failed to earn a commission. One year later Wiener again tried to join the military, but the government again rejected him due to his poor eyesight. In the summer of 1918, Oswald Veblen invited Wiener to work on ballistics at the Aberdeen Proving Ground in Maryland.[2] Living and working with other mathematicians strengthened his interest in mathematics. However, Wiener was still eager to serve in uniform, and decided to make one more attempt to enlist, this time as a common soldier. Wiener wrote in a letter to his parents, "I should consider myself a pretty cheap kind of a swine if I were willing to be an officer but unwilling to be a soldier".[3] This time the army accepted Wiener into its ranks and assigned him, by coincidence, to a unit stationed at Aberdeen, Maryland. World War I ended just days after Wiener's return to Aberdeen and Wiener was discharged from the military in February 1919.[4]
Wiener was unable to secure a permanent position at Harvard, a situation he blamed largely on anti-semitism at the university and in particular on the antipathy of Harvard mathematician G. D. Birkhoff.[5] He was also rejected for a position at the University of Melbourne. At W. F. Osgood's suggestion, Wiener became an instructor of mathematics at MIT, where he spent the remainder of his career, becoming promoted eventually to Professor.
In 1926, Wiener returned to Europe as a Guggenheim scholar. He spent most of his time at Göttingen and with Hardy at Cambridge, working on Brownian motion, the Fourier integral, Dirichlet's problem, harmonic analysis, and the Tauberian theorems.
In 1926, Wiener's parents arranged his marriage to a German immigrant, Margaret Engemann; they had two daughters.
During World War II, his work on the automatic aiming and firing of anti-aircraft guns caused Wiener to investigate information theory independently of Claude Shannon and to invent the Wiener filter. (To him is due the now standard practice of modeling an information source as a random process.) His anti-aircraft work eventually led him to formulate cybernetics. Unlike many of his contemporaries, Wiener was not invited to participate in the Manhattan Project.[6] After the war, his fame helped MIT to recruit a research team in cognitive science, composed of researchers in neuropsychology and the mathematics and biophysics of the nervous system, including Warren Sturgis McCulloch and Walter Pitts. These men later made pioneering contributions to computer science and artificial intelligence. Soon after the group was formed, Wiener suddenly ended all contact with its members, mystifying his colleagues. In their biography of Wiener, Conway and Siegelman suggest that Wiener's wife Margaret, who detested McCulloch's bohemian lifestyle, engineered the breach.[7]
Wiener later helped develop the theories of cybernetics, robotics, computer control, and automation. He shared his theories and findings with other researchers, and credited the contributions of others. These included Soviet researchers and their findings. Wiener's acquaintance with them caused him to be regarded with suspicion during the "Cold War". He was a strong advocate of automation to improve the standard of living, and to end economic underdevelopment. His ideas became influential in India, whose government he advised during the 1950s.
After the war, Wiener became increasingly concerned with what he believed was political interference with scientific research, and the militarization of science. His article "A Scientist Rebels" for the January 1947 issue of The Atlantic Monthly[8] urged scientists to consider the ethical implications of their work. After the war, he refused to accept any government funding or to work on military projects. The way Wiener's beliefs concerning nuclear weapons and the Cold War contrasted with that of John von Neumann is the major theme of the book John Von Neumann and Norbert Wiener Heims (1980).[9][citation needed]
Wiener was a core participant of the Macy conferences.
Information is information, not matter or energy.—Norbert Wiener, Cybernetics: Or the Control and Communication in the Animal and the Machine
Wiener was an early studier of stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.
Wiener is regarded as the originator of cybernetics, a formalization of the notion of feedback, with many implications for engineering, systems control, computer science, biology, philosophy, and the organization of society.
Wiener's work with cybernetics influenced Gregory Bateson and Margaret Mead, and through them, anthropology, sociology, and education.[12]
A simple mathematical representation of Brownian motion, the Wiener equation, named after Wiener, assumes the current velocity of a fluid particle fluctuates.
For signal processing, the Wiener filter is a filter proposed by Wiener during the 1940s and published in 1949. Its purpose is to reduce the amount of noise present in a signal by comparison with an estimation of the desired noiseless signal.
Wiener took a great interest in the mathematical theory of Brownian motion (named after Robert Brown) proving many results now widely known such as the non-differentiability of the paths. As a result the one-dimensional version of Brownian motion became known as the Wiener process. It is the best known of the Lévy processes, càdlàg stochastic processes with stationary statistically independent increments, and occurs frequently in pure and applied mathematics, physics and economics (e.g. on the stock-market).
Wiener's Tauberian theorem, a 1932 result of Wiener, developed Tauberian theorems in summability theory, on the face of it a chapter of real analysis, by showing that most of the known results could be encapsulated in a principle taken from harmonic analysis. As now formulated, the theorem of Wiener does not have any obvious association with Tauberian theorems, which deal with infinite series; the translation from results formulated for integrals, or using the language of functional analysis and Banach algebras, is however a relatively routine process.
The Paley–Wiener theorem relates growth properties of entire functions on Cn and Fourier transformation of Schwartz distributions of compact support.
The Wiener–Khinchin theorem, (or Wiener – Khintchine theorem or Khinchin – Kolmogorov theorem), states that the power spectral density of a wide-sense-stationary random process is the Fourier transform of the corresponding autocorrelation function.
An abstract Wiener space is a mathematical object in measure theory, used to construct a "decent", strictly positive and locally finite measure on an infinite-dimensional vector space. Wiener's original construction only applied to the space of real-valued continuous paths on the unit interval, known as classical Wiener space. Leonard Gross provided the generalization to the case of a general separable Banach space.
The notion of a Banach space itself was discovered independently by both Wiener and Stefan Banach at around the same time.[13]
Wiener wrote many books and hundreds of articles:[14]
Fiction:
Autobiography:
Under the name "W. Norbert"
A brief profile of Dr. Wiener is given in The Observer newspaper, Sunday, 28 January 1951.
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