Everything about Norbert Wiener totally explained
Norbert Wiener (
November 26,
1894,
Columbia, Missouri –
March 18,
1964,
Stockholm Sweden) was an
American theoretical and
applied mathematician.
Wiener was a pioneer in the study of
stochastic and
noise processes, contributing work relevant to
electronic engineering,
electronic communication, and
control systems.
Wiener also founded
cybernetics, a field that formalizes the notion of
feedback and has implications for
engineering,
systems control,
computer science,
biology,
philosophy, and the organization of
society.
Biography
Youth
Wiener was the first child of Leo Wiener, a
Polish-
Jewish immigrant, and Bertha Kahn, of
German-
Jewish descent. Employing teaching methods of his own invention, Leo educated Norbert at home until 1903, except for a brief interlude when Norbert was 7 years of age. Thanks to his father's tutelage and his own abilities, Wiener became a
child prodigy. Earning his living teaching
German and
Slavic languages, Leo read widely and accumulated a personal library from which the young Norbert benefited much. 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 in
zoology at
Harvard. In 1910 he transferred to
Cornell to study philosophy.
Harvard
The next year he returned to Harvard, while still continuing his philosophical studies. Back at Harvard, Wiener came under the influence of
Edward Vermilye Huntington, whose mathematical interests ranged from axiomatic foundations to problems posed by engineering. Harvard awarded Wiener a
Ph.D. in 1912, when he was a mere 18, for a dissertation on
mathematical logic, supervised by
Karl Schmidt, whose essential results were published as Wiener (1914). In that dissertation, he was the first to see that the
ordered pair can be defined in terms of elementary
set theory. Hence
relations can be wholly grounded in
set theory, so that the theory of relations doesn't require any axioms or primitive notions distinct from those of set theory. In 1921,
Kuratowski proposed a simplification of Wiener's definition of the ordered pair, and that simplification has been in common use ever since.
In 1914, Wiener travelled to Europe, to study under
Bertrand Russell and
G. H. Hardy at
Cambridge University, and under
David Hilbert and
Edmund Landau at the
University of Göttingen. In 1915-16, he taught philosophy at Harvard, then worked for
General Electric and wrote for the
Encyclopedia Americana. When
World War I broke out,
Oswald Veblen invited him to work on
ballistics at the
Aberdeen Proving Ground in Maryland. Thus Wiener, an eventual pacifist, wore a uniform 1917-18. Living and working with other mathematicians strengthened and deepened his interest in mathematics.
After the war
After the war, Wiener was unable to secure a position at Harvard because he was Jewish (despite his father being the first tenured Jew at Harvard), and was rejected for a position at the
University of Melbourne. At
W. F. Osgood's invitation, Wiener became an instructor in mathematics at
MIT, where he spent the remainder of his career, rising 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, who wasn't Jewish; they'd two daughters.
During and after World War II
During
World War II, his work on the automatic aiming and firing of
anti-aircraft guns led Wiener to
communication theory and eventually to formulate
cybernetics. After the war, his prominence helped MIT to recruit a research team in
cognitive science, made up of researchers in
neuropsychology and the mathematics and
biophysics of the nervous system, including
Warren Sturgis McCulloch and
Walter Pitts. These men went on to make pioneering contributions to
computer science and
artificial intelligence. Shortly after the group was formed, Wiener broke off all contact with its members. Speculation still flourishes as to why this split occurred.
Wiener went on to break new ground in 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 connections with them placed him under suspicion during the
Cold War. He was a strong advocate of automation to improve the standard of living, and to overcome economic underdevelopment. His ideas became influential in
India, whose government he advised during the 1950s.
Wiener declined an invitation to join the
Manhattan Project. After the war, he became increasingly concerned with what he saw as political interference in scientific research, and the militarization of science. His article "A Scientist Rebels" in the January 1947 issue of
The Atlantic Monthly 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 stance towards nuclear weapons and the Cold War contrasted with that of
John von Neumann is the central theme of Heims (1980).
Awards and honors
Work
Wiener was as a pioneer in the study of
stochastic and
noise processes, contributing work relevant to
electronic engineering,
electronic communication, and
control systems.
Wiener also founded
cybernetics, a field that formalizes the notion of
feedback and has implications for
engineering,
systems control,
computer science,
biology,
philosophy, and the organization of
society.
Wiener equation
A simple mathematical representation of
Brownian motion, the
Wiener equation, named after Wiener, assumes the current
velocity of a
fluid particle fluctuates.
Wiener filter
In 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.
In mathematics
The
Wiener process is a continuous-time
stochastic process named in honor of Wiener. It is often called
Brownian motion', after
Robert Brown. It is one of the best known
Lévy processes, càdlàg stochastic processes with stationary statistical independence increments, and occurs frequently in pure and applied mathematics, economics and physics.
Wiener's tauberian theorem is a 1932 result of Wiener. It put the capstone on the field of
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 from
harmonic analysis. As now formulated, the theorem of Wiener has no obvious connection to 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 once the idea is grasped.
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, also known as the
Wiener–Khintchine theorem and sometimes as the
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.
Publications
Wiener wrote a dozen books and hundreds of articles:
1914, "A simplification in the logic of relations" in Jean van Heijenoort, 1967. From Frege to Godel: A Source Book in Mathematical Logic, 1879-1931. Harvard Univ. Press: 224-27.
1930, Extrapolation, Interpolation and Smoothing of Stationary Time Series with Engineering Applications. MIT Press. (Originally classified, finally published in 1949; the 1942 version of this monograph was nicknamed "the yellow peril" because of the color of the cover and the difficulty of the subject. (External Link
))
1948, Cybernetics: Or the Control and Communication in the Animal and the Machine. Cambridge, MA: MIT Press.
1950, The Human Use of Human Beings. Da Capo Press.
1958, Nonlinear Problems in Random Theory. MIT Press & Wiley.
1966, Generalized Harmonic Analysis and Tauberian Theorems. MIT Press.
1966, . MIT Press.
1988, The Fourier Integral and Certain of its Applications (Cambridge Mathematical Library). Cambridge Univ. Press.
1994, Invention: The Care and Feeding of Ideas. MIT Press.
Autobiography:
1953. Ex-Prodigy: My Childhood and Youth. MIT Press.
1956. I am a Mathematician. MIT Press.Further Information
Get more info on 'Norbert Wiener'.
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