Norbert Wiener (November 26,
1894, Columbia,
Missouri – March 18, 1964, Stockholm, Sweden) was an
American pure and
applied mathematician.
A famous
child prodigy, Wiener went on
to become a pioneer in the study of
stochastic and
noise processes, contributing work relevant to
electronic engineering,
electronic communication,
and
control systems.
Wiener is the founder of
cybernetics, a
field that formalizes the notion of
feedback, with many 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. Wiener became a
child prodigy in part due to his father's
tutelage. 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 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,
the essential results of which 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 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 the ordered pair, and that
simplification has been in common use ever since.
In 1914, Wiener traveled 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's 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 was not Jewish; they had 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 ``John Von Neumann and Norbert Wiener" 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. He was
influenced by
William Ross
Ashby.
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
C^{n} 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.
The notion of a Banach space itself was independently discovered by
both Wiener and
Stefan Banach at
around the same time.
Publications
Wiener wrote many 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.
[9962])
- 1948, Cybernetics: Or Control and Communication in the
Animal and the Machine. Paris, France: Librairie Hermann &
Cie, and Cambridge, MA: MIT Press.Cambridge, MA: MIT Press.
- 1950, The Human Use of Human Beings. The Riverside
Press (Houghton Mifflin Co.).
- 1958, Nonlinear Problems in Random Theory. MIT Press
& Wiley.
- 1966, Generalized Harmonic Analysis and Tauberian
Theorems. MIT Press.
- 1966,
God & Golem, Inc.: A Comment on Certain Points Where
Cybernetics Impinges on Religion. 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.
Fiction:
- 1959,The Tempter. Random House.
Autobiography:
- 1953. Ex-Prodigy: My Childhood and Youth. MIT
Press.
- 1956. I am a Mathematician. MIT Press.
Under the name "W. Norbert"
- 1952 The Brain and other short science fiction in Tech
Engineering News
References
Further reading
- Bynum, Terrell W., " Norbert Wiener's Vision: The impact of "the
automatic age" on our moral lives."
- Conway, F., and Siegelman, J., 2005. Dark Hero of the
Information Age: in search of Norbert Wiener, the father of
cybernetics. Basic Books, New York. 423pp. ISBN
0-7382-0368-8
- Ivor Grattan-Guinness,
2000. The Search for Mathematical Roots 1870-1940.
Princeton Uni. Press.
- Bluma, Lars, 2005. Norbert Wiener und die Entstehung der
Kybernetik im Zweiten Weltkrieg. Münster.
- Michel Faucheux, Nobert Wiener, le Golem et la cybernetique,
Editions du Sandre,2008
- Heims, Steve J., 1980. John von Neumann and Norbert Wiener:
From Mathematics to the Technologies of Life and Death. MIT
Press.
- Heims, Steve J., 1993. Constructing a Social Science for
Postwar America. The Cybernetics Group, 1946-1953.
MIT Press.
- Ilgauds, Hans Joachim, 1980. Norbert Wiener.
- Masani, P. Rustom, 1990. Norbert Wiener 1894-1964.
Birkhauser.
A brief profile of Dr. Wiener is given in
The Observer newspaper, Sunday, 28 January 1951.
External links