Norbert Wiener (November 26, 1894 – March 18, 1964) was an American
mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems.
Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change.
History
On ...
and
philosopher
A philosopher is a person who practices or investigates philosophy. The term ''philosopher'' comes from the grc, φιλόσοφος, , translit=philosophos, meaning 'lover of wisdom'. The coining of the term has been attributed to the Greek th ...
. He was a professor of mathematics at the
Massachusetts Institute of Technology
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the ...
(MIT). A
child prodigy
A child prodigy is defined in psychology research literature as a person under the age of ten who produces meaningful output in some domain at the level of an adult expert. The term is also applied more broadly to young people who are extraor ...
, Wiener later became an early researcher in
stochastic
Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...
and mathematical
noise
Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...
processes, contributing work relevant to
electronic engineering
Electronics engineering is a sub-discipline of electrical engineering which emerged in the early 20th century and is distinguished by the additional use of active components such as semiconductor devices to amplify and control electric current ...
,
electronic communication
Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that ...
, and
control system
A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial c ...
s.
Wiener is considered the originator of
cybernetics
Cybernetics is a wide-ranging field concerned with circular causality, such as feedback, in regulatory and purposive systems. Cybernetics is named after an example of circular causal feedback, that of steering a ship, where the helmsperson m ...
, the science of communication as it relates to living things and machines, with implications for
engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
,
systems control Systems control, in a communications system, is the control and implementation of a set of functions that:
# prevent or eliminate Degradation (telecommunications), degradation of any part of the system,
# initiate immediate response to demands tha ...
,
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
,
biology
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
,
neuroscience
Neuroscience is the scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions and disorders. It is a multidisciplinary science that combines physiology, anatomy, molecular biology, development ...
,
philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
, and the organization of
society
A society is a group of individuals involved in persistent social interaction, or a large social group sharing the same spatial or social territory, typically subject to the same political authority and dominant cultural expectations. Socie ...
.
Norbert Wiener is credited as being one of the first to theorize that all intelligent behavior was the result of feedback mechanisms, that could possibly be simulated by machines and was an important early step towards the development of modern
artificial intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech re ...
.
Biography
Youth
Wiener was born in
Columbia, Missouri
Columbia is a city in the U.S. state of Missouri. It is the county seat of Boone County and home to the University of Missouri. Founded in 1821, it is the principal city of the five-county Columbia metropolitan area. It is Missouri's fourth ...
, the first child of
Leo Wiener
Leo Wiener (1862–1939) was an American historian, linguist, author and translator.
Biography
Wiener was born in Białystok (then in the Russian Empire), of Lithuanian Jewish origin. His father was Zalmen (Solomon) Wiener, and his mother w ...
and Bertha Kahn, Jewish immigrants from
Lithuania
Lithuania (; lt, Lietuva ), officially the Republic of Lithuania ( lt, Lietuvos Respublika, links=no ), is a country in the Baltic region of Europe. It is one of three Baltic states and lies on the eastern shore of the Baltic Sea. Lithuania ...
and
Germany
Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
, respectively. Through his father, he was related to
Maimonides
Musa ibn Maimon (1138–1204), commonly known as Maimonides (); la, Moses Maimonides and also referred to by the acronym Rambam ( he, רמב״ם), was a Sephardic Jewish philosopher who became one of the most prolific and influential Torah ...
, the famous
rabbi
A rabbi () is a spiritual leader or religious teacher in Judaism. One becomes a rabbi by being ordained by another rabbi – known as ''semikha'' – following a course of study of Jewish history and texts such as the Talmud. The basic form of ...
, philosopher and physician from
Al Andalus, as well as to
Akiva Eger
Rabbi Akiva Eiger (, also spelled Eger; , yi, עקיבא אייגער), or Akiva Güns (17611837) was an outstanding Talmudic scholar, influential halakhic decisor and foremost leader of European Jewry during the early 19th century. He was also ...
, chief rabbi of
Posen from 1815 to 1837. 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
The Slavic languages, also known as the Slavonic languages, are Indo-European languages spoken primarily by the Slavic peoples and their descendants. They are thought to descend from a proto-language called Proto-Slavic, spoken during the Ear ...
, 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. In his autobiography, Norbert described his father as calm and patient, unless he (Norbert) failed to give a correct answer, at which his father would lose his temper.
A child prodigy, he graduated from
Ayer High School
Ayer Shirley Regional High School is a high school located in Ayer, Massachusetts. The school colors are maroon and white, and the mascot is the Panther. The student body contains about 350 students in 9th-12th grade.
School Support
The school b ...
in 1906 at 11 years of age, and Wiener then entered
Tufts College
Tufts University is a private research university on the border of Medford and Somerville, Massachusetts. It was founded in 1852 as Tufts College by Christian universalists who sought to provide a nonsectarian institution of higher learning. ...
. He was awarded a
BA in mathematics in 1909 at the age of 14, whereupon he began graduate studies of
zoology
Zoology ()The pronunciation of zoology as is usually regarded as nonstandard, though it is not uncommon. is the branch of biology that studies the Animal, animal kingdom, including the anatomy, structure, embryology, evolution, Biological clas ...
at
Harvard
Harvard University is a private Ivy League research university in Cambridge, Massachusetts. Founded in 1636 as Harvard College and named for its first benefactor, the Puritan clergyman John Harvard, it is the oldest institution of higher le ...
. In 1910 he transferred to
Cornell
Cornell University is a private statutory land-grant research university based in Ithaca, New York. It is a member of the Ivy League. Founded in 1865 by Ezra Cornell and Andrew Dickson White, Cornell was founded with the intention to teach an ...
to study philosophy. He graduated in 1911 at 17 years of age.
Harvard and World War I
The next year he returned to Harvard, while still continuing his philosophical studies. Back at Harvard, Wiener became influenced by
Edward Vermilye Huntington
Edward Vermilye Huntington (April 26, 1874November 25, 1952) was an American mathematician.
Biography
Huntington was awarded the B.A. and the M.A. by Harvard University in 1895 and 1897, respectively. After two years' teaching at Williams College ...
, whose mathematical interests ranged from axiomatic foundations to engineering problems. Harvard awarded Wiener a
PhD in June 1913, when he was only 19 years old, for a dissertation on
mathematical logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...
(a comparison of the work of
Ernst Schröder with that of
Alfred North Whitehead
Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher. He is best known as the defining figure of the philosophical school known as process philosophy, which today has found applicat ...
and
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ...
), supervised by Karl Schmidt, the essential results of which were published as Wiener (1914). He was one of the youngest to achieve such a feat. In that dissertation, he was the first to state publicly that
ordered pair
In mathematics, an ordered pair (''a'', ''b'') is a pair of objects. The order in which the objects appear in the pair is significant: the ordered pair (''a'', ''b'') is different from the ordered pair (''b'', ''a'') unless ''a'' = ''b''. (In con ...
s can be defined in terms of elementary
set theory
Set theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly conce ...
. 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
Kazimierz Kuratowski (; 2 February 1896 – 18 June 1980) was a Polish mathematician and logician. He was one of the leading representatives of the Warsaw School of Mathematics.
Biography and studies
Kazimierz Kuratowski was born in Warsaw, (t ...
proposed a simplification of Wiener's definition of ordered pairs, and that simplification has been in common use ever since. It is (x, y) = .
In 1914, Wiener traveled to Europe, to be taught by
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ...
and
G. H. Hardy
Godfrey Harold Hardy (7 February 1877 – 1 December 1947) was an English mathematician, known for his achievements in number theory and mathematical analysis. In biology, he is known for the Hardy–Weinberg principle, a basic principle of pop ...
at
Cambridge University
, mottoeng = Literal: From here, light and sacred draughts.
Non literal: From this place, we gain enlightenment and precious knowledge.
, established =
, other_name = The Chancellor, Masters and Schola ...
, and by
David Hilbert
David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
and
Edmund Landau
Edmund Georg Hermann Landau (14 February 1877 – 19 February 1938) was a German mathematician who worked in the fields of number theory and complex analysis.
Biography
Edmund Landau was born to a Jewish family in Berlin. His father was Leopold ...
at the
University of Göttingen
The University of Göttingen, officially the Georg August University of Göttingen, (german: Georg-August-Universität Göttingen, known informally as Georgia Augusta) is a public research university in the city of Göttingen, Germany. Founded ...
. At Göttingen he also attended three courses with
Edmund Husserl
, thesis1_title = Beiträge zur Variationsrechnung (Contributions to the Calculus of Variations)
, thesis1_url = https://fedora.phaidra.univie.ac.at/fedora/get/o:58535/bdef:Book/view
, thesis1_year = 1883
, thesis2_title ...
"one on Kant's ethical writings, one on the principles of Ethics, and the seminary on Phenomenology." (Letter to Russell, c. June or July, 1914). During 1915–16, he taught philosophy at Harvard, then was an engineer for
General Electric
General Electric Company (GE) is an American multinational conglomerate founded in 1892, and incorporated in New York state and headquartered in Boston. The company operated in sectors including healthcare, aviation, power, renewable energ ...
and wrote for the ''
Encyclopedia Americana
''Encyclopedia Americana'' is a general encyclopedia written in American English. It was the first major multivolume encyclopedia that was published in the United States. With ''Collier's Encyclopedia'' and ''Encyclopædia Britannica, Encyclo ...
''. Wiener was briefly a journalist for the ''
Boston Herald
The ''Boston Herald'' is an American daily newspaper whose primary market is Boston, Massachusetts, and its surrounding area. It was founded in 1846 and is one of the oldest daily newspapers in the United States. It has been awarded eight Pulit ...
'', 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.
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
Oswald Veblen (June 24, 1880 – August 10, 1960) was an American mathematician, geometer and topologist, whose work found application in atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905; while this was lon ...
invited Wiener to work on
ballistics
Ballistics is the field of mechanics concerned with the launching, flight behaviour and impact effects of projectiles, especially ranged weapon munitions such as bullets, unguided bombs, rockets or the like; the science or art of designing and a ...
at the
Aberdeen Proving Ground
Aberdeen Proving Ground (APG) (sometimes erroneously called Aberdeen Proving ''Grounds'') is a U.S. Army facility located adjacent to Aberdeen, Harford County, Maryland, United States. More than 7,500 civilians and 5,000 military personnel work at ...
in Maryland. 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." 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.
After the war
Wiener was unable to secure a permanent position at Harvard, a situation he attributed largely to
anti-Semitism
Antisemitism (also spelled anti-semitism or anti-Semitism) is hostility to, prejudice towards, or discrimination against Jews. A person who holds such positions is called an antisemite. Antisemitism is considered to be a form of racism.
Antis ...
at the university and in particular the antipathy of Harvard mathematician
G. D. Birkhoff. He was also rejected for a position at the
University of Melbourne
The University of Melbourne is a public research university located in Melbourne, Australia. Founded in 1853, it is Australia's second oldest university and the oldest in Victoria. Its main campus is located in Parkville, an inner suburb nor ...
. At
W. F. Osgood's suggestion, Wiener was hired as an instructor of mathematics at
MIT
The Massachusetts Institute of Technology (MIT) is a private land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern technology and science, and is one of the m ...
, where, after his promotion to professor, he spent the remainder of his career. For many years his photograph was prominently displayed in the
Infinite Corridor
The Infinite Corridor 203 pp. is a hallway that runs through the main buildings of the Massachusetts Institute of Technology, specifically parts of the buildings numbered 7, 3, 10, 4, and 8 (from west to east).
Twice a year, in mid-November a ...
and often used in giving directions, but , it has been removed.
In 1926, Wiener returned to Europe as a
Guggenheim scholar
Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...
. He spent most of his time at Göttingen and with Hardy at Cambridge, working on
Brownian motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas).
This pattern of motion typically consists of random fluctuations in a particle's position insi ...
, the
Fourier integral
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
,
Dirichlet's problem, harmonic analysis, and the
Tauberian theorems In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named after Niels Henrik Abel and Alfred Tauber. The original examples are Abel's theorem showing tha ...
.
In 1926, Wiener's parents arranged his marriage to a German immigrant, Margaret Engemann; they had two daughters. His sister, Constance (1898–1973), married
Philip Franklin
Philip Franklin (October 5, 1898 – January 27, 1965) was an American mathematician and professor whose work was primarily focused in analysis.
Dr. Franklin received a B.S. in 1918 from City College of New York (who later awarded him ...
. Their daughter, Janet, Wiener's niece, married
Václav E. Beneš
Václav Edvard "Vic" Beneš (born January 1, 1931) is a Czech-American mathematician, known for his contributions to the theory of stochastic processes, queueing theory and control theory, as well as the design of telecommunications switches.
...
. Norbert Wiener's sister, Bertha (1902–1995), married the botanist
Carroll William Dodge
Carroll William Dodge (January 20, 1895 – July 21, 1988) was an American mycologist and lichenologist. His major fields of study included human and mammalian parasitic fungi, lichen-associated fungi, and fungi forming subterranean sporophores. ...
.
Many tales, perhaps apocryphal, were told of Norbert Wiener at MIT, especially concerning his absent-mindedness. It was said that he returned home once to find his house empty. He inquired of a neighborhood girl the reason, and she said that the family had moved elsewhere that day. He thanked her for the information and she replied, "That's why I stayed behind, Daddy!"
Asked about the story, Wiener's daughter reportedly asserted that "he never forgot who his children were! The rest of it, however, was pretty close to what actually happened…"
In the run-up to
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
(1939–45) Wiener became a member of the
China Aid Society
The China Aid Society was organized by a group of progressive Koreans in the United States after Japan invaded China in 1937. It advocated anti-Japanese political action in the US, helped refugees from the Japanese invasion and supported Korean gu ...
and the Emergency Committee in Aid of Displaced German Scholars.
He was interested in placing scholars such as
Yuk-Wing Lee
Lee Yuk-wing (; April 14, 1904 – November 8, 1989) was a Professor of Electrical Engineering at the Massachusetts Institute of Technology. He is best known for adapting and popularizing the pioneering work of Norbert Wiener and for his own resea ...
and
Antoni Zygmund
Antoni Zygmund (December 25, 1900 – May 30, 1992) was a Polish mathematician. He worked mostly in the area of mathematical analysis, including especially harmonic analysis, and he is considered one of the greatest analysts of the 20th century. ...
who had lost their positions.
During and after World War II
During
World War II
World War II or the Second World War, often abbreviated as WWII or WW2, was a world war that lasted from 1939 to 1945. It involved the vast majority of the world's countries—including all of the great powers—forming two opposin ...
, his work on the automatic aiming and firing of
anti-aircraft gun
Anti-aircraft warfare, counter-air or air defence forces is the battlespace response to aerial warfare, defined by NATO as "all measures designed to nullify or reduce the effectiveness of hostile air action".AAP-6 It includes surface based, ...
s caused Wiener to investigate
information theory
Information theory is the scientific study of the quantification (science), quantification, computer data storage, storage, and telecommunication, communication of information. The field was originally established by the works of Harry Nyquist a ...
independently of
Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American people, American mathematician, electrical engineering, electrical engineer, and cryptography, cryptographer known as a "father of information theory".
As a 21-year-o ...
and to invent the
Wiener filter
In signal processing, the Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant ( LTI) filtering of an observed noisy process, assuming known stationary signal and noise spectra, and ...
. (To him is due the now standard practice of modeling an information source as a random process—in other words, as a variety of noise.) Initially his anti-aircraft work led him to write, with
Arturo Rosenblueth
Arturo Rosenblueth Stearns (October 2, 1900 – September 20, 1970) was a Mexican researcher, physician and physiologist, who is known as one of the pioneers of cybernetics.
Biography
Rosenblueth was born in 1900 in Ciudad Guerrero, Chihuahua. ...
and
Julian Bigelow
Julian Bigelow (March 19, 1913 – February 17, 2003) was a pioneering American computer engineer. Life
Bigelow was born in 1913 in Nutley, New Jersey. He obtained a master's degree at the Massachusetts Institute of Technology, studying electrica ...
the 1943 article 'Behavior, Purpose and Teleology', which was published in
Philosophy of Science
Philosophy of science is a branch of philosophy concerned with the foundations, methods, and implications of science. The central questions of this study concern what qualifies as science, the reliability of scientific theories, and the ultim ...
. Subsequently his anti-aircraft work led him to formulate
cybernetics
Cybernetics is a wide-ranging field concerned with circular causality, such as feedback, in regulatory and purposive systems. Cybernetics is named after an example of circular causal feedback, that of steering a ship, where the helmsperson m ...
. After the war, his fame helped MIT to recruit a research team in
cognitive science, composed of researchers in
neuropsychology
Neuropsychology is a branch of psychology concerned with how a person's cognition and behavior are related to the brain and the rest of the nervous system. Professionals in this branch of psychology often focus on how injuries or illnesses of t ...
and the mathematics and
biophysics
Biophysics is an interdisciplinary science that applies approaches and methods traditionally used in physics to study biological phenomena. Biophysics covers all scales of biological organization, from molecular to organismic and populations. ...
of the nervous system, including
Warren Sturgis McCulloch
Warren Sturgis McCulloch (November 16, 1898 – September 24, 1969) was an American neurophysiologist and cybernetician, known for his work on the foundation for certain brain theories and his contribution to the cybernetics movement.Ken Aizawa ( ...
and
Walter Pitts
Walter Harry Pitts, Jr. (23 April 1923 – 14 May 1969) was a logician who worked in the field of computational neuroscience.Smalheiser, Neil R"Walter Pitts", ''Perspectives in Biology and Medicine'', Volume 43, Number 2, Winter 2000, pp. 21 ...
. These men later made pioneering contributions to
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
and
artificial intelligence
Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machines, as opposed to intelligence displayed by animals and humans. Example tasks in which this is done include speech re ...
. Soon after the group was formed, Wiener suddenly ended all contact with its members, mystifying his colleagues. This emotionally traumatized Pitts, and led to his career decline. In their biography of Wiener,
Conway and
Siegelman suggest that Wiener's wife Margaret, who detested McCulloch's
bohemian
Bohemian or Bohemians may refer to:
*Anything of or relating to Bohemia
Beer
* National Bohemian, a brand brewed by Pabst
* Bohemian, a brand of beer brewed by Molson Coors
Culture and arts
* Bohemianism, an unconventional lifestyle, origin ...
lifestyle, engineered the breach.
Wiener later helped develop the theories of cybernetics,
robotics
Robotics is an interdisciplinary branch of computer science and engineering. Robotics involves design, construction, operation, and use of robots. The goal of robotics is to design machines that can help and assist humans. Robotics integrat ...
, computer control, and
automation
Automation describes a wide range of technologies that reduce human intervention in processes, namely by predetermining decision criteria, subprocess relationships, and related actions, as well as embodying those predeterminations in machines ...
. He discussed the modeling of neurons with
John von Neumann
John von Neumann (; hu, Neumann János Lajos, ; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, engineer and polymath. He was regarded as having perhaps the widest cove ...
, and in a letter from November 1946 von Neumann presented his thoughts in advance of a meeting with Wiener.
Wiener always shared his theories and findings with other researchers, and credited the contributions of others. These included
Soviet
The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, it was nominally a federal union of fifteen nation ...
researchers and their findings. Wiener's acquaintance with them caused him to be regarded with suspicion during the
Cold War
The Cold War is a term commonly used to refer to a period of geopolitical tension between the United States and the Soviet Union and their respective allies, the Western Bloc and the Eastern Bloc. The term '' cold war'' is used because the ...
. He was a strong advocate of automation to improve the standard of living, and to end economic underdevelopment. His ideas became influential in
India
India, officially the Republic of India (Hindi: ), is a country in South Asia. It is the seventh-largest country by area, the second-most populous country, and the most populous democracy in the world. Bounded by the Indian Ocean on the so ...
, 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" from the January 1947 issue of ''
The Atlantic Monthly
''The Atlantic'' is an American magazine and multi-platform publisher. It features articles in the fields of politics, foreign affairs, business and the economy, culture and the arts, technology, and science.
It was founded in 1857 in Boston, ...
'' 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 those of von Neumann is the major theme of the book ''John Von Neumann and Norbert Wiener''.
Wiener was a participant of the
Macy conferences.
Personal life
In 1926 Wiener married Margaret Engemann, an assistant professor of modern languages at
Juniata College
Juniata College is a private liberal arts college in Huntingdon, Pennsylvania. Founded in 1876 as a co-educational school, it was the first college started by members of the Church of the Brethren as a center for vocational learning for those wh ...
. They had two daughters. Opinions are not all positive on Margaret's impacts on Wiener's career.
Wiener admitted in his autobiography ''I Am a Mathematician: The Later Life of a Prodigy'' to abusing
benzadrine throughout his life without being fully aware of its dangers.
Wiener died in March 1964, aged 69, in
Stockholm
Stockholm () is the Capital city, capital and List of urban areas in Sweden by population, largest city of Sweden as well as the List of urban areas in the Nordic countries, largest urban area in Scandinavia. Approximately 980,000 people liv ...
, from a heart attack. Wiener and his wife are buried at the Vittum Hill Cemetery in
Sandwich, New Hampshire
Sandwich is a town in Carroll County, New Hampshire, United States. Its population was 1,466 at the 2020 census. Sandwich includes the villages of Center Sandwich and North Sandwich. Part of the White Mountain National Forest is in the north, a ...
.
Awards and honors
* Wiener was a Plenary Speaker of the
ICM in 1936 at Oslo and in 1950 at Cambridge, Massachusetts.
* Wiener won the
Bôcher Memorial Prize
The Bôcher Memorial Prize was founded by the American Mathematical Society in 1923 in memory of Maxime Bôcher with an initial endowment of $1,450 (contributed by members of that society). It is awarded every three years (formerly every five year ...
in 1933 and the
National Medal of Science
The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social scienc ...
in 1963, presented by President Johnson at a White House Ceremony in January, 1964, shortly before Wiener's death.
* Wiener won the 1965 U.S.
National Book Award
The National Book Awards are a set of annual U.S. literary awards. At the final National Book Awards Ceremony every November, the National Book Foundation presents the National Book Awards and two lifetime achievement awards to authors.
The Nat ...
in Science, Philosophy and Religion for ''
God & Golem, Inc.: A Comment on Certain Points where Cybernetics Impinges on Religion''.
["National Book Awards – 1965"](_blank)
. National Book Foundation
The National Book Foundation (NBF) is an American nonprofit organization established, "to raise the cultural appreciation of great writing in America". Established in 1989 by National Book Awards, Inc.,Edwin McDowell. "Book Notes: 'The Joy Luc ...
. Retrieved 2012-03-05.
* The
Norbert Wiener Prize in Applied Mathematics
The Norbert Wiener Prize in Applied Mathematics is a $5000 prize awarded, every three years, for an outstanding contribution to "applied mathematics in the highest and broadest sense." It was endowed in 1967 in honor of Norbert Wiener by MIT's m ...
was endowed in 1967 in honor of Norbert Wiener by MIT's mathematics department and is provided jointly by the
American Mathematical Society
The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...
and
Society for Industrial and Applied Mathematics.
* The
awarded annually by
CPSR, was established in 1987 in honor of Wiener to recognize contributions by computer professionals to socially responsible use of computers.
* The crater
Wiener on the
far side
''The Far Side'' is a single-panel comic created by Gary Larson and syndicated by Chronicle Features and then Universal Press Syndicate, which ran from December 31, 1979, to January 1, 1995 (when Larson retired as a cartoonist). Its surrealis ...
of the
Moon
The Moon is Earth's only natural satellite. It is the fifth largest satellite in the Solar System and the largest and most massive relative to its parent planet, with a diameter about one-quarter that of Earth (comparable to the width of ...
is named after him.
* The Norbert Wiener Center for Harmonic Analysis and Applications, at the
University of Maryland, College Park
The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland. Founded in 1856, UMD is the flagship institution of the University System of Mary ...
, is named in his honor.
* Robert A. Heinlein named a spaceship after him in his 1957 novel ''
Citizen of the Galaxy
''Citizen of the Galaxy'' is a science fiction novel by American writer Robert A. Heinlein, originally serialized in ''Astounding Science Fiction'' (September, October, November, and December 1957) and published in hardcover in 1957 as one of t ...
'', a "Free Trader" ship called the ''Norbert Wiener'' mentioned in Chapter 14.
Doctoral students
*
Shikao Ikehara
was a Japanese mathematician. He was a student of Norbert Wiener at MIT ( PhD 1930).
Following Wiener in 1928, in 1931 Ikehara used Wiener's Tauberian theory to derive another proof of the prime number theorem, demonstrated solely via the non-v ...
(PhD 1930)
*
Dorothy Walcott Weeks (PhD 1930)
*
Norman Levinson
Norman Levinson (August 11, 1912 in Lynn, Massachusetts – October 10, 1975 in Boston) was an American mathematician. Some of his major contributions were in the study of Fourier transforms, complex analysis, non-linear differential equation ...
(Sc.D. 1935)
*
Brockway McMillan
Brockway McMillan (March 30, 1915 – December 3, 2016) was an American government official and scientist, who served as the eighth Under Secretary of the Air Force and the second Director of the National Reconnaissance Office.
McMillan was ...
(PhD 1939)
*
Abe Gelbart
Abraham Markham Gelbart (December 2, 1911 – September 7, 1994) was an American mathematician, the founding dean of the Belfer Graduate School of Science at Yeshiva University and the namesake of the International Research Institute for Mathematic ...
(PhD 1940)
*
John P. Costas (engineer)
John Peter Costas (1923 in Wabash, Indiana – August 9, 2008) was an American electrical engineer. Costas invented, among other things, the Costas loop and Costas arrays.
Biography
Costas studied at Purdue University as an undergraduate. During ...
(PhD 1951)
*
Amar Bose
Amar Gopal Bose (November 2, 1929 – July 12, 2013) was an American entrepreneur and academic. An electrical engineer and sound engineer, he was a professor at the Massachusetts Institute of Technology for over 45 years. He was also the found ...
(Sc.D. 1956)
*
Colin Cherry
Edward Colin Cherry (23 June 1914 – 23 November 1979) was a British cognitive scientist whose main contributions were in focused auditory attention, specifically the cocktail party problem regarding the capacity to follow one conversatio ...
(PhD 1956)
Work
Wiener was an early studier of
stochastic
Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselv ...
and mathematical
noise
Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...
processes, contributing work relevant to
electronic engineering
Electronics engineering is a sub-discipline of electrical engineering which emerged in the early 20th century and is distinguished by the additional use of active components such as semiconductor devices to amplify and control electric current ...
,
electronic communication
Telecommunication is the transmission of information by various types of technologies over wire, radio, optical, or other electromagnetic systems. It has its origin in the desire of humans for communication over a distance greater than that ...
, and
control system
A control system manages, commands, directs, or regulates the behavior of other devices or systems using control loops. It can range from a single home heating controller using a thermostat controlling a domestic boiler to large industrial c ...
s. It was Wiener's idea to model a signal as if it were an exotic type of noise, giving it a sound mathematical basis. The example often given to students is that English text could be modeled as a random string of letters and spaces, where each letter of the alphabet (and the space) has an assigned probability. But Wiener dealt with analog signals, where such a simple example doesn't exist. Wiener's early work on information theory and signal processing was limited to analog signals, and was largely forgotten with the development of the digital theory.
Wiener is one of the key originators of
cybernetics
Cybernetics is a wide-ranging field concerned with circular causality, such as feedback, in regulatory and purposive systems. Cybernetics is named after an example of circular causal feedback, that of steering a ship, where the helmsperson m ...
, a formalization of the notion of
feedback
Feedback occurs when outputs of a system are routed back as inputs as part of a chain of cause-and-effect that forms a circuit or loop. The system can then be said to ''feed back'' into itself. The notion of cause-and-effect has to be handled ...
, with many implications for
engineering
Engineering is the use of scientific method, scientific principles to design and build machines, structures, and other items, including bridges, tunnels, roads, vehicles, and buildings. The discipline of engineering encompasses a broad rang ...
,
systems control Systems control, in a communications system, is the control and implementation of a set of functions that:
# prevent or eliminate Degradation (telecommunications), degradation of any part of the system,
# initiate immediate response to demands tha ...
,
computer science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
,
biology
Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of cells that process hereditary i ...
,
philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
, and the organization of
society
A society is a group of individuals involved in persistent social interaction, or a large social group sharing the same spatial or social territory, typically subject to the same political authority and dominant cultural expectations. Socie ...
.
Wiener's work with cybernetics influenced
Gregory Bateson and
Margaret Mead
Margaret Mead (December 16, 1901 – November 15, 1978) was an American cultural anthropologist who featured frequently as an author and speaker in the mass media during the 1960s and the 1970s.
She earned her bachelor's degree at Barnard Co ...
, and through them,
anthropology
Anthropology is the scientific study of humanity, concerned with human behavior, human biology, cultures, societies, and linguistics, in both the present and past, including past human species. Social anthropology studies patterns of behavi ...
,
sociology
Sociology is a social science that focuses on society, human social behavior, patterns of Interpersonal ties, social relationships, social interaction, and aspects of culture associated with everyday life. It uses various methods of Empirical ...
, and
education
Education is a purposeful activity directed at achieving certain aims, such as transmitting knowledge or fostering skills and character traits. These aims may include the development of understanding, rationality, kindness, and honesty. Va ...
.
Wiener equation
A simple mathematical representation of
Brownian motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas).
This pattern of motion typically consists of random fluctuations in a particle's position insi ...
, the
Wiener equation
A simple mathematical representation of Brownian motion, the Wiener equation, named after Norbert Wiener, assumes the current velocity of a fluid particle fluctuates randomly:
:\mathbf = \frac = g(t),
where v is velocity, x is position, ''d/dt'' ...
, named after Wiener, assumes the current
velocity
Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
of a
fluid
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
particle fluctuates randomly.
Wiener filter
For signal processing, the
Wiener filter
In signal processing, the Wiener filter is a filter used to produce an estimate of a desired or target random process by linear time-invariant ( LTI) filtering of an observed noisy process, assuming known stationary signal and noise spectra, and ...
is a
filter
Filter, filtering or filters may refer to:
Science and technology
Computing
* Filter (higher-order function), in functional programming
* Filter (software), a computer program to process a data stream
* Filter (video), a software component tha ...
proposed by Wiener during the 1940s and published in 1942 as a classified document. Its purpose is to reduce the amount of
noise
Noise is unwanted sound considered unpleasant, loud or disruptive to hearing. From a physics standpoint, there is no distinction between noise and desired sound, as both are vibrations through a medium, such as air or water. The difference arise ...
present in a signal by comparison with an estimate of the desired noiseless signal. Wiener developed the filter at the Radiation Laboratory at MIT to predict the position of German bombers from radar reflections. It is necessary to predict the position, because by the time the shell reaches the vicinity of the target, the target will have moved, and may have changed direction slightly. They even modeled the muscle response of the pilot, which led eventually to cybernetics. The unmanned V1's were particularly easy to model, and on a good day, American guns fitted with Wiener filters would shoot down 99 out of 100 V1's as they entered Britain from the English channel, on their way to London. What emerged was a mathematical theory of great generality—a theory for predicting the future as best one can on the basis of incomplete information about the past. It was a statistical theory that included applications that did not, strictly speaking, predict the future, but only tried to remove noise. It made use of Wiener's earlier work on
integral equations
In mathematics, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus be expressed as being of the form: f(x_1,x_2,x_3,...,x_n ; u(x_1,x_2,x_3,...,x_n) ...
and
Fourier transforms
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, ...
.
In mathematics
Wiener took a great interest in the mathematical theory of
Brownian motion
Brownian motion, or pedesis (from grc, πήδησις "leaping"), is the random motion of particles suspended in a medium (a liquid or a gas).
This pattern of motion typically consists of random fluctuations in a particle's position insi ...
(named after
Robert Brown) proving many results now widely known such as the non-differentiability of the paths. Consequently, the one-dimensional version of Brownian motion was named the
Wiener process
In mathematics, the Wiener process is a real-valued continuous-time stochastic process named in honor of American mathematician Norbert Wiener for his investigations on the mathematical properties of the one-dimensional Brownian motion. It is ...
. It is the best known of the
Lévy process
In probability theory, a Lévy process, named after the French mathematician Paul Lévy, is a stochastic process with independent, stationary increments: it represents the motion of a point whose successive displacements are random, in which disp ...
es,
càdlàg In mathematics, a càdlàg (French: "''continue à droite, limite à gauche''"), RCLL ("right continuous with left limits"), or corlol ("continuous on (the) right, limit on (the) left") function is a function defined on the real numbers (or a subset ...
stochastic processes with stationary statistically
independent increments In probability theory, independent increments are a property of stochastic processes and random measures. Most of the time, a process or random measure has independent increments by definition, which underlines their importance. Some of the stochas ...
, and occurs frequently in pure and applied mathematics, physics and economics (e.g. on the stock-market).
Wiener's tauberian theorem In mathematical analysis, Wiener's tauberian theorem is any of several related results proved by Norbert Wiener in 1932. They provide a necessary and sufficient condition under which any function in or can be approximated by linear combination ...
, a 1932 result of Wiener, developed
Tauberian theorem In mathematics, Abelian and Tauberian theorems are theorems giving conditions for two methods of summing divergent series to give the same result, named after Niels Henrik Abel and Alfred Tauber. The original examples are Abel's theorem showing th ...
s in
summability theory
In mathematics, a divergent series is an infinite series that is not convergent, meaning that the infinite sequence of the partial sums of the series does not have a finite limit.
If a series converges, the individual terms of the series must ...
, on the face of it a chapter of
real analysis
In mathematics, the branch of real analysis studies the behavior of real numbers, sequences and series of real numbers, and real functions. Some particular properties of real-valued sequences and functions that real analysis studies include conv ...
, by showing that most of the known results could be encapsulated in a principle taken from
harmonic analysis. In its present formulation, the theorem of Wiener does not have any obvious association with Tauberian theorems, which deal with
infinite series
In mathematics, a series is, roughly speaking, a description of the operation of adding infinitely many quantities, one after the other, to a given starting quantity. The study of series is a major part of calculus and its generalization, math ...
; the translation from results formulated for integrals, or using the language of
functional analysis
Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. Inner product space#Definition, inner product, Norm (mathematics)#Defini ...
and
Banach algebra
In mathematics, especially functional analysis, a Banach algebra, named after Stefan Banach, is an associative algebra A over the real or complex numbers (or over a non-Archimedean complete normed field) that at the same time is also a Banach ...
s, is however a relatively routine process.
The
Paley–Wiener theorem In mathematics, a Paley–Wiener theorem is any theorem that relates decay properties of a function or distribution at infinity with analyticity of its Fourier transform. The theorem is named for Raymond Paley (1907–1933) and Norbert Wiener (189 ...
relates growth properties of
entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic on the whole complex plane. Typical examples of entire functions are polynomials and the exponential function, and any fin ...
s on C
n and Fourier transformation of Schwartz distributions of compact support.
The
Wiener–Khinchin theorem
In applied mathematics, the Wiener–Khinchin theorem or Wiener–Khintchine theorem, also known as the Wiener–Khinchin–Einstein theorem or the Khinchin–Kolmogorov theorem, states that the autocorrelation function of a wide-sense-stationary ...
, (also known as the ''Wiener – Khintchine theorem'' and 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 The concept of an abstract Wiener space is a mathematical construction developed by Leonard Gross to understand the structure of Gaussian measures on infinite-dimensional spaces. The construction emphasizes the fundamental role played by the Camer ...
is a mathematical object in
measure theory
In mathematics, the concept of a measure is a generalization and formalization of geometrical measures ( length, area, volume) and other common notions, such as mass and probability of events. These seemingly distinct concepts have many simil ...
, 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
In mathematics, classical Wiener space is the collection of all continuous functions on a given domain (usually a subinterval of the real line), taking values in a metric space (usually ''n''-dimensional Euclidean space). Classical Wiener space i ...
. Leonard Gross provided the generalization to the case of a general
separable Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced ) is a complete normed vector space. Thus, a Banach space is a vector space with a metric that allows the computation of vector length and distance between vector ...
.
The notion of a Banach space itself was discovered independently by both Wiener and
Stefan Banach
Stefan Banach ( ; 30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the 20th century's most important and influential mathematicians. He was the founder of modern functional analysis, and an origina ...
at around the same time.
The
Norbert Wiener Center for Harmonic Analysis and Applications
The Norbert Wiener Center for Harmonic Analysis and Applications (NWC) is a division of the Mathematics Department in the University of Maryland College of Computer, Mathematical, and Natural Sciences devoted to research and education in pure and ...
(NWC) in the Department of Mathematics at the University of Maryland, College Park is devoted to the scientific and mathematical legacy of Norbert Wiener. Th
NWC websitehighlights the research activities of the center. Further, each year the Norbert Wiener Center hosts the February Fourier Talks, a two-day national conference displaying advances in pure and applied harmonic analysis in industry, government, and academia.
In popular culture
His work with
Mary Brazier is referred to in
Avis DeVoto
Avis is Latin for bird and may refer to:
Aviation
* Auster Avis, a 1940s four-seat light aircraft developed from the Auster Autocrat (abandoned project)
*Avro Avis, a two-seat biplane
* Scottish Aeroplane Syndicate Avis, an early aircraft built b ...
's ''As Always, Julia''.
A flagship named after him appears briefly in ''
Citizen of the Galaxy
''Citizen of the Galaxy'' is a science fiction novel by American writer Robert A. Heinlein, originally serialized in ''Astounding Science Fiction'' (September, October, November, and December 1957) and published in hardcover in 1957 as one of t ...
'' by
Robert Heinlein
Robert Anson Heinlein (; July 7, 1907 – May 8, 1988) was an American science fiction author, aeronautical engineer, and naval officer. Sometimes called the "dean of science fiction writers", he was among the first to emphasize scientific accu ...
.
The song ''Dedicated to Norbert Wiener'' appears as the second track on the 1980 album ''Why?'' by G.G. Tonet (Luigi Tonet), released on the Italian ''It Why'' label.
Publications
Wiener wrote many books and hundreds of articles:
* 1914, Reprinted in
* 1930,
* 1933,
The Fourier Integral and Certain of its Applications' Cambridge Univ. Press; reprint by Dover, CUP Archive 1988
* 1942, ''Extrapolation, Interpolation and Smoothing of Stationary Time Series''. A war-time classified report nicknamed "the yellow peril" because of the color of the cover and the difficulty of the subject. Published postwar 1949
MIT Press
The MIT Press is a university press affiliated with the Massachusetts Institute of Technology (MIT) in Cambridge, Massachusetts (United States). It was established in 1962.
History
The MIT Press traces its origins back to 1926 when MIT publish ...
. http://www.isss.org/lumwiener.htm ])
* 1948, ''
Cybernetics: Or Control and Communication in the Animal and the Machine.'' Paris, (Hermann & Cie) & Camb. Mass. (MIT Press) ; 2nd revised ed. 1961.
* 1950, ''
The Human Use of Human Beings''. The Riverside Press (Houghton Mifflin Co.).
* 1958, ''Nonlinear Problems in Random Theory''. MIT Press & Wiley.
* 1964, ''Selected Papers of Norbert Wiener''. Cambridge Mass. 1964 (MIT Press & SIAM)
* 1964, ''
God & Golem, Inc.: A Comment on Certain Points Where Cybernetics Impinges on Religion''. MIT Press.
* 1966, Published in book form.
* 1966, ''Generalized Harmonic Analysis and Tauberian Theorems''. MIT Press.
* 1993, This was written in 1954 but Wiener abandoned the project at the editing stage and returned his advance. MIT Press published it posthumously in 1993.
* 1976–84, ''The Mathematical Work of Norbert Wiener''. Masani P (ed) 4 vols, Camb. Mass. (MIT Press). This contains a complete collection of Wiener's mathematical papers with commentaries.
Fiction:
* 1959, ''The Tempter''. Random House.
Autobiography:
* 1953, ''Ex-Prodigy: My Childhood and Youth''. MIT Press.
* 1956, ''I am a Mathematician''. London (Gollancz).
Under the name "W. Norbert":
* 1952, ''The Brain'' and other short science fiction in
Tech Engineering News.
See also
*
Autowave
*
Box–Muller transform
The Box–Muller transform, by George Edward Pelham Box and Mervin Edgar Muller, is a random number sampling method for generating pairs of independent, standard, normally distributed (zero expectation, unit variance) random numbers, given a ...
*
Cellular automaton
A cellular automaton (pl. cellular automata, abbrev. CA) is a discrete model of computation studied in automata theory. Cellular automata are also called cellular spaces, tessellation automata, homogeneous structures, cellular structures, tesse ...
*
Functional integration
Functional integration is a collection of results in mathematics and physics where the domain of an integral is no longer a region of space, but a space of functions. Functional integrals arise in probability, in the study of partial differentia ...
*
Operational calculus Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation.
History
Th ...
*
Smoothing problem (stochastic processes)
The smoothing problem (not to be confused with smoothing in statistics, image processing and other contexts) is the problem of estimating an unknown probability density function recursively over time using incremental incoming measurements. It i ...
*
List of things named after Norbert Wiener {{Short description, none
In mathematics, there are a large number of topics named in honor of Norbert Wiener (1894 – 1964).
* Abstract Wiener space
* Classical Wiener space
* Paley–Wiener integral
* Paley–Wiener theorem
* Wiener algebra
* ...
Notes
Further reading
*
*
*
*
*
*
*
*
*
*
*
* ''.''
*
*
External links
*
Norbert Wiener Center for Harmonic Analysis and Applications– Living Internet
*
*
*
"Norbert Wiener" in ''Complete Dictionary of Scientific Biography''
{{DEFAULTSORT:Wiener, Norbert
1894 births
1964 deaths
20th-century American mathematicians
American agnostics
American pacifists
American people of German-Jewish descent
American people of Polish-Jewish descent
Control theorists
Cornell University alumni
Cyberneticists
General Electric people
Harvard Graduate School of Arts and Sciences alumni
Harvard University faculty
Jewish agnostics
Jewish American scientists
Jewish philosophers
Jewish American academics
Jewish pacifists
Massachusetts Institute of Technology School of Science faculty
National Book Award winners
National Medal of Science laureates
People from Belmont, Massachusetts
People from Columbia, Missouri
Probability theorists
American systems scientists
Tufts University School of Arts and Sciences alumni
Analysands of Helene Deutsch
Scientists from Missouri
Mathematicians from Missouri