Norbert Wiener
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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, mathematical structure, structure, space, Mathematica ...
and philosopher. He was a professor of mathematics at the
Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private Land-grant university, land-grant research university in Cambridge, Massachusetts. Established in 1861, MIT has played a key role in the development of modern t ...
(MIT). A child prodigy, 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 themselve ...
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 aris ...
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, 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 ...
s. Wiener is considered the originator of cybernetics, 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,
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 practical disciplines (includin ...
,
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 hereditar ...
,
neuroscience Neuroscience is the science, scientific study of the nervous system (the brain, spinal cord, and peripheral nervous system), its functions and disorders. It is a Multidisciplinary approach, multidisciplinary science that combines physiology, an ...
, philosophy, and the organization of
society A society is a Social group, group of individuals involved in persistent Social relation, social interaction, or a large social group sharing the same spatial or social territory, typically subject to the same Politics, political authority an ...
. 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 machine A machine is a physical system using Power (physics), power to apply Force, forces and control Motion, moveme ...
.


Biography


Youth

Wiener was born in Columbia, Missouri, the first child of Leo Wiener and Bertha Kahn, Jewish immigrants from Lithuania and
Germany Germany, officially the Federal Republic of Germany (FRG),, is a country in Central Europe. It is the most populous member state of the European Union. Germany lies between the Baltic and North Sea to the north and the Alps to the sou ...
, 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, 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 Slavs, Slavic peoples and their descendants. They are thought to descend from a proto-language called Proto-Slavic language, Proto ...
, 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 in 1906 at 11 years of age, and Wiener then entered Tufts College. 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 kingdom, including the structure, embryology, evolution, classification, habits, and ...
at Harvard. 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 teac ...
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, whose mathematical interests ranged from axiomatic foundations to engineering problems. Harvard awarded Wiener a
PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * ''Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. albu ...
in June 1913, when he was only 19 years old, for a dissertation on
mathematical logic Mathematical logic is the study of 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 formal ...
(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 applic ...
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, ar ...
), 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 co ...
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 concer ...
. Hence
relations Relation or relations may refer to: General uses *International relations, the study of interconnection of politics, economics, and law on a global level *Interpersonal relationship, association or acquaintance between two or more people *Public ...
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. 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, ar ...
and G. H. Hardy 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 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 Leopo ...
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 i ...
. 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''. 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 Puli ...
'', where he wrote a feature story on the poor labor conditions for mill workers in
Lawrence, Massachusetts Lawrence is a city located in Essex County, Massachusetts Massachusetts (Massachusett language, Massachusett: ''Muhsachuweesut assachusett writing systems, məhswatʃəwiːsət'' English: , ), officially the Commonwealth of Massachuset ...
, 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 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 ...
at the Aberdeen Proving Ground 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. Ant ...
at the university and in particular the antipathy of Harvard mathematician
G. D. Birkhoff George David Birkhoff (March 21, 1884 – November 12, 1944) was an American mathematician best known for what is now called the ergodic theorem. Birkhoff was one of the most important leaders in American mathematics in his generation, and durin ...
. 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 n ...
. At W. F. Osgood's suggestion, Wiener was hired as an instructor of mathematics at MIT, 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 and often used in giving directions, but , it has been removed. 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 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,
Dirichlet's problem In mathematics, a Dirichlet problem is the problem of finding a function which solves a specified partial differential equation (PDE) in the interior of a given region that takes prescribed values on the boundary of the region. The Dirichlet prob ...
, harmonic analysis, and the Tauberian theorems. 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. Their daughter, Janet, Wiener's niece, married Václav E. Beneš. Norbert Wiener's sister, Bertha (1902–1995), married the botanist Carroll William Dodge. 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 World War II by country, vast majority of the world's countries—including all of the great power ...
(1939–45) Wiener became a member of the China Aid Society and the Emergency Committee in Aid of Displaced German Scholars. He was interested in placing scholars such as Yuk-Wing Lee and Antoni Zygmund 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 World War II by country, vast majority of the world's countries—including all of the great power ...
, his work on the automatic aiming and firing of anti-aircraft guns caused Wiener to investigate
information theory Information theory is the scientific study of the quantification, storage, and communication of information. The field was originally established by the works of Harry Nyquist and Ralph Hartley, in the 1920s, and Claude Shannon in the 1940s. ...
independently of
Claude Shannon Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, and cryptographer known as a "father of information theory". As a 21-year-old master's degree student at the Massachusetts In ...
and to invent the Wiener filter. (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 and Julian Bigelow 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 ulti ...
. Subsequently his anti-aircraft work led him to formulate cybernetics. 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 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 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 practical disciplines (includin ...
and
artificial intelligence Artificial intelligence (AI) is intelligence—perceiving, synthesizing, and inferring information—demonstrated by machine A machine is a physical system using Power (physics), power to apply Force, forces and control Motion, moveme ...
. 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 lifestyle, engineered the breach. Wiener later helped develop the theories of cybernetics,
robotics Robotics is an interdisciplinarity, 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 human ...
, 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 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 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 ...
, 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 Amphetamine (contracted from alpha- methylphenethylamine) is a strong central nervous system (CNS) stimulant that is used in the treatment of attention deficit hyperactivity disorder (ADHD), narcolepsy, and obesity. It is also commonly us ...
throughout his life without being fully aware of its dangers. Wiener died in March 1964, aged 69, in Stockholm, 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 ...
.


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 in 1933 and the National Medal of Science 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 N ...
in Science, Philosophy and Religion for '' God & Golem, Inc.: A Comment on Certain Points where Cybernetics Impinges on Religion''."National Book Awards – 1965"
. National Book Foundation. Retrieved 2012-03-05.
* The Norbert Wiener Prize in Applied Mathematics 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 Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific soci ...
. * The Norbert Wiener Award for Social and Professional Responsibility 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 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 ...
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 ...
, is named in his honor. * Robert A. Heinlein named a spaceship after him in his 1957 novel '' Citizen of the Galaxy'', a "Free Trader" ship called the ''Norbert Wiener'' mentioned in Chapter 14.


Doctoral students

* Shikao Ikehara (PhD 1930) *
Dorothy Walcott Weeks Dorothy Walcott Weeks (May 3, 1893 – June 4, 1990) was an American mathematician and physicist. Weeks was born in Philadelphia, Pennsylvania. She earned degrees from Wellesley College, the Massachusetts Institute of Technology, and Simmons ...
(PhD 1930) * Norman Levinson (Sc.D. 1935) * Brockway McMillan (PhD 1939) * Abe Gelbart (PhD 1940) * John P. Costas (engineer) (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 fo ...
(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 conversati ...
(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 themselve ...
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 aris ...
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, 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 ...
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, 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,
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 practical disciplines (includin ...
,
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 hereditar ...
, philosophy, and the organization of
society A society is a Social group, group of individuals involved in persistent Social relation, social interaction, or a large social group sharing the same spatial or social territory, typically subject to the same Politics, political authority an ...
. 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 C ...
, 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 be ...
, sociology, and education.


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, named after Wiener, assumes the current velocity of a fluid particle fluctuates randomly.


Wiener filter

For signal processing, the Wiener filter is a filter (signal processing), filter proposed by Wiener during the 1940s and published in 1942 as a classified document. Its purpose is to reduce the amount of noise 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 and Fourier transforms.


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 (Scottish botanist from Montrose), 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. 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. In its present formulation, 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, (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 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 space, separable Banach space. The notion of a Banach space itself was discovered independently by both Wiener and Stefan Banach at around the same time. The Norbert Wiener Center for Harmonic Analysis and Applications (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 website
highlights 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's ''As Always, Julia''. A flagship named after him appears briefly in '' Citizen of the Galaxy'' by Robert Heinlein. 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. 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 * Cellular automaton * Functional integration * Operational calculus * Smoothing problem (stochastic processes) * List of things named after Norbert Wiener


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