Norbert Wiener
Photo: Konrad Jacobs, CC BY-SA 2.0 de, via Wikimedia Commons16

Norbert Wiener

American mathematician and philosopher (1894–1964)

Norbert Wiener (November 26, 1894 – March 18, 1964) was an American computer scientist, mathematician, and philosopher. He became a professor of mathematics at the Massachusetts Institute of Technology (MIT).2

From Wikipedia’s article on Norbert Wiener (this version), CC BY-SA 4.0.

Born Nov 26, 1894, died Mar 18, 1964.1

About

A child prodigy, Wiener later became an early researcher in stochastic and mathematical noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.

Wiener is considered the originator of cybernetics, the science of communication as it relates to living things and machines, with implications for engineering, systems control, computer science, biology, neuroscience, philosophy, and the organization of society. His work heavily influenced computer pioneer John von Neumann, information theorist Claude Shannon, anthropologists Margaret Mead and Gregory Bateson, and others.

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, an important early step towards the development of modern artificial intelligence.

From Wikipedia’s article on Norbert Wiener, shared under CC BY-SA 4.0.2

Companies

Early life and education

  • 1901 to 1903Peabody School3
  • 1903 to 1906Ayer High School3
  • 1906 to 1909Tufts University3
  • 1909 to 1910Harvard University3
  • 1910 to 1911Cornell University3
  • 1911 to 1913Harvard University3
  • 1913 to 1914University of Cambridge3
  • 1914 to 1915University of Göttingen3
  • Date not recordedTufts University School of Engineering3

Family and youth

Wiener was born in Columbia, Missouri, the first child of Leo Wiener and Bertha Kahn, Jewish immigrants from Lithuania and Germany, respectively. Through his father, he was related to Maimonides, the famous 12th century rabbi, philosopher and physician from al-Andalus, as well as to Akiva Eger, chief rabbi of Posen from 1815 to 1837.

He met his paternal grandfather—Solomon Wiener, whom he describes as a scholarly journalist incapable of keeping the family together—only once in New York. Despite this, he was impressed by his grandfather's efforts to replace Yiddish in his lived environment with German. Solomon was born in Krotoschin, but married his wife—who came from a family of Jewish tanners—before settling in Byelostok where Wiener's father was born in 1862. Wiener was told they had originally been minor nobles in Russia, such that when the Russian Tzar came to visit Byelostok it was his grandmother's house which was selected as a place of temporary residence.

His paternal grandmother's side of the family was very different to his grandfather's side, and Wiener suggests that his father developed "solid, business-like habits that gave my father a firm footing in life", which made him a better custodian of the family than his grandfather. Nonetheless, his father still displayed an idealist streak. By the age of thirteen and because of their family situation—and because according to Wiener there is a tendency within the Jewish community to give adolescent boys the responsibilities of men—his father Leo had begun to support his family as a private tutor. Due to the German bias of his grandfather, Wiener's father went to a Lutheran school and learnt several languages.

His father later left the Minsk Gymnasium for Warsaw in Poland, where Wiener claims his father developed good relations with his Polish schoolmates—so much so that his father became privy to the underground Polish resistance movement. His father became a contemporary of Zamenhof, the inventor of Esperanto, to which Wiener claims: "my father was one of the first to study the new artificial language". His father later went to the University of Warsaw to study medicine, although could not handle the profession so went to study at the Polytechnicum in Berlin to study engineering. Relatives in Berlin with connections to Mendelssohn bank tried to get his father to pursue a career in banking, but his father declined. Instead, his father had begun to develop a Tolstoyan ethic which was reinforced through his attendance of a humanitarian student meeting, which would eventually led to him emigrating to the United States, as well as Wiener's vegetarianism. Wiener, however, expressed resentment over his father's dogmatism over this later point during his childhood, which in his view led to emotional abuse from his father.

However, assuming for the sake of argument that all these events had occurred in their due sequence, I should still not have been brought up as a vegetarian, should not have lived in a house in which I was surrounded by horrible and hair raising vegetarian tracts concerning cruelty to animals, and should not have been subjected to the overwhelming precept and example of my father in such matters.

His father planned to set up a commune in Central America based on these ideas. However, his companion abandoned him, leaving him on a ship to Hartlepool. His father then went to Liverpool, Havana and New Orleans—picking up both on English and Spanish during his trip. Eventually, his father decided to teach languages and went into Philology. He later met Wiener's mother Bertha Kahn, the daughter of department store owner Henry Kahn, in St. Joseph, Missouri.

His maternal grandfather was a German Jewish immigrant from Rhineland. His wife, whose maiden name was Ellinger, had settled in the United States a few generations beforehand. He notes that his maternal grandmother's mother was not Jewish, and suggests that while women in that side of the family tended to marry inside the Jewish community, men from that side of the family tended to marry Gentiles. The family could also trace its roots to the American South. He notes that many men from this side of the family tended to leave some "career of impeccable propriety by suddenly leaving his family and taking to the great open spaces", with rumours that one family member ended up becoming a Western bandit and was shot trying to evade capture. In his autobiography, Wiener contrasted the melting pot culture that he was brought up in with the more socially homogeneous Old American culture that had been predominant before. He saw this culture as offering greater freedom and opportunity compared to the serfdom that was found for many in Eastern Europe.

He writes of his youth: "Child as I was, I absorbed a real understanding of many things, and my childish point of view is not totally devoid of significance". Leo had educated Norbert at home until 1903, employing teaching methods of his own invention, except for a brief interlude when Norbert was seven years of age. Earning his living teaching German and Slavic languages, Leo read widely and accumulated a personal library from which the young Norbert benefited greatly. Leo also had ample ability in mathematics and tutored his son in the subject until he left home. 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.

In "The Theory of Ignorance", a paper Wiener wrote at the age of 10, he disputed "man's presumption in declaring that his knowledge has no limits", arguing that all human knowledge "is based on an approximation", and acknowledging "the impossibility of being certain of anything."

Wiener graduated from Ayer High School in 1906 at age 11, at which point he entered Tufts College, being awarded a BA in mathematics in 1909 at the age of 14. He began graduate studies of zoology at Harvard, before transferring to Cornell in 1910 to study philosophy. He graduated in 1911 at 17 years of age.

From Wikipedia’s article on Norbert Wiener (this version), CC BY-SA 4.0.

Career

Occupation: founder, autobiographer, scientist, psychologist, university teacher, computer scientist, mathematician.6

Known for: The Human Use of Human Beings, The Theory of Ignorance, Paley–Wiener theorem, abstract Wiener space, classical Wiener space, Wiener algebra, Wiener equation, Wiener filter, God & Golem, Inc..7

Information is information, not matter or energy.

Wiener was an early studier of stochastic and mathematical noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems. 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 does not 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, with many implications for engineering, systems control, computer science, biology, philosophy, and the organization of society. While he claims the field arose during his personal development, it has roots in the works of Leibnitz, Kierkegaard, Babbage, Maxwell, and Gibbs. His work with cybernetics influenced Gregory Bateson and Margaret Mead, and through them, anthropology, sociology, and education.

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Wiener equation

A simple mathematical representation of Brownian motion, 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 proposed by Wiener during the 1940s and published in 1942 as a classified document, which was funded by the National Defense Research Committee. 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. 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.

Nonlinear control theory

Wiener studied polynomial chaos, a key piece of which is the Hermite-Laguerre expansion. This was developed in detail in Nonlinear Problems in Random Theory.

Wiener applied Hermite-Laguerre expansion to nonlinear system identification and control. Specifically, a nonlinear system can be identified by inputting a white noise process and computing the Hermite-Laguerre expansion of its output. The identified system can then be controlled.

In mathematics

Wiener took a great interest in the mathematical theory of Brownian motion (named after Robert Brown) proving many results now widely known, such as the non-differentiability of the paths. 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 Banach space.

The notion of a Banach space itself was discovered independently by both Wiener and Stefan Banach at around the same time.

From Wikipedia’s article on Norbert Wiener (this version), CC BY-SA 4.0.

Personal life

  • BornNov 26, 1894, Columbia8
  • DiedMar 18, 1964, Stockholm9
  • CitizenshipUnited States10
  • SpouseMargaret Engemann11

In 1926, Wiener married Margaret Engemann, an assistant professor of modern languages at Juniata College. They had two daughters.

Wiener admitted in his autobiography I Am a Mathematician: The Later Life of a Prodigy to abusing Benzedrine throughout his life without being fully aware of its dangers.

A famous anecdote demonstrates his dedication to teaching:

One day, [he] was walking across the campus of Massachusetts Institute of Technology. While he was walking, someone stopped him and asked a question about Fourier analysis. Wiener didn't hesitate. He took out a small piece of paper and carefully wrote down the answer, explaining it step by step. The person was very thankful, said thanks, and started to leave. But Wiener stopped him and asked, "Just one moment—which direction was I walking when you met me?" The man pointed in the direction Wiener had been heading. Wiener smiled and said, "Good. That means I've already had my lunch."

Wiener died on March 18, 1964, aged 69, in Stockholm, from a heart attack. Wiener and his wife are buried at the Vittum Hill Cemetery in Sandwich, New Hampshire.

From Wikipedia’s article on Norbert Wiener (this version), CC BY-SA 4.0.

Awards

  • 1965National Book Award for God & Golem, Inc.12
  • 1963National Medal of Science12 14
  • 1951Honorary Doctorate from the National Autonomous University of Mexico12
  • 1949Josiah Willard Gibbs Lectureship12
  • 1933Bôcher Memorial Prize12 13
  • 1926Guggenheim Fellowship12