There was a catch, though: This symbolic abstraction made the world transparent but the brain opaque. Once everything had been reduced to information governed by logic, the actual mechanics ceased to matter—the tradeoff for universal computation was ontology. Von Neumann was the first to see the problem. He expressed his concern to Wiener in a letter that anticipated the coming split between artificial intelligence on one side and neuroscience on the other. “After the great positive contribution of Turing-cum-Pitts-and-McCulloch is assimilated,” he wrote, “the situation is rather worse than better than before. Indeed these authors have demonstrated in absolute and hopeless generality that anything and everything … can be done by an appropriate mechanism, and specifically by a neural mechanism—and that even one, definite mechanism can be ‘universal.’ Inverting the argument: Nothing that we may know or learn about the functioning of the organism can give, without ‘microscopic,’ cytological work any clues regarding the further details of the neural mechanism.”

By the fall of 1943, Pitts had moved into a Cambridge apartment, was enrolled as a special student at MIT, and was studying under one of the most influential scientists in the world.

it had been Wiener who discovered a precise mathematical definition of information: The higher the probability, the higher the entropy and the lower the information content.

1956. I am a Mathematician. London (Gollancz).

1950, The Human Use of Human Beings. The Riverside Press (Houghton Mifflin Co.).

The Wiener–Khinchin theorem, (or Wiener – Khintchine theorem or 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.

The Paley–Wiener theorem relates growth properties of entire functions on Cn and Fourier transformation of Schwartz distributions of compact support.

iener'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.

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 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

What emerged was a mathematical theory of great generality---a theory for predicting the future as best as one can on the basis of incomplete information about the past. It was a statistical theory that included applications that didn't 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.[22] [23]

A simple mathematical representation of Brownian motion, the Wiener equation, named after Wiener, assumes the current velocity of a fluid particle fluctuates randomly.

In the mathematical field of probability, the "Wiener sausage" is a neighborhood of the trace of a Brownian motion up to a time t, given by taking all points within a fixed distance of Brownian motion. It can be visualized as a cylinder of fixed radius the centerline of which is Brownian motion.

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.

Information is information, not matter or energy. — Norbert Wiener, Cybernetics: Or Control and Communication in the Animal and the Machine

Bernard Friedman (Ph.D. 1936)

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.

Norman Levinson (Sc.D. 1935)

The Norbert Wiener Center for Harmonic Analysis and Applications, at the University of Maryland, College Park, is named in his honor.[18]

The crater Wiener on the far side of the Moon is named after him.

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 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 and Society for Industrial and Applied Mathematics.

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" for the January 1947 issue of The Atlantic Monthly[15] 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 John von Neumann is the major theme of the book John Von Neumann and Norbert Wiener.[16][citation needed]

During World War II, his work on the automatic aiming and firing of anti-aircraft guns caused Wiener to investigate information theory independently of Claude Shannon 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.)

Many tales, perhaps apocryphal, were told of him 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!"[9]

Wiener is considered the originator of cybernetics, a formalization of the notion of feedback, with implications for engineering, systems control, computer science, biology, neuroscience, philosophy, and the organization of society.