Claude Elwood Shannon (April 30th, 1916 with Gaylord, Michigan - February 24th, 2001) is a Engineer electrician and American Mathématicien . It is one of the fathers, if it is not the founding father, of the Information theory. Its name is attached to famous “a diagram of Shannon” very much used in social sciences, which he constantly repudiated.

Biography

He studies the Electronic engineering and the Mathématiques with the Université of Michigan in 1932. He off uses in particular the Boolean algebra for his control supported in 1938 with the Massachusetts Institute Technology (MIT). He explains there how to build machines with relay by using the Boolean algebra to describe the state of the relays (1: closed, 0: opened).

Shannon works twenty years with the MIT, of 1958 with 1978. Parallel to its academic activities, he also works with the Laboratoires Beautiful of 1941 with 1972.

Claude Shannon is known not only for his work in telecommunications, but also for the extent and the originality of his hobbies, like the Jonglerie, the practice of the Monocycle and the invention of eccentric machines: a mechanical mouse knowing to find its way in a labyrinth, a robot juggler, a player of failures (king turn against king), etc

Suffering from the disease of Alzheimer in the last years of his life, Claude Shannon died in 84 years on February 24th, 2001.

Its work

During the Second world war, Shannon works for the secret services of the army, in cryptography, charged to locate in an automatic way in the enemy code the meaning parts hidden in the middle of jamming. Its work is exposed in a secret report/ratio (déclassifié in the years 1980 only), which gives birth post-war period in an article, has Mathematical Theory off Communications (1948), which was shown in 1949 in the form of book with an addition of Warren Weaver, its superior in the secret services. This work is centered around the problems of the transmission of the signal.

The diagram of Shannon

To describe the communication between machines, the article of 1948 and delivers it of 1949 begin both with a “diagram” which consequently knew an astonishing posterity in Information sciences and communication, so much so that Shannon was astonished some and dissociated some. The diagram models the communication between machines in 6 elements:

• source --> transmitting --> message --> receiving --> recipient, in a context of noise.

This diagram is the “civil” translation of a preliminary diagram, used in the military context:

• source --> coder --> signal --> decoder --> recipient, in a context of jamming.

Adequate to describe the communication between machines, this diagram is unsuitable with the modeling of the human communication. However, its success is striking down, and it took part largely in the creation of a disciplinary field, the Information sciences and communication. One of the explanations of this success is the fact that it is melted perfectly in an approach Béhavioriste of the media, heavy tendency inherited a linear and reductionistic approach of the social phenomena. Moreover, this diagram known as canonical gives a consistency and an appearance of scientificity which the social sciences cannot resist.

Shannon: the measuring unit

In the article as in the book, it popularizes the use of the word bit which measures the basic unit of information Numérique, although he is not the inventor (John Tukey was the first to use the term).

The bit is a measuring unit indicating the number of binary digits necessary to code a quantity of information.

To code 2 states (pile or face), 1 Shannon (or 1 bit) is necessary: 0 or 1

To code 4 states, one must use 2 Shannon (2 bits): 00,01,10,11.

5 bits minimum are essential to code the 26 letters of the alphabet, because:

More generally, P the number of possible states is , N the number of bits:

$P\; =\; 2^n$

$n\; =\; log\_2\; (P)$

The relation of Shannon

In the field of telecommunications, the relation of Shannon makes it possible to calculate the valence (or maximum number of states) in disturbed medium:

That is to say S the signal, NR noise:

$N\; =\; \backslash \; sqrt\; \{1\; +\; \backslash \; frac\; \{S\}\; \{NR\}\}$

There is then the maximum flow:

$H\; log\_2\; (1+\; \backslash \; frac\; \{S\}\; \{NR\})$

This result is independent the speed of sampling and of the number of level of a sample (the valence).

Entropy within the meaning of Shannon

See also: Entropy of Shannon

An essential contribution of work of Shannon relates to the concept of Entropie. If one considers NR events of probability p ₁, p ₂… p _N, independent from/to each other, then their entropy of Shannon is defined like:

Entropy = $-\; \backslash \; sum\_\; \{i=1\}\; ^N\; p\_i\; \backslash \; log\_2\; (p\_i)$

It has in addition:

• drawn up a relationship between increase in entropy and profit of information;
• shown the equivalence of this concept with the Entropy of Ludwig Boltzmann in Thermodynamic.

The discovery of the concept thus opened the way with the methods known as of maximum Entropie (see Probabilité), therefore with the medical scanner, the automatic recognition of the characters and with the machine Learning.

Anecdotes

• In 1981, Claude Shannon started to off write an article entitled Scientific Aspects Juggling , on the art of the Jonglerie. This article was designed to be published in Scientific American , but it was not finally the case. Nevertheless, this outline was used as a basis for formalization of the movements of juggling by the Siteswap .

See too

Related articles

• Theorem of sampling of Nyquist-Shannon

• Information theory
• Communication
• Message (communication)
• Cybernetic Inference bayésienne

External bonds

• Claude E. Shannon, has off Symbolic Analysis Relay and Switching Circuits , Thesis (M.S.), Massachusetts Institute off Technology, Dept. off Electrical Engineering, 1940 (to read)
• Claude E. Shannon, has Mathematical Theory off Communication , Bell System Technical Journal , vol. 27, pp. 379-423 and 623-656, July and October, 1948 (to read)
• Claude E. Shannon, Communication Theory off Secrecy Systems ], Bell System Technical Journal, Vol 28, pp. 656-715, Oct. 1949. (to read)
• J. Segal, the Zero and the One , Syllepse, Paris, 2003 (to read)

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