Claude Elwood Shannon

American mathematician (1916–)

Born in Gaylord, Michigan, Shannon graduated from the University of Michigan in 1936. He later worked both at the Massachusetts Institute of Technology and the Bell Telephone Laboratories. In 1958 he returned to MIT as Donner Professor of Science, a post he held until his retirement in 1978.

Shannon's greatest contribution to science has been in laying the mathematical foundations of communication theory. The central problem of communication theory is to determine the most efficient ways of transmitting messages. What Shannon did was to show a precise way of quantifying the information content of a message, thus making the study of information flow amenable to exact mathematical treatment. He first published his ideas in 1948 in A Mathematical Theory of Communication, written in collaboration with Warren Weaver. The resulting theory found wide application in such wide-ranging fields as circuit design, computer design, communication technology in general, and even in biology, psychology, semantics, and linguistics. Shannon's work made extensive use of the theory of probability; he also extended the concept of entropy from thermodynamics and applied it to lack of information.

Shannon has also made important contributions to computer science. In his paper A Symbolic Analysis of Relay and Switching Circuits (1938) he drew the analogy between truth values in logic and the binary states of circuits. He also coined the term ‘bit’ for a unit of information.

The American mathematician Claude Elwood Shannon (born 1916) was the first to apply symbolic logic to the design of switching circuits, and his work on the mathematics of communication is central to modern information theory.

Claude Shannon was born on April 30, 1916, in Gaylord, Michigan. After graduating from the University of Michigan in 1936, he went to the Massachusetts Institute of Technology. There he made a mathematical discovery of considerable potential in the field of technology, and one which pointed the direction of his subsequent career. While studying the design of switching circuits, he saw how to apply symbolic logic to establish an economy of design. By employing the language of logic in plotting the alternative flow paths of the electric current through a switching series, redundant controls could be discovered and eliminated.

On completion of his doctorate in 1940, Shannon joined Bell Telephone Laboratories. He was interested in the problem of ascertaining the efficiency of various electrical devices for the transmission of information, with a view to the selection of the most efficient one - and the increase of its efficiency. Involved in this problem is that of communication in general, and in applying mathematics to this problem, Shannon, following H. Nyquist and R. V. L. Hartley, laid the foundations of information theory.

In a communication system, a source information selects a message which is transformed into a signal by a transmitter, which in turn directs the signal along a channel to a receiver. The receiver converts the signal back into a message which is then available at its destination. In any system, and especially a mechanized one, there is a tendency for distortions, errors, and redundant signals to affect the accuracy of the signal, and these may all be classed as noise." The problems associated with the system may be concerned with the amount of information; the capacity of transmitter, channel, and receiver; the encoding process; and noise. Information" in this sense is a measure of the freedom of choice available when selecting a message, and the theory of probability involved in estimating the freedom of choice. The capacity of the transmitter and of the channel may be related in a theorem by means of which the maximum transmission rate possible may be calculated. And, further, by introducing the noise factor it is possible to calculate under what conditions transmissions low in error may be achieved.

Shannon's work on information systems not only had important implications in the whole theory of communications but was of considerable value in the development of computers. His demonstration of the central importance of a knowledge of symbolic logic as basic to understanding of circuit design has ensured a level of efficiency essential to the increasingly complex computer systems. He remained as a consultant with Bell Laboratories until 1972. Shannon was also a Donner Professor of Science from 1958-78, becoming Professor Emeritus in 1978 (he was also a visiting fellow at All Souls College in Oxford, England that year). Shannon was awarded the Kyoto Prize in 1985.

Further Reading

Some information on Shannon appears in Mathematics in the Modern World: Readings from Scientific American, with an introduction by Morris Kline (1968). The importance of his work in the computer age is also highlighted in On the Shoulders of Giants: From Boole to Shannon to Taube (June, 1993) in Information Technology and Library.

For more information on Claude Elwood Shannon, visit Britannica.com.

Shannon, Claude Elwood, 1916–2001, American applied mathematician, b. Gaylord, Michigan. A student of Vannevar Bush at the Massachusetts Institute of Technology (MIT), he was the first to propose the application of symbolic logic to the design of relay circuitry with his paper “A Symbolic Analysis of Relay and Switching Circuits” (1938). His insight that all data could be encoded as a series of 1's and 0's pioneered the breakthrough in digital electronics that led to the modern digital computer and telecommunications networks. Shannon worked at Bell Telephone Laboratories from 1941–72 and initiated the field of information theory with his 1948 paper “A Mathematical Theory of Communication,” which was retitled The Mathematical Theory of Communication when published in 1949 with a preface by Warren Weaver. Shannon returned to MIT in 1958, although he remained a consultant with Bell Telephone. Over the next two decades his curiosity about the fledgling field of artificial intelligence led him to build and experiment with such things as chess-playing, maze-solving, juggling, and mind-reading machines.

Bibliography

See C. E. Shannon et al., Claude Elwood Shannon: Collected Papers (1993).

(1912–2001). American mathematician, engineer, and computer scientist, born in Petoskey, Michigan. Shannon was a graduate of the University of Michigan, being awarded a degree in mathematics and electrical engineering in 1936. He then went to the Massachusetts Institute of Technology where he obtained a master's degree in electrical engineering and his Ph.D. in mathematics in 1940. Shannon wrote a master's thesis 'A symbolic analysis of relay and switching circuits' on the use of Boole's algebra to analyse and optimize relay switching circuits. In 1940 it was awarded the Alfred Nobel Prize of the combined engineering societies of the United States, an award given each year to a person not over 30 for a paper published in one of the journals of the participating societies. A quarter of a century later H. H. Goldstine, in his book The Computer from Pascal to Von Neumann, called this work 'one of the most important master's theses ever written ... a landmark in that it helped to change digital circuit design from an art to a science'. Shannon's doctoral thesis was on theoretical genetics and was supervised by Professor Frank L. Hitchcock, an algebraist at MIT.

He joined AT&T Bell Telephones in New Jersey in 1941 as a research mathematician and remained there until 1972. During his time at the Bell laboratories, Shannon worked most notably on information theory, a development that was published in 1948 as 'A mathematical theory of communication'. In this paper it was shown that all information sources, telegraph keys, people speaking, television cameras, and so on, have a 'source rate' associated with them which can be measured in bits per second. Communication channels have a 'capacity' measured in the same units. The information can be transmitted over the channel if and only if the source rate does not exceed the channel capacity. This work on communication is generally considered to be Shannon's most important scientific contribution.

Information theory has now infiltrated fields outside communications, including linguistics, psychology, economics, biology, even the arts. In the early 1950s the IEEE Transactions on Information Theory published an editorial, titled 'Information theory, photosynthesis and religion', decrying this trend. Yet Shannon himself suggested that applying information theory to biological systems might not be so far fetched, because he believed common principles underlie mechanical and living things.

In 1952 Shannon devised an experiment illustrating the capabilities of telephone relays. He had held a position as a visiting professor of communication sciences and mathematics at the Massachusetts Institute of Technology in 1956, then from 1957 he was appointed to the faculty there, but remained a consultant with Bell Telephones. In 1958 he became Donner Professor of science.

Shannon's later work looked at ideas in artificial intelligence. He devised chess-playing programs and an electronic mouse, which could solve maze problems. The chess-playing program appeared in the paper 'Programming a computer for playing chess' published in 1950. This proposal led to the first game played by the Los Alamos MANIAC computer in 1956. This was the year that Shannon published a paper showing that a universal Turing machine may be constructed with only two states.

Marvin Minsky described Shannon as follows: 'Whatever came up, he engaged it with joy, and he attacked it with some surprising resource which might be some new kind of technical concept or a hammer and saw with some scraps of wood. For him, the harder a problem might seem, the better the chance to find something new.'

Shannon died on 24 February 2001 in Medford, Massachusetts.

(Published 2004)

See also information theory.

Bibliography
• McMillan, B. (1994). 'Scientific impact of the work of C. E. Shannon'. In Proceedings of the Norbert Wiener Centenary Congress, East Lansing, MI.
• Price, R. (1985). 'A conversation with Claude Shannon: one man's approach to problem solving', Cryptologia, 9.
• Slepian, D. (ed.) (1974). Key Papers in the Development of Information Theory.
• Sloane, N. J. A., and Wyner, A. D. (1993). Claude Elwood Shannon: Collected Papers.

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