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 Elwood Shannon

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 on Claude Elwood Shannon

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.*

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