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definitions - Claude_E._Shannon

Claude E. Shannon (n.)

1.United States electrical engineer who pioneered mathematical communication theory (1916-2001)

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Claude Shannon

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Claude Shannon

Claude Elwood Shannon (1916-2001)
BornApril 30, 1916(1916-04-30)
Petoskey, Michigan, United States
DiedFebruary 24, 2001 (aged 84)
Medford, Massachusetts, United States
ResidenceUnited States
FieldsElectronic engineer and mathematician
InstitutionsBell Laboratories
Massachusetts Institute of Technology
Institute for Advanced Study
Alma materUniversity of Michigan
Massachusetts Institute of Technology
Doctoral advisorFrank Lauren Hitchcock
Doctoral studentsDanny Hillis
Ivan Edward Sutherland
William Robert Sutherland
Heinrich Ernst
Known forInformation Theory

Shannon–Fano coding
Shannon–Hartley law
Nyquist–Shannon sampling theorem
Noisy channel coding theorem
Shannon switching game
Shannon number
Shannon index
Shannon's source coding theorem
Shannon's expansion
Shannon-Weaver model of communication

Whittaker–Shannon interpolation formula
Notable awardsAlfred Noble Prize
IEEE Medal of Honor
Kyoto Prize

Claude Elwood Shannon (April 30, 1916 – February 24, 2001), an American electronic engineer and mathematician, is known as "the father of information theory".[1]

Shannon is famous for having founded information theory with one landmark paper published in 1948. But he is also credited with founding both digital computer and digital circuit design theory in 1937, when, as a 21-year-old master's student at MIT, he wrote a thesis demonstrating that electrical application of Boolean algebra could construct and resolve any logical, numerical relationship. It has been claimed that this was the most important master's thesis of all time.[2]



Shannon was born in Petoskey, Michigan. His father, Claude Sr (1862–1934), a descendant of early New Jersey settlers, was a businessman and for a while, Judge of Probate. His mother, Mabel Wolf Shannon (1890–1945), daughter of German immigrants, was a language teacher and for a number of years principal of Gaylord High School, Michigan. The first sixteen years of Shannon's life were spent in Gaylord, Michigan, where he attended public school, graduating from Gaylord High School in 1932. Shannon showed an inclination towards mechanical things. His best subjects were science and mathematics, and at home he constructed such devices as models of planes, a radio-controlled model boat and a telegraph system to a friend's house half a mile away. While growing up, he worked as a messenger for Western Union. His childhood hero was Thomas Edison, who he later learned was a distant cousin. Both were descendants of John Ogden, a colonial leader and an ancestor of many distinguished people.[3][4]

Boolean theory

In 1932 he entered the University of Michigan, where he took a course that introduced him to the works of George Boole. He graduated in 1936 with two bachelor's degrees, one in electrical engineering and one in mathematics, then began graduate study at the Massachusetts Institute of Technology (MIT), where he worked on Vannevar Bush's differential analyzer, an analog computer.

While studying the complicated ad hoc circuits of the differential analyzer, Shannon saw that Boole's concepts could be used to great utility. A paper drawn from his 1937 master's thesis, A Symbolic Analysis of Relay and Switching Circuits[5], was published in the 1938 issue of the Transactions of the American Institute of Electrical Engineers. It also earned Shannon the Alfred Noble American Institute of American Engineers Award in 1940. Howard Gardner, of Harvard University, called Shannon's thesis "possibly the most important, and also the most famous, master's thesis of the century."

Victor Shestakov, at Moscow State University, had proposed a theory of electric switches based on Boolean logic a little bit earlier than Shannon, in 1935, but the first publication of Shestakov's result took place in 1941, after the publication of Shannon's thesis.

In this work, Shannon proved that Boolean algebra and binary arithmetic could be used to simplify the arrangement of the electromechanical relays then used in telephone routing switches, then turned the concept upside down and also proved that it should be possible to use arrangements of relays to solve Boolean algebra problems. Exploiting this property of electrical switches to do logic is the basic concept that underlies all electronic digital computers. Shannon's work became the foundation of practical digital circuit design when it became widely known among the electrical engineering community during and after World War II. The theoretical rigor of Shannon's work completely replaced the ad hoc methods that had previously prevailed.

Flush with this success, Vannevar Bush suggested that Shannon work on his dissertation at Cold Spring Harbor Laboratory, funded by the Carnegie Institution headed by Bush, to develop similar mathematical relationships for Mendelian genetics, which resulted in Shannon's 1940 PhD thesis at MIT, An Algebra for Theoretical Genetics[6].

In 1940, Shannon became a National Research Fellow at the Institute for Advanced Study in Princeton, New Jersey. At Princeton, Shannon had the opportunity to discuss his ideas with influential scientists and mathematicians such as Hermann Weyl and John von Neumann, and even had the occasional encounter with Albert Einstein. Shannon worked freely across disciplines, and began to shape the ideas that would become information theory.[7]

Wartime research

Shannon then joined Bell Labs to work on fire-control systems and cryptography during World War II, under a contract with section D-2 (Control Systems section) of the National Defense Research Committee (NDRC).

For two months early in 1943, Shannon came into contact with the leading British cryptanalyst and mathematician Alan Turing. Turing had been posted to Washington to share with the US Navy's cryptanalytic service the methods used by the British Government Code and Cypher School at Bletchley Park to break the ciphers used by the German U-boats in the North Atlantic.[8] He was also interested in the encipherment of speech and to this end spent time at Bell Labs. Shannon and Turing met every day at teatime in the cafeteria.[8] Turing showed Shannon his seminal 1936 paper that defined what is now known as the "Universal Turing machine"[9][10] which impressed him, as many of its ideas were complementary to his own.

In 1945, as the war was coming to an end, the NDRC was issuing a summary of technical reports as a last step prior to its eventual closing down. Inside the volume on fire control a special essay titled Data Smoothing and Prediction in Fire-Control Systems, coauthored by Shannon, Ralph Beebe Blackman, and Hendrik Wade Bode, formally treated the problem of smoothing the data in fire-control by analogy with "the problem of separating a signal from interfering noise in communications systems."[11] In other words it modeled the problem in terms of data and signal processing and thus heralded the coming of the information age.

His work on cryptography was even more closely related to his later publications on communication theory.[12] At the close of the war, he prepared a classified memorandum for Bell Telephone Labs entitled "A Mathematical Theory of Cryptography," dated September, 1945. A declassified version of this paper was subsequently published in 1949 as "Communication Theory of Secrecy Systems" in the Bell System Technical Journal. This paper incorporated many of the concepts and mathematical formulations that also appeared in his A Mathematical Theory of Communication. Shannon said that his wartime insights into communication theory and cryptography developed simultaneously and "they were so close together you couldn’t separate them".[13] In a footnote near the beginning of the classified report, Shannon announced his intention to "develop these results ... in a forthcoming memorandum on the transmission of information."[14]

Postwar contributions

In 1948 the promised memorandum appeared as "A Mathematical Theory of Communication", an article in two parts in the July and October issues of the Bell System Technical Journal. This work focuses on the problem of how best to encode the information a sender wants to transmit. In this fundamental work he used tools in probability theory, developed by Norbert Wiener, which were in their nascent stages of being applied to communication theory at that time. Shannon developed information entropy as a measure for the uncertainty in a message while essentially inventing the field of information theory.

The book, co-authored with Warren Weaver, The Mathematical Theory of Communication, reprints Shannon's 1948 article and Weaver's popularization of it, which is accessible to the non-specialist. Shannon's concepts were also popularized, subject to his own proofreading, in John Robinson Pierce's Symbols, Signals, and Noise.

Information theory's fundamental contribution to Natural language processing and Computational linguistics was further established in 1951, in his article "Prediction and Entropy of Printed English", proving that treating whitespace as the 27th letter of the alphabet actually lowers uncertainty in written language, providing a clear quantifiable link between cultural practice and probabilistic cognition.

Another notable paper published in 1949 is "Communication Theory of Secrecy Systems", a declassified version of his wartime work on the mathematical theory of cryptography, in which he proved that all theoretically unbreakable ciphers must have the same requirements as the one-time pad. He is also credited with the introduction of Sampling Theory, which is concerned with representing a continuous-time signal from a (uniform) discrete set of samples. This theory was essential in enabling telecommunications to move from analog to digital transmissions systems in the 1960s and later.

He returned to MIT to hold an endowed chair in 1956.

Hobbies and inventions

Outside of his academic pursuits, Shannon was interested in juggling, unicycling, and chess. He also invented many devices, including rocket-powered flying discs, a motorized pogo stick, and a flame-throwing trumpet for a science exhibition[citation needed]. One of his more humorous devices was a box kept on his desk called the "Ultimate Machine", based on an idea by Marvin Minsky. Otherwise featureless, the box possessed a single switch on its side. When the switch was flipped, the lid of the box opened and a mechanical hand reached out, flipped off the switch, then retracted back inside the box. Renewed interest in the "Ultimate Machine" has emerged on YouTube and Thingiverse. In addition he built a device that could solve the Rubik's cube puzzle.[3]

He is also considered the co-inventor of the first wearable computer along with Edward O. Thorp.[15] The device was used to improve the odds when playing roulette.

Legacy and tributes

Shannon came to MIT in 1956 to join its faculty and to conduct work in the Research Laboratory of Electronics (RLE). He continued to serve on the MIT faculty until 1978. To commemorate his achievements, there were celebrations of his work in 2001, and there are currently five statues of Shannon: one at the University of Michigan; one at MIT in the Laboratory for Information and Decision Systems; one in Gaylord, Michigan; one at the University of California, San Diego; and another at Bell Labs. After the breakup of the Bell system, the part of Bell Labs that remained with AT&T was named Shannon Labs in his honor.

Robert Gallager has called Shannon the greatest scientist of the 20th century. According to Neil Sloane, an AT&T Fellow who co-edited Shannon's large collection of papers in 1993, the perspective introduced by Shannon's communication theory (now called information theory) is the foundation of the digital revolution, and every device containing a microprocessor or microcontroller is a conceptual descendant of Shannon's 1948 publication:[16] "He's one of the great men of the century. Without him, none of the things we know today would exist. The whole digital revolution started with him."[17]

Shannon developed Alzheimer's disease, and spent his last few years in a Massachusetts nursing home. He was survived by his wife, Mary Elizabeth Moore Shannon; a son, Andrew Moore Shannon; a daughter, Margarita Shannon; a sister, Catherine S. Kay; and two granddaughters.[18][19]

Shannon was oblivious to the marvels of the digital revolution because his mind was ravaged by Alzheimer's disease. His wife mentioned in his obituary that had it not been for Alzheimer's "he would have been bemused" by it all.[17]

Other work

Shannon and his famous electromechanical mouse Theseus (named after Theseus from Greek mythology) which he tried to have solve the maze in one of the first experiments in artificial intelligence

Shannon's mouse

Theseus, created in 1950, was a magnetic mouse controlled by a relay circuit that enabled it to move around a maze of 25 squares. Its dimensions were the same as an average mouse.[1] The maze configuration was flexible and it could be modified at will.[1] The mouse was designed to search through the corridors until it found the target. Having travelled through the maze, the mouse would then be placed anywhere it had been before and because of its prior experience it could go directly to the target. If placed in unfamiliar territory, it was programmed to search until it reached a known location and then it would proceed to the target, adding the new knowledge to its memory thus learning.[1] Shannon's mouse appears to have been the first learning device of its kind.[1]

Shannon's computer chess program

In 1950 Shannon published a groundbreaking paper on computer chess entitled Programming a Computer for Playing Chess. It describes how a machine or computer could be made to play a reasonable game of chess. His process for having the computer decide on which move to make is a minimax procedure, based on an evaluation function of a given chess position. Shannon gave a rough example of an evaluation function in which the value of the black position was subtracted from that of the white position. Material was counted according to the usual relative chess piece relative value (1 point for a pawn, 3 points for a knight or bishop, 5 points for a rook, and 9 points for a queen). He considered some positional factors, subtracting ½ point for each doubled pawns, backward pawn, and isolated pawn. Another positional factor in the evaluation function was mobility, adding 0.1 point for each legal move available. Finally, he considered checkmate to be the capture of the king, and gave the king the artificial value of 200 points. Quoting from the paper:

The coefficients .5 and .1 are merely the writer's rough estimate. Furthermore, there are many other terms that should be included. The formula is given only for illustrative purposes. Checkmate has been artificially included here by giving the king the large value 200 (anything greater than the maximum of all other terms would do).

The evaluation function is clearly for illustrative purposes, as Shannon stated. For example, according to the function, pawns that are doubled as well as isolated would have no value at all, which is clearly unrealistic.

The Las Vegas connection: Information theory and its applications to game theory

Shannon and his wife Betty also used to go on weekends to Las Vegas with M.I.T. mathematician Ed Thorp,[20] and made very successful forays in blackjack using game theory type methods co-developed with fellow Bell Labs associate, physicist John L. Kelly Jr. based on principles of information theory.[21] They made a fortune, as detailed in the book Fortune's Formula by William Poundstone and corroborated by the writings of Elwyn Berlekamp,[22] Kelly's research assistant in 1960 and 1962.[2] Shannon and Thorp also applied the same theory, later known as the Kelly criterion, to the stock market with even better results.[23]

Shannon's maxim

Shannon formulated a version of Kerckhoffs' principle as "the enemy knows the system". In this form it is known as "Shannon's maxim".

Biographical Notes

He met his wife Betty when she was a numerical analyst at Bell Labs.

Awards and honors list

See also


  1. ^ a b c d e Bell Labs website: "For example, Claude Shannon, the father of Information Theory, had a passion..."
  2. ^ a b Poundstone, William: Fortune's Formula : The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street
  3. ^ a b MIT Professor Claude Shannon dies; was founder of digital communications, MIT - News office, Cambridge, Massachusetts, February 27, 2001
  4. ^ CLAUDE ELWOOD SHANNON, Collected Papers, Edited by N.J.A Sloane and Aaron D. Wyner, IEEE press, ISBN 0-7803-0434-9
  5. ^ Claude Shannon, "A Symbolic Analysis of Relay and Switching Circuits," unpublished MS Thesis, Massachusetts Institute of Technology, Aug. 10, 1937.
  6. ^ C. E. Shannon, "An algebra for theoretical genetics", (Ph.D. Thesis, Massachusetts Institute of Technology, 1940), MIT-THESES//1940–3 Online text at MIT
  7. ^ Erico Marui Guizzo, “The Essential Message: Claude Shannon and the Making of Information Theory” (M.S. Thesis, Massachusetts Institute of Technology, Dept. of Humanities, Program in Writing and Humanistic Studies, 2003), 14.
  8. ^ a b Hodges, Andrew (1992), [Expression error: Missing operand for > Alan Turing: The Enigma], London: Vintage, pp. 243–252, ISBN 978-0099116417 
  9. ^ Turing, A.M. (1936), [Expression error: Missing operand for > "On Computable Numbers, with an Application to the Entscheidungsproblem"], Proceedings of the London Mathematical Society, 2 42: 230–65, 1937 
  10. ^ Turing, A.M. (1937), [Expression error: Missing operand for > "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction"], Proceedings of the London Mathematical Society, 2 43: 544–6 
  11. ^ David A. Mindell, Between Human and Machine: Feedback, Control, and Computing Before Cybernetics, (Baltimore: Johns Hopkins University Press), 2004, pp. 319-320. ISBN 0801880572.
  12. ^ David Kahn, The Codebreakers, rev. ed., (New York: Simon and Schuster), 1996, pp. 743-751. ISBN 0684831309.
  13. ^ quoted in Kahn, The Codebreakers, p. 744.
  14. ^ quoted in Erico Marui Guizzo, "The Essential Message: Claude Shannon and the Making of Information Theory," unpublished MS thesis, Massachusetts Institute of Technology, 2003, p. 21.
  15. ^ The Invention of the First Wearable Computer Online paper by Edward O. Thorp of Edward O. Thorp & Associates
  16. ^ C. E. Shannon: A mathematical theory of communication. Bell System Technical Journal, vol. 27, pp. 379–423 and 623–656, July and October, 1948
  17. ^ a b Bell Labs digital guru dead at 84 — Pioneer scientist led high-tech revolution (The Star-Ledger, obituary by Kevin Coughlin 27 February 2001)
  18. ^ Shannon, Claude Elwood (1916-2001)
  19. ^ Claude Elwood Shannon April 30, 1916
  20. ^ American Scientist online: Bettor Math, article and book review by Elwyn Berlekamp
  21. ^ John Kelly by William Poundstone website
  22. ^ Elwyn Berlekamp (Kelly's Research Assistant) Bio details
  23. ^ William Poundstone website

Further reading

  • Claude E. Shannon: A Mathematical Theory of Communication, Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, 1948.
  • Claude E. Shannon and Warren Weaver: The Mathematical Theory of Communication. The University of Illinois Press, Urbana, Illinois, 1949. ISBN 0-252-72548-4
  • Rethnakaran Pulikkoonattu - Eric W. Weisstein: Mathworld biography of Shannon, Claude Elwood (1916-2001) [1]
  • Claude E. Shannon: Programming a Computer for Playing Chess, Philosophical Magazine, Ser.7, Vol. 41, No. 314, March 1950. (Available online under External links below)
  • David Levy: Computer Gamesmanship: Elements of Intelligent Game Design, Simon & Schuster, 1983. ISBN 0-671-49532-1
  • Mindell, David A., "Automation's Finest Hour: Bell Labs and Automatic Control in World War II", IEEE Control Systems, December 1995, pp. 72-80.
  • David Mindell, Jérôme Segal, Slava Gerovitch, "From Communications Engineering to Communications Science: Cybernetics and Information Theory in the United States, France, and the Soviet Union" in Walker, Mark (Ed.), Science and Ideology: A Comparative History, Routledge, London, 2003, pp. 66-95.
  • Poundstone, William, Fortune's Formula, Hill & Wang, 2005, ISNB-13 978-0-8090-4599-0

Shannon videos

External links

External links

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