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Claude Shannon

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Claude Shannon
File:Claude Elwood Shannon (1916-2001).jpg
Claude Elwood Shannon (1916-2001)
Born(1916-04-30)April 30, 1916
Petoskey, Michigan, United States
DiedFebruary 24, 2001(2001-02-24) (aged 84)
Medford, Massachusetts, United States
NationalityAmerican
Alma materUniversity of Michigan
Massachusetts Institute of Technology
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
AwardsIEEE Medal of Honor
Kyoto Prize
Harvey Prize (1972)
Scientific career
FieldsMathematics and electronic engineering
InstitutionsBell Laboratories
Massachusetts Institute of Technology
Institute for Advanced Study
Doctoral advisorFrank Lauren Hitchcock
Doctoral studentsDanny Hillis
Ivan Edward Sutherland
William Robert Sutherland
Heinrich Ernst

Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electronic engineer, and cryptographer known as "the father of information theory".[1][2]

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.[3] Shannon contributed to the field of cryptanalysis during World War II and afterwards, including basic work on code breaking.

Biography

Shannon was born in Petoskey, Michigan. His father, Claude Sr (1862–1934), a descendant of early New Jersey settlers, was a self-made 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 16 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 wireless 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.[4][5]

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. Later he began his graduate studies at the Massachusetts Institute of Technology (MIT), where he worked on Vannevar Bush's differential analyzer, an analog computer.[6]

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,[7] 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 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 expanded the concept 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.

Vannevar Bush suggested that Shannon, flush with this success, 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.[8]

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.[9]

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).

He met his wife Betty when she was a numerical analyst at Bell Labs. They married in 1949.[10]

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.[11] He was also interested in the encipherment of speech and to this end spent time at Bell Labs. Shannon and Turing met at teatime in the cafeteria.[11] Turing showed Shannon his seminal 1936 paper that defined what is now known as the "Universal Turing machine"[12][13] 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."[14] 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.[15] 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".[16] 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."[17]

While at Bell Labs, he proved that the one-time pad is unbreakable in his World War II research that was later published in October 1949. He also proved that any unbreakable system must have essentially the same characteristics as the one-time pad: the key must be truly random, as large as the plaintext, never reused in whole or part, and kept secret.[18]

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", showing upper and lower bounds of entropy on the statistics of English - giving a statistical foundation to language analysis. In addition, he proved 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.[4]

He is also considered the co-inventor of the first wearable computer along with Edward O. Thorp.[19] 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 six statues of Shannon sculpted by Eugene L. Daub: 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; one at Bell Labs; and another at AT&T Shannon Labs.[20] After the breakup of the Bell system, the part of Bell Labs that remained with AT&T was named Shannon Labs in his honor.

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:[21] "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."[22]

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.[10][23]

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.[22]

Other work

File:Shannonmouse.PNG
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.[2] The maze configuration was flexible and it could be modified at will.[2] 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.[2] Shannon's mouse appears to have been the first artificial learning device of its kind.[2]

Shannon's computer chess program

In 1950 Shannon published a 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).[24] 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,[25] 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.[26] They made a fortune, as detailed in the book Fortune's Formula by William Poundstone and corroborated by the writings of Elwyn Berlekamp,[27] Kelly's research assistant in 1960 and 1962.[3] Shannon and Thorp also applied the same theory, later known as the Kelly criterion, to the stock market with even better results.[28] Over the decades, Kelly's scientific formula has become a part of mainstream investment theory[29] and the most prominent users, well-known and successful billionaire investors Warren Buffett,[30][31] Bill Gross[32], and Jim Simons use Kelly methods. Warren Buffett met Thorp the first time in 1968. It's said that Buffett uses a form of the Kelly criterion in deciding how much money to put into various holdings. Also Elwyn Berlekamp had applied the same logical algorithm for Axcom Trading Advisors, an alternative investment management company, that he had founded. Berlekamp's company was acquired by Jim Simons and his Renaissance Technologies Corp hedge fund in 1992, whereafter its investment instruments were either subsumed into (or essentially renamed as) Renaissance's flagship Medallion Fund. But as Kelly's original paper demonstrates, the criterion is only valid when the investment or "game" is played many times over, with the same probability of winning or losing each time, and the same payout ratio.[33]

The theory was also exploited by the famous MIT Blackjack Team, which was a group of students and ex-students from the Massachusetts Institute of Technology, Harvard Business School, Harvard University, and other leading colleges who used card-counting techniques and other sophisticated strategies to beat casinos at blackjack worldwide. The team and its successors operated successfully from 1979 through the beginning of the 21st century. Many other blackjack teams have been formed around the world with the goal of beating the casinos.

Claude Shannon's card count techniques were explained in Bringing Down the House, the best-selling book published in 2003 about the MIT Blackjack Team by Ben Mezrich. In 2008, the book was adapted into a drama film titled 21.

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".

Awards and honors list

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See also

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References

  1. ^ Attention: This template ({{cite doi}}) is deprecated. To cite the publication identified by doi:10.1098/rsbm.2009.0015, please use {{cite journal}} (if it was published in a bona fide academic journal, otherwise {{cite report}} with |doi=10.1098/rsbm.2009.0015 instead.
  2. ^ a b c d e Bell Labs website: "For example, Claude Shannon, the father of Information Theory, had a passion..."
  3. ^ a b Poundstone, William: Fortune's Formula : The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street
  4. ^ a b MIT Professor Claude Shannon dies; was founder of digital communications, MIT — News office, Cambridge, Massachusetts, February 27, 2001
  5. ^ CLAUDE ELWOOD SHANNON, Collected Papers, Edited by N.J.A Sloane and Aaron D. Wyner, IEEE press, ISBN 0-7803-0434-9
  6. ^ Robert Price (1982). "Claude E. Shannon, an oral history". IEEE Global History Network. IEEE. Retrieved 14 July 2011.
  7. ^ Claude Shannon, "A Symbolic Analysis of Relay and Switching Circuits," unpublished MS Thesis, Massachusetts Institute of Technology, Aug. 10, 1937.
  8. ^ C. E. Shannon, "An algebra for theoretical genetics", (Ph.D. Thesis, Massachusetts Institute of Technology, 1940), MIT-THESES//1940–3 Online text at MIT
  9. ^ 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.
  10. ^ a b Shannon, Claude Elwood (1916-2001)
  11. ^ a b Hodges, Andrew (1992), Alan Turing: The Enigma, London: Vintage, pp. 243–252, ISBN 978-0-09-911641-7
  12. ^ Turing, A.M. (1936), "On Computable Numbers, with an Application to the Entscheidungsproblem", Proceedings of the London Mathematical Society, 2, vol. 42 (published 1937), pp. 230–65, doi:10.1112/plms/s2-42.1.230
  13. ^ Turing, A.M. (1938), "On Computable Numbers, with an Application to the Entscheidungsproblem: A correction", Proceedings of the London Mathematical Society, 2, vol. 43, no. 6 (published 1937), pp. 544–6, doi:10.1112/plms/s2-43.6.544
  14. ^ David A. Mindell, Between Human and Machine: Feedback, Control, and Computing Before Cybernetics, (Baltimore: Johns Hopkins University Press), 2004, pp. 319-320. ISBN 0-8018-8057-2.
  15. ^ David Kahn, The Codebreakers, rev. ed., (New York: Simon and Schuster), 1996, pp. 743-751. ISBN 0-684-83130-9.
  16. ^ quoted in Kahn, The Codebreakers, p. 744.
  17. ^ 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.
  18. ^ Shannon, Claude (1949). "Communication Theory of Secrecy Systems". Bell System Technical Journal 28 (4): 656–715.
  19. ^ The Invention of the First Wearable Computer Online paper by Edward O. Thorp of Edward O. Thorp & Associates
  20. ^ Shannon Statue Dedications
  21. ^ C. E. Shannon: A mathematical theory of communication. Bell System Technical Journal, vol. 27, pp. 379–423 and 623–656, July and October, 1948
  22. ^ 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)
  23. ^ Claude Elwood Shannon April 30, 1916
  24. ^ Hamid Reza Ekbia (2008), Artificial dreams: the quest for non-biological intelligence, Cambridge University Press, p. 46, ISBN 978-0-521-87867-8
  25. ^ American Scientist online: Bettor Math, article and book review by Elwyn Berlekamp
  26. ^ John Kelly by William Poundstone website
  27. ^ Elwyn Berlekamp (Kelly's Research Assistant) Bio details
  28. ^ William Poundstone website
  29. ^ Zenios, S. A.; Ziemba, W. T. (2006), Handbook of Asset and Liability Management, North Holland, ISBN 978-0-444-50875-1
  30. ^ Pabrai, Mohnish (2007), The Dhandho Investor: The Low-Risk Value Method to High Returns, Wiley, ISBN 978-0-470-04389-9
  31. ^ "Ed Thorp's Genius Detailed In Scott Patterson's The Quants", book review by Bill Freehling for gurufocus.com, February 5, 2010
  32. ^ Thorp, E. O. (2008), "The Kelly Criterion: Part II", Wilmott Magazine {{citation}}: Unknown parameter |month= ignored (help)
  33. ^ J. L. Kelly, Jr, A New Interpretation of Information Rate, Bell System Technical Journal, 35, (1956), 917–926
  34. ^ "IEEE Morris N. Liebmann Memorial Award Recipients" (PDF). IEEE. Retrieved February 27, 2011 (2011-02-27). {{cite web}}: Check date values in: |accessdate= (help)
  35. ^ "IEEE Medal of Honor Recipients" (PDF). IEEE. Retrieved February 27, 2011 (2011-02-27). {{cite web}}: Check date values in: |accessdate= (help)
  36. ^ "Award Winners (chronological)". Eduard Rhein Foundation. Retrieved February 20, 2011 (2011-02-20). {{cite web}}: Check date values in: |accessdate= (help)

Further reading

  • Claude E. Shannon: A Mathematical Theory of Communication, Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, 1948. [1] [2]
  • 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) [3]
  • 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, ISBN 978-0-8090-4599-0
  • Gleick, James, The Information: A History, A Theory, A Flood, Pantheon, 2011, ISBN 978-0-375-42372-7

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