Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an Americanmathematician,electrical engineer,computer scientist,cryptographer and inventor, known as the "father ofinformation theory" and credited with laying the foundations of theInformation Age.[1][2][3] Shannon was the first to describe the use of Boolean algebra that are essential to all digital electronic circuits, and was one of the founding fathers ofartificial intelligence.[4][5][6] RoboticistRodney Brooks declared that Shannon was the 20th century engineer who contributed the most to 21st century technologies,[7] and mathematicianSolomon W. Golomb described his intellectual achievement as "one of the greatest of the twentieth century".[8]
At theUniversity of Michigan, Shannondual degreed, graduating with a Bachelor of Science in both electrical engineering and mathematics in 1936. A 21-year-oldmaster's degree student in electrical engineering atMIT, his thesis "A Symbolic Analysis of Relay and Switching Circuits" demonstrated that electrical applications ofBoolean algebra could construct any logical numerical relationship,[9] thereby establishing the theory behinddigital computing anddigital circuits.[10] The thesis has been claimed to be the most important master's thesis of all time,[9] having been called the "birth certificate of the digital revolution",[11] and winning the1939 Alfred Noble Prize.[12] He graduated from MIT in 1940 with a PhD in mathematics;[13] his thesis focusing ongenetics contained important results, while initially going unpublished.[14]
Shannon contributed to the field ofcryptanalysis for national defense of the United States duringWorld War II, including his fundamental work on codebreaking and securetelecommunications, writing apaper which is considered one of the foundational pieces of modern cryptography,[15] with his work described as "a turning point, and marked the closure of classical cryptography and the beginning of modern cryptography".[16] The work of Shannon was foundational forsymmetric-key cryptography, including the work ofHorst Feistel, theData Encryption Standard (DES), and theAdvanced Encryption Standard (AES).[16] As a result, Shannon has been called the "founding father of modern cryptography".[17]
His 1948 paper "A Mathematical Theory of Communication" laid the foundations for the field of information theory,[18][13] referred to as a "blueprint for the digital era" by electrical engineerRobert G. Gallager[19] and "theMagna Carta of the Information Age" byScientific American.[20][21] Golomb compared Shannon's influence on the digital age to that which "the inventor of the alphabet has had on literature".[18] Advancements across multiple scientific disciplines utilized Shannon's theory—including the invention of thecompact disc, the development of theInternet, the commercialization of mobile telephony, and the understanding ofblack holes.[22][23] He also formally introduced the term "bit",[24][2] and was a co-inventor of bothpulse-code modulation and the firstwearable computer.
Shannon made numerous contributions to the field of artificial intelligence,[4] including co-organizing the 1956Dartmouth workshop considered to be the discipline's founding event,[25][26] and papers on the programming of chess computers.[27][28] His Theseus machine was the first electrical device to learn by trial and error, being one of the first examples of artificial intelligence.[7][29]
The Shannon family lived inGaylord, Michigan, and Claude was born in a hospital that was nearbyPetoskey.[5] His father, Claude Sr. (1862–1934), was a businessman and, for a while, a judge ofprobate inGaylord. His mother, Mabel Wolf Shannon (1880–1945), was a language teacher, who also served as the principal ofGaylord High School.[30] Claude Sr. was a descendant ofNew Jersey settlers, while Mabel was a child of German immigrants.[5] Shannon's family was active in their Methodist Church during his youth.[31]
Most of the first 16 years of Shannon's life were spent in Gaylord, where he attended public school, graduating from Gaylord High School in 1932. Shannon showed an inclination towards mechanical and electrical things. His best subjects were science and mathematics. At home, he constructed such devices as models of planes, a radio-controlled model boat and a barbed-wiretelegraph system to a friend's house a half-mile away.[32] While growing up, he also worked as a messenger for theWestern Union company.
Shannon's childhood hero wasThomas Edison, who he later learned was a distant cousin. Both Shannon and Edison were descendants ofJohn Ogden (1609–1682), a colonial leader and an ancestor of many distinguished people.[33][34]
In 1936, Shannon began his graduate studies inelectrical engineering at theMassachusetts Institute of Technology (MIT), where he worked onVannevar Bush'sdifferential analyzer, which was an earlyanalog computer that was composed of electromechanical parts and could solvedifferential equations.[35] While studying the complicatedad hoc circuits of this analyzer, Shannon designedswitching circuits based onBoole's concepts. In 1937, he wrote hismaster's degree thesis,A Symbolic Analysis of Relay and Switching Circuits,[36] with a paper from this thesis published in 1938.[36] A revolutionary work forswitching circuit theory, Shannon diagramed switching circuits that could implement the essential operators ofBoolean algebra. Then he proved that his switching circuits could be used to simplify the arrangement of theelectromechanicalrelays that were used during that time intelephone call routing switches. Next, he expanded this concept, proving that these circuits could solve all problems that Boolean algebra could solve. In the last chapter, he presented diagrams of several circuits, including a digital 4-bit full adder.[36] His work differed significantly from the work of previous engineers such asAkira Nakashima, who still relied on the existent circuit theory of the time and took a grounded approach.[37] Shannon's idea were more abstract and relied on mathematics, thereby breaking new ground with his work, with his approach dominating modern-day electrical engineering.[37]
Using electrical switches to implement logic is the fundamental concept that underlies allelectronic digital computers. Shannon's work became the foundation ofdigital circuit design, as it became widely known in the electrical engineering community during and afterWorld War II. The theoretical rigor of Shannon's work superseded thead hoc methods that had prevailed previously.Howard Gardner hailed Shannon's thesis "possibly the most important, and also the most famous, master's thesis of the century."[38]Herman Goldstine described it as "surely ... one of the most important master's theses ever written ... It helped to change digital circuit design from an art to a science."[39] One of the reviewers of his work commented that "To the best of my knowledge, this is the first application of the methods of symbolic logic to so practical an engineering problem. From the point of view of originality I rate the paper as outstanding."[40] Shannon's master's thesis won the1939 Alfred Noble Prize.
Shannon received his PhD in mathematics from MIT in 1940.[33] Vannevar Bush had suggested that Shannon should work on his dissertation at theCold Spring Harbor Laboratory, in order to develop a mathematical formulation forMendeliangenetics. This research resulted in Shannon's PhD thesis, calledAn Algebra for Theoretical Genetics.[41] However, the thesis went unpublished after Shannon lost interest, but it did contain important results.[14] Notably, he was one of the first to apply an algebraic framework to study theoretical population genetics.[42] In addition, Shannon devised a general expression for the distribution of several linked traits in a population after multiple generations under a random mating system, which was original at the time,[43] with the new theorem unworked out by otherpopulation geneticists of the time.[44]
Shannon is credited with the invention ofsignal-flow graphs, in 1942. He discovered the topological gain formula while investigating the functional operation of an analog computer.[47]
For two months early in 1943, Shannon came into contact with the leading British mathematicianAlan Turing. Turing had been posted to Washington to share with theU.S. Navy's cryptanalytic service the methods used by theBritish Government Code and Cypher School atBletchley Park to break the cyphers used by theKriegsmarineU-boats in the northAtlantic Ocean.[48] 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.[48] Turing showed Shannon his 1936 paper that defined what is now known as the "universal Turing machine".[49][50] This impressed Shannon, as many of its ideas complemented his own.
Shannon and his team developed anti-aircraft systems that tracked enemy missiles and planes, while also determining the paths for intercepting missiles.[51]
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 titledData Smoothing and Prediction in Fire-Control Systems, coauthored by Shannon,Ralph Beebe Blackman, andHendrik 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."[52] In other words, it modeled the problem in terms ofdata andsignal processing and thus heralded the coming of theInformation Age.
Shannon's work on cryptography was even more closely related to his later publications oncommunication theory.[53] At the close of the war, he prepared a classified memorandum forBell Telephone Labs entitled "A Mathematical Theory of Cryptography", dated September 1945. A declassified version of this paper was published in 1949 as "Communication Theory of Secrecy Systems" in theBell System Technical Journal. This paper incorporated many of the concepts and mathematical formulations that also appeared in hisA Mathematical Theory of Communication. Shannon said that his wartime insights into communication theory and cryptography developed simultaneously, and that "they were so close together you couldn't separate them".[54] 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."[55]
While he was at Bell Labs, Shannon proved that thecryptographicone-time pad is unbreakable in his classified research that was later published in 1949. The same article 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.[56]
In 1948, the promised memorandum appeared as "A Mathematical Theory of Communication", an article in two parts in the July and October issues of theBell System Technical Journal. This work focuses on the problem of how best to encode the message a sender wants to transmit. Shannon developedinformation entropy as a measure of theinformation content in a message, which is a measure of uncertainty reduced by the message. In so doing, he essentially invented the field ofinformation theory.
The bookThe Mathematical Theory of Communication[57] reprints Shannon's 1948 article andWarren Weaver's popularization of it, which is accessible to the non-specialist. Weaver pointed out that the word "information" in communication theory is not related to what you do say, but to what you could say. That is, information is a measure of one's freedom of choice when one selects a message. Shannon's concepts were also popularized, subject to his own proofreading, inJohn Robinson Pierce'sSymbols, Signals, and Noise.
Information theory's fundamental contribution tonatural language processing andcomputational 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 treatingspace 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 cyphers must have the same requirements as the one-time pad. He is credited with the introduction ofsampling theorem, which he had derived as early as 1940,[58] and 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 further wrote a paper in 1956 regarding coding for a noisy channel, which also became a classic paper in the field of information theory.[59] However, also in 1956 he wrote a one-page editorial for the "IRE Transactions on Information Theory" entitled "The Bandwagon" which he began by observing: "Information theory has, in the last few years, become something of a scientific bandwagon" and which he concluded by warning: "Only by maintaining a thoroughly scientific attitude can we achieve real progress in communication theory and consolidate our present position."[60]
Claude Shannon's influence has been immense in the field, for example, in a 1973 collection of the key papers in the field of information theory, he was author or coauthor of 12 of the 49 papers cited, while no one else appeared more than three times.[61] Even beyond his original paper in 1948, he is still regarded as the most important post-1948 contributor to the theory.[61]
In May 1951,Mervin Kelly received a request from the director of theCIA, generalWalter Bedell Smith, regarding Shannon and the need for him, as Shannon was regarded as, based on "the best authority", the "most eminently qualified scientist in the particular field concerned".[62] As a result of the request, Shannon became part of the CIA's Special Cryptologic Advisory Group or SCAG.[62]
In 1950, Shannon designed and built, with the help of his wife, a learning machine named Theseus. It consisted of a maze on a surface, through which a mechanical mouse could move. Below the surface were sensors that followed the path of a mechanical mouse through the maze. After much trial and error, this device would learn the shortest path through the maze, and direct the mechanical mouse through the maze. The pattern of the maze could be changed at will.[29]
Mazin Gilbert stated that Theseus "inspired the whole field of AI. This random trial and error is the foundation of artificial intelligence."[29]
Shannon wrote multiple influential papers on artificial intelligence, such as his 1950 paper titled "Programming a Computer for Playing Chess", and his 1953 paper titled "Computers and Automata".[65] AlongsideJohn McCarthy, he co-edited a book titledAutomata Studies, which was published in 1956.[59] The categories in the articles within the volume were influenced by Shannon's own subject headings in his 1953 paper.[59] Shannon shared McCarthy's goal of creating a science of intelligent machines, but also held a broader view of viable approaches in automata studies, such as neural nets, Turing machines, cybernetic mechanisms, and symbolic processing by computer.[59]
In 1956 Shannon joined the MIT faculty, holding an endowed chair. He worked in the Research Laboratory of Electronics (RLE). He continued to serve on the MIT faculty until 1978.
Shannon developedAlzheimer's disease and spent the last few years of his life in anursing home; he died in 2001, survived by his wife, a son and daughter, and two granddaughters.[67][68]
Shannon also invented flame-throwingtrumpets, rocket-poweredfrisbees, and plastic foamshoes for navigating a lake, and which to an observer, would appear as if Shannon was walking on water.[71]
Shannon marriedNorma Levor, a wealthy, Jewish, left-wing intellectual in January 1940. The marriage ended in divorce a year later. Levor later marriedBen Barzman.[74]
Shannon met his second wife,Mary Elizabeth Moore (Betty), when she was a numerical analyst at Bell Labs. They were married in 1949.[67] Betty assisted Claude in building some of his most famous inventions.[75] They had three children.[76]
In June 1954, Shannon was listed as one of the top 20 most important scientists in America byFortune.[80] In 2013, information theory was listed as one of the top 10 revolutionary scientific theories byScience News.[81]
According toNeil Sloane, anAT&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 thedigital revolution, and every device containing amicroprocessor ormicrocontroller is a conceptual descendant of Shannon's publication in 1948:[82] "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."[83] Thecryptocurrency unitshannon (a synonym for gwei) is named after him.[84]
Shannon is credited by many as single-handedly creating information theory and for laying the foundations for theDigital Age.[85][86][14][87][88][2]
A Mind at Play, a biography of Shannon written byJimmy Soni and Rob Goodman, was published in 2017.[91] They described Shannon as "the most important genius you’ve never heard of, a man whose intellect was on par withAlbert Einstein andIsaac Newton".[92] Consultant and writer Tom Rutledge, writing forBoston Review, stated that "Of the computer pioneers who drove the mid-20th-century information technology revolution—an elite men’s club of scholar-engineers who also helped crack Nazi codes and pinpoint missile trajectories—Shannon may have been the most brilliant of them all."[89] Electrical engineerRobert Gallager stated about Shannon that "He had this amazing clarity of vision. Einstein had it, too – this ability to take on a complicated problem and find the right way to look at it, so that things become very simple."[19] In an obituary by Neil Sloane andRobert Calderbank, they stated that "Shannon must rank near the top of the list of major figures of twentieth century science".[93] Due to his work in multiple fields, Shannon is also regarded as apolymath.[94][95]
HistorianJames Gleick noted the importance of Shannon, stating that "Einstein looms large, and rightly so. But we’re not living in the relativity age, we’re living in the information age. It’s Shannon whose fingerprints are on every electronic device we own, every computer screen we gaze into, every means of digital communication. He’s one of these people who so transform the world that, after the transformation, the old world is forgotten."[3] Gleick further noted that "he created a whole field from scratch, from the brow ofZeus".[3]
On April 30, 2016, Shannon was honored with aGoogle Doodle to celebrate his life on what would have been his 100th birthday.[96][97][98][99]
The Bit Player, a feature film about Shannon directed byMark Levinson premiered at theWorld Science Festival in 2019.[100] Drawn from interviews conducted with Shannon in his house in the 1980s, the film was released on Amazon Prime in August 2020.
Shannon'sThe Mathematical Theory of Communication,[57] begins with an interpretation of his own work byWarren Weaver. Although Shannon's entire work is about communication itself, Warren Weaver communicated his ideas in such a way that those not acclimated to complex theory and mathematics could comprehend the fundamental laws he put forth. The coupling of their unique communicational abilities and ideas generated theShannon-Weaver model, although the mathematical and theoretical underpinnings emanate entirely from Shannon's work after Weaver's introduction. For the layman, Weaver's introduction better communicatesThe Mathematical Theory of Communication,[57] but Shannon's subsequent logic, mathematics, and expressive precision was responsible for defining the problem itself.
Shannon and hiselectromechanical mouseTheseus (named afterTheseus from Greek mythology) which he tried to have solve the maze in one of the first experiments inartificial intelligenceTheseus Maze in MIT Museum
"Theseus", created in 1950, was a mechanical mouse controlled by an electromechanical relay circuit that enabled it to move around alabyrinth of 25 squares.[101] The maze configuration was flexible and it could be modified arbitrarily by rearranging movable partitions.[101] The mouse was designed to search through the corridors until it found the target. Having travelled through the maze, the mouse could 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 and learning new behavior.[101] Shannon's mouse appears to have been the first artificial learning device of its kind.[101]
In 1949 Shannon completed a paper (published in March 1950) which estimates thegame-tree complexity ofchess, which is approximately 10120. This number is now often referred to as the "Shannon number", and is still regarded today as an accurate estimate of the game's complexity. The number is often cited as one of the barriers tosolving the game of chess using an exhaustive analysis (i.e.brute force analysis).[102][103]
On March 9, 1949, Shannon presented a paper called "Programming a Computer for playing Chess". The paper was presented at the National Institute for Radio Engineers Convention in New York. He described how to program a computer to play chess based on position scoring and move selection. He proposed basic strategies for restricting the number of possibilities to be considered in a game of chess. In March 1950 it was published inPhilosophical Magazine, and is considered one of the first articles published on the topic of programming a computer for playing chess, and using a computer to solve the game.[102][104] In 1950, Shannon wrote an article titled "A Chess-Playing Machine",[105] which was published inScientific American. Both papers have had immense influence and laid the foundations for future chess programs.[27][28]
His process for having the computer decide on which move to make was aminimax procedure, based on anevaluation 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 usualchess 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).[106] He considered some positional factors, subtracting ½ point for eachdoubled pawn,backward pawn, andisolated pawn;mobility was incorporated by adding 0.1 point for each legal move available.
Shannon also contributed tocombinatorics anddetection theory.[107] His 1948 paper introduced many tools used in combinatorics. He did work on detection theory in 1944, with his work being one of the earliest expositions of the “matched filter” principle.[107]
He was known as a successful investor who gave lectures on investing. A report fromBarron's on August 11, 1986, detailed the recent performance of 1,026 mutual funds, and Shannon achieved a higher return than 1,025 of them. Comparing the portfolio of Shannon from the late 1950s to 1986, toWarren Buffett's of 1965 to 1995, Shannon had a return of about 28% percent, compared to 27% for Buffett.[108] One such method of Shannon's was labeledShannon's demon, which was to form a portfolio of equal parts cash and a stock, and rebalance regularly to take advantage of the stock's randomly jittering price movements.[109] Shannon reportedly long thought of publishing about investing, but ultimately did not, despite giving multiple lectures.[109] He was one of the first investors to download stock prices, and a snapshot of his portfolio in 1981 was found to be $582,717.50, translating to $1.5 million in 2015, excluding another one of his stocks.[109]
This section needs to beupdated. Please help update this article to reflect recent events or newly available information.(April 2016)
Claude Shannon centenary
The Shannon centenary, 2016, marked the life and influence of Claude Elwood Shannon on the hundredth anniversary of his birth on April 30, 1916. It was inspired in part by theAlan Turing Year. An ad hoc committee of theIEEE Information Theory Society includingChristina Fragouli, Rüdiger Urbanke,Michelle Effros, Lav Varshney andSergio Verdú,[110] coordinated worldwide events. The initiative was announced in the History Panel at the 2015 IEEE Information Theory Workshop Jerusalem[111][112] and the IEEE Information Theory Society newsletter.[113]
A detailed listing of confirmed events was available on the website of the IEEE Information Theory Society.[114]
Some of the activities included:
Bell Labs hosted the First Shannon Conference on the Future of the Information Age on April 28–29, 2016, in Murray Hill, New Jersey, to celebrate Claude Shannon and the continued impact of his legacy on society. The event includes keynote speeches by global luminaries and visionaries of the information age who will explore the impact of information theory on society and our digital future, informal recollections, and leading technical presentations on subsequent related work in other areas such as bioinformatics, economic systems, and social networks. There is also a student competition
Bell Labs launched aWeb exhibit on April 30, 2016, chronicling Shannon's hiring at Bell Labs (under an NDRC contract with US Government), his subsequent work there from 1942 through 1957, and details of Mathematics Department. The exhibit also displayed bios of colleagues and managers during his tenure, as well as original versions of some of the technical memoranda which subsequently became well known in published form.
The Republic of Macedonia issued a commemorative stamp.[115] AUSPS commemorative stamp is being proposed, with an active petition.[116]
A trans-Atlantic celebration of both George Boole's bicentenary and Claude Shannon's centenary that is being led by University College Cork and the Massachusetts Institute of Technology. A first event was a workshop in Cork, When Boole Meets Shannon,[118] and will continue with exhibits at theBoston Museum of Science and at theMIT Museum.[119]
Many organizations around the world are holding observance events, including the Boston Museum of Science, the Heinz-Nixdorf Museum, the Institute for Advanced Study, Technische Universität Berlin, University of South Australia (UniSA), Unicamp (Universidade Estadual de Campinas), University of Toronto, Chinese University of Hong Kong, Cairo University, Telecom ParisTech, National Technical University of Athens, Indian Institute of Science, Indian Institute of Technology Bombay,Indian Institute of Technology Kanpur,Nanyang Technological University of Singapore, University of Maryland, University of Illinois at Chicago, École Polytechnique Federale de Lausanne, The Pennsylvania State University (Penn State), University of California Los Angeles, Massachusetts Institute of Technology,Chongqing University of Posts and Telecommunications, and University of Illinois at Urbana-Champaign.
A logo that appears on this page was crowdsourced on Crowdspring.[120]
The Math Encounters presentation of May 4, 2016, at theNational Museum of Mathematics in New York, titledSaving Face: Information Tricks for Love and Life, focused on Shannon's work in information theory. A video recording and other material are available.[121]
Claude E. Shannon: "A Mathematical Theory of Communication",Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, 1948 (abstract).
Claude E. Shannon and Warren Weaver:The Mathematical Theory of Communication. The University of Illinois Press, Urbana, Illinois, 1949.ISBN0-252-72548-4
^abPoundstone, William (2005).Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street. Hill & Wang. p. 20.ISBN978-0-8090-4599-0.
^Rioul, Olivier (2021), Duplantier, Bertrand; Rivasseau, Vincent (eds.), "This is IT: A Primer on Shannon's Entropy and Information",Information Theory: Poincaré Seminar 2018, Progress in Mathematical Physics, vol. 78, Cham: Springer, pp. 49–86,doi:10.1007/978-3-030-81480-9_2,ISBN978-3-030-81480-9
^Shannon, Claude Elwood (1940).An Algebra for Theoretical Genetics (Thesis). Massachusetts Institute of Technology.hdl:1721.1/11174. — Contains a biography on pp. 64–65.
^Guizzo, Erico Marui (2003).The Essential Message: Claude Shannon and the Making of Information Theory (Thesis). Massachusetts Institute of Technology.hdl:1721.1/39429.
^Gertner, Jon (2013).The idea factory: Bell Labs and the great age of American innovation. London: Penguin Books. p. 118.ISBN978-0-14-312279-1.
^Okrent, Howard; McNamee, Lawrence P. (1970)."3. 3 Flowgraph Theory"(PDF).NASAP-70 User's and Programmer's manual. Los Angeles, California: School of Engineering and Applied Science, University of California at Los Angeles. pp. 3–9. RetrievedMarch 4, 2016.
^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,S2CID73712
^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
^Mindell, David A. (October 15, 2004).Between Human and Machine: Feedback, Control, and Computing Before Cybernetics. JHU Press. pp. 319–320.ISBN0801880572.
^Stanković, Raromir S.; Astola, Jaakko T.; Karpovsky, Mark G. (September 2006).Some Historic Remarks On Sampling Theorem(PDF). Proceedings of the 2006 International TICSP Workshop on Spectral Methods and Multirate Signal Processing.
^Boehm, George A. W. (March 1, 1953). "GYPSY, MODEL VI, CLAUDE SHANNON, NIMWIT, AND THE MOUSE".Computers and Automation 1953-03: Vol 2 Iss 2. Internet Archive. Berkeley Enterprises. pp. 1–4.
^Thorp, Edward (October 1998). "The invention of the first wearable computer".Digest of Papers. Second International Symposium on Wearable Computers (Cat. No.98EX215). pp. 4–8.doi:10.1109/iswc.1998.729523.ISBN0-8186-9074-7.S2CID1526.
^Jimmy Soni; Rob Goodman (2017).A Mind At Play: How Claude Shannon Invented the Information Age. Simon and Schuster. pp. 63, 80.
^William Poundstone (2010).Fortune's Formula: The Untold Story of the Scientific Betting System. Macmillan. p. 18.ISBN978-0-374-70708-8.Shannon described himself as an atheist and was outwardly apolitical.
^Shannon, C. E. (1948). "A mathematical theory of communication".Bell System Technical Journal.27 (3):379–423,623–656.doi:10.1002/j.1538-7305.1948.tb01338.x.
^Coughlin, Kevin (February 27, 2001). "Bell Labs digital guru dead at 84— Pioneer scientist led high-tech revolution".The Star-Ledger.
Claude E. Shannon:Programming a Computer for Playing Chess, Philosophical Magazine, Ser.7, Vol. 41, No. 314, March 1950. (Available online underExternal links below)
David Levy:Computer Gamesmanship: Elements of Intelligent Game Design, Simon & Schuster, 1983.ISBN0-671-49532-1
Mindell, David A., "Automation's Finest Hour: Bell Labs and Automatic Control in World War II",IEEE Control Systems, December 1995, pp. 72–80.
Nahin, Paul J.,The Logician and the Engineer: How George Boole and Claude Shannon Created the Information Age, Princeton University Press, 2013,ISBN978-0691151007
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