Editing Claude Shannon (section)

===Information theory===
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 message a sender wants to transmit. Shannon developed [[information entropy]] as a measure of the [[information]] content in a message, which is a measure of uncertainty reduced by the message. In so doing, he essentially invented the field of [[information theory]].

The book ''The Mathematical Theory of Communication''<ref name=":0" /> reprints Shannon's 1948 article and [[Warren 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, 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 [[space (punctuation)|space]] 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 of [[Nyquist–Shannon sampling theorem|sampling theorem]], which he had derived as early as 1940,<ref>{{Cite conference |last1=Stanković |first1=Raromir S. |last2=Astola |first2=Jaakko T. |last3=Karpovsky |first3=Mark G. |date=September 2006 |title=Some Historic Remarks On Sampling Theorem |url=https://sites.bu.edu/mark/files/2018/02/196.pdf |conference=Proceedings of the 2006 International TICSP Workshop on Spectral Methods and Multirate Signal Processing}}</ref> 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.<ref name=":16" /> 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."<ref>{{cite journal |last1=Shannon |first1=Claude E. |title=The Bandwagon |journal=IRE Transactions on Information Theory |date=1956 |volume=2 |issue=1 |page=3 |doi=10.1109/TIT.1956.1056774 |url=https://www.jonglage.net/theorie/notation/siteswap-avancee/refs/books/Claude%20Shannon%20-%20Collected%20Papers.pdf |access-date=18 February 2025}}</ref>

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.<ref name=":19">{{Cite book |last=McEliece |first=Robert J. |author-link=Robert McEliece |url=https://books.google.com/books?id=bQ9fWH7fh3IC |title=The Theory of Information and Coding |date=2004 |publisher=Cambridge University Press |isbn=978-0-521-83185-7 |edition=Student |series= |location=Cambridge |pages=13 |language=en}}</ref> Even beyond his original paper in 1948, he is still regarded as the most important post-1948 contributor to the theory.<ref name=":19" />

In May 1951, [[Mervin Kelly]] received a request from the director of the [[Central Intelligence Agency|CIA]], general [[Walter 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".<ref name="Soni Goodman 2017 p. 63">{{cite book |last1=Soni |first1=J. |url=https://books.google.com/books?id=gygsDwAAQBAJ&dq=special+cryptologic+advisory+group+claude+shannon&pg=PA196 |title=A Mind at Play: How Claude Shannon Invented the Information Age |last2=Goodman |first2=R. |publisher=Simon & Schuster |year=2017 |isbn=978-1-4767-6668-3 |pages=193–198 |language=en |access-date=}}</ref> As a result of the request, Shannon became part of the CIA's Special Cryptologic Advisory Group or SCAG.<ref name="Soni Goodman 2017 p. 63" />

In his time at Bell Labs, he also co-developed [[pulse-code modulation]] alongside [[Bernard M. Oliver]], and [[John R. Pierce]].<ref>{{Cite book |last=Noll |first=A. Michael |url=https://books.google.com/books?id=rpkuAgAAQBAJ&pg=PA50 |title=Highway of Dreams: A Critical View Along the Information Superhighway |date=1997 |publisher=Erlbaum |isbn=978-0-8058-2557-2 |edition=Revised |series=Telecommunications |location=Mahwah, NJ |pages=50 |language=en}}</ref><ref>{{Cite book |last=Barrett |first=G. Douglas |url=https://books.google.com/books?id=r9-SEAAAQBAJ&pg=PA102 |title=Experimenting the Human: Art, Music, and the Contemporary Posthuman |publisher=[[The University of Chicago Press]] |year=2023 |isbn=978-0-226-82340-9 |location=Chicago London |pages=102 |language=en}}</ref>