A Mathematical Theory of Communication

{{Short description|1948 scholarly article by Claude Shannon}} {{use dmy dates|date=August 2019|cs1-dates=y}} {{Infobox book | italic title =  | name = A Mathematical Theory of Communication | image = The Mathematical Theory Of Communication title page.jpg | image_size = | border = | alt = | caption = 1949 full book edition | author = Claude E. Shannon | audio_read_by = | title_orig = | orig_lang_code = en | title_working = | translator = | illustrator = | cover_artist = | country = United States | language = English | series = | release_number = | subject = Communication theory | genre = | set_in = | publisher = | publisher2 = | pub_date = 1948 | english_pub_date = | published = | media_type = | pages = | awards = | isbn = | isbn_note = | oclc = | dewey = | congress = | preceded_by = | followed_by = | native_wikisource = | wikisource = | notes = | exclude_cover = | website = }} "'''A Mathematical Theory of Communication'''" is an article by mathematician Claude Shannon published in ''Bell System Technical Journal'' in 1948.<ref name="Shannon_1948_1"/><ref name="Shannon_1948_2"/><ref>{{cite book| title=Information Theory: Tracts in Pure & Applied Mathematics| last=Ash| first=Robert B.| location=New York| publisher=John Wiley & Sons Inc| year=1966| isbn=0-470-03445-9}}</ref><ref>{{Cite book| title=Information Theory and Network Coding| url=https://archive.org/details/informationtheor00yeun| url-access=limited| last=Yeung| first=Raymond W.| year=2008| publisher=Springer| isbn=978-0-387-79233-0| chapter=The Science of Information| pages=[https://archive.org/details/informationtheor00yeun/page/n18 1]–4| doi=10.1007/978-0-387-79234-7_1}}</ref> It was renamed '''''The Mathematical Theory of Communication''''' in the 1949 book of the same name,<ref name="Shannon_1949"/> a small but significant title change after realizing the generality of this work. It has tens of thousands of citations, being one of the most influential and cited scientific papers of all time,<ref>{{Cite book |last=Yan |first=Zheng |url=https://books.google.com/books?id=eEgFEAAAQBAJ&pg=PA7 |title=Publishing Journal Articles: A Scientific Guide for New Authors Worldwide |date=2020 |publisher=Cambridge University Press |isbn=978-1-108-27742-6 |location= |pages=7 |language=en}}</ref> as it gave rise to the field of information theory, with ''Scientific American'' referring to the paper as the "Magna Carta of the Information Age",<ref>{{Cite web |last1=Goodman |first1=Rob |last2=Soni |first2=Jimmy |date=2018 |title=Genius in Training |url=https://alumni.umich.edu/michigan-alum/genius-in-training/ |access-date=2023-10-31 |website=Alumni Association of the University of Michigan |language=en-US}}</ref> while the electrical engineer Robert G. Gallager called the paper a "blueprint for the digital era".<ref>{{Cite web |date=2001-07-01 |title=Claude Shannon: Reluctant Father of the Digital Age |url=https://www.technologyreview.com/2001/07/01/235669/claude-shannon-reluctant-father-of-the-digital-age/ |access-date=2024-06-26 |website=MIT Technology Review |language=en}}</ref> Historian James Gleick rated the paper as the most important development of 1948, placing the transistor second in the same time period, with Gleick emphasizing that the paper by Shannon was "even more profound and more fundamental" than the transistor.<ref>{{Cite book |last=Gleick |first=James |author-link=James Gleick |url=https://books.google.com/books?id=WAKWDwAAQBAJ&pg=PA3 |title=The Information: A History, a Theory, a Flood |publisher=Vintage Books |year=2011 |isbn=978-1-4000-9623-7 |edition=1st |location=New York |pages=3–4 |language=en}}</ref>

It is also noted that "as did relativity and quantum theory, information theory radically changed the way scientists look at the universe".<ref>{{Cite book |last=Watson |first=Peter |author-link=Peter Watson (intellectual historian) |url=https://books.google.com/books?id=gC6MDAAAQBAJ&pg=PA392 |title=Convergence: The Idea at the Heart of Science |date=2018 |publisher=Simon & Schuster |isbn=978-1-4767-5434-5 |edition= |location=New York London Toronto Sydney New Delhi |pages=392 |language=en}}</ref> The paper also formally introduced the term "bit" and serves as its theoretical foundation.<ref>{{Cite book |last=Nicolelis |first=Miguel A. L. |author-link=Miguel Nicolelis |url=https://books.google.com/books?id=my7EDwAAQBAJ&pg=PA34 |title=The True Creator of Everything: How the Human Brain Shaped the Universe as We Know it |date=2020 |publisher=Yale University Press |isbn=978-0-300-24463-2 |location=New Haven |pages=34 |language=en |oclc=on1090423259}}</ref>

==Publication== The article was the founding work of the field of information theory. It was later published in 1949 as a book titled ''The Mathematical Theory of Communication'' ({{ISBN|0-252-72546-8}}), which was published as a paperback in 1963 ({{ISBN|0-252-72548-4}}). The book contains an additional article by Warren Weaver, providing an overview of the theory for a more general audience.<ref>{{cite web |title=The Mathematical Theory of Communication |url=https://monoskop.org/images/b/be/Shannon_Claude_E_Weaver_Warren_The_Mathematical_Theory_of_Communication_1963.pdf |website=Monoskop Digital Libraries |access-date=28 May 2024}}</ref>

==Contents== [[File:Shannon communication system.svg|thumb|right|343px|Shannon's diagram of a general communications system, showing the process by which a message sent becomes the message received (possibly corrupted by noise)]] This work is known for introducing the concepts of channel capacity as well as the noisy channel coding theorem.

Shannon's article laid out the basic elements of communication: *An information source that produces a message *A transmitter that operates on the message to create a signal which can be sent through a channel *A channel, which is the medium over which the signal, carrying the information that composes the message, is sent *A receiver, which transforms the signal back into the message intended for delivery *A destination, which can be a person or a machine, for whom or which the message is intended

It also developed the concepts of information entropy, redundancy and the source coding theorem, and introduced the term bit (which Shannon credited to John Tukey) as a unit of information. It was also in this paper that the Shannon–Fano coding technique was proposed – a technique developed in conjunction with Robert Fano.

==References== {{Reflist|refs= <ref name="Shannon_1948_1">{{cite journal |author-last=Shannon |author-first=Claude Elwood |author-link=Claude Elwood Shannon |title=A Mathematical Theory of Communication |journal=Bell System Technical Journal |volume=27 |issue=3 |pages=379–423 |date=July 1948 |doi=10.1002/j.1538-7305.1948.tb01338.x |hdl=11858/00-001M-0000-002C-4314-2 |url=http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |archive-url=https://web.archive.org/web/19980715013250/http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |url-status=dead |archive-date=1998-07-15 |quote=The choice of a logarithmic base corresponds to the choice of a unit for measuring information. If the base 2 is used the resulting units may be called binary digits, or more briefly ''bits'', a word suggested by J. W. Tukey.|hdl-access=free }}</ref> <ref name="Shannon_1948_2">{{cite journal |author-last=Shannon |author-first=Claude Elwood |author-link=Claude Elwood Shannon |title=A Mathematical Theory of Communication |journal=Bell System Technical Journal |volume=27 |issue=4 |pages=623–656 |date=October 1948 |doi=10.1002/j.1538-7305.1948.tb00917.x |hdl=11858/00-001M-0000-002C-4314-2|hdl-access=free }}</ref> <ref name="Shannon_1949">{{cite book |author-last1=Shannon |author-first1=Claude Elwood |author-link1=Claude Elwood Shannon |author-first2=Warren |author-last2=Weaver |author-link2=Warren Weaver |title=The Mathematical Theory of Communication |publisher=University of Illinois Press |date=1949 |url=http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |archive-url=https://web.archive.org/web/19980715013250/http://cm.bell-labs.com/cm/ms/what/shannonday/shannon1948.pdf |url-status=dead |archive-date=1998-07-15}}</ref> }}

== External links == * [https://people.math.harvard.edu/~ctm/home/text/others/shannon/entropy/entropy.pdf (PDF) "A Mathematical Theory of Communication" by C. E. Shannon] (reprint with corrections) hosted by the [https://www.math.harvard.edu/ Harvard Mathematics Department], at Harvard University ** Original publications: {{Cite book |url=https://archive.org/details/sim_att-technical-journal_1948-07_27_3/page/n2/ |title=The Bell System Technical Journal 1948-07: Vol 27 Iss 3 |date=1948-07-01 |publisher=AT & T Bell Laboratories |pages=379–423 |language=en}}, {{Cite book |url=https://archive.org/details/sim_att-technical-journal_1948-10_27_4/page/623/ |title=The Bell System Technical Journal 1948-10: Vol 27 Iss 4 |date=1948-10-01 |publisher=AT & T Bell Laboratories |pages=623–656 |language=en}} * [https://www.khanacademy.org/computing/computer-science/informationtheory/moderninfotheory/v/a-mathematical-theory-of-communication Khan Academy video about "A Mathematical Theory of Communication"]

{{DEFAULTSORT:Mathematical Theory of Communication}} Category:1963 non-fiction books Category:Information theory Category:Computer science books Category:Mathematics books Category:Mathematics papers Category:Works originally published in American magazines Category:1948 documents Category:Works originally published in science and technology magazines Category:Texts related to the history of the Internet Category:Claude Shannon