Claude Elwood Shannon

# Claude Elwood Shannon

Overview
Claude Elwood Shannon was an American mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, electronic engineer, and cryptographer
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...

known as "the father of information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

".
Discussion
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Quotations

I visualize a time when we will be to robots what dogs are to humans. And I am rooting for the machines.

Omni Magazine 1987
Encyclopedia
Claude Elwood Shannon was an American mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, electronic engineer, and cryptographer
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...

known as "the father of information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

".

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
Digital circuit
Digital electronics represent signals by discrete bands of analog levels, rather than by a continuous range. All levels within a band represent the same signal state...

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. Shannon contributed to the field of cryptanalysis
Cryptanalysis
Cryptanalysis is the study of methods for obtaining the meaning of encrypted information, without access to the secret information that is normally required to do so. Typically, this involves knowing how the system works and finding a secret key...

during World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

and afterwards, including basic work on code breaking.

## Biography

Shannon was born in Petoskey, Michigan
Petoskey, Michigan
Petoskey is a city and coastal resort community in the U.S. state of Michigan. As of the 2000 census, the city population was 6,080. It is the county seat of Emmet County....

. His father, Claude Sr (1862–1934), a descendant of early New Jersey
New Jersey
New Jersey is a state in the Northeastern and Middle Atlantic regions of the United States. , its population was 8,791,894. It is bordered on the north and east by the state of New York, on the southeast and south by the Atlantic Ocean, on the west by Pennsylvania and on the southwest by Delaware...

settlers, was a self-made businessman and for a while, Judge of Probate
Probate
Probate is the legal process of administering the estate of a deceased person by resolving all claims and distributing the deceased person's property under the valid will. A probate court decides the validity of a testator's will...

. 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
Gaylord High School
Gaylord High School is located in Gaylord, Michigan, United States. It is the fifth-largest high school in the Big North Athletic Conference, serving approximately 1019 students in grades 9-12. This classifies it as a "Class A" high school. GHS is part of Gaylord Community Schools. Its location...

, Michigan. The first 16 years of Shannon's life were spent in Gaylord, Michigan
Gaylord, Michigan
Gaylord is a city in the U.S. state of Michigan. As of the 2000 census, the city population was 3,681. It is the county seat of Otsego County. The city is also the seat of the Roman Catholic Diocese of Gaylord; it is by far the smallest settlement serving as the location of an active Roman...

, 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
Western Union
The Western Union Company is a financial services and communications company based in the United States. Its North American headquarters is in Englewood, Colorado. Up until 2006, Western Union was the best-known U.S...

. His childhood hero was Thomas Edison
Thomas Edison
Thomas Alva Edison was an American inventor and businessman. He developed many devices that greatly influenced life around the world, including the phonograph, the motion picture camera, and a long-lasting, practical electric light bulb. In addition, he created the world’s first industrial...

, who he later learned was a distant cousin. Both were descendants of John Ogden, a colonial leader and an ancestor of many distinguished people.

### Boolean theory

In 1932 he entered the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...

, where he took a course that introduced him to the works of George Boole
George Boole
George Boole was an English mathematician and philosopher.As the inventor of Boolean logic—the basis of modern digital computer logic—Boole is regarded in hindsight as a founder of the field of computer science. Boole said,...

. He graduated in 1936 with two bachelor's degree
Bachelor's degree
A bachelor's degree is usually an academic degree awarded for an undergraduate course or major that generally lasts for three or four years, but can range anywhere from two to six years depending on the region of the world...

s, one in electrical engineering
Electrical engineering
Electrical engineering is a field of engineering that generally deals with the study and application of electricity, electronics and electromagnetism. The field first became an identifiable occupation in the late nineteenth century after commercialization of the electric telegraph and electrical...

and one in mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

. Later he began his graduate studies at the Massachusetts Institute of Technology
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...

(MIT), where he worked on Vannevar Bush
Vannevar Bush
Vannevar Bush was an American engineer and science administrator known for his work on analog computing, his political role in the development of the atomic bomb as a primary organizer of the Manhattan Project, the founding of Raytheon, and the idea of the memex, an adjustable microfilm viewer...

's differential analyzer, an analog computer
Analog computer
An analog computer is a form of computer that uses the continuously-changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved...

.

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
Thesis
A dissertation or thesis is a document submitted in support of candidature for an academic degree or professional qualification presenting the author's research and findings...

, A Symbolic Analysis of Relay and Switching Circuits
A Symbolic Analysis of Relay and Switching Circuits
A Symbolic Analysis of Relay and Switching Circuits is the title of a master's thesis written by computer science pioneer Claude E. Shannon while attending the Massachusetts Institute of Technology in 1937...

, 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
Alfred Noble Prize
The Alfred Noble Prize is an award presented by the combined engineering societies of the United States, given each year to a person not over thirty-five for a paper published in one of the journals of the participating societies....

in 1940. Howard Gardner
Howard Gardner
Howard Earl Gardner is an American developmental psychologist who is a professor of Cognition and Education at Harvard Graduate School of Education at Harvard University, Senior Director of Harvard Project Zero and author of over twenty books translated into thirty languages. Since 1995, he has...

, of Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...

, called Shannon's thesis "possibly the most important, and also the most famous, master's thesis of the century."

Victor Shestakov
Victor Shestakov
Victor Ivanovich Shestakov was a Russian/Soviet logician and theoretician of electrical engineering. In 1935 he discovered the possible interpretation of Boolean algebra of logic in electro-mechanical relay circuits...

, 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 relay
Relay
A relay is an electrically operated switch. Many relays use an electromagnet to operate a switching mechanism mechanically, but other operating principles are also used. Relays are used where it is necessary to control a circuit by a low-power signal , or where several circuits must be controlled...

s 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
Digital circuit
Digital electronics represent signals by discrete bands of analog levels, rather than by a continuous range. All levels within a band represent the same signal state...

design when it became widely known among the electrical engineering community during and after World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

. 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
Cold Spring Harbor Laboratory
The Cold Spring Harbor Laboratory is a private, non-profit institution with research programs focusing on cancer, neurobiology, plant genetics, genomics and bioinformatics. The Laboratory has a broad educational mission, including the recently established Watson School of Biological Sciences. It...

, funded by the Carnegie Institution headed by Bush, to develop similar mathematical relationships for Mendelian
Gregor Mendel
Gregor Johann Mendel was an Austrian scientist and Augustinian friar who gained posthumous fame as the founder of the new science of genetics. Mendel demonstrated that the inheritance of certain traits in pea plants follows particular patterns, now referred to as the laws of Mendelian inheritance...

genetics
Genetics
Genetics , a discipline of biology, is the science of genes, heredity, and variation in living organisms....

, which resulted in Shannon's 1940 PhD
PHD
PHD may refer to:*Ph.D., a doctorate of philosophy*Ph.D. , a 1980s British group*PHD finger, a protein sequence*PHD Mountain Software, an outdoor clothing and equipment company*PhD Docbook renderer, an XML renderer...

thesis at MIT, An Algebra for Theoretical Genetics.

In 1940, Shannon became a National Research Fellow at the Institute for Advanced Study
The Institute for Advanced Study, located in Princeton, New Jersey, United States, is an independent postgraduate center for theoretical research and intellectual inquiry. It was founded in 1930 by Abraham Flexner...

in Princeton, New Jersey. At Princeton, Shannon had the opportunity to discuss his ideas with influential scientists and mathematicians such as Hermann Weyl
Hermann Weyl
Hermann Klaus Hugo Weyl was a German mathematician and theoretical physicist. Although much of his working life was spent in Zürich, Switzerland and then Princeton, he is associated with the University of Göttingen tradition of mathematics, represented by David Hilbert and Hermann Minkowski.His...

and John von Neumann
John von Neumann
John von Neumann was a Hungarian-American mathematician and polymath who made major contributions to a vast number of fields, including set theory, functional analysis, quantum mechanics, ergodic theory, geometry, fluid dynamics, economics and game theory, computer science, numerical analysis,...

, and even had the occasional encounter with Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...

. Shannon worked freely across disciplines, and began to shape the ideas that would become information theory.

### Wartime research

Shannon then joined Bell Labs
Bell Labs
Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...

to work on fire-control system
Fire-control system
A fire-control system is a number of components working together, usually a gun data computer, a director, and radar, which is designed to assist a weapon system in hitting its target. It performs the same task as a human gunner firing a weapon, but attempts to do so faster and more...

s and cryptography
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...

during World War II, under a contract with section D-2 (Control Systems section) of the National Defense Research Committee (NDRC
National Defense Research Committee
The National Defense Research Committee was an organization created "to coordinate, supervise, and conduct scientific research on the problems underlying the development, production, and use of mechanisms and devices of warfare" in the United States from June 27, 1940 until June 28, 1941...

).

He met his wife Betty when she was a numerical analyst at Bell Labs
Bell Labs
Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...

. They married in 1949.

For two months early in 1943, Shannon came into contact with the leading British cryptanalyst and mathematician Alan Turing
Alan Turing
Alan Mathison Turing, OBE, FRS , was an English mathematician, logician, cryptanalyst, and computer scientist. He was highly influential in the development of computer science, providing a formalisation of the concepts of "algorithm" and "computation" with the Turing machine, which played a...

. 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
The Government Communications Headquarters is a British intelligence agency responsible for providing signals intelligence and information assurance to the UK government and armed forces...

at Bletchley Park
Bletchley Park
Bletchley Park is an estate located in the town of Bletchley, in Buckinghamshire, England, which currently houses the National Museum of Computing...

to break the ciphers used by the German U-boats in the North Atlantic. 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. Private archives from Bell Labs suggest that a Visual Binary encoding system was developed via their collaboration at this time.
Turing showed Shannon his seminal 1936 paper that defined what is now known as the "Universal Turing machine
Universal Turing machine
In computer science, a universal Turing machine is a Turing machine that can simulate an arbitrary Turing machine on arbitrary input. The universal machine essentially achieves this by reading both the description of the machine to be simulated as well as the input thereof from its own tape. Alan...

" 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
Ralph Beebe Blackman
Ralph Beebe Blackman was an American mathematician and engineer who was among thepioneers of the information age along with Claude E. Shannon, Hendrik Wade Bode, and John Tukey. He worked at Bell Laboratories in the 1960s and authored books on the topic of spectrum estimation.- Books :* R. B....

Hendrik Wade Bode , was an American engineer, researcher, inventor, author and scientist], of Dutch ancestry. As a pioneer of modern control theory and electronic telecommunications he revolutionized both the content and methodology of his chosen fields of research.He made important contributions...

, 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." In other words it modeled the problem in terms of data
Data processing
Computer data processing is any process that a computer program does to enter data and summarise, analyse or otherwise convert data into usable information. The process may be automated and run on a computer. It involves recording, analysing, sorting, summarising, calculating, disseminating and...

and signal processing
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...

and thus heralded the coming of the information age
Information Age
The Information Age, also commonly known as the Computer Age or Digital Age, is an idea that the current age will be characterized by the ability of individuals to transfer information freely, and to have instant access to knowledge that would have been difficult or impossible to find previously...

.

His work on cryptography was even more closely related to his later publications on communication theory
Communication theory
Communication theory is a field of information and mathematics that studies the technical process of information and the human process of human communication.- History :- Origins :...

. 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
Communication Theory of Secrecy Systems
Communication Theory of Secrecy Systems is a paper published in 1949 by Claude Shannon discussing cryptography from the viewpoint of information theory. It is one of the foundational treatments of modern cryptography...

" in the Bell System Technical Journal
Bell System Technical Journal
The Bell System Technical Journal was the in-house scientific journal of Bell Labs that was published from 1922 to 1983.- Notable papers :...

. This paper incorporated many of the concepts and mathematical formulations that also appeared in his A Mathematical Theory of Communication
A Mathematical Theory of Communication
"A Mathematical Theory of Communication" is an influential 1948 article by mathematician Claude E. Shannon. As of November 2011, Google Scholar has listed more than 48,000 unique citations of the article and the later-published book version...

. Shannon said that his wartime insights into communication theory and cryptography developed simultaneously and "they were so close together you couldn’t separate them". 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."

While at Bell Labs, he proved that the one-time pad
In cryptography, the one-time pad is a type of encryption, which has been proven to be impossible to crack if used correctly. Each bit or character from the plaintext is encrypted by a modular addition with a bit or character from a secret random key of the same length as the plaintext, resulting...

is unbreakable in his World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...

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.

### Postwar contributions

In 1948 the promised memorandum appeared as "A Mathematical Theory of Communication
A Mathematical Theory of Communication
"A Mathematical Theory of Communication" is an influential 1948 article by mathematician Claude E. Shannon. As of November 2011, Google Scholar has listed more than 48,000 unique citations of the article and the later-published book version...

", 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
Information
Information in its most restricted technical sense is a message or collection of messages that consists of an ordered sequence of symbols, or it is the meaning that can be interpreted from such a message or collection of messages. Information can be recorded or transmitted. It can be recorded as...

a sender wants to transmit. In this fundamental work he used tools in probability theory, developed by Norbert Wiener
Norbert Wiener
Norbert Wiener was an American mathematician.A famous child prodigy, Wiener later became an early researcher in stochastic and noise processes, contributing work relevant to electronic engineering, electronic communication, and control systems.Wiener is regarded as the originator of cybernetics, a...

, which were in their nascent stages of being applied to communication theory at that time. Shannon developed information entropy
Information entropy
In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits...

as a measure for the uncertainty in a message while essentially inventing the field of information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

.

The book, co-authored with Warren Weaver
Warren Weaver
Warren Weaver was an American scientist, mathematician, and science administrator...

, 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
John Robinson Pierce
John Robinson Pierce , was an American engineer and author. He worked extensively in the fields of radio communication, microwave technology, computer music, psychoacoustics, and science fiction. Born in Des Moines, Iowa, he earned his Ph.D...

's Symbols, Signals, and Noise.

Information theory's fundamental contribution to natural language processing
Natural language processing
Natural language processing is a field of computer science and linguistics concerned with the interactions between computers and human languages; it began as a branch of artificial intelligence....

and computational linguistics
Computational linguistics
Computational linguistics is an interdisciplinary field dealing with the statistical or rule-based modeling of natural language from a computational perspective....

was further established in 1951, in his article "Prediction and Entropy of Printed English", proving that treating whitespace
Whitespace (computer science)
In computer science, whitespace is any single character or series of characters that represents horizontal or vertical space in typography. When rendered, a whitespace character does not correspond to a visual mark, but typically does occupy an area on a page...

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
Communication Theory of Secrecy Systems
Communication Theory of Secrecy Systems is a paper published in 1949 by Claude Shannon discussing cryptography from the viewpoint of information theory. It is one of the foundational treatments of modern cryptography...

", a declassified version of his wartime work on the mathematical theory of cryptography
Cryptography
Cryptography is the practice and study of techniques for secure communication in the presence of third parties...

, in which he proved that all theoretically unbreakable ciphers must have the same requirements as the one-time pad
In cryptography, the one-time pad is a type of encryption, which has been proven to be impossible to crack if used correctly. Each bit or character from the plaintext is encrypted by a modular addition with a bit or character from a secret random key of the same length as the plaintext, resulting...

. 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
Juggling
Juggling is a skill involving moving objects for entertainment or sport. The most recognizable form of juggling is toss juggling, in which the juggler throws objects up to catch and toss up again. This may be one object or many objects, at the same time with one or many hands. Jugglers often refer...

, unicycling, and chess
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...

. He also invented many devices, including rocket-powered flying discs, a motorized pogo stick
Pogo stick
A pogo stick is a device for jumping off the ground in a standing position with the aid of a spring, used as a toy or exercise equipment. It consists of a pole with a handle at the top and footrests near the bottom, and a spring located somewhere along the pole...

, and a flame-throwing trumpet for a science exhibition. One of his more humorous devices was a box kept on his desk called the "Ultimate Machine", based on an idea by Marvin Minsky
Marvin Minsky
Marvin Lee Minsky is an American cognitive scientist in the field of artificial intelligence , co-founder of Massachusetts Institute of Technology's AI laboratory, and author of several texts on AI and philosophy.-Biography:...

. 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
YouTube is a video-sharing website, created by three former PayPal employees in February 2005, on which users can upload, view and share videos....

and Thingiverse
MakerBot Industries
MakerBot Industries is a Brooklyn, New York-based company founded in January 2009 by Bre Pettis, Adam Mayer, and Zach "Hoeken" Smith producing open source hardware, specifically 3D printers...

. In addition he built a device that could solve the Rubik's cube
Rubik's Cube
Rubik's Cube is a 3-D mechanical puzzle invented in 1974 by Hungarian sculptor and professor of architecture Ernő Rubik.Originally called the "Magic Cube", the puzzle was licensed by Rubik to be sold by Ideal Toy Corp. in 1980 and won the German Game of the Year special award for Best Puzzle that...

puzzle.

He is also considered the co-inventor of the first wearable computer
Wearable computer
Wearable computers are miniature electronic devices that are worn by the bearer under, with or on top of clothing. This class of wearable technology has been developed for general or special purpose information technologies and media development...

along with Edward O. Thorp
Edward O. Thorp
Edward Oakley Thorp is an American mathematics professor, author, hedge fund manager, and blackjack player. He was a pioneer in modern applications of probability theory, including the harnessing of very small correlations for reliable financial gain.He was the author of Beat the Dealer, the first...

. The device was used to improve the odds when playing roulette
Roulette
Roulette is a casino game named after a French diminutive for little wheel. In the game, players may choose to place bets on either a single number or a range of numbers, the colors red or black, or whether the number is odd or even....

.

### Legacy and tributes

Shannon came to MIT in 1956 to join its faculty and to conduct work in the Research Laboratory of Electronics
Research Laboratory of Electronics at MIT
The Research Laboratory of Electronics at the Massachusetts Institute of Technology was founded in 1946 as the successor to the famed MIT Radiation Laboratory of World War II....

(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
Eugene L. Daub
Eugene L. Daub is a recognized contemporary figure sculptor. He attended the Pennsylvania Academy of the Fine Arts in Philadelphia, and taught there...

: one at the University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...

; one at MIT in the Laboratory for Information and Decision Systems
MIT Laboratory for Information and Decision Systems
The MIT Laboratory for Information and Decision Systems is an interdisciplinary research laboratory of MIT, working on research in the areas of communications, control, and signal processing combining faculty from the School of Engineering, the Department of Aeronautics and Astronautics, the...

; one in Gaylord, Michigan; one at the University of California, San Diego
University of California, San Diego
The University of California, San Diego, commonly known as UCSD or UC San Diego, is a public research university located in the La Jolla neighborhood of San Diego, California, United States...

; one at Bell Labs
Bell Labs
Bell Laboratories is the research and development subsidiary of the French-owned Alcatel-Lucent and previously of the American Telephone & Telegraph Company , half-owned through its Western Electric manufacturing subsidiary.Bell Laboratories operates its...

; and another at AT&T Shannon Labs
AT&T Laboratories
AT&T Laboratories, Inc. was the research & development division of AT&T Corporation. It was founded in 1925 as Bell Telephone Laboratories, Inc., following the merger of the research & development divisions of American Telephone & Telegraph and Western Electric.-History:In 1996, most of Bell Labs...

. After the breakup
Bell System divestiture
The Bell System divestiture, or the breakup of AT&T, was initiated by the filing in 1974 by the U.S. Department of Justice of an antitrust lawsuit against AT&T. The case, United States v...

of the Bell system, the part of Bell Labs that remained with AT&T
AT&T
AT&T Inc. is an American multinational telecommunications corporation headquartered in Whitacre Tower, Dallas, Texas, United States. It is the largest provider of mobile telephony and fixed telephony in the United States, and is also a provider of broadband and subscription television services...

was named Shannon Labs in his honor.

Robert Gallager
Robert G. Gallager
Robert Gray Gallager is an American electrical engineer known for his work on information theory and communications networks. He was elected an IEEE Fellow in 1968 and a member of the National Academy of Engineering in 1979. He received the Claude E. Shannon Award from the IEEE Information Theory...

has called Shannon the greatest scientist of the 20th century. According to Neil Sloane
Neil Sloane
Neil James Alexander Sloane is a British-U.S. mathematician. His major contributions are in the fields of combinatorics, error-correcting codes, and sphere packing...

, an AT&T Fellow who co-edited Shannon's large collection of papers in 1993, the perspective introduced by Shannon's communication theory
Communication theory
Communication theory is a field of information and mathematics that studies the technical process of information and the human process of human communication.- History :- Origins :...

(now called information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

) is the foundation of the digital revolution, and every device containing a microprocessor
Microprocessor
A microprocessor incorporates the functions of a computer's central processing unit on a single integrated circuit, or at most a few integrated circuits. It is a multipurpose, programmable device that accepts digital data as input, processes it according to instructions stored in its memory, and...

or microcontroller
Microcontroller
A microcontroller is a small computer on a single integrated circuit containing a processor core, memory, and programmable input/output peripherals. Program memory in the form of NOR flash or OTP ROM is also often included on chip, as well as a typically small amount of RAM...

is a conceptual descendant of Shannon's 1948 publication: "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
Digital Revolution
The Digital Revolution is the change from analog mechanical and electronic technology to digital technology that has taken place since c. 1980 and continues to the present day. Implicitly, the term also refers to the sweeping changes brought about by digital computing and communication technology...

started with him."

Shannon developed Alzheimer's disease
Alzheimer's disease
Alzheimer's disease also known in medical literature as Alzheimer disease is the most common form of dementia. There is no cure for the disease, which worsens as it progresses, and eventually leads to death...

, 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.

Shannon was oblivious to the marvels of the digital revolution because his mind was ravaged by Alzheimer's disease
Alzheimer's disease
Alzheimer's disease also known in medical literature as Alzheimer disease is the most common form of dementia. There is no cure for the disease, which worsens as it progresses, and eventually leads to death...

. His wife mentioned in his obituary that had it not been for Alzheimer's "he would have been bemused" by it all.

## Other work

### Shannon's mouse

Theseus, created in 1950, was a magnetic mouse controlled by a relay circuit that enabled it to move around a maze
Maze
A maze is a tour puzzle in the form of a complex branching passage through which the solver must find a route. In everyday speech, both maze and labyrinth denote a complex and confusing series of pathways, but technically the maze is distinguished from the labyrinth, as the labyrinth has a single...

of 25 squares. Its dimensions were the same as an average mouse. The maze configuration was flexible and it could be modified at will. 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. Shannon's mouse appears to have been the first artificial learning device of its kind.

### Shannon's computer chess program

In 1950 Shannon published a paper on computer chess
Computer chess
Computer chess is computer architecture encompassing hardware and software capable of playing chess autonomously without human guidance. Computer chess acts as solo entertainment , as aids to chess analysis, for computer chess competitions, and as research to provide insights into human...

entitled Programming a Computer for Playing Chess. It describes how a machine or computer could be made to play a reasonable game of chess
Chess
Chess is a two-player board game played on a chessboard, a square-checkered board with 64 squares arranged in an eight-by-eight grid. It is one of the world's most popular games, played by millions of people worldwide at home, in clubs, online, by correspondence, and in tournaments.Each player...

. His process for having the computer decide on which move to make is a minimax
Minimax
Minimax is a decision rule used in decision theory, game theory, statistics and philosophy for minimizing the possible loss for a worst case scenario. Alternatively, it can be thought of as maximizing the minimum gain...

procedure, based on an evaluation function
Evaluation function
An evaluation function, also known as a heuristic evaluation function or static evaluation function, is a function used by game-playing programs to estimate the value or goodness of a position in the minimax and related algorithms...

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
Backward pawn
In chess, a backward pawn is a pawn that is behind the pawns of the same color on the adjacent files and that cannot be advanced without loss of material, usually the backward pawn itself....

, and isolated pawn
Isolated pawn
In chess, an isolated pawn is a pawn which has no friendly pawn on an adjacent file. An isolated queen's pawn is often called an isolani. Isolated pawns are usually a weakness because they cannot be protected by other pawns...

. Another positional factor in the evaluation function was mobility, adding 0.1 point for each legal move available. Finally, he considered checkmate
Checkmate
Checkmate is a situation in chess in which one player's king is threatened with capture and there is no way to meet that threat. Or, simply put, the king is under direct attack and cannot avoid being captured...

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
Las Vegas metropolitan area
The Las Vegas Valley is the heart of the Las Vegas-Paradise, NV MSA also known as the Las Vegas–Paradise–Henderson MSA which includes all of Clark County, Nevada, and is a metropolitan area in the southern part of the U.S. state of Nevada. The Valley is defined by the Las Vegas Valley landform, a ...

with M.I.T. mathematician Ed Thorp
Edward O. Thorp
Edward Oakley Thorp is an American mathematics professor, author, hedge fund manager, and blackjack player. He was a pioneer in modern applications of probability theory, including the harnessing of very small correlations for reliable financial gain.He was the author of Beat the Dealer, the first...

, and made very successful forays in blackjack
Blackjack
Blackjack, also known as Twenty-one or Vingt-et-un , is the most widely played casino banking game in the world...

using game theory
Game theory
Game theory is a mathematical method for analyzing calculated circumstances, such as in games, where a person’s success is based upon the choices of others...

type methods co-developed with fellow Bell Labs associate, physicist John L. Kelly Jr.
John Larry Kelly, Jr
John Larry Kelly, Jr. , was a scientist who worked at Bell Labs. He is best known for formulating the Kelly criterion, an algorithm for maximally investing money....

based on principles of information theory. They made a fortune, as detailed in the book Fortune's Formula by William Poundstone
William Poundstone
William Poundstone is an American author, columnist, and skeptic. He has written a number of books including the Big Secrets series and a biography of Carl Sagan...

and corroborated by the writings of Elwyn Berlekamp
Elwyn Berlekamp
Elwyn Ralph Berlekamp is an American mathematician. He is a professor emeritus of mathematics and EECS at the University of California, Berkeley. Berlekamp is known for his work in information theory and combinatorial game theory....

, Kelly's research assistant in 1960 and 1962. Shannon and Thorp also applied the same theory, later known as the Kelly criterion
Kelly criterion
In probability theory, the Kelly criterion, or Kelly strategy or Kelly formula, or Kelly bet, is a formula used to determine the optimal size of a series of bets. In most gambling scenarios, and some investing scenarios under some simplifying assumptions, the Kelly strategy will do better than any...

, to the stock market with even better results. Over the decades, Kelly's scientific formula has become a part of mainstream investment theory and the most prominent users, well-known and successful billionaire investors Warren Buffett
Warren Buffett
Warren Edward Buffett is an American business magnate, investor, and philanthropist. He is widely regarded as one of the most successful investors in the world. Often introduced as "legendary investor, Warren Buffett", he is the primary shareholder, chairman and CEO of Berkshire Hathaway. He is...

, Bill Gross and Jim Simons
James Harris Simons
James Harris "Jim" Simons is an American hedge fund manager, mathematician, and philanthropist.In 1982, Simons founded Renaissance Technologies, a private investment firm based in New York with over \$15 billion under management; Simons is still at the helm, as CEO, of what is now one of the...

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
Elwyn Berlekamp
Elwyn Ralph Berlekamp is an American mathematician. He is a professor emeritus of mathematics and EECS at the University of California, Berkeley. Berlekamp is known for his work in information theory and combinatorial game theory....

Axcom Trading Advisors was an early alternative investment management company founded by Elwyn Berlekamp and based in Berkeley, CA. It was acquired by Renaissance Technologies Corp in 1992, whereafter its investment instruments were either subsumed into Renaissance's flagship Medallion Fund. The...

, an alternative investment management company, that he had founded. Berlekamp's company was acquired by Jim Simons
James Harris Simons
James Harris "Jim" Simons is an American hedge fund manager, mathematician, and philanthropist.In 1982, Simons founded Renaissance Technologies, a private investment firm based in New York with over \$15 billion under management; Simons is still at the helm, as CEO, of what is now one of the...

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.

The theory was also exploited by the famous MIT Blackjack Team
MIT Blackjack Team
The MIT Blackjack Team 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 more sophisticated strategies to beat casinos at blackjack worldwide...

, which was a group of students and ex-students from the Massachusetts Institute of Technology
Massachusetts Institute of Technology
The Massachusetts Institute of Technology is a private research university located in Cambridge, Massachusetts. MIT has five schools and one college, containing a total of 32 academic departments, with a strong emphasis on scientific and technological education and research.Founded in 1861 in...

Harvard Business School is the graduate business school of Harvard University in Boston, Massachusetts, United States and is widely recognized as one of the top business schools in the world. The school offers the world's largest full-time MBA program, doctoral programs, and many executive...

, Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...

, and other leading colleges who used card-counting
Card counting
Card counting is a casino card game strategy used primarily in the blackjack family of casino games to determine whether the next hand is likely to give a probable advantage to the player or to the dealer. Card counters, also known as advantage players, attempt to decrease the inherent casino house...

techniques and other sophisticated strategies to beat casinos at blackjack
Blackjack
Blackjack, also known as Twenty-one or Vingt-et-un , is the most widely played casino banking game in the world...

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
Bringing Down the House (book)
Bringing Down the House: The Inside Story of Six MIT Students Who Took Vegas for Millions is a book by Ben Mezrich about a group of MIT card counters commonly known as the MIT Blackjack Team. While represented as non-fiction by Mezrich and Free Press, the book contains significant fictional elements...

, the best-selling book published in 2003 about the MIT Blackjack Team
MIT Blackjack Team
The MIT Blackjack Team 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 more sophisticated strategies to beat casinos at blackjack worldwide...

by Ben Mezrich
Ben Mezrich
Ben Mezrich is an American author from Princeton, New Jersey. He graduated magna-cum-laude with a degree in Social Studies from Harvard University in 1991. Some of his books have been written under the pseudonym Holden Scott. Mezrich attended Princeton Day School, in Princeton, New Jersey...

. In 2008 the book was adapted into a drama film
Drama film
A drama film is a film genre that depends mostly on in-depth development of realistic characters dealing with emotional themes. Dramatic themes such as alcoholism, drug addiction, infidelity, moral dilemmas, racial prejudice, religious intolerance, poverty, class divisions, violence against women...

titled 21
21 (2008 film)
21 is a 2008 drama film directed by Australian director Robert Luketic and stars Jim Sturgess, Kevin Spacey, Laurence Fishburne, Kate Bosworth, Liza Lapira, Jacob Pitts, and Aaron Yoo. The film is inspired by the true story of the MIT Blackjack Team as told in Bringing Down the House, the...

.

### Shannon's maxim

Shannon formulated a version of Kerckhoffs' principle
Kerckhoffs' principle
In cryptography, Kerckhoffs's principle was stated by Auguste Kerckhoffs in the 19th century: A cryptosystem should be secure even if everything about the system, except the key, is public knowledge.Kerckhoffs's principle was reformulated by Claude Shannon as...

as "the enemy knows the system". In this form it is known as "Shannon's maxim".

## Awards and honors list

• Alfred Noble Prize
Alfred Noble Prize
The Alfred Noble Prize is an award presented by the combined engineering societies of the United States, given each year to a person not over thirty-five for a paper published in one of the journals of the participating societies....

, 1939
• Morris Liebmann Memorial Prize of the Institute of Radio Engineers
The Institute of Radio Engineers was a professional organization which existed from 1912 until January 1, 1963, when it merged with the American Institute of Electrical Engineers to form the Institute of Electrical and Electronics Engineers .-Founding:Following several attempts to form a...

, 1949
• Yale University
Yale University
Yale University is a private, Ivy League university located in New Haven, Connecticut, United States. Founded in 1701 in the Colony of Connecticut, the university is the third-oldest institution of higher education in the United States...

(Master of Science), 1954
• Stuart Ballantine Medal of the Franklin Institute
Franklin Institute
The Franklin Institute is a museum in Philadelphia, Pennsylvania, and one of the oldest centers of science education and development in the United States, dating to 1824. The Institute also houses the Benjamin Franklin National Memorial.-History:On February 5, 1824, Samuel Vaughn Merrick and...

, 1955
• Research Corporation Award, 1956
• University of Michigan
University of Michigan
The University of Michigan is a public research university located in Ann Arbor, Michigan in the United States. It is the state's oldest university and the flagship campus of the University of Michigan...

, honorary doctorate, 1961
• Rice University
Rice University
William Marsh Rice University, commonly referred to as Rice University or Rice, is a private research university located on a heavily wooded campus in Houston, Texas, United States...

Medal of Honor, 1962
• Princeton University
Princeton University
Princeton University is a private research university located in Princeton, New Jersey, United States. The school is one of the eight universities of the Ivy League, and is one of the nine Colonial Colleges founded before the American Revolution....

, honorary doctorate, 1962
• Marvin J. Kelly Award, 1962
• University of Edinburgh
University of Edinburgh
The University of Edinburgh, founded in 1583, is a public research university located in Edinburgh, the capital of Scotland, and a UNESCO World Heritage Site. The university is deeply embedded in the fabric of the city, with many of the buildings in the historic Old Town belonging to the university...

, honorary doctorate, 1964
• University of Pittsburgh
University of Pittsburgh
The University of Pittsburgh, commonly referred to as Pitt, is a state-related research university located in Pittsburgh, Pennsylvania, United States. Founded as Pittsburgh Academy in 1787 on what was then the American frontier, Pitt is one of the oldest continuously chartered institutions of...

, honorary doctorate, 1964
• Medal of Honor
IEEE Medal of Honor
The IEEE Medal of Honor is the highest recognition of the Institute of Electrical and Electronics Engineers . It has been awarded since 1917, when its first recipient was Major Edwin H. Armstrong. It is given for an exceptional contribution or an extraordinary career in the IEEE fields of...

of the Institute of Electrical and Electronics Engineers
Institute of Electrical and Electronics Engineers
The Institute of Electrical and Electronics Engineers is a non-profit professional association headquartered in New York City that is dedicated to advancing technological innovation and excellence...

, 1966
• National Medal of Science
National Medal of Science
The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social sciences, biology, chemistry, engineering, mathematics and...

, 1966, presented by President Lyndon B. Johnson
Lyndon B. Johnson
Lyndon Baines Johnson , often referred to as LBJ, was the 36th President of the United States after his service as the 37th Vice President of the United States...

• Golden Plate Award, 1967

• Northwestern University
Northwestern University
Northwestern University is a private research university in Evanston and Chicago, Illinois, USA. Northwestern has eleven undergraduate, graduate, and professional schools offering 124 undergraduate degrees and 145 graduate and professional degrees....

, honorary doctorate, 1970
• Harvey Prize
Harvey Prize
The Harvey Prize is awarded by the Technion in Haifa, Israel. It is awarded in different disciplines of Science, Technology, Human Health, and Contributions to Peace in the Middle East. Two awards - each of \$75,000 - are given away annually...

, the Technion of Haifa
Haifa
Haifa is the largest city in northern Israel, and the third-largest city in the country, with a population of over 268,000. Another 300,000 people live in towns directly adjacent to the city including the cities of the Krayot, as well as, Tirat Carmel, Daliyat al-Karmel and Nesher...

, Israel
Israel
The State of Israel is a parliamentary republic located in the Middle East, along the eastern shore of the Mediterranean Sea...

, 1972
• Royal Netherlands Academy of Arts and Sciences
Royal Netherlands Academy of Arts and Sciences
The Royal Netherlands Academy of Arts and Sciences is an organisation dedicated to the advancement of science and literature in the Netherlands...

(KNAW), foreign member, 1975
• University of Oxford
University of Oxford
The University of Oxford is a university located in Oxford, United Kingdom. It is the second-oldest surviving university in the world and the oldest in the English-speaking world. Although its exact date of foundation is unclear, there is evidence of teaching as far back as 1096...

, honorary doctorate, 1978
• Joseph Jacquard Award, 1978
• Harold Pender
Harold Pender
Harold Pender was an American academic, author, and inventor. He was the first Dean of the University of Pennsylvania's Moore School of Electrical Engineering, a position he held from the founding of the School in 1923 until his retirement in 1949...

Award, 1978
• University of East Anglia
University of East Anglia
The University of East Anglia is a public research university based in Norwich, United Kingdom. It was established in 1963, and is a founder-member of the 1994 Group of research-intensive universities.-History:...

, honorary doctorate, 1982
• Carnegie Mellon University
Carnegie Mellon University
Carnegie Mellon University is a private research university in Pittsburgh, Pennsylvania, United States....

, honorary doctorate, 1984
• Audio Engineering Society
Audio Engineering Society
Established in 1948, the Audio Engineering Society draws its membership from amongst engineers, scientists, other individuals with an interest or involvement in the professional audio industry. The membership largely comprises engineers developing devices or products for audio, and persons working...

Gold Medal, 1985
• Kyoto Prize
Kyoto Prize
The has been awarded annually since 1985 by the Inamori Foundation, founded by Kazuo Inamori. The prize is a Japanese award similar in intent to the Nobel Prize, as it recognizes outstanding works in the fields of philosophy, arts, science and technology...

, 1985
• Tufts University
Tufts University
Tufts University is a private research university located in Medford/Somerville, near Boston, Massachusetts. It is organized into ten schools, including two undergraduate programs and eight graduate divisions, on four campuses in Massachusetts and on the eastern border of France...

, honorary doctorate, 1987
• University of Pennsylvania
University of Pennsylvania
The University of Pennsylvania is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Penn is the fourth-oldest institution of higher education in the United States,Penn is the fourth-oldest using the founding dates claimed by each institution...

, honorary doctorate, 1991
• Basic Research Award, Eduard Rhein Foundation, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...

, 1991
• National Inventors Hall of Fame
National Inventors Hall of Fame
The National Inventors Hall of Fame is a not-for-profit organization dedicated to recognizing, honoring and encouraging invention and creativity through the administration of its programs. The Hall of Fame honors the men and women responsible for the great technological advances that make human,...

inducted, 2004

• Shannon–Fano coding
Shannon–Fano coding
In the field of data compression, Shannon–Fano coding, named after Claude Elwood Shannon and Robert Fano, is a technique for constructing a prefix code based on a set of symbols and their probabilities...

• Shannon–Hartley theorem
Shannon–Hartley theorem
In information theory, the Shannon–Hartley theorem tells the maximum rate at which information can be transmitted over a communications channel of a specified bandwidth in the presence of noise. It is an application of the noisy channel coding theorem to the archetypal case of a continuous-time...

• Nyquist–Shannon sampling theorem
Nyquist–Shannon sampling theorem
The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular telecommunications and signal processing. Sampling is the process of converting a signal into a numeric sequence...

• Noisy channel coding theorem
Noisy channel coding theorem
In information theory, the noisy-channel coding theorem , establishes that for any given degree of noise contamination of a communication channel, it is possible to communicate discrete data nearly error-free up to a computable maximum rate through the channel...

• Rate distortion theory
Rate distortion theory
Rate–distortion theory is a major branch of information theory which provides the theoretical foundations for lossy data compression; it addresses the problem of determining the minimal amount of entropy R that should be communicated over a channel, so that the source can be approximately...

• Information theory
Information theory
Information theory is a branch of applied mathematics and electrical engineering involving the quantification of information. Information theory was developed by Claude E. Shannon to find fundamental limits on signal processing operations such as compressing data and on reliably storing and...

• Channel Capacity
Channel capacity
In electrical engineering, computer science and information theory, channel capacity is the tightest upper bound on the amount of information that can be reliably transmitted over a communications channel...

• Confusion and diffusion
Confusion and diffusion
In cryptography, confusion and diffusion are two properties of the operation of a secure cipher which were identified by Claude Shannon in his paper Communication Theory of Secrecy Systems, published in 1949....

In cryptography, the one-time pad is a type of encryption, which has been proven to be impossible to crack if used correctly. Each bit or character from the plaintext is encrypted by a modular addition with a bit or character from a secret random key of the same length as the plaintext, resulting...

• Shannon switching game
Shannon switching game
The Shannon switching game is an abstract strategy game for two players, invented by Claude Shannon, and independently invented by David Gale; it has also been known as Gale, Bridg-It, and Bird Cage....

• Shannon number
Shannon number
The Shannon number, named after Claude Shannon, is an estimated lower bound on the game-tree complexity of chess. Shannon calculated it as an aside in his 1950 paper "Programming a Computer for Playing Chess"...

• Claude E. Shannon Award
Claude E. Shannon Award
The Claude E. Shannon Award of the IEEE Information Theory Society was instituted to honour consistent and profound contributions to the field of information theory. Each Shannon Award winner is expected to present a Shannon Lecture at the following IEEE International Symposium on Information Theory...

• Shannon index
Shannon index
The Shannon index, sometimes referred to as the Shannon-Wiener Index or the Shannon-Weaver Index, is one of several diversity indices used to measure diversity in categorical data. It is simply the Information entropy of the distribution, treating species as symbols and their relative population...

• Shannon's source coding theorem
• Information entropy
Information entropy
In information theory, entropy is a measure of the uncertainty associated with a random variable. In this context, the term usually refers to the Shannon entropy, which quantifies the expected value of the information contained in a message, usually in units such as bits...

• Shannon's expansion

• Claude E. Shannon: A Mathematical Theory of Communication, Bell System Technical Journal, Vol. 27, pp. 379–423, 623–656, 1948. http://www.alcatel-lucent.com/bstj/vol27-1948/articles/bstj27-3-379.pdf http://www.alcatel-lucent.com/bstj/vol27-1948/articles/bstj27-4-623.pdf
• 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) http://scienceworld.wolfram.com/biography/Shannon.html
• 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
The Information: A History, a Theory, a Flood
The Information: A History, a Theory, a Flood is a book by science history writer James Gleick, author of Chaos: Making a New Science. It covers the genesis of our current information age. The Information has also been published in ebook formats by Fourth Estate and Random House, and as an...

, Pantheon, 2011, ISBN 9780375423727