Claude Shannon
Claude Elwood Shannon (April 30, 1916 – February 24, 2001) was an American mathematician, electrical engineer, computer scientist and cryptographer known as the "father of information theory" and as the "father of the Information Age".[1][2] Shannon was the first to describe the Boolean gates (electronic circuits) that are essential to all digital electronic circuits, and was an important pioneer of artificial intelligence.[3][4][1][5] He is credited alongside George Boole for laying the foundations of the Information Age.[6][7][8][5]
Claude Shannon
February 24, 2001 (aged 84)
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Information theory
"A Mathematical Theory of Communication"
A Symbolic Analysis of Relay and Switching Circuits
"Communication Theory of Secrecy Systems"
Artificial intelligence
Beta distribution
Binary code
Block cipher
Boolean algebra
Channel capacity
Computer chess
Data compression
Digital electronics
Digital Revolution
Digital subscriber line
Edge coloring
Entropy in information theory
Entropy (information theory)
Entropy power inequality
Error-correcting codes with feedback
Evaluation function
Financial signal processing
Information processing
Information-theoretic security
Innovation (signal processing)
Key size
Logic gate
Logic synthesis
Minivac 601
Models of communication
n-gram
Noisy channel coding theorem
Nyquist–Shannon sampling theorem
One-time pad
Product cipher
Pulse-code modulation
Rate–distortion theory
Sampling
Shannon–Fano coding
Shannon–Hartley law
Shannon capacity
Shannon entropy
Shannon's expansion
Shannon index
Shannon's Maxim
Shannon multigraph
Shannon number
Shannon security
Shannon's source coding theorem
Shannon switching game
Shannon-Weaver model of communication
Stream cipher
Switching circuit theory
Symbolic dynamics
Uncertainty coefficient
Units of information
Useless machine
Wearable computer
Whittaker–Shannon interpolation formula
Norma Levor (1940–41)
Betty Shannon (1949–2001)
- Stuart Ballantine Medal (1955)
- IEEE Medal of Honor (1966)
- National Medal of Science (1966)
- Harvey Prize (1972)
- Claude E. Shannon Award (1972)
- Harold Pender Award (1978)
- John Fritz Medal (1983)
- Kyoto Prize (1985)
- Marconi Society Lifetime Achievement Award (2000)
- National Inventors Hall of Fame (2004)
At the University of Michigan, Shannon dual degreed, graduating with a Bachelor of Science in both electrical engineering and mathematics in 1936. As a 21-year-old master's degree student at the Massachusetts Institute of Technology (MIT) in electrical engineering, Shannon wrote his thesis demonstrating that electrical applications of Boolean algebra could construct any logical numerical relationship,[9] thereby establishing the theory behind digital computing and digital circuits.[10] The thesis has been claimed to be the most important master's thesis of all time,[9] as in 1985, Howard Gardner described it as "possibly the most important, and also the most famous, master's thesis of the century",[11] while 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."[12] Shannon then graduated with a PhD in mathematics from MIT in 1940.[13]
Shannon contributed to the field of cryptanalysis for national defense of the United States during World War II, including his fundamental work on codebreaking and secure telecommunications, writing a paper which is considered one of the foundational pieces of modern cryptography,[14] and whose work "was a turning point, and marked the closure of classical cryptography and the beginning of modern cryptography."[15]
His mathematical theory of communication laid the foundations for the field of information theory,[16][13] with his famous paper being called the "Magna Carta of the Information Age" by Scientific American,[8][17] along with his work being described as being at "the heart of today's digital information technology".[18] Robert G. Gallager referred to the paper as a "blueprint for the digital era".[19] Regarding the influence that Shannon had on the digital age, Solomon W. Golomb remarked "It's like saying how much influence the inventor of the alphabet has had on literature."[16]
His Theseus machine was the first electrical device to learn by trial and error, being one of the first examples of artificial intelligence.[20][21] He co-organized and participated in the Dartmouth workshop of 1956, considered the founding event of the field of artificial intelligence.[22][23]
Rodney Brooks declared that Shannon was the 20th century engineer who contributed the most to 21st century technologies.[20] Shannon's achievements are considered to be on par with those of Albert Einstein and Sir Isaac Newton in their fields.[6][16][4][24][25]
Biography[edit]
Childhood[edit]
The Shannon family lived in Gaylord, Michigan, and Claude was born in a hospital in nearby Petoskey.[3] His father, Claude Sr. (1862–1934), was a businessman and, for a while, a judge of probate in Gaylord. His mother, Mabel Wolf Shannon (1880–1945), was a language teacher, who also served as the principal of Gaylord High School.[26] Claude Sr. was a descendant of New Jersey settlers, while Mabel was a child of German immigrants.[3] Shannon's family was active in their Methodist Church during his youth.[27]
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-wire telegraph system to a friend's house a half-mile away.[28] While growing up, he also worked as a messenger for the Western Union company.
Shannon's childhood hero was Thomas Edison, whom he later learned was a distant cousin. Both Shannon and Edison were descendants of John Ogden (1609–1682), a colonial leader and an ancestor of many distinguished people.[29][30]
Logic circuits[edit]
In 1932, Shannon entered the University of Michigan, where he was introduced to the work of George Boole. He graduated in 1936 with two bachelor's degrees: one in electrical engineering and the other in mathematics.
In 1936, Shannon began his graduate studies in electrical engineering at the Massachusetts Institute of Technology (MIT), where he worked on Vannevar Bush's differential analyzer, which was an early analog computer that was composed of electromechanical parts and could solve differential equations.[31] While studying the complicated ad hoc circuits of this analyzer, Shannon designed switching circuits based on Boole's concepts. In 1937, he wrote his master's degree thesis, A Symbolic Analysis of Relay and Switching Circuits,[32] with a paper from this thesis published in 1938.[33] A revolutionary work for switching circuit theory, Shannon diagramed switching circuits that could implement the essential operators of Boolean algebra. Then he proved that his switching circuits could be used to simplify the arrangement of the electromechanical relays that were used during that time in telephone 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.[32]
Using this property of electrical switches to implement logic is the fundamental concept that underlies all electronic digital computers. Shannon's work became the foundation of digital circuit design, as it became widely known in the electrical engineering community during and after World War II. The theoretical rigor of Shannon's work superseded the ad hoc methods that had prevailed previously. Howard Gardner hailed Shannon's thesis "possibly the most important, and also the most noted, master's thesis of the century."[34]
Shannon received his PhD in mathematics from MIT in 1940.[29] Vannevar Bush had suggested that Shannon should work on his dissertation at the Cold Spring Harbor Laboratory, in order to develop a mathematical formulation for Mendelian genetics. This research resulted in Shannon's PhD thesis, called An Algebra for Theoretical Genetics.[35]
In 1940, Shannon became a National Research Fellow at the Institute for Advanced Study in Princeton, New Jersey. In Princeton, Shannon had the opportunity to discuss his ideas with influential scientists and mathematicians such as Hermann Weyl and John von Neumann, and he also had occasional encounters with Albert Einstein and Kurt Gödel. Shannon worked freely across disciplines, and this ability may have contributed to his later development of mathematical information theory.[36]
Wartime research[edit]
Shannon had worked at Bell Labs for a few months in the summer of 1937,[37] and returned there to work on fire-control systems and cryptography during World War II, under a contract with section D-2 (Control Systems section) of the National Defense Research Committee (NDRC).
Shannon is credited with the invention of signal-flow graphs, in 1942. He discovered the topological gain formula while investigating the functional operation of an analog computer.[38]
For two months early in 1943, Shannon came into contact with the leading British mathematician Alan Turing. Turing had been posted to Washington to share with the U.S. Navy's cryptanalytic service the methods used by the British Government Code and Cypher School at Bletchley Park to break the cyphers used by the Kriegsmarine U-boats in the north Atlantic Ocean.[39] 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.[39] Turing showed Shannon his 1936 paper that defined what is now known as the "universal Turing machine".[40][41] This impressed Shannon, as many of its ideas complemented his own.
In 1945, as the war was coming to an end, the NDRC was issuing a summary of technical reports as a last step prior to its eventual closing down. Inside the volume on fire control, a special essay titled Data Smoothing and Prediction in Fire-Control Systems, coauthored by Shannon, Ralph Beebe Blackman, and Hendrik Wade Bode, formally treated the problem of smoothing the data in fire-control by analogy with "the problem of separating a signal from interfering noise in communications systems."[42] In other words, it modeled the problem in terms of data and signal processing and thus heralded the coming of the Information Age.
Shannon's work on cryptography was even more closely related to his later publications on communication theory.[43] 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 published in 1949 as "Communication Theory of Secrecy Systems" in the Bell System Technical Journal. This paper incorporated many of the concepts and mathematical formulations that also appeared in his A Mathematical Theory of Communication. Shannon said that his wartime insights into communication theory and cryptography developed simultaneously, and that "they were so close together you couldn't separate them".[44] 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."[45]
While he was at Bell Labs, Shannon proved that the cryptographic one-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.[46]
The Mathematical Theory of Communication[edit]
Weaver's Contribution[edit]
Shannon's The Mathematical Theory of Communication,[76] begins with an interpretation of his own work by Warren 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 the Shannon-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 communicates The Mathematical Theory of Communication,[76] but Shannon's subsequent logic, mathematics, and expressive precision was responsible for defining the problem itself.
