# Alan Turing

**Alan Mathison Turing** (June 23, 1912 – June 7, 1954) was a British mathematician, logician, and cryptographer.

Turing is often considered to be a father of modern computer science. With the Turing Test, he made a significant and characteristically provocative contribution to the debate regarding artificial intelligence: whether it will ever be possible to say that a machine is conscious and can think. He provided an influential formalisation of the concept of algorithm and computation with the Turing machine, formulating the now widely accepted "Turing" version of the Church-Turing thesis, namely that any practical computing model has either the equivalent or a subset of the capabilities of a Turing machine.

During World War II, Turing worked at Bletchley Park, Britain's codebreaking centre. He devised a number of techniques for breaking German ciphers and became head of the section responsible for German Naval cryptanalysis (Hut 8). He invented the bombe, an electromechanical machine which could find settings for the Enigma machine.

After the war, he worked at the National Physical Laboratory, creating one of the first designs for a stored program computer, although it was never actually built. In 1947 he moved to the University of Manchester to work, largely on software, on the Manchester Mark I then emerging as one of the world's earliest true computers.

In 1952, Turing was convicted of acts of gross indecency because of his homosexuality. He was placed on probation and required to undergo hormone therapy.

Turing died in 1954; the inquest found that he had committed suicide by eating an apple laced with cyanide.

## Contents

- 1 Childhood and youth
- 2 College and his work on computability
- 3 Cryptanalysis
- 4 Work on early computers and the Turing Test
- 5 Work on pattern formation and mathematical biology
- 6 Prosecution for homosexuality and Turing's death
- 7 Recognition
- 8 Turing in fiction
- 9 See also
- 10 References
- 11 External links

## Childhood and youth

Turing was conceived in 1911 in Chatrapur, India. His father, Julius Mathison Turing, was a member of the Indian civil service. Julius and wife Ethel (*née* Stoney) wanted Alan to be brought up in Britain, so they returned to Paddington, London. His father's civil service commission was still active, and during Turing's childhood years his parents travelled between Guildford, England and India, leaving their two sons to stay with friends in England, rather than risk their health in the British colony. Very early in life, Turing showed signs of the genius he was to display more prominently later. He is said to have taught himself to read in three weeks, and to have shown an early affinity for numbers and puzzles.

His parents enrolled him at St. Michael's, a day school, at six years of age. The headmistress recognized his genius early on, as did many of his subsequent educators. In 1926, at the age of 14, he went on to Sherborne School in Dorset. His first day of term coincided with a general strike in England, and so determined was he to attend his first day that he rode his bike unaccompanied over sixty miles from Southampton to school, stopping overnight at an inn — a feat reported in the local press.

Turing's natural inclination toward mathematics and science did not earn him respect with the teachers at Sherborne, a famous and expensive public school (a British private school with charitable status), whose definition of education placed more emphasis on the classics. His headmaster wrote to his parents: "I hope he will not fall between two schools. If he is to stay at Public School, he must aim at becoming *educated*. If he is to be solely a *Scientific Specialist*, he is wasting his time at a Public School," (Hodges, 2000, p26).

But despite this, Turing continued to show remarkable ability in the studies he loved, solving advanced problems in 1927 without having even studied elementary calculus. In 1928, aged sixteen, Turing encountered Albert Einstein's work; not only did he grasp it, but he extrapolated Einstein's questioning of Newton's laws of motion from a text in which this was never made explicit.

Turing's hopes and ambitions at school were raised by his strong feelings for his friend Christopher Morcom, with whom he fell in love, though the feeling was not reciprocated. Morcom died only a few weeks into their last term at Sherborne, from complications of bovine tuberculosis, contracted after drinking infected cow's milk as a boy. Turing was heart-broken.

## College and his work on computability

Due to his unwillingness to work as hard on his classical studies as on science and mathematics, Turing failed to win a scholarship to Trinity College, Cambridge, and went on to the college of his second choice, King's College, Cambridge. He was an undergraduate from 1931 to 1934, graduating with a distinguished degree, and in 1935 was elected a Fellow at King's on the strength of a dissertation on the Gaussian error function.

In his momentous paper "On Computable Numbers, with an Application to the Entscheidungsproblem" (submitted on May 28, 1936), Turing reformulated Kurt Gödel's 1931 results on the limits of proof and computation, substituting Gödel's universal arithmetics-based formal language by what are now called Turing machines, formal and simple devices. He proved that such a machine would be capable of performing any conceivable mathematical problem if it were representable as an algorithm, even if no actual Turing machine would be likely to have practical applications, being much slower than alternatives. Turing machines are to this day the central object of study in theory of computation. He went on to prove that there was no solution to the *Entscheidungsproblem* by first showing that the halting problem for Turing machines is uncomputable: it is not possible to algorithmically decide whether a given Turing machine will ever halt. While his proof was published subsequent to Alonzo Church's equivalent proof in respect to his lambda calculus, Turing's work is considerably more accessible and intuitive. It was also novel in its notion of a "Universal (Turing) Machine," the idea that such a machine could perform the tasks of any other machine. The paper also introduces the notion of definable numbers.

Most of 1937 and 1938 he spent at Princeton University, studying under Alonzo Church. In 1938 he obtained his Ph.D. from Princeton; his dissertation introduced the notion of hypercomputation where Turing machines are augmented with so-called oracles, allowing a study of problems that cannot be solved algorithmically.

Back in Cambridge in 1939, he attended lectures by Ludwig Wittgenstein about the foundations of mathematics. The two argued and disagreed vehemently, with Turing defending formalism and Wittgenstein arguing that mathematics is overvalued and does not discover any absolute truths (Wittgenstein 1932/1976).

## Cryptanalysis

During World War II, Turing was a major participant in the efforts at Bletchley Park to break German ciphers. Turing's codebreaking work was kept secret until the 1970s; not even his close friends knew about it. He contributed several mathematical insights into breaking both the Enigma machine and the Lorenz SZ 40/42 (a teletype cipher attachment codenamed "Tunny" by the British), and was, for a time, head of Hut 8, the section responsible for reading German Naval signals.

Since September 1938, Turing had been recruited to work part-time for the Government Code and Cypher School. Turing reported to Bletchley Park when war was declared in September 1939. To break Enigma, Turing devised an electromechanical machine which searched for the correct settings of the Enigma rotors. The machine was called the bombe, named after the Polish-designed *bomba*. Using a bombe, it was possible to ignore the effect of the Enigma plugboard and consider the settings of its rotors alone, and eliminate most of them from consideration. For each possible setting, a chain of logical deductions was implemented electrically, and it was possible to detect when a contradiction had occurred and rule out that setting. Turing's bombe was first installed on 18 March 1940, and, with an enhancement suggested by mathematician Gordon Welchman, was the primary tool used to read Enigma traffic. Over 200 bombes were in operation by the end of the war.

In December 1940, Turing solved the naval Enigma indicator system, which was more complex than the indicator systems used by the other services. Turing also invented a Bayesian statistical technique termed "Banburismus" to assist in breaking Naval Enigma. Banburismus could rule out certain orders of the Enigma rotors, reducing time needed to test settings on the bombes. Against the Lorenz cipher, Turing devised a technique termed *Turingismus* or *Turingery*, although other methods were also used.

In the spring of 1941, Turing proposed marriage to fellow Hut 8 co-worker Joan Clarke, although the engagement was broken off by mutual agreement in the summer.

In late November 1942, Turing visited the US to work on secure speech devices and Naval Enigma, returning in March 1943. During his absence, Hugh Alexander had assumed the position of head of Hut 8, although Alexander had been *de facto* head for some time, Turing having little interest in the day-to-day running of the section. Turing became a general consultant for cryptanalysis at Bletchley Park.

In the later part of the war, Turing undertook (assisted with engineer Donald Bayley) the design of a portable machine codenamed *Delilah* to allow secure voice communications, teaching himself electronics at the same time. Intended for different applications, Delilah lacked the ability to be used over long-distance radio transmissions, and Delilah was completed too late to be used in the war. While Turing demonstrated it to officials by encoding/decoding a recording of a Winston Churchill speech, it was not adopted for use.

## Work on early computers and the Turing Test

From 1945 to 1947 he was at the National Physical Laboratory, where he worked on the design of ACE (Automatic Computing Engine). He presented a paper on February 19, 1946, which was the first complete design of a stored-program computer. Although he succeeded in designing the ACE, there were delays in starting the project and he became disillusioned. In late 1947 he returned to Cambridge for a 'sabbatical' year. While he was at Cambridge work on building the ACE stopped before it was ever begun. In 1949 he became deputy director of the computing laboratory at the University of Manchester, and worked on software for one of the earliest true computers — the Manchester Mark I. During this time he continued to do more abstract work, and in "Computing machinery and intelligence" (Mind, October 1950), Turing addressed the problem of artificial intelligence, and proposed an experiment now known as the Turing test, an attempt to define a standard for a machine to be called "sentient". In 1948, Turing, working with his former undergraduate colleague, D.G. Champernowne, began writing a chess program for a computer that did not yet exist. In 1952, lacking a computer powerful enough to execute the program, Turing played a game in which he simulated the computer, taking about half an hour per move. The game was recorded; the program lost to a colleague of Turing, Alick Glennie, however, it is said that the program won a game against Champernowne's wife.

## Work on pattern formation and mathematical biology

Turing worked from 1952 until his death in 1954 on mathematical biology, specifically morphogenesis. He published one paper on the subject called "The Chemical Basis of Morphogenesis" in 1952. His central interest in the field was understanding Fibonacci phyllotaxis, the existence of Fibonacci numbers in plant structures. He used reaction-diffusion equations which are now central to the field of pattern formation. Later papers went unpublished until 1992 when *Collected Works of A.M. Turing* was published.

## Prosecution for homosexuality and Turing's death

Turing was a homosexual man during a period when homosexuality was illegal. In 1952, his lover Arnold Murray helped an accomplice to break into Turing's house, and Turing went to the police to report the crime. As a result of the police investigation, Turing acknowledged a sexual relationship with Murray, and they were charged with gross indecency under Section 11 of the Criminal Law Amendment Act of 1885. Turing was unrepentant and was convicted. Although he could have been sent to prison, he was placed on probation, conditional on him undergoing hormonal treatment designed to reduce libido. He accepted the oestrogen hormone injections, which lasted for a year, with side effects including the development of breasts. Although there is no direct evidence, it is possible that his conviction led to a removal of his security clearance and may have prevented him from continuing consultancy on cryptographic matters.

In 1954, he died of cyanide poisoning, apparently from a cyanide-laced apple he left half-eaten. The apple itself was never tested for contamination with cyanide, and cyanide poisoning as a cause of death was established by a post-mortem. Most believe that his death was intentional, and the death was ruled a suicide. It is rumoured that this method of self-poisoning was in tribute to Turing's beloved film *Snow White and the Seven Dwarfs*. His mother, however, strenuously argued that the ingestion was accidental due to his careless storage of laboratory chemicals. Friends of his have said that Turing may have killed himself in this ambiguous way quite deliberately, to give his mother some plausible deniability. The possibility of assassination has also been suggested, owing to Turing's involvement in the secret service and the perception of Turing as a security risk due to his homosexuality.

*See also*: Sodomy law, Category:LGBT civil rights

## Recognition

On 23 June 1998, on what would have been Turing's 86th birthday, Andrew Hodges, his biographer, unveiled an official English Heritage Blue Plaque on his birthplace in Warrington Crescent, London, now the Colonnade hotel [1], [2].

A statue of Turing was unveiled in Manchester on June 23 2001. It is in Sackville Park, between the University of Manchester building on Whitworth Street and the Canal Street gay village. To mark the 50th anniversary of his death, a memorial plaque was unveiled at his former residence, Hollymeade, in Wilmslow on June 7 2004.

The Turing Award is given by the Association for Computing Machinery to a person for technical contributions to the computing community. It is widely considered to be the equivalent of the Nobel Prize in the computing world.

The Alan Turing Institute was initiated by UMIST and University of Manchester in Summer 2004.

A celebration of Turing's life and achievements was held at the University of Manchester on 5 June 2004; it was arranged by the British Logic Colloquium and the British Society for the History of Mathematics.

On October 28 2004 a bronze statue of Alan Turing sculpted by John W. Mills was unveiled at the University of Surrey [3]. The statue marks the 50th anniversary of Turing's death. It portrays Turing carrying his books across the campus.

Holtsoft produces a programming language named for Turing. The language is designed for beginner programmers and has no direct access to the hardware.

## Turing in fiction

- Turing appears as a character in Neal Stephenson's
*Cryptonomicon*. - In another one of Stephenson's books,
*The Diamond Age*, there is a very good explanation of Turing's work put into the format of a child's book. - The play
*Breaking the Code*by Hugh Whitemore deals with the life and death of Turing. In the original West End and Broadway runs, the role of Turing was played by Derek Jacobi, who also played Turing in a 1995 television adaptation of the play. - "Turing Police" (Artificial Intelligence law enforcers) appear in William Gibson's
*Neuromancer*. - In White Wolf Game Studio's World of Darkness role-playing universe, Turing was a leading member of the mage faction known as the Virtual Adepts.
- An FBI agent named Alan Turing made an appearance in the webcomic
*Questionable Content*as a homage to Turing. - Appears in
*Enigma*by Robert Harris - A young Alan Turing introduces the title character to Gödel's first incompleteness theorem in Apostolos Doxiadis's novel
*Uncle Petros and Goldbach's Conjecture*. - In the 1989
*Doctor Who*serial*The Curse of Fenric*, the character of Dr. Judson is based on Turing. Turing himself is the narrator of the*Doctor Who*spin-off novel*The Turing Test*by Paul Leonard. - Greg Egan's novella,
*Oracle*, is about an alternate universe version of Turing

## See also

## References

- Copeland, B. Jack (2004) "Colossus: Its Origins and Originators".
*IEEE Annals of the History of Computing*, 26(4):38–45. - Copeland, B. Jack (editor, 2004)
*The Essential Turing*. Oxford University Press, ISBN 0-19-825079-7 (hardback) and ISBN 0-19-825080-0 (paperback). - Copeland, B. Jack (editor, 2005),
*Alan Turing's Automatic Computing Engine*. Oxford University Press, ISBN 0-19-856593-3. - Hodges, Andrew (1983/2000).
*Alan Turing: The Enigma*. Simon & Schuster, 1983, ISBN 0-671-49207-1. Also: Walker Publishing Company, 2000. - Christof Teuscher (editor 2004),
*Alan Turing: Life and Legacy of a Great Thinker*. Springer-Verlag, ISBN 3540200207. - Yates, David M. (1997)
*Turing's Legacy: A history of computing at the National Physical Laboratory 1945—1995*. London: Science Museum, ISBN 0-901805-94-7. - Ludwig Wittgenstein (1932/1976)
*Wittgenstein's Lectures on the Foundations of Mathematics (1932-1935)*. Edited by Cora Diamond. Cornell University Press.

## External links

- MacTutor biography of Turing
- Alan Turing Home Page by Andrew Hodges including a short biography
- AlanTuring.net Turing Archive for the History of Computing by Jack Copeland
- A short biography
- Alan Turing – Towards a Digital Mind: Part 1
- Computing machinery and intelligence — full text of article.
- Skyscraper song inspired by Alan Turing
- Hollymeade unveiling of memorial plaque marking 50th anniversary of Turing's untimely death
- Alan Turing and morphogenesis
- The Turing Archive
- Turing Day 2002
- Turing 2004: A celebration of his life and achievements
- Stanford Encyclopedia of Philosophy entry
- Photos

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