Alan Turing

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Alan Turing
OBE, FRS
Alan Turing photo.jpg
Turing at the time of his election to Fellowship of the Royal Society
Born Alan Mathison Turing
(1912-06-23)23 June 1912
Maida Vale, London, England
Died 7 June 1954(1954-06-07) (aged 41)
Wilmslow, Cheshire, England
Residence Wilmslow, Cheshire, England
Favorite places KFC + Mellat park
Fields Mathematics, cryptanalysis, computer science, Biology
Institutions University of Manchester
Government Code and Cypher School
National Physical Laboratory
University of Cambridge
Alma mater Sherborne School
King's College, Cambridge
Princeton University
Thesis Systems of Logic based on Ordinals (1938)
Doctoral advisor Alonzo Church[1]
Doctoral students Robin Gandy[1]
Known for
Notable awards

Alan Mathison Turing, OBE, FRS (/ˈtjʊərɪŋ/ TEWR-ing; 23 June 1912 – 7 June 1954) was a British mathematician, logician, cryptanalyst, philosopher, pioneering computer scientist, mathematical biologist, and marathon and ultra distance runner. 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 can be considered a model of a general purpose computer.[2][3][4] Turing is widely considered to be the father of theoretical computer science and artificial intelligence.[5]

During World War II, Turing worked for the Government Code and Cypher School (GC&CS) at Bletchley Park, Britain's codebreaking centre. For a time he led Hut 8, the section responsible for German naval cryptanalysis. He devised a number of techniques for breaking German ciphers, including improvements to the pre-war Polish bombe method, an electromechanical machine that could find settings for the Enigma machine. Winston Churchill said that Turing made the single biggest contribution to Allied victory in the war against Nazi Germany.[6] Turing's pivotal role in cracking intercepted coded messages enabled the Allies to defeat the Nazis in several crucial battles. It has been estimated that Turing's work shortened the war in Europe by as many as two to four years.[7]

After the war, he worked at the National Physical Laboratory, where he designed the ACE, among the first designs for a stored-program computer. In 1948 Turing joined Max Newman's Computing Laboratory at Manchester University, where he assisted development of the Manchester computers[8] and became interested in mathematical biology. He wrote a paper on the chemical basis of morphogenesis, and predicted oscillating chemical reactions such as the Belousov–Zhabotinsky reaction, first observed in the 1960s.

Turing was prosecuted for homosexuality in 1952, when such acts were still criminalised in the UK. He accepted treatment with oestrogen injections (chemical castration) as an alternative to prison. Turing died in 1954, 16 days before his 42nd birthday, from cyanide poisoning. An inquest determined his death a suicide; his mother and some others believed it was accidental.[9] On 10 September 2009, following an Internet campaign, British Prime Minister Gordon Brown made an official public apology on behalf of the British government for "the appalling way he was treated." The Queen granted him a posthumous pardon on 24 December 2013.[10][11]

Early life and career[edit]

Turing was born in Paddington, London, while his father was on leave from his position with the Indian Civil Service (ICS) at Chhatrapur, Bihar and Orissa Province, in British India.[12][13] Turing's father, Julius Mathison Turing (1873–1947), was the son of a clergyman from a Scottish family of merchants which had been based in the Netherlands and included a baronet. Julius's wife, Alan's mother, was Ethel Sara (née Stoney; 1881–1976), daughter of Edward Waller Stoney, chief engineer of the Madras Railways. The Stoneys were a Protestant Anglo-Irish gentry family from both County Tipperary and County Longford, while Ethel herself had spent much of her childhood in County Clare.[14] Julius' work with the ICS brought the family to British India, where his grandfather had been a general in the Bengal Army. However, both Julius and Ethel wanted their children to be brought up in England, so they moved to Maida Vale,[15] London, where Turing was born on 23 June 1912, as recorded by a blue plaque on the outside of the house of his birth,[16][17] later the Colonnade Hotel.[12][18] He had an elder brother, John (the father of Sir John Dermot Turing, 12th Baronet of the Turing baronets).

His father's civil service commission was still active, and during Turing's childhood years his parents travelled between Hastings in England[19] and India, leaving their two sons to stay with a retired Army couple. At Hastings, Turing stayed at Baston Lodge, Upper Maze Hill, St Leonards-on-Sea, now marked with a blue plaque.[20]

Very early in life, Turing showed signs of the genius he was later to display prominently.[21] His parents purchased a house in Guildford in 1927, and Turing lived there during school holidays. The location is also marked with a blue plaque.[22]

His parents enrolled him at St Michael's, a day school at 20 Charles Road, St Leonards-on-Sea, at the age of six. The headmistress recognised his talent early on, as did many of his subsequent educators. In 1926, at the age of 13, he went on to Sherborne School, a well known independent school in the market town of Sherborne in Dorset. The first day of term coincided with the 1926 General Strike in Britain, but so determined was he to attend that he rode his bicycle unaccompanied more than 60 miles (97 km) from Southampton to Sherborne, stopping overnight at an inn.[23]

King's College, Cambridge, where the computer room is named after Turing, who became a student there in 1931 and a Fellow in 1935

Turing's natural inclination toward mathematics and science did not earn him respect from some of the teachers at Sherborne, whose definition of education placed more emphasis on the classics. His headmaster wrote to his parents: "I hope he will not fall between two stools. 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".[24] Despite this, Turing continued to show remarkable ability in the studies he loved, solving advanced problems in 1927 without having studied even elementary calculus. In 1928, aged 16, 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.[25]

At Sherborne, Turing formed an important friendship with fellow pupil Christopher Morcom, which provided inspiration in Turing's future endeavours. However, the friendship was cut short by Morcom's death in February 1930 from complications of bovine tuberculosis contracted after drinking infected cow's milk some years previously.[26][27] This event shattered Turing's religious faith. He became an atheist. He believed that all phenomena, including the workings of the human brain, must be materialistic,[28] while maintaining a belief that the spirit survives after death.[29]

University and work on computability[edit]

After Sherborne, Turing studied as an undergraduate from 1931 to 1934 at King's College, Cambridge, from where he gained first-class honours in mathematics. In 1935, at the young age of 22, he was elected a fellow at King's on the strength of a dissertation in which he proved the central limit theorem,[30] despite the fact that he had failed to find out that it had already been proved in 1922 by Jarl Waldemar Lindeberg.[31]

Alan Turing memorial statue in Sackville Park, Manchester

In 1928, German mathematician David Hilbert had called attention to the Entscheidungsproblem (decision problem). In his momentous paper "On Computable Numbers, with an Application to the Entscheidungsproblem" (submitted on 28 May 1936 and delivered 12 November),[32] Turing reformulated Kurt Gödel's 1931 results on the limits of proof and computation, replacing Gödel's universal arithmetic-based formal language with the formal and simple hypothetical devices that became known as Turing machines. He proved that some such machine would be capable of performing any conceivable mathematical computation if it were representable as an algorithm. He went on to prove that there was no solution to the Entscheidungsproblem by first showing that the halting problem for Turing machines is undecidable: in general, it is not possible to decide algorithmically whether a given Turing machine will ever halt.

Although Turing's proof was published shortly after Alonzo Church's equivalent proof[33] using his lambda calculus, Turing had been unaware of Church's work.[34] Turing's approach is considerably more accessible and intuitive than Church's. It was also novel in its notion of a 'Universal Machine' (now known as a Universal Turing machine), with the idea that such a machine could perform the tasks of any other computation machine, or in other words, it is provably capable of computing anything that is computable. Von Neumann acknowledged that the central concept of the modern computer was due to this paper.[35] Turing machines are to this day a central object of study in theory of computation.

From September 1936 to July 1938, he spent most of his time studying under Church at Princeton University. In addition to his purely mathematical work, he studied cryptology and also built three of four stages of an electro-mechanical binary multiplier.[36] In June 1938, he obtained his PhD from Princeton;[37] his dissertation, Systems of Logic Based on Ordinals,[38][39] introduced the concept of ordinal logic and the notion of relative computing, where Turing machines are augmented with so-called oracles, allowing a study of problems that cannot be solved by a Turing machine.

When Turing returned to Cambridge, he attended lectures given by Ludwig Wittgenstein about the foundations of mathematics.[40] The two argued and disagreed, with Turing defending formalism and Wittgenstein propounding his view that mathematics does not discover any absolute truths but rather invents them.[41] He also started to work part-time with the Government Code and Cypher School (GC&CS).

Cryptanalysis[edit]

Two cottages in the stable yard at Bletchley Park. Turing worked here in 1939 and 1940, before moving to Hut 8.

During the Second World War, Turing was a leading participant in the breaking of German ciphers at Bletchley Park. The historian and wartime codebreaker Asa Briggs has said, "You needed exceptional talent, you needed genius at Bletchley and Turing's was that genius."[42]

From September 1938, Turing had been working part-time with the GC&CS, the British code breaking organisation. He concentrated on cryptanalysis of the Enigma, with Dilly Knox, a senior GC&CS codebreaker.[43] Soon after the July 1939 Warsaw meeting at which the Polish Cipher Bureau had provided the British and French with the details of the wiring of Enigma rotors and their method of decrypting Enigma messages, Turing and Knox started to work on a less fragile approach to the problem.[44] The Polish method relied on an insecure indicator procedure that the Germans were likely to change, which they did in May 1940. Turing's approach was more general, using crib-based decryption for which he produced the functional specification of the bombe (an improvement of the Polish Bomba).[45]

On 4 September 1939, the day after the UK declared war on Germany, Turing reported to Bletchley Park, the wartime station of GC&CS.[46] Specifying the bombe was the first of five major cryptanalytical advances that Turing made during the war. The others were: deducing the indicator procedure used by the German navy; developing a statistical procedure for making much more efficient use of the bombes dubbed Banburismus; developing a procedure for working out the cam settings of the wheels of the Lorenz SZ 40/42 (Tunny) dubbed Turingery and, towards the end of the war, the development of a portable secure voice scrambler at Hanslope Park that was codenamed Delilah.

By using statistical techniques to optimise the trial of different possibilities in the code breaking process, Turing made an innovative contribution to the subject. He wrote two papers discussing mathematical approaches which were entitled Report on the applications of probability to cryptography[47] and Paper on statistics of repetitions,[48] which were of such value to GC&CS and its successor GCHQ, that they were not released to the UK National Archives until April 2012, shortly before the centenary of his birth. A GCHQ mathematician said at the time that the fact that the contents had been restricted for some 70 years demonstrated their importance.[49]

Turing had something of a reputation for eccentricity at Bletchley Park. He was known to his colleagues as 'Prof' and his treatise on Enigma was known as 'The Prof's Book'.[50] Jack Good, a cryptanalyst who worked with him, is quoted by Ronald Lewin as having said of Turing:

In the first week of June each year he would get a bad attack of hay fever, and he would cycle to the office wearing a service gas mask to keep the pollen off. His bicycle had a fault: the chain would come off at regular intervals. Instead of having it mended he would count the number of times the pedals went round and would get off the bicycle in time to adjust the chain by hand. Another of his eccentricities is that he chained his mug to the radiator pipes to prevent it being stolen.[51]

While working at Bletchley, Turing, who was a talented long-distance runner, occasionally ran the 40 miles (64 km) to London when he was needed for high-level meetings,[52] and he was capable of world-class marathon standards.[53][54] Turing tried out for the 1948 British Olympic team, hampered by an injury. His tryout time for the marathon was only 11 minutes slower than British silver medalist Thomas Richards' Olympic race time of 2 hours 35 minutes. He was Walton Athletic Club's best runner, a fact discovered when he passed the group while running alone.[55] [56] [57]

In 1945, Turing was awarded the OBE by King George VI for his wartime services, but his work remained secret for many years.[58]

Turing–Welchman bombe[edit]

Within weeks of arriving at Bletchley Park,[46] Turing had specified an electromechanical machine that could help break Enigma more effectively than the Polish bomba kryptologiczna, from which its name was derived. The bombe, with an enhancement suggested by mathematician Gordon Welchman, became one of the primary tools, and the major automated one, used to attack Enigma-enciphered messages.

Jack Good opined:

Turing's most important contribution, I think, was of part of the design of the bombe, the cryptanalytic machine. He had the idea that you could use, in effect, a theorem in logic which sounds to the untrained ear rather absurd; namely that from a contradiction, you can deduce everything.[59]

A complete and working replica of a bombe at the National Codes Centre at Bletchley Park

The bombe searched for possible correct settings used for an Enigma message (i.e. rotor order, rotor settings and plugboard settings), using a suitable crib: a fragment of probable plaintext. For each possible setting of the rotors (which had of the order of 1019 states, or 1022 for the four-rotor U-boat variant),[60] the bombe performed a chain of logical deductions based on the crib, implemented electrically. The bombe detected when a contradiction had occurred, and ruled out that setting, moving on to the next. Most of the possible settings would cause contradictions and be discarded, leaving only a few to be investigated in detail. The first bombe was installed on 18 March 1940.[61]

By late 1941, Turing and his fellow cryptanalysts Gordon Welchman, Hugh Alexander, and Stuart Milner-Barry were frustrated. Building on the brilliant work of the Poles, they had set up a good working system for decrypting Enigma signals but they only had a few people and a few bombes so they did not have time to translate all the signals. In the summer they had had considerable success and shipping losses had fallen to under 100,000 tons a month but they were still on a knife-edge. They badly needed more resources to keep abreast of German adjustments. They had tried to get more people and fund more bombes through the proper channels but they were getting nowhere. Finally, breaking all the rules, on 28 October they wrote directly to Churchill spelling out their difficulties. They emphasised how small their need was compared with the vast expenditure of men and money by the forces and compared with the level of assistance they could offer to the forces.[62]

The effect was electric. Churchill wrote a memo to General Ismay which read: "ACTION THIS DAY. Make sure they have all they want on extreme priority and report to me that this has been done." On 18 November the chief of the secret service reported that every possible measure was being taken.[63] More than two hundred bombes were in operation by the end of the war.[64]

Hut 8 and Naval Enigma[edit]

Turing decided to tackle the particularly difficult problem of German naval Enigma "because no one else was doing anything about it and I could have it to myself".[65] In December 1939, Turing solved the essential part of the naval indicator system, which was more complex than the indicator systems used by the other services.[65][66] That same night he also conceived of the idea of Banburismus, a sequential statistical technique (what Abraham Wald later called sequential analysis) to assist in breaking naval Enigma, "though I was not sure that it would work in practice, and was not in fact sure until some days had actually broken".[65] For this he invented a measure of weight of evidence that he called the ban. Banburismus could rule out certain sequences of the Enigma rotors, substantially reducing the time needed to test settings on the bombes.

Statue of Turing by Stephen Kettle at Bletchley Park, commissioned by the American philanthropist Sidney Frank.[67]

In 1941, Turing proposed marriage to Hut 8 co-worker Joan Clarke, a fellow mathematician and cryptanalyst, but their engagement was short-lived. After admitting his homosexuality to his fiancée, who was reportedly "unfazed" by the revelation, Turing decided that he could not go through with the marriage.[68]

Turing travelled to the United States in November 1942[69] and worked with US Navy cryptanalysts on Naval Enigma and bombe construction in Washington. He visited their Computing Machine Laboratory at Dayton, Ohio. His reaction to the American Bombe design was far from enthusiastic:

It seems a pity for them to go out of their way to build a machine to do all this stopping if it is not necessary. I am now converted to the extent of thinking that starting from scratch on the design of a Bombe, this method is about as good as our own. The American Bombe program was to produce 336 Bombes, one for each wheel order. I used to smile inwardly at the conception of test (of commutators) can hardly be considered conclusive as they were not testing for the bounce with electronic stop finding devices.[70]

During this trip, he also assisted at Bell Labs with the development of secure speech devices.[71]

He returned to Bletchley Park in March 1943. During his absence, Hugh Alexander had officially 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.

Alexander wrote as follows about his contribution:

There should be no question in anyone's mind that Turing's work was the biggest factor in Hut 8's success. In the early days he was the only cryptographer who thought the problem worth tackling and not only was he primarily responsible for the main theoretical work within the Hut but he also shared with Welchman and Keen the chief credit for the invention of the Bombe. It is always difficult to say that anyone is absolutely indispensable but if anyone was indispensable to Hut 8 it was Turing. The pioneer's work always tends to be forgotten when experience and routine later make everything seem easy and many of us in Hut 8 felt that the magnitude of Turing's contribution was never fully realised by the outside world.[72]

Turingery[edit]

In July 1942, Turing devised a technique termed Turingery (or jokingly Turingismus)[73] for use against the Lorenz cipher messages produced by the Germans' new Geheimschreiber (secret writer) machine. This was a teleprinter rotor cipher attachment codenamed Tunny at Bletchley Park. Turingery was a method of wheel-breaking, i.e. a procedure for working out the cam settings of Tunny's wheels.[74] He also introduced the Tunny team to Tommy Flowers who, under the guidance of Max Newman, went on to build the Colossus computer, the world's first programmable digital electronic computer, which replaced a simpler prior machine (the Heath Robinson), and whose superior speed allowed the statistical decryption techniques to be applied usefully to the messages.[75] Some have mistakenly said that Turing was a key figure in the design of the Colossus computer. Turingery and the statistical approach of Banburismus undoubtedly fed into the thinking about cryptanalysis of the Lorenz cipher,[76][77] but he was not directly involved in the Colossus development.[78]

Secure speech device (Delilah)[edit]

Following his work at Bell Labs in the US,[79] Turing pursued the idea of electronic enciphering of speech in the telephone system, and in the latter part of the war, he moved to work for the Secret Service's Radio Security Service (later HMGCC) at Hanslope Park. There he further developed his knowledge of electronics with the assistance of engineer Donald Bayley. Together they undertook the design and construction of a portable secure voice communications machine codenamed Delilah.[80] It was intended for different applications, lacking capability for use with long-distance radio transmissions, and in any case, Delilah was completed too late to be used during the war. Though the system worked fully, with Turing demonstrating it to officials by encrypting and decrypting a recording of a Winston Churchill speech, Delilah was not adopted for use.[81]

Turing also consulted with Bell Labs on the development of SIGSALY, a secure voice system that was used in the later years of the war.

Early computers and the Turing test[edit]

From 1945 to 1947, Turing lived in Richmond, London[82] while he worked on the design of the ACE (Automatic Computing Engine) at the National Physical Laboratory (NPL). He presented a paper on 19 February 1946, which was the first detailed design of a stored-program computer.[83] Von Neumann's incomplete First Draft of a Report on the EDVAC had predated Turing's paper, but it was much less detailed and, according to John R. Womersley, Superintendent of the NPL Mathematics Division, it "contains a number of ideas which are Dr. Turing's own".[84] Although ACE was a feasible design, the secrecy surrounding the wartime work at Bletchley Park led to delays in starting the project and he became disillusioned. In late 1947 he returned to Cambridge for a sabbatical year during which he produced a seminal work on Intelligent Machinery that was not published in his lifetime.[85] While he was at Cambridge, the Pilot ACE was being built in his absence. It executed its first program on 10 May 1950. Although the full version of Turing's ACE was never built, a number of computers around the world owe much to it, for example, the English Electric DEUCE and the American Bendix G-15.

According to the memoirs of the German computer pioneer Heinz Billing from the Max Planck Institute for Physics, published by Genscher, Düsseldorf (1997), there was a meeting between Alan Turing and Konrad Zuse.[86] It took place in Göttingen in 1947. The interrogation had the form of a colloquium. Participants were Womersley, Turing, Porter from England and a few German researchers like Zuse, Walther, and Billing. (For more details see Herbert Bruderer, Konrad Zuse und die Schweiz).

In 1948, he was appointed Reader in the Mathematics Department at the University of Manchester. In 1949, he became Deputy Director of the Computing Laboratory there, working on software for one of the earliest stored-program computers—the Manchester Mark 1. During this time he continued to do more abstract work in mathematics,[87] and in "Computing machinery and intelligence" (Mind, October 1950), Turing addressed the problem of artificial intelligence, and proposed an experiment which became known as the Turing test, an attempt to define a standard for a machine to be called "intelligent". The idea was that a computer could be said to "think" if a human interrogator could not tell it apart, through conversation, from a human being.[88] In the paper, Turing suggested that rather than building a program to simulate the adult mind, it would be better rather to produce a simpler one to simulate a child's mind and then to subject it to a course of education. A reversed form of the Turing test is widely used on the Internet; the CAPTCHA test is intended to determine whether the user is a human or a computer.

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. By 1950, the program was completed and dubbed the Turbochamp.[89] In 1952, he tried to implement it on a Ferranti Mark 1, but lacking enough power, the computer was unable to execute the program. Instead, Turing played a game in which he simulated the computer, taking about half an hour per move. The game was recorded.[90] The program lost to Turing's colleague Alick Glennie, although it is said that it won a game against Champernowne's wife.

His Turing test was a significant, characteristically provocative and lasting contribution to the debate regarding artificial intelligence, which continues after more than half a century.[91]

He also invented the LU decomposition method in 1948, used today for solving matrix equations.[92]

Pattern formation and mathematical biology[edit]

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, putting forth the Turing hypothesis of pattern formation[93][94] (the theory was experimentally confirmed 60 years after his death[95] ). His central interest in the field was understanding Fibonacci phyllotaxis, the existence of Fibonacci numbers in plant structures.[96] He used reaction–diffusion equations which are central to the field of pattern formation. Later papers went unpublished until 1992 when Collected Works of A.M. Turing was published. His contribution is considered a seminal piece of work in this field.[97] Removal of Hox genes causes an increased number of digits (up to 14) in mice, demonstrating a Turing-type mechanism in the development of the hand.[98]

Conviction for indecency[edit]

In January 1952, Turing, then 39, started a relationship with Arnold Murray, a 19-year-old unemployed man. Turing met Murray just before Christmas outside the Regal Cinema when walking down Manchester's Oxford Road and had invited him to lunch. On 23 January Turing's house was burgled. Murray told Turing that the burglar was an acquaintance of his, and Turing reported the crime to the police. During the investigation he acknowledged a sexual relationship with Murray. Homosexual acts were criminal offences in the United Kingdom at that time,[99] and both men were charged with gross indecency under Section 11 of the Criminal Law Amendment Act 1885.[100] Initial committal proceedings for the trial occurred on 27 February, where Turing's solicitor "reserved his defence".

Later, convinced by the advice of his brother and other lawyers, Turing entered a plea of "guilty", in spite of the fact that he felt no remorse or guilt for having committed acts of homosexuality.[101] The case, Regina v. Turing and Murray, was brought to trial on 31 March 1952,[102] when Turing was convicted and given a choice between imprisonment and probation, which would be conditional on his agreement to undergo hormonal treatment designed to reduce libido. He accepted the option of treatment via injections of stilboestrol, a synthetic oestrogen; this treatment was continued for the course of one year. The treatment rendered Turing impotent and caused gynaecomastia,[103] fulfilling in the literal sense, Turing's prediction that "no doubt I shall emerge from it all a different man, but quite who I've not found out".[104][105] Murray was given a conditional discharge.[106]

Turing's conviction led to the removal of his security clearance and barred him from continuing with his cryptographic consultancy for the Government Communications Headquarters (GCHQ), the British signals intelligence agency that had evolved from GC&CS in 1946 (though he kept his academic job). He was denied entry into the United States after his conviction in 1952, but was free to visit other European countries, even though this was viewed by some as a security risk. At the time, there was acute public anxiety about homosexual entrapment of spies by Soviet agents,[107] because of the recent exposure of the first two members of the Cambridge Five, Guy Burgess and Donald Maclean, as KGB double agents. Turing was never accused of espionage, but in common with all who had worked at Bletchley Park, he was prevented by the Official Secrets Act from discussing his war work.[108]

Death[edit]

On 8 June 1954, Turing's housekeeper found him dead. He had died the previous day. A post-mortem examination established that the cause of death was cyanide poisoning. When his body was discovered, an apple lay half-eaten beside his bed, and although the apple was not tested for cyanide,[109] it was speculated that this was the means by which a fatal dose was consumed. An inquest determined that he had committed suicide, and he was cremated at Woking Crematorium on 12 June 1954.[110] Turing's ashes were scattered there, just as his father's had been.

Philosophy professor Jack Copeland has questioned various aspects of the coroner's historical verdict, suggesting the alternative explanation of the accidental inhalation of cyanide fumes from an apparatus for gold electroplating spoons, using potassium cyanide to dissolve the gold, which Turing had set up in his tiny spare room. Copeland notes that the autopsy findings were more consistent with inhalation than with ingestion of the poison. Turing also habitually ate an apple before bed, and it was not unusual for it to be discarded half-eaten.[111] In addition, Turing had reportedly borne his legal setbacks and hormone treatment (which had been discontinued a year previously) "with good humour" and had shown no sign of despondency prior to his death, in fact, setting down a list of tasks he intended to complete upon return to his office after the holiday weekend.[111] At the time, Turing's mother believed that the ingestion was accidental, caused by her son's careless storage of laboratory chemicals.[112] Biographer Andrew Hodges suggests that Turing may have arranged the cyanide experiment deliberately, to give his mother some plausible deniability.[113]

Turing's biographers Andrew Hodges and David Leavitt have suggested that Turing was re-enacting a scene from the 1937 Walt Disney film Snow White, his favourite fairy tale, both noting that (in Leavitt's words) he took "an especially keen pleasure in the scene where the Wicked Queen immerses her apple in the poisonous brew".[114]

Recognition and tributes[edit]

A blue plaque marking Turing's home at Wilmslow, Cheshire

A biography published by the Royal Society shortly after Turing's death, while his wartime work was still subject to the Official Secrets Act, recorded:

Three remarkable papers written just before the war, on three diverse mathematical subjects, show the quality of the work that might have been produced if he had settled down to work on some big problem at that critical time. For his work at the Foreign Office he was awarded the OBE.[2]

Since 1966, the Turing Award has been given annually by the Association for Computing Machinery for technical or theoretical contributions to the computing community. It is widely considered to be the computing world's highest honour, equivalent to the Nobel Prize.[115]

Breaking the Code is a 1986 play by Hugh Whitemore about Alan Turing. The play ran in London's West End beginning in November 1986 and on Broadway from 15 November 1987 to 10 April 1988. There was also a 1996 BBC television production (broadcast in the United States by PBS). In all three performances Turing was played by Derek Jacobi. The Broadway production was nominated for three Tony Awards including Best Actor in a Play, Best Featured Actor in a Play, and Best Direction of a Play, and for two Drama Desk Awards, for Best Actor and Best Featured Actor.

On 23 June 1998, on what would have been Turing's 86th birthday, his biographer, Andrew Hodges, unveiled an official English Heritage blue plaque at his birthplace and childhood home in Warrington Crescent, London, later the Colonnade Hotel.[116][117] To mark the 50th anniversary of his death, a memorial plaque was unveiled on 7 June 2004 at his former residence, Hollymeade, in Wilmslow, Cheshire.[118]

On 13 March 2000, Saint Vincent and the Grenadines issued a set of postage stamps to celebrate the greatest achievements of the 20th century, one of which carries a portrait of Turing against a background of repeated 0s and 1s, and is captioned: "1937: Alan Turing's theory of digital computing". On 1 April 2003, Turing's work at Bletchley Park was named an IEEE Milestone.[119] On 28 October 2004, a bronze statue of Alan Turing sculpted by John W. Mills was unveiled at the University of Surrey in Guildford, marking the 50th anniversary of Turing's death; it portrays him carrying his books across the campus.[120] In 2006, Boston Pride named Turing their Honorary Grand Marshal.[121]

Turing was one of four mathematicians examined in the 2008 BBC documentary entitled "Dangerous Knowledge".[122] The Princeton Alumni Weekly named Turing the second most significant alumnus in the history of Princeton University, second only to President James Madison. A 1.5-ton, life-size statue of Turing was unveiled on 19 June 2007 at Bletchley Park. Built from approximately half a million pieces of Welsh slate, it was sculpted by Stephen Kettle, having been commissioned by the late American billionaire Sidney Frank.[123]

Turing has been honoured in various ways in Manchester, the city where he worked towards the end of his life. In 1994, a stretch of the A6010 road (the Manchester city intermediate ring road) was named "Alan Turing Way". A bridge carrying this road was widened, and carries the name Alan Turing Bridge. A statue of Turing was unveiled in Manchester on 23 June 2001 in Sackville Park, between the University of Manchester building on Whitworth Street and the Canal Street gay village. The memorial statue, depicts the "father of Computer Science" sitting on a bench at a central position in the park.

Turing memorial statue plaque in Sackville Park, Manchester

Turing is shown holding an apple. The cast bronze bench carries in relief the text 'Alan Mathison Turing 1912–1954', and the motto 'Founder of Computer Science' as it could appear if encoded by an Enigma machine: 'IEKYF ROMSI ADXUO KVKZC GUBJ'.

A plinth at the statue's feet says 'Father of computer science, mathematician, logician, wartime codebreaker, victim of prejudice'. There is also a Bertrand Russell quotation saying 'Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere, like that of sculpture.' The sculptor buried his old Amstrad computer, which was an early popular home computer, under the plinth, as a tribute to "the godfather of all modern computers".[124]

In 1999, Time Magazine named Turing as one of the 100 Most Important People of the 20th century and stated: "The fact remains that everyone who taps at a keyboard, opening a spreadsheet or a word-processing program, is working on an incarnation of a Turing machine."[3] Turing is featured in the 1999 Neal Stephenson novel Cryptonomicon.

In 2002, a new building named after Alan Turing was constructed on the Malvern site of QinetiQ. It houses about 200 scientists and engineers, some of whom work on big data computing.

In 2002, Turing was ranked twenty-first on the BBC nationwide poll of the 100 Greatest Britons.[125] In 2006 British writer and mathematician Ioan James chose Turing as one of twenty people to feature in his book about famous historical figures who may have had some of the traits of Asperger syndrome.[126] In 2010, actor/playwright Jade Esteban Estrada portrayed Turing in the solo musical, ICONS: The Lesbian and Gay History of the World, Vol. 4. In 2011, in The Guardian's "My hero" series, writer Alan Garner chose Turing as his hero and described how they had met whilst out jogging in the early 1950s. Garner remembered Turing as "funny and witty" and said that he "talked endlessly". [127]

In 2006, Alan Turing was named with online resources as an LGBT History Month Icon.[128]

In February 2011, Turing's papers from the Second World War were bought for the nation with an 11th-hour bid by the National Heritage Memorial Fund, allowing them to stay at Bletchley Park.[129]

In November 2011, Channel 4 aired the docudrama Britain's Greatest Codebreaker about the life of Turing.

The logo of Apple Computer is often erroneously referred to as a tribute to Alan Turing, with the bite mark a reference to his death.[130] Both the designer of the logo[131] and the company deny that there is any homage to Turing in the design of the logo.[132] Stephen Fry has recounted asking Steve Jobs whether the design was intentional, saying that Jobs' response was, "God, we wish it were."[133]

The Turing Rainbow Festival, held in Madurai, India in 2012 for celebrating the LGBT and Genderqueer cause, was named in honour of Alan Turing by Gopi Shankar of Srishti Madurai.[134]

Also in 2012 Turing was inducted into the Legacy Walk, an outdoor public display which celebrates LGBT history and people. His marker here is the only such marker to mention his sexual orientation.[135][136]

The francophone singer-songwriter Salvatore Adamo makes a tribute to Turing with his song "Alan et la Pomme".[137]

Turing's life and work featured in a BBC children's programme about famous scientists - Absolute Genius with Dick and Dom - the episode was first broadcast on 12 March 2014.

On 26 April 2014, a choral work written by James McCarthy depicting the life of Alan Turing is premiered in the Barbican hall, London, by the Hertfordshire Chorus.[138]

Tributes by universities[edit]

The Alan Turing Building at the University of Manchester

Government apology and pardon[edit]

In August 2009, John Graham-Cumming started a petition urging the British Government to apologise for Turing's prosecution as a homosexual.[151][152] The petition received more than 30,000 signatures.[153][154] Prime Minister Gordon Brown acknowledged the petition, releasing a statement on 10 September 2009 apologising and describing the treatment of Turing as "appalling":[153][155]

Thousands of people have come together to demand justice for Alan Turing and recognition of the appalling way he was treated. While Turing was dealt with under the law of the time and we can't put the clock back, his treatment was of course utterly unfair and I am pleased to have the chance to say how deeply sorry I and we all are for what happened to him ... So on behalf of the British government, and all those who live freely thanks to Alan's work I am very proud to say: we're sorry, you deserved so much better.[153][156]

In December 2011, William Jones created an e-petition[157] requesting the British Government pardon Turing for his conviction of "gross-indecency":[158]

We ask the HM Government to grant a pardon to Alan Turing for the conviction of "gross indecency". In 1952, he was convicted of "gross indecency" with another man and was forced to undergo so-called "organo-therapy" – chemical castration. Two years later, he killed himself with cyanide, aged just 41. Alan Turing was driven to a terrible despair and early death by the nation he'd done so much to save. This remains a shame on the UK government and UK history. A pardon can go to some way to healing this damage. It may act as an apology to many of the other gay men, not as well-known as Alan Turing, who were subjected to these laws.[159]

The petition gathered over 37,000 signatures,[10][157] but the request was discouraged by Lord McNally, who gave the following opinion in his role as the Justice Minister:[160]

A posthumous pardon was not considered appropriate as Alan Turing was properly convicted of what at the time was a criminal offence. He would have known that his offence was against the law and that he would be prosecuted. It is tragic that Alan Turing was convicted of an offence which now seems both cruel and absurd—particularly poignant given his outstanding contribution to the war effort. However, the law at the time required a prosecution and, as such, long-standing policy has been to accept that such convictions took place and, rather than trying to alter the historical context and to put right what cannot be put right, ensure instead that we never again return to those times.[161]

On 26 July 2012, a bill was introduced in the House of Lords to grant a statutory pardon to Turing for offences under section 11 of the Criminal Law Amendment Act 1885, of which he was convicted on 31 March 1952.[162] Late in the year in a letter to The Daily Telegraph, the physicist Stephen Hawking and 10 other signatories including the Astronomer Royal Lord Rees, President of the Royal Society Sir Paul Nurse, Lady Trumpington (who worked for Turing during the war), and Lord Sharkey (the bill's sponsor) called on Prime Minister David Cameron to act on the pardon request.[163] The Government indicated it would support the bill,[164][165][166] and it passed its third reading in the Lords in October.[167]

Wikinews has related news: Alan Turing given posthumous pardon

Before the bill could be debated in the House of Commons,[168] the Government elected to proceed under the royal prerogative of mercy. On 24 December 2013, Queen Elizabeth II signed a pardon[11] for Turing's conviction for gross indecency, with immediate effect. Announcing the pardon, Justice Secretary Chris Grayling said Turing deserved to be "remembered and recognised for his fantastic contribution to the war effort" and not for his later criminal conviction.[10] The Queen then officially pronounced Turing pardoned in August 2014.[169] The Queen's action is only the fourth royal pardon granted since the conclusion of World War II.[170] This case is unusual in that pardons are normally granted only when the person is technically innocent, and a request has been made by the family or other interested party. Neither condition was met in regard to Turing's conviction.[171]

In a letter to Prime Minister David Cameron after announcement of the pardon, human rights advocate Peter Tatchell criticised the decision to single out Turing due to his fame and achievements, when thousands of others convicted under the same law have not received pardons.[172] Tatchell also called for a new investigation into Turing's death:

A new inquiry is long overdue, even if only to dispel any doubts about the true cause of his death – including speculation that he was murdered by the security services (or others). I think murder by state agents is unlikely. There is no known evidence pointing to any such act. However, it is a major failing that this possibility has never been considered or investigated.[173]

Centenary celebrations[edit]

Main article: Alan Turing Year
David Chalmers on stage for an Alan Turing Year conference at De La Salle University, Manila, 27 March 2012

To mark the 100th anniversary of Turing's birth, the Turing Centenary Advisory Committee (TCAC) co-ordinated the Alan Turing Year, a year-long programme of events around the world honouring Turing's life and achievements. The TCAC, chaired by S. Barry Cooper with Alan Turing's nephew Sir John Dermot Turing acting as Honorary President, worked with the University of Manchester faculty members and a broad spectrum of people from Cambridge University and Bletchley Park.

On 23 June 2012, Google featured an interactive doodle where visitors had to change the instructions of a Turing Machine, so when run, the symbols on the tape would match a provided sequence, featuring "Google" in Baudot-Murray code.[174]

The Bletchley Park Trust collaborated with Winning Moves to publish an Alan Turing edition of the board game Monopoly. The game's squares and cards have been revised to tell the story of Alan Turing's life, from his birthplace in Maida Vale to Hut 8 at Bletchley Park.[175] The game also includes a replica of an original hand-drawn board created by William Newman, son of Turing's mentor, Max Newman, which Turing played on in the 1950s.[176]

In the Philippines, the Department of Philosophy at De La Salle University-Manila hosted Turing 2012, an international conference on philosophy, artificial intelligence, and cognitive science from 27 to 28 March 2012 to commemorate the centenary birth of Turing.[177][178] Madurai, India held celebrations, in conjunction with Asia's first Gay Pride festival, with a programme attended by 6000 students.[179]

UK celebrations[edit]

The London 2012 Olympic Torch flame was passed on in front of Turing's statue in Manchester on his 100th birthday.

There was a three-day conference in Manchester, UK in June, a two-day conference in San Francisco, organised by the ACM, and a birthday party and Turing Centenary Conference in Cambridge organised at King's College, Cambridge and the University of Cambridge, the latter organised by the association Computability in Europe.[180]

The Science Museum in London launched a free exhibition devoted to Turing's life and achievements in June 2012, to run until July 2013.[181] In February 2012, the Royal Mail issued a stamp featuring Turing as part of its "Britons of Distinction" series.[182] The London 2012 Olympic Torch flame was passed on in front of Turing's statue in Sackville Gardens, Manchester, on the evening of 23 June 2012, the 100th anniversary of his birth.

On 22 June 2012 Manchester City Council, in partnership with the Lesbian and Gay Foundation, launched the Alan Turing Memorial Award which will recognise individuals or groups who have made a significant contribution to the fight against homophobia in Manchester.[183]

At the University of Oxford, a new course in Computer Science and Philosophy was established to coincide with the centenary of Turing's birth.[184]

Previous events have included a celebration of Turing's life and achievements, at the University of Manchester, arranged by the British Logic Colloquium and the British Society for the History of Mathematics on 5 June 2004.[185]

Portrayal in adaptations[edit]

Benedict Cumberbatch has portrayed Turing in the film The Imitation Game (2014).

Turing was portrayed by Derek Jacobi in the 1996 television movie Breaking the Code.[186] The drama-documentary Codebreaker, about Turing's life, was aired by UK's Channel 4 in 2011 and was released in the US in October 2012. The film features Ed Stoppard as Turing and Henry Goodman as Franz Greenbaum.[187]

A musical work inspired by Turing's life, written by Neil Tennant and Chris Lowe of the Pet Shop Boys, entitled A Man from the Future, was announced in late 2013.[188] A Man from the Future was performed by the Pet Shop Boys and Juliet Stevenson (narrator), the BBC Singers, and the BBC Concert Orchestra conducted by Dominic Wheeler at the BBC Proms in Royal Albert Hall on 23 July 2014.[189]

Codebreaker, a choral work written by James McCarthy to the settings of texts by poets Wilfred Owen, Sara Teasdale, Walt Whitman, Oscar Wilde and Robert Burns, received its world premier on 26 April 2014 at the Barbican Centre in London. It was performed by the Hertfordshire Chorus, who commissioned the work, led by David Temple with a soprano soloist (sung by Naomi Harvey) providing the voice of Turing's mother.[190]

The historical drama The Imitation Game, directed by Morten Tyldum and starring Benedict Cumberbatch as Turing, is set for cinematic release on 28 November 2014.[191][192]

See also[edit]

Portal icon Biography portal
Portal icon Logic portal

Notes[edit]

  1. ^ Jump up to: a b Alan Turing at the Mathematics Genealogy Project
  2. ^ Jump up to: a b c Newman, M. H. A. (1955). "Alan Mathison Turing. 1912–1954". Biographical Memoirs of Fellows of the Royal Society 1: 253–226. doi:10.1098/rsbm.1955.0019. JSTOR 769256. 
  3. ^ Jump up to: a b Gray, Paul (29 March 1999). "Alan Turing – Time 100 People of the Century". Time Magazine. "Providing a blueprint for the electronic digital computer. The fact remains that everyone who taps at a keyboard, opening a spreadsheet or a word-processing program, is working on an incarnation of a Turing machine." 
  4. Jump up ^ Sipser 2006, p. 137
  5. Jump up ^ Beavers 2013, p. 481
  6. Jump up ^ Spencer, Clare (2009-09-11). "Profile: Alan Turing". BBC. Archived from the original on 2014-04-20. Retrieved 2014-07-22. "According to Winston Churchill, Turing made the single biggest contribution to Allied victory in the war against Nazi Germany." 
  7. Jump up ^ Copeland, J. Alan Turing: The codebreaker who saved 'millions of lives' (June 18, 2012) BBC News archive. Retrieved October 26, 2014.
  8. Jump up ^ Leavitt 2007, pp. 231–233
  9. Jump up ^ Pease, Roland (26 June 2012). "Alan Turing: Inquest's suicide verdict 'not supportable'". BBC News. Retrieved 25 December 2013. 
  10. ^ Jump up to: a b c Oliver Wright (23 December 2013). "Alan Turing gets his royal pardon for 'gross indecency' – 61 years after he poisoned himself". The Independent (London). 
  11. ^ Jump up to: a b "(Archived copy of) Royal Pardon for Alan Turing". 
  12. ^ Jump up to: a b Hodges 1983, p. 5
  13. Jump up ^ "The Alan Turing Internet Scrapbook". Turing.org.uk. Retrieved 2 January 2012. 
  14. Jump up ^ Phil Maguire, "An Irishman's Diary", page 5. The Irish Times, 23 June 2012
  15. Jump up ^ "London Blue Plaques". English Heritage. Archived from the original on 13 September 2009. Retrieved 10 February 2007. 
  16. Jump up ^ The Scientific Tourist In London: #17 Alan Turing's Birth Place, Nature.com London Blog
  17. Jump up ^ Plaque #381 on Open Plaques.
  18. Jump up ^ "The Alan Turing Internet Scrapbook". Retrieved 26 September 2006. 
  19. Jump up ^ Hodges 1983, p. 6
  20. Jump up ^ "Baston Lodge". 
  21. Jump up ^ Jones, G. James (11 December 2001). "Alan Turing – Towards a Digital Mind: Part 1". System Toolbox. Archived from the original on 3 August 2007. Retrieved 27 July 2007. 
  22. Jump up ^ Name * (29 November 2012). "Guildford Dragon NEWS". The Guildford Dragon. Retrieved 31 October 2013. 
  23. Jump up ^ Hofstadter, Douglas R. (1985). Metamagical Themas: Questing for the Essence of Mind and Pattern. Basic Books. ISBN 0-465-04566-9. OCLC 230812136. 
  24. Jump up ^ Hodges 1983, p. 26
  25. Jump up ^ Hodges 1983, p. 34
  26. Jump up ^ Rachel Hassall, 'The Sherborne Formula: The Making of Alan Turing' 'Vivat!' 2012/13
  27. Jump up ^ Teuscher, Christof (ed.) (2004). Alan Turing: Life and Legacy of a Great Thinker. Springer-Verlag. ISBN 3-540-20020-7. OCLC 53434737 62339998. 
  28. Jump up ^ Paul Gray, Alan Turing Time Magazine's Most Important People of the Century, p.2
  29. Jump up ^ The Inspiration of Life and Death, 1928–1932 Alan Turing Scrapbook
  30. Jump up ^ See Section 3 of John Aldrich, "England and Continental Probability in the Inter-War Years", Journal Electronique d'Histoire des Probabilités et de la Statistique, vol. 5/2 Decembre 2009 Journal Electronique d'Histoire des Probabilités et de la Statistique
  31. Jump up ^ Hodges 1983, pp. 88,94
  32. Jump up ^ Turing 1937
  33. Jump up ^ Church 1936
  34. Jump up ^ Hodges 1983, p. 111
  35. Jump up ^ "von Neumann ... firmly emphasised to me, and to others I am sure, that the fundamental conception is owing to Turing—insofar as not anticipated by Babbage, Lovelace and others." Letter by Stanley Frankel to Brian Randell, 1972, quoted in Jack Copeland (2004) The Essential Turing, p22.
  36. Jump up ^ Hodges 1983, p. 138
  37. Jump up ^ Turing, A. M. (1939). "Systems of Logic Based on Ordinals". Proceedings of the London Mathematical Society: 161–228. doi:10.1112/plms/s2-45.1.161.  edit
  38. Jump up ^ Turing, Alan (1938). Systems of Logic Based on Ordinals (PhD thesis). Princeton University. doi:10.1112/plms/s2-45.1.161. 
  39. Jump up ^ Turing, A. M. (1938). "Systems of Logic Based on Ordinals". 
  40. Jump up ^ Hodges 1983, p. 152
  41. Jump up ^ Hodges 1983, pp. 153–154
  42. Jump up ^ Briggs, Asa (21 November 2011). Britain's Greatest Codebreaker (TV broadcast). UK Channel 4. 
  43. Jump up ^ Copeland, Jack, "Colossus and the Dawning of the Computer Age", p. 352 in Action This Day, 2001.
  44. Jump up ^ Copeland 2004a, p. 217
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  46. ^ Jump up to: a b Copeland, 2006 p. 378.
  47. Jump up ^ Turing, Alan (c. 1941). "Report on the applications of probability to cryptography". The National Archives of the UK: HW 25/37. 
  48. Jump up ^ Turing, Alan (c. 1941). "Paper on statistics of repetitions". The National Archives of the UK: HW 25/38. 
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  50. Jump up ^ Hodges 1983, p. 208
  51. Jump up ^ Lewin 1978, p. 57
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  54. Jump up ^ Pat Butcher: In Praise of Great Men. 14 September 2009
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  59. Jump up ^ "The Men Who Cracked Enigma", Episode 4 in the UKTV History Channel documentary series "Heroes of World War II"
  60. Jump up ^ Professor Jack Good in "The Men Who Cracked Enigma", 2003: with his caveat: "if my memory is correct".
  61. Jump up ^ Oakley 2006, p. 40/03B
  62. Jump up ^ Hodges 1983, p. 218
  63. Jump up ^ Hodges 1983, p. 221
  64. Jump up ^ Copeland, Jack; Proudfoot, Diane (May 2004). "Alan Turing, Codebreaker and Computer Pioneer". alanturing.net. Retrieved 27 July 2007. 
  65. ^ Jump up to: a b c Mahon 1945, p. 14
  66. Jump up ^ Leavitt 2007, pp. 184–186
  67. Jump up ^ "Bletchley Park Unveils Statue Commemorating Alan Turing". Retrieved 30 June 2007. 
  68. Jump up ^ Leavitt 2007, pp. 176–178
  69. Jump up ^ Hodges 1983, pp. 242–245
  70. Jump up ^ "BOMBE PROJECT HISTORY, MAY 44". Retrieved 2 May 2012. 
  71. Jump up ^ Hodges 1983, pp. 245–253
  72. Jump up ^ Alexander circa 1945, p. 42
  73. Jump up ^ Copeland 2006, p. 380
  74. Jump up ^ Copeland 2006, p. 381
  75. Jump up ^ Copeland 2006, p. 72
  76. Jump up ^ Gannon 2007, p. 230
  77. Jump up ^ Hilton 2006, pp. 197–199
  78. Jump up ^ Copeland 2006, pp. 382, 383
  79. Jump up ^ Hodges 1983, pp. 245–250
  80. Jump up ^ Hodges 1983, p. 273
  81. Jump up ^ Hodges 1983, p. 346
  82. Jump up ^ Plaque #1619 on Open Plaques.
  83. Jump up ^ Copeland 2006, p. 108
  84. Jump up ^ Randell, B (1980). "A History of Computing in the Twentieth Century: Colossus". Retrieved 27 January 2012.  citing Womersley, J. R. (13 February 1946). "'ACE' Machine Project". Executive Committee, National Physical Laboratory, Teddington, Middlesex. 
  85. Jump up ^ See Copeland 2004b, pp. 410–432
  86. Jump up ^ Herbert Bruderer. "Did Alan Turing interrogate Konrad Zuse in Göttingen in 1947?". Retrieved 7 February 2013. 
  87. Jump up ^ Turing, A. M. (1948). "Rounding-Off Errors in Matrix Processes". The Quarterly Journal of Mechanics and Applied Mathematics 1: 287–308. doi:10.1093/qjmam/1.1.287.  edit
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  91. Jump up ^ Pinar Saygin, A.; Cicekli, I.; Akman, V. (2000). Minds and Machines 10 (4): 463. doi:10.1023/A:1011288000451.  edit
  92. Jump up ^ "SPICE 1 2 3 and beyond ... Intusoft Newsletter, August 2003". Intusoft.com. 16 August 2001. Archived from the original on 11 June 2011. Retrieved 29 May 2011. 
  93. Jump up ^ Turing, A. M. (1952). "The Chemical Basis of Morphogenesis". Philosophical Transactions of the Royal Society B: Biological Sciences 237 (641): 37–64. doi:10.1098/rstb.1952.0012.  edit
  94. Jump up ^ "Control Mechanism For Biological Pattern Formation Decoded" ScienceDaily, 30 November 2006
  95. Jump up ^ Tompkins, Li, et al (10 March 2014). "Testing Turing's theory of morphogenesis in chemical cells". Proceedings of the National Academy of Sciences. doi:10.1073/pnas.1322005111. Retrieved 18 March 2014. 
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  97. Jump up ^ Turing's Last, Lost work at the Wayback Machine (archived 23 August 2003)
  98. Jump up ^ Sheth, R.; Marcon, L.; Bastida, M. F.; Junco, M.; Quintana, L.; Dahn, R.; Kmita, M.; Sharpe, J.; Ros, M. A. (2012). "Hox Genes Regulate Digit Patterning by Controlling the Wavelength of a Turing-Type Mechanism". Science 338 (6113): 1476–1480. doi:10.1126/science.1226804. PMID 23239739.  edit
  99. Jump up ^ Hodges 1983, p. 458
  100. Jump up ^ Leavitt 2007, p. 268
  101. Jump up ^ Hodges, Andrew (27 May 2012). Alan Turing: The Enigma. p. 463. ISBN 0-691-15564-X. 
  102. Jump up ^ Hodges, Andrew (27 May 2012). Alan Turing: The Enigma. p. 471. ISBN 0-691-15564-X. 
  103. Jump up ^ Andrew Hodges (2012). Alan Turing: The Enigma The Centenary Edition. Princeton University. 
  104. Jump up ^ Turing, Alan (1952). "Letters of Note: Yours in distress, Alan". Archived from the original on 16 December 2012. 
  105. Jump up ^ Hodges, Andrew (27 May 2012). Alan Turing: The Enigma. p. xxviii. ISBN 0-691-15564-X. 
  106. Jump up ^ Hodges 1983, p. 473
  107. Jump up ^ Leavitt 2007, p. 269
  108. Jump up ^ Copeland 2006, p. 143
  109. Jump up ^ Hodges 1983, p. 488
  110. Jump up ^ Hodges 1983, p. 529
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  112. Jump up ^ Letter to Robin Gandy, 28 July 1954, http://www.christies.com/lotfinder/books-manuscripts/turing-ethel-sara-series-of-11-5685694-details.aspx
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  150. Jump up ^ "Turing Hörsaal at University of Würzburg". Retrieved 21 July 2014. 
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  152. Jump up ^ Petition seeks apology for Enigma code-breaker Turing. CNN. 1 September 2009. Archived from the original on 5 October 2009. Retrieved 1 September 2009. 
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References[edit]

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