Alan Turing

Alan Mathison Turing, OBE, FRS (/ˈtjʊərɪŋ/; 23 June 1912 – 7 June 1954) was a British pioneering computer scientist, mathematician, logician, cryptanalyst and theoretical biologist. 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. Turing is widely considered to be the father of theoretical computer science and artificial intelligence.

During the Second World War, 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 and an electromechanical machine that could find settings for the Enigma machine. Turing played a pivotal role in cracking intercepted coded messages that enabled the Allies to defeat the Nazis in many crucial engagements, including the Battle of the Atlantic; it has been estimated that this work shortened the war in Europe by as many as two to four years.

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 the University of Manchester, where he helped develop the Manchester computers 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 in 1952 for homosexual acts, when such behaviour was still a criminal act 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 as suicide, but it has been noted that the known evidence is equally consistent with accidental poisoning. In 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". Queen Elizabeth II granted him a posthumous pardon in 2013.

    Early life and family

    Turing was born in Maida Vale, London, while his father, Julius Mathison Turing (1873–1947), was on leave from his position with the Indian Civil Service (ICS) at Chhatrapur, Bihar and Orissa Province, in British India. Turing's father was the son of a clergyman, the Rev. John Robert Turing, from a Scottish family of merchants which had been based in the Netherlands and included a baronet. Turing's mother, Julius' wife, 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.

    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 Britain, so they moved to Maida Vale, London, where Turing was born on 23 June 1912, as recorded by a blue plaque on the outside of the house of his birth, later the Colonnade Hotel. He had an elder brother, John (the father of Sir John Dermot Turing, 12th Baronet of the Turing baronets).

    Turing's father's civil service commission was still active and during Turing's childhood years Turing's parents travelled between Hastings in England 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.

    Very early in life, Turing showed signs of the genius that he was later to display prominently. 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.

    Education

    School

    Turing's 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 he was so determined to attend that he rode his bicycle unaccompanied more than 60 miles (97 km) from Southampton to Sherborne, stopping overnight at an inn.

    Turing's natural inclination towards 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". 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 might even have extrapolated Einstein's questioning of Newton's laws of motion from a text in which this was never made explicit.

    At Sherborne, Turing formed an important friendship with fellow pupil Christopher Morcom, who has been described as Turing's "first love". Their relationship provided inspiration in Turing's future endeavours, but it 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.

    The event caused Turing great sorrow. He coped with his grief by working that much harder on the topics of science and maths that he had shared with Morcom. In a letter to Morcom's mother Turing said:

    I am sure I could not have found anywhere another companion so brilliant and yet so charming and unconceited. I regarded my interest in my work, and in such things as astronomy (to which he introduced me) as something to be shared with him and I think he felt a little the same about me ... I know I must put as much energy if not as much interest into my work as if he were alive, because that is what he would like me to do.

    Some have speculated that Morcom's death was the cause of Turing's atheism and materialism, but this seems unlikely. Apparently, at this point in his life he still believed in such concepts as a spirit, independent of the body and surviving death. In a later letter, also written to Morcom's mother, Turing said:

    Personally, I believe that spirit is really eternally connected with matter but certainly not by the same kind of body ... as regards the actual connection between spirit and body I consider that the body [can] hold on to a 'spirit', whilst the body is alive and awake the two are firmly connected. When the body is asleep I cannot guess what happens but when the body dies, the 'mechanism' of the body, holding the spirit is gone and the spirit finds a new body sooner or later, perhaps immediately.

    University and work on computability

    After Sherborne, Turing studied as an undergraduate from 1931 to 1934 at King's College, Cambridge, whence 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, despite the fact that the committee had failed to identify that it had already been proven, in 1922, by Jarl Waldemar Lindeberg.

    In 1928, German mathematician David Hilbert had called attention to the Entscheidungsproblem (decision problem). In his paper "On Computable Numbers, with an Application to the Entscheidungsproblem" (submitted on 28 May 1936 and delivered 12 November), 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.

    King's College, Cambridge, where Turing was a student in 1931 and became a Fellow in 1935. The computer room is named after him.

    Although Turing's proof was published shortly after Alonzo Church's equivalent proof using his lambda calculus, Turing's approach is considerably more accessible and intuitive than Church's.[] It also included a 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 (as indeed could Church's lambda calculus). According to the Church–Turing thesis, Turing machines and the lambda calculus are capable of computing anything that is computable. John von Neumann acknowledged that the central concept of the modern computer was due to Turing's paper. To this day, Turing machines are a central object of study in theory of computation.

    From September 1936 to July 1938, Turing 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. In June 1938, he obtained his PhD from Princeton; his dissertation, Systems of Logic Based on Ordinals, 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 in 1939 by Ludwig Wittgenstein about the foundations of mathematics. Remarkably, the lectures have been reconstructed verbatim, including interjections from Turing and other students, from students' notes. Turing and Wittgenstein argued and disagreed, with Turing defending formalism and Wittgenstein propounding his view that mathematics does not discover any absolute truths but rather invents them.

    Cryptanalysis

    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."

    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. 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 code messages, Turing and Knox started to work on a less fragile approach to the problem. 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).

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

    On 4 September 1939, the day after the UK declared war on Germany, Turing reported to Bletchley Park, the wartime station of GC&CS. 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 The Applications of Probability to Cryptography and Paper on Statistics of Repetitions, 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.

    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'.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.

    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, and he was capable of world-class marathon standards. 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.

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

    Bombe

    Within weeks of arriving at Bletchley Park, 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.

    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 on the order of 1019 states, or 1022 states for the four-rotor U-boat variant), 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.

    By late 1941, Turing and his fellow cryptanalysts Gordon Welchman, Hugh Alexander, and Stuart Milner-Barry were frustrated. Building on the 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 Winston Churchill spelling out their difficulties, with Turing as the first named. 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.

    As Andrew Hodges, biographer of Turing, later wrote, "This letter had an electric effect." 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. The cryptographers at Bletchley Park did not know of the prime minister's response, but as Milner-Barry later recalled, "All that we did notice was that almost from that day the rough ways began miraculously to be made smooth." More than two hundred bombes were in operation by the end of the war.

    Hut 8 and Naval Enigma

    Turing by Stephen Kettle at Bletchley Park, commissioned by Sidney Frank, built from half a million pieces of Welsh slate.

    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". 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. 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." 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.

    In 1941, Turing proposed marriage to Hut 8 colleague 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.

    Joan Clarke, friend and colleague of Turing at Hut 8, to whom he proposed marriage in the spring of 1941

    Turing travelled to the United States in November 1942 and worked with US Navy cryptanalysts on naval Enigma and bombe construction in Washington; he also visited their Computing Machine Laboratory in 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.

    — Alan Turing

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

    — Hugh Alexander

    Turingery

    In July 1942, Turing devised a technique termed Turingery (or jokingly Turingismus) 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. 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. 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, but he was not directly involved in the Colossus development.

    Delilah

    Following his work at Bell Labs in the US, 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. 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.

    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

    Plaque, 78 High Street, Hampton

    From 1945 to 1947, Turing lived in Hampton, London 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.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". 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. While he was at Cambridge, the Pilot ACE was being built in his absence. It executed its first program on 10 May 1950, and a number of later computers around the world owe much to it, including the English Electric DEUCE and the American Bendix G-15. The full version of Turing's ACE was not built until after his death.

    According to the memoirs of the German computer pioneer Heinz Billing from the Max Planck Institute for Physics, published by Genscher, Düsseldorf, there was a meeting between Alan Turing and Konrad Zuse. 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, Turing 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-programme computers—the Manchester Mark 1. During this time he continued to do more abstract work in mathematics, 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. In the paper, Turing suggested that rather than building a programme 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 programme was completed and dubbed the Turochamp. In 1952, he tried to implement it on a Ferranti Mark 1, but lacking enough power, the computer was unable to execute the programme. Instead, 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 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.

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

    Pattern formation and mathematical biology

    Towards the end of his life, Turing turned to mathematical biology, publishing the "The Chemical Basis of Morphogenesis" in 1952. He was interested in morphogenesis, the development of patterns and shapes in biological organisms. His central interest in the field was understanding Fibonacci phyllotaxis, the existence of Fibonacci numbers in plant structures. He suggested that a system of chemicals reacting with each other and diffusing across space, termed a reaction-diffusion system, could account for "the main phenomena of morphogenesis." Instability in the system of linear partial differential equations used to model the system allows for small random perturbations to homogeneous initial state to drive the development of patterns. Though published before even the structure or role of DNA was understood, Turing's work on morphogenesis remains relevant today, and is considered a seminal piece of work in mathematical biology. Experiments suggest that Turing's work can partially explain growth of "feathers, hair follicles, the branching pattern of lungs, and even the left-right asymmetry that puts the heart on the left side of the chest." In 2012, Sheh, et al. found that in mice, removal of Hox genes causes an increase in the number of digits without an increase in the overall size of the limb, suggesting that Hox genes control digit formation by tuning the wavelength of a Turing-type mechanism. Later papers, though promised, were not available until Collected Works of A. M. Turing was published in 1992.

    Conviction for indecency

    In January 1952, Turing, then 39, started a relationship with Arnold Murray, a 19-year-old unemployed man. Turing had met Murray just before Christmas outside the Regal Cinema when walking down Manchester's Oxford Road and 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, and both men were charged with gross indecency under Section 11 of the Criminal Law Amendment Act 1885. Initial committal proceedings for the trial were held on 27 February during which Turing's solicitor "reserved his defence".

    Later, convinced by the advice of his brother and his own solicitor, Turing entered a plea of guilty. The case, Regina v. Turing and Murray, was brought to trial on 31 March 1952, 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, 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". Murray was given a conditional discharge.

    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, 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.

    Death

    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, 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. Turing's ashes were scattered there, just as his father's had been.

    Alternative death theories

    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. 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, setting down, in fact, a list of tasks he intended to complete upon return to his office after the holiday weekend. At the time, Turing's mother believed that the ingestion was accidental, resulting from her son's careless storage of laboratory chemicals. Biographer Andrew Hodges suggests that Turing may have arranged the cyanide experiment deliberately, to give his mother some plausible deniability.

    Andrew Hodges, and another biographer, David Leavitt, have both suggested that Turing was re-enacting a scene from the Walt Disney film Snow White and the Seven Dwarfs (1937), 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".

    Recognition and tributes

    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.

    Since 1966, the Turing Award has been given annually by the Association for Computing Machinery (ACM) 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.

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

    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. 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.

    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. 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. In 2006, Boston Pride named Turing their Honorary Grand Marshal.

    Turing was one of four mathematicians examined in the BBC documentary entitled Dangerous Knowledge (2008). 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 American billionaire Sidney Frank.

    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 Canal Street. The memorial statue depicts the "father of Computer Science" sitting on a bench at a central position in the park. 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'.

    Turing memorial statue plaque in Sackville Park, Manchester

    A plaque at the statue's feet reads '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 own old Amstrad computer under the plinth as a tribute to "the godfather of all modern computers".

    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." Turing is featured in the Neal Stephenson novel Cryptonomicon (1999).

    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. 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. 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".

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

    Alan Turing memorial statue in Sackville Park, Manchester.

    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.

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

    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.

    Also in 2012 Turing was inducted into the Legacy Walk, an outdoor public display which celebrates LGBT history and people.

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

    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 17 May 2014, the world's first work of public art to recognise Alan Turing as gay was commissioned in Bletchley, close by to Bletchley Park where his war-time work was carried out. The commission was announced by the owners of Milton Keynes-based LGBT venue and nightclub, Pink Punters to mark International Day Against Homophobia and Transphobia. The work was unveiled at a ceremony on Turing's birthday, 23 June 2014, and is placed outside Pink Punter's alongside the busy Watling Street, the old main road to London where Turing himself would have passed by on many occasions.

    On 22 October 2014, Turing was inducted into the NSA Hall of Honor.

    Tributes by universities and research institutions

    • The computer room at King's College, Cambridge, Alan Turing's alma mater, is called the Turing Room.
    • The Turing Room at the University of Edinburgh's School of Informatics houses a bust of Turing by Eduardo Paolozzi, and a set (No. 42/50) of his Turing prints (2000).
    • The University of Surrey has a statue of Turing on their main piazza and one of the buildings of Faculty of Engineering and Physical Sciences is named after him.
    • Istanbul Bilgi University organises an annual conference on the theory of computation called "Turing Days".
    • The University of Texas at Austin has an honours computer science programme named the Turing Scholars.
    • In the early 1960s Stanford University named the sole lecture room of the Polya Hall Mathematics building "Alan Turing Auditorium".
    • One of the amphitheatres of the Computer Science department (LIFL) at the University of Lille in Northern France is named in honour of Alan M. Turing (the other amphitheatre is named after Kurt Gödel).
    The Alan Turing Building at the University of Manchester
    • The Department of Computer Science at Pontifical Catholic University of Chile, the University of Buenos Aires, the Polytechnic University of Puerto Rico, Los Andes University in Bogotá, Colombia, King's College, Cambridge, Bangor University in Wales, the Universities of Ghent and Mons in Belgium, the University of Turin (Università degli Studi di Torino), the University of Puerto Rico at Humacao, Keele University and the University of Washington have computer laboratories named after Turing.[]
    • The University of Manchester, the Open University, Oxford Brookes University and Aarhus University (in Aarhus, Denmark) all have buildings named after Turing.[]
    • Alan Turing Road in the Surrey Research Park and the Alan Turing Way, part of the Manchester inner ring road are named after Alan Turing.
    • Carnegie Mellon University has a granite bench, situated in the Hornbostel Mall, with the name "A. M. Turing" carved across the top, "Read" down the left leg, and "Write" down the other.
    • The École Internationale des Sciences du Traitement de l'Information has named its third building "Turing".[]
    • The University of Oregon has a bust of Turing on the side of the Deschutes Hall, the computer science building.
    • The École Polytechnique Fédérale de Lausanne has a road and a square named after Alan Turing (Chemin de Alan Turing and Place de Alan Turing).
    • The Faculty of Informatics and Information Technologies Slovak University of Technology in Bratislava, Slovakia has a lecture room named "Turing Auditorium".
    • The Paris Diderot University has a lecture room named "Amphithéâtre Turing".[]
    • The Paul Sabatier University has a lecture room named "Amphithéâtre Turing" (Bâtiment U4).
    • The Department of Computer Science at the College of Engineering, Guindy has named its lecture hall as the "Turing Hall".[]
    • The Faculty of Mathematics and Computer Science at the University of Würzburg has a lecture hall named "Turing Hörsaal".
    • The largest conference hall at the Amsterdam Science Park is named Turingzaal.
    • In the summer of 2014, King's College London's School of Natural and Mathematical Sciences awarded the Alan Turing Centenary Prize to "the student ... who has not only achieved outstanding academic performance, but also made a significant contribution to the life of [the department]".[]
    • The University of Kent will open a brand new college, named Turing College at their Canterbury campus, to provide more than 800 new rooms to accommodate undergraduate and postgraduate students and keep up with increased demand for 'on campus living'. Other features of the new college include a hub to provide a social space for residents, study areas, office space and catering. Scientist George McVittie, an Honorary Professor at Kent from 1972 to 1988, worked with Alan Turing at Bletchley Park.[]
    • The campus of the École polytechnique has a building named after Alan Turing; it is a research centre of which premises are shared by the École Polytechnique, the INRIA and Microsoft.
    • The University of Toronto developed the Turing programming language in 1982, named after Alan Turing

    Government apology and pardon

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

    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.

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

    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 British government and British 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.

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

    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.

    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. 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. The Government indicated it would support the bill, and it passed its third reading in the Lords in October.

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