Turing, A

Alan Mathison Turing, OBE, FRS (/ˈtjʊərɪŋ / ***tewr**-ing*; 23 June 1912 – 7 June 1954) was a British pioneering computer scientist, mathematician, logician, cryptanalyst, philosopher, 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 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 ledHut 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. Turing's pivotal role in cracking intercepted coded messages enabled the Allies to defeat the Nazis in many crucial engagements, including the Battle of the Atlantic; it has been estimated that the work at Bletchley Park shortened the war in Europe by as many as two to four years.^[6]

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 helped develop the Manchester computers^[7] 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 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, but it has been noted that the known evidence is equally consistent with accidental poisoning.^[8] In 2009, following an Internet campaign, British Prime Minister Gordon Brownmade 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.^[9][10][11]

Early life and family

Turing was born in Paddington, 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.^[12][13] Turing's father was the son of a clergyman, 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.^[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).

Turing's father's civil service commission was still active and during Turing's childhood years Turing's parents travelled between Hastings in England^[19] and India, leaving their two sons to stay with a retired Armycouple. 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 that 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]

Education

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 12, 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.^[23]

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".^[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, 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.^[26][27][28] 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.^[29]

University and work on computability

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 afellow 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 proven in 1922 by Jarl Waldemar Lindeberg.^[31]

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 theEntscheidungsproblem" (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.

...

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."^[43]

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.^[44]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 codemessages, Turing and Knox started to work on a less fragile approach to the problem.^[45] 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).^[46]

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^[48] and Paper on Statistics of Repetitions,^[49] 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.^[50]On 4 September 1939, the day after the UK declared war on Germany, Turing reported to Bletchley Park, the wartime station of GC&CS.^[47] 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.

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'.^[51]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.^[52]

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,^[53] and he was capable of world-class marathon standards.^[54][55] 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.^[56][57][58]

In 1945, Turing was awarded the OBE by King George VI for his wartime services, but his work remained secret for many years.^[59]

Bombe

Within weeks of arriving at Bletchley Park,^[47] 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.*^[60]

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 10^19 states, or 10²² for the four-rotor U-boat variant),^[61] 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.^[62]

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 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.^[63]

As Andrew Hodges, biographer of Turing, later wrote, "This letter had an electric effect."^[64] 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.^[64] 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."^[65] More than two hundred bombes were in operation by the end of the war.^[66]

Hut 8 and Naval Enigma

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.^[70]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".^[68] 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.^[68][69] 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".^[68] 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.

"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".^[74]Turing travelled to the United States in November 1942^[73] 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:

—Alan Turing

During this trip, he also assisted at Bell Labs with the development of secure speech devices.^[75] He returned to Bletchley Park in March 1943. During his absence, Hugh Alexanderhad 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".^[76]

—Hugh Alexander

Turingery

In July 1942, Turing devised a technique termed Turingery (or jokingly Turingismus)^[77] 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.^[78] 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.^[79] 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,^[80][81] but he was not directly involved in the Colossus development.^[82]

Delilah

Following his work at Bell Labs in the US,^[83] 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.^[84] 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.^[85]

Turing also consulted withBell 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

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.^[90] 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).From 1945 to 1947, Turing lived in Hampton, London^[86] 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.^[87] 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".^[88] 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.^[89] 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.

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-program computers—the Manchester Mark 1. During this time he continued to do more abstract work in mathematics,^[91] 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.^[92]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 Turochamp.^[93] 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.^[94] 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.^[95]

He also invented the LU decomposition method in 1948,^[91] used today for solving matrix equations.^[96]

Pattern formation and mathematical biology

Turing worked from 1952 until his death in 1954 on mathematical biology, specifically morphogenesis. He published one paper on the subject called The Chemical Basis of Morphogenesis in 1952, putting forth the Turing hypothesis of pattern formation^[97][98] (the theory was experimentally confirmed 60 years after his death^[99]). His central interest in the field was understanding Fibonacci phyllotaxis, the existence of Fibonacci numbers in plant structures.^[100] 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.^[101] 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.^[102]

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,^[103] and both men were charged with gross indecency under Section 11 of theCriminal Law Amendment Act 1885.^[104] 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.^[105] The case, Regina v. Turing and Murray, was brought to trial on 31 March 1952,^[106] 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 ofstilboestrol, a synthetic oestrogen; this treatment was continued for the course of one year. The treatment rendered Turing impotent and caused gynaecomastia,^[107] 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".^[108][109] Murray was given a conditional discharge.^[110]

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,^[111] 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.^[112]

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,^[113] 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.^[114] 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 goldelectroplating 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.^[115] 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.^[115] At the time, Turing's mother believed that the ingestion was accidental, resulting from her son's careless storage of laboratory chemicals.^[116] Biographer Andrew Hodges suggests that Turing may have arranged the cyanide experiment deliberately, to give his mother some plausible deniability.^[117]

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".^[118]

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.^[2]

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.^[119]

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