Alan Turing: The Man Who Took On Enigma

Alan Turing went to King’s College, Cambridge, in 1931 and earned first-class honours in mathematics in 1934. The central limit theorem is a basic result in probability theory. He proved a version of it while still an undergraduate and described it in a fellowship dissertation, “On the Gaussian Error Function”. The mathematician J. W. Lindeberg had proved a similar result in 1922. In 1936 Turing also won a Smith’s Prize, one of Cambridge’s prizes for mathematics. He remained a Fellow of King’s until 1952.

The paper was called “On Computable Numbers, with an Application to the Entscheidungsproblem”. The German word means “decision problem”. The mathematician David Hilbert had asked whether a definite method could decide, for any mathematical statement, whether it can be proved. Alan Turing learned of the question in 1935 from lectures by the Cambridge mathematician Max Newman, and answered no. At Princeton, the logician Alonzo Church reached the same result independently, by a method that did not use machines. Church published a few months earlier. Church was the first to call Turing’s imaginary device a “Turing machine”. The same paper described a universal machine that could do the work of any other such machine, the basic idea behind the modern computer.

Poland’s Cipher Bureau first read Enigma messages at the end of 1932. The mathematician Marian Rejewski reconstructed the wiring of the machine’s rotors using mathematics. In 1938 the Poles built the bomba, a machine that searched automatically through Enigma settings. Alan Turing’s bombe borrowed that idea but tested settings against guessed message text. Britain sent Alastair Denniston, the head of its codebreaking service, and Dilly Knox, who led its work on Enigma, to the meeting near Warsaw. By July 1939, Britain and France had promised to support Poland if it were invaded, and the Poles agreed to share what they knew. In January 1940, Turing met the Polish codebreakers in France, where they had escaped after Poland fell.

The liner Athenia was torpedoed by the U-boat U-30 on the evening of 3 September 1939, the day Britain declared war. More than 110 people died. Experts thought naval Enigma could not be broken. One reason was that the German navy used Enigma in more complex ways than the Army and Air Force did. Army and Air Force operators chose three rotors from a set of five. Each rotor was a wheel that scrambled the letters, and rotor order mattered. Navy operators chose from eight. That raised the possible rotor orders from 60 to 336, and a full search on the bombes took far longer. Naval Enigma became the work of Hut 8, the section Alan Turing led.

Banburismus took its name from Banbury, the town where the long paper sheets were printed. Letters of an intercepted message were punched into a sheet as holes. The codebreakers slid two sheets over each other and counted the holes that matched. The count gave a clue to how the machine settings of the two messages were related. Alan Turing measured the strength of that evidence in units he called “bans”, and in tenths of a ban, “decibans”. The method reduced the number of rotor orders the bombes had to try, and so saved scarce bombe time. Banburismus was skilled work. Joan Clarke, who joined Hut 8 in 1940, became adept at it.

Alan Turing designed the bombe to test possible Enigma settings at high speed. The bombe worked against a “crib”, a short stretch of text the codebreakers guessed a message contained. Each set of spinning drums copied the rotors of an Enigma machine. When the bombe found a setting that fitted the crib, it stopped, and the setting was checked. The British Tabulating Machine Company built the bombes at its works in Letchworth, Hertfordshire, where the engineering was led by Harold “Doc” Keen. Most bombes were run by members of the Women’s Royal Naval Service, the Wrens. By the end of the war in Europe, about 210 bombes had been built.

Gordon Welchman was a Cambridge mathematician who ran Hut 6, the section that attacked the German Army and Air Force Enigma codes. The diagonal board used a rule of Enigma’s plugboard, a panel of cables that swapped letters in pairs before and after the rotors. If A was wired to E, then E was wired to A. With that rule built into the bombe, each guess produced extra checks. Wrong settings were rejected faster, and the bombe could work from simpler cribs. The first bombe fitted with the board, nicknamed “Agnus”, began work in August 1940. From late 1940, the improved bombe made reading the German Air Force’s messages routine.

Joan Clarke studied mathematics at Newnham College, Cambridge, and earned a double first. At the time, Cambridge did not let women graduate in full. Gordon Welchman, one of her supervisors, recruited her to Bletchley Park, where she worked with Alan Turing in Hut 8. Turing and Clarke became engaged in the spring of 1941. Their families were told, but the engagement was kept secret from their colleagues. After it ended, the two stayed friends for the rest of Turing’s life. According to GCHQ, she was one of the first people Turing wrote to after his arrest in 1952. She later rejoined GCHQ, Bletchley Park’s successor.

Captured material helped in two ways. Key tables gave Hut 8 the exact settings for the days they covered, and codebooks helped the codebreakers guess the wording of later messages. On 9 May 1941, British warships forced the U-boat U-110 to the surface in the North Atlantic. A boarding party took its papers and Enigma material. U-110’s captain, Fritz-Julius Lemp, the officer who had sunk the Athenia, died in the action. U-110 sank the next day while under tow, and the capture was kept secret for decades. From August 1941, Hut 8 could break the main naval cipher without captured keys.

The four signatories were Alan Turing, Gordon Welchman, Hugh Alexander and Stuart Milner-Barry, senior codebreakers in Hut 8 and Hut 6. Winston Churchill had visited Bletchley Park in September 1941, and the letter opened by recalling that visit. The letter then listed the shortages section by section. In Hut 8, the punched-card (Hollerith) section that helped find the naval keys had stopped working night shifts for lack of staff. As a result, the letter said, the naval keys were found at least 12 hours later every day. Because the work was so secret, Milner-Barry delivered the letter to 10 Downing Street by hand.

Winston Churchill sent the four codebreakers’ letter, with his handwritten order, to General Hastings Ismay, his chief military assistant. The order also asked Ismay to report to Churchill once the order had been completed. According to the file at The National Archives, Ismay contacted the Ministry of Labour and the Admiralty department that ran the Women’s Royal Naval Service. Members of the service ran many of the bombes. The file records that Ismay gave instructions for Bletchley’s staff needs to be given extreme priority. Ismay’s reply of 18 November 1941 is in the same file. It said the head of the secret service had reported that the needs were being met very fast, though not completely.

The U-boats in the Atlantic and Mediterranean began using a new machine, the four-rotor M4 Enigma. The M4 ran on a separate cipher network that Hut 8 called Shark. The rest of the German navy’s Enigma traffic could still be read, so the blackout was limited to the U-boats’ traffic. Hut 8’s bombes were built for three-rotor machines and could not handle the fourth rotor. In November 1942, Alan Turing crossed the Atlantic to work with the Americans on the crisis. British and American four-rotor bombes did not enter service until the summer of 1943.

U-559 was sinking in the eastern Mediterranean, near Port Said in Egypt, when sailors from HMS Petard boarded it. Lieutenant Anthony Fasson and Able Seaman Colin Grazier went inside the sinking submarine to collect its papers. A 16-year-old canteen assistant, Tommy Brown, also boarded U-559 and was the only one of the three to survive. Tommy Brown had lied about his age to enlist. Fasson and Grazier were awarded the George Cross after their deaths, and Brown the George Medal. The papers included the U-boats’ weather codebook and the short-signal book used for sighting reports. The historian Ralph Erskine judged that without the three sailors’ bravery, Shark would not have been broken before four-rotor bombes arrived, if at all.

U-boats sent short weather reports with the fourth rotor set in a neutral position, so the machine behaved like a three-rotor Enigma. A weather codebook captured from U-559 let Hut 8 guess the wording of those reports. Hut 8’s existing three-rotor bombes could then find the day’s settings. On 13 December 1942, Bletchley again sent the Admiralty the positions of Atlantic U-boats from the previous week. According to the historian Ralph Erskine, there were more than a dozen. In March 1943 the Germans changed the weather codebook, but Hut 8 found a new way to break Shark within about 10 days. Erskine also writes that intelligence from Shark, though sometimes badly delayed, played a critical part in the Battle of the Atlantic.

The National Physical Laboratory, at Teddington near London, was a government science institute. In 1945, an American report on a planned computer, the EDVAC, spurred the laboratory to start a British project. The laboratory hired Alan Turing to design the machine. ACE stood for Automatic Computing Engine. According to the biographer Andrew Hodges, Turing imagined a machine that could switch from arithmetic to algebra, codebreaking or chess just by changing its program. Construction stalled. Hodges writes that Turing found the lack of cooperation deeply frustrating. A smaller trial version, the Pilot ACE, was built from Turing’s designs and ran in 1950, after Turing had left. The Pilot ACE is now in the Science Museum Group collection.

The OBE, Officer of the Order of the British Empire, is a British honour. The London Gazette listed Alan Turing among the additional officers of the Order’s Civil Division. The Gazette described him only as working in a department of the Foreign Office, with no mention of Bletchley Park. Joan Clarke, Turing’s Hut 8 colleague, was made an MBE for her war work. The secret of Bletchley Park’s work held until 1974, when Frederick Winterbotham’s book The Ultra Secret revealed it. By then, Turing had been dead for 20 years.

Alan Turing began running seriously after the war, while working at the National Physical Laboratory, and joined Walton Athletic Club. The race was the marathon championship of the Amateur Athletic Association, held at Loughborough. It served as a trial for the 1948 Olympic Games in London. Delfo Cabrera of Argentina won the Olympic marathon a year later in 2 hours 34 minutes 51.6 seconds. An injury then ended Turing’s serious running.

Mind is a journal of philosophy, and the paper was called “Computing Machinery and Intelligence”. Alan Turing based the test on a party game in which a questioner, typing questions, tries to tell a man from a woman. In his version, a machine takes one of the places. He also predicted that within about 50 years, computers would play the game well. An average questioner would then have no more than a 70 per cent chance of spotting the machine after five minutes. The test the paper describes is now known as the Turing test.

The young man was Arnold Murray, a 19-year-old from Manchester whom Alan Turing had met in December 1951. Murray told Turing that the burglar was an acquaintance of his. Under police questioning, Turing at first gave a false description of his informant, then admitted the relationship. Both men were charged with “gross indecency”. The offence came from the Criminal Law Amendment Act of 1885 and was used to prosecute any sexual contact between men. Turing had moved to Manchester University in 1948 and had bought his first house, in Wilmslow, Cheshire, south of the city.

The trial was held at the court in Knutsford, Cheshire. Alan Turing pleaded guilty, though, as the biographer Andrew Hodges writes, Turing saw nothing wrong in what he had done. The judge placed Turing on probation for a year, on condition that Turing accept oestrogen injections meant to suppress his sex drive. Losing his security clearance meant Turing could no longer work for GCHQ, the post-war successor to Bletchley Park. He had continued to work for GCHQ in secret. He kept his post at Manchester University and continued his research. Sex between men in private, if both were over 21, stopped being a crime in England and Wales only in 1967.

The paper, “The Chemical Basis of Morphogenesis”, appeared in the Philosophical Transactions of the Royal Society. Morphogenesis is the study of how living things develop their shape and pattern. Alan Turing showed how two chemicals could, on their own, change an even mixture into spots or stripes. In his model, the two chemicals react with each other and spread at different speeds. To test the idea, he ran the calculations on Manchester’s electronic computer. The biographer Andrew Hodges calls this the first serious use of a computer for mathematical research. Biologists now call such patterns “Turing patterns”, and studies of zebrafish skin have found such patterns.

Alan Turing’s housekeeper found him dead in bed, with a half-eaten apple beside the bed. The coroner recorded a verdict of suicide. Turing’s mother believed the death was an accident: Turing ran chemistry experiments at home and could have swallowed cyanide by mistake. The scholar Jack Copeland notes that the apple was never tested for cyanide. Copeland also notes that Turing kept cyanide at home for experiments in a small spare room. Copeland argues that the evidence would not support a suicide verdict today, and that an accident is equally likely. The biographer Andrew Hodges finds suicide more credible, arranged so that Turing’s mother alone could believe it was an accident.

The petition was started by the computer scientist John Graham-Cumming, and more than 30,000 people signed it. Gordon Brown telephoned Graham-Cumming before the apology was published as a statement from 10 Downing Street. In it, Brown wrote of Alan Turing: “Without his outstanding contribution, the history of World War Two could well have been very different.” Brown added that Turing and many thousands of other gay men convicted, as Turing was, under laws against sex between men “were treated terribly”. Brown ended: “We’re sorry, you deserved so much better.” The apology did not overturn Turing’s conviction.

Alan Turing’s pardon in 2013 was granted by the Queen, under the Royal Prerogative of Mercy, at the request of the Justice Secretary, Chris Grayling. His relatives then campaigned for pardons for other men convicted under historical indecency laws. The new law was created by amendments to the Policing and Crime Bill, first proposed by Lord Sharkey and other peers. About 49,000 men convicted under the old laws were pardoned after their deaths. Living men could get the same pardon, but only after applying to have their convictions removed. Justice minister Sam Gyimah called it “a truly momentous day”.

The Bank of England announced Alan Turing as the face of the new £50 note in July 2019. The Bank said its public call for scientists had drawn 227,299 nominations covering 989 eligible people. The £50 completed the Bank of England’s switch from paper to polymer, a thin plastic. The note carries a line Turing gave The Times in 1949. “This is only a foretaste of what is to come and only the shadow of what is going to be.” A strip of ticker tape shows his birth date in binary code. The note also shows the Pilot ACE computer and technical drawings of the bombe.