On 27 May 1941, fresh from gaining his doctorate at Cambridge, Good walked into Hut Eight, scene of Bletchley Park's attack on German naval ciphers, for his first shift. This was the day that the Royal Navy caught, and destroyed, the battleship Bismarck after it had sunk HMS Hood, the British fleet flagship. Bletchley's contribution had been tangential but important: the discovery by wireless-traffic analysis that the German flagship was bound for Brest in France rather than Wilhelmshaven, from which she had set out, when signals to her started coming from the French port instead of the German one.
But Hut Eight had not been able to decipher in real time the 22 messages sent to the Bismarck because the Kriegsmarine was better at protecting its wireless traffic than the German army or the Luftwaffe, whose ciphers had been well penetrated the previous year. Naval signals were taking three to seven days to decipher, which usually made them operationally useless for the British. Yet this was about to change.
In his book Enigma: the Battle for the Code, Hugh Sebag-Montefiore describes how Good annoyed Alan Turing, the great mathematician and guiding intelligence of the Bletchley operation, by taking a nap on the floor of Hut Eight during his first night shift. Turing refused to speak to him afterwards - until the new boy used his statistical expertise to demonstrate how an essential trial-and-error method of attacking Enigma traffic could be accelerated .
The two men were thus reconciled. On another night shift, Good made a discovery missed by the old hands at Hut Eight. This helped them to work out which pairs of dummy letters the German encoders were adding to the twice enciphered, three-letter group at the start of each signal, telling the recipient how to set his machine to decipher it (for the British this became the achilles heel of the system). Good worked out that the "padding" was not random but came from a table, just as the setting itself did.
Some sensitive or important Enigma messages were enciphered twice, once in a special variation cipher and again in the normal cipher. Clearly a man who needed his sleep, Good dreamed one night that the process had been reversed: normal cipher first, special cipher second. When he woke up he tried his theory on an unbroken message - and promptly broke it. He also worked closely with Turing and others on the pioneering Colossus computers used to tackle other German ciphers. By now he was principal statistician.
Good was born Isidore Jacob Gudak to Polish-Jewish parents in London. His father was a watchmaker. He was educated at the Haberdashers' Aske's boys' school then in Hampstead, north London, where he effortlessly outpaced the mathematics teaching curriculum.
In 1938 he graduated with first-class honours in mathematics from Jesus College, Cambridge and stayed on to work for his PhD. While still at Cambridge, in 1941, he was approached by Bletchley recruiters. These included Hugh Alexander, twice British national chess champion, with whom he was to work closely, Good had won the 1939 Cambridgeshire chess championship. He reported for work within days. His service with Turing lasted nearly two years until he transferred to a team led by Max Newman, working on Colossus.
In 1947 Newman invited Good to join him and Turing at Manchester University. There for three years he lectured in mathematics and researched computers - including the Manchester Mark 1. Then, in 1948, he was recruited by the Government Communications Headquarters (GCHQ), the successor to Bletchley Park, where he stayed until 1959. This did not prevent him from taking up a brief associate professorship at Princeton University and a short consultancy with IBM.
From 1959 until he moved to the US in 1967 he held various government-funded posts and a senior research fellowship at Trinity College, Oxford. He was made a doctor of science at Cambridge in 1963 and at Oxford in 1964. Three years later he was appointed professor of statistics at Virginia Polytechnic Institute and State University.
As the author of such treatises as Speculations Concerning the First Ultraintelligent Machine and Logic of Man and Machine (both 1965), Good must have seemed the obvious man for Kubrick to consult when making 2001; one of the main characters in the film is the super-computer HAL 9000, which shows intelligence and emotions but goes rogue. Good's published work ran to more than three million words.
Slender and sporting a bushy moustache, Good was not without humour. He published one paper under the names IJ Good and K Caj Doog, his own nickname spelt backwards. In one paper in 1988 he solemnly reviewed other writings on the subject, mainly his own, on the grounds that: "I have read them all carefully." In Virginia, where car owners can invent their own numberplates, he chose 007 IJG in a coy reference to his wartime intelligence role.
Irving John "Jack" Good, mathematician, born 9 December 1916; died 5 April 2009.
Dan van der Vat
29 April 2009 © Guardian Newspapers Limited