A film about a mathematician: “The Imitation Game”

The new Hollywood blockbuster film about the mathematician Alan Turing is well-made, covers an interesting true story, and is shaped to promote some valid and important ideas.

Yet the shaping for dramatic effect twists the story in a way which inadvertently undercuts the film’s messages, and which purveys misunderstanding about Turing’s ideas.

[Click here for a review of the 2005 film Proof, about a fictional mathematician, in many ways superior to The Imitation Game, but having with it some similar problems.]

Turing was one of the founders of computer science. He studied maths at Cambridge from 1931 to 1934, then became a lecturer there. In 1936-8 he studied at Princeton University in the USA with Alonzo Church, another key figure in the science of computation.

He returned to Cambridge in 1938, started working part-time for the government’s code-breaking operation (forerunner of GCHQ), and then at the outbreak of war became one of the first employees at the government’s new code-breaking centre at Bletchley Park.

Bletchley Park eventually broke the Germans’ formidable Enigma code. Its effort was secret at the time and for decades afterwards, but is now what Turing is most famous for.

In 1945 he moved to work for the National Physical Laboratory, and then in 1948 to Manchester University. There the world’s first general-purpose electronic computer was built. A special-purpose forerunner, Colossus, had been built at Bletchley Park.

After about 1951 Turing worked more on biology. In 1952 he was prosecuted for homosexuality, and sentenced to chemical castration. In June 1954 he killed himself.

More or less every incident in the film is loosely based on something in the real history, and the film does not claim to be a documentary.

But the film has Turing as a tortured genius, relying on an emotional connection with machines rather than with other people to escape loneliness, and dedicated to the idea that machines can solve every problem.

It is sympathetic to Turing. As the film industry magazine Variety puts it, “the film ultimately celebrates anyone who is not ‘normal’.” It tells us that we need not-normal people to do more-than-normal things, as Turing did. Weird people may be geniuses.

But then what of weird people who are not geniuses, as most aren’t? And when the film-makers’ pitch their plea for gay rights – surely sincere – in terms of generous appreciation for the weird, doesn’t that sustain an inaccurate stereotype of LGBT people? Turing was open about his sexuality and about the joy he got from his gay lovers: why isn’t that unweird openness and joy in the film?

The film inadvertently nourishes the stereotype of the mathematician as necessarily socially-awkward, emotionally-crippled, and anguished, a stereotype already nurturing and nurtured by a nasty culture in a male-dominated IT industry. And of mathematical “genius” as a mysterious faculty available only to the tortured few.

In truth, exceptionally talented and dedicated people in any field, from carpentry through socialist politics to singing, may seem off-beat to a conformist majority. But many talented and pioneering mathematicians have been calm, affable people in their everyday life. And mathematical “genius”, like “genius” in carpentry, is only an extension and honing-by-practice of talents available in some measure or other to everyone.

The real Turing was not a stereotype tortured genius. According to his sympathetic biographer Andrew Hodges, he was habitually dishevelled, and “sometimes halting in speech and awkward of manner”, but had many friends.

The film’s presentation of Turing’s supposed fixation on machines is compiled from two sources. After World War 2 (that is, after the main period covered by the film), Turing pondered the question of whether machines could “think”. In a 1950 article (Computing machinery and intelligence, in the journal Mind), he proposed the “Turing Test”, namely to have humans question both the computer and a human and see if they could distinguish.

Turing’s own opinion in 1950 was that: “in about fifty years’ time it will be possible, to programme computers, with a storage capacity of about 109, to make them play the imitation game so well that an average interrogator will not have more than 70 per cent chance of making the right identification after five minutes of questioning. The original question, ‘Can machines think?’ I believe to be too meaningless to deserve discussion. Nevertheless I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted”.

Earlier this year some researchers claimed (controversially) to have done the first successful Turing Test. Arguably Turing was just jumping ahead too far. But in any case his argument was not at all that machines could do everything; and it was an argument he developed after the main period covered by the film, not one which shaped his actions in that period.

The film talks of the “Universal Turing Machine”, a concept coined by Turing in 1936-7 to describe, essentially, the common-core functioning of digital computers (which had not yet been invented), as if the term “universal” implied a claim that those machines could do everything.


On the contrary: Turing’s work in the 1930s, together with that of Alonzo Church and Kurt Gödel, showed two things. First, that all computers would have essentially the same range of competence. A quicker and bigger computer, better programmed, can do larger calculations, and maybe fast where a smaller one would be impossibly slow, but essentially it does the same sort of calculations.

Second, that some functions are not calculable on such machines. Some propositions are true or false but not decidable by such machines. This result follows essentially from Georg Cantor’s discovery that the points on a line form an infinity “too big” for them to be enumerated one by one.

Keira Knightley gives a tremendous performance as Joan Clarke, a woman code-breaker at Bletchley Park, and I like the film-makers’ evident wish to instruct us that women can be as mathematically able as men, yet glamorous and sassy with it.

Yet there are problems here too with the film’s reshaping of historical facts to dramatic effect. The real Joan Clarke was an able mathematician, but “shy, gentle and kind, non-aggressive and always subordinate to the men in her life”, and unremarkable in appearance. She did get engaged to be married to Turing, but only much more briefly than the film suggests.

The problem with the Clarke character is a flipside problem to that with the Turing character. The way she is portrayed in the film cannot but nourish the prejudice that women can of course function as only slightly-subordinate colleagues with men – but only if they combine smartness (assumed to be something short of the tortured genius of the man, Turing) with film-star looks, dress sense, sharp wit, and social poise. What about women who are smart, but ordinary in other respects?

Of the many twists to the story made for dramatic effect, some should be mentioned. Turing had been off the “chemical-castration” drugs for a year when he committed suicide, and was then working on mathematical biology, not computers. The code-breaking “bombes” in out-stations of Bletchley Park were special-purpose devices, not pioneer computers, and based on ideas not of Turing’s but of Polish mathematicians such as Marian Rejewski, who had made progress in breaking the Enigma code even before World War 2. Turing was the main designer, but he did not build them personally, and Denniston did not threaten to smash them up and sack Turing. Bletchley Park and its out-stations employed about 10,000 people, not, as the film suggests, half a dozen code-breakers and a couple of dozen secretaries.

The “bombes”, once functioning, did not solve the code problem once and for all. It was a constant struggle for Bletchley Park to keep up with the Germans’ changes in code procedures, and that struggle led to it developing the Colossus proto-computer to tackle problems the “bombes” couldn’t.

Joan Clarke was recruited to Bletchley Park not from doing a crossword, but by personal recommendation of one of her teachers at Cambridge University, Gordon Welchman, who worked with Turing at Bletchley Park and knew him from Cambridge.

However, if this film encourages more people to visit the museum now housed at Bletchley Park, or to read Andrew Hodges’s biography of Turing, it will have done good.