The Imitation Game and Turing's Legacy

[The Sloan Foundation supported The Imitation Game via their partnership with the Tribeca Film Institute]

Computer scientists and mathematicians around the world know all about Alan Turing, and his “Turing machine,” a hypothetical prototype for the modern computer. Now, thanks to the Weinstein Company, their new film The Imitation Game, and actor Benedict Cumberbatch, who plays Turing in the film, the legendary cryptanalyst and mathematician is likely to win some news fans, including gay activists, art-house film-goers and Oscar-prognosticators.

But it wasn’t the case in his lifetime. Despite Turing’s success working at the UK’s code-breaking center Bletchley Park in WWII and his pioneering experiments in early computing, his life wasn’t one of celebrated scientific breakthroughs, but shame and ignominy after being convicted of the criminal offense of homosexuality in 1952.

Sloan Science and Film asked S. Barry Cooper, Professor of Mathematics at the University of Leeds and author of the award-winning book Alan Turing: His Work and Impact, about Turing’s legacy, his lesser-known research areas, and whether his personal life should be mentioned in conjunction with his science.

Sloan Science and Film: Can you explain the significance of Turing and the Turing machine?

S. Barry Cooper: What was interesting about Turing was the drive to make everything algorithmic and computable. He clarified the model, if you like, of what it is to compute something. And if you were to get out of that model, you discovered that not everything was computable. So I think, more or less, the whole of his life was more or less involved with incomputability in different ways. Nowadays, we’re looking at Big Data, which is all about the struggle to control information. And these are the things that Turing paid attention to in his career that turned out to be very seminal. I wouldn’t say he was the best mathematician who ever lived, but he had a knack for spotting what was key and fundamental and his work fed very much into modern research and intuitions about directions to go.

SSF: What were some of those specific areas that he foresaw?

SBC: It depends on what community you’re looking at, whether it’s biology—morphogenesis—or if it’s logic or computer science, they know about the Turing Machine and they may know about the universal Turing Machine. His first big contribution was the research about what it meant to become computable known as the Church-Turing thesis [ They discovered computability and incomputability appeared in a very kind of mathematically trivial way. You don’t have to be terribly excellent in mathematics to understand incomputable objects. And incomputability is still being digested in science. More and more, physicists and biologists and economists are coming across this… like string theory. Just as Alan Turing tells you that you cannot compute everything, you can’t always prove your conjectures are true. I think there’s a classic dichotomy between artists and scientists, and nowadays, we’re following this path, influenced by Turing, where we’re getting this convergence, with scientists coming up with quite heretical thoughts about the limitations of science and people in the arts interested in computability. I wonder what Turing would make of it. I think he’d be quite amazed to get the level of recognition and respect that he has.

SSF: Because he didn’t in his lifetime, yes?

SBC: At Bletchley Park, all these people came together and the history was buried under the Official Secrets Act, and people weren’t allowed to even tell their own family about what they were doing. Turing was a solitary person. And there was no sense of the remarkable person he was. He didn’t get the support he wanted at the National Physical Laboratory, so he went away and left them to get on with developing the ACE Computer. But people didn’t know what his expertise really was, so he was limited to writing programs and watching other people doing stuff; being a geeky character, he didn’t always find it easy to work with other people. This kind of anonymity and burying of the history must have had a big impact on his life. And when he lost the respect through the court case, I think it hurt him very badly.

SSF: Do you think his personal life was an aspect of this idea of incomputablity? Is his personal life connected to his science?

SBC: This is something I feel strongly about. On the one hand, there’s a cohesion of the science, and I think it all hangs together in the sense of trying to get a grip on higher levels of computation. But a lot of what we say about Turing as a person is conjecture. He didn’t leave any diaries, so there’s a lot we don’t know about what went on in his head. But I think it impacted him that his parents were off in India, while he was fostered in the south of England, so I think the search for identity is a powerful thing in his life.

I think Turing wanted everything to be a Turing machine. He did want to pin everything down. He had this wonderful insecurity and uncertainty, so he was always able to take onboard things that didn’t quite fit what he was thinking. At one point, he would say that he was building a brain—some kind of computer chip—and at other times, he’s writing quite mysterious postcards about phenomenon effecting the real world. This search for control and higher order runs right through his career. I’ve corresponded with a gay mathematician and we’ve puzzled about the way his sexuality feeds into the science. You can say very reductive things. But we have this feeling that there is a connection, and the whole personality is part of the science, so you wouldn‘t have the science if Turing wasn’t Turing.

SSF: Are you concerned that the film will be reductive, and simplify this relationship?

SBC: One has concerns about the engagement with Turing. Are they using him for some kind of opportunist reason? But the vibrations I got from the filmmakers is that these were people who were intent on doing things right by Turing. But you can’t spend all this money and not take into account commercial concerns. I think there’s a lot of wrong stuff about Turing on the web and I think it could be misrepresented, but I think Turing’s personality is robust enough to deal with it.

SSF: As a mathematician, what would you like to see captured on film correctly about Turing’s work?

SBC: I’d be interested in the things that are not so well known—the offshoots of artificial intelligence are very exciting. And the biology is really interesting. Turing’s ideas about very simple computational events. The last stuff that Turing did, his one paper that he wrote on morphogenesis and the emergence of patterns in nature, this is actually his most cited paper.

Turing was also very interested in statistics, and it fits within all the other things. Because at Bletchley Park, you’re faced with all these coded messages from Germany, and you have to find the meaning in them. He brought to the decoding process sampling techniques from statistics called Data Reduction. So there’s this fundamental role for statistics, and it’s very important for Big Data right now.