The Imitation Game: A Philosophical Review

January 20, 2015 Picture: touchedmuch/Flickr.

This article is part of The Critique’s exclusive series on the Alan Turing Biopic The Imitation Game

The Imitation Game is loosely based on the life of Alan Mathison Turing (1912-1954), a distinguished British mathematician. In a landmark paper published in 1936, Turing laid the conceptual and mathematical foundations of computer science. During WWII, he played a pivotal role in designing and running special purpose computers that cracked German secret codes, thereby helping the Allies’ victory in WWII. He also designed one of the earliest universal computers, argued that computers can become as intelligent as human beings, was tried and sentenced for homosexuality, and tragically died of cyanide poisoning at age 41. Since Turing used cyanide for chemical experiments in his house and left no indication that he committed suicide, it is disputed whether his death was a suicide or an accident.

When a film is inspired by a true story, one possible evaluation standard is historical accuracy. There are major differences between the real Turing and the way he is portrayed in the film. So if you are looking for a precise representation of the real Turing and his life, The Imitation Game is not for you. But historical accuracy is not the aim of this movie, so historical accuracy is a dubious evaluation standard.

If you are looking for a candid representation of Turing’s homosexuality, this isn’t the film for you either. Although the movie makes clear that he was gay, no homosexual acts of any kind are displayed—not even a tame kiss. But no sexual acts are displayed at all, so again this doesn’t seem like the most appropriate evaluation standard.

If you are looking for a highly digestible, emotionally compelling depiction of how Turing’s intellectual and technological achievements contributed to winning WWII, followed by the tragedy of Turing being unfairly convicted for his homosexuality, you will probably like this narrative. The film makes clear that Turing was a brilliant mathematician, that he contributed to the foundations of computer science, that he contributed to the Allies’ victory in WWII, that he believed in machine intelligence, and that he was unfairly persecuted for his sexual orientation. All of this is wrapped in the stereotype of the socially awkward mathematical genius and a conventional dramatic framework that is probably compelling to a mainstream audience. It will help make more people aware of Turing and his significance. That seems to be its creators’ aim. So by the standards of its creators, the film does its job. But I will ignore all of that.

“If you are looking for a precise representation of the real Turing and his life, The Imitation Game is not for you. But historical accuracy is not the aim of this movie, so historical accuracy is a dubious evaluation standard”

I will discuss how well The Imitation Game captures the philosophically significant aspects of Turing’s work. Such a discussion seems fair because Turing’s intellectual achievements are tightly bound to their philosophical significance. Specifically, I will focus on the powers and limitations of universal computers, including whether such computers can think.

One of Turing’s achievements was to devise a general formalism—now known as Turing machines—for characterizing algorithms or mechanical computation procedures. A Turing machine is a device that writes and erases letters on a tape. It works a little like an automatic typewriter. Unlike a typewriter, though, it also reads what’s written on the tape and decides what to type next based on both what it reads and its own internal state.

A second achievement was to argue persuasively that his formalism was sufficient—that any algorithm whatsoever could be carried out by one of his machines. In other words, for any algorithm performing any calculation over discrete symbols (addition, multiplication, prime factorization, you name it) you can design a Turing machine that performs the same calculation. This is known as the Church-Turing thesis. (It was also almost simultaneously proposed, in an equivalent form, by fellow mathematician Alonzo Church).

“If you are looking for a highly digestible, emotionally compelling depiction of how Turing’s intellectual and technological achievements contributed to winning WWII, followed by the tragedy of Turing being unfairly convicted for his homosexuality, you will probably like this narrative”

A third achievement was to show that there are universal Turing machines—namely, Turing machines that can execute any algorithm on any input so long as the algorithm and input are appropriately encoded and fed to the machine. The electronic computers we use every day, of which Turing designed one of the first, are concrete approximations of universal Turing machines.

A fourth achievement was to prove that there are many mathematical functions that cannot be computed by following an algorithm—and therefore they cannot be computed by universal Turing machines/modern computers. For example, the function that returns, for any Turing machine and any input, whether that Turing machine will ever halt while processing that input, is an uncomputable function. These uncomputable functions vastly outnumber the computable functions.

A fifth philosophically important contribution was to argue that, in spite of computers’ limitations, a computer could be as intelligent as a human being. Turing made many other contributions but I will focus on these five.

The film makes no attempt to describe Turing’s contributions in depth, but it does include scenes that hint at some of them. Uncomputable functions are not mentioned at all. Turing machines are mentioned, and their concrete counterparts—computers—play a central role in the movie. It is implied that universal Turing machines/computers are sufficient for computing all computable functions and that computers are more powerful than traditional computing machines such as desk calculators. In one of the most relevant scenes, Turing’s character explains that he wants to build a machine that will do more than just follow algorithms (for example, a multiplication algorithm) chosen by its user to compute specific functions. Instead, his computer will decide what to do next in light of the circumstances, like a human being does. In another passage, Turing’s character admits that computers think differently from human beings, but he immediately suggests that this doesn’t show computers don’t think. Turing’s character is also portrayed as developing an emotional bond towards his own private computer, which he is building inside his house. He points out that his computer is “learning so much!” Turing thought the ability to learn is necessary for computers to become as intelligent as human beings. Turing’s character seems to treat his computer as a person—while this is almost certainly historically inaccurate, it forcefully conveys Turing’s belief that machines can think.

The screenplay is based on Andrew Hodges’s main biography of Turing (Hodges 1983), which is valuable in many ways though not always accurate. Specifically, Hodges argues that Turing went back and forth on whether computers can be as intelligent as human beings. According to Hodges, young Turing believed that human beings are more intelligent than computers, because computers are limited to following fixed algorithms and fixed algorithms cannot solve all mathematical problems. (The latter statement is a consequence of mathematical results by Turing himself.) But later in his life, again according to Hodges, Turing somehow convinced himself that computers can be as intelligent as human beings after all. This alleged flip-flopping on machine intelligence appears to be due to a misunderstanding of some passages in Turing’s writings.

“Turing’s character seems to treat his computer as a person—while this is almost certainly historically inaccurate, it forcefully conveys Turing’s belief that machines can think”

A more plausible interpretation goes as follows. Turing concerned himself with the power and limitations of human mathematical faculties as early as the 1930s. By then, Kurt Gödel and others — including Turing himself — had shown that no finite set of rules, i.e. no algorithm, could be used to generate all mathematical truths. And yet intelligent human beings, Turing maintained, could invent new methods of proof by which an unbounded number of mathematical truths could be proved. But computers contain only finite instructions so it may seem that they cannot reproduce human intelligence. Or can they? Turing called this the mathematical objection to his view that machines can think. In reply, he proposed designing computers that can learn and discover new instructions, overcoming the limitations imposed by Gödel’s results in the same way that human mathematicians presumably do (Piccinini 2003).

Here is how Turing himself puts it:

“Let us suppose we have set up a machine with certain initial instruction tables [i.e., computer programs], so constructed that these tables might on occasion, if good reason arose, modify those tables. One can imagine that after the machine has been operating for some time, the instructions would have altered out of all recognition, but nevertheless still be such that one would have to admit that the machine was still doing very worthwhile calculations. Possibly it might still be getting results of the type desired when the machine was first set up, but in a much more efficient manner. In such a case one would have to admit that the progress of the machine had not been foreseen when its original instructions were put in. It would be like a pupil who had learnt much from his master, but had added much more by his own work. When this happens I feel that one is obliged to regard the machine as showing intelligence … What we want is a machine that can learn from experience. The possibility of letting the machine alter its own instructions provides the mechanism for this” (1947, pp. 122–123, emphasis added).

In summary, Turing argued that a computer can be as intelligent as a human being so long as it can modify its own instructions (in a non-algorithmic way) in a way that constitutes learning from experience.

Although there is no evidence that those who wrote the movie’s script went in any way beyond Hodges’s biography, they also ignored Hodges’s view that Turing changed his mind on machine intelligence. This is good because, by ignoring this part of Hodge’s story, they avoided reproducing Hodges’s mistake.

The movie does not explore whether machines can think, let alone whether computers can be people, in much depth. A more nuanced encapsulation of that debate may be found in episode 9 of Star Trek: The Next Generation, entitled “The Measure of a Man.” There, the protagonists wrestle with whether a machine can be a person, what it takes to be a person, how we can tell, and what the moral implications are. That Star Trek episode is a great way to expand on philosophical themes that are barely touched on in The Imitation Game.

Footnotes & References

Hodges, A. (1983). Alan Turing: The Enigma, New York: Simon and Schuster.

Piccinini, G. (2003). “Alan Turing and the Mathematical Objection,” Minds and Machines, 13.1: 23-48.

Turing, A.M. (1947). “Lecture to the London Mathematical Society on 20 February 1947.” Reprinted in D.C. Ince (1992), ed., Collected Works of A.M. Turing: Mechanical Intelligence, Amsterdam: North Ho