I propose to consider the question, “Can machines think?”

— Alan Turing, “Computing Machinery and Intelligence” (1950)

So begins the paper Turing published in 1950 in the philosophy journal Mind. In the very next sentence he gives up on the question. To answer it, one would have to define “machine” and “think”, and any definition would turn into an endless argument about words. Turing proposes replacing it with another question, which has the advantage that it can be tested.

The rules of the game

The original game has three players: a man, a woman and an interrogator, in separate rooms. The interrogator communicates with the other two only through written messages and has to find out which is the man and which is the woman. The man tries to deceive him; the woman tries to help him.

Now replace the man with a machine. The question becomes: does the interrogator get it wrong just as often when one of the players is a machine? If the machine converses so well that the interrogator cannot tell it from a person, Turing proposes that we set aside the argument about whether it “really” thinks. This is the imitation game, known today as the Turing test.

The text even includes a sample conversation. To the question “add 34957 to 70764”, the machine waits about 30 seconds and answers “105621”. The correct sum is 105,721. Further on in the paper, Turing explains that a machine good at the game would get sums wrong on purpose, now and then, to seem human.

The prediction

Turing did not say the machines of his time would pass the test. He made a prediction with numbers:

I believe 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.

— Alan Turing, “Computing Machinery and Intelligence” (1950)

The “$10^9$” is the capacity in binary digits, or bits. In today’s language, $10^9$ bits are $\frac{10^9}{8}=1.25\times10^8$ bytes, about 125 megabytes: less than the memory of any phone. Turing was close on the memory and too cautious on the timing: convincing conversations with machines only came in the 2020s, with large language models, which use thousands of times more memory than he imagined.

The objections

Half the paper answers objections. Some of them:

  • The theological objection: thinking is a function of the immortal soul, which God gave to men and not to machines. Turing replies that, if God wished, he could give a soul to a machine.
  • The mathematical objection: Turing’s theorem and Gödel’s show that there are questions no machine can answer. Turing agrees, but notes that nothing suggests human beings do not have similar limits.
  • Lady Lovelace’s objection: in 1843 Ada Lovelace wrote that Babbage’s analytical engine “has no pretensions whatever to originate anything; it can do whatever we know how to order it to perform”. Turing replies that machines often surprised him, and that a machine capable of learning would do things its programmer did not foresee.

That last reply is the most prophetic. At the end of the paper Turing suggests that, instead of programming an adult brain, it would be better to program a “child machine” and educate it, with rewards and punishments. That is, in a few lines, the idea of machine learning.

Exercise: how much is 10⁹ bits?

How many 500-page books fit in $10^9$ bits, if each page has 2,000 characters and each character takes 8 bits?

One book is $500\cdot2000\cdot8=8\times10^6$ bits. In $10^9$ bits there is room for $\frac{10^9}{8\times10^6}=125$ books. Turing thought the memory of a small library would be enough to converse like a person.

Exercise: what does 70% mean?

If the interrogator guessed at random between the two players, what would the chance of being right be? What does “not more than 70%” mean?

Guessing, they would be right 50% of the time. “Not more than 70%” means that, after five minutes, the average interrogator is wrong in at least 30% of the games: the machine fools plenty of people, though not everyone.

Sources: Alan Turing, “Computing Machinery and Intelligence”, Mind, 59 (1950), pp. 433–460 · Ada Lovelace, notes to the translation of Menabrea’s paper on the analytical engine (1843) · The Turing Test, Stanford Encyclopedia of Philosophy.

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