Alan Turing

Alan Turing: the machine that imitates any machine

Almost everything we argue about today when we argue about AI —whether a machine can surprise the person who programmed it, whether behaviour is enough as a criterion of intelligence, whether the brain is a computer— is already set out in three pieces Alan Turing wrote between 1936 and 1950. They are worth reading in order, because the sequence shows how a question about the foundations of mathematics turns into a question about the mind.

1936: modelling the human computer

From the seventeenth century, “computer” named a person: someone who did calculations. They were easy calculations but extremely long ones, and they were tied to the production of scientific knowledge —predicting the path of Halley’s comet, compiling the logarithm tables that scientists and engineers used.

Turing’s move was to model that activity. His machine is abstract and mathematical, but what guides the modelling is a person with a pencil:

Computing is normally done by writing certain symbols on paper. We may suppose this paper is divided into squares like a child’s arithmetic book. […] I assume then that the computation is carried out on one-dimensional paper, i.e. on a tape divided into squares. I shall also suppose that the number of symbols which may be printed is finite. […] The behaviour of the computer at any moment is determined by the symbols which he is observing, and his “state of mind” at that moment.

Putting a “state of mind” into a piece of mathematical logic, at a time when the mental was being pushed out of the domain of the scientific, is odd and does not look like an oversight. The paper can be read as an investigation into the nature of mind and its relation to a physical substrate.

The most important thing here is not the negative answer to the decision problem, but a by-product: the universal machine, a machine that takes instructions to behave as if it were any other machine. In 1936, almost in passing, Turing discovers the software industry.

1939-1945: Enigma, or finding patterns in noise

(Yes, the one from the film.) Turing’s contribution was decisive in breaking the Enigma machine the German military used to encipher its communications.

What matters here is the kind of reasoning the task demanded, closer to detective work and statistics than to logic: guessing the configuration of a machine from a string of characters that looks random but hides a message. Finding a regularity that will then work for any message enciphered with that same configuration.

Finding meaningful patterns in what looks like randomness, by trial and error. It is the most economical description there is of what a machine learning system does.

And the Bombe, the electromechanical device that did the work, had one feature the other wartime computers lacked: it did not compute numbers. It simulated being another machine.

1947: the brain as a computer without a clock

After the war, Turing turned officially to building a digital computer for the British government: the ACE (Automatic Computing Engine, a name that betrays the debt to Babbage).

In the lecture he gave that year to the London Mathematical Society, after explaining why the clock is central to the ACE’s design, he drops this:

We might say that the clock enables us to introduce a discreteness into time, so that time for some purposes can be regarded as a succession of instants instead of a continuous flow. A digital machine must essentially deal with discrete objects, and in the case of the ACE this is possible through the use of a clock. All other digital computing machines except for human and other brains that I know of do the same.

The brain joins the list of digital machines, with the peculiarity of computing without a central clock.

The same lecture contains the objection you still hear, and its refutation:

It has been said that computing machines can only carry out the processes that they are instructed to do. This is certainly true in the sense that if they do something other than what they were instructed then they have just made some mistake. It is also true that the intention in constructing these machines in the first instance is to treat them as slaves, giving them only jobs which have been thought out in detail, jobs such that the user of the machine fully understands in principle what is going on all the time. Up till the present machines have only been used in this way. But is it necessary that they should always be used in such a manner?

The “user” Turing means is the person programming, who can in principle know everything the machine does at the level of abstraction they are working in. (The distinction between user and programmer arrives later, when the computer becomes a product for non-experts.)

Universality lets Turing suggest that this servile mode of use, the most natural one at first, need not be the only one. Under a different kind of programming, the program can include instructions that modify its own configuration: not just the state, but the transition rules between states. If such a machine reaches the expected results by a more efficient route than the one foreseen, Turing is willing to call that behaviour intelligent. It is probably the first formulation of what we now call machine learning, and it arrives fifteen years before the phrase exists.

1950: the imitation game

In Computing machinery and intelligence, Turing returns to the problem with a strategy that resembles the Enigma work: putting himself in the position of someone who has to determine whether they are dealing with a machine.

Since defining “intelligence” is a swamp, he proposes an operational definition by way of a test procedure. The game has three parties: a judge, a human being playing a human being, and a computer playing a human being. The judge communicates with both in writing —today it would be a chat window—, knows one of the two is not human, and has to work out which.

Turing predicted:

I believe that in about fifty years’ time it will be possible to programme computers, with a storage capacity of about 10^9, 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.

That 10 followed by nine zeros is barely a gigabyte. Today it sounds like nothing; in 1950 it was an enormous figure. The ACE was to have some 25 kilobytes, and the EDVAC —the machine of the period closest to it in architecture— had around 5.6 kilobytes of fast memory.

Turing adds, in the same prediction, something that gets quoted less and has aged better: that by the end of the century the use of words would have changed enough that one could speak of thinking machines without expecting to be contradicted. He did not predict a technical capability. He predicted a shift in language. He was right.

Lady Lovelace’s objection

The most valuable part of the 1950 paper is the objections Turing takes the trouble to consider, from the theological (“thinking is a function of man’s immortal soul”) to those resting on Gödel’s incompleteness theorems. The one most pertinent to today’s argument is the one he attributes to Ada Lovelace:

In this she states, “The Analytical Engine has no pretensions to originate anything. It can do whatever we know how to order it to perform” (her italics).

That is: the machine can do only what we know how to break into steps and instruct precisely. Does it resemble the 1956 Dartmouth conjecture from the previous entry? It resembles it closely, though one states it as a limit and the other as a research programme.

Turing’s answer is not that the machine is creative. It is more modest and harder to dodge: machines surprised him many times, and not through faults. The error is in how we think about consequences.

The view that machines cannot give rise to surprises is due, I believe, to a fallacy to which philosophers and mathematicians are particularly subject. This is the assumption that as soon as a fact is presented to a mind all consequences of that fact spring into the mind simultaneously with it. It is a very useful assumption under many circumstances, but one too easily forgets that it is false.

There is an epistemological thesis there and not just a reply to an objection: deriving consequences from data and general principles is work, and it produces knowledge that was not available before the work was done. That is the subject of Epistemology?, a couple of entries further on.

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