“Machines take me by surprise with great frequency”

Alan Turing

If some time ago we had gone around asking, “Do you know who Alan Turing was?”, few would have answered us, since it is a name that recurs almost exclusively among scholars of mathematics, computer science and philosophy. But towards the end of 2014, suddenly, the figure of this scientist became a cinematic phenomenon, with the release of a film titled “The Imitation Game”, dedicated to the English mathematician and to his life (1912-1954). Since then people have begun to talk about him, about the Enigma machine, the Bombe computer, Colossus, cryptography, etc. To many, all this seemed to resemble what had happened with John Nash, whose life and vicissitudes had, some years ago, inspired the cult movie A Beautiful Mind. Both events sometimes lead one to suspect that, around the troubled yet scientifically extraordinarily fruitful lives of two scholars fundamental to the intellectual landscape of their time (and of ours as well), someone wanted to build a marketing operation, a commercial operation that has very little to do with the true worth of the two figures in question. Yes, it is true, a cinema is not the most suitable place to recount game theory, mathematical equations, flip-flops, formal logic and the tedious considerations about machines and the reproducibility of human thought. But it is also true, let us take Alan Turing as an example, that everyone ought to know that, besides having been homosexual, having taken his own life because he could bear neither prison nor the chemical castration to which he had been subjected, and besides having, as an expert in cryptography, invented a machine that, by decoding the enemy's ciphered messages during the Second World War, made it possible to sink a considerable number of enemy submarines, Alan Turing has long been unanimously regarded as the father of the modern computer and of computer science: everyone, therefore, should know something more about his contribution to the logical and functional design of these extraordinary (though at times infernal) machines that today populate our homes, our schools, our workplaces.

The Turing Machine

Turing is the author of an extraordinary logical and mathematical discovery: the idea of the universal machine; a celebrated 1936 article titled “On Computable Numbers” describes its features and its workings.
But what had happened before? Turing was not, in fact, the first to conceive the idea of a machine for calculation and logical programming. Let us look briefly at what had happened some time earlier.
By a strange coincidence, it was two philosophers who attempted to build calculating machines.
The first, a very young Blaise Pascal, managed to show how the operations of calculation could be carried out in a purely mechanical way, building a machine that performed additions and subtractions and made the carry operation automatic, one of the main obstacles to the speed of mental calculation.
Some years later Gottfried Wilhelm von Leibniz, aware that it was unworthy of ingenious men to waste hours like slaves in the labour of calculation, work that could be entrusted to someone else who could make use of a machine, conceived a calculating machine able to perform multiplications and divisions in the form of repeated additions and subtractions. But Leibniz's contribution does not stop here: convinced of the possibility of mechanizing reasoning, he promoted the attempt to build a kind of symbolic language based on the combination of elementary propositions, a sort of “alphabet of thought”, a universal language capable of representing all possible concepts and of resolving any intellectual dispute with his famous calculemus. In the work De scientia universali seu calculo philosophico, Leibniz states:

“Quo facto, quando orientur controversiae, non magis disputatione opus erit inter duos philosophos, quam inter duos computistas. Sufficiet enim calamos in manus sumere sedereque ad abacos, et sibi mutuo (accito si placet amico) dicere: calculemus!”

(When controversies arise, there will be no more need of disputation between two philosophers than between two accountants. For it will suffice for them to take their pens in hand and sit down at the abacus and say to one another (calling in a friend as witness, if they wish): let us calculate!)

Naturally, there are many other events and many other figures who developed ideas relating to automatic calculation, but it would be impossible to cite them all here, because we would have to retrace the whole history of scientific and technological thought from antiquity to yesterday; two of them, however, must be given a place of prominence.
The first is Charles Babbage (1792-1871), an English mathematician who took up an idea of the French inventor Joseph-Marie Jacquard, who in 1805 had revolutionized the textile industry by inventing a device to be combined with the loom in order to obtain designs on cloth by means of punched cards that automated the process of warping the fabric (the famous Jacquard loom). In the analytical engine the sequences of cards made it possible to regulate the various operations automatically, but the most revolutionary aspect was its logical and functional scheme: the central part, called the “store”, was made up of various stacks of toothed wheels capable of representing up to 1000 numbers and gathered the data to be calculated; the “intermediate unit”, consisting of a system of levers and gears, transferred the data from the store to the third unit, called the “mill”, where the four arithmetic operations were carried out by a mechanical procedure. One glimpses here a scheme that would be kept in mind right up to the present day for the construction of modern computers.
The second figure is Ada Augusta Byron (1815-1851), the poet's daughter, who intuited the potential of Babbage's analytical engine and wrote the first programs to make it work. The English noblewoman, particularly interested in the ideas of the English mathematician and in their dissemination, was the first to introduce certain algorithmic concepts that govern today's structured programming of computers, and more precisely the idea of sequence, repetition, conditional jump and the concept of subroutine. Even though all this remained at the level of a project, Ada Byron understood that the machine could exploit the formalization of logic to build a symbolic system and a language capable of expressing the laws that govern the relations between any two things.

Alan Turing constitutes a bridge between the events described above and, with a single thread, ties together Pascal's desire to perform rapid calculations, Leibniz's idea of making demonstrations automatic, Babbage's concept of the machine and Ada Augusta Byron's idea of programming: these ideas converge in the so-called Turing machine, which was to be endowed, at least in its author's intentions, with powers of extension equal to those of a human brain.
The Turing machine was essentially a theoretical formulation, very simple but very powerful: it consisted of a tape of infinite length, divided into cells, each of which could contain a single symbol, and of a head under which the tape could run in both directions; the machine was able to perform only elementary operations and, despite its apparent simplicity, was physically realizable in an almost infinite number of different ways and was able to carry out any function computable by the most powerful of electronic computers. A machine conceived in this way could be considered entirely automatic, in the sense that human intervention was not envisaged in its operation, as instead happened in the attempts that had preceded it: it could work without external interference, in an autonomous way; moreover, it was also an abstract machine, in the sense that it left aside the possibility of actually being built, and therefore set aside problems and constraints of a technical nature, such as the characteristics of the hardware, the speed of calculation, the size of the memory, etc. With the extended description of all the information intended to define such an automatic machine, one obtained a kind of “behaviour table” of finite dimensions that completely defined the machine: it was this behaviour table that was the machine proper, not the physical apparatus in which it was realized from time to time. Each of the possible behaviour tables defines a machine different from all the others, with a different behaviour, so there exists an infinite number of possible tables, and therefore an infinite number of possible and realizable machines[1].

We might define Turing's project as the attempt to build an ideal reasoning machine, characterized by logical omnipotence, precisely because, through it, one came to distinguish the logical form of a machine from its material realization. If the initial problem was simply to add, subtract, multiply and divide rapidly, with Turing the attention shifts definitively to the mechanization of reasoning and to the machine's powers of deduction. The calculating machine turns into a computer: the two terms resemble each other, but they refer to two totally different ways of conceiving a machine; the former is designed to deal exclusively with numbers, the latter is programmed to carry out logical operations according to whether or not certain conditions are met; the former is a dedicated machine, the latter a universal machine able to perform very different operations without, for this reason, changing its physical structure.

The Turing Test

Turing's second fundamental contribution consists of his considerations on the relations between thought and machine. Turing, in a famous article that appeared in the journal “Mind” in 1950[2], opens with a sentence through which he sets in motion a reflection that would remain at the centre of philosophical debate up to our own day and that concerns, on the one hand, artificial intelligence and, on the other, the mind-body problem. The question at issue is the following: “Can machines think?”.
Confident in his conviction that a computer could be compared to a human brain, he tries to reflect on the differences in the behaviour of a man and of a computer and proposes a test. The so-called Turing test is based on a game, called the “imitation game” (it is from this game that the film mentioned above takes its name), in which the participants are three players who do not know one another; the first two are the so-called candidates, a man and a woman, while the third player, called the interrogator, tries to establish the identity of the two candidates simply on the basis of the answers they give to his questions. The male candidate, for example, may try to confuse the interrogator by pretending to be the woman, while the female candidate tries to help the interrogator. If the interrogator guesses the identity of the candidates, it is the woman who wins the game, otherwise the man wins the match. To avoid any clue (e.g. the register of the voice), the three players are in three different rooms and converse with one another by means of a teleprinter, without the presence of computers. Turing's idea, however, is to substitute a computer for the male candidate and to see whether, faced with average female opponents, it is able to confuse the average (human) interrogator as often as an average man does. If this happens, the computer passes the test and can be considered “intelligent”[3].
It is also true that machines are at ease only in circumscribed domains, such as that of the game of chess, where the possibilities of examining a given situation are a finite number, albeit a very high one.
The imitation game serves, of course, to test the machine's aptitudes because, Turing states, “if the man were to try and pretend to be the machine he would clearly make a very poor showing, because he would be given away at once by slowness and inaccuracy in arithmetic”. In this regard, in the 1950 article Turing reports the following dialogue between man (question) and computer (answer):

Question: Please write me a sonnet on the subject of the Forth Bridge.
Answer: Count me out on this one. I never could write poetry.
Question: Add 34957 to 70764.
Answer: (pause of about thirty seconds and then the answer): 105721.
Question: Do you play chess?
Answer: Yes.
Question: I have my King on e1 and no other piece. You have only your King on c3 and a Rook on h8. It is your move. What do you play?
Answer: (after a pause of fifteen seconds): Rook to h1, mate.

Turing's convictions about the emulation of a human brain by a computer have been sorely tested by a series of scholars: one above all, John Searle, who through various demonstrations (one of which is the experiment of the so-called Chinese room) noted precisely that it is from a linguistic point of view that no parallel can be drawn between machine and man: the former easily controls the syntax of a discourse, the latter, besides the syntax, is able to attach meanings to words within a context known to him; the computer, in this case, is nothing but a sophisticated simulator of human conversations.
Any attempt to emulate human intelligence comes up against a series of problems of a philosophical nature, but perhaps the debate set off by Turing's famous sentence around artificial intelligence has served, and still serves, on the one hand to distinguish what we can ask of a machine and what instead remains a human prerogative, and on the other to define a better and more adequate concept of intelligence than the one we have used until now.
Turing's insights are in any case summed up in the sentence with which he closes the 1950 article, and which foreshadows the extraordinary technological development that took place in very few years and that, since then, continues down to our own day: “We can only see a short distance ahead, but we can see plenty there that needs to be done”.

Notes

[1] Cf. M. Capponi, Il computer come ambiente di apprendimento, Morlacchi, Perugia 2003.

[2] A.M. Turing, Computing machinery and intelligence, Mind, 59 (1950) 433-460, It. transl. in: V. Somenzi, R. Cordeschi, La filosofia degli automi. Origini dell’intelligenza artificiale, Bollati Boringhieri, Torino 1986, pp. 157-183.

[3] J. Haugeland, Artificial Intelligence. The Very Idea, Mit Press, Cambridge 1985, It. transl. Intelligenza artificiale. Il significato di un’idea, Bollati Boringhieri, Torino 1988.

Massimo Capponi is a tenured university researcher at the University of Perugia; he teaches Computer Science Applied to Education in the degree course in Educational Sciences.