In this third period

In this third period (as it may be termed) of my mental progress, which now went hand in hand with hers, my opinions gained equally in breadth and depth, I understood more things, and those which I had understood before, I now understood more thoroughly. I had now completely turned back from what there had been of excess in my reaction against Benthamism. I had, at the height of that reaction, certainly become much more indulgent to the common opinions of society and the world, and more willing to be content with seconding the superficial improvement which had begun to take place in those common opinions, than became one whose convictions on so many points, differed fundamentally from them. I was much more inclined, than I can now approve, to put in abeyance the more decidedly heretical part of my opinions, which I now look upon as almost the only ones, the assertion of which tends in any way to regenerate society.

He is a dreamer of ancient...

He is a dreamer of ancient times, or rather, of the myths of what ancient times used to be. Such men are harmless in themselves, but their queer lack of realism makes them fools for others.

The object of desire

What is at stake here is precisely the problem of the fulfillment of desire: when we encounter in reality an object which has all the properties of the fantasized object of desire, we are nevertheless necessarily somewhat disappointed; we experience a certain this is not it; it becomes evident that the finally found real object is not the reference of desire even though it possesses all the required properties.

Consistency of being

The analysis achieves its end when the patient is able to recognize, in the Real of his symptom, the only support of his being. That is how we must read Freud's 'wo we war, soll ich werden:' you, the subject, must identify yourself with the place where your symptom already was; in its pathological particularity you must recognize the element which gives consistency to your being.

Mathematical reasoning may be regarded...

Mathematical reasoning may be regarded rather schematically as the exercise of a combination of two facilities, which we may call intuition and ingenuity. The activity of the intuition consists in making spontaneous judgements which are not the result of conscious trains of reasoning... The exercise of ingenuity in mathematics consists in aiding the intuition through suitable arrangements of propositions, and perhaps geometrical figures or drawings.

Instruction tables will have to...

Instruction tables will have to be made up by mathematicians with computing experience and perhaps a certain puzzle-solving ability. There need be no real danger of it ever becoming a drudge, for any processes that are quite mechanical may be turned over to the machine itself.

A man provided with paper,...

A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine.

There is a remarkably close...

There is a remarkably close parallel between the problems of the physicist and those of the cryptographer. The system on which a message is enciphered corresponds to the laws of the universe, the intercepted messages to the evidence available, the keys for a day or a message to important constants which have to be determined. The correspondence is very close, but the subject matter of cryptography is very easily dealt with by discrete machinery, physics not so easily.

This is only a foretaste...

This is only a foretaste of what is to come, and only the shadow of what is going to be. We have to have some experience with the machine before we really know its capabilities. It may take years before we settle down to the new possibilities, but I do not see why it should not enter any one of the fields normally covered by the human intellect, and eventually compete on equal terms.

Science is a differential equation....

Science is a differential equation. Religion is a boundary condition.

The Exclusion Principle is laid...

The Exclusion Principle is laid down purely for the benefit of the electrons themselves, who might be corrupted (and become dragons or demons) if allowed to associate too freely.

Let us now assume, for...

Let us now assume, for the sake of argument, that these machines are a genuine possibility, and look at the consequences of constructing them. To do so would of course meet with great opposition, unless we have advanced greatly in religious toleration from the days of Galileo. There would be great opposition from the intellectuals who were afraid of being put out of a job. It is probable though that the intellectuals would be mistaken about this. There would be plenty to do, trying to understand what the machines were trying to say, i.e. in trying to keep one’s intelligence up to the standard set by the machines, for it seems probable that once the machine thinking method had started, it would not take long to outstrip our feeble powers. There would be no question of the machines dying, and they would be able to converse with each other to sharpen their wits. At some stage therefore we should have to expect the machines to take control, in the way that is mentioned in Samuel Butler’s “Erewhon”.

The "computable" numbers may be...

The "computable" numbers may be described briefly as the real numbers whose expressions as a decimal are calculable by finite means. ...According to my definition, a number is computable if its decimal can be written down by a machine. ...I show that certain large classes of numbers are computable. They include, for instance, the real parts of all s, the real parts of the zeros of the Bessel functions, the numbers π, e, etc. The computable numbers do not, however, include all definable numbers. ...[C]onclusions are reached which are superficially similar to those of Gödel. ...[I]t is shown ...that the Hilbertian can have no solution. In a recent paper ... reaches similar conclusions...

We may compare a man...

We may compare a man in the process of computing a real number to a machine which is only capable of a finite number of conditions q1, q2, ..., qK which will be called " m-configurations ".

The machine is supplied with...

The machine is supplied with a "tape" (the analogue of paper) running through it, and divided into sections (called "squares") each capable of bearing a "symbol".

The "scanned symbol" is the...

The "scanned symbol" is the only one of which the machine is... "directly aware". However, by altering its m-configuration the machine can effectively remember some of the symbols which it has "seen" (scanned) previously.

In some of the configurations...

In some of the configurations in which the scanned square is blank... the machine writes down a new symbol on the scanned square: in other configurations it erases the scanned symbol.

The machine may also change...

The machine may also change the square which is being scanned, but only by shifting it one place to right or left.

[T]he m-configuration may be changed.

[T]he m-configuration may be changed.

Some of the symbols written...

Some of the symbols written down will form the sequence of figures which is the decimal of the real number... being computed. The others are just rough notes to "assist the memory ". ...[O]nly ...these rough notes ...will be liable to erasure.

[T]hese operations include all those...

[T]hese operations include all those which are used in the computation...

For some purposes we might...

For some purposes we might use machines (choice... or c-machines) whose motion is only partially determined by the configuration... When such a machine reaches... ambiguous configurations, it cannot go on until some arbitrary choice has been made by an external operator. This would be the case if we were using machines to deal with axiomatic systems.

In this paper I deal...

In this paper I deal only with automatic machines, and will therefore often omit the prefix ɑ-.

If an ɑ-machine prints two...

If an ɑ-machine prints two kinds of symbols, of which the first kind (called figures) consists entirely of 0 and 1 (the others being called symbols of the second kind), then the machine will be called a computing machine.

It will be useful to...

It will be useful to put... tables into a... standard form. ...The lines of the table are... of formm-config. | Symbol | Operations | Final m-config. In this way we obtain a complete description of the machine. ...This new description of the machine may be called the standard description (S.D). ...[W]e shall have a description of the machine in the form of an arabic numeral. The integer represented by this numeral may be called a description number (D.N) of the machine. The D.N determine the S.D and the structure of the machine uniquely. The machine whose D.N is n may be described as \mathcal{M}(n).

To each computable sequence there...

To each computable sequence there corresponds at least one description number, while to no description number does there correspond more than one computable sequence. The computable sequences and numbers are therefore enumerable.

It is possible to invent...

It is possible to invent a single machine which can be used to compute any computable sequence. If this machine \mathcal{U} is supplied with a tape on the beginning of which is written the S.D of some computing machine \mathcal{M}, then \mathcal{U} will compute the same sequence as \mathcal{M}.

"Can machines think?"... The new...

"Can machines think?"... The new form of the problem can be described in terms of a game which we call the 'imitation game." It is played with three people, a man (A), a woman (B), and an interrogator (C) who may be of either sex. The interrogator stays in a room apart from the other two. The object of the game for the interrogator is to determine which of the other two is the man and which is the woman. He knows them by labels X and Y, and at the end of the game he says either "X is A and Y is B" or "X is B and Y is A." The interrogator is allowed to put questions to A and B... We now ask the question, "What will happen when a machine takes the part of A in this game?" Will the interrogator decide wrongly as often when the game is played like this as he does when the game is played between a man and a woman? These questions replace our original, "Can machines think?"

We do not wish to...

We do not wish to penalise the machine for its inability to shine in beauty competitions, nor to penalise a man for losing in a race against an aeroplane. The conditions of our game make these disabilities irrelevant.

May not machines carry out...

May not machines carry out something which ought to be described as thinking but which is very different from what a man does?

We are not asking whether...

We are not asking whether all digital computers would do well in the game nor whether the computers at present available would do well, but whether there are imaginable computers which would do well.

The idea behind digital computers...

The idea behind digital computers may be explained by saying that these machines are intended to carry out any operations which could be done by a human computer.

A digital computer can usually...

A digital computer can usually be regarded as consisting of three parts: (i) Store. (ii) Executive unit. (iii) Control. ...The executive unit is the part which carries out the various individual operations involved in a calculation. ...It is the duty of the control to see that...[the table of] instructions are obeyed correctly and in the right order. ...A typical instruction might say—"Add the number stored in position 6809 to that in 4302 and put the result back into the latter storage position." Needless to say it would not occur in the machine expressed in English. It would more likely be coded in a form such as 6809430217. Here 17 says which of various possible operations [add] is to be performed on the two numbers. ...It will be noticed that the instruction takes up 10 digits and so forms one packet of information...

Suppose Mother wants Tommy to...

Suppose Mother wants Tommy to call at the cobbler's every morning on his way to school to see if her shoes are done, she can ask him afresh every morning. Alternatively she can stick up a notice once and for all in the hall which he will see when he leaves for school and which tells him to call for the shoes, and also to destroy the notice when he comes back if he has the shoes with him.

If one wants to make...

If one wants to make a machine mimic the behaviour of the human computer in some complex operation one has to ask him how it is done, and then translate the answer into the form of an instruction table. Constructing instruction tables is usually described as "programming."

I believe that at the...

I believe that at the end of the century the use of words and general educated opinion will have altered so much that one will be able to speak of machines thinking without expecting to be contradicted.

I am not very impressed...

I am not very impressed with theological arguments whatever they may be used to support. Such arguments have often been found unsatisfactory in the past. In the time of Galileo it was argued that the texts, "And the sun stood still... and hasted not to go down about a whole day" (Joshua x. 13) and "He laid the foundations of the earth, that it should not move at any time" (Psalm cv. 5) were an adequate refutation of the Copernican theory.

Machines take me by surprise...

Machines take me by surprise with great frequency.

Here’s the thing. Alan Turing...

Here’s the thing. Alan Turing never got to stand on a stage like this and look out at all of these disconcertingly attractive faces. I do. And that’s the most unfair thing I’ve ever heard. So in this brief time here, what I wanted to do was say this: When I was 16-years-old, I tried to kill myself because I felt weird and I felt different, and I felt like I did not belong. And now I’m standing here — and so I would like this moment to be for this kid out there who feels like she’s weird or she’s different or she doesn’t fit in anywhere: Yes, you do. I promise you do. Stay weird, stay different — and then, when it’s your turn, and you are standing on this stage, please pass the same message to the next person who comes along.

I’m not gay, but I...

I’m not gay, but I don’t think you have to be gay to have a gay hero. Growing up, Alan Turing was certainly mine. … I’m also not the greatest mathematician of my generation. We have lots of biographical differences, but nonetheless I always identified with him so much.

His high-pitched voice already stood...

His high-pitched voice already stood out above the general murmur of well-behaved junior executives grooming themselves for promotion within the Bell corporation. Then he was suddenly heard to say: "No, I'm not interested in developing a powerful brain. All I'm after is just a mediocre brain, something like the President of the American Telephone and Telegraph Company."

He wondered what one might...

He wondered what one might ask in a structured conversation to decide if one's interlocutor was a human being or a computer. ...but the ultimate Turing test might be to pose the question "How would a guilt-stricken homosexual commit suicide?" Would a computer ever conceive of eating an apple laced with cyanide?

Although a mathematician, Turing took...

Although a mathematician, Turing took quite an interest in the engineering side of computer design. There was some discussion in 1947 as to whether a cheaper substance than mercury could not be found for use as an ultrasonic delay medium. Turing's contribution to this discussion was to advocate the use of gin, which he said contained alcohol and water in just the right proportions to give a zero temperature coefficient of propagation velocity at room temperature.

Turing had a strong predeliction...

Turing had a strong predeliction for working things out from first principles, usually in the first instance without consulting any previous work on the subject, and no doubt it was this habit which gave his work that characteristically original flavor. I was reminded of a remark which Beethoven is reputed to have made when he was asked if he had heard a certain work of Mozart which was attracting much attention. He replied that he had not, and added "neither shall I do so, lest I forfeit some of my own originality."

He was particularly fond of...

He was particularly fond of little programming tricks (some people would say that he was too fond of them to be a "good" programmer) and would chuckle with boyish good humor at any little tricks I may have used.

The Imitation Game

The Imitation Game

[http://www.time.com/time/time100/scientist/profile/turing.html Time 100: Alan Turing]

[http://www.time.com/time/time100/scientist/profile/turing.html Time 100: Alan Turing]

[http://plato.stanford.edu/entries/turing/ Stanford Encyclopedia of Philosophy...

[http://plato.stanford.edu/entries/turing/ Stanford Encyclopedia of Philosophy entry]

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Turing.html Profile at the University...

[http://www-history.mcs.st-andrews.ac.uk/Biographies/Turing.html Profile at the University of St. Andrews]

[http://www.turing.org.uk/bio/part1.html Profile at Turing.org]

[http://www.turing.org.uk/bio/part1.html Profile at Turing.org]