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Alan Turing

39 quotes

“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.”
Alan Turing (1912–1954) first seen 1938 wikiquote, CC BY-SA 4.0 source
Recorded in: Systems of Logic Based on Ordinals," section 11: The purpose of ordinal logics (1938), published in Proceedings of the London Mathematical Society, series 2, vol. 45 (1939)
“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.”
Alan Turing (1912–1954) first seen 1946 wikiquote, CC BY-SA 4.0 source
Recorded in: Proposed Electronic Calculator" (1946), a report for National Physical Laboratory, Teddington; published in A. M. Turing's ACE Report of 1946 and Other Papers (1986), edited by B. E. Carpenter and R. W. Doran, and in Th…
“A man provided with paper, pencil, and rubber, and subject to strict discipline, is in effect a universal machine.”
Alan Turing (1912–1954) first seen 1948 wikiquote, CC BY-SA 4.0 source
Recorded in: Intelligent Machinery: A Report by A. M. Turing," (Summer 1948), submitted to the National Physical Laboratory (1948) and published in Key Papers: Cybernetics, ed. C. R. Evans and A. D. J. Robertson (1968) and, in varia…
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) first seen 1949 wikiquote, CC BY-SA 4.0 source
Recorded in: 'The Mechanical Brain. Answer Found to 300 Year Old Problem' The Times newspaper, 11 June 1949 page 4 column 5.
“Science is a differential equation. Religion is a boundary condition.”
Alan Turing (1912–1954) first seen 1954 wikiquote, CC BY-SA 4.0 source
Recorded in: Epigram to Robin Gandy (1954); reprinted in Andrew Hodges, Alan Turing: the Enigma (Vintage edition 1992), p. 513.
“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.”
Alan Turing (1912–1954) first seen 1954 wikiquote, CC BY-SA 4.0 source
Recorded in: Epigram to Robin Gandy (1954).
“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 ".”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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".”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“The machine may also change the square which is being scanned, but only by shifting it one place to right or left.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“[T]he m-configuration may be changed.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“[T]hese operations include all those which are used in the computation...”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“In this paper I deal only with automatic machines, and will therefore often omit the prefix ɑ-.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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}.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“May not machines carry out something which ought to be described as thinking but which is very different from what a man does?”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“Machines take me by surprise with great frequency.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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. A natural consequence of doing so is that one then assumes that there is no virtue in the mere working out of consequences from data and general principles.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“Presumably the child-brain is something like a note-book as one buys it from the stationer's. Rather little mechanism, and lots of blank sheets.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“We can only see a short distance ahead, but we can see plenty there that needs to be done.”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“It is customary... to offer a grain of comfort, in the form of a statement that some peculiarly human characteristic could never be imitated by a machine. ... I cannot offer any such comfort, for I believe that no such bounds can be set.”
Alan Turing (1912–1954) first seen 1951 wikiquote, CC BY-SA 4.0 source
Recorded in: 'Can digital computers think?'. Talk broadcast on BBC Third Programme, 15 May 1951.
“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”.”
Alan Turing (1912–1954) first seen 1951 wikiquote, CC BY-SA 4.0 source
Recorded in: Intelligent Machinery, A Heretical Theory" (1951), from a BBC radio discussion programme, The ’51 Society.
“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...”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“It will be useful to put... tables into a... standard form. ...The lines of the table are... of form m-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).”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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?”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“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...”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source
“Another simile would be an atomic pile of less than critical size: an injected idea is to correspond to a neutron entering the pile from without. Each such neutron will cause a certain disturbance which eventually dies away. If, however, the size of the pile is sufficiently increased, the disturbance caused by such an incoming neutron will very likely go on and on increasing until the whole pile is destroyed. Is there a corresponding phenomenon for minds, and is there one for machines? There does seem to be one for the human mind. The majority of them seem to be "sub-critical," i.e., to correspond in this analogy to piles of sub-critical size. An idea presented to such a mind will on average give rise to less than one idea in reply. A smallish proportion are super-critical. An idea presented to such a mind may give rise to a whole "theory" consisting of secondary, tertiary and more remote ideas. Animals minds seem to be very definitely sub-critical. Adhering to this analogy we ask, "Can a machine be made to be super-critical?”
Alan Turing (1912–1954) said by 1954 at the latest wikiquote, CC BY-SA 4.0 source