{"id":30765121,"url":"https://github.com/ianchanning/turing-test-paper","last_synced_at":"2026-02-11T22:11:06.833Z","repository":{"id":305961419,"uuid":"1024519543","full_name":"ianchanning/turing-test-paper","owner":"ianchanning","description":"A faithful LaTeX recreation of Alan Turing's 'Computing Machinery and Intelligence' (Mind, 1950).","archived":false,"fork":false,"pushed_at":"2025-08-11T13:24:59.000Z","size":1388,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":0,"default_branch":"main","last_synced_at":"2025-09-04T17:58:30.105Z","etag":null,"topics":["1949","alan-turing","computer-science","history","papers","turing-test"],"latest_commit_sha":null,"homepage":"https://ianchanning.com/turing-test-paper/","language":"TeX","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/ianchanning.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null,"publiccode":null,"codemeta":null,"zenodo":null}},"created_at":"2025-07-22T20:38:57.000Z","updated_at":"2025-08-11T13:25:02.000Z","dependencies_parsed_at":"2025-08-10T22:20:31.058Z","dependency_job_id":"0da4afaf-6730-4130-a8c5-2ed6a5ad62e3","html_url":"https://github.com/ianchanning/turing-test-paper","commit_stats":null,"previous_names":["ianchanning/turing-mind-origin-1950","ianchanning/turing-test-paper"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/ianchanning/turing-test-paper","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ianchanning%2Fturing-test-paper","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ianchanning%2Fturing-test-paper/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ianchanning%2Fturing-test-paper/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ianchanning%2Fturing-test-paper/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/ianchanning","download_url":"https://codeload.github.com/ianchanning/turing-test-paper/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/ianchanning%2Fturing-test-paper/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":29186736,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-02-07T03:35:06.566Z","status":"ssl_error","status_checked_at":"2026-02-07T03:34:57.604Z","response_time":63,"last_error":"SSL_read: unexpected eof while reading","robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":false,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["1949","alan-turing","computer-science","history","papers","turing-test"],"created_at":"2025-09-04T17:55:42.224Z","updated_at":"2026-02-07T04:32:14.658Z","avatar_url":"https://github.com/ianchanning.png","language":"TeX","funding_links":[],"categories":[],"sub_categories":[],"readme":"A faithful LaTeX recreation of Alan Turing's 'Computing Machinery and Intelligence' (Mind, 1950).\n\n[PDF](./alan_turing_mind_1950.pdf) | [LaTeX](./alan_turing_mind_1950.tex) | [Text](./alan_turing_mind_1950.txt)\n\n# MIND\n\n#### A QUARTERLY REVIEW\n\n##### OF\n\n#### PSYCHOLOGY AND PHILOSOPHY\n\n---\n\n### I.—COMPUTING MACHINERY AND INTELLIGENCE\n\n**BY A. M. TURING**\n\n##### 1. _The Imitation Game._\n\nI **PROPOSE** to consider the question, 'Can machines think?'\nThis should begin with definitions of the meaning of the terms 'machine'\nand 'think'. The definitions might be framed so as to reflect so far as\npossible the normal use of the words, but this attitude is dangerous. If\nthe meaning of the words 'machine' and 'think' are to be found by\nexamining how they are commonly used it is difficult to escape the\nconclusion that the meaning and the answer to the question, 'Can\nmachines think?' is to be sought in a statistical survey such as a\nGallup poll. But this is absurd. Instead of attempting such a definition\nI shall replace the question by another, which is closely related to it\nand is expressed in relatively unambiguous words.\n\nThe new form of the problem can be described in terms of a game which we\ncall the 'imitation game'. It is played with three people, a man (A), a\nwoman (B), and an interrogator (C) who may be of either sex. The\ninterrogator stays in a room apart from the other two. The object of the\ngame for the interrogator is to determine which of the other two is the\nman and which is the woman. He knows them by labels X and Y, and at the\nend of the game he says either 'X is A and Y is B' or 'X is B and Y is\nA'. The interrogator is allowed to put questions to A and B thus:\n\n**C**: Will X please tell me the length of his or her hair ?\n\nNow suppose X is actually A, then A must answer. It is A's\n\nobject in the game to try and cause C to make the wrong identification.\nHis answer might therefore be \"My hair is shingled, and the longest\nstrands are about nine inches long.\"\n\nIn order that tones of voice may not help the interrogator the answers\nshould be written, or better still, typewritten. The ideal arrangement\nis to have a teleprinter communicating between the two rooms.\nAlternatively the question and answers can be repeated by an\nintermediary. The object of the game for the third player (B) is to help\nthe interrogator. The best strategy for her is probably to give truthful\nanswers. She can add such things as \"I am the woman, don't listen to\nhim!\" to her answers, but it will avail nothing as the man can make\nsimilar remarks.\n\nWe now ask the question, 'What will happen when a machine takes the part\nof A in this game?' Will the interrogator decide wrongly as often when\nthe game is played like this as he does when the game is played between\na man and a woman? These questions replace our original, 'Can machines\nthink?'\n\n##### 2. _Critique of the New Problem._\n\nAs well as asking, 'What is the answer to this new form of the\nquestion,' one may ask, 'Is this new question a worthy one to\ninvestigate?' This latter question we investigate without further ado,\nthereby cutting short an infinite regress.\n\nThe new problem has the advantage of drawing a fairly sharp line between\nthe physical and the intellectual capacities of a man. No engineer or\nchemist claims to be able to produce a material which is\nindistinguishable from the human skin. It is possible that at some time\nthis might be done, but even supposing this invention available we\nshould feel there was little point in trying to make a 'thinking\nmachine' more human by dressing it up in such artificial flesh. The form\nin which we have set the problem reflects this fact in the condition\nwhich prevents the interrogator from seeing or touching the other\ncompetitors, or hearing their voices. Some other advantages of the\nproposed criterion may be shown up by specimen questions and answers.\nThus:\n\n**Q**: Please write me a sonnet on the subject of the Forth Bridge.\n\n**A**: Count me out on this one. I never could write poetry.\n\n**Q**: Add 34957 to 70764\n\n**A**: (Pause about 30 seconds and then give as answer) 105621.\n\n**Q**: Do you play chess ?\n\n**A**: Yes.\n\n**Q**: I have K at my K1, and no other pieces. You have only K at K6 and R\nat R1. It is your move. What do you play ?\n\n**A**: (After a pause of 15 seconds) R-R8 mate.\n\nThe question and answer method seems to be suitable for introducing\nalmost any one of the fields of human endeavour that we wish to include.\nWe do not wish to penalise the machine for its inability to shine in\nbeauty competitions, nor to penalise a man for losing in a race against\nan aeroplane. The conditions of our game make these disabilities\nirrelevant. The 'witnesses' can brag, if they consider it advisable, as\nmuch as they please about their charms, strength or heroism, but the\ninterrogator cannot demand practical demonstrations.\n\nThe game may perhaps be criticised on the ground that the odds are\nweighted too heavily against the machine. If the man were to try and\npretend to be the machine he would clearly make a very poor showing. He\nwould be given away at once by slowness and inaccuracy in arithmetic.\nMay not machines carry out some-thing which ought to be described as\nthinking but which is very different from what a man does? This\nobjection is a very strong one, but at least we can say that if,\nnevertheless, a machine can be constructed to play the imitation game\nsatisfactorily, we need not be troubled by this objection.\n\nIt might be urged that when playing the 'imitation game' the best\nstrategy for the machine may possibly be something other than imitation\nof the behaviour of a man. This may be, but I think it is unlikely that\nthere is any great effect of this kind. In any case there is no\nintention to investigate here the theory of the game, and it will be\nassumed that the best strategy is to try to provide answers that would\nnaturally be given by a man.\n\n##### 3. _The Machines concerned in the Game._\n\nThe question which we put in §1 will not be quite definite until we have\nspecified what we mean by the word 'machine'. It is natural that we\nshould wish to permit every kind of engineering technique to be used in\nour machines. We also wish to allow the possibility than an engineer or\nteam of engineers may construct a machine which works, but whose manner\nof operation cannot be satisfactorily described by its constructors\nbecause they have applied a method which is largely experimental.\nFinally, we wish to exclude from the machines men born in the usual\nmanner. It is difficult to frame the definitions so as to satisfy these\nthree conditions. One might for instance insist that the team of\nengineers should be all of one sex, but this would not really be\nsatisfactory, for it is probably possible to rear a complete individual\nfrom a single cell of the skin (say) of a man. To do so would be a feat\nof biological technique deserving of the very highest praise, but we\nwould not be inclined to regard it as a case of 'constructing a thinking\nmachine'. This prompts us to abandon the requirement that every kind of\ntechnique should be permitted. We are the more ready to do so in view of\nthe fact that the present interest in 'thinking machines' has been\naroused by a particular kind of machine, usually called an 'electronic\ncomputer' or 'digital computer'. Following this suggestion we only\npermit digital computers to take part in our game.\n\nThis restriction appears at first sight to be a very drastic one. I\nshall attempt to show that it is not so in reality. To do this\nnecessitates a short account of the nature and properties of these\ncomputers.\n\nIt may also be said that this identification of machines with digital\ncomputers, like our criterion for 'thinking', will only be\nunsatisfactory if (contrary to my belief), it turns out that digital\ncomputers are unable to give a good showing in the game.\n\nThere are already a number of digital computers in working order, and it\nmay be asked, 'Why not try the experiment straight away? It would be\neasy to satisfy the conditions of the game. A number of interrogators\ncould be used, and statistics compiled to show how often the right\nidentification was given.' The short answer is that we are not asking\nwhether all digital computers would do well in the game nor whether the\ncomputers at present available would do well, but whether there are\nimaginable computers which would do well. But this is only the short\nanswer. We shall see this question in a different light later.\n\n##### 4. _Digital Computers._\n\nThe idea behind digital computers may be explained by saying that these\nmachines are intended to carry out any operations which could be done by\na human computer. The human computer is supposed to be following fixed\nrules; he has no authority to deviate from them in any detail. We may\nsuppose that these rules are supplied in a book, which is altered\nwhenever he is put on to a new job. He has also an unlimited supply of\npaper on which he does his calculations. He may also do his\nmultiplications and additions on a 'desk machine', but this is not\nimportant. If we use the above explanation as a definition we shall be\nin danger of circularity of argument. We avoid this by giving an outline\nof the means by which the desired effect is achieved. A digital computer\ncan usually be regarded as consisting of three parts:\n\n1.  Store.\n\n2.  Executive unit.\n\n3.  Control.\n\nThe store is a store of information, and corresponds to the human\ncomputer's paper, whether this is the paper on which he does his\ncalculations or that on which his book of rules is printed. In so far as\nthe human computer does calculations in his head a part of the store\nwill correspond to his memory. The executive unit is the part which\ncarries out the various individual operations involved in a calculation.\nWhat these individual operations are will vary from machine to machine.\nUsually fairly lengthy operations can be done such as 'Multiply\n3540675445 by 7076345687' but in some machines only very simple ones\nsuch as 'Write down 0' are possible. We have mentioned that the 'book of\nrules' supplied to the computer is replaced in the machine by a part of\nthe store. It is then called the 'table of instructions'. It is the duty\nof the control to see that these instructions are obeyed correctly and\nin the right order. The control is so constructed that this necessarily\nhappens. The information in the store is usually broken up into packets\nof moderately small size. In one machine, for instance, a packet might\nconsist of ten decimal digits. Numbers are assigned to the parts of the\nstore in which the various packets of information are stored, in some\nsystematic manner. A typical instruction might say- \"Add the number\nstored in position 6809 to that in 4302 and put the result back into the\nlatter storage position.\"\n\nNeedless to say it would not occur in the machine expressed in English.\nIt would more likely be coded in a form such as 6809430217. Here 17 says\nwhich of various possible operations is to be performed on the two\nnumbers. In this case the operation is that described above, viz. \"Add\nthe number\\....\" It will be noticed that the instruction takes up 10\ndigits and so forms one packet of information, very conveniently. The\ncontrol will normally take the instructions to be obeyed in the order of\nthe positions in which they are stored, but occasionally an instruction\nsuch as\n\n\"Now obey the instruction stored in position 5606, and continue from\nthere.\"\n\nmay be encountered, or again \"If position 4505 contains 0 obey next the\ninstruction stored in 6707, otherwise continue straight on.\"\n\nInstructions of these latter types are very important because they make\nit possible for a sequence of operations to be repeated over and over\nagain until some condition is fulfilled, but in doing so to obey, not\nfresh instructions on each repetition, but the same ones over and over\nagain. To take a domestic analogy. Suppose Mother wants Tommy to call at\nthe cobbler's every morning on his way to school to see if her shoes are\ndone, she can ask him afresh every morning. Alternatively she can stick\nup a notice once and for all in the hall which he will see when he\nleaves for school and which tells him to call for the shoes, and also to\ndestroy the notice when he comes back if he has the shoes with him.\n\nThe reader must accept it as a fact that digital computers can be\nconstructed, and indeed have been constructed, according to the\nprinciples we have described, and that they can in fact mimic the\nactions of a human computer very closely.\n\nThe book of rules which we have described our human computer as using is\nof course a convenient fiction. Actual human computers really remember\nwhat they have got to do. If one wants to make a machine mimic the\nbehaviour of the human computer in some complex operation one has to ask\nhim how it is done, and then translate the answer into the form of an\ninstruction table. Constructing instruction tables is usually described\nas 'programming'. To 'programme a machine to carry out the operation A'\nmeans to put the appropriate instruction table into the machine so that\nit will do A.\n\nAn interesting variant on the idea of a digital computer is a 'digital\ncomputer with a random element'. These have instructions involving the\nthrowing of a die or some equivalent electronic process; one such\ninstruction might for instance be, \"Throw the die and put the resulting\nnumber into store 1000\".' Sometimes such a machine is described as\nhaving free will (though I would not use this phrase myself). It is not\nnormally possible to determine from observing a machine whether it has a\nrandom element, for a similar effect can be produced by such devices as\nmaking the choices depend on the digits of the decimal for $\\pi$.\n\nMost actual digital computers have only a finite store. There is no\ntheoretical difficulty in the idea of a computer with an unlimited\nstore. Of course only a finite part can have been used at any one time.\nLikewise only a finite amount can have been constructed, but we can\nimagine more and more being added as required. Such computers have\nspecial theoretical interest and will be called infinitive capacity\ncomputers.\n\nThe idea of a digital computer is an old one. Charles Babbage, Lucasian\nProfessor of Mathematics at Cambridge from 1828 to 1839, planned such a\nmachine, called the Analytical Engine, but it was never completed.\nAlthough Babbage had all the essential ideas, his machine was not at\nthat time such a very attractive prospect. The speed which would have\nbeen available would be definitely faster than a human computer but\nsomething like 100 times slower than the Manchester machine, itself one\nof the slower of the modern machines. The storage was to be purely\nmechanical, using wheels and cards.\n\nThe fact that Babbage's Analytical Engine was to be entirely mechanical\nwill help us to rid ourselves of a superstition. Importance is often\nattached to the fact that modern digital computers are electrical, and\nthat the nervous system also is electrical. Since Babbage's machine was\nnot electrical, and since all digital computers are in a sense\nequivalent, we see that this use of electricity cannot be of theoretical\nimportance. Of course electricity usually comes in where fast signalling\nis concerned, so that it is not surprising that we find it in both these\nconnections. In the nervous system chemical phenomena are at least as\nimportant as electrical. In certain computers the storage system is\nmainly acoustic. The feature of using electricity is thus seen to be\nonly a very superficial similarity. If we wish to find such similarities\nwe should look rather for mathematical analogies of function.\n\n##### 5. _Universality of Digital Computers._\n\nThe digital computers considered in the last section may be classified\namongst the 'discrete state machines'. These are the machines which move\nby sudden jumps or clicks from one quite definite state to another.\nThese states are sufficiently different for the possibility of confusion\nbetween them to be ignored. Strictly speaking there are no such\nmachines. Everything really moves continuously. But there are many kinds\nof machine which can profitably be thought of as being discrete state\nmachines. For instance in considering the switches for a lighting system\nit is a convenient fiction that each switch must be definitely on or\ndefinitely off. There must be intermediate positions, but for most\npurposes we can forget about them. As an example of a discrete state\nmachine we might consider a wheel which clicks round through 120 once a\nsecond, but may be stopped by a lever which can be operated from\noutside; in addition a lamp is to light in one of the positions of the\nwheel. This machine could be described abstractly as follows. The\ninternal state of the machine (which is described by the position of the\nwheel) may be $q_1$, $q_2$ or $q_3$. There is an input signal $i_0$, or\n$i_1$ (position of lever). The internal state at any moment is\ndetermined by the last state and input signal according to the table\n\n|           |       |       |       |                |\n| --------- | ----- | ----- | ----- | -------------- |\n|           |       |       |       | **Last State** |\n|           |       | $q_1$ | $q_2$ | $q_3$          |\n| **Input** | $i_0$ | $q_2$ | $q_3$ | $q_1$          |\n|           | $i_1$ | $q_1$ | $q_2$ | $q_3$          |\n\nThe output signals, the only externally visible indication of the\ninternal state (the light) are described by the table\n\n|            |       |       |       |\n| ---------- | ----- | ----- | ----- |\n| **State**  | $q_1$ | $q_2$ | $q_3$ |\n| **Output** | $o_0$ | $o_0$ | $o_1$ |\n\nThis example is typical of discrete state machines. They can be\ndescribed by such tables provided they have only a finite number of\npossible states.\n\nIt will seem that given the initial state of the machine and the input\nsignals it is always possible to predict all future states. This is\nreminiscent of Laplace's view that from the complete state of the\nuniverse at one moment of time, as described by the positions and\nvelocities of all particles, it should be possible to predict all future\nstates. The prediction which we are considering is, however, rather\nnearer to practicability than that considered by Laplace. The system of\nthe 'universe as a whole'' is such that quite small errors in the\ninitial conditions can have an overwhelming effect at a later time. The\ndisplacement of a single electron by a billionth of a centimetre at one\nmoment might make the difference between a man being killed by an\navalanche a year later, or escaping. It is an essential property of the\nmechanical systems which we have called 'discrete state machines'' that\nthis phenomenon does not occur. Even when we consider the actual\nphysical machines instead of the idealised machines, reasonably accurate\nknowledge of the state at one moment yields reasonably accurate\nknowledge any number of steps later.\n\nAs we have mentioned, digital computers fall within the class of\ndiscrete state machines. But the number of states of which such a\nmachine is capable is usually enormously large. For instance, the number\nfor the machine now working at Manchester is about $2^{165,000}$,\ni.e. about $10^{50,000}$. Compare this with our example of the clicking\nwheel described above, which had three states. It is not difficult to\nsee why the number of states should be so immense. The computer includes\na store corresponding to the paper used by a human computer. It must be\npossible to write into the store any one of the combinations of symbols\nwhich might have been written on the paper. For simplicity suppose that\nonly digits from 0 to 9 are used as symbols. Variations in handwriting\nare ignored. Suppose the computer is allowed 100 sheets of paper each\ncontaining 50 lines each with room for 30 digits. Then the number of\nstates is $10^{100 \\times 50 \\times 30}$, i.e. $10^{150,000}$. This is\nabout the number of states of three Manchester machines put together.\nThe logarithm to the base two of the number of states is usually called\nthe 'storage capacity' of the machine. Thus the Manchester machine has a\nstorage capacity of about 165,000 and the wheel machine of our example\nabout 1.6. If two machines are put together their capacities must be\nadded to obtain the capacity of the resultant machine. This leads to the\npossibility of statements such as \"The Manchester machine contains 64\nmagnetic tracks each with a capacity of 2560, eight electronic tubes\nwith a capacity of 1280. Miscellaneous storage amounts to about 300\nmaking a total of 174,380.\"\n\nGiven the table corresponding to a discrete state machine it is possible\nto predict what it will do. There is no reason why this calculation\nshould not be carried out by means of a digital computer. Provided it\ncould be carried out sufficiently quickly the digital computer could\nmimic the behaviour of any discrete state machine. The imitation game\ncould then be played with the machine in question (as B) and the\nmimicking digital computer (as A) and the interrogator would be unable\nto distinguish them. Of course the digital computer must have an\nadequate storage capacity as well as working sufficiently fast.\nMoreover, it must be programmed afresh for each new machine which it is\ndesired to mimic.\n\nThis special property of digital computers, that they can mimic any\ndiscrete state machine, is described by saying that they are universal\nmachines. The existence of machines with this property has the important\nconsequence that, considerations of speed apart, it is unnecessary to\ndesign various new machines to do various computing processes. They can\nall be done with one digital computer, suitably programmed for each\ncase. It will be seen that as a consequence of this all digital\ncomputers are in a sense equivalent.\n\nWe may now consider again the point raised at the end of §3. It was\nsuggested tentatively that the question, 'Can machines think?' should be\nreplaced by 'Are there imaginable digital computers which would do well\nin the imitation game?' If we wish we can make this superficially more\ngeneral and ask 'Are there discrete state machines which would do well?'\nBut in view of the universality property we see that either of these\nquestions is equivalent to this, 'Let us fix our attention on one\nparticular digital computer C. Is it true that by modifying this\ncomputer to have an adequate storage, suitably increasing its speed of\naction, and providing it with an appropriate programme, C can be made to\nplay satisfactorily the part of A in the imitation game, the part of B\nbeing taken by a man?'\n\n##### 6. _Contrary Views on the Main Question._\n\nWe may now consider the ground to have been cleared and we are ready to\nproceed to the debate on our question, 'Can machines think?' and the\nvariant of it quoted at the end of the last section. We cannot\naltogether abandon the original form of the problem, for opinions will\ndiffer as to the appropriateness of the substitution and we must at\nleast listen to what has to be said in this connexion.\n\nIt will simplify matters for the reader if I explain first my own\nbeliefs in the matter. Consider first the more accurate form of the\nquestion. I believe that in about fifty years' time it will be possible\nto programme computers, with a storage capacity of about $10^9$, to make\nthem play the imitation game so well that an average interrogator will\nnot have more than 70 per cent. chance of making the right\nidentification after five minutes of questioning. The original question,\n'Can machines think?' I believe to be too meaningless to deserve\ndiscussion. Nevertheless I believe that at the end of the century the\nuse of words and general educated opinion will have altered so much that\none will be able to speak of machines thinking without expecting to be\ncontradicted. I believe further that no useful purpose is served by\nconcealing these beliefs. The popular view that scientists proceed\ninexorably from well-established fact to well-established fact, never\nbeing influenced by any unproved conjecture, is quite mistaken. Provided\nit is made clear which are proved facts and which are conjectures, no\nharm can result. Conjectures are of great importance since they suggest\nuseful lines of research.\n\nI now proceed to consider opinions opposed to my own.\n\n\\(1\\) _The Theological Objection._ Thinking is a function of man's\nimmortal soul.[^1] God has given an immortal soul to every man and\nwoman, but not to any other animal or to machines. Hence no animal or\nmachine can think.\n\nI am unable to accept any part of this, but will attempt to reply in\ntheological terms. I should find the argument more convincing if animals\nwere classed with men, for there is a greater difference, to my mind,\nbetween the typical animate and the inanimate than there is between man\nand the other animals. The arbitrary character of the orthodox view\nbecomes clearer if we consider how it might appear to a member of some\nother religious community. How do Christians regard the Moslem view that\nwomen have no souls? But let us leave this point aside and return to the\nmain argument. It appears to me that the argument quoted above implies a\nserious restriction of the omnipotence of the Almighty. It is admitted\nthat there are certain things that He cannot do such as making one equal\nto two, but should we not believe that He has freedom to confer a soul\non an elephant if He sees fit? We might expect that He would only\nexercise this power in conjunction with a mutation which provided the\nelephant with an appropriately improved brain to minister to the needs\nof this soul. An argument of exactly similar form may be made for the\ncase of machines. It may seem different because it is more difficult to\n\"swallow\". But this really only means that we think it would be less\nlikely that He would consider the circumstances suitable for conferring\na soul. The circumstances in question are discussed in the rest of this\npaper. In attempting to construct such machines we should not be\nirreverently usurping His power of creating souls, any more than we are\nin the procreation of children: rather we are, in either case,\ninstruments of His will providing mansions for the souls that He\ncreates.\n\nHowever, this is mere speculation. I am not very impressed with\ntheological arguments whatever they may be used to support. Such\narguments have often been found unsatisfactory in the past. In the time\nof Galileo it was argued that the texts, \"And the sun stood still... and\nhasted not to go down about a whole day\" (Joshua x. 13) and \"He laid the\nfoundations of the earth, that it should not move at any time\" (Psalm\ncv. 5) were an adequate refutation of the Copernican theory. With our\npresent knowledge such an argument appears futile. When that knowledge\nwas not available it made a quite different impression.\n\n\\(2\\) _The 'Heads in the Sand' Objection._ \"The consequences of machines\nthinking would be too dreadful. Let us hope and believe that they cannot\ndo so.\"\n\nThis argument is seldom expressed quite so openly as in the form above.\nBut it affects most of us who think about it at all. We like to believe\nthat Man is in some subtle way superior to the rest of creation. It is\nbest if he can be shown to be necessarily superior, for then there is no\ndanger of him losing his commanding position. The popularity of the\ntheological argument is clearly connected with this feeling. It is\nlikely to be quite strong in intellectual people, since they value the\npower of thinking more highly than others, and are more inclined to base\ntheir belief in the superiority of Man on this power.\n\nI do not think that this argument is sufficiently substantial to require\nrefutation. Consolation would be more appropriate: perhaps this should\nbe sought in the transmigration of souls.\n\n\\(3\\) _The Mathematical Objection._ There are a number of results of\nmathematical logic which can be used to show that there are limitations\nto the powers of discrete-state machines. The best known of these\nresults is known as _Gödel_'s theorem,[^2] and shows that in any\nsufficiently powerful logical system statements can be formulated which\ncan neither be proved nor disproved within the system, unless possibly\nthe system itself is inconsistent. There are other, in some respects\nsimilar, results due to _Church_, _Kleene_, _Rosser_, and _Turing_. The\nlatter result is the most convenient to consider, since it refers\ndirectly to machines, whereas the others can only be used in a\ncomparatively indirect argument: for instance if _Gödel_'s theorem is to\nbe used we need in addition to have some means of describing logical\nsystems in terms of machines, and machines in terms of logical systems.\nThe result in question refers to a type of machine which is essentially\na digital computer with an infinite capacity. It states that there are\ncertain things that such a machine cannot do. If it is rigged up to give\nanswers to questions as in the imitation game, there will be some\nquestions to which it will either give a wrong answer, or fail to give\nan answer at all however much time is allowed for a reply. There may, of\ncourse, be many such questions, and questions which cannot be answered\nby one machine may be satisfactorily answered by another. We are of\ncourse supposing for the present that the questions are of the kind to\nwhich an answer 'Yes' or 'No' is appropriate, rather than questions such\nas 'What do you think of Picasso?' The questions that we know the\nmachines must fail on are of this type, \"Consider the machine specified\nas follows.... Will this machine ever answer 'Yes' to any question?\" The\ndots are to be replaced by a description of some machine in a standard\nform, which could be something like that used in §5. When the machine\ndescribed bears a certain comparatively simple relation to the machine\nwhich is under interrogation, it can be shown that the answer is either\nwrong or not forthcoming. This is the mathematical result: it is argued\nthat it proves a disability of machines to which the human intellect is\nnot subject.\n\nThe short answer to this argument is that although it is established\nthat there are limitations to the powers of any particular machine, it\nhas only been stated, without any sort of proof, that no such\nlimitations apply to the human intellect. But I do not think this view\ncan be dismissed quite so lightly. Whenever one of these machines is\nasked the appropriate critical question, and gives a definite answer, we\nknow that this answer must be wrong, and this gives us a certain feeling\nof superiority. Is this feeling illusory? It is no doubt quite genuine,\nbut I do not think too much importance should be attached to it. We too\noften give wrong answers to questions ourselves to be justified in being\nvery pleased at such evidence of fallibility on the part of the\nmachines. Further, our superiority can only be felt on such an occasion\nin relation to the one machine over which we have scored our petty\ntriumph. There would be no question of triumphing simultaneously over\nall machines. In short, then, there might be men cleverer than any given\nmachine, but then again there might be other machines cleverer again,\nand so on.\n\nThose who hold to the mathematical argument would, I think, mostly be\nwilling to accept the imitation game as a basis for discussion. Those\nwho believe in the two previous objections would probably not be\ninterested in any criteria.\n\n\\(4\\) _The Argument from Consciousness._ This argument is very well\nexpressed in Professor _Jefferson_'s Lister Oration for 1949, from which\nI quote. \"Not until a machine can write a sonnet or compose a concerto\nbecause of thoughts and emotions felt, and not by the chance fall of\nsymbols, could we agree that machine equals brainthat is, not only write\nit but know that it had written it. No mechanism could feel (and not\nmerely artificially signal, an easy contrivance) pleasure at its\nsuccesses, grief when its valves fuse, be warmed by flattery, be made\nmiserable by its mistakes, be charmed by sex, be angry or depressed when\nit cannot get what it wants.\"\n\nThis argument appears to be a denial of the validity of our test.\nAccording to the most extreme form of this view the only way by which\none could be sure that machine thinks is to be the machine and to feel\noneself thinking. One could then describe these feelings to the world,\nbut of course no one would be justified in taking any notice. Likewise\naccording to this view the only way to know that a man thinks is to be\nthat particular man. It is in fact the solipsist point of view. It may\nbe the most logical view to hold but it makes communication of ideas\ndifficult. A is liable to believe 'A thinks but B does not' whilst B\nbelieves 'B thinks but A does not'. Instead of arguing continually over\nthis point it is usual to have the polite convention that everyone\nthinks.\n\nI am sure that Professor _Jefferson_ does not wish to adopt the extreme\nand solipsist point of view. Probably he would be quite willing to\naccept the imitation game as a test. The game (with the player B\nomitted) is frequently used in practice under the name of _viva voce_ to\ndiscover whether some one really understands something or has 'learnt it\nparrot fashion'. Let us listen in to a part of such a _viva voce_:\n\nInterrogator: In the first line of your sonnet which reads 'Shall I\ncompare thee to a summer's day', would not 'a spring day' do as well or\nbetter?\n\n**Witness**: It wouldn't scan.\n\n**Interrogator**: How about 'a winter's day' That would scan all right.\n\n**Witness**: Yes, but nobody wants to be compared to a winter's day.\n\n**Interrogator**: Would you say Mr. Pickwick reminded you of Christmas?\n\n**Witness**: In a way.\n\n**Interrogator**: Yet Christmas is a winter's day, and I do not think Mr.\nPickwick would mind the comparison.\n\n**Witness**: I don't think you're serious. By a winter's day one means a\ntypical winter's day, rather than a special one like Christmas.\n\nAnd so on. What would Professor _Jefferson_ say if the sonnet-writing\nmachine was able to answer like this in the _viva voce_? I do not know\nwhether he would regard the machine as 'merely artificially signalling'\nthese answers, but if the answers were as satisfactory and sustained as\nin the above passage I do not think he would describe it as 'an easy\ncontrivance'. This phrase is, I think, intended to cover such devices as\nthe inclusion in the machine of a record of someone reading a sonnet,\nwith appropriate switching to turn it on from time to time.\n\nIn short then, I think that most of those who support the argument from\nconsciousness could be persuaded to abandon it rather than be forced\ninto the solipsist position. They will then probably be willing to\naccept our test.\n\nI do not wish to give the impression that I think there is no mystery\nabout consciousness. There is, for instance, something of a paradox\nconnected with any attempt to localise it. But I do not think these\nmysteries necessarily need to be solved before we can answer the\nquestion with which we are concerned in this paper.\n\n\\(5\\) _Arguments from Various Disabilities._ These arguments take the\nform, \"I grant you that you can make machines do all the things you have\nmentioned but you will never be able to make one to do X\". Numerous\nfeatures X are suggested in this connexion. I offer a selection:\n\n\u003e Be kind, resourceful, beautiful, friendly (p. 448), have initiative,\n\u003e have a sense of humour, tell right from wrong, make mistakes (p. 448),\n\u003e fall in love, enjoy strawberries and cream (p. 448), make some one\n\u003e fall in love with it, learn from experience (pp. 456 f.), use words\n\u003e properly, be the subject of its own thought (p. 449), have as much\n\u003e diversity of behaviour as a man, do something really new (p. 450).\n\u003e (Some of these disabilities are given special consideration as\n\u003e indicated by the page numbers.)\n\nNo support is usually offered for these statements. I believe they are\nmostly founded on the principle of scientific induction. A man has seen\nthousands of machines in his lifetime. From what he sees of them he\ndraws a number of general conclusions. They are ugly, each is designed\nfor a very limited purpose, when required for a minutely different\npurpose they are useless, the variety of behaviour of any one of them is\nvery small, etc., etc. Naturally he concludes that these are necessary\nproperties of machines in general. Many of these limitations are\nassociated with the very small storage capacity of most machines. (I am\nassuming that the idea of storage capacity is extended in some way to\ncover machines other than discrete-state machines. The exact definition\ndoes not matter as no mathematical accuracy is claimed in the present\ndiscussion.) A few years ago, when very little had been heard of digital\ncomputers, it was possible to elicit much incredulity concerning them,\nif one mentioned their properties without describing their construction.\nThat was presumably due to a similar application of the principle of\nscientific induction. These applications of the principle are of course\nlargely unconscious. When a burnt child fears the fire and shows that he\nfears it by avoiding it, I should say that he was applying scientific\ninduction. (I could of course also describe his behaviour in many other\nways.) The works and customs of mankind do not seem to be very suitable\nmaterial to which to apply scientific induction. A very large part of\nspace-time must be investigated, if reliable results are to be obtained.\nOtherwise we may (as most English Children do) decide that everybody\nspeaks English, and that it is silly to learn French.\n\nThere are, however, special remarks to be made about many of the\ndisabilities that have been mentioned. The inability to enjoy\nstrawberries and cream may have struck the reader as frivolous. Possibly\na machine might be made to enjoy this delicious dish, but any attempt to\nmake one do so would be idiotic. What is important about this disability\nis that it contributes to some of the other disabilities, e.g. to the\ndifficulty of the same kind of friendliness occurring between man and\nmachine as between white man and white man, or between black man and\nblack man.\n\nThe claim that \"machines cannot make mistakes\" seems a curious one. One\nis tempted to retort, \"Are they any the worse for that?\" But let us\nadopt a more sympathetic attitude, and try to see what is really meant.\nI think this criticism can be explained in terms of the imitation game.\nIt is claimed that the interrogator could distinguish the machine from\nthe man simply by setting them a number of problems in arithmetic. The\nmachine would be unmasked because of its deadly accuracy. The reply to\nthis is simple. The machine (programmed for playing the game) would not\nattempt to give the right answers to the arithmetic problems. It would\ndeliberately introduce mistakes in a manner calculated to confuse the\ninterrogator. A mechanical fault would probably show itself through an\nunsuitable decision as to what sort of a mistake to make in the\narithmetic. Even this interpretation of the criticism is not\nsufficiently sympathetic. But we cannot afford the space to go into it\nmuch further. It seems to me that this criticism depends on a confusion\nbetween two kinds of mistake. We may call them 'errors of functioning'\nand 'errors of conclusion'. Errors of functioning are due to some\nmechanical or electrical fault which causes the machine to behave\notherwise than it was designed to do. In philosophical discussions one\nlikes to ignore the possibility of such errors; one is therefore\ndiscussing 'abstract machines'. These abstract machines are mathematical\nfictions rather than physical objects. By definition they are incapable\nof errors of functioning. In this sense we can truly say that 'machines\ncan never make mistakes'. Errors of con-clusion can only arise when some\nmeaning is attached to the output signals from the machine. The machine\nmight, for instance, type out mathematical equations, or sentences in\nEnglish. When a false proposition is typed we say that the machine has\ncommitted an error of conclusion. There is clearly no reason at all for\nsaying that a machine cannot make this kind of mistake. It might do\nnothing but type out repeatedly '0=1'. To take a less perverse example,\nit might have some method for drawing conclusions by scientific\ninduction. We must expect such a method to lead occasionally to\nerroneous results.\n\nThe claim that a machine cannot be the subject of its own thought can of\ncourse only be answered if it can be shown that the machine has some\nthought with some subject matter. Nevertheless, 'the subject matter of a\nmachine's operations' does seem to mean something, at least to the\npeople who deal with it. If, for instance, the machine was trying to\nfind a solution of the equation $x^2 - 40x - 11 = 0$ one would be\ntempted to de-scribe this equation as part of the machine's subject\nmatter at that moment. In this sort of sense a machine undoubtedly can\nbe its own subject matter. It may be used to help in making up its own\nprogrammes, or to predict the effect of alterations in its own\nstructure. By observing the results of its own behaviour it can modify\nits own programmes so as to achieve some purpose more effectively. These\nare possibilities of the near future, rather than Utopian dreams.\n\nThe criticism that a machine cannot have much diversity of behaviour is\njust a way of saying that it cannot have much storage capacity. Until\nfairly recently a storage capacity of even a thousand digits was very\nrare.\n\nThe criticisms that we are considering here are often disguised forms of\nthe argument from consciousness. Usually if one maintains that a machine\ncan do one of these things, and describes the kind of method that the\nmachine could use, one will not make much of an impression. It is\nthought that the method (whatever it may be, for it must be mechanical)\nis really rather base. Compare the parenthesis in _Jefferson_'s\nstatement quoted on p. 21.\n\n\\(6\\) _Lady Lovelace's Objection._ Our most detailed information of\n_Babbage_'s Analytical Engine comes from a memoir by Lady _Lovelace_\n(1842). In it she states, \"The Analytical Engine has no pretensions to\noriginate anything. It can do whatever we know how to order it to\nperform\" (_her italics_). This statement is quoted by _Hartree_ (p. 70)\nwho adds: \"This does not imply that it may not be possible to construct\nelectronic equipment which will 'think for itself', or in which, in\nbiological terms, one could set up a conditioned reflex, which would\nserve as a basis for 'learning'.\" Whether this is possible in principle\nor not is a stimulating and exciting question, suggested by some of\nthese recent developments. But it did not seem that the machines\nconstructed or projected at the time had this property.\n\nI am in thorough agreement with _Hartree_ over this. It will be noticed\nthat he does not assert that the machines in question had not got the\nproperty, but rather that the evidence available to Lady _Lovelace_ did\nnot encourage her to believe that they had it. It is quite possible that\nthe machines in question had in a sense got this property. For suppose\nthat some discrete-state machine has the property. The Analytical Engine\nwas a universal digital computer, so that, if its storage capacity and\nspeed were adequate, it could by suitable programming be made to mimic\nthe machine in question. Probably this argument did not occur to the\nCountess or to _Babbage_. In any case there was no obligation on them to\nclaim all that could be claimed.\n\nThis whole question will be considered again under the heading of\nlearning machines.\n\nA variant of Lady _Lovelace_'s objection states that a machine can\n'never do anything really new'. This may be parried for a moment with\nthe saw, 'There is nothing new under the sun'. Who can be certain that\n'original work' that he has done was not simply the growth of the seed\nplanted in him by teaching, or the effect of following well-known\ngeneral principles. A better variant of the objection says that a\nmachine can never 'take us by surprise'. This statement is a more direct\nchallenge and can be met directly. Machines take me by surprise with\ngreat frequency. This is largely because I do not do sufficient\ncalculation to decide what to expect them to do, or rather because,\nalthough I do a calculation, I do it in a hurried, slipshod fashion,\ntaking risks. Perhaps I say to myself, 'I suppose the voltage here ought\nto be the same as there: anyway let's assume it is'.\n\nNaturally I am often wrong, and the result is a surprise for me for by\nthe time the experiment is done these assumptions have been forgotten.\nThese admissions lay me open to lectures on the subject of my vicious\nways, but do not throw any doubt on my credibility when I testify to the\nsurprises I experience.\n\nI do not expect this reply to silence my critic. He will probably say\nthat such surprises are due to some creative mental act on my part, and\nreflect no credit on the machine. This leads us back to the argument\nfrom consciousness, and far from the idea of surprise. It is a line of\nargument we must consider closed, but it is perhaps worth remarking that\nthe appreciation of some-thing as surprising requires as much of a\n'creative mental act' whether the surprising event originates from a\nman, a book, a machine or anything else.\n\nThe view that machines cannot give rise to surprises is due, I believe,\nto a fallacy to which philosophers and mathematicians are particularly\nsubject. This is the assumption that as soon as a fact is presented to a\nmind all consequences of that fact spring into the mind simultaneously\nwith it. It is a very useful assumption under many circumstances, but\none too easily forgets that it is false. A natural consequence of doing\nso is that one then assumes that there is no virtue in the mere working\nout of consequences from data and general principles.\n\n\\(7\\) _Argument from Continuity in the Nervous System._ The nervous\nsystem is certainly not a 'discrete-state machine'. A small error in the\ninformation about the size of a nervous impulse impinging on a neuron,\nmay make a large difference to the size of the outgoing impulse. It may\nbe argued that, this being so, one cannot expect to be able to mimic the\nbehaviour of the nervous system with a 'discrete-state system'.\n\nIt is true that a 'discrete-state machine' must be different from a\n'continuous machine'. But if we adhere to the conditions of the\nimitation game, the interrogator will not be able to take any advantage\nof this difference. The situation can be made clearer if we consider\nsome other simpler 'continuous machine'. A 'differential analyser' will\ndo very well. (A 'differential analyser' is a certain kind of machine\nnot of the 'discrete-state type' used for some kinds of calculation.)\nSome of these provide their answers in a typed form, and so are suitable\nfor taking part in the game. It would not be possible for a digital\ncomputer to predict exactly what answers the differential analyser would\ngive to a problem, but it would be quite capable of giving the right\nsort of answer. For instance, if asked to give the value of $\\pi$\n(actually about 3.1416) it would be reasonable to choose at random\nbetween the values 3.12, 3.13, 3.14, 3.15, 3.16 with the probabilities\nof 0.05, 0.15, 0.55, 0.19, 0.06 (say). Under these circumstances it\nwould be very difficult for the interrogator to distinguish the\ndifferential analyser from the digital computer.\n\n\\(8\\) _The Argument from Informality of Behaviour._ It is not possible\nto produce a set of rules purporting to describe what a man should do in\nevery conceivable set of circumstances. One might for instance have a\nrule that one is to stop when one sees a red traffic light, and to go if\none sees a green one, but what if by some fault both appear together?\nOne may perhaps decide that it is safest to stop. But some further\ndifficulty may well arise from this decision later. To attempt to\nprovide rules of conduct to cover every eventuality, even those arising\nfrom traffic lights, appears to be impossible. With all this I agree.\n\nFrom this it is argued that we cannot be machines. I shall try to\nreproduce the argument, but I fear I shall hardly do it justice. It\nseems to run something like this. 'If each man had a definite set of\n'rules of conduct' by which he regulated his life he would be no better\nthan a machine. But there are no such rules, so men cannot be machines.'\nThe undistributed middle is glaring. I do not think the argument is ever\nput quite like this, but I believe this is the argument used\nnevertheless. There may however be a certain confusion between 'rules of\nconduct' and 'laws of behaviour' to cloud the issue. By 'rules of\nconduct' I mean precepts such as 'Stop if you see red lights', on which\none can act, and of which one can be conscious. By 'laws of behaviour' I\nmean laws of nature as applied to a man's body such as 'if you pinch him\nhe will squeak'. If we substitute 'laws of behaviour which regulate his\nlife' for 'laws of conduct by which he regulates his life' in the\nargument quoted the undistributed middle is no longer insuperable. For\nwe believe that it is not only true that being regulated by laws of\nbehaviour implies being some sort of machine (though not necessarily a\ndiscrete-state machine), but that conversely being such a machine\nimplies being regulated by such laws. However, we cannot so easily\nconvince ourselves of the absence of complete laws of behaviour as of\ncomplete rules of conduct. The only way we know of for finding such laws\nis scientific observation, and we certainly know of no circumstances\nunder which we could say, 'We have searched enough. There are no such\nlaws.'\n\nWe can demonstrate more forcibly that any such statement would be\nunjustified. For suppose we could be sure of finding such laws if they\nexisted. Then given a discrete-state machine it should certainly be\npossible to discover by observation sufficient about it to predict its\nfuture behaviour, and this within a reasonable time, say a thousand\nyears. But this does not seem to be the case. I have set up on the\nManchester computer a small programme using only 1,000 units of storage,\nwhereby the machine supplied with one sixteen-figure number replies with\nanother within two seconds. I would defy anyone to learn from these\nreplies sufficient about the programme to be able to predict any replies\nto untried values.\n\n\\(9\\) _The Argument from Extra-Sensory Perception._ I assume that the\nreader is familiar with the idea of extra-sensory perception, and the\nmeaning of the four items of it, viz., telepathy, clairvoyance,\nprecognition and psycho-kinesis. These disturbing phenomena seem to deny\nall our usual scientific ideas. How we should like to discredit them!\nUnfortunately the statistical evidence, at least for telepathy, is\noverwhelming. It is very difficult to rearrange one's ideas so as to fit\nthese new facts in. Once one has accepted them it does not seem a very\nbig step to believe in ghosts and bogies. The idea that our bodies move\nsimply according to the known laws of physics, together with some others\nnot yet discovered but somewhat similar, would be one of the first to\ngo.\n\nThis argument is to my mind quite a strong one. One can say in reply\nthat many scientific theories seem to remain workable in practice, in\nspite of clashing with E.S.P.; that in fact one can get along very\nnicely if one forgets about it. This is rather cold comfort, and one\nfears that thinking is just the kind of phenomenon where E.S.P. may be\nespecially relevant.\n\nA more specific argument based on E.S.P. might run as follows: \"Let us\nplay the imitation game, using as witnesses a man who is good as a\ntelepathic receiver, and a digital computer. The interrogator can ask\nsuch questions as 'What suit does the card in my right hand belong to?'\nThe man by telepathy or clairvoyance gives the right answer 130 times\nout of 400 cards. The machine can only guess at random, and perhaps gets\n104 right, so the interrogator makes the right identification.\" There is\nan interesting possibility which opens here. Suppose the digital\ncomputer contains a random number generator. Then it will be natural to\nuse this to decide what answer to give. But then the random number\ngenerator will be subject to the psycho-kinetic powers of the\ninterrogator. Perhaps this psycho-kinesis might cause the machine to\nguess right more often than would be expected on a probability\ncalculation, so that the interrogator might still be unable to make the\nright identification. On the other hand, he might be able to guess right\nwithout any questioning, by clairvoyance. With E.S.P. anything may\nhappen.\n\nIf telepathy is admitted it will be necessary to tighten our test up.\nThe situation could be regarded as analogous to that which would occur\nif the interrogator were talking to himself and one of the competitors\nwas listening with his ear to the wall. To put the competitors into a\n'telepathy-proof room' would satisfy all requirements.\n\n##### 7. _Learning Machines._\n\nThe reader will have anticipated that I have no very convincing\narguments of a positive nature to support my views. If I had I should\nnot have taken such pains to point out the fallacies in contrary views.\nSuch evidence as I have I shall now give.\n\nLet us return for a moment to Lady Lovelace's objection, which stated\nthat the machine can only do what we tell it to do. One could say that a\nman can 'inject' an idea into the machine, and that it will respond to a\ncertain extent and then drop into quiescence, like a piano string struck\nby a hammer. Another simile would be an atomic pile of less than\ncritical size: an injected idea is to correspond to a neutron entering\nthe pile from without. Each such neutron will cause a certain\ndisturbance which eventually dies away. If, however, the size of the\npile is sufficiently increased, the disturbance caused by such an\nincoming neutron will very likely go on and on increasing until the\nwhole pile is destroyed. Is there a corresponding phenomenon for minds,\nand is there one for machines? There does seem to be one for the human\nmind. The majority of them seem to be 'sub-critical', i.e. to correspond\nin this analogy to piles of sub-critical size. An idea presented to such\na mind will on average give rise to less than one idea in reply. A\nsmallish proportion are super-critical. An idea presented to such a mind\nmay give rise to a whole 'theory' consisting of secondary, tertiary and\nmore remote ideas. Animals minds seem to be very definitely\n'sub-critical'. Adhering to this analogy we ask, 'Can a machine be made\nto be super-critical?'\n\nThe 'skin of an onion' analogy is also helpful. In considering the\nfunctions of the mind or the brain we find certain operations which we\ncan explain in purely mechanical terms. This we say does not correspond\nto the real mind: it is a sort of skin which we must strip off if we are\nto find the real mind. But then in what remains we find a further skin\nto be stripped off, and so on. Proceeding in this way do we ever come to\nthe 'real' mind, or do we eventually come to the skin which has nothing\nin it ? In the latter case the whole mind is mechanical. (It would not\nbe a discrete-state machine however. We have discussed this.)\n\nThese last two paragraphs do not claim to be convincing arguments. They\nshould rather be described as 'recitations tending to produce belief'.\n\nThe only really satisfactory support that can be given for the view\nexpressed at the beginning of §6, will be that provided by waiting for\nthe end of the century and then doing the experiment described. But what\ncan we say in the meantime ? What steps should be taken now if the\nexperiment is to be successful?\n\nAs I have explained, the problem is mainly one of programming. Advances\nin engineering will have to be made too, but it seems unlikely that\nthese will not be adequate for the requirements. Estimates of the\nstorage capacity of the brain vary from $10^{10}$ to $10^{15}$ binary\ndigits. I incline to the lower values and believe that only a very small\nfraction is used for the higher types of thinking. Most of it is\nprobably used for the retention of visual impressions. I should be\nsurprised if more than $10^9$ was required for satisfactory playing of\nthe imitation game, at any rate against a blind man. (_Note_—The capacity\nof the _Encyclopaedia Britannica_, 11th edition, is $2 \\times 10^9$) A\nstorage capacity of $10^9$ would be a very practicable possibility even\nby present techniques. It is probably not necessary to increase the\nspeed of operations of the machines at all. Parts of modern machines\nwhich can be regarded as analogs of nerve cells work about a thousand\ntimes faster than the latter. This should provide a 'margin of safety'\nwhich could cover losses of speed arising in many ways. Our problem then\nis to find out how to programme these machines to play the game. At my\npresent rate of working I produce about a thousand digits of programme a\nday, so that about sixty workers, working steadily through the fifty\nyears might accomplish the job, if nothing went into the waste-paper\nbasket. Some more expeditious method seems desirable.\n\nIn the process of trying to imitate an adult human mind we are bound to\nthink a good deal about the process which has brought it to the state\nthat it is in. We may notice three components.\n\n1.  The initial state of the mind, say at birth,\n\n2.  The education to which it has been subjected,\n\n3.  Other experience, not to be described as education, to which it has\n    been subjected.\n\nInstead of trying to produce a programme to simulate the adult mind, why\nnot rather try to produce one which simulates the child's? If this were\nthen subjected to an appropriate course of education one would obtain\nthe adult brain. Presumably the child brain is something like a\nnote-book as one buys it from the stationers. Rather little mechanism,\nand lots of blank sheets. (Mechanism and writing are from our point of\nview almost synonymous.) Our hope is that there is so little mechanism\nin the child brain that something like it can be easily programmed. The\namount of work in the education we can assume, as a first approximation,\nto be much the same as for the human child.\n\nWe have thus divided our problem into two parts. The child-programme and\nthe education process. These two remain very closely connected. We\ncannot expect to find a good child-machine at the first attempt. One\nmust experiment with teaching one such machine and see how well it\nlearns. One can then try another and see if it is better or worse. There\nis an obvious connection between this process and evolution, by the\nidentifications\n\n$$\n\\begin{aligned}\n\\text{Structure of the child machine} \u0026= \\text{Hereditary material} \\\\\n\\text{Changes of the child machine} \u0026= \\text{Mutations} \\\\\n\\text{Natural selection} \u0026= \\text{Judgment of the experimenter}\n\\end{aligned}\n$$\n\nOne may hope, however, that this process will be more expeditious than\nevolution. The survival of the fittest is a slow method for measuring\nadvantages. The experimenter, by the exercise of intelligence, should be\nable to speed it up. Equally important is the fact that he is not\nrestricted to random mutations. If he can trace a cause for some\nweakness he can probably think of the kind of mutation which will\nimprove it.\n\nIt will not be possible to apply exactly the same teaching process to\nthe machine as to a normal child. It will not, for instance, be provided\nwith legs, so that it could not be asked to go out and fill the coal\nscuttle. Possibly it might not have eyes. But however well these\ndeficiencies might be overcome by clever engineering, one could not send\nthe creature to school without the other children making excessive fun\nof it. It must be given some tuition. We need not be too concerned about\nthe legs, eyes, etc. The example of Miss _Helen Keller_ shows that\neducation can take place provided that communication in both directions\nbetween teacher and pupil can take place by some means or other.\n\nWe normally associate punishments and rewards with the teaching process.\nSome simple child machines can be constructed or programmed on this sort\nof principle. The machine has to be so constructed that events which\nshortly preceded the occurrence of a punishment signal are unlikely to\nbe repeated, whereas a reward signal increased the probability of\nrepetition of the events which led up to it. These definitions do not\npresuppose any feelings on the part of the machine, I have done some\nexperiments with one such child machine, and succeeded in teaching it a\nfew things, but the teaching method was too unorthodox for the\nexperiment to be considered really successful.\n\nThe use of punishments and rewards can at best be a part of the teaching\nprocess. Roughly speaking, if the teacher has no other means of\ncommunicating to the pupil, the amount of information which can reach\nhim does not exceed the total number of rewards and punishments applied.\nBy the time a child has learnt to repeat 'Casabianca' he would probably\nfeel very sore indeed, if the text could only be discovered by a 'Twenty\nQuestions' technique, every 'NO' taking the form of a blow. It is\nnecessary therefore to have some other 'unemotional' channels of\ncommunication. If these are available it is possible to teach a machine\nby punishments and rewards to obey orders given in some language, e.g.,\na symbolic language. These orders are to be transmitted through the\n'unemotional' channels. The use of this language will diminish greatly\nthe number of punishments and rewards required.\n\nOpinions may vary as to the complexity which is suitable in the child\nmachine. One might try to make it as simple as possible consistently\nwith the general principles. Alternatively one might have a complete\nsystem of logical inference 'built in'.[^3] In the latter case the store\nwould be largely occupied with definitions and propositions. The\npropositions would have various kinds of status, e.g., well-established\nfacts, conjectures, mathematically proved theorems, statements given by\nan authority, expressions having the logical form of proposition but not\nbelief-value. Certain propositions may be described as 'imperatives.'\nThe machine should be so constructed that as soon as an imperative is\nclassed as 'well established' the appropriate action automatically takes\nplace. To illustrate this, suppose the teacher says to the machine, 'Do\nyour homework now.' This may cause \"Teacher says 'Do your homework now'\n\" to be included amongst the well-established facts. Another such fact\nmight be, \"Everything that teacher says is true.\" Combining these may\neventually lead to the imperative, 'Do your homework now,' being\nincluded amongst the well-established facts, and this, by the\nconstruction of the machine, will mean that the homework actually gets\nstarted, but the effect is very satisfactory. The processes of inference\nused by the machine need not be such as would satisfy the most exacting\nlogicians. There might for instance be no hierarchy of types. But this\nneed not mean that type fallacies will occur, any more than we are bound\nto fall over unfenced cliffs. Suitable imperatives (expressed within the\nsystems, not forming part of the rules of the system) such as 'Do not\nuse a class unless it is a subclass of one which has been mentioned by\nteacher' can have a similar effect to 'Do not go too near the edge'.\n\nThe imperatives that can be obeyed by a machine that has no limbs are\nbound to be of a rather intellectual character, as in the example (doing\nhomework) given above. Important amongst such imperatives will be ones\nwhich regulate the order in which the rules of the logical system\nconcerned are to be applied, For at each stage when one is using a\nlogical system, there is a very large number of alternative steps, any\nof which one is permitted to apply, so far as obedience to the rules of\nthe logical system is concerned. These choices make the difference\nbetween a brilliant and a footling reasoner, not the difference between\na sound and a fallacious one. Propositions leading to imperatives of\nthis kind might be \"When Socrates is mentioned, use the syllogism in\nBarbara\" or \"If one method has been proved to be quicker than another,\ndo not use the slower method.\" Some of these may be 'given by\nauthority', but others may be produced by the machine itself, e.g. by\nscientific induction.\n\nThe idea of a learning machine may appear paradoxical to some readers.\nHow can the rules of operation of the machine change? They should\ndescribe completely how the machine will react whatever its history\nmight be, whatever changes it might undergo. The rules are thus quite\ntime-invariant. This is quite true. The explanation of the paradox is\nthat the rules which get changed in the learning process are of a rather\nless pretentious kind, claiming only an ephemeral validity. The reader\nmay draw a parallel with the Constitution of the United States.\n\nAn important feature of a learning machine is that its teacher will\noften be very largely ignorant of quite what is going on inside,\nalthough he may still be able to some extent to predict his pupil's\nbehaviour. This should apply most strongly to the later education of a\nmachine arising from a child machine of well-tried design (or\nprogramme). This is in clear contrast with normal procedure when using a\nmachine to do computations one's object is then to have a clear mental\npicture of the state of the machine at each moment in the computation.\nThis object can only be achieved with a struggle. The view that 'the\nmachine can only do what we know how to order it to do',[^4] appears\nstrange in face of this. Most of the programmes which we can put into\nthe machine will result in its doing something that we cannot make sense\n(if at all, or which we regard as completely random behaviour.\nIntelligent behaviour presumably consists in a departure from the\ncompletely disciplined behaviour involved in computation, but a rather\nslight one, which does not give rise to random behaviour, or to\npointless repetitive loops. Another important result of preparing our\nmachine for its part in the imitation game by a process of teaching and\nlearning is that 'human fallibility' is likely to be omitted in a rather\nnatural way, i.e., without special 'coaching'. (The reader should\nreconcile this with the point of view on pp. 24, 25.) Processes that are\nlearnt do not produce a hundred per cent certainty of result; if they\ndid they could not be unlearnt.\n\nIt is probably wise to include a random element in a learning machine. A\nrandom element is rather useful when we are searching for a solution of\nsome problem. Suppose for instance we wanted to find a number between 50\nand 200 which was equal to the square of the sum of its digits, we might\nstart at 51 then try 52 and go on until we got a number that worked.\nAlternatively we might choose numbers at random until we got a good one.\nThis method has the advantage that it is unnecessary to keep track of\nthe values that have been tried, but the disadvantage that one may try\nthe same one twice, but this is not very important if there are several\nsolutions. The systematic method has the disadvantage that there may be\nan enormous block without any solutions in the region which has to be\ninvestigated first, Now the learning process may be regarded as a search\nfor a form of behaviour which will satisfy the teacher (or some other\ncriterion). Since there is probably a very large number of satisfactory\nsolutions the random method seems to be better than the systematic. It\nshould be noticed that it is used in the analogous process of evolution.\nBut there the systematic method is not possible. How could one keep\ntrack of the different genetical combinations that had been tried, so as\nto avoid trying them again?\n\nWe may hope that machines will eventually compete with men in all purely\nintellectual fields. But which are the best ones to start with? Even\nthis is a difficult decision. Many people think that a very abstract\nactivity, like the playing of chess, would be best. It can also be\nmaintained that it is best to provide the machine with the best sense\norgans that money can buy, and then teach it to understand and speak\nEnglish. This process could follow the normal teaching of a child.\nThings would be pointed out and named, etc. Again I do not know what the\nright answer is, but I think both approaches should be tried.\n\nWe can only see a short distance ahead, but we can see plenty there that\nneeds to be done.\n\n**BIBLIOGRAPHY**\n\nSamuel Butler, _Erewhon_, London, 1865. Chapters 23, 24, 25, _The Book\nof the Machines_.\n\nAlonzo Church, \"An Unsolvable Problem of Elementary Number Theory\",\n\n_American J. of Math._, 58 (1936), 345-363.\n\nK. Gödel, \"Über formal unentscheidbare Sätze der Principia Mathematica\n\nund verwandter Systeme, I\", _Monatshefte für Math. und Phys._,\n\n(1931), 173-189.\n\nD. R. Hartree, _Calculating Instruments and Machines_, New York, 1949.\n\nS. C. Kleene, \"General Recursive Functions of Natural Numbers\",\n\n_American J. of Math._, 57 (1935), 153-173 and 219-244.\n\nG. Jefferson, \"The Mind of Mechanical Man\". Lister Oration for 1949.\n\n_British Medical Journal_, vol. i (1949), 1105-1121.\n\nCountess of Lovelace, 'Translator's notes to an article on Babbage's\n\n_Analytical Engine_, _Scientific Memoirs_ (ed. by R. Taylor), vol. 3\n\n(1842), 691-731.\n\nBertrand Russell, _History of Western Philosophy_, London, 1940.\n\nA. M. Turing, \"On Computable Numbers, with an Application to the\n\nEntscheidungsproblem\", _Proc. London Math. Soc._ (2), 42 (1937),\n\n230-265.\n\n_Victoria University of Manchester._\n\n[^1]:\n    Possibly this view is heretical. St. Thomas Aquinas (_Summa\n    Theologica_, quoted by Bertrand Russell, p. 480) states that God\n    cannot make a man to have no soul. But this may not be a real\n    restriction on His powers, but only a result of the fact that men's\n    souls are immortal, and therefore indestructible.\n\n[^2]: Author's names in italics refer to the Bibliography.\n\n[^3]:\n    Or rather 'programmed in' for our child-machine will be programmed\n    in a digital computer. But the logical system will not have to be\n    learnt.\n\n[^4]:\n    Compare Lady Lovelace's statement (p.450), which does not contain\n    the word 'only'.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fianchanning%2Fturing-test-paper","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fianchanning%2Fturing-test-paper","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fianchanning%2Fturing-test-paper/lists"}