Turing, Computing (Mind)

8/13/2019 Turing, Computing (Mind)

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Mind Association

Computing Machinery and IntelligenceAuthor(s): A. M. TuringSource: Mind, New Series, Vol. 59, No. 236 (Oct., 1950), pp. 433-460Published by: Oxford University Presson behalf of the Mind Association

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VOL. LIX. No. 236.] [October, 950

M INDA QUARTERLY REVIEW

OFPSYCHOLOGY AND PHILOSOPHYI.-COMPUTING MACHINERY ANDINTELLIGENCE

BY A. M. TURING1. The mitation ame.I PROPOSE tO considerthe question, Can machines hinkThis shouldbeginwith definitionsfthemeaning fthe terms'machine' and think'. Thedefinitions ight eframed o as toreflect o far as possiblethe normaluse ofthe words,but thisattitude s dangerous. If the meaning f thewords machine'and think are tobefound y examining ow hey recommonlyused it is difficulto escape the conclusion hat the meaningand theanswer o tliequestion, Can machines hink isto besought n a statistical urvey uch as a Gallup poll. But this sabsurd. Instead f ttemptinguch definitionshallreplace hequestion yanother, hichs closely elated o it andisexpressedinrelativelynambiguous ords.The newform f the problem an be describedn termsofa game whichwe call the imitationgame'. It is played withthree eople, man A),a womanB), andaninterrogatorC)whomay be of either ex. The interrogatortays n a roomapartfrom heother wo. The objectofthegamefor he nterrogatoris to determine hich f the other wois the man and which sthe woman. He knows hembylabelsX and Y, and at the endofthegamehesayseither X isA andY is B ' or X is B and Yis A'. The interrogators allowedto put questions o A and Bthus:C: Will X pleasetellmethe ength f his or herhairNow supposeX is aetually A, then A mustanswer. It is A's28 433

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COMPUTING MACHINERY AND INTELLIGENCE 435Q: I have K at my Ki, and no otherpieces. You have onlyK at K6 and R at RI. It is yourmove. What do youplay?A: (After pauseof 15seconds)R-R8 mate.The question and answer methodseems to be suitable forintroducinglmost ny one ofthe fields fhuman ndeavour hatwe wish to include. We do not wish to penalise themachinefor ts inability o shine nbeautycompetitions,or to penalisea man for osing n a raceagainst n aeroplane. Theconditionsofourgame makethesedisabilitiesrrelevant. The 'witnesses'can brag, f they consider t advisable, s muchas theypleaseabout theircharms, trength r heroism, ut the interrogatorcannotdemandpracticaldemonstrations.The gamemay perhapsbe criticised n the ground hat theodds areweightedoo heavily gainst hemachine. If the manwere o try ndpretend o be themachine ewouldclearlymakea very oor howing. He wouldbegiven way t onceby slownessand inaccuracynarithmetic.May notmachinesarry ut some-thingwhich ught o be describeds thinking utwhich s verydifferentromwhat mandoes? Thisobjection s a very trongone,but at least we can say that f,nevertheless, machine anbe constructedo play the mitation amesatisfactorily,e neednotbe troubled y thisobjection.It mightbe urgedthat whenplaying he 'imitationgame'the best strategy orthe machinemay possiblybe somethingother han mitation f hebehaviour f man. Thismaybe, butI think t is unlikely hatthere s anygreateffect f thiskind.

In any case there s no intention o investigate erethetheoryof the game,and it will be assumedthat the best strategystotry oprovide nswers hatwouldnaturally egivenbya man.3. TheMlachinesoncernedntheGame.

The questionwhich we put in ?1 will not be quitedefiniteuntilwe have specified hatwe meanby theword machine'.It isnatural hatweshouldwish opermitvery ind f ngineeringtechniqueo beused n ourmachines. We also wish o allowthepossibilityhan an engineerrteamofengineersmayconstructa machinewhichworks, ut whosemanner foperation annotbe satisfactorilyescribed yits constructorsecausetheyhaveapplied a methodwhich s largelyexperimental.Finally,wewish oexclude romhemachinesmenbornntheusual manner.It is difficulto frame he definitionso as to satisfyhesethreeconditions. One mightfor instance nsistthat the team of



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436 A. M. TURING:engineers hould be all of one sex, but this would not reallybe satisfactory,or t is probablypossible to rear a completeindividual rom singlecell of the skin say) of a man. To doso would be a feat of biological echnique eserving f the veryhighestpraise,but we would not be inclined o regard t as acase of constructing thinkingmachine'. This prompts s toabandonthe requirementhat everykind of technique houldbe permitted. We are the moreready to do so in view of thefact that the present nterestn 'thinkingmachines' has beenaroused by a particularkind of machine, usually called an' electronic omputer' or 'digital computer'. Following thissuggestion e only permit igitalcomputers o take part n ourgame.This restrictionppears at first ight o be a verydrastic ne.I shall attempt o showthat t is not so in reality. To do thisnecessitates short ccountof the nature nd properties f thesecomputers.It may also be said that this dentificationfmachineswithdigital computers,ike our criterion or thinking',will onlybe unsatisfactoryf (contrary o my belief), t turns out thatdigitalcomputersre unableto givea good showingn thegame.There are alreadya number fdigital computersn workingorder,ndit maybe asked, Why nottry heexperimenttraightaway ? It wouldbe easyto satisfy he conditionsfthegame.A number f nterrogatorsouldbe used,and statisticsompiledto showhow often herightdentificationasgiven.' The- hortanswer s that we are not askingwhether ll digital computerswoulddo well nthegamenor whether hecomputerst presentavailablewould do well,butwhether here re imaginable om-puterswhichwould do well. But this s onlythe short'nswer.We shall seethisquestionn a diflerentight ater.4. DigitalComputers.

The idea behinddigitalcomputersmaybe explained y sayingthat thesemachines re intended o carryout any operationswhich ouldbe donebya human omputer. Thehuman omputeris supposedto be following ixedrules; he has no authorityto deviatefrom hem nanydetail. Wemay suppose hat theserules re suppliedn a book,which s alteredwhenever e is puton to a new ob. He has also an unlimitedupply fpaperonwhich edoeshiscalculations. He may lso do hismultiplicationsand additions n a 'desk machine',butthis s not mportant.If we use theabove explanation s a definition e shallbe in



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COMPUTING MACHINERY AND INTELLIGENCE 437dangerof circularity f argument. We avoid this by givingan outline fthemeansbywhich hedesired ffects achieved.A digital omputeranusuallybe regardeds consistingfthreeparts:

(i) Store.(ii) Executive nit.(iii) Control.The store s a store f nformation,ndcorrespondso thehumancomputer's aper,whetherhis s thepaperonwhichhe doeshiscalculations rthatonwhichhisbookofrules s printed. In sofar as thehuman omputeroescalculationsnhisheada partofthe storewillcorrespondohismemory.The executive nit is the partwhichcarriesout the variousindividualoperations nvolved n a calculation. What theseindividualoperations re will varyfrommachineto machine.Usuallyfairlyengthyperations an be donesuch as 'Multiply3540675445by 7076345687' but in somemachinesonly verysimple nessuch s 'Writedown0 ' arepossible.We have mentionedhat the ' bookofrules-' upplied o thecomputers replaced n themachineby a partof the store. Itis thencalledthe table of nstructions'. It is thedutyofthecontrol o seethatthese nstructionsre obeyed orrectlynd intheright rder. Thecontrolssoconstructedhat hisnecessarilyhappens.The informationn thestore s usuallybroken p intopacketsofmoderatelymallsize. In onemachine, ornstance, packetmight onsist ftendecimaldigits. Numbers reassigned otheparts ofthe store n whichthe variouspackets of informationare stored, n somesystematicmanner. A typical nstructionmight ay-'Add the number tored n position 809 to that n 4302 andput theresultbackintothelatter torage osition'.Needlessto say it wouldnot occur n themachine xpressedin English. It would more ikelybe coded in a form uch as6809430217. Here 17 sayswhichofvariouspossibleoperationsis to be performednthetwonumbers. In thiscase theopera-tion is that described bove, viz. 'Add the number. . .' Itwill be noticedthat the instructionakes up 10 digitsand soformsnepacketof nformation,ery onveniently.The controlwillnormally ake theinstructionso be obeyed n the order fthe positions n which heyare stored,but occasionally n in-structionuch as



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438 A. M. TURING:' Now obey the instructiontored n position5606, and con-tinuefrom heremaybe encountered,ragain'If position 505 contains obey next the instructiontoredin 6707,otherwiseontinue traightn.'Instructionsfthese atter ypes revery mportant ecause heymake t possible or sequence foperations o be repeated verand over again untilsomeconditions fulfilled,utin doing oto obey,notfreshnstructionsn each repetition,ut the sameonesover nd over gain. To takea domesticnalogy. Suppose

MotherwantsTommy o call at the cobbler's verymorningnhiswayto school o see ifher shoes are done,she can ask himafresh verymorning.Alternativelyhe can stick up a noticeonce and for ll in thehall whichhe willseewhenhe leavesforschool nd which ellshim o call for he shoes, nd also to destroythenoticewhenhe comesback f hehas theshoeswithhim.The readermust ccept t as a factthat digital omputers anbe constructed,nd indeed have been constructed, ccordingto theprincipleswe have described,nd thattheycan in factmimic he actions fa human omputer ery losely.Thebookofruleswhichwe havedescribedurhuman omputeras using s of course convenient iction. Actual humancom-puters eally ememberhat heyhavegot odo. Ifone wants omake a machinemimic he behaviour f the humancomputerinsomecomplex peration ne hasto askhimhow tis done, ndthen translate he answer ntotheform fan instructionable.Constructingnstruction ables is usually describedas 'pro-gramming'. To 'programme machine o carry utthe opera-tion A' meansto putthe appropriatenstructionable into themachine o that twilldo A.An interestingarianton the idea of a digital computers a'digital omputer ith random lement'.Thesehave nstructionsinvolving he throwing f a die or some equivalentelectronicprocess;one uch nstruction ight or nstance e,' Throw hedieand puttheresulting umberntostore1000 . Sometimesucha machine s described s havingfreewill (though would notusethisphrasemyself). It is notnormally ossible o determinefromobserving machine whethert has a random element,fora similar ffect an be producedby suchdevices as makingthe choicesdependonthe digits fthedecimal orw.Most actual digital omputers ave only a finite tore. Thereis no theoretical ifficultyn the dea of a computerwith n un-limited tore. Of courseonly a finite art can have been usedat any one time. Likewise nly a finite mount an have been



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COMPUTING MACHINERY AND INTELLIGENCE 439constructed,ut we can imaginemore nd morebeing dded asrequired. Such computers ave special theoretical nterest ndwillbe called nfinitiveapacity omputers.The dea of digital omputers an old one. Charles abbage,Lucasian Professor f Mathematics t Cambiidgefrom1828 to1839, planned such a machine,called the AnalyticalEngine,but it was never completed. AlthoughBabbage had all theessential deas, his machinewas not at that time such a veryattractive rospect. The speed whichwouldhave been availablewould be definitelyaster han a human omputer ut somethinglike 100 times lower han the Manchestermachine, tself ne ofthe slower of the modernmachines. The storage was to bepurelymechanical, singwheels nd cards.The factthatBabbage's Analytical nginewas to be entirelymechanicalwillhelpus to ridourselves f supers,tition.mport-ance is often ttached o the factthat modern igital omputersareelectrical,nd thatthe nervous ystem lso s electrical. Sinc',Babbage'smachinewas not electrical, nd since ll digital om-puters rein a senseequivalent,we see thatthisuse ofelectricitycannotbe of heoreticalmportance. Ofcourse lectricitysuallycomes in wherefast signallings concerned, o that it is notsurprising hat we find t in both these connections. n thenervous ystem hemicalphenomena re at least as importantas electrical. In certain omputers he storage ystem s mainlyacoustic. The feature of using electricitys thus seen to beonly a very superficial imilarity. If we wish to find suchsimilaritieswe should ook rather ormathematical nalogiesoffunction.5. UniversalityfDigitalComputers.

The digital computers onsideredn the last sectionmay beclassifiedmongst he discrete tate machines. Theseare themachineswhichmoveby sudden umpsor clicksfrom ne quitedefinitetate oanother. Thesestates resufficientlyifferentorthepossibilityf confusionetween hem obe ignored. Strictlyspeaking here re no such machines. Everything eallymovescontinuously.But there remanykindsofmachinewhich anprofitably e thoughtf as beingdiscrete tatemachines. Forinstance n consideringhe switches or a lighting ystem t isa convenient iction hat each switchmustbe definitelyn ordefinitely ff. Theremust be intermediate ositions,but formostpurposeswe can forget bout them. As an exampleofadiscrete tatemachinewe mightconsider wheelwhichclicks



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440 A. M. TURING:round through 20?once a second, but may be stoppedby aleverwhich an be operated rom utside; in addition lamp sto light noneofthepositions fthe wheel. Thismachine ouldbe described bstractly s follows. The internal tate of themachinewhich s described ythe position fthe wheel)maybeql, q2or q3. There s an inputsignal 0or i1 position f ever).The internaltateat anymoment s determined y the ast stateand input ignal ccordingo thetable

Last Stateq1 q2 q3

i0 q2 q3 q1Input?i q1 q2 q3

The output signals, the only externallyvisible indicationofthe nternal tate the ight) re described ythetableState q1 q2 q3Output 00 0? 01

Thisexample s typical f discrete tatemachines. Theycan bedescribed y suchtablesprovided heyhaveonly finite umberofpossible tates.It willseemthat given the initial state ofthe machine ndthe nput ignals t is always possible o predict ll future tates.This is reminiscent f Laplace's view that from he completestate of theuniverse t onemoment f time, s described y thepositions nd velocities f all particles,t shouldbe possibletopredict ll futuretates. Thepredictioil hichwe areconsideringis, however, athernearer o practicabilityhanthat consideredby Laplace. The system fthe 'universe as a whole is suchthat quite small errors n the initial conditions an have anoverwhelmingffect t a later time. The displacement f asingle electronby a billionth f a centimetret one momentmightmake the differenceetween man beingkilledby anavalanche a year ater,or escaping. It is an essential ropertyofthe mechanical ystemswhichwe have called 'discrete statemachines'thatthisphenomenonoesnotoccur. Even whenweconsider he actual physicalmachines nsteadof the idealisedmachines, easonably ccurateknowledge f the state at onemomentyieldsreasonably ccurateknowledge ny numberofsteps ater.



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COMPUTING MACHINERY AND INTELLIGENCE 441As we have mentioned, igitalcomputersall within he classof discrete tate machines. But the number f states of whichsuch a machine s capable is usually enormouslyarge. Forinstance, he number or he machine owworkingt Manchesterit about2165,000, i.e. about 1505?.??.omparehiswith ur exampleof the clickingwheeldescribed bove,which had three states.It is notdifficulto see whythenumber f states shouldbe soimmense. The computerncludes storecorrespondingo thepaperusedbya humancomputer. It mustbe possible o writeinto the store any one of the combinations f symbolswhich

mighthave beenwritten n thepaper. For simplicityupposethat onlydigits rom to 9 are used as symbols. Variationsnhandwritingre ignored. Supposethe computer s allowed 100sheets of paper each containing 0 lines each withroomfor 30digits. Then thenumber f states is 10100X5OX30, i.e. 10150,000.This is aboutthenumber fstatesof threeManchestermachinesput together.The logarithm o the base two of the numberof states s usuallycalledthe storagecapacity' of the machine.Thus theManchestermachinehas a storagecapacityof about165,000and the wheelmachineof our exampleabout 1-6. Iftwo machines re put together heircapacitiesmustbe addedto obtain the capacityofthe resultantmachine. This leads tothe possibilityf statements uchas 'The Manchestermachinecontains64 magnetic rackseach witha capacityof2560, eightelectronic ubeswitha capacityof 1280. Miscellaneous torageamounts oabout300making totalof174,380.'Giventhe table correspondingo a discrete tate machine tis possibleto predictwhat it will do. There s no reason whythiscalculation houldnot be carried ut bymeans of a digitalcomputer. Provided t couldbe carried ut sufficientlyuicklythedigitalcomputerould mimic he behaviour fanydiscretestatemachine. The mitation amecould henbe playedwith hemachine n question as B) and themimicking igital computer(as A) and the nterrogatorouldbe unableto distinguishhem.Of course the digital computermust have an adequate storagecapacityas well as working ufficientlyast. Moreover,t mustbe programmedfresh oreach new machinewhich t is desiredto mimic.This special property f digital computers, hat they canmimic any discretestate machine, is describedby sayingthat they are universalmachines. The existenceof machineswiththis property as the important onsequence hat, consi-derations fspeed apart, t is unnecessaryo designvariousnewmachines o do variouscomputing rocesses. They can all.be



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442 A. M. TURING:done with one digital computer,uitablyprogrammed or eachcase. It willbe seen hatas a consequence f his ll digital om-puters re na sense quivalent.We may nowconsider-gainthe pointraisedat the end of ?3.It was suggested entativelyhat the question,Can machinesthink should be replaced by 'Are there maginabledigitalcomputerswhich would do well in the imitationgame ? Ifwe wishwe can make this superficially ore general nd ask'Are there discretestate machines which would do well?But in viewof the universality ropertywe see that either fthesequestions s equivalent o this, Let us fix ourattentionononeparticularigital omputer . Is it true hatby modifyingthiscomputer ohavean adequate storage,uitably ncreasingtsspeed of ction, nd providingtwith n appropriate rogramme,C canbe madetoplaysatisfactorilyhe partofA inthe mitationgame,thepartof B being akenbya man?6. Contrary iews n theMain Question.Wemaynowconsider he ground ohave beencleared nldweareready oproceed o the debateonourquestion,Can machinesthink andthevariant f t quoted t theendof he ast section.We cannot ltogether bandontheoriginal orm f the problem,foropinionswilldiffers to theappropriatenessfthe substitu-tion and we mustat least listen o what has to be said in thisconnexion.It willsimplify atters or hereaderf explainfirstmyownbeliefsnthematter. Consider irst hemore ccurate ormf hequestion. I believe hat na-boutifty ears' ime t willbepossibleto programmeomputers, itha storage apacityof about 109,to makethemplay the imitation ame so well that an averageinterrogatorillnothave more han70 percent. hance fmakingthe right dentificationfterfiveminutes f questioning.Theoriginalquestion, Can machines hink I believe to be toomeaninglesso deserve iscussion. Nevertheless believe hatattheendof he enturyheuseofwords ndgeneralducated pinionwillhave altered o much hatonewillbe able to speakofmachinesthinking ithout xpecting o be contradicted. believefurtherthat no usefulpurpose s served by concealing hese beliefs.The popularviewthat scientists roceed nexorably romwell-established act to well-establishedact,neverbeing nfluencedby any unproved onjecture,s quitemistaken. Provided t ismade clear whichare proved facts and whichare conjectures,no harm can result. Conjecturesre of great mportance incethey uggest seful inesof research.



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COMPUTING MACHINERY AND INTELLIGENCE 443I now proceed o consider pinions pposed o my own.(1) The Theological bjection. Thinkings a function f man'simmortal oul. God hasgiven n immortaloul to everymanandwoman,but not to anyother nimal or to machines. Hencenoanimalor machine anthink.I am unable to acceptany part of this,but will attempt oreply n theological erms. I should findthe argumentmoreconvincingfanimalswere lassedwithmen, or here s a greaterdifference,o my mind,between he typical animateand theinanimatethan there s betweenman and the otheranimals.

The arbitraryharacter f the orthodox iew becomes learer fwe considerhow it might ppear to a member f some otherreligious ommunity.How do Christiansegard heMoslem iewthat womenhave no souls? But let us leave thispointasideand return o the main argument. It appears to me that theargument uotedaboveimplies serious estrictionf the omni-potenceofthe Almighty. It is admitted hat there re certainthings hat He cannotdo suchas making neequal to two,butshould we not believethat He has freedomo confer soulonan elephant fHe sees fit We mightexpect thatHe wouldonly exercise hispower n conjunctionwitha mutationwhichprovided he elephantwith an appropriatelymproved raintoministerotheneedsof his oul. Anargument fexactly imilarformmaybe madefor hecase ofmachines. It may eemdifferentbecauseit is moredifficulto " swallow . But this reallyonlymeansthatwe think-t would be lesslikely hat He would con-sider the circumstancesuitableforconferring soul. The cir-cumstancesn question re discussed n the rest of this paper.In attempting o construct uch machineswe should not beirreverentlysurping is power fcreating ouls, ny more hanwe are in the procreationf children: ratherwe a-re, n eithercase, nstrumentsfHiswillprovidingmansions or he soulsthatHe creates.However, hisis merespeculation. I am notvery mpressedwith heological rguments hatever heymaybeused to support.Sucharguments ave often eenfound nsatisfactorynthe past.In the time of Galileo it was arguedthatthe texts," And thesun stood still . . . and hasted not to go down about a wholeday" (Joshuax. 13) and " He laid thefoundations f theearth,

1Possibly hisview sheretical.St. ThomasAquinas Summa heologica,quoted byBertrand ussell,p. 480) states hatGodcannotmakea manto havenosoul. But thismaynotbe a realrestrictionnHispowers, utonly a resultof the factthatmen'ssouls are immortal, nd thereforeindestructible.



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444 A. M. TURING:that it shouldnot moveat anytime (Psalm cv. 5) wereanadequaterefutationftheCopernicanheory. Withour presentknowledge uchan argumentppearsfutile. When thatknow-ledgewasnotavailable tmadea quitedifferentmpression.(2) The 'Heads in theSand' Objection." The consequencesof machines hinking ouldbe too dreadful. Let us hope andbelieve hatthey annotdo so."This arguments seldomexpressed uite so openly s in theformbove. But it affectsmostofus whothink boutit at all.We liketo believe hatMan is in some ubtlewaysuperiorotherestofcreation. It is best fhe can be shown o be necessarilysuperior,or hen heresno danger fhim osing iscommandingposition. The popalarity f the theological rguments clearlyconnectedwith hisfeeling. It is likely o be quitestrongn in-tellectualpeople,sincetheyvalue the powerof thinkingmorehighly han others, nd are more nclined o base theirbeliefinthesuperiorityfManon this ower.I do not thinkthat this arguments sufficientlyubstantialto require efutation.Consolationwould be moreappropriate:perhaps his houldbe soughtnthetransmigrationf souls.(3) The Mathematicalbjection.There rea number fresultsof mathematicalogic whichcan be used to showthat thereare limitations o the powersof discrete-state achines. Thebest knownoftheseresults s known s G6del'stheorem,' ndshows hat n any sufficientlyowerfulogical ystem tatementscan be formulated hichcan neither e provednordisprovedwithin hesystem, nlesspossiblyhesystemtselfs inconsistent.There are other,n some respects imilar, esults ue to Church,Kleene,Rosser, nd Turing. The latterresult s the mostcon-venient o consider,ince t refers irectlyo machines,whereastheothers anonlybeused na comparativelyndirectrgument:for nstancefG6del'stheorems to be usedwe need n additionto have somemeansof describingogical systemsn termsofmachines,nd machinesnterms f ogical ystems. Theresultnquestion efersoa typeofmachinewhich s essentially digitalcomputerwith an infinite apacity. It statesthat therearecertainhingshat such machine annot o. If it srigged ptogiveanswers o questions s in the imitation ame,therewill besomequestions owhichtwilleither ivea wrong nswer, rfailtogivean answer t all howevermuch ime s allowedfor reply.Theremay,of course,be manysuch questions, nd questionswhich annotbe answered yone machinemaybe satisfactorily

1Author's ames nitalics efero theBibliography.



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COMPUTING MACHINEkY AND INTELLIGENCE 445answered yanother. Weare ofcourse upposing or hepresentthat the questions re of the kind to whichan answer Yes 'or No' is appropriate,ather hanquestions uchas 'What doyou think of Picasso ?-' The questions that we know themachinesmust fail on are of this type," Consider hemachinespecified s follows. . . Will this machineever answer Yes'to any question " The dots are to be replaced by a des-cription f somemachine n a standardform,which could besomethingike that used in ? 5. Whenthemachinedescribedbears a certaincomparatively implerelation o the machinewhich s under nterrogation,t can be shown hat the answeris eitherwrong r not forthcoming. his is the mathematicalresult: it is argued that it proves a disability f machines owhich hehuman ntellects not subject.The shortanswer to this arguments that although t isestablished hat there are limitations o the powers of anyparticularmachine, t has only been stated,without ny sortofproof, hatno such imitations pply to thehuman ntellect.But I do not think his viewcan be dismissed uite so lightly.Wheneverone of these machines is asked the appropriatecritical uestion, nd givesa definite nswer,we know hat thisanswermust be wrong, nd this gives us a certainfeeling fsuperiority. s this feeling llusory? It is no doubt quitegenuine,buit do not thinktoo muchimportance hould beattachedto it. We too oftengive wrong nswers o questionsourselves o be justifiedn beingverypleasedat such evidence ffallibility nthe part of the machines. Further, ur superioritycanonlybefelt nsuch n occasionnrelationotheone machineover which we have scored our pettytriumph. Therewouldbe no question ftriumphingimultaneouslyverall machines.In short,then,there mightbe men cleverer han any givenmachine, utthen gain theremight e othermachines levereragain, and so on.Those whohold to the mathematicalrgument ouLld, think,mostlybe willing o accept the imitation ame as a basis fordiscussion. Those who believein the two previousobjectionswouldprobablynot be interestedn any criteria.(4) TheAryumentfromonsciousness.Thisarguments verywell expressedn Professor efferson'sisterOrationfor1949,fromwhich quote. " Not untila machine an write sonnetor composea concerto ecause of thoughts nd emotions elt,and not by the chance fall of symbols, ould we agree thatmachine quals brain-that is, not onlywrite t but Inow thatit had writtent. No mechanism ould feel (and not merely



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446 A. M. TURING:artificiallyignal, n easy contrivance) leasure t its successes,griefwhen its valves fuse,be warmed by flattery, e mademiserable y its mistakes, e charmedby sex, be angryor de-pressedwhen t cannot getwhat t wants."This argument ppears to be a denial of the validityof ourtest. According o the mostextreme orm f this view the onlyway by whichone could be sure that a machine hinks s to bethemachine nd to feeloneself hinking. One could then des-cribethese feelings o the world,but of course no one wouldbe justified n taking any notice. Likewise according o thisview the only way to knowthat a man thinks s to be thatparticularman. It is infact hesolipsist ointofview. It maybe the most ogicalview to hold but it makes communicationfideas difficult. is liable to believe A thinksbut B does not'whilstB believes B thinks utA does not . Instead ofarguingcontinually ver this point t is usual to have the polite con-vention hat everyone hinks.I am surethat ProfessorJeffersonoes not wishto adoptthe extremend solipsist ointof view. Probablyhe would bequite willing o accept the mitation ameas a test. The game(with the player B omitted) s frequently sed in practiceunder he name of viva voce odiscoverwhetheromeonereallyunderstands omethingr has ' learnt t parrotfashion'. Letus listen n to a partofsucha vivavoce:Interrogator: In the first ine of your sonnet which reads' Shall I compare hee to a summer's ay , would not ' aspring ay do as well orbetterWitness: It wouldn't can.Interrogator:How about ' a winter's ay' That wouldscanall right.Witness: Yes, but nobodywantsto be compared o a winter'sday.Interroga.tor:Would you say Mr. Pickwickremindedyou ofChristmasWitness: In a way.Interrogator:Yet Christmass a winter'sday, and I do not

thinkMr. Pickwickwouldmindthe comparison.Witness: I don'tthinkyou'reserious. By a winter's ay onemeansa typicalwinter's ay,rather hana specialonelikeChristmas.Andso on. WhatwouldProfessor effersonayifthesonnet-writingmachinewas ableto answer ikethis n thevivavoce Ido notknowwhether e wouldregard hemachine s 'merely



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448 A. M. TURING:Theexactdefinitionoes notmatter s nomathematicalccuracyis claimedin thepiresent iscussion.) A fewyearsago, whenvery ittle had beenheardof digitalcomputers,t was possibleto elicitmuchincredulity oncerninghem, f one mentionedtheir propertieswithoutdescribing heir construction.Thatwas presumably ue to a similar pplicationof the principleof scientificnduction. These applications f the principle reof course argelyunconscious. When a burntchild fearsthefire nd shows hathe fears t byavoiding t, I should aythathe was applying cientificnduction. (I could of coursealsodescribehis behaviour n manyother ways.) The works ndcustomsofmankinddo not seem to be verysuitablematerialto whichto apply scientificnduction. A verylargepart ofspace-timemustbe investigated,f reliableresultsare to beobtained. Otherwisewe may (as most Englishchildrendo)decide that everybody peaks English,and that it is silly tolearnFrench.Thereare,however,pecialremarks o be made about manyofthe disabilities hathave beenmentioned. The inability oenjoy strawberriesnd cream may have struck he readerasfrivolous. Possibly a machinemightbe made to enjoy thisdeliciousdish,but any attemptto make one do so would beidiotic. Whatis importantbout this disabilitys that it con-tributesosome f heother isabilities,.g.to thedifficultyf hesamekindoffriendlinessccurringetweenmanand machine sbetweenwhitemanand whiteman,or betweenblackman andblackman.The claimthat " machines annotmake mistakes seemsacurious ne. Oneis tempted o retort, Arethey nytheworsefor hat ? " But let us adopta more ympatheticttitude, ndtryto see whatis reallymeant. I think hiscriticisman beexplainedn terms fthe mitation amne. t is claimed hattheinterrogatoroulddistinguishhemachine rom hemansimplyby settingthema numberof problems n arithmetic. Themachinewould be unmaskedbecause of its deadly accuracy.The replyto this is simple. The machine programmed orplaying he game)wouldnot attempt o givethe rightnswersto the arithmetic roblems. It would deliberatelyntroducemistakes na manner alculatedto confuse heinterrogator.Amechanical aultwouldprobably-how tself hroughn unsuit-able decisionas to what sort of a mistaketo make in tbearithmetic. Even this interpretationf the criticism s notsufficientlyympathetic.But we cannotaffordhe space to gointo tmuchfurther. t seems o methatthiscriticismepends



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COMPUTING MACHINERY AND INTELLIGENCE 449on a confusion etweentwo kinds of mistake. We may callthem errorsffunctioningand ' errors fconclusion. Errorsof functioningre due to some mechanical or electricalfaultwhich causes the machineto behave otherwise han it wasdesigned to do. In philosophicaldiscussionsone likes toignore he possibilityf such errors; one is therefore iscussing'abstract machines'. These bstractmachinesre mathematicalfictions atherthan physicalobjects. By definition heyareincapable of errors f functioning. n this sense we can trulysay that machinescan nevermake mistakes'. Errorsof con-clusion can only arise whensome meaning s attached to theoutput signals from the machine. The machine might,forinstance, type out mathematicalequations, or sentences nEnglish. When a false proposition s typedwe say that themachinehascommittedn error f conclusion. There s clearlyno reason at all for sayingthat a machine cannot make thiskind of mistake. It mightdo nothing uttype out repeatedly' 0 - 1 . To takea lessperverse xample, t mighthave somemethod for drawingconclusionsby scientificnduction. Wemust expect such a methodto lead occasionally o erroneousresults.The claimthat a machinecannotbe the subjectof its ownthought an of courseonlybe answeredf t can be shown hatthe machine as some houghtwith ome ubjectmatter. Never-theless, the subject matterof a machine'soperations doesseemtomeansomething,t leastto thepeoplewhodeal with t.If, for nstance, he machinewas trying o finda solutionofthe equationx2 40x - 11 0 onewoald be tempted o de-scribethisequationas partof themachine's ubjectmatter tthatmoment. In thissortof sensea machine ndoubtedlyanbe its ownsubjectmatter. It maybe used to help in makingup its ownprogrammes,r to predict heeffect f alterationsnits ownstructure. By observingheresults f ts ownbehaviourit canmodifytsownprogrammeso as to achieve omepurposemore effectively. hese are possibilities f the near future,rather han Utopiandreams.The criticism hat a machine cannothave much diversityof behaviour s just a way ofsayingthat it cannothave muchstorage capacity. Until fairlyrecently storage capacity ofeven a thousanddigitswas very are.The criticismshatweare consideringere reoften isguisedforms ftheargumentrom onsciousness. Usually f onemain-tainsthata machine ando oneofthese hings,nd describes hekind ofmethod hatthemachine oulduse, one willnotmake29



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450 A. M. TURING:muchof n impression. It isthought hatthemethodwhateverit may be, for t must be mechanical) s really ratherbase.Compare heparenthesisnJefferson'statementuotedonp. 21.(6) LadyLovelace'sObjection.Ourmostdetailed nformationofBabbage's AnalyticalEngine omesfrom memoir y LadyLovelace. In it shestates, The AnalyticalEnginehas no pre-tensions o originatenything. It can do whatevereknow owtoorder t to perform (her talics). Thisstatements quotedby Hartree p. 70) who adds: " This does notimplythat itmay not be possible to construct lectronic quipmentwhichwill thinkfor tself, or nwhich,n biological erms, ne couldset up a conditionedeflex,whichwould serveas a basis for'learning . Whether his is possible n principle r not is astimulatingnd excitingquestion, uggested y someof theserecentdevelopments. But it did not seemthatthe machinesconstructedrprojected t thetime had thisproperty.I am in thoroughgreement ithHartreeoverthis. It willbe noticed hathe does notassert hatthemachinesn questionhad notgot theproperty,utrather hat theevidence vailabletoLady Lovelacedid notencourage er obelieve hat heyhad t.It is quitepossible hatthe machines n questionhad ina sensegotthisproperty. Forsuppose hat somediscrete-state achinehas the property. The Analytical Engine was a universaldigitalcomputer,o that, f ts storage apacity nd speedwereadequate, it couldby suitableprogramminge made to mimicthe machinein question. Probablythis argumentdid notoccurto theCountess rto Babbage. In anycase therewasnoobligation nthem o claimall that couldbe claimed.

Thiswhole uestionwillbe consideredgainunder heheadingoflearningmachines.A variant fLady Lovelace'sobjection tatesthat a machinecan ' neverdo anythingeallynew'. Thismaybe parried ormomentwith thesaw, 'There is nothingnewunderthe sun'.Who can be certain hat originalwork' thathe has donewasnot simply hegrowth fthe seedplanted n himby teaching,or the effect f followingwell-known eneralprinciples. Abettervariantofthe objection ays that a machinecan never'take us bysurprise'. Thisstatements a moredirect hallengeand can be metdirectly. Machines ake me by surprisewithgreatfrequency. This is largelybecauseI do notdo sufficientcalculationodecidewhat oexpect hem odo,orrather ecause,although do a calculation, do it ina hurried,lipshod ashion,takingrisks. Perhaps say to myself, I supposethe voltagehereought o be the sameas there: anywayet'sassume tis .



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COMPUTING MACHINERY AND INTELLIGENCE 451Naturally amoftenwrong,nd theresults a surpriseormeforbythe timetheexperiments done theseassumptions avebeenforgotten.These admissions ay me open to lectureson thesubjectof myviciousways,but do notthrow ny doubton mycredibility hen testifyo the surprises experience.I do not expect thisreply o silencemy critic. He will pro-bablysaythatsuchsurprisesredue to somecreativemental cton my part, nd reflect o credit n the machine. This eadsusbackto the argument rom onsciousness,nd farfrom he ideaof surprise. It is a line of argumentwe mustconsider losed,but t is perhapsworth emarkinghat the appreciationf some-thing s surprisingequires s muchof a ' creativemental ct 'whether he surprising,ventoriginates rom man, a book,amachine ranything lse.The viewthatmachines annotgiveriseto surprisess due,I believe, o a fallacy owhichphilosophersndmathematiciansareparticularlyubject. Thisis theassumptionhatas soon asa fact is presentedto a mind all consequencesof that factspring nto the mindsimultaneously ith t. It is a veryuse-ful assumptionundermanycircumstances,ut one too easilyforgetshat tisfalse. A natural onsequence fdoing o is thatone thenassumesthat there s no virtue n the mereworkingout of consequences rom ata andgeneral rinciples.(7) ArgumentromContitnuityn the NervousSystem. Thenervoussystem s certainlynot a discrete-statemachine. Asmallerrornthe nformationboutthesizeof nervousmpulseimpingingn a neuron,maymakea largedifferenceo the sizeoftheoutgoingmpulse. It maybe arguedthat,thisbeing o,one cannotexpectto be able to mimic the behaviourof thenervous ystemwith discrete-stateystem.It is truethata discrete-state achinemustbe differentroma continuousmachine. But ifweadhere o theconditionsftheimitation ame,the interrogator ill not be able to take anyadvantageofthis difference.The situation anbe made clearerif we considersome other simplercontinuousmachine. Adifferentialnalyserwill do verywell. (A differentialnalyseris a certainkind ofmachinenot of the discrete-stateypeusedfor some kinds of calculation.) Some of these provide theiranswers n a typed form, nd so are suitablefortaking partin the game. It wouldnotbe possiblefora digital computerto predict exactly what answers the differential nalyserwould give to a problem,but it would be quite capable ofgiving he right ort of answer. For instance,faskedto givethe value of r (actuallyabout 3.1416) it wouldbe reasonable



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452 A. M. TURING:to chooseat randombetween he values 3*12,3*13,3*14,3-15,3 16 withthe probabilities f005, 0O15, .55, 019, 006 (say).Under these circumstancest would be very difficultor theinterrogatoro distinguish he differentialnalyserfromthedigital computer.(8) The Argumentrom nformalityf Behaviour. It is notpossibleto producea set of rulespurportingo describewhata man should do in every conceivableset of circumstances.One mightfor nstancehave a rule that one is to stop whenone sees a red trafficight, nd to go if one sees a greenone,but what if by some fault both appear together One mayperhaps decide that it is safest to stop. But some furtherdifficultyay well arisefrom hisdecisionater. To attempt oproviderulesof conduct o cover every ventuality,ven thosearisingfrom rafficights, ppearsto be impossible. Withallthis agree.Fromthis t is arguedthat we cannotbe machines. I shalltryto reproducehe argument, ut I fear shall hardlydo itjustice. It seems to run somethingike this. 'If each manhad a definiteet of rules of conductby whichhe regulated islifehe wouldbe no better han a machine. But thereare nosuch rules, so men cannotbe machines.' The undistributedmiddle s glaring. I do notthink hearguments everput quitelikethis,but I believethis s the argument sed nevertheless.There may howeverbe a certainconfusion etween rules ofconduct and laws ofbehaviour to cloudthe ssue. By ' rulesof conduct I meanpreceptsuch as ' Stopifyousee red ights,on whichone can act, and of whichone can be conscious. By'laws ofbehaviour' mean aws of nature s appliedto a man'sbody uch s ' ifyou pinchhimhe will queak . If we substitute'laws ofbehaviourwhich egulatehis life' for laws of conductbywhichhe regulateshis life' in the argumentuotedthe un-distributedmiddle is no longer nsuperable. For we believethatit is notonly rue hatbeingregulated y aws of behaviourimpliesbeingsome sort of machine thoughnot necessarilydiscrete-stateachine), utthatconversely eing uch machineimpliesbeing regulatedby such laws. However,we cannotso easilyconvince urselves fthe absence ofcompleteaws ofbehaviour s of complete ules of conduct. The only wayweknow offorfindinguch laws is scientificbservation,nd wecertainly nowof no circumstances nder whichwe could say,'We have searched nough. Thereareno such aws.'We can demonstratemoreforciblyhat any such statementwouldbe unjustified.For supposewe couldbe sure of; inding



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COMPUTING MACHINERY AND INTELLIGENCE 453such aws ifthey existed. Then givena discrete-s,,ateachineit should ertainlye possible odiscover yobservationufficentabout t to predictts future ehaviour,nd thiswithin reason-able time, ay a thousandyears. But thisdoesnot seem to bethe case. I have set up on theManchester omputer smallprogrammesing nly1000units f torage,wherebyhemachinesuppliedwith one sixteenfigurenumberreplieswith anotherwithin wo seconds. I would defy nyoneto learn from hesereplies ufficientbouttheprogrammeo be able to predict nyreplies o untried alues.

(9) The ArgumentromExtra-Sensoryerception.I assumethat the reader s familiarwiththe idea of extra-sensoryer-ception, nd themeaning f the four temsof t,viz.telepathy,clairvoyance, recognitionnd psycho-kinesis.These disturb-ing phenomenaseem to deny all our usual scientificdeas.How we should like to discreditthem Unfortunatelyhestatistical vidence,t leastfor elepathy,s overwhelming.t isverydifficulto rearrangene'sideas so as to fit hesenew factsin. Onceone has accepted hem t does notseem verybig stepto believe nghosts nd bogies. The idea that our bodiesmovesimply ccording o the known aws of physics, ogetherwithsome othersnot yet discoveredbut somewhat imilar,wouldbe one ofthe first o go.Thisarguments to mymindquitea strong ne. One can sayin reply hatmanyscientificheories eem to remainworkablein practice,n spiteof clashingwithE.S.P.; that in factonecan get alongverynicely f one forgetsbout it. Thisis rathercold comfort,nd one fears that thinkings just the kind ofphenomenon hereE.S.P. maybe especially elevant.A more pecificrgument asedonE.S.P. might un s follows:"Let us playtheimitation ame,usingas witnesses manwhois good as a telepathicreceiver,nd a digitalcomputer. Theinterrogatoran ask such questions s 'What suitdoes thecardinmy righthandbelong o ? The manbytelepathy rclair-voyancegivestheright nswer 30times ut of400 cards. Themachine an onlyguessat random, nd perhapsgets 104right,so theinterrogator akestherightdentification."There s aninterestingossibility hich penshere. Suppose hedigital om-putercontains randomnumbergenerator. Then it will benatural o usethisto decidewhatanswer o give. But then herandomnumber eneratorwillbe subjectto thepsycho-kineticpowersof the interrogator.Perhapsthispsycho-kinesis ightcause the machineto guess rightmoreoftenthan would beexpectedon a probability alculation, o that the interrogator



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454 A. M. TURING:might tillbe unable to make the right dentification.On theotherhand,he might e ableto guessrightwithout ny question-ing, by clairvoyance. WithE.S.P. anythingmay happen.If telepathy s admitted t will be necessary o tightenourtest up. The situation ouldbe regarded s analogousto thatwhich would occur if the interrogator eretalking o himselfand one ofthe competitors as listening ithhisearto thewall.To put the competitorsnto a 'telep-thy-proofoom' wouldsatisfy ll requirements.7. LearningMachines.The readerwill have anticipatedhat havenovery onvincingargumentsf a positivenature o supportmy views. If I had Ishould nothave taken suchpains to pointout the fallacies ncontrary iews. Such evidence s I have I shallnowgive.Let us returnfor a moment o Lady Lovelace's objection,which tated hat the machine an onlydo whatwetell t to do.One could say that a mancan inject' an idea intothemachine,and that it will respondto a certainextent and then dropintoquiescence,ike pianostring truck ya hammer. Anothersimile would be an atomicpile of less than criticalsize aninjected dea is to correspond o a neutron ntering he pilefromwithout. Each suchneutron ill ausea certain isturbancewhich ventually ies away. If, however, hesize ofthepile ssufficientlyncreased,he disturbanceausedby such n incomingneutronwillvery ikelygo on and on increasing ntilthewholepile is destroyed. Is there a correspondinghenomenon orminds, and is there one for machines There does seem tobe one for hehumanmind. The majority fthem seem to be' sub-critical', .e. to correspondn this analogyto pilesof sub-critical ize. An idea presentedo such a mindwillon averagegiveriseto less than one idea in reply. A smallish roportionare super-critical.An idea presentedo sucha mindmay giverise to a whole theory' consisting f secondary, ertiary ndmoreremote deas. Animalsminds seem to be verydefinitelysub-critical.Adhering o thisanalogy we ask, Can a machinebe made to be super-critical'The skin of n onion' analogy s alsohelpful. In consideringthefunctions f the mindorthebrainwe find ertain perationswhichwe can explain n purelymechanical erms. Thiswe saydoesnot correspondo therealmind: it is a sortofskinwhichwe must stripoff f we are to find hereal mind. But then nwhatremainswe find furtherkin o be stripped ff, nd so on.



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COMPUTING MACHINERY AND INTELLIGENCE 455Proceedingn thiswaydo we ever cometo the real' mind,ordo we eventuallyometo the skinwhichhas nothingn it ? Inthe latter case the wholemind s mechanical. (It would notbe a discrete-state achinehowever. We have discussed his.)These last two paragraphsdo not claim to be convincingarguments. They should ratherbe describedas 'recitationstending o producebelief .The onlyreally atisfactoryupport hat can be givenfor heviewexpressedt thebeginningrf? 6, willbe thatprovided ywaiting or he end ofthecenturynd thendoing heexperimentdescribed. But what can we say -in the meantime Whatsteps should be taken now if the experiment s to besuccessfulAs I haveexplained,heproblemsmainly neofprogramming.Advances' n engineering illhave to be madetoo,but it seemsunlikely hatthesewillnot be adeqaate for the requirements.Estimatesofthe storagecapacityofthe brainvaryfrom1010to 1015binary igits. I incline o the lowervalues and believethat only a verysmall fractions used forthehigher ypesofthinking.Mostof t is probably sedfor heretention fvisualimpressions. shouldbe surprisedfmore han109wasrequiredfor atisfactorylaying f he mitation ame, t anyrateagainsta blind man. (Note-The capacity of the EncyclopaediaBritannica, 1thedition,s 2 X 109.) A storage apacityof107would be a very practicablepossibility ven by present ech-niques. It is probablynot necessary o increase he speed ofoperations f the machines t all. Parts of modernmachineswhichcan be regarded s analoguesofnervecellsworkaboata thousand imesfaster hanthe latter. Thisshouldprovide' marginof sa.fety whichcould cover losses of speed arisinginmanyways. Ourproblemhensto find uthow oprogrammethesemachines oplaythegame. Atmypresent ateofworkingI produce bouta thousanddigitsofprogramme day,so thatabout sixtyworkers,working teadilythrough he fifty earsmight ccomplishhe job, ifnothingwent ntothewaste-paperbasket. Some more expeditiousmethodseemsdesirable.In the processoftrying o imitate n adulthiumanmind weare bound to think good deal about the processwhichhasbrought t to the state that it is in. We may notice threecomponents,(a) The initial tateof themind, ayat birth,(b) The education owhich thas beensubjected,(e) Otherexperience, ot to be described s education,towhich t has beensubjected.



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456 A. M. TURING:Instead of trying o producea programmeo simulate headult mind,whynot rather ry o produce ne which imulatesthe child's? If this were then subjected to an appropriatecourseof educationone would obtain the adult brain. Pre-sumablythe child-brains somethingike a note-book s onebuys t from hestationers. Rather ittlemechanism,nd lotsof blanksheets. (Mechanismnd writingre from ur pointofview almost synonymous.)Our hope is that there s so littlemechanismn thechild-brainhat somethingike t can be easilyprogrammed.The amountof work in the educationwe can

assume, s a firstpproximation,o be much hesame as for hehuman child.We have thus divided our problem nto two parts. Thechild-programmend the educationprocess. Thesetwo remainveryclosely onnected. We cannotexpectto find good child-machine-athefirstttempt. One must xperiment ith eachingone suchmachine nd see howwell t learns. One can thentryanother nd see if it is betteror worse. There s an obviousconnection etween his process nd evolution, y the identifi-cationsStructuref hechildmachine HereditarymaterialChanges ,, ,, = MutationsNaturalselection = JudgmentftheexperimenterOnemayhope,however,hat hisprocesswillbemore xpeditiousthan evolution. The survival f thefittests a slowmethod ormeasuring dvantages. The experimenter,y the exerciseofintelligence,houldbe able to speed t up. Equallyimportantsthe factthat he is not restrictedo randommutations. If hecantracea cause for omeweakness e can probably hink fthekindofmutationwhichwill mprove t.It will not be possible to apply exactlythe same teachingprocessto the machineas to a normalchild. It will not,forinstance,be providedwith legs,so that it couldnot be askedto go out and fill he coal scuttle. Possibly t mightnot haveeyes. But howeverwell these deficienciesmightbe overcomebycleverengineering,ne could notsendthecreature o schoolwithout heother hildrenmaking xcessivefunof t. It mustbe givensometuition. We need not be too concerned boutthe legs, eyes,etc. The example of Miss HelenKellershowsthat educationcan take place providedthat communicationin bothdirections etween eacher nd pupil can take place bysome meansor other.



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COMPUTING AMACHINERY AND INTELLIGENCE 457We normally ssociate punishmentsnd rewardswith theteachingprocess. Some simple child-machines an be con-structed rprogrammednthissortofprinciple. Themachinehas to be so constructedhat eventswhich hortly receded heoccurrence fa punishment-signalre unlikely o be repeated,whereas a reward-signalncreased he probability frepetitionofthe eventswhich ed up to it. Thesedefinitionso not pre-supposeanyfeelings n thepartofthemachine. I have donesome experiments ith one suchchild-machine,nd succeededin teaching t a fewthings,but the teachingmethodwas toounorthodoxor heexperimento be consideredeally uccessful.The use ofpunishmentsnd rewards an at best be a partofthe teachingprocess. Roughly peaking,fthe teacherhas noothermeans of communicatingo the pupil, the amount ofinformationhich anreachhimdoesnotexceedthetotalnum-ber ofrewards nd punishmentspplied. By the time a childhas learnt o repeat Casabianca' he wouldprobablyfeelverysore ndeed, fthetextcouldonlybe discovered y a 'TwentyQuestions' technique, very NO' takingthe form f a blow.

It is necessary hereforeo have some other unemotionalchannels fcommunication. f these are availableit is possibleto teacha machine y punishmentsnd rewards o obeyordersgiven n some anguage, .g.a symbolicanguage. Theseordersare to be transmitted hrough he 'unemotional' channels.The use of this languagewill diminish reatly he number fpunishmentsnd rewards equired.Opinionsmayvaryas to the complexitywhich s suitable nthe child machine. One mighttry'to make it as simpleaspossibleconsistently ith thegeneralprinciples. Alternativelyonemight ave a completeystem f ogical nferencebuilt n .,In the lattercase the storewouldbe largely ccupiedwithde-finitionsndpropositions.Thepropositions ouldhavevariouskinds of status,e.g. well-establishedacts,conjectures,mathe-maticallyprovedtheorems,tatements iven by an authority,expressions aving helogicalform fpropositionut notbelief-value. Certain ropositionsmaybe described s 'imperatives'.The machine houldbe so constructedhat as soon as an im-perative s classed as 'well-established the appropriate ctionautomatically akesplace. Toillustratehis, uppose heteachersays to the machine, Do yourhomework ow'. This maycause " Teacher ays Do yourhomework ow " to be includedamongst hewell-establishedacts. Another uchfactmight e,1Orratherprogrammedn' for urchild-machineillbeprogrammedina digital omputer.But the ogical ystemwillnothave to be learnt.



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458 A. M. TURING:"Everything hat teacher ays s true . Combininghesemayeventually ead to the imperative,Do your homework ow',being included amongst the well-established acts, and this,by theconstructionf hemachine,willmeanthat the homeworkactually getsstarted, ut the effect s very satisfactory. Theprocessesof inference sed by the machineneed not be suchas wouldsatisfy he most exacting ogicians. There mightforinstancebe nohierarchy f types. But thisneed not mean thattype fallacieswill occur, any morethan we are bound to fallover unfencedcliffs. Suitable imperatives expressedwithinthe systems, ot forming art of the rules of the system) uchas ' Do notuse a class unless t is a subclass of one whichhasbeenmentioned y teacher' can have a similar ffecto 'Do notgo tooneartheedge'.The imperatives hat can be obeyedby a machinethat hasno limbs reboundto be of a rather ntellectual haracter, s intheexampledoinghomework) iven bove. Important mongstsuch mperatives ill be ones whichregulate he order n whichthe rules of the logical system concerned re to be applied.For at each stagewhenone is usinga logical system,here s avery largenumberof alternative teps, any of which one ispermittedo apply, o far s obedience otherulesofthe ogicalsystems concerned. These choicesmakethe differenceetweena brilliant nd a footling easoner, otthe differenceetweensound nda fallacious ne. Propositionseadingto imperativesof this kindmightbe " When Socrates s mentioned, se thesyllogismnBarbara" or" If one methodhas been proved o bequicker than another, o not use the slowermethod . Someofthese maybe 'given by authority',but othersmaybe pro-ducedby themachine tself, .g. by scientificnduction.The idea of a learningmachinemay appear paradoxicaltosomereaders. How can the rules of operation fthemachinechange They shoulddescribecompletelyhow the machinewill react whatever ts historymightbe, whateverchangesit mightundergo. The rules are thus quite time-invariant.This is quite true. The explanation ftheparadoxis that therules whichget changed n the learning rocess re of a ratherlesspretentious ind, laiming nly n ephemeral alidity. Thereadermaydraw a parallelwiththeConstitutionf theUnitedStates.Aln mportant eature fa learningmachines that tsteacherwill oftenbe very argely gnorant f quite what is goingoninside, lthoughhe may stillbe able to some extent o predicthis pupil'sbehaviour. This shouldapplymoststronglyo the



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460 A. M. TURING: COMPUTING MACHINERY AND INTELLIGENCEof the differentenetical ombinations hat had been tried, oas to avoidtrying hemagain ?We mayhope thatmachineswilleventuallyompetewithmenin all purely ntellectual ields. But which re the best onestostart with Even this is a difficult ecision. Many peoplethinkthat a veryabstract activity, ike the playingof chess,would be best. It can also be maintained hat it is best toprovide hemachinewith he best sense organs hat money anbuy, and then teach it to understandnd speakEnglish. Thisprocesscould followthe normalteaching of a child. Thingswould be pointed out and named, etc. Again I do not knowwhat theright nswer s, but I thinkbothapproaches houldbetried.We can only ee a short istance head, butwe can see plentythere hatneeds to be done.

BIBLIOGRAPHYSamuel Butler, Erewhon, London, 1865. Chapters 23, 24, 25, The Bookof theMachines.Alonzo Church, An Unsolvable Problemof ElementaryNumberTheory ",AmericanJ. of Math., 58 (1936), 345-363.K. G6del, " Vber formalunentscheidbareSatze derPrincipia Mathematicaund verwandter Systeme, I ", Monatshefte uirMath. und Phys.,(1931), 173-189.D. R. Hartree, Calculating Instruments nd Machines, New York, 1949.S. C. Kleene, " General Recursive Functions of Natural Numbers ",AmericanJ. of Math., 57 (1935), 153-173 and 219-244.G. Jefferson, The Mind of Mechanical Man ". Lister Oration for 1949.

BritishMedical Journal,vol. i (1949), 1105-1121.Countess of Lovelace, ' Translator's notes to an article on Babbage'sAnalytical Engire', ScientificMemoirs (ed. by R. Taylor), vol. 3(1842), 691-731.Bertrand Russell, Historyof Western hilosophy,London, 1940.A. M. Turing, " On Computable Numbers, with an Application to theEntscheidungsproblem , Proc. London Math. Soc. (2), 42 (1937),230-265.V7ictoria niversittyf Manchester.

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Turing, Computing (Mind)