Alan Turing (1912–1954) never described himself as a philosopher, buthis 1950 paper “Computing Machinery and Intelligence” is one of themost frequently cited in modern philosophical literature. It gave afresh approach to the traditional mind-body problem, by relating it tothe mathematical concept of computability he himself had introduced inhis 1936–7 paper “On computable numbers, with an application to theEntscheidungsproblem.” His work can be regarded as the foundation ofcomputer science and of the artificial intelligence program.

• 1. Outline of Life
• 2. The Turing Machine and Computability
• 3. The Logical and the Physical
• 4. The Uncomputable
• 5. Building a Universal Machine
• 6. Building a Brain
• 7. Machine Intelligence
• 8. Unfinished Work
• 9. Alan Turing: the Unknown Mind
• Bibliography
• Academic Tools
• Other Internet Resources
• Related Entries

1. Outline of Life

Alan Turing's short and extraordinary life has attracted wide interest.It has inspired his mother's memoir (E. S. Turing 1959), a detailedbiography (Hodges 1983), a play and television film (Whitemore 1986),and various other works of fiction and art.

There are many reasons for this interest, but one is that in everysphere of his life and work he made unexpected connections betweenapparently unrelated areas. His central contribution to science andphilosophy came through his treating the subject of symbolic logic as anew branch of applied mathematics, giving it a physical and engineeringcontent. Unwilling or unable to remain within any standard role ordepartment of thought, Alan Turing continued a life full ofincongruity. Though a shy, boyish, man, he had a pivotal role in worldhistory through his role in Second World War cryptology. Though thefounder of the dominant technology of the twentieth century, hevariously impressed, charmed or disturbed people with his unworldlyinnocence and his dislike of moral or intellectual compromise.

Alan Mathison Turing was born in London, 23 June 1912, toupper-middle-class British parents. His schooling was of a traditionalkind, dominated by the British imperial system, but from earliest lifehis fascination with the scientific impulse—expressed by him asfinding the ‘commonest in nature’—found him at oddswith authority. His scepticism, and disrespect for worldly values, werenever tamed and became ever more confidently eccentric. His moodyhumour swung between gloom and vivacity. His life was also notable asthat of a gay man with strong emotions and a growing insistence on hisidentity.

His first true home was at King's College, Cambridge University,noted for its progressive intellectual life centred on J. M. Keynes.Turing studied mathematics with increasing distinction and was electeda Fellow of the college in 1935. This appointment was followed by aremarkable and sudden début in an area where he was an unknownfigure: that of mathematical logic. The paper “On ComputableNumbers…” (Turing 1936–7) was his first and perhaps greatesttriumph. It gave a definition of computation and an absolute limitationon what computation could achieve, which makes it the founding work ofmodern computer science. It led him to Princeton for more advanced workin logic and other branches of mathematics. He had the opportunity toremain in the United States, but chose to return to Britain in 1938,and was immediately recruited for the British communications war.

From 1939 to 1945 Turing was almost totally engaged in the masteryof the German enciphering machine, Enigma, and other cryptologicalinvestigations at now-famous Bletchley Park, the British government'swartime communications headquarters. Turing made a unique logicalcontribution to the decryption of the Enigma and became the chiefscientific figure, with a particular responsibility for reading theU-boat communications. As such he became a top-level figure inAnglo-American liaison, and also gained exposure to the most advancedelectronic technology of the day.

Combining his ideas from mathematical logic, his experience incryptology, and some practical electronic knowledge, his ambition, atthe end of the war in Europe, was to create an electronic computer inthe full modern sense. His plans, commissioned by the National PhysicalLaboratory, London, were overshadowed by the more powerfully supportedAmerican projects. Turing also laboured under the disadvantage that hiswartime achievements remained totally secret. His ideas led the fieldin 1946, but this was little recognised. Frustrated in his work, heemerged as a powerful marathon runner, and almost qualified for theBritish team in the 1948 Olympic games.

Turing's motivations were scientific rather than industrial orcommercial, and he soon returned to the theoretical limitations ofcomputation, this time focussing on the comparison of the power ofcomputation and the power of the human brain. His contention was thatthe computer, when properly programmed, could rival the brain. Itfounded the ‘Artificial Intelligence’ program of comingdecades.

In 1948 he moved to Manchester University, where he partly fulfilledthe expectations placed upon him to plan software for the pioneercomputer development there, but still remained a free-ranging thinker.It was here that his famous 1950 paper, “Computing Machinery andIntelligence,” (Turing 1950b) was written. In 1951 he was elected aFellow of the Royal Society for his 1936 achievement, yet at the sametime he was striking into entirely new territory with a mathematicaltheory of biological morphogenesis (Turing 1952).

This work was interrupted by Alan Turing's arrest in February 1952for his sexual affair with a young Manchester man, and he was obliged,to escape imprisonment, to undergo the injection of oestrogen intendedto negate his sexual drive. He was disqualified from continuing secretcryptological work. His general libertarian attitude was enhancedrather than suppressed by the criminal trial, and his intellectualindividuality also remained as lively as ever. While remaining formallya Reader in the Theory of Computing, he not only embarked on moreambitious applications of his biological theory, but advanced new ideasfor fundamental physics.

For this reason his death, on 7 June 1954, at his home in Wilmslow,Cheshire, came as a general surprise. In hindsight it is obvious thatTuring's unique status in Anglo-American secret communication workmeant that there were pressures on him of which his contemporaries wereunaware; there was certainly another ‘security’ conflictwith government in 1953 (Hodges 1983, p. 483). Some commentators, e.g.Dawson (1985), have argued that assassination should not be ruled out.But he had spoken of suicide, and his death, which was by cyanidepoisoning, was most likely by his own hand, contrived so as to allowthose who wished to do so to believe it a result of his penchant forchemistry experiments. The symbolism of its dramatic element—apartly eaten apple—has continued to haunt the intellectual Edenfrom which Alan Turing was expelled.

2. The Turing Machine and Computability

Alan Turing drew much between 1928 and 1933 from the work of themathematical physicist and populariser A. S. Eddington, from J. vonNeumann's account of the foundations of quantum mechanics, and thenfrom Bertrand Russell's mathematical logic. Meanwhile, his lastingfascination with the problems of mind and matter was heightened byemotional elements in his own life (Hodges 1983, p. 63). In 1934 hegraduated with an outstanding degree in mathematics from CambridgeUniversity, followed by a successful dissertation in probability theorywhich won him a Fellowship of King's College, Cambridge, in 1935. Thiswas the background to his learning, also in 1935, of the problem whichwas to make his name.

It was from the lectures of the topologist M. H. A. (Max) Newman inthat year that he learnt of Gödel's 1931 proof of the formalincompleteness of logical systems rich enough to include arithmetic,and of the outstanding problem in the foundations of mathematics asposed by Hilbert: the “Entscheidungsproblem” (decision problem). Wasthere a method by which it could be decided, for any given mathematicalproposition, whether or not it was provable?

The principal difficulty of this question lay in giving anunassailably correct and general definition of what was meant by suchexpressions as ‘definite method’ or ‘effectiveprocedure.’ Turing worked on this alone for a year until April1936; independence and isolation was to be both his strength, informulating original ideas, and his weakness, when it came to promotingand implementing them.

The word ‘mechanical’ had often been used of theformalist approach lying behind Hilbert's problem, and Turing seized onthe concept of themachine.Turing's solution lay in definingwhat was soon to be named theTuring machine. With this hedefined the concept of ‘the mechanical’ in terms of simpleatomic operations. The Turing machine formalism was modelled on theteleprinter, slightly enlarged in scope to allow a paper tape thatcould move in both directions and a ‘head’ that could read,erase and print new symbols, rather than only read and punch permanentholes.

The Turing machine is ‘theoretical,’ in the sense thatit is not intended actually to be engineered (there being no point indoing so), although it is essential that its atomic components (thepaper tape, movement to left and right, testing for the presence of asymbol) are such ascould actually be implemented. The wholepoint of the formalism is to reduce the concept of ‘method’to simple operations that can unquestionably be‘effected.’

Nevertheless Turing's purpose was to embody the most generalmechanical process as carried out by ahuman being. Hisanalysis began not with any existing computing machines, but with thepicture of a child's exercise book marked off in squares. From thebeginning, the Turing machine concept aimed to capture what thehuman mind can do when carrying out a procedure.

In speaking of ‘the’ Turing machine it should be madeclear that there areinfinitely many Turing machines, eachcorresponding to a different method or procedure, by virtue of having adifferent ‘table of behaviour.’ Nowadays it is almostimpossible to avoid imagery which did not exist in 1936: that of thecomputer. In modern terms, the ‘table of behaviour’ of aTuring machine is equivalent to a computer program.

If a Turing machine corresponds to a computer program, what is theanalogy of the computer? It is what Turing described as auniversal machine (Turing 1936, p. 241). Again, there areinfinitely many universal Turing machines, forming a subset ofTuring machines; they are those machines with ‘tables ofbehaviour’ complex enough to read the tables of other Turingmachines, and then do what those machines would have done. If thisseems strange, note the modern parallel that any computer can besimulated by software on another computer. The way that tables can readand simulate the effect of other tables is crucial to Turing's theory,going far beyond Babbage's ideas of a hundred years earlier. It alsoshows why Turing's ideas go to the heart of the modern computer, inwhich it is essential that programs are themselves a form of data whichcan be manipulated by other programs. But the reader must alwaysremember that in 1936 there were no such computers; indeed the moderncomputer aroseout of the formulation of ‘behavingmechanically’ that Turing found in this work.

Turing's machine formulation allowed the precise definition of thecomputable: namely, as what can be done by a Turing machineacting alone. More exactly, computable operations are those which canbe effected by what Turing calledautomatic machines. Thecrucial point here is that the action of an automatic Turing machine istotally determined by its ‘table of behaviour’. (Turingalso allowed for ‘choice machines’ which call for humaninputs, rather than being totally determined.) Turing then proposedthat this definition of ‘computable’ captured preciselywhat was intended by such words as ‘definite method, procedure,mechanical process’ in stating theEntscheidungsproblem.

In applying his machine concept to theEntscheidungsproblem, Turing took the step of definingcomputable numbers. These are those real numbers, consideredas infinite decimals, say, which it is possible for a Turing machine,starting with an empty tape, to print out. For example, the Turingmachine which simply prints the digit 1 and moves to the right, thenrepeats that action for ever, can thereby compute the number.1111111… A more complicated Turing machine can compute theinfinite decimal expansion of π.

Turing machines, like computer programs, are countable; indeed theycan be ordered in a complete list by a kind of alphabetical ordering oftheir ‘tables of behaviour’. Turing did this by encodingthe tables into ‘description numbers’ which can then beordered in magnitude. Amongst this list, a subset of them (those with‘satisfactory’ description numbers) are the machines whichhave the effect of printing out infinite decimals. It is readily shown,using a ‘diagonal’ argument first used by Cantor andfamiliar from the discoveries of Russell and Gödel, that there canbe no Turing machine with the property of deciding whether adescription number is satisfactory or not. The argument can bepresented as follows. Suppose that such a Turing machine exists. Thenit is possible to construct a new Turing machine which works out inturn the Nth digit from the Nth machine possessing a satisfactorydescription number. This new machine then prints an Nth digit differingfrom that digit. As the machine proceeds, it prints out an infinitedecimal, and therefore has a ‘satisfactory’ descriptionnumber. Yet this number must by construction differ from the outputs ofevery Turing machine with a satisfactory description number. This is acontradiction, so the hypothesis must be false (Turing 1936, p. 246).From this, Turing was able to answer Hilbert'sEntscheidungsproblem in the negative: there can be no suchgeneral method.

Turing's proof can be recast in many ways, but the core idea dependson theself-reference involved in a machine operating onsymbols, which is itself described by symbols and so can operate on itsown description. Indeed, the self-referential aspect of the theory canbe highlighted by a different form of the proof, which Turing preferred(Turing 1936, p. 247). Suppose that such a machine for decidingsatisfactoriness does exist; then apply it to its own descriptionnumber. A contradiction can readily be obtained. However, the‘diagonal’ method has the advantage of bringing out thefollowing: that a real number may bedefined unambiguously,yet beuncomputable. It is a non-trivial discovery thatwhereas some infinite decimals (e.g. π) may be encapsulated in afinite table, other infinite decimals (in fact, almost all) cannot.Likewise there are decision problems such as ‘is this numberprime?’ in which infinitely many answers are wrapped up in afinite recipe, while there are others (again, almost all) which arenot, and must be regarded as requiring infinitely many differentmethods. ‘Is this a provable proposition?’ belongs to thelatter category.

This is what Turing established, and into the bargain the remarkablefact that anything thatis computable can in fact be computedbyone machine, a universal Turing machine.

It was vital to Turing's work that he justified the definition byshowing that it encompassed the most general idea of‘method’. For if it did not, theEntscheidungproblem remained open: there might be some morepowerful type of method than was encompassed by Turing computability.One justification lay in showing that the definition included manyprocesses a mathematician would consider to be natural in computation(Turing 1936, p. 254). Another argument involved a human calculatorfollowing written instruction notes. (Turing 1936, p. 253). But in abolder argument, the one he placed first, he considered an‘intuitive’ argument appealing to thestates ofmind of a human computer. (Turing 1936, p. 249). The entry of‘mind’ into his argument was highly significant, but atthis stage it was only a mind following a rule.

To summarise: Turing found, and justified on very general andfar-reaching grounds, a precise mathematical formulation of theconception of a general process or method. His work, as presented toNewman in April 1936, argued that his formulation of‘computability’ encompassed ‘the possible processeswhich can be carried out in computing a number.’ (Turing 1936,p. 232). This opened up new fields of discovery both in practicalcomputation, and in the discussion of human mental processes. However,although Turing had worked as what Newman called ‘a confirmedsolitary’ (Hodges 1983, p 113), he soon learned that he was notalone in what Gandy (1988) has called ‘the confluence of ideas in1936.’

The Princeton logician Alonzo Church had slightly outpaced Turing infinding a satisfactory definition of what he called ‘effectivecalculability.’ Church's definition required the logicalformalism of thelambda-calculus. This meant that from theoutset Turing's achievement merged with and superseded the formulationofChurch's Thesis, namely the assertion that thelambda-calculus formalism correctly embodied the concept of effectiveprocess or method. Very rapidly it was shown that the mathematicalscope of Turing computability coincided with Church's definition (andalso with the scope of thegeneral recursive functions definedby Gödel). Turing wrote his own statement (Turing 1939, p. 166) ofthe conclusions that had been reached in 1938; it is in the Ph.D.thesis that he wrote under Church's supervision, and so this statementis the nearest we have to a joint statement of the ‘Church-Turingthesis’:

A function is said to be ‘effectivelycalculable’ if its values can be found by some purely mechanicalprocess. Although it is fairly easy to get an intuitive grasp of thisidea, it is nevertheless desirable to have some more definite,mathematically expressible definition. Such a definition was firstgiven by Gödel at Princeton in 1934… These functions weredescribed as ‘general recursive’ by Gödel…Another definition of effective calculability has been given byChurch… who identifies it with lambda-definability. The author[i.e. Turing] has recently suggested a definition corresponding moreclosely to the intuitive idea… It was stated above that ‘afunction is effectively calculable if its values can be found by apurely mechanical process.’ We may take this statement literally,understanding by a purely mechanical process one which could be carriedout by a machine. It is possible to give a mathematical description, ina certain normal form, of the structures of these machines. Thedevelopment of these ideas leads to the author's definition of acomputable function, and to an identification of computability witheffective calculability. It is not difficult, though somewhatlaborious, to prove that these three definitions areequivalent.

Church accepted that Turing's definition gave a compelling, intuitivereason for why Church's thesis was true. The recent exposition byDavis (2000) emphasises that Gödel also was convinced by Turing'sargument that an absolute concept had been identified (Gödel1946). The situation has not changed since 1937. (For furthercomment, see the article on theChurch-Turing Thesis. The recent selection of Turing's papers edited by Copeland (2004),and the review of Hodges (2006), continue this discussion.)

Turing himself did little to evangelise his formulation in the worldof mathematical logic and early computer science. The textbooks ofDavis (1958) and Minsky (1967) did more. Nowadays Turing computabilityis often reformulated (e.g. in terms of ‘registermachines’). However, computer simulations (e.g., Turing's World, from Stanford) have brought Turing'soriginal imagery to life.

Turing's work also opened new areas for decidability questionswithin pure mathematics. From the 1970s, Turing machines also took onnew life in the development ofcomplexity theory, and as suchunderpin one of the most important research areas in computer science.This development exemplifies the lasting value of Turing's specialquality of giving concrete illustration to abstract concepts.

3. The Logical and the Physical

As put by Gandy (1988), Turing's paper was ‘a paradigm ofphilosophical analysis,’ refining a vague notion into a precisedefinition. But it was more than being an analysiswithin theworld of mathematical logic: in Turing's thought the question thatconstantly recurs both theoretically and practically is therelationship of the logical Turing machine to the physical world.

‘Effective’ meansdoing, not merely imaginingor postulating. At this stage neither Turing nor any other logicianmade a serious investigation into the physics of such‘doing.’ But Turing's image of a teleprinter-like machinedoes inescapably refer to something that could actually be physically‘done.’ His concept is a distillation of the idea that onecan only ‘do’ one simple action, or finite number of simpleactions, at a time. How ‘physical’ a concept is it?

The tape never holds more than a finite number of marked squares atany point in a computation. Thus it can be thought of as being finite,but always capable of further extension as required. Obviously thisunbounded extendibility is unphysical, but the definition is still ofpractical use: it means that anything done on a finite tape, howeverlarge, is computable. (Turing himself took such a finitistic approachwhen explaining the practical relevance of computability in his 1950paper.) One aspect of Turing's formulation, however, involves absolutefiniteness: the table of behaviour of a Turing machine must be finite,since Turing allows only a finite number of‘configurations’ of a Turing machine, and only a finiterepertoire of symbols which can be marked on the tape. This isessentially equivalent to allowing only computer programs with finitelengths of code.

‘Calculable by finite means’ was Turing'scharacterisation of computability, which he justified with the argumentthat ‘the human memory is necessarily limited.’ (Turing1936, p. 231). The whole point of his definition lies in encodinginfinite potential effects, (e.g. the printing of an infinite decimal)into finite ‘tables of behaviour’. There would be no pointin allowing machines with infinite ‘tables of behaviour’.It is obvious, for instance, that any real number could be printed bysuch a ‘machine’, by letting the Nth configuration be‘programmed’ to print the Nth digit, for example. Such a‘machine’ could likewise store any countable number ofstatements about all possible mathematical expressions, and so make theEntscheidungsproblem trivial.

Church (1937), when reviewing Turing's paper while Turing was inPrinceton under his supervision, actually gave a boldercharacterisation of the Turing machine as anarbitrary finitemachine.

The author [i.e. Turing] proposes as a criterion that aninfinite sequence of digits 0 and 1 be “computable” that it shall bepossible to devise a computing machine, occupying a finite space andwith working parts of finite size, which will write down the sequenceto any desired number of terms if allowed to run for a sufficientlylong time. As a matter of convenience, certain further restrictions areimposed on the character of the machine, but these are of such a natureas obviously to cause no loss of generality—in particular, ahuman calculator, provided with pencil and paper and explicitinstructions, can be regarded as a kind of Turing machine.

Church (1940) repeated this characterisation. Turing neitherendorsed it nor said anything to contradict it, leaving the generalconcept of ‘machine’ itself undefined. The work of Gandy(1980) did more to justify this characterisation, by refining thestatement of what is meant by ‘a machine.’ His resultssupport Church's statement; they also argue strongly for the view thatnatural attempts to extend the notion of computability lead totrivialisation: if Gandy's conditions on a ‘machine’ aresignificantly weakened then every real number becomes calculable (Gandy1980, p. 130ff.). (For a different interpretation of Church'sstatement, see the article on theChurch-Turing Thesis.)

Turing did not explicitly discuss the question of thespeedof his elementary actions. It is left implicit in his discussion, byhis use of the word ‘never,’ that it is not possible forinfinitely many steps to be performed in a finite time. Others haveexplored the effect of abandoning this restriction. Davies (2001), forinstance, describes a ‘machine’ with an infinite number ofparts, requiring components of arbitrarily small size, running atarbitrarily high speeds. Such a ‘machine’ could performuncomputable tasks. Davies emphasises that such a machine cannot bebuilt in our own physical world, but argues that it could beconstructed in a universe with different physics. To the extent that itrules out such ‘machines’, the Church-Turing thesis musthave at least some physical content.

True physics is quantum-mechanical, and this implies a differentidea of matter and action from Turing's purely classical picture. It isperhaps odd that Turing did not point this out in this period, since hewas well versed in quantum physics. Instead, the analysis and practicaldevelopment of quantum computing was left to the 1980s. Quantumcomputation, using the evolution of wave-functions rather thanclassical machine states, is the most important way in which Turingmachine model has been challenged. The standard formulation of quantumcomputing (Deutsch 1985, following Feynman 1982) does not predictanything beyond computable effects, although within the realm of thecomputable, quantum computations may be very much more efficient thanclassical computations. It is possible that a deeper understanding ofquantum mechanical physics may further change the picture of what canbe physically ‘done.’

4. The Uncomputable

Turing turned to the exploration of theuncomputable for hisPrinceton Ph.D. thesis (1938), which then appeared asSystems ofLogic based on Ordinals (Turing 1939).

It is generally the view, as expressed by Feferman (1988), that thiswork was a diversion from the main thrust of his work. But from anotherangle, as expressed in (Hodges 1997), one can see Turing's developmentas turning naturally from considering the mind when following a rule,to the action of the mind whennot following a rule. Inparticular this 1938 work considered the mind when seeing the truth ofone of Gödel's true but formally unprovable propositions, andhence going beyond rules based on the axioms of the system. As Turingexpressed it (Turing 1939, p. 198), there are ‘formulae, seenintuitively to be correct, but which the Gödel theorem shows areunprovable in the original system.’ Turing's theory of‘ordinal logics’ was an attempt to ‘avoid as far aspossible the effects of Gödel's theorem’ by studying theeffect of adding Gödel sentences as new axioms to create strongerand stronger logics. It did not reach a definitive conclusion.

In his investigation, Turing introduced the idea of an‘oracle’ capable of performing, as if by magic, anuncomputable operation. Turing's oracle cannot be considered as some‘black box’ component of a new class of machines, to be puton a par with the primitive operations of reading single symbols, ashas been suggested by (Copeland 1998). An oracle isinfinitely morepowerful than anything a modern computer can do, and nothing likean elementary component of a computer. Turing defined‘oracle-machines’ as Turing machines with an additionalconfiguration in which they ‘call the oracle’ so as to takean uncomputable step. But these oracle-machines arenot purelymechanical. They are only partially mechanical, like Turing'schoice-machines. Indeed thewhole point of the oracle-machineis to explore the realm of whatcannot be done by purelymechanical processes. Turing emphasised (Turing 1939, p. 173):

We shall not go any further into the nature of this oracleapart from saying that it cannot be a machine.

Turing's oracle can be seen simply as a mathematical tool, usefulfor exploring the mathematics of the uncomputable. The idea of anoracle allows the formulation of questions ofrelative ratherthan absolute computability. Thus Turing opened new fields ofinvestigation in mathematical logic. However, there is also a possibleinterpretation in terms of human cognitive capacity. On thisinterpretation, the oracle is related to the ‘intuition’involved in seeing the truth of a Gödel statement. M. H. A.Newman, who introduced Turing to mathematical logic and continued tocollaborate with him, wrote in (Newman 1955) that the oracle resemblesa mathematician ‘having an idea’, as opposed to using amechanical method. However, Turing's oracle cannot actually beidentified with a human mental faculty. It is too powerful: itimmediately supplies the answer as to whether any given Turing machineis ‘satisfactory,’ something no human being could do. Onthe other hand, anyone hoping to see mental ‘intuition’captured completely by an oracle, must face the difficulty that Turingshowed how his argument for the incompleteness of Turing machines couldbe applied with equal force to oracle-machines (Turing 1939, p. 173).This point has been emphasised by Penrose (1994, p. 380). Newman'scomment might better be taken to refer to the different oraclesuggested later on (Turing 1939, p. 200), which has the property ofrecognising ‘ordinal formulae.’ One can only safely saythat Turing's interest at this time in uncomputable operations appearsin thegeneral setting of studying the mental‘intuition’ of truths which are not established byfollowing mechanical processes (Turing 1939, p. 214ff.).

In Turing's presentation, intuition is in practice present in everypart of a mathematician's thought, but when mathematical proof isformalised, intuition has an explicit manifestation in those stepswhere the mathematician sees the truth of a formally unprovablestatement. Turing did not offer any suggestion as to what he consideredthe brain was physically doing in a moment of such‘intuition’; indeed the word ‘brain’ did notappear in his writing in this era. This question is of interest becauseof the views of Penrose (1989, 1990, 1994, 1996) on just this issue:Penrose holds that the ability of the mind to see formally unprovabletruths shows that there must be uncomputable physical operations in thebrain. It should be noted that there is widespread disagreement aboutwhether the human mind is really seeing the truth of a Gödelsentence; see for instance the discussion in (Penrose 1990) and thereviews following it. However Turing's writing at this period acceptedwithout criticism the concept of intuitive recognition of thetruth.

It was also at this period that Turing met Wittgenstein, and thereis a full record of their 1939 discussions on the foundations ofmathematics in (Diamond 1976). To the disappointment of many, there isno record of any discussions between them, verbal or written, on theproblem of Mind.

In 1939 Turing's various energetic investigations were broken offfor war work. This did, however, have the positive feature of leadingTuring to turn his universal machine into the practical form of themodern digital computer.

5. Building a Universal Machine

When apprised in 1936 of Turing's idea for a universal machine,Turing's contemporary and friend, the economist David Champernowne,reacted by saying that such a thing was impractical; it would need‘the Albert Hall.’ If built from relays as then employed intelephone exchanges, that might indeed have been so, and Turing made noattempt at it. However, in 1937 Turing did work with relays on asmaller machine with a special cryptological function (Hodges 1983, p.138). World history then led Turing to his unique role in the Enigmaproblem, to his becoming the chief figure in the mechanisation oflogical procedures, and to his being introduced to ever faster and moreambitious technology as the war continued.

After 1942, Turing learnt that electronic components offered thespeed, storage capacity and logical functions required to be effectiveas ‘tapes’ and instruction tables. So from 1945, Turingtried to use electronics to turn his universal machine into practicalreality. Turing rapidly composed a detailed plan for a modernstored-program computer: that is, a computer in which data andinstructions are stored and manipulated alike. Turing's ideas led thefield, although his report of 1946 postdated von Neumann's more famousEDVAC report (von Neumann 1945). It can however be argued, as doesDavis (2000), that von Neumann gained his fundamental insight into thecomputer through his pre-war familiarity with Turing's logical work. Atthe time, however, these basic principles were not much discussed. Thedifficulty of engineering the electronic hardware dominatedeverything.

It therefore escaped observers that Turing was ahead of von Neumannand everyone else on the future of software, or as he called it, the‘construction of instruction tables.’ Turing (1946) foresawat once:

Instruction tables will have to be made up bymathematicians with computing experiences and perhaps a certainpuzzle-solving ability. There will probably be a great deal of work tobe done, for every known process has got to be translated intoinstruction table form at some stage.

The process of constructing instruction tables should be veryfascinating. There need be no real danger of it ever becoming a drudge,for any processes that are quite mechanical may be turned over to themachine itself.

These remarks, reflecting the universality of the computer, and itsability to manipulate its own instructions, correctly described thefuture trajectory of the computer industry. However, Turing had in mindsomething greater: ‘building a brain.’

6. Building a Brain

The provocative words ‘building a brain’ from the outsetannounced the relationship of Turing's technical computer engineeringto a philosophy of Mind. Even in 1936, Turing had given aninterpretation of computability in terms of ‘states ofmind’. His war work had shown the astounding power of thecomputable in mechanising expert human procedures and judgments. From1941 onwards, Turing had also discussed the mechanisation ofchess-playing and other ‘intelligent’ activities with hiscolleagues at Bletchley Park (Hodges 1983, p. 213). But moreprofoundly, it appears that Turing emerged in 1945 with a convictionthat computable operations were sufficient to embraceallmental functions performed by the brain. As will become clear from theensuing discussion, the uncomputable ‘intuition’ of 1938disappeared from Turing's thought, and was replaced by new ideas alllying within the realm of the computable. This change shows even in thetechnical prospectus of (Turing 1946), where Turing referred to thepossibility of making a machine calculate chess moves, and thencontinued:

This … raises the question ‘Can a machine playchess?’ It could fairly easily be made to play a rather bad game.It would be bad because chess requires intelligence. We stated …that the machine should be treated as entirely without intelligence.There are indications however that it is possible to make the machinedisplay intelligence at the risk of its making occasional seriousmistakes. By following up this aspect the machine could probably bemade to play very good chess.

The puzzling reference to ‘mistakes’ is made clear by atalk Turing gave a year later (Turing 1947), in which the issue ofmistakes is linked to the issue of the significance of seeing the truthof formally unprovable statements.

…I would say that fair play must be given to themachine. Instead of it giving no answer we could arrange that it givesoccasional wrong answers. But the human mathematician would likewisemake blunders when trying out new techniques… In other wordsthen, if a machine is expected to be infallible, it cannot also beintelligent. There are several mathematical theorems which say almostexactly that. But these theorems say nothing about how muchintelligence may be displayed if a machine makes no pretence atinfallibility.

Turing's post-war view was that mathematicians make mistakes, and sodo not in fact see the truth infallibly. Once the possibility ofmistakes is admitted, Gödel's theorem become irrelevant.Mathematicians and computers alike apply computable processes to theproblem of judging the correctness of assertions; both will thereforesometimes err, since seeing the truth is known not to be a computableoperation, but there is no reason why the computer need do worse thanthe mathematician. This argument is still very much alive. Forinstance, Davis (2000) endorses Turing's view and attacks Penrose(1989, 1990, 1994, 1996) who argues against the significance of humanerror on the grounds of a Platonist account of mathematics.

Turing also pursued more constructively the question of howcomputers could be made to perform operations which did not appear tobe ‘mechanical’ (to use common parlance). His guidingprinciple was that it should be possible to simulate the operation ofhuman brains. In an unpublished report (Turing 1948), Turing explainedthat the question was that of how to simulate ‘initiative’in addition to ‘discipline’—comparable to the needfor ‘intuition’ as well as mechanical ingenuity expressedin his pre-war work. He announced ideas for how to achieve this: hethought ‘initiative’ could arise from systems where thealgorithm applied is not consciously designed, but is arrived at bysome other means. Thus, he now seemed to think that the mind whennot actually following any conscious rule or plan, wasnevertheless carrying out some computable process.

He suggested a range of ideas for systems which could be said tomodify their own programs. These ideas included nets of logicalcomponents (‘unorganised machines’) whose properties couldbe ‘trained’ into a desired function. Thus, as expressedby (Ince 1989), he predicted neural networks. However, Turing's netsdid not have the ‘layered’ structure of the neuralnetworks that were to be developed from the 1950s onwards. By theexpression ‘genetical or evolutionary search’, he alsoanticipated the ‘genetic algorithms’ which since the late1980s have been developed as a less closely structured approach toself-modifying programs. Turing's proposals were not well developed in1948, and at a time when electronic computers were only barely inoperation, could not have been. Copeland and Proudfoot (1996) havedrawn fresh attention to Turing’s connectionist ideas, whichhave since been tried out (Teuscher 2001).

It is important to note that Turing identified his prototype neuralnetworks and genetic algorithms ascomputable. This has to beemphasised since the word ‘nonalgorithmic’ is often nowconfusingly employed for computer operations that are not explicitlyplanned. Indeed, his ambition was explicit: he himself wanted toimplement them as programs on a computer. Using the term UniversalPractical Computing Machine for what is now called a digital computer,he wrote in (Turing 1948):

It should be easy to make a model of any particular machinethat one wishes to work on within such a UPCM instead of having to workwith a paper machine as at present. If one also decided on quitedefinite ‘teaching policies’ these could also be programmedinto the machine. One would then allow the whole system to run for anappreciable period, and then break in as a kind of ‘inspector ofschools’ and see what progress had been made. One might also beable to make some progress with unorganisedmachines…

The upshot of this line of thought is that all mental operations arecomputable and hence realisable on a universal machine: thecomputer. Turing advanced this view with increasing confidence in thelate 1940s, perfectly aware that it represented what he enjoyed calling‘heresy’ to the believers in minds or souls beyond materialdescription.

Turing was not a mechanical thinker, or a stickler for convention;far from it. Of all people, he knew the nature of originality andindividual independence. Even in tackling the U-boat Enigma problem,for instance, he declared that he did so because no-one else waslooking at it and he could have it to himself. Far from being trainedor organised into this problem, he took it on despite the prevailingwisdom in 1939 that it was too difficult to attempt. His arrival at athesis of ‘machine intelligence’ was not the outcome ofsome dull or restricted mentality, or a lack of appreciation ofindividual human creativity.

7. Machine Intelligence

Turing relished the paradox of ‘Machine Intelligence’: anapparent contradiction in terms. It is likely that he was alreadysavouring this theme in 1941, when he read a theological book by theauthor Dorothy Sayers (Sayers 1941). In (Turing 1948) he quoted fromthis work to illustrate his full awareness that in common parlance‘mechanical’ was used to to mean ‘devoid ofintelligence.’ Giving a date which no doubt had his highlysophisticated Enigma-breaking machines secretly in mind, he wrote that‘up to 1940’ only very limited machinery had been used, andthis ‘encouraged the belief that machinery was necessarilylimited to extremely straightforward, possibly even to repetitious,jobs.’ His object was to dispel these connotations.

In 1950, Turing wrote on the first page of his Manual for users ofthe Manchester University computer (Turing 1950a):

Electronic computers are intended to carry out any definiterule of thumb process which could have been done by a human operatorworking in a disciplined but unintelligent manner.

This is, of course, just the 1936 universal Turing machine, now inelectronic form. On the other hand, he also wrote in the more famouspaper of that year (Turing 1950b, p. 460)

We may hope that machines will eventually compete with menin all purely intellectual fields.

How could theintelligent arise from operations which werethemselves totallyroutine and mindless—‘entirely without intelligence’? This is the core of theproblem Turing faced, and the same problem faces ArtificialIntelligence research today. Turing's underlying argument was that thehuman brain must somehow be organised for intelligence, and that theorganisation of the brain must be realisable as a finite discrete-statemachine. The implications of this view were exposed to a wider circlein his famous paper, “Computing Machinery and Intelligence,” whichappeared inMind in October 1950.

The appearance of this paper, Turing's first foray into a journal ofphilosophy, was stimulated by his discussions at Manchester Universitywith Michael Polanyi. It also reflects the general sympathy of GilbertRyle, editor ofMind, with Turing's point of view.

Turing's 1950 paper was intended for a wide readership, and its fresh anddirect approach has made it one of the most frequently cited and republishedpapers in modern philosophical literature. Not surprisingly,the paper has attracted many critiques. Not all commentators note thecareful explication of computability which opens the paper, with anemphasis on the concept of the universal machine. This explains why ifmental function can be achieved by any finite discrete state machine,then the same effect can be achieved by programming a computer (Turing1950b, p. 442). (Note, however, that Turing makes no claim that thenervous system should resemble a digital computer in its structure.)Turing's treatment has a severely finitistic flavour: his argument isthat the relevant action of the brain is not only computable, butrealisable as a totally finite machine, i.e. as a Turing machine thatdoes not use any ‘tape’ at all. In his account, the fullrange of computable functions, defined in terms of Turing machines thatuse an infinite tape, only appears as being of ‘specialtheoretical interest.’ (Of uncomputable functions there is,afortiori, no mention.) Turing uses the finiteness of the nervoussystem to give an estimate of about 10⁹ bitsof storage required for a limited simulation of intelligence (Turing1950b, p. 455).

The wit and drama of Turing's ‘imitation game’ hasattracted more fame than his careful groundwork. Turing's argument wasdesigned to bypass discussions of the nature of thought, mind, andconsciousness, and to give a criterion in terms of external observationalone. His justification for this was that one only judges that otherhuman beings are thinking by external observation, and he applied aprinciple of ‘fair play for machines’ to argue that thesame should hold for machine intelligence. He dramatised this viewpointby a thought-experiment (which nowadays can readily be tried out). Ahuman being and a programmed computer compete to convince an impartialjudge, using textual messages alone, as to which is the human being.If the computer wins, it must be credited with intelligence.

Turing introduced his ‘game’ confusingly with a pooranalogy: a party game in which a man pretends to be a woman. His loosewording (Turing 1950b, p. 434) has led some writers wrongly to supposethat Turing proposed an ‘imitation game’ in which a machinehas to imitate a man imitating a woman. Others, like Lassègue(1998), place much weight on this game of gender pretence and its realor imaginary connotations. In fact, the whole point of the‘test’ setting, with its remote text-message link, was toseparate intelligence from other human faculties andproperties. But it may fairly be said that this confusion reflectsTuring's richly ambitious concept of what is involved in human‘intelligence’. It might also be said to illustrate his ownhuman intelligence, in particular a delight in the Wildean reversal ofroles, perhaps reflecting, as in Wilde, his homosexual identity. Hisfriends knew an Alan Turing in whom intelligence, humour and sex wereoften intermingled.

Turing was in fact sensitive to the difficulty of separating‘intelligence’ from other aspects of human senses andactions; he described ideas for robots with sensory attachments andraised questions as to whether they might enjoy strawberries and creamor feel racial kinship. In contrast, he paid scant attention to thequestions of authenticity and deception implicit in his test,essentially because he wished to by-pass questions about the reality ofconsciousness. A subtle aspect of one of his imagined‘intelligent’ conversations (Turing 1950b, p. 434) is wherethe computer imitates human intelligence by giving thewronganswer to a simple arithmetic problem. But in Turing's setting weare not supposed to ask whether the computer ‘consciously’deceives by giving the impression of innumerate humanity, nor why itshould wish to do so. There is a certain lack of seriousness in thisapproach. Turing took on a second-rank target in countering thepublished views of the brain surgeon G. Jefferson, as regards theobjectivity of consciousness. Wittgenstein's views on Mind would havemade a more serious point of departure.

Turing's imitation principle perhaps also assumes (like‘intelligence tests’ of that epoch) too much of a sharedlanguage and culture for his imagined interrogations. Neither does itaddress the possibility that there may be kinds of thought, by animalsor extra-terrestrial intelligences, which are not amenable tocommunication.

A more positive feature of the paper lies in its constructiveprogram for research, culminating in Turing's ideas for ‘learningmachines’ and educating ‘child’ machines (Turing1950b, p. 454). It is generally thought (e.g. in Dreyfus and Dreyfus1990) that there was always an antagonism between programming and the‘connectionist’ approach of neural networks. But Turingnever expressed such a dichotomy, writing that both approaches shouldbe tried. Donald Michie, the British AI research pioneer profoundlyinfluenced by early discussions with Turing, has called this suggestion‘Alan Turing's Buried Treasure’, in an allusion to abizarre wartime episode in which Michie was himself involved (Hodges1983, p. 345). The question is still highly pertinent.

It is also a commonly expressed view that Artificial Intelligenceideas only occurred to pioneers in the 1950safter the successof computers in large arithmetical calculations. It is hard to see whyTuring's work, which was rooted from the outset in the question ofmechanising Mind, has been so much overlooked. But through his failureto publish and promote work such as that in (Turing 1948) he largelylost recognition and influence.

It is also curious that Turing's best-known paper should appear in ajournal of philosophy, for it may well be said that Turing, alwayscommitted to materialist explanation, was not really a philosopher atall. Turing was a mathematician, and what he had to offer philosophylay in illuminating its field with what had been discovered inmathematics and physics. In the 1950 paper this was surprisinglycursory, apart from his groundwork on the concept of computability. Hisemphasis on the sufficiency of the computable to explain the action ofthe mind was stated more as a hypothesis, even a manifesto, than arguedin detail. Of his hypothesis he wrote (Turing 1950b, p. 442):

…I believe that at the end of the century the use ofwords and general educated opinion will have altered so much that onewill be able to speak of machines thinking without expecting to becontradicted. I believe further that no useful purpose is served byconcealing these beliefs. The popular view that scientists proceedinexorably from established fact to established fact, never beinginfluenced by any unproved conjecture, is quite mistaken. Provided itis made clear which are proved facts and which are conjecture, no harmcan result. Conjectures are of great importance since they suggestuseful lines of research.

Penrose (1994, p.21), probing into Turing's conjecture, haspresented it as ‘Turing's thesis’ thus:

It seems likely that he viewed physical action in general—which would include the action of a human brain—to bealways reducible to some kind of Turing-machine action.

The statement that all physical action is in effect computable goesbeyond Turing's explicit words, but is a fair characterisation of theimplicit assumptions behind the 1950 paper. Turing's consideration of‘The Argument from Continuity in the Nervous System,’ inparticular, simply asserts that the physical system of the brain can beapproximated as closely as is desired by a computer program (Turing1950b, p. 451). Certainly there is nothing in Turing's work in the1945–50 period to contradict Penrose's interpretation. The moretechnical precursor papers (Turing 1947, 1948) include wide-rangingcomments on physical processes, but make no reference to thepossibility of physical effects being uncomputable.

In particular, a section of (Turing 1948) is devoted to a generalclassification of ‘machines.’ The period between 1937 and1948 had given Turing much more experience of actual machinery than hehad in 1936, and his post-war remarks reflected this in a down-to-earthmanner. Turing distinguished ‘controlling’ from‘active’ machinery, the latter being illustrated by‘a bulldozer’. Naturally it is the former—in modernterms ‘information-based machinery’—with whichTuring's analysis is concerned. It is noteworthy that in 1948 as in1936, despite his knowledge of physics, Turing made no mention of howquantum mechanics might affect the concept of‘controlling’. His concept of ‘controlling’remained entirely within the classical framework of the Turing machine(which he called a Logical Computing Machine in this paper.)

The same section of (Turing 1948) also drew the distinction betweendiscrete andcontinuous machinery, illustrating thelatter with ‘the telephone’ as a continuous, controllingmachine. He made light of the difficulty of reducing continuous physicsto the discrete model of the Turing machine, and though citing‘the brain’ as a continuous machine, stated that it couldprobably be treated as if discrete. He gave no indication that physicalcontinuity threatened the paramount role of computability. In fact, histhrust in (Turing 1947) was to promote the digital computer asmorepowerful than analog machines such as the differential analyser.When he discussed this comparison, he gave the following informalversion of the Church-Turing thesis:

One of my conclusions was that the idea of a ‘rule ofthumb’ process and a ‘machine process’ weresynonymous. The expression ‘machine process’ of coursemeans one which could be carried out by the type of machine I wasconsidering [i.e. Turing machines]

Turing gave no hint that the discreteness of the Turing machineconstituted a real limitation, or that the non-discrete processes ofanalog machines might be of any deep significance.

Turing also introduced the idea of ‘random elements’ buthis examples (using the digits of π) showed that he consideredpseudo-random sequences (i.e. computable sequences withsuitable ‘random’ properties) quite adequate for hisdiscussion. He made no suggestion that randomness implied somethinguncomputable, and indeed gave no definition of the term‘random’. This is perhaps surprising in view of the factthat his work in pure mathematics, logic and cryptography all gave himconsiderable motivation to approach this question at a seriouslevel.

8. Unfinished Work

From 1950 Turing worked on a new mathematical theory of morphogenesis,based on showing the consequences of non-linear equations for chemicalreaction and diffusion (Turing 1952). He was a pioneer in using acomputer for such work. Some writers have referred to this theory asfounding Artificial Life (A-life), but this is a misleadingdescription, apt only to the extent that the theory was intended, asTuring saw it, to counter the Argument from Design. A-life since the1980s has concerned itself with using computers to explore the logicalconsequences of evolutionary theory without worrying about specificphysiological forms. Morphogenesis is complementary, being concerned toshow which physiological pathways are feasible for evolution toexploit. Turing's work was developed by others in the 1970s and is nowregarded as central to this field.

It may well be that Turing's interest in morphogenesis went back toa primordial childhood wonder at the appearance of plants and flowers.But in another late development, Turing went back to other stimuli ofhis youth. For in 1951 Turing did consider the problem, hithertoavoided, of setting computability in the context of quantum-mechanicalphysics. In a BBC radio talk of that year (Turing 1951) he discussedthe basic groundwork of his 1950 paper, but this time dealing ratherless certainly with the argument from Gödel's theorem, and thistime also referring to the quantum-mechanical physics underlying thebrain. Turing described the universal machine property, applying it tothe brain, but said that its applicability required that the machinewhose behaviour is to be imitated

…should be of the sort whose behaviour is inprinciple predictable by calculation. We certainly do not know how anysuch calculation should be done, and it was even argued by Sir ArthurEddington that on account of the indeterminacy principle in quantummechanics no such prediction is even theoreticallypossible.

Copeland (1999) has rightly drawn attention to this sentence in hispreface to his edition of the 1951 talk. However, Copeland's criticalcontext suggests some connection with Turing's ‘oracle.’There is is in fact no mention of oracles here (nor anywhere inTuring's post-war discussion of mind and machine.) Turing here isdiscussing the possibility that, when seen as as aquantum-mechanical machine rather than a classical machine,the Turing machine model is inadequate. The correct connection to drawis not with Turing's 1938 work on ordinal logics, but with hisknowledge of quantum mechanics from Eddington and von Neumann in hisyouth. Indeed, in an early speculation, influenced by Eddington, Turinghad suggested that quantum mechanical physics could yield the basis offree-will (Hodges 1983, p. 63). Von Neumann's axioms of quantummechanics involve two processes: unitary evolution of the wavefunction, which is predictable, and the measurement or reductionoperation, which introduces unpredictability. Turing's reference tounpredictability must therefore refer to the reduction process. Theessential difficulty is that still to this day there is no agreed orcompelling theory of when or how reduction actually occurs. (It shouldbe noted that ‘quantum computing,’ in the standard modernsense, is based on the predictability of the unitary evolution, anddoes not, as yet, go into the question of how reduction occurs.) Itseems that this single sentence indicates the beginning of a new fieldof investigation for Turing, this time into the foundations of quantummechanics. In 1953 Turing wrote to his friend and student Robin Gandythat he was ‘trying to invent a new Quantum Mechanics but itwon't really work.’

At Turing's death in June 1954, Gandy reported in a letter to Newmanon what he knew of Turing's current work (Gandy 1954). He wrote ofTuring having discussed a problem in understanding the reductionprocess, in the form of

…‘the Turing Paradox’; it is easy toshow using standard theory that if a system start in an eigenstate ofsome observable, and measurements are made of that observable N times asecond, then, even if the state is not a stationary one, theprobability that the system will be in the same state after, say, 1second, tends to one as N tends to infinity; i.e. that continualobservation will prevent motion. Alan and I tackled one or twotheoretical physicists with this, and they rather pooh-poohed it bysaying that continual observation is not possible. But there is nothingin the standard books (e.g., Dirac's) to this effect, so that at least theparadox shows up an inadequacy of Quantum Theory as usuallypresented.

Turing's investigations take on added significance in view of theassertion of Penrose (1989, 1990, 1994, 1996) that the reductionprocess must involve something uncomputable. Probably Turing was aimingat the opposite idea, of finding a theory of the reduction process thatwould be predictive and computable, and so plug the gap in hishypothesis that the action of the brain is computable. However Turingand Penrose are alike in seeing this as an important question affectingthe assumption that all mental action is computable; in this they bothdiffer from the mainstream view in which the question is accordedlittle significance.

Alan Turing's last postcards to Robin Gandy, in March 1954, headed‘Messages from the Unseen World’ in allusion to Eddington,hinted at new ideas in the fundamental physics of relativity andparticle physics (Hodges 1983, p. 512). They illustrate the wealth ofideas with which he was concerned at that last point in his life, butwhich apart from these hints are entirely lost. A review of such lostideas is given in (Hodges 2004), as part of a larger volume onTuring's legacy (Teuscher 2004).

9. Alan Turing: the Unknown Mind

It is a pity that Turing did not write more about his ethicalphilosophy and world outlook. As a student he was an admirer of BernardShaw's plays of ideas, and to friends would openly voice both thehilarities and frustrations of his many difficult situations. Yet thenearest he came to serious personal writing, apart from occasionalcomments in private letters, was in penning a short story about his1952 crisis (Hodges 1983, p. 448). His last two years were particularlyfull of Shavian drama and Wildean irony. In one letter (to his friendNorman Routledge; the letter is now in the Turing Archive at King'sCollege, Cambridge) he wrote:

Turing believes machines think
Turing lies with men
Therefore machines do not think

The syllogistic allusion to Socrates is unmistakeable, and hisdemise, with cyanide rather than hemlock, may have signalled somethingsimilar. A parallel figure in World War II, Robert Oppenheimer,suffered the loss of his reputation during the same week that Turingdied. Both combined the purest scientific work and the most effectiveapplication of science in war. Alan Turing was even more directly onthe receiving end of science, when his sexual mind was treated as amachine, against his protesting consciousness and will. But amidst allthis human drama, he left little to say about what he really thought ofhimself and his relationship to the world of human events.

Alan Turing did not fit easily with any of the intellectual movementsof his time, aesthetic, technocratic or marxist. In the 1950s,commentators struggled to find discreet words to categorise him: as‘a scientific Shelley,’ as possessing great ‘moralintegrity’. Until the 1970s, the reality of his life wasunmentionable. He is still hard to place within twentieth-centurythought. He exalted the science that according to existentialists hadrobbed life of meaning. The most original figure, the most insistenton personal freedom, he held originality and will to be susceptible tomechanisation. The mind of Alan Turing continues to be anenigma.

But it is an enigma to which the twenty-first century seemsincreasingly drawn. The year of his centenary, 2012, witnessednumerous conferences, publications, and cultural events in hishonor. Some reasons for this explosion of interest are obvious. One isthat the question of the power and limitations of computation nowarises in virtually every sphere of human activity. Another is thatissues of sexual orientation have taken on a new importance in moderndemocracies. More subtly, the interdisciplinary breadth of Turing'swork is now better appreciated. A landmark of the centenary period wasthe publication ofAlan Turing, his work and impact(eds. Cooper and van Leeuwen, 2013), which made available almost allaspects of Turing's scientific oeuvre, with a wealth of moderncommentary. In this new climate, fresh attention has been paid toTuring's lesser-known work, and new light shed upon hisachievements. He has emerged from obscurity to become one of the mostintensely studied figures in modern science.

Bibliography

Selected Works by Turing

• 1936, ‘On computable numbers, with anapplication to the Entscheidungsproblem’,Proc. London Maths.Soc. (Series 2), 42: 230–265; also in Davis 1965 and Gandy andYates 2001; [Available online].
• 1939, ‘Systems of logic defined by ordinals’,Proc. Lond. Math. Soc., Ser. 2, 45: 161–228; This wasTuring's Ph.D. thesis, Princeton University (1938), published asAlan Turing's systems of logic: The Princeton thesis,A. W. Appel (ed.), Princeton: Princeton University Press, 2012; alsoin Davis 1965 and in Gandy and Yates 2001.
• 1946,Proposed Electronic Calculator,report for National Physical Laboratory, Teddington; published inA. M. Turing's ACE report of 1946 and other papers, B. E.Carpenter and R. W. Doran (eds.), Cambridge, Mass.: MIT Press, 1986; also inCollected Works (Volume 1).
• 1947, ‘Lecture to the London Mathematical Society on 20February 1947’, inA. M. Turing's ACE report of 1946 andother papers, B. E. Carpenter and R. W. Doran (eds.), Cambridge,Mass.: MIT Press, 1986; also inCollected Works (Volume1).
• 1948, ‘Intelligent Machinery’, reportfor National Physical Laboratory, inMachine Intelligence 7,B. Meltzer and D. Michie (eds.) 1969; also inCollected Works (Volume 1).
• 1950a,Programmers' Handbook for the ManchesterElectronic Computer, Manchester University Computing Laboratory. [Available online in PDF].
• 1950b, ‘Computing machinery andintelligence’,Mind, 50: 433–460; also in Boden 1990,Collected Works (Volume 1), and [Available online].
• 1951, BBC radio talk, inThe EssentialTuring, B. J. Copeland (ed.), Oxford: Clarendon Press, 2004.
• 1952, ‘The chemical basis ofmorphogenesis’,Phil. Trans. R. Soc. London B 237:37–72; also inThe Collected Works of A. M. Turing:Morphogenesis, P. T. Saunders (ed.), Amsterdam: North-Holland,1992.

The Collected Works of A. M. Turing consists of4 volumes:

• Volume 1:Mechanical Intelligence, D.C. Ince (ed.),Amsterdam: North-Holland, 1992.
• Volume 2:Morphogenesis, P. T. Saunders (ed.), Amsterdam: North-Holland, 1992.
• Volume 3:Pure Mathematics, J. L. Britton (ed.), Amsterdam: North-Holland, 1992.
• Volume 4:Mathematical Logic, R. O. Gandy andC. E. M. Yates, Amsterdam: North-Holland, 2001.

The following, single-volume work contains much of theCollectedWorks and adds extensive modern commentary:

• Alan Turing, his work and impact, S. B. Cooper and J. vanLeeuwen (eds.), Amsterdam: Elsevier, 2013.

Secondary Literature

• Boden, M. (ed.), 1990,The Philosophy of ArtificialIntelligence, Oxford: Oxford University Press.
• Church, A., 1937, Review of Turing 1936–7,Journal of SymbolicLogic, 2: 42.
• –––, 1940, ‘On the concept of a randomsequence’,Bull. Amer. Math. Soc., 46: 130–135.
• Copeland, B. J., 1998, ‘Turing's o-machines, Searle, Penroseand the brain’,Analysis, 58(2): 128–138.
• –––, 1999, ‘A lecture and two radio broadcasts onmachine intelligence by Alan Turing’, inMachine Intelligence15, K. Furukawa, D. Michie, and S. Muggleton (eds.), Oxford:Oxford University Press.
• ––– (ed.), 2004,The Essential Turing, Oxford:Clarendon Press.
• Copeland, B. J. and D. Proudfoot, 1996, ‘On Alan Turing'santicipation of connectionism’,Synthese, 108:361–377.
• Davies, E. B., 2001, ‘Building infinite machines’,British Journal for the Philosophy of Science,52 (4): 671–682.
• Davis, M., 2000,The Universal Computer, New York:Norton.
• ––– (ed.), 1958,Computability and Unsolvability,New York: McGraw-Hill; New York: Dover (1982).
• ––– (ed.), 1965,The Undecidable, New York:Raven.
• Dawson, J. W., 1985, Review of Hodges (1983),Journal ofSymbolic Logic, 50: 1065–1067.
• Deutsch, D., 1985, ‘Quantum theory, the Church-Turingprinciple and the universal quantum computer’,Proc. Roy.Soc. A, 400: 97–115.
• Diamond, C. (ed.), 1976,Wittgenstein's Lectures on theFoundations of Mathematics, Cambridge, 1939, Hassocks: HarvesterPress.
• Dreyfus, H. L. and S. E. Dreyfus, 1990, ‘Making a mind versusmodelling the brain: artificial intelligence back at abranch-point’, in Boden 1990.
• Feferman, S., 1988, ‘Turing in the Land of O(Z)’, in(Herken 1988); also in Gandy and Yates (eds.) 2001.
• Feynman, R. P., 1982, ‘Simulating physics withcomputers’,Int. Journal of Theoretical Physics, 21:467–488.
• Gandy, R. O., 1954, Letter to M. H. A. Newman, in Gandy and Yates,2001.
• –––, 1980, ‘Principles of Mechanisms’, inThe Kleene Symposium, J. Barwise, H. J. Keisler and K.Kunen (eds.), Amsterdam: North-Holland.
• –––, 1988, ‘The confluence of ideas in1936’, in Herken 1988.
• Gandy, R. O. and C. E. M. Yates (eds.), 2001,The CollectedWorks of A M. Turing: Mathematical Logic, Amsterdam:North-Holland.
• Gödel, K., 1946, ‘Remarks before the PrincetonBicentennial Conference on problems in mathematics’, in Davis1965.
• Herken R., (ed.), 1988,The Universal Turing Machine: AHalf-Century Survey, Berlin: Kammerer und Unverzagt; Oxford:Oxford University Press.
• Hodges, A., 1983,Alan Turing: the Enigma, London:Burnett; New York: Simon & Schuster; London: Vintage,1992, 2012; Princeton University Press, 2012.
• –––, 1997,Turing, a naturalphilosopher, London: Phoenix; New York: Routledge (1999);included inThe great philosophers, R. Monk andF. Raphael (eds.), London: Weidenfeld and Nicolson (2000).
• –––, 2004, What would Alan Turing have doneafter 1954, inAlan Turing: life and legacy of a great thinker,C. Teuscher (ed.), Berlin: Springer Verlag.
• –––, 2006, Review of Copeland2004,Notices of the American Mathematical Society, 53:1190–1199.
• Ince, D. C., 1989, Preface to Turing 1948, in Ince (ed.)1992.
• Lassègue, J., 1998,Turing, Paris: les BellesLettres.
• Minsky, M. L., 1967,Computation: Finite and InfiniteMachines, Englewood Cliffs, N.J.: Prentice-Hall.
• Newman, M. H. A., 1955, ‘Alan Mathison Turing’,Biographical memoirs of the Royal Society (1955), 253–263.
• Penrose, R., 1989,The Emperor's New Mind, Oxford: OxfordUniversity Press.
• –––, 1990, Précis ofThe Emperor's NewMind,Behavioral and Brain Sciences, 13: 643–655.
• –––, 1994,Shadows of the Mind, Oxford: OxfordUniversity Press.
• ––– 1996, ‘Beyond the doubting of a shadow: A Replyto Commentaries onShadows of the Mind’, inPsyche:An Interdisciplinary Journal of Research on Consciousness, Volume2.
• Sayers, D., 1941,The Mind of the Maker, London:Methuen.
• Teuscher, C., 2001,Turing's Connectionism, London:Springer-Verlag UK.
• ––– (ed.), 2004,Alan Turing: Life andLegacy of a Great Thinker, Berlin: Springer-Verlag.
• Turing, E. S., 1959,Alan M. Turing, Cambridge:Heffers; republished by Cambridge University Press, 2012.
• von Neumann, J., 1945, ‘First draft of a report on theEDVAC’, University of Pennsylvania; first printed in N. Stern,From Eniac to Univac: an appraisal of the Eckert-Mauchlymachines, Bedford MA: Digital Press, 1981.
• Whitemore, H., 1986,Breaking the Code, London: S.French.

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