Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  Nor did he compromise with Manchester society by associating with the small homosexual set centred on the university, the BBC and the Manchester Guardian. In this respect life centred still on Cambridge. The exile in Manchester meant in particular a separation from Neville, whom over the next two years he would visit at Cambridge every few weeks. Neville was taking a two-year postgraduate course in statistics. At Easter 1949 they had another short holiday together in France, cycling and visiting the Lascaux Caves. (The prehistoric paintings rather suited Alan, who always wanted to draw nature from scratch himself.) Alan also spent the August of each year back for the long vacation in King’s, rather as he had in 1937.

  So King’s retained its protective role, and Robin in particular was the White Knight in the forest, as the most helpful character in the story. In other ways, Robin was not the White Knight at all, being rather dashing and energetic. Later he acquired a powerful motor-cycle and a full set of black leathers, and sometimes took Alan for rides in the Peak District. Alan told his friends about the Princeton treasure hunts, and he, with Robin, Nick Furbank and Keith Roberts, organised several of them over the next few years. Alan would run round in search of the clues, while the others would cycle. Once Noel Annan joined in, and made a great hit by producing a bottle of champagne to match a clue which involved an Old French text with the word champaigne. Keith Roberts had many discussions with Alan about science and computers, but was innocent of other matters which Alan shared with his friends. He never deciphered the coded messages that passed between the others. Nick Furbank, on the other hand, did not have the scientific background, but he was very interested in rationalism and game theory and the imitation principle

  Alan and Robin and Nick devised a new game called Presents. The idea was that one person went out of the room and the others made up a list of imaginary presents that they believed he would like to have. Then he came back and could ask questions about the presents before choosing them, and here the game of bluff and double bluff came in, for one of the presents would secretly be designated ‘Tommy’ and once Tommy was chosen, the turn was finished. The imaginary presents moved after a while into a more probing realm. Alan tentatively dropped ‘Tea in Knightsbridge Barracks’ into the game at one point, perhaps reflecting fantasies of twenty years before. The Manchester computer had, in its unexpected and back-handed way, realised one of the products of his imagination. There still remained other dreams; no less hard to fulfil; no less liable to go awry.

  The arrangement at Manchester was that the university engineers were to build a prototype machine, which Ferranti would use as ‘the instructions of Professor F.C. Williams’, So throughout 1949 the engineers, who were now able to recruit more staff, were adding to the original ‘baby machine’. By April it had been fitted with three more cathode ray tubes for fast store, multiplier and ‘β-tube’, and by that time a small magnetic drum was being tested. Another change was that each line on the cathode ray tube store now held forty spots, an instruction taking up twenty of them. These were conveniently thought of as grouped in fives, and a sequence of five binary digits as forming a single digit in the base of 32

  Meanwhile Newman made an ingenious choice of problem with which to demonstrate the machine as it stood with only a tiny store but with a multiplier. It was something that had been discussed at Bletchley – finding large prime numbers. In 1644 the French mathematician Mersenne had conjectured that 217-1, 219-1, 231 – 1, 267-1, 2127- 1, 2257- 1 were all prime, and that these were the only primes of that form within the range. In the eighteenth century, Euler laboriously established that 231 — 1 = 2,146,319,807 was indeed prime, but the list would not have progressed further without a fresh theory. In 1876 the French mathematician E. Lucas proved that there was a way to decide whether 2p – 1 was prime by a process of p operations of squaring and taking of remainders. He announced that 2127 – 1 was prime. In 1937, the American D.H. Lehmer attacked 2257 – 1 on a desk calculator and after a couple of years of work showed that Mersenne had been mistaken. In 1949 Lucas’s number was still the largest known prime.

  Lucas’s method was tailor-made for a computer using binary numbers. They had only to chop up the huge numbers being squared into 40-digit sections and to program all the carrying. Newman explained the problem to Tootill and Kilburn and in June 1949 they managed to pack a program into the four cathode ray tubes and still leave enough space for working up to P = 353. En route they checked all that Euler and Lucas and Lehmer had done, but did not discover any more primes.*

  This was part of an uneasy treaty of alliance, according to which the zones of ‘engineers’ and ‘mathematicians’ were agreed. Newman took little further interest in the machine, and Alan took on the role of ‘the mathematician’. It was for him to specify the range of operations that should be performed by the machine, although his list was in fact cut back by the engineers. He had no part in the internal logical design, which was done by Geoff Tootill, but had control over the input and output mechanism, which lay more in the province of the user.

  At the NPL he had chosen punched cards for input since they already had a punched card section; here he preferred to generate a teleprinter tape which could later be run off on a printer. He was, of course, very familiar with the teleprinter system from Bletchley and Hanslope, and people knew it was from ‘a place you mustn’t talk about’ that he obtained a paper tape punch, which ran off a dry battery, and ‘had a tendency to replace 1 by 0’. After it had been attached, those 32 different combinations of 0s and Is in five-row teleprinter tape became the language of the Manchester machine, haunting the days and dreams alike of its users.

  It was Alan’s job to make the Manchester machine convenient to use, but his ideas of convenience were not always shared by others. He had, of course, attacked the principle on which Wilkes was working according to which the hardware of the machine would be designed to make the instructions easy for a human user to follow – so that in the EDSAC design, the letter ‘A’ was used as the symbol for the instruction to add. In contrast, Alan held that human convenience should be catered for by programming techniques, not by electronics. In his 1947 talk he had referred to such matters of convenience as ‘fussy little details’, and had stressed how they could be taken care of by ‘pure paperwork’. Now at Manchester, he had the opportunity, in principle, to put this into practice – for the machine hardware had not been designed to pander to the programmer. However, by 1949 he had lost interest in doing this kind of work. The ‘fussy little detail* of binary to decimal conversion, for instance, he now found not worth bothering about. He himself found it simple to work directly in the base-32 arithmetic in which the machine could be regarded as working, and expected other people to do the same.

  To use base-32 arithmetic it was necessary to find 32 symbols for the 32 different ‘digits’. Here he took over the system already used by the engineers, in which they labelled the five-bit combinations according to the Baudot teleprinter code. Thus the ‘twenty-two’ digit, corresponding to the sequence 10110 of binary digits, would be written as ‘P’, the letter that the sequence 10110 encoded for an ordinary teleprinter. To work in this system meant memorising the Baudot code and the multiplication table as expressed in it – something he, but few others, found easy.

  The ostensible reason for sticking to this hideously primitive form of coding, which entailed so much work for the user, was that the cathode ray tube storage made it possible – indeed necessary – to check the contents of the store by ‘peeping’, as Alan called it, at a monitor tube. He insisted that what one saw as spots on the tube had to correspond digit by digit to the program that had been written out. To maintain this principle of correspondence it was actually necessary to write out the base-32 numbers backwards, with the least significant digit first. This was for technical electronic engineering reasons, the same as those which obliged cathode ray tubes always to scan from left to right. Another awkwardness arose on account of the five-bit combinations which did not
correspond to a letter of the alphabet on the Baudot code. (It was the same problem that the Rockex system overcame.) Geoff Tootill had already introduced extra symbols for these, the zero of the base-32 notation being represented by a stroke ‘/’. The result was that pages of programs were covered with strokes – an effect which at Cambridge was said to reflect the Manchester rain lashing at the windows.

  By October 1949 the machine was ready, bar some details, for Ferranti to manufacture. The prototype remained in place while this was done, and the idea was to use the time to write an operations manual and basic programs ready to use on the computer (the Mark I, it would be called), when it arrived.

  This was Alan’s next job, and he must have spent a great deal of time in checking the operation of every single function on the prototype, arguing over their efficiency with the engineers. By October he had written out an input routine: that is, a means to persuade the machine when first switched on and empty of instructions, to read in new instructions from a tape, to store them in the right place, and to begin executing them.

  But this was low-level work; and on this level the Programmers’ Handbook7 that he wrote, though full of helpful and practical advice, involved few new ideas. Indeed, it had nothing as sophisticated as the routines he had devised at the NPL for floating-point numbers. Nor did he do anything inspired in connection with the organisation of sub-routines. This, in the Manchester development, was dominated by the existence of two kinds of storage: on the Ferranti-built machine this would amount to eight cathode ray tubes each with their 1280 digits, and the magnetic drum promising no fewer than 655360 digits, arranged in 256 tracks of 2560 digits each.* Programming revolved around the process of ‘bringing down’ data and instructions from the drum to the tubes, and sending them back again, and the hardware more or less obliged each sub-routine to be stored on a new track of the drum, to be transferred in toto as required. The Turing scheme coped with this, but he did not bother with a system for subroutines nested to any depth. He referred to this possibility in a rather flippant passage of the Handbook:

  The sub-routines of any routine may themselves have sub-routines. This is like the case of the bigger and lesser fleas. I am not sure of the exact meaning the poet attached to the phrase ‘and so ad infinitum’, but am inclined to think that he meant there was no limit that one could assign to the length of a parasitic chain of fleas, rather than that he believed in infinitely long chains. This certainly is the case with sub-routines. One always eventually comes down to a routine without sub-routines.

  but he left this for the user to organise. His own ‘Scheme A’ only allowed for one level of sub-routine calling.

  The Handbook brought out many of the problems of communication that he faced at Manchester. To Williams and the other engineers, a mathematician was someone who knew how to do calculations; in particular they saw binary notation as something new introduced to them by ‘mathematics’. To Alan Turing, however, all their schemes with base-32 arithmetic and the rest were merely simple illustrations of the deeper fact that mathematicians were free to employ symbolism in any way they chose. To him it was obvious that a symbol had no intrinsic connection with the entity that it symbolised, and so a long paragraph at the beginning of the Handbook explained how it was that there existed a convention according to which sequences of pulses could be interpreted as numbers. While this was a far more accurate and also more creative idea than the usual statement that the machine ‘stored the numbers’, it was not immediately helpful to the person who had never before known that numbers could be expressed other than in the scale of ten. It was not that Alan despised doing routine, detailed work within a symbolism such as the Manchester machine demanded: but as in Computable Numbers arid the ACE report he tended to veer from the abstract to the detailed in a way that made sense to him, but not to others. The development that could have absorbed both his liberated understanding of symbolism, and his willingness to do the donkey work when necessary, was that of designing programming languages, the development he described as ‘obvious’ in 1947. But this was precisely what he did not do; and thus he failed to exploit the advantage that a grasp of abstract mathematics gave him.*

  In writing the standard routines for square roots and so forth, he had two assistants after October 1949. One was Audrey Bates, a postgraduate student. The other was Cicely Popplewell, whom he had interviewed for the advertised post in summer 1949. She was a Cambridge mathematics graduate with experience of punched cards used in housing statistics. They both shared his office in that Victorian fortress, the university Main Building, pending the construction of the new Computing Laboratory to house the Ferranti machine. It was not a happy arrangement, for he never really acknowledged their right to exist. On Cicely’s first day he said ‘Lunch!’ and marched out of the room without telling Cicely where the Refectory was. He would talk away himself to anyone who visited, but would be very annoyed if either of them did. Sometimes the shell would crack; they persuaded him to play tennis once, and they were amazed the first time they saw him arrive apparently wearing a raincoat and nothing else, which caused some laughs. Once there was some business of him borrowing a ten-shilling note to pin on his shorts when he went home. But usually they were glad when, as often happened, he did not come in. He made no allowance for the amount they had to learn, and did nothing to mitigate what Cicely felt as ‘an acute inferiority complex’ in terms of speed of brain. Cicely also had the job of smoothing things over with the engineers, when interdepartmental tension was running high.

  Using the prototype machine was no smooth operation. It was comparable with the use of the Robinsons. According to Cicely Popplewell,8 it

  …required considerable physical stamina. Starting in the machine room you alerted the engineer and then used the hand switches to bring down and enter the input program. A bright band on the monitor tube indicated that the waiting loop had been entered. When this had been achieved, you ran upstairs and put the tape in the tape reader and then returned to the machine room. If the machine was still obeying the input loop you called to the engineer to switch on the writing current, and cleared the accumulator (allowing the control to emerge from the loop). With luck, the tape was read. As soon as the pattern on the monitor showed that input was ended the engineer switched off the write current to the drum. Programs which wrote to the drum during the execution phase were considered very daring. As every vehicle that drove past was a potential source of spurious digits, it usually took many attempts to get a tape in - each attempt needing another trip up to the tape room.

  In fact, writing from the tubes on to the magnetic drum was all but impossible on the prototype. Alan wrote9:

  Judged from the point of view of the programmer, the least reliable part of the machine appeared to be the magnetic writing facilities. It is not known whether the writing was more often done wrong than the reading or less. The effects of incorrect writing were however so much more disastrous than any other mistake which could be made by the machine, that automatic writing was practically never done. …Other serious sources of error were the failure of storage tubes and the multiplier. …

  In the hot summer of 1950 it was not unknown for computer users to be sweltering in 90°F heat, and banging the racks with a hammer to detect loose valves.

  The autumn of 1949 saw what was to be Alan’s only titbit of hardware design for the Ferranti machine.10 One of the hardware functions on which he had insisted was that of a random number generator - a feature not included in his ACE design. His own electronic knowledge stopped short of the necessary practical detail, but with Geoff Tootill’s collaboration he was still able to design his own system. It was one that produced truly random digits from noise, as opposed to something like a cipher key generator that would produce apparently random but actually determined digits. (That, if he wanted it, he would surely program for himself.) Perhaps he based his design on the circuit that produced the Rockex key-tapes at Hanslope.

  Geoff Tootill was intereste
d in Alan’s ideas, but some of them were particularly impractical in view of the limited time and effort available. There was, for instance, a scheme he devised for computer character recognition, which would involve an elaborate system with a television camera in order to transfer a visual image to the cathode ray tube store, and reduce it to a standard size. Geoff Tootill was probably the most tolerant of such dreams, but to him as to all on the engineering side, Alan Turing was the brilliant mathematician (or so they heard) but embarrassingly half-baked engineer. The year 1949 meant the end of his groping efforts to be the academic engineer; there were few who appreciated that the remarkable thing for a British pure mathematician was not a deficiency in electronics, but the willingness to dirty his hands at all.

  Meanwhile the more theoretical side of computer development had become a more public question. In 1948 Norbert Wiener had published a book called Cybernetics, defining this word to mean ‘Control and Communication in the Animal and the Machine’. It meant the description of the world in which information and logic, rather than energy or material constitution, was what mattered. As such it was heavily influenced by the massive wartime technological developments, although the basic ideas, such as feedback, were hardly new. Wiener and von Neumann had led a conference in the winter of 1943–4 on ‘cybernetic’ ideas, but Wiener’s book marked the opening up of the subject outside the narrow domain of technical papers. In fact Cybernetics was still very technical, incoherent, and almost unreadable, but the public seized upon it as a magic key which would unlock the secrets of what had happened to the world in the past decade.