Alan Turing: The Enigma The Centenary Edition

by Andrew Hodges

  As McTaggart shews matter is meaningless in the absence of spirit (throughout I do not mean by matter that which can be a solid a liquid or a gas so much as that which is dealt with by physics e.g. light and gravitation as well, i.e. that which forms the universe). Personally I think that spirit is really eternally connected with matter but certainly not always by the same kind of body. I did believe it possible for a spirit at death to go to a universe entirely separate from our own, but I now consider that matter and spirit are so connected that this would be a contradiction in terms. It is possible however but unlikely that such universes may exist.

  Then as regards the actual connection between spirit and body I consider that the body by reason of being a living body can ‘attract’ and hold on to a ‘spirit’, whilst the body is alive and awake the two are firmly connected. When the body is asleep I cannot guess what happens but when the body dies the ‘mechanism’ of the body, holding the spirit is gone and the spirit finds a new body sooner or later perhaps immediately.

  As regards the question of why we have bodies at all; why we do not or cannot live free as spirits and communicate as such, we probably could do so but there would be nothing whatever to do. The body provides something for the spirit to look after and use.

  Alan could have found many of these ideas in his reading of Eddington while still at school. He had told Mrs Morcom that she would like The Nature of the Physical World, and this would have been because of the olive branch that Eddington held out from the throne of science towards the claims of religion. He had found a resolution of the classical problem of determinism and free will, of mind and matter, in the new quantum mechanics.

  The idea that Alan said ‘used to be supposed in Science’ was familiar to anyone who studied applied mathematics. In any school or university problem, there would always be just sufficient information supplied about some physical system to determine its entire future. In practice, predictions could not be performed except in the most simple of cases, but in principle there was no dividing line between these and systems of any complexity. It was also true that some sciences, thermodynamics and chemistry for instance, considered only averaged-out quantities, and in those theories information could appear and disappear. When the sugar has dissolved in the tea, there remains no evidence, on the level of averages, that it was ever in the form of a cube. But in principle, at a sufficiently detailed level of description, the evidence would remain in the motion of the atoms. That was the view as summed up by Laplace13 in 1795:

  Given for one instant an intelligence which could comprehend all the forces by which nature is animated and the respective situations of the beings who compose it – an intelligence sufficiently vast to submit these data to analysis – it would embrace in the same formula the movements of the greatest bodies and those of the lightest atom; for it, nothing would be uncertain and the future, as the past, would be present to its eyes.

  From this point of view, whatever might be said about the world on other levels of description (whether of chemistry, or biology, or psychology, or anything else), nevertheless, there was one level of description, that of microscopic physical detail, in which every event was completely determined by the past. In the Laplacian view, there was no possibility of any undetermined events. They might appear undetermined, but that would only be because one could not in practice perform the necessary measurements and predictions.

  The difficulty was that there was one kind of description of the world to which people were strongly attached, namely that of ordinary language, with deciding and choosing, justice and responsibility. The problem lay in the lack of any connection between the two kinds of description. The physical ‘must’ had no connection with the psychological ‘must’, for no one would feel like a puppet pulled by strings because of physical law. As Eddington declared:

  I have an intuition much more immediate than any relating to the objects of the physical world; this tells me that nowhere in the world as yet is there any trace of a deciding factor as to whether I am going to lift my right hand or my left. It depends on the unfettered act of volition not yet made or foreshadowed. My intuition is that the future is able to bring forth deciding factors which are not secretly hidden from the past.

  But he was not content to keep ‘science and religion in watertight compartments’, as he put it. For there was no obvious way in which the body was excused obedience to the laws of matter. There had to be some connection between the descriptions – some unity, some integrity of vision. Eddington was not a dogmatic Christian, but a Quaker who wished to preserve some idea of free consciousness, and an ability to perceive a ‘spiritual’ or ‘mystical’ truth directly. He had to reconcile this with the scientific view of physical law. And how, he asked, could ‘this collection of ordinary atoms be a thinking machine?’ Alan’s problem was the same, only with the intensity of youth. For he believed that Christopher was still helping him – perhaps by ‘an intuition much more immediate than any relating to the objects of the physical world.’ But if there was no immaterial mind, independent of the physics of the brain, then there was nothing to survive, nor any way in which a surviving spirit might act upon his brain.

  The new quantum physics offered such a reconciliation, because it seemed that certain phenomena were absolutely undetermined. If a beam of electrons were directed at a plate in which there were two holes, then the electrons would divide between the two, but there seemed no way of predicting the path that any particular electron would follow, not even in principle. Einstein, who in 1905 had made a very important contribution to the early quantum theory with a description of the related photo-electric effect, was never convinced that this was really so. But Eddington was more readily persuaded, and was not shy of turning his expressive pen to explain to a general audience that determinism was no more. The Schrödinger theory, with its waves of probability, and the Heisenberg Uncertainty Principle (which, formulated independently, turned out to be equivalent to Schrödinger’s ideas) gave him the idea that mind could act upon matter without in any way breaking physical laws. Perhaps it could select the outcome of otherwise undetermined events.

  It was not as simple as that. Having painted the picture of mind controlling the matter of the brain in this way, Eddington admitted that he found it impossible to believe that manipulating the wave-function of just one atom could possibly give rise to a mental act of decision. ‘It seems that we must attribute to the mind power not only to decide the behaviour of atoms individually but to affect systematically large groups – in fact to tamper with the odds on atomic behaviour.’ But there was nothing in quantum mechanics to explain how that was to be done. At this point his argument became suggestive in character, rather than precise – and Eddington did tend to revel in the obscurity of the new theories. As he went on, the concepts of physics became more and more nebulous, until he compared the quantum-mechanical description of the electron with the ‘Jabberwocky’ in Through the Looking Glass:

  Something unknown is doing we don’t know what – that is what our theory amounts to. It does not sound a particularly illuminating theory. I have read something like it elsewhere:-

  The slithy toves

  Did gyre and gimble in the wabe.

  Eddington was careful to say that in some sense the theory actually worked, for it produced numbers which agreed with the outcome of experiments. Alan had grasped this point back in 1929: ‘Of course he does not believe that there are really about 1070 dimensions, but that this theory will explain the behaviour of an electron. He thinks of 6 dimensions, or 9, or whatever it may be without forming any mental picture.’ But it seemed no longer possible to ask what waves or particles really were, for their hard nineteenth century billiard-ball concreteness had evaporated. Physics had become a symbolic representation of the world, and nothing more, Eddington argued, edging towards a philosophical idealism (in the technical sense) in which everything was in the mind.

  This was the background of Alan’s assertion that ‘We
have a will which is able to determine the action of the atoms probably in a small portion of the brain, or possibly all over it.’ Eddington’s ideas had bridged the gap between the ‘mechanism’ of the body, which Alan had learnt from Natural Wonders, and the ‘spirit’ in which he wanted to believe. He had found another source of support in the Idealist philosopher McTaggert, and added ideas about reincarnation. But he had in no way advanced upon or even clarified Eddington’s view, having ignored the difficulties which Eddington had pointed out in discussing the action of the ‘will’. Instead, he had taken a slightly different direction, one fascinated with the idea of the body amplifying the action of the will, and more generally concerned with the nature of the connection between mind and body in life and death.

  These ideas did, in fact, show the shape of things to come, though in 1932 there was little outward evidence of future development. In June he had found himself placed in the second class in the Part I of the Tripos. ‘I can hardly look anyone in the face after it. I won’t try to offer an explanation, I shall just have to get a 1st in Mays* to shew I’m not really so bad as that,’ he wrote to Mrs Morcom. But more significant, in reality, was the fact that he had ordered as his last prize from Sherborne a book that promised a serious account of the interpretation of quantum mechanics. It was an ambitious choice of study, a book only published in 1932. It was the Mathematische Grundlagen der Quantenmechanik, the Mathematical Foundations of Quantum Mechanics, by the young Hungarian mathematician John von Neumann.

  On 23 June it was his twentieth birthday, and then on 13 July what would have been Christopher’s twenty-first. Mrs Morcom sent Alan a ‘Research’ fountain pen, such as Christopher had shown off, as a present. Alan wrote from Cambridge, where he spent the ‘Long Vacation Term’:

  14/7/32

  My dear Mrs Morcom,

  … I remembered Chris’ birthday and would have written to you but for the fact that I found myself quite unable to express what I wanted to say. Yesterday should I suppose have been one of the happiest days of your life.

  How very kind of you it was to think of sending me a ‘Research’ pen. I don’t think anything else (of that kind) could remind me better of Chris; his scientific appreciation and dexterous manipulation of it. I can so well remember him using it.

  But if he was twenty, and preparing to confront the work of European mathematicians, he was still a boy away from home, away from Sherborne. The summer holidays were spent much as those of the previous year:

  Daddy and I have just been to Germany, for just over a fortnight. We spent most of the time walking in the Schwarzwald, though Daddy of course was not up to much more than 10 miles a day. My knowledge of the language wasn’t altogether of the kind that [was] most wanted. I have learnt nearly all my German by reading half a German mathematical book.† I got home somehow or other…

  Yours affectionately, Alan M. Turing

  Alan had another holiday camping with John in Ireland, where he amazed his family by turning up at Cork in a pig-boat. Then for the first two weeks of September he joined O’Hanlon for a second and last time on Sark. Alan was ‘a lively companion even to the extent of mixed bathing at midnight,’ wrote14 O’Hanlon, who had struck a modern note by allowing two girls on the party. Alan had taken some fruit-flies with him, as he was studying genetics in a rather haphazard way. Back at Guildford the Drosophilae escaped and infested the Turing home for weeks, not at all to Mrs Turing’s pleasure. O’Hanlon was sufficiently detached from the ‘nation in miniature’ to write15 of Alan as ‘human and lovable’, saying:

  † Not the von Neumann book, however, which he only received in October 1932.

  I look back on holidays in Cornwall and Sark among the great enjoyments of my life: in all his companionship and whimsical humour, and the diffident shake of the head and rather high pitched voice as he propounded some question or objection or revealed that he had proved Euclid’s postulates or was studying decadent flies – you never knew what was coming.

  The all-encompassing system still allowed some moments of freedom. And Sherborne had also left Alan with one friendship that lasted – with Victor. Alan’s younger friend had been obliged to leave school at the same time, his father suffering from financial loss at what was the worst of the Depression. He had failed his School Certificate (telling Alan that it was because of too much time spent on chess and codes) but quickly caught up by passing it at a London crammers, and began what Alan called ‘his grim life as a chartered accountant’. At Christmas 1932 Alan stayed with the Beuttells for two weeks and worked in Alfred Beuttell’s office near Victoria. The visit was overshadowed by the fact that Victor’s mother had died on 5 November. The deep shadow was a link, for both boys were having to deal with the fact of early death. The link was close enough to break Alan’s usual reserve as to his beliefs – just as Mrs Morcom had broken it – and rather grudgingly to discuss his ideas about religion and survival. Victor believed very strongly, not only in the essential Christian ideas, but in extra-sensory perception and in reincarnation. To him, Alan appeared as one who wanted so much to believe, but whose scientific mind made him an unwilling agnostic, and who was under great tension as a result. Victor saw himself as a ‘crusader’, trying to keep Alan on the straight and narrow, and they had fierce arguments, the more so as Alan did not like being challenged by a boy of seventeen. They talked about who had rolled the stone away, and how the five thousand had really been fed. What was myth and what was fact? They argued about the after-life, and the pre-life too. Victor would say to Alan, ‘Look, no one has ever been able to teach you any mathematics – perhaps you have remembered it from a previous life.’ But, as Victor saw it, Alan could not believe in such a thing ‘without a mathematical formula’.

  Victor’s father, meanwhile, had thrown himself into research and work to overcome his bereavement. Alan’s work in his office was concerned with calculations required for his commission as lighting consultant to the Freemasons’ new headquarters in Great Queen Street. Alfred Beuttell was a pioneer in the scientific measurement of illumination, and the development of a lighting code16 based on ‘first principles’ as part of the ‘reduction of the physiology of vision to a scientific and mathematical basis’. His work for the Masons involved elaborate calculations to estimate the illumination at the floor level, in terms of the candle power of lights installed and the reflecting properties of the walls. Alan, who was not allowed into the Masonic building, had to work from imagination to check Mr Beuttell’s figures.

  Alan became friendly with Mr Beuttell, who told him about his success in Monte Carlo as a young man, when he had managed to live for a month on his winnings. He showed Alan his gambling system, which Alan took back to Cambridge and studied. On 2 February 1933 he wrote back with the result of his analysis, which was that the system yielded an expected gain of exactly zero, and that accordingly Mr Beuttell’s winnings had been entirely due to luck and not to skill. He also sent a formula he had worked out for the illumination of the floor of a hemispheric room lit from its centre – not, admittedly, an immediately useful result, but a very neat one.

  Standing up to Mr Beuttell’s ideas about his gambling system took some courage, as he was a forceful man, whose heart of gold was buried deep, with strong opinions on many subjects. An eclectic Christian tending to Theosophy, he was a great believer in the unseen world, and told Alan that his invention of the Linolite electric lamp had been sent to him from beyond. This Alan found too much to swallow. But he also had ideas about the brain, which he had formed since the early 1900s, according to which it worked on electric principles, with differences of potential determining moods. An electric brain! – there lay a more scientific idea. They had long discussions on these lines.

  Alan and Victor also went down to Sherborne together for the house supper, and after Christmas Alan wrote to Blamey, saying:

  I still haven’t quite decided what I am going to do when I grow up. My ambition is to become a don at King’s. I am afraid it may b
e more ambition than profession though. I mean it is not very likely I shall ever become one.

  Glad you had a good beano for your coming of age. Personally when my time comes I shall retire into a corner of England far from home and sulk. In other words I don’t want to come of age (Happiest days of my life at school etc.)

  Sherborne was part of him; and, essentially loyal to his past, he did not make the mistake of trying to cast it out. Although, indeed, the official speeches about training, leadership and the future of the Empire had left him almost untouched, there were aspects of the distinctive English public school culture in which he genuinely shared. Its dowdy, Spartan amateurism, in which possessions and consumption played a small role, were his. So was its combination of conventionality and weird eccentricity; so too, to some degree, was its anti-intellectualism. For Alan Turing did not think of himself as placed in a superior category by virtue of his brains, and only insisted upon playing what happened to be his own special part. And if the public school was founded upon deprivation and suppression, this was of a kind which gave its products the privilege of knowing that their thoughts and actions were considered significant. In setting out to do something in life, Alan exhibited in a pure form the sense of moral mission that headmasterly sermons sought so laboriously to inculcate.

  But he could not stay with one foot in the nineteenth century; Cambridge had introduced him to the twentieth. There had been a moment in 1932 when after a college Feast, Alan wandered quite drunk into David Champernowne’s rooms, only to be told to ‘get a grip on himself’. ‘I must get a grip on myself, I must get a grip on myself,’ Alan repeated in a very droll fashion, so that Champ always liked to think that this had marked a turning point. Be this as it may, it was indeed the year 1933 which brought Alan closer to the problems of the modern world, and in which he began to interact with it.