But there were also the university lectures, which on the whole were of a high standard; the Cambridge tradition was to cover the entire mathematics course with lectures which were in effect definitive textbooks, by lecturers who were themselves world authorities. One of these was G. H. Hardy, the most distinguished British mathematician of his time, who returned in 1931 from Oxford to take up the Sadleirian Chair at Cambridge.
Alan was now at the centre of scientific life, where there were people such as Hardy and Eddington who at school had been only names. Besides himself, there were eighty-five students who thus embarked upon the mathematics degree course, or ‘Tripos’ as Cambridge had it, in 1931. But these fell into two distinct groups: those who would offer Schedule A, and those who would sit for Schedule B as well. The former was the standard honours degree, taken like all Cambridge degrees in two Parts, Part I after one year, and Part II two years later. The Schedule B candidates would do the same, but in the final year they would also offer for examination an additional number – up to five or six – of more advanced courses. It was a cumbersome system, which was changed the following year, the Schedule B becoming ‘Part III’. But for Alan Turing’s year it meant neglecting study for Part I, which was something of a historical relic, hard questions on school mathematics, and instead beginning immediately on the Part II courses, leaving the third year free to study for the advanced Schedule B papers.
The scholars and exhibitioners would be expected to offer Schedule B, and Alan par excellence was among them, one of those who could feel themselves entering another country, in which social rank, money and politics were insignificant, and in which the greatest figures, Gauss and Newton, had both been born farm boys. David Hilbert, the towering mathematical intellect of the previous thirty years, had put it thus:9 ‘Mathematics knows no races … for mathematics, the whole cultural world is a single country’, by which he meant no idle platitude, for he spoke as the leader of the German delegation at the 1928 international congress. The Germans had been excluded in 1924 and many refused to attend in 1928.
Alan responded with joy to the absolute quality of mathematics, its apparent independence of human affairs, which G. H. Hardy expressed another way:10
317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.
Hardy was himself a ‘pure’ mathematician, meaning that he worked in those branches of the subject independent not only of human life, but of the physical world itself. The prime numbers, in particular, had this immaterial character. The emphasis of pure mathematics also lay upon absolutely logical deduction.
On the other hand, Cambridge also laid emphasis on what it called ‘applied’ mathematics. This did not mean the application of mathematics to industry, economics or the useful arts, there being in English universities no tradition of combining high academic status with practical benefits. It referred instead to the interface of mathematics and physics, generally physics of the most fundamental and theoretical kind. Newton had developed the calculus and the theory of gravitation together, and in the 1920s there had been a similar fertile period, when it was discovered that the quantum theory demanded techniques which were miraculously to be found in some of the newer developments of pure mathematics. In this area the work of Eddington, and of others such as P. A. M. Dirac, placed Cambridge second only to Göttingen, where much of the new theory of quantum mechanics had been forged.
Alan was no foreigner to an interest in the physical world. But at this point, what he needed most was a grip on rigour, on intellectual toughness, on something that was absolutely right. While the Cambridge Tripos – half ‘pure’ and half ‘applied’ – kept him in touch with science, it was to pure mathematics that he turned as to a friend, to stand against the disappointments of the world.
Alan did not have many other friends – particularly in this first year, in which he still mentally belonged to Sherborne. The King’s scholars mostly formed a self-consciously élite group, but he was one of the exceptions. He was a shy boy of nineteen, who had had an education more to do with learning silly poems by rote, or writing formal letters, than with ideas or self-expression. His first friend, and link with the others of the group, was David Champernowne, one of the other two mathematical scholars. He came from the mathematical sixth form of Winchester College, where he had been a scholar, and was more confident socially than Alan. But the two shared a similar ‘sense of humour’, being alike unimpressed by institutions or traditions. They also shared a hesitancy in speech, although David Champernowne’s was more slight than Alan’s. It was and remained a rather detached, public school kind of friendship, but important to Alan was that ‘Champ’ was not shocked by unconventionality. Alan told him about Christopher, showing him a diary that he had kept of his feelings since the death.
They would go to college tutorials together. To begin with, it was a case of Alan catching up, for David Champernowne had been much better taught, and Alan’s work was still poorly expressed and muddled. Indeed, his friend ‘Champ’ had the distinction of publishing a paper11 while still an undergraduate, which was more than Alan did. The two supervisors of mathematics at King’s were A. E. Ingham, serious but with a wry humour, the embodiment of mathematical rigour, and Philip Hall, only recently elected a Fellow, under whose shyness lay a particular friendly disposition. Philip Hall liked taking Alan, and found him full of ideas, talking excitedly in his own strange way, in which his voice went up and down in pitch rather than in stress. By January 1932 Alan was able to write in an impressively off-hand way:
I pleased one of my lecturers rather the other day by producing a theorem, which he found had previously only been proved by one Sierpinski, using a rather difficult method. My proof is quite simple so Sierpinski* is scored off.
But it was not all work, because Alan joined the college Boat Club. This was unusual for a scholar, for the university was stuck with the polarising effect of the public schools, and students were supposed to be either ‘athletes’ or ‘aesthetes’. Alan fitted into neither category. There was also the other problem of mental and physical balance, for he fell in love again, this time with Kenneth Harrison, who was another King’s scholar of his year, studying the Natural Sciences Tripos. Alan talked to him a good deal about Christopher, and it became clear that Kenneth, who also had fair hair and blue eyes, and who also was a scientist, had become a sort of reincarnation of his first great flame. One difference, however, was that Alan did speak up for his own feelings, as he would never have dared with Christopher. They did not meet with reciprocation, but Kenneth admired the straightforwardness of his approach, and did not let it stop them from talking about science.
At the end of January 1932, Mrs Morcom sent back to Alan all the letters between him and Christopher which he had surrendered to her in 1931. She had copied them out – quite literally – in facsimile. It was the second anniversary of his death. Mrs Morcom sent a card asking him to dinner on 19 February at Cambridge, and he in turn made the arrangements for her stay. It was not the most convenient weekend, he being engaged with the Lent boat races and obliged to be abstemious at dinner. But Alan found time to show her round: Mrs Morcom noted that his rooms were ‘very untidy’, and they went on to see where Alan and Christopher had stayed in Trinity for the scholarship examination, and where Mrs Morcom imagined Christopher would have sat in Trinity chapel.
In the first week of April, Alan went to stay at the Clock House again, this time with his father. Alan slept in Christopher’s sleeping bag. They all went together to see the window of St Christopher, now installed in Catshill parish church, and Alan said that he could not have imagined anything more beautiful of its kind. Christopher’s face had been incorporated into the window – not as the sturdy St Christopher fording the stream, but as the secret Christ. On Sunday he went to communion there, and at the house they held an evening gramophone concert. Mr Turing read and played billiard
s with Colonel Morcom, while Alan played parlour games with Mrs Morcom. Alan went out one day for a long walk with his father, and they had another day at Stratford-upon-Avon. On the last evening, Alan asked Mrs Morcom to come and say goodnight to him, as he lay in Christopher’s place in bed.
The Clock House still held the spirit of Christopher Morcom. But how could this be? Could the atoms of Alan’s brain be excited by a non-material ‘spirit’, like a wireless set resonating to a signal from the unseen world? It was probably on this visit12 that Alan wrote out for Mrs Morcom the following explanation:
NATURE OF SPIRIT
It used to be supposed in Science that if everything was known about the Universe at any particular moment then we can predict what it will be through all the future. This idea was really due to the great success of astronomical prediction. More modern science however has come to the conclusion that when we are dealing with atoms and electrons we are quite unable to know the exact state of them; our instruments being made of atoms and electrons themselves. The conception then of being able to know the exact state of the universe then really must break down on the small scale. This means then that the theory which held that as eclipses etc. are predestined so were all our actions breaks down too. 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. The rest of the body acts so as to amplify this. There is now the question which must be answered as to how the action of the other atoms of the universe are regulated. Probably by the same law and simply by the remote effects of spirit but since they have no amplifying apparatus they seem to be regulated by pure chance. The apparent non-predestination of physics is almost a combination of chances.
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 was 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 i
t 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 McTaggart, 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.
Alan Turing: The Enigma: The Book That Inspired the Film The Imitation Game Page 13
