Department of Mathematics and Statistics

### A Necessary Balance: Alec and Harry Aitken 1920-1935P.C. Fenton

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#### 22.   D’Arcy Thompson; Edwin Muir

D’Arcy Wentworth Thompson FRS (1860-1948) was a biologist and classicist with a bent for mathematics: ‘neither a naturalist nor a Hellenist nor a mathematician, but all three in one’.184 His book Growth and Form (1917) is famous as a pioneering attempt to explain biological growth from physical and mathematical principles, and by Aitken’s time he was a patriarchal figure in science and letters. He looked the part, white-haired and -bearded, a child’s image of a kindly God. He was older than Aitken by a good margin, ten years older than his father in fact. A correspondence between the two was underway by 31 January 1934, the date of the first surviving letter from Aitken to Thompson. Aitken’s tone was deferential, almost courtly, perhaps reflecting the emotional strain he was under.

It is, of course, no inconvenience whatever to me to have, for company in my room, your trunk & its contents. It serves to remind me, if such reminder were needed, of your virtuosic lecture of last Friday evening – of which the only disappointing feature was that you had to depart in such haste for your other appointment that you missed the many expressions of praise which you should rightly have heard in person.185

In time he loosened up, especially when the subject took his fancy – the frequency of dactyls and spondees in Virgil for example, and the possibility of using such an analysis to test the authenticity of the Appendix Vergiliana. (As it happened Thompson had already considered this question.186) Stimulated by Thompson’s interest in Fibonacci numbers, Aitken launched into a tour of recurrence relations, including an anecdote that says much about his approach to mathematics.

Take my own case. As a youth, knowing nothing of theory of numbers but being good at mental arithmetic, I read in the puzzle column of the “Strand” Magazine the statement that $17^2$ is twice $12^2$ plus 1; challenge, to find two pairs of higher numbers possessing this property. Well, with trial and error and some slight scribbling, I soon found the pair 99 and 70, noting with interest the intermediate pair 41 and 29 and the minus 1 in their case; and soon after that I noticed the recurrence 12 + 17 = 29, 12 + 12 + 17 = 41, 29 + 41 = 70 and so on, and building on it got 577 and 408, noting 239 and 169 of the other type. All this in some quarter of an hour in a public library in Dunedin, New Zealand. Going home, I proved the recurrence algebraically, worked out 7/5, 17/12, 41/19, 99/70, … up to 1393/985, compared them with $\sqrt{2}$ and observed that the errors diminished successively in something which seemed to be tending to a G.P. of common ratio about –1 : 6. Now if I did that from natural interest and without preconceived ideas, I can easily believe the Greeks (or the Babylonians, whom, according to Dr Neugebauer, we have greatly underestimated) worked by a like instinct.187

Later letters brought out some of Aitken’s most vivid writing.

Each year, up to 1939, I used to make a kind of pilgrimage, centred upon the Waverley Novels and “The Bride of Lammermoor”. This was to the Fast Castle. It is true that Sir Walter had never been there, though he had seen it from the sea while on a voyage from Leith in 1810 (so far as I recall); but he says, in his notes on the novel, that Fast Castle will sufficiently stand for Wolf’s Crag; and so each year I used to walk over Coldingham Moor to this wild and romantic spot, which I have seen in all weathers; sometimes when the sea was a smooth sheet of sun-burnished lead, stretching without ripple to the horizon, with the Bass Rock, ten miles to the north, suspended upon it like an enormous nugget of antimony; sometimes in the teeth of the wind, and sometimes when the seagulls, jealous of their young in the breeding season, made vicious repeated swoops much too close for comfort; but always with the thought that here was the outer edge of an enchanted country, stretching across the Lammermoors to the Eildons and the Tweed.188

When Thompson wrote offering his congratulations on Aitken’s FRS, Aitken replied with one of his rarest confidences, a glimpse of his father.

Indeed I have found that the pleasure given me by such kind messages from friends who are “in the know” is fully equal to the natural pleasure I feel in the occasion of their congratulations. But chiefly I am glad – and I think you will well understand and be in sympathy with this sentiment – chiefly I am glad for the sake of my father in New Zealand, whose pride in the matter may atone in some small degree for the pang of separation by half a world.189

He last wrote to Thompson in late 1946 to wish him well on his forthcoming trip to India, as a Royal Society delegate to the Indian Science Congress. Thompson contracted pneumonia during the conference and died shortly afterwards.

Perhaps the deepest of Aitken’s relationships was with the poet Edwin Muir, an account of which is included here, though it lies just beyond the chronological limits of our narrative. Muir himself caught the drama of their first meeting.

[W]e both felt at once an affinity with you, which probably goes deeper than any of us knows yet, and I assure you that such spontaneous friendship is rare to us, as to you. I want it to continue, and I’ll do anything I can to make it continue. I feel that in some ways our experience coincides, though I feel that yours, in the things you mention, has gone farther than mine and is more exact.190

Muir’s early life, in its material poverty and emotional upheaval, its disconnection from the culture in which he later found a prominent place, has points of correspondence with Aitken’s. He was born in 1887 on a farm in Orkney, where he spent an idyllic childhood. In 1901 the family moved to Glasgow. His father died when Muir was 15, and in the following two years his mother and two of his brothers also died. Muir worked unhappily as an office clerk until his marriage to Willa Anderson in 1919; it was she who gave him the confidence to concentrate on writing. His poetry conveys a transcendent view of the world in which the unity and timelessness of his Edenic childhood is partially recovered.

Aitken met Muir at St Andrews, where Muir was living, during the 1938 Mathematics Colloquium. At once they fell into shared confidences. Aitken spoke about his breakdowns and visionary experiences, and his recent dream about St Andrew’s crosses, which he was later to decipher in mathematical terms. Muir responded:

The most strange and the most beautiful experience I have ever had was a waking trance, a long, very rapid series of vivid pictures, which may have actually occupied a very short space of time: including a fight with a curious heraldic monster, and ending up on the shoulder of God, a huge figure sitting on a throne, with rings of the blessed round him.191

They were on secure ground; each trusted his dream life and the intuitions to which he had been privy, and each recognized the deepest parts of himself in the other.

But when you came I was too moved by some of the things you said to consider that I was a poet, or to care about it, except essentially, in recognizing that the world you spoke about was the world from which what I like best in my poetry was drawn, largely unconsciously.192

Aitken was never shy of sharing his convictions but his encounter with Muir may have been the only time in his life in which he arrived at complete communion with another human being. It was an auspicious moment for their lives to intersect. Muir was in the later stages of a period of struggle, on the verge of a realization of his Christianity, after which his life became ever more integrated and complete. Aitken was about to experience the fragmentation of another breakdown, and others followed that in his later years left part of him hollowed out. A letter of 28 June 1951 points subtly to differences between them, though it was in response to Aitken’s words of support for views expressed by Muir in a public broadcast.

It is necessary for us to have a picture, an image of our life, if our life is to have any significance; and my complaint is that the ability to produce the picture is declining, and that when it is produced it tends more and more to be confused and inconclusive; and one of the reasons I put down for this (perhaps wrongly) was that the mental energy of mankind had gone more and more into the pursuit of knowledge, more and more exact, about such things as the universe. You write in your letter, my dear Alec, about the universe; but I want to know something about Tom and Dick and Jane ...193

Aitken’s letter would have been written at a time of stress, if not breakdown. Muir concluded, evidently puzzled:

But, my dear Alec, what do you mean by saying so mysteriously that I am being weighed in the balance? Aren’t we all, and the world along with us? And what is the verdict, with its harshness, that you cannot give me? [...] But what does it matter, in any case? We shall pass, and our works with us. Yet I should very much like to know that verdict.194

It is not beside the point to observe that those to whom Aitken responded most deeply were all, in various ways, outsiders. Schlapp, who suffered as a schoolboy for his German parentage and whose family circle Aitken evoked so warmly for its ‘Gemütlichkeit’; Aitken’s Polish research student, Dr Stanisław Kołodzieczyk – ‘Kwodge’ as the children knew him – his ‘younger friend’ who touched Aitken to the core;195 and Muir, the exile from Eden.

 184 Clifford Dobell, D’Arcy Wentworth Thompson, Obit. Notices of Fellows R.S., 1949, 611. 185 Aitken to Thompson, 22 Jan 1935. The Thompson-Aitken letters are held at the University of St Andrews Library. Photocopies were obtained by Walter Ledermann who very kindly (and with the Library’s permission) passed them on to the author. 186 Aitken to Thompson, 29, 31 Dec 1937. 187 Aitken to Thompson, 23 Dec 1938. 188 Aitken to Thompson, 30 June 1946. 189 Aitken to Thompson, 15 Mar. 1936, after Aitken’s FRS. 190 P.H. Butter (ed.), Selected Letters of Edwin Muir (London, 1974), 102. Muir includes his wife, Willa. 191 Ibid, 102. 192 Ibid, 103. 193 Ibid, 159. 194 Ibid, 160. 195 Memoir, 107-8.

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