| Department of Mathematics and Statistics |
A Necessary Balance: Alec and Harry Aitken 1920-1935
P.C. Fenton
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10. Schlapp; Tovey; Whittaker; Lidstone
Robert Schlapp, known as Robin, took up a lectureship at the University of Edinburgh in 1925, the year Aitken was appointed. Schlapp and C.G. Darwin, the Head, were at that time all of Applied Mathematics at Edinburgh. Schlapp was a ‘sensitive man, diffident, a truly good and kind man’,77 and became Aitken’s closest friend.
Aitken’s social circle in Edinburgh was drawn mainly from those he met through music or the University. Willie Macnaughton for example, the director of a tweed factory, was an excellent pianist. He holidayed with the Aitkens at the seaside (Margaret remembers riding on his back as he simultaneously whistled and swam) and was with Aitken on the evening of the fateful ‘emotional disturbance’ between Herbert Read and Margaret Ludwig.78 Aitken’s connection with Donald Tovey, to whom he introduced himself in his first days in Edinburgh, was, according to Aitken,
very much “au sérieux”, and not much diversified by Toveyan quips. Self-taught amateur though I was, he treated me as on the same level of discussion as himself, and never showed a trace of condescension. What I learned from him, permanently altering, enriching, deepening my understanding, cannot be summed in words.
(In a speech to honorary graduands, Sidney Newman quoted a Toveyan quip that may have slipped Aitken’s mind. ‘Sir Edmund Whittaker, whose beauty of voice compelled belief; or his successor in office, the beloved Alec. Aitken, mathematician, musician and poet, who squared or factorized car numbers as asides in his conversation, as one walked to pick blackberries; or that leg entwiner Sir Donald Tovey, whom I was privileged to succeed, who confounded Aitken, as they were absorbed in Parsifal together at the piano with the question whether he had ever insured a cat. Aitken’s perplexed hesitation was resolved as Tovey continued “It’s a devilish business, you have to sign everything nine times”!’)
Aitken’s relationship with Whittaker remained politely formal.
In the diary [Memoir] there is mentioned Whittaker’s kindness to him, and this is all carefully written in, but Whittaker was I would say cold and Cambridge.79
George Lidstone, perhaps the foremost actuary of his time, was not a colleague of Aitken’s, but their mathematical interests overlapped; a problem of Lidstone’s was the topic of Aitken’s DSc. When Aitken met him, Lidstone was manager and actuary of the Scottish Widows Fund and a wealthy man.80 Margaret and George recalled childhood visits to the Lidstones’ 17th century mansion at Hermiston, fetched by a chauffeur in a Rolls Royce; one Christmas especially, with flaming pudding, games and a treasure hunt. Lidstone was twenty-five years Aitken’s senior. Recalling the circumstances in which he had set one of Housman’s poems81 to music, Aitken wrote to Sidney Newman,
“Hailes 1934” at the end [of the manuscript] means in fact Broomhouse Road 1933; it was just after my brother had been left at Epsom. I had been out at Hermiston House telling G.J. Lidstone (who stood to me rather in loco parentis then) of some of it. I walked back the whole way to Corstorphine, where we lived at that time. It was exactly as in Housman’s poem, the dry road, the hedges, the moonlight.82
Robin Schlapp was born in Edinburgh on 18 July 1899.83 His parents were German and his father was Reader (later Professor) of German at the University of Edinburgh. Of musical evenings at the home of the elder Schlapps, Aitken wrote
Those evenings are gone into the long ago: but the insight they gave me into the great and kindly Germany of former time will always stand to me as counter, in face of whatever detraction or condemnation Hitler and his like have brought on that nation. The highest degree of humanity and civilization was not merely reached, but normal, in the household at 1 Peel Terrace; and one must believe that the soil which grew those virtues cannot have lost the power of making them flower again.84
A correspondence developed between Aitken and Schlapp in the early thirties,85 if ‘correspondence’ is an appropriate term for what appears to have been entirely one-directional.86 Though the letters are largely mathematical, they are curiously intimate. Aitken was a natural letter-writer and fell easily into the rhythms of speech. Conversational asides abound.
‘Take (- I had almost said “the oboe”) the problem of repeated trials’; ‘Let me interpolate a meaning for this’; ‘I myself, by nature and predilection (and nationality perhaps), am strongly inclined to a different method’; ‘you would suppose, offhand, few things more hopeless than to get a reasonable approximation to π, the area of a polygon of unit half-diagonal and an infinite number of sides, from the special cases of a triangle, a square and a hexagon’; ‘I am using you as an anvil, for I feel a kind of momently generating function myself’; ‘does Southwellian opportunism really ensure in the long run the optimum convergence at which it aims? Does it not perhaps, by eating the largest bananas first, lay up for itself a slow diet of small bananas?’; ‘At any rate, light will be shed on the matter if we go through a simple example, and subject each detail to haruspicial scrutiny”.87
Apart from the first few letters, which were answers to questions from Schlapp, the mathematical ones were commentaries on Aitken’s research, and certain sequences of them amount to freehand drafts of papers that were published at about the same time. Others served to clarify ideas in Aitken’s mind.
Do not trouble to acknowledge this; for I am using you, not for the first time, as a target pour fixer les idées.88
He used argument sparingly, typically laying out examples to carry the point. One is repeatedly astonished at his facility at rapid calculation. Arithmetic complications never become obstacles but, being quickly done, painlessly reveal the patterns he prepares us for. Schlapp must have read the letters carefully, for though Aitken occasionally excused himself (as in the preceding quote) for barging in, each time he wrote it was with the clear confidence that the previous letter has been understood.
These letters, like any others, are conversations by other means. Setting aside the elegant structure Aitken created to accommodate his arguments, the idea that exchanges between mathematical collaborators – even those in the same place, who may be neighbours in the same building, talking to each other every day – should take a written form is commonplace. Only writing can provide the clarity and possibility for reflection that intricate arguments demand. We need not, then, be surprised at the existence of such a correspondence.
And yet a feeling of strangeness remains. For this is not a collaboration in any real sense, unless we identify Schlapp as a silent partner; neither the problems nor the solutions were his. Aitken too was not a collaborative writer. Of the seventy-two publications listed in his bibliography, only four were jointly written: his first, with G.L. Frewin, a fellow research student (1923-24); one each with H.T. Gonin (1933-35) and H. Silverstone (1941-43), two of his students; and the book Canonical Matrices (1932) with Herbert Turnbull, in which Aitken and Turnbull eliminated the possibility of territorial disputes by writing alternate chapters.
In reading the letters we cannot help but register their egoism, unconscious though it may be, and what is nearly the same thing, the assumption underpinning them, that whatever compels Aitken’s interest is compellingly interesting in itself. But this does not detract from their underlying meaning, that they are a sustained hymn to friendship.
There was a similar correspondence later with W.L. Edge, another of Aitken’s colleagues, but unlike the letters to Edge, which were overwhelmingly mathematical, some among those to Schlapp take on a more conventional form. Two are worth quoting in full, one zestful, the other, a decade later following Aitken’s professorship, more restrained, but both typical of Aitken, especially in their evocations of place.
The first, dated 27 September 1943, was written from D.E. Rutherford’s holiday retreat in the Highlands. Rutherford was Professor at St Andrews and held informal mathematical gatherings for invited guests at his cottage. On this occasion the only participant apart from Rutherford and Aitken was Ivor Etherington, Aitken’s colleague at Edinburgh.
Dear Robin,
You see by the address89 where I have been since last Saturday. D.E.R., Etherington and I occupy this two-roomed cottage to the north of the Lyon, some twenty miles west of Aberfeldy, a place marked Bruach on the map. Some 650 feet above sea-level, the river at 610 ft lying below the road 100 yards in front of us, the steep quartz-studded slope of Creag nan Eildeag (2087 ft) fronting us due south, and a similar spur of another Creag or Meall or Beinn, on the slope of which we actually are, behind us due north. Westward the glen continues indefinitely, range after range alternately déchiquetés behind each other on the skyline. Something brooding and autumnal exhales from the scene. No young men are to be seen, or at least only one in a wheeled invalid chair. The farming activities seem random and lost, defeated partly by a stinting and churlish soil, but chiefly overwhelmed and dwarfed by the sphinxlike frown of the mountains, Meall a Choire Leith (3033ʹ) and Meall Garbh (3661ʹ) lying high, remote and disdainful behind the nearer crags. Magnificent as the scene is, a sameness pervades it, the kind of sameness one would feel pursuing a long journey from some Inveralloch to an Invergalloch, passing some Invershalloch on the way. Eadem, mutata sed eadem. So much for background. The cottage itself, of grey substantial quartzy granite, has, as I said, two rooms, one about 18 ft by 12 ft, a living, cooking and general purpose room; a picture gallery also, since Dan paints his visitors and tacks the resulting portraits on the western wall, as well as certain scenery rendered in a “poster”-like style. The portraits and the landscapes, the former including such subjects as R.P. Gillespie, Lederman, Coulson, Graham, & Etherington with a five weeks growth of beard (as in one of Van Gogh’s self-portraits), these efforts reflect Dan’s own abrupt and farouche manner; while a self-portrait was so farouche that I took it to be some brother of Dan, who stood to him in some such ratio as my youngest brother Alan, sheepshearer, gold-miner, roadsman and N.Z. infantryman, stands to me. In a smaller room on the east side, half the size of the other, I sleep; each room has two beds placed parallel.
The arrangements are bachelorial, but of a rather slatternly civilian bachelorishness, which is abhorrent to me as an old campaigner. I feel at times the “orderly officer” complex rise in me, with a desire to bawl, “Here, ’shun! Sergeant, put these men on the mat for an untidy tent! Bedding not laid out, and look at those mess-tins!” etc etc. Still, we fare well. Two eggs and bacon each for yesterday’s breakfast, two boiled eggs each for today’s, and so on I presume. Washing facilities are exterior and al fresco, consisting of an artificially made waterfall between two table-like quartz rocks, on one of which some soap reposes: – “Cover the soap when you’ve done with it, otherwise the sheep eat it” – I think this injunction gives the keynote of our domestic life here. There is a tablecloth, with a “J’y suis et j’y reste” air about it.
There is an “utile” to all this “dolci”; and that “utile” is the notion of mental mathematical improvement. I do not myself subscribe to the idea of repairing to the wilds in order to gain the detachment of mind conducive to the study of J.E. Campbell’s “Theory of Continuous Groups”, or A. Adrian Albert’s “Modern Higher Algebra”. None the less that is the serious idea held by my co-celibants [sic] here, and I render an outward lip-service to it. When we may perhaps have heard the nine o’clock news at the farmer’s (Mr Campbell) close at hand (on an inferior set which oscillates and gives the impression of an announcer intermittently affected by a combination of cleft palate and loose false teeth), we return after pleasant conversation at, let us say, 10.30 p.m. Then Dan will say, “I begin to feel like some maths”, and perhaps some coffee is made, and another chapter of “Continuous Groups” is broached, knotty points being elucidated in chalk on a 5 feet by 2 ft 6 in “blackboard” of linoleum. This, as a matter of fact, is where my lip-service breaks away; for I like to be in bed before 11.30 (indeed, before 11) and I plead heaviness and leave the enthusiasts to it.
What is our life? Well, that is it for these few days; but I shall be very ready to return to 23 Stirling Road, tele.83419, when they end. I did not much want to come in any case; but a kind of conspiracy, in which my wife had a hand, was set afoot.
Rentonhall90 is already far in the past, though near in every detail. I left it in such state as befitted, so I thought, a place so beautiful and with such associations, into which the names of your mother and father were not least interwoven. It has now declined, I fear, on worse times and much worse occupancy; and with no little poignancy will I, if I ever traverse the Morham Road, glance towards the house and ridge, whether or not the gracious trees still stand about it. The sense of place is no light thing with me. Cramond, Corstorphine, Braids, Eskdalemuir and Rentonhall, each several name evokes a whole lifetime of common and uncommon experience.
We were not quite settled when I left home, but our things were moving towards stability in their places. Then we shall see more of you. Meanwhile, to you and Mary and little Katherine!
Yours ever, Alec
The context of the second letter was a short excursion Aitken took into Galloway, rendered yet shorter by sudden illness. Aitken often took off alone, mostly for day trips.
If he was free on a fine day he would decide, often on the spur of the moment, to go out. Mother would rustle him up a few sandwiches, he’d put them in a haversack & go out to catch a bus. So, a bus, sufficiently frequent along by the Pentlands, & get off where the mood of the moment took him.91
The letter is headed 74 Trinity Road, Edinburgh 5, 3 April 1954.
My dear Robin,
Thank you for the birthday greetings. I could wish, anno sexagesimo aetatis, that I were in better fettle to receive them. It was disappointing to have to return from the southwest after so brief a visit.
I was sorry to have missed your talk on Newton. Not that Newton appeals to me much as a man at all. He is deficient in something – call it vaguely warmth; he is an enigma, something of a Martian. Who has called him a mystic? Certainly not William Blake, for whom Newton and Locke were the enemies of life. A magnificent brain; but something disquieting, in that research into Biblical chronology.
To return to Galloway. As you say, there is something “different” about that quarter of Scotland. I was strongly conscious of it in that peninsula, lying between Urr and Dee, of which Kirkcudbright is the western mark and, for all that it is the name-town of its shire, is really cut off from Castle Douglas, the virtual county town and the main highway. An irregular range of rough hills – Ben Gairn is the chief – looming apparently much higher than their 1250 feet – completes the isolation. On the Saturday morning, just a week ago, I took a short bus-run to Dundrennan, south of these, a mere four houses on a slope, a post office and a manse below the road, principally to view the ruins of Dundrennan Abbey and to form an intuitive opinion as to whether it was really likely that Mary Queen of Scots had spent her last night in Scotland there, as romance and the history-books assert. I had the morning and the Abbey and the caretaker, a veteran of the Leicestershire Regiment incapacitated in the third battle of Ypres (and therefore a bond established between us at once) to myself.
The Cistercians, who founded the Abbey in A.D. 1142, had marvellously chosen the site, a flat of ground breaking the uniformity if the incline before it falls again into the groove of the Abbey Burn. In ruins, its pillars lopped short, open to the winds, the Abbey is still spacious, noble and impressive, too full of detail for brief description; it is astonishing to learn that it is only since 1920 that it has been scheduled as an ancient monument and cared for. It is interesting to see the supersession, as additions were made over more than a hundred years, of Norman architecture by Gothic – and I will say that I am not a Goth; a supersession only partial, for at one place a range of Gothic windows is surmounted at the next flight by one of Norman, as though old habit had reasserted itself. There are recumbent effigies, one of them a “belted knight”, none other than the father of Devorguilla, the wife of John Baliol. I mounted to the guest-room, now wall-less and roofless, where Mary Queen of Scots is said to have spent that last night; but it is hard to believe this tradition, the place is too conspicuously romantic and would moreover, considering the epoch and the circumstances, be a dangerous hiding-place. An alternative and less colourful tradition favours a farmhouse, Hazelfield, a mile or two off; from either place it would be easy for a fugitive to reach the small cove of Abbeyburnfoot, where the boat is said to have put in. I walked east four miles to Auchencairn, a village straggling in a slatternly way down to mudflat level, had an indifferent lunch at Auchencairn Arms (it needed no Heraclitus to tell me this would not occur a second time!) and fortunately found a local bus run by private enterprise. This took me north through wooded valleys under the eastern lee of Ben Gairn to Castle Douglas, and I then completed the circuit.
My fellow-resident was in the same position and angle. He opened one benignant eye, shut it again, indicated a smile by a contraction of the right cheek, and continued to drowse softly. A tray of tea things had clearly been brought to him in that position. He vanished on the Sunday, and I know no more about him. I saw him once going down for breakfast at 9.45. A gentle and unimportant mystery.
What chiefly remains of my brief visit is a walk on a starlit night. And I need not have truncated my Virgilian quotation (one line of which must have been a favourite with Virgil, since he uses it twice in the Aeneid), but should have given it whole:*
Arcturum pluriasque Hyadas geminosque Triones
Armatumque auro circumspicit Oriona,
(* Palinurus setting a course by the stars.)
since I had the geminos Triones on the way back. Consider what Virgil can do with night and the sea:
Ruit oceano nox.
Reading in the Scotsman, by the way, Douglas Percy Bliss on Dante and his illustrators, Blake and Gustave Doré and the rest, and in particular on Dante’s Simile of the cranes, I was half tempted to write myself pointing out their Virgilian origin,
quales sub nubibus atris
Strymoniae dant signagrues, atque aethera tranant
Cum sonitu, fuguintque Notos clamore secundo,
but I withheld my hand. Aliis memoranda relinquo.
W.L.E. will be disappointed that I am not going to the Mathematical Colloquium at Cambridge. So am I, though only partly; I am not gregarious, and I often think there is too much talking shop at these Colloquia!
Yours ever, A.
One wonders whether here too, as in the mathematical correspondence, Aitken is writing principally for himself, as it were to ‘hold the mood and fix it’. Did he have friends in the usual sense, or are they better thought of as personifications of aspects of himself, with whom he could continue his lifelong interior monologue in a socially acceptable way? Margaret raised the question explicitly. ‘I think Robin Schlapp was a close friend, very close. I have even so wondered, how close? How close was he?’92 One is reminded of a passage from Dobell’s account of D’Arcy Thompson (a later correspondent of Aitken’s), though Thompson was an utterly different personality and wildly sociable compared with Aitken.
He often recalled how Michael Foster once said to him, while they were sitting by the old bowling green in Trinity, “You know, D’Arcy, you haven’t got many friends!” He was ‘shocked and startled’ by this casual remark, ‘for I thought I knew everybody and had not an enemy in the world […] Yet so it was and so it still is. Of real friends I have had none.’ Retelling this tale in his last years he added ‘And what’s more, I can see that precisely the same was true of my own Father. He was the most harmless of men. He never hurt man, woman or child, he never did a mean thing, he had a smile and a pleasant word for everybody, from the Bishop to the apple-woman at his gate. But yet I can see clearly that he had no friends.’93
Margaret wrote:
Those letters to Robin are very elegantly written. I’ve sometimes wondered if Father ever let his hair down, at least in writing; he did sometimes in speaking – to me anyway; George has said he was “distant”.94
Ian Hunter commented that Aitken was almost autistic in his self-absorption. He talked charmingly about himself, and of the world insofar as it acquired shape and expression through him, but was bored if the conversation strayed to other topics. Just as, he said, motioning at our surroundings, Aitken would be bored by a visit to the local pub.
| 77 | MM to me, 23 Jan 1998. |
| 78 | Memoir, 100-102. |
| 79 | MM to me, June 1996. |
| 80 | According to George Aitken, Lidstone’s annual income was about £5000 plus directors fees of £1000; with, in addition, taxes paid by the company. At the same time (according to George) Whittaker would have been earning about £$1200 pa. |
| 81 | White in the moon the long road lies, The moon stands blank above; White in the moon the long road lies That leads me from my love. Still hangs the hedge without a gust, Still, still the shadows stay: My feet upon the moonlit dust Pursue the ceaseless way. The world is round, so travellers tell, And straight though reach the track, Trudge on, trudge on, 'twill all be well, The way will guide one back. But ere the circle homeward hies Far, far must it remove: White in the moon the long road lies That leads me from my love. |
| 82 | A.C.A. to Sidney Newman, 28 April 1961. |
| 83 | W.L. Edge, Obituary of Robert Schlapp, Proc Ed. Math. Soc., 35 (1992), 329-334. |
| 84 | Memoir, 87-88. |
| 85 | The first of the twenty-nine letters I have is dated 28 October 1933. The last was written on 19 November 1960. |
| 86 | Only one of the letters mentions a message from Schlapp, and that was a birthday greeting. |
| 87 | 7 March 1934; 21 March, 1945; 8 December 1945; 14 January 1946; 16 January 1949; 21 January 1949. |
| 88 | 20 October 1951. |
| 89 | c/o D.E. Rutherford, Ballinloan, Glenlyon, Perthshire. |
| 90 | The Aitkens’ house from December 1940 to September 1943. For the context of Aitken's comments, see Memoir, 111-112. |
| 91 | MM to me, 20 Nov 1997. |
| 92 | Ibid. |
| 93 | Clifford Dobell, op.cit., 613-4. |
| 94 | MM to me, 22 Oct 1995. |
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