Prepare Problems for the Brain to Solve

Bernardo Gonçalves has a nice new paper out on the Turing Test, partly making use of a couple of letters to Beatrice Worsley noticed by Mark Priestley in the Smithsonian archive. I don’t have much to add to Bernardo’s paper, but Mark’s generosity in sharing this source does help me illustrate that Turing had a major blind-spot: he didn’t generally take women seriously as mathematicians. Worsley is notable as the only female mathematical thinker for whom there’s any evidence of any intellectual traffic with Turing. (According to Hollywood, Joan Clarke achieved the same respect, but there’s little evidence for that beyond the desire to see Turing as a sympathetic figure.) In this of course he was hardly alone in this among his professional male peers: see this contemporary US report about how his mentor Max Newman was a superb manager at Bletchley Park save for the fact he didn’t make good use of female talent.

In 1950, Turing was still committed to the idea of using the new electronic computers to do thinking with in mathematical logic. That - rather than building a fast calculator - was why Max Newman had succumbed to Patrick Blackett’s enticement move to coal-black Manchester, over the objections of his wife Lyn, and why Max had in turn recruited Turing there in 1948. But Newman never did any active research on the computer and Turing was left, intellectually, entirely on his own. As the engineers took control, the project of doing research in mathematical logic on the new electronic computers was running into the ground while mathematical resources went, instead, into numerical calculations.

There were two young, enthusiastic and First-class mathematically trained women Turing could have used to build a research group around. Audrey Bates and Cicely Popplewell shared Turing’s office, and indeed Audrey Bates’s first job was to implement a version of ‘lambda-calculus’ - the tool of choice of mathematical logicians on the Manchester computer. But as soon as her MSc was finished, Bates defined herself as a programmer, not a mathematician. It can hardly have helped her lack of engagement with Turing’s intellectual program that Turing barely thought she and Popplewell had a right to exist, as Bates once told Andrew Hodges.

So how did Worsley establish this right to exist? Perhaps she came to Manchester because she was interested in Turing. Worsley was registered for a PhD in Cambridge from 1949, working on the EDSAC electronic computer there that Turing largely avoided engaging with. Whilst in Cambridge she took and - notably - kept some intriguing notes on a talk she later labelled as a ‘physiology colloquium - Univ of Cambridge 1949’ that discussed a number of issues that were occupying Turing at the time. There are references to information theory, and to the Rashevsky house journal from Chicago, the Bulletin of Mathematical Biophysics, and one diagram headed ‘flow diagram for a thinking mechanism’. (The five relevant sheets are displayed in the gallery nearby: these papers are in the National Museum of American History Worsley papers Box 1 Folder 1).

It’s unclear who the speaker was; I’d say not Turing, but the notes have a Ratio-y Club feel. Perhaps Woodger or McCulloch? If Worsley’s later annotation is correct then the only recorded candidate for the meeting is the Society for Experimental Biology’s ‘Physiological Mechanisms in Animal Behaviour’ which was held in Cambridge in July 1949. But the proceedings of that, though it has a contents list with star names such as Tinbergen, Lorenz and Lashley, don’t contain any paper that the notes are a recognisable version of. There is a mini-clue [I am unusually sensitive to these at the moment, being more or less completely unable to get any grip on John Finnemore’s new thing] in that JH Woodger is thanked reading one of the articles by WH Thorpe.

The fact that Worsley chose to preserve these notes, gives some hint that it may have been for reasons of intellectual interest in and perhaps from Turing, rather than commercial or academic reasons, that led her to work with the Manchester computer rather than the Cambridge one from 1950 onwards; by the end of 1950 she was living in Manchester. It was unlikely to have been a fleeing from Cambridge misogyny; the historiographic consensus is that Hartree, the professor in Cambridge, was much more sympathetic to female graduate students than supervisor in Manchester was.

The most substantial biographical article on Worsley (indeed it is the only one) says that

Worsley started writing her dissertation at Cambridge, but in 1951 for some unknown reason she returned to Canada with the text unfinished. She arranged to complete the work with the supervision of Byron A. Griffith, a professor of Mathematics at the University of Toronto and a member of the Computation Centre. Worsley wrapped up the writing quickly and was rehired as a staff mathematician at was rehired as a staff mathematician at the Centre in July 1951. Hartree approved the dissertation in Cambridge, and Worsley’s doctorate was awarded in 1952 after Hartree made a visit to Toronto. (Cambell, 2003)

A letter of December 1950 from Worsley to Turing, now in the University of Manchester (in the Special Collections TUR/Add 13 and 91), does indeed says that she intended to return to Canada because of medical advice to ‘take a prolonged change from academic work’. The same archive confirms that by 1952 she was working again, partly on the University of Toronto’s new computer. The correspondence with Turing restarted on practical career matters and applied mathematical issues, but also, notably, on Worsley’s ambition to find the simplest program which would ‘provide the functions necessary for the calculation of a computable number consistent with your theory’. This seems to have been intended to end up as a chapter in her Cambridge PhD thesis.

Beatrice Worsley in the Toronto Star, 1952, helping to 'prepare problems for Brain to Solve'. (The star puzzle was a newspaper circulation gimmick, not a cosmological model). 

Quite why Worsley rather abruptly left first Cambridge and then the UK to finish her PhD in Canada, and how the University of Cambridge thought that an acceptable idea, is not explained in print anywhere. In fact Worsley’s inner life remains pretty opaque beyond an enquiring mathematical brain. As far as the world knew, she never had any romantic partners, and all we know about her family life is that she barely spoke to her sister-in-law. One of the few glimpses was noted in Scott Campbell’s 2003 biography: at Worsley’s death in 1971 she left her decent sized estate not to her living siblings but to the University of Cambridge she had left in a hurry twenty years earlier. (Worsley died of a heart attack at the age of 50 so this Will might have been made much earlier.) Moreover this was specifically to found a ‘Helge Lundgren’ studentship. In 2003 Campbell didn’t know who Lundgren was so by implication the sister-in-law either wasn’t telling or didn’t know, but it seems likely to me that this was in memory or honour to the Helge Lundgren who was a prominent Danish canal engineer. A romantic speculation might link that to the flight from Cambridge, but is very unlikely. The likeliest time for any personal connection with Lundgren was after the Cambridge years, as the the major application for the Toronto computer, Ferut, was simulation of the hydraulic behaviour of the St Lawrence Seaway, Beyond that, there’s not much.

Bernardo uses Turing’s letters to Worsley of 1951, now in Washington, to good effect in explaining Turing’s opinion of his Test, but to see an early reception of these ideas it is the letters in Manchester (which run through 1952) that show how Worsley responded with her own ideas:

In connection with your paper on computing machinery and intelligence I'm still trying to think of some property of the human mind which could not be duplicated by The Imitation Game. I feel intuitively that if there is one it must be in the direction of spontaneity. McCulloch and Pitts in an article in the Bulletin of Mathematical Physics postulate a brain mechanism in which the threshold of excitement of the neuron can be determined by the neuron itself.

It’s not a ground-breaking response but it is an engaged one, and as such rather unusual among mathematicians of the time.

Thanks to Jonathan Dawes for investigating the SSEB proceedings and identifying the 1949 meeting. For the Ratio Club, I have taken my view from Husbands and Hollands 2008 article. At more length I have only just read Andrew Pickering’s superb book, both readable and indigestible, The cybernetic brain: sketches of another future. The day this was first posted, Colin Williams, who I had a great drink with in the pub once in Oxford, has shared with me for the first time his completed PhD on British cybernetics, which claims to be ‘archivally rich and methodologically innovative’, and changing ‘our understanding of post-war British history so that’s something to look forward to reading properly. Naturally I have ctrl-F-ed to check that my Turing book was cited (it was, thanks), and as a consequence I discover I am thanked for my support, which I don’t recall giving. One more superficial response: I don’t think I’d agree with Colin’s claim that Pickering’s book was merely in the service of sociological intervention; it is packed with vivid and well sourced history.

Must have been alluring

An interesting little fragment from the Keynes archive on King’s view of itself and of Turing, in 1939. The context is a debate between two King’s dons discussing the problem of what to do with the College’s young Research Fellows as they came towards the end of their Fellowships. The business model of the College rested on earning undergraduate tutorial fees, and there was no significant equivalent of modern PhD or postdoc funding. A surplus from the College’s endowment, which was incorrectly believed - then and now - to have come from Keynes’ magical money powers, was used to support young men as Research Fellows at the start of research careers. The older man, economic historian John Clapham wrote

Image by permission of King’s College Cambridge.

One of the 6 [non-permanent King’s Fellows] is Turing, a most brilliant fellow I should like to see kept in Cambridge, for Cambridge’s sake if not his. As our mathematical staff is overfull his proper destiny is the staff of another College. Several are weak in mathematics… [22 May 1939; Keynes KC/2/384]

In a similarly polite and collegiate reply - although I sense an underlying tension in the correspondence - the younger and more worldly Keynes responded that he had

a little doubt as to whether we have been strict enough in the past’ [about terminating Fellowships] ‘the average quality is by no means bad; it is the comparative lack of outstanding figures which is so striking. The prospect of going on with substantially the current staff … is death to the College’. The real test case on your list, because it will come to a head fairly soon, is to my mind Turing. If another College elects him to a Fellowship, well and good. But if not I would consider it absolutely disgraceful if we should drop him after six years, and we should take the earliest opportunity of giving him some small emolument beyond his Fellowship. He is, in your words, ‘a most brilliant Fellow’…if the expert reports on him turn out to be what I and I gather you expect them to be, I would feel a blight had fallen on our prospects if we were to drop him. [23 May 1939; Keynes KC/2/389]

Clapham in turn responded

Turing I am quite prepared to consider under the nine-year rule. I am not at present prepared to put him on the Tutorial Fund (unless for next year in Ingham’s absence; in which case of course I would).. I am prepared to carry on men of the Turing stamp now and then. [25 May 1939; Keynes KC/2/397].

Turing certainly had made a brilliant contribution with his 1936 paper on computable numbers, but neither Clapham nor Keynes were in a position to judge its value in a then small field of mathematical logic thought to have no practical application. (It would have helped, though, that there was a lineage from GE Moore and Bertrand Russell.) I wonder who the experts were who persuaded Clapham that Turing was a ‘most brilliant fellow’. My guess would be a Cambridge mathematician capable of impressing a historian with the civilised nature of their High Table conversation, so probably it wasMax Newman. But it’s odd that Keynes seemed to be expecting ‘expert reports’ on Turing in May 1939. I wonder if Turing was being tested out, with or without his knowledge, for a university promotion to a permanent job at the time. Four months later, of course, Turing reported for duty at Bletchley Park and everything changed. When he returned to King’s in 1947 to take up the final year of his Fellowship both Keynes and Clapham were dead, and there is no record of whether anyone still wanted to carry on with ‘men of the Turing stamp’. Whatever King’s or the ‘weak in mathematics’ colleges thought, Turing left for Manchester and for good at the end of the year.

There is a caricature of post-First World War King’s as populated by elderly dons desperately trying to re-elect young men as beautiful and brilliant as Rupert Brooke into vacancies in the Apostles and the Fellowship; it is a caricature I’ve both seen written as a homophobic slur, and alternatively heard as a point of some Pride. I doubt there’s much truth in the caricature, and in my view it’s more interesting to think about the class and national backgrounds of those who did and didn’t (Gray Walter, say) get chosen for these prestige positions. But I don’t think it’s entirely irrelevant to finish with a ditty said to have circulated a few years earlier. Andrew Hodges recorded this as oral history in 1983 and did not name his source. My guess would be Richard Braithwaite, himself elected in 1924, and whose own interviews with Laurie Khan about Frank Ramsey reveal him as someone who would have found this amusing in the 1980s:

Turing

Must have been alluring

To get made a don

So early on

Alan Turing's bathtub

Institutional memory in of Turing in King’s College (about which I have written here) tends, not wrongly, to point to a rather nice set of rooms by the river as ‘Turing’s room’ and I thought it was finally time to check.

True, for Alan Turing by Antony Gormley, with information plinth (critique? homage?) by King’s College Entrepreneurship Laboratory. It was revisiting King’s to watch the unveiling of this sculpture which prompted me to reflect on Turing’s bed and bath…

Turing’s first year room in the 1931 plans preserved in the Archive Centre, King’s College, Cambridge, KCAC/1/3/2/1.

The archive research, then: The College still hold schematic room allocations from the period. In his first year at King’s in 1931/1932, Turing had rooms in J.11 at the top of the Scott Building; in his second year on the ground floor of Webb’s Court in Q.2, and in his final undergraduate year he moved into S.8 at the top of S staircase in Bodley’s Court, paying a termly rent of £9 5’. He stayed there in the following year as a graduate student before winning his Fellowship in 1935 and moving into rent-free rooms in X.8, also on the top floor but with windows opening onto a view of the Cam. The floor plan records stop in 1938, but chances are Turing was re-assigned this room upon his return from Princeton in August 1938 until he finally relinquished his Fellowship in the spring of 1947; he went on visiting Cambridge for long periods from then until his death in 1954 and it is unclear where he stayed when he did but very strong chances are it was a room in King’s.

The title of this post was briefly ‘I had sex in Alan Turing’s bedroom’ as I had first thought that the 20 year old Jonathan Swinton had spent a year in what had once been the bedroom of Q.2, and that Turing’s ghost would have encountered my coming to terms with the physical realities of two bodies in one single bed. After a bit I borrowed a double mattress off someone; I vividly recall four of us carrying it across King’s Parade in something of a visible challenge to the don’t-ask-don’t-tell attitude to extramural overnight visitors then prevalent. But I was wrong (about Q.2: the mattress definitely worked) as I had miscalculated how the rooms were renumbered in the 1950s when the sets of sitting-room and bedroom had been split into two separate bedrooms to double the accommodation for students. So I didn’t ever sleep in Turing’s bed in Q.2, alone or not. (In any case, the college didn’t provide furniture in Turing’s time: students had to rent or buy their own, often from the previous occupant) But Turing’s first year room, J.11, I now realise from seeing the maps, was later converted into what was my shared bathroom in my final year. And the bath was huge. And the water was boiling hot and I could lie in that bath for hours and hours and I did, instead of revising. Unfortunately Turing’s ghost was no good at helping me out with my finals, which I hated and did very much worse in than Turing’s extremely good First.

Please don’t be tempted to try and take a bath in any of these rooms yourself: they still function as student and staff accommodation and even if you can conquer both the locked doors and your own respect for privacy half of them have changed numbering anyway, so you wouldn’t even be seeing the correct shrine. And making a pilgrimage to a shrine won’t get you a First any more than it did me.

Some slightly more historically relevant observations on these room allocations. Firstly, in the language which often introduces elite male friendships of the time, Turing ‘shared a staircase’ in that impressionable first year with, among others, the zoologist JWS Pringle. Pringle went on to be a significant zoologist who was one of Turing’s post war links with the Ratio Club, and perhaps more significantly for his thinking on morphogenesis, with the Society for Experimental Biology. (As an aside, I’ve just recently noticed this oral history which if accurate pushes back the date when Turing talking in public about morphogenesis to the first British Mathematics Colloquium in the summer of 1949. It would be great if a printed programme for that emerged). Also on that staircase was the grammar school boy Fred Clayton, who would become a significant friend, although Hodges asserts this wasn’t until their third year.

The room plans, which are far from forgotten and do come out on show regularly, are potentially quite interesting for the (relative) social gradations on display. There was a set of rather dark and dank buildings on the other side of King’s Lane, swept away in the 1970s, and the plans show that the rents for these were slightly cheaper at £8 a term rather than £9 for the rather nice sets in Bodley’s or the very grand (but austere and bath-less) staircases in the Gibbs building at £10. I wonder if there’s a correlation between the desirability of the rooms and the perceived prestige of the occupants. King’s in the 1930s had for decades been taking more than Etonians but it would be interesting to see where they, or students who had done well in the entrance examination, were placed spatially: in particular I wonder if they were the only ones allowed to live in the Gibbs building. That prestige space has now long been reserved only for Fellows. I’ve also sometimes wondered why Keynes had rooms in the (currently) less valued Webb’s Court development of 1909; perhaps he thought they were more contemporary and stylish than Gibbs, or perhaps he liked the fact there were toilets (in the basement). He was a vigorously modern man, though I bet he only had a single mattress.

Morphotexts

Just for morphonerds, a link to some reference documents on Turing’s morphogenesis work.