Oxford Road Show

A map of the central Manchester University precincts around 1950. The four brown regions are, top to bottom,

• the ‘lavatorial’ room where Williams and Kilburn’s 1948 ‘Baby’ prototyped the earliest practicable electronic memory bits, and in the process generated a plausible claim to run the worlds first computer programme.

• the 1950/51 (?) Computing Laboratory, partly built with Max Newman’s £35000 Royal Society grant and the ‘little steel’ he extracted from a reluctant Ministry of (war) Supply. This housed both the successor to the Baby, the Manchester Mark I and its human labourers including individual offices for both Kilburn and Turing.

• The offices of the mathematics Professor, on the top floor of the original Waterhouse lecture building

• A lecture room in the Arts Building, possibly the site of the 1950 discussion on ‘Mind and the Computing Machine’ that seems to have provoked Turing into writing his Mind paper introducing the Turing Test.

None of these interiors are open to the public, though all can be clearly seen from public spaces. The University has in the past run walking tours that offer access, though they may have lapsed at the same time as the post of University Historian.

I post this partly because a publisher’s error has corrupted the map in the second printing of the book.

I drew this map and it specifically is freely copiable under a CC-BY copyright license (in fact I am happy to share the Adobe Illustrator files if you want to add anything). It is partly based on a 1926 booklet, The Victoria University of Manchester: a short historical and descriptive account; there is a copy of this in Universty of Manchester Special Collections. Aspects are mildly speculative, I should perhaps add offices for a (human) pre-war computer in the basement of the Christie Building and the wartime location of Hartree’s differential analyser in the basement of the 1909 Physics building. (It also seems a bit odd not to mention that building is where the atom got split.) Further references are in the book. The buildings south of Burlington Street have largely now disappeared.

Sometimes it is the People Paid to Imagine Stuff

Not for the first time I was asked the other day if Alan Turing had ever said the following quote:

Sometimes it is the people who no one imagines anything of who do the things that no one can imagine.

The answer is no, Alan Turing the historical figure is not on record as ever having said this, and he very probably never did. Benedict Cumberbatch, on the other hand, definitely did say it.

It doesn’t really matter much, but:

• Both Andrew Hodges and Dermot Turing, the two of Alan Turing’s biographers I respect the most, have told me that they don’t recognise the quote from any primary source material.

• The quote does appear in the 2014 film The Imitation Game. In fact it is said first to Turing by Christopher Morcom, Turing’s first love at school, and then repeated later in the film when Alan Turing (Cumberbatch) is asked by Joan Clarke (Keira Knightley) why he has singled her out for a key role at Bletchley Park. The Imitation Game is a Hollywood narrative, crafted to make emotional sense to audiences, in this case by making Turing more sympathetic through letting us see a paying forward of his debt of support from Morcom to Clarke.

• The film certainly fictionalises very many aspects of the historical source material. Opinions have differed on how morally legitimate this fictionalisation was, but in any case it is overwhelmingly likely to me that this particular phrase was conceived in the mind of the script writer.

• More broadly, Turing is drawn on today as a hero in a modern drive to offer inspiration to a more diverse set of students than he ever encountered in 1930s Cambridge. It might be worth remembering that Turing was as embedded in the sexist and classist assumptions of that time as much as anyone. If Turing did offer a helping hand in recruiting Joan Clarke (which I don’t think there is any evidence for) it was because she had a Cambridge First, and because he knew her brother from High Table…

• By 2015, the quote was being discussed, as a quote from the movie in at least one blog. One comment on the blog suggested the line also appeared in Tim Burton’s 2010 Alice in Wonderland though the copies of that script I can find online don’t seem to contain the quote.

• Sometime around 2019 I saw the following different quote in the wild, but credited again to Alan Turing

Those who can imagine anything, can create the impossible

• Again, I don’t know of any primary historical source for this quote. Dermot Turing thinks that this one originated in the 2006 fiction A Madman Dreams of Turing Machines by Janna Levin. which I have not read. Unlike the first quote, which is so blandly banal that anyone could have said it, I think mathematical logicians are the one class of people who definitely would not write this second sentence. (I can though imagine a Max Newman exploding while a Ludwig Wittgenstein expounded this). I can imagine that it is meaningful, I suppose, but only by creating an impossibility. To be fair, there is no provably terminating algorithm to verify my claim.

• Unfortunately, the place where I spotted this unsourced quote was.. the newly redecorated reception area of the Turing Building, home to the University of Manchester’s Department of Mathematics. How on earth it came to be installed I don’t know. At the time the University had a professional historian in place as University Historian, who might have enquired about the source, but he wasn’t consulted, and the University have since decided they don’t need such a post anyway.

Filming Dr Who in Manchester Town Hall

…never happened, as far as I know. But I think it will once the location scouts see this production still from the 1935 Manchester of Commerce handbook.

The photo is credited to GR Hinks. I’ve not been able to confirm the connection, but a Manchester engineer named George Ryder Hinks (1886-1949) might well be him in which case I think it comes out of copyright today 1 Jan 2020. Happy New Year!

Skewed research

A previously unpublished Turing letter on number theory

After I’d finished the research on Turing and was working on someone quite different I turned up a previously unpublished letter by Turing on number theory. For the record here it is.

The letter is in Trinity College Cambridge. Turing wrote it at home in Wilmslow to a Cambridge mathematician named Albert Ingham and it is undated though almost certainly written around Christmas 1951. That’s because it is a response to a letter Ingham wrote to Turing on 19 Dec 1950 and in turn it got a response on 2 Jan 1951: both of these letter’s are in King’s and online and they have been excellently put in context by Denis Hejhala and Andrew Odlyzko.  The letter has long been catalogued as from Turing in the printed Trinity catalogue for AE Ingham’s papers, but they’ve never put that catalogue online and the two sides of the correspondence have not been connected before. (It’s one of those libraries where research can tend to the serendipitous.) I don’t think the editors of Turing’s Collected Works knew about it.

I’m not going to comment on the details of the maths so as not to bore you. Also because I don’t understand them. The rough problem is estimating how big a number now called Skewes’ number is. That was a characteristically ambitious problem for Turing: it turns out that Skewes’ number is the largest interesting number in the universe. (**)

Like all of Turing’s writings this letter is copyright by King’s College. Although the copyright in Turing’s published work expires at the beginning of 2025 you will need their permission until 2039 to reproduce this unpublished material for non-fair-use reasons. King’s are responsible and generous copyright holders and it’s not their fault that copyright law is quite badly broken.. I record my thanks to Trinity College Cambridge for allowing me to view this letter. and making it possible to reproduce.

 (**) Skewes’ original bound was for the first sign change of the difference between the number of primes up to a point and a well known and very good approximation for that number given by a logarithmic integral. The characterisation of this crossing as happening at less than 1.397x10^316 was described by GH Hardy as requiring ‘the largest number that has ever served any definite purpose in mathematics’.  There have been a number of versions of Skewes’ number related to the behaviour of the Riemann zeta function and the distribution of primes. But actually a decently robust definition would be the largest interesting number which has ever appeared in any mathematical research not intended to define a largest interesting number. And before you all write, I am aware of the proof that all numbers are interesting, though personally I am bored of 1729. Stanley Skewes was a South African-born mathematician who was a contemporary of Alan Turing’s at King’s. As well as collecting a PhD in number theory  from Cambridge, Skewes also went home with a wife, Ena Allen, who Wikipedia tells us was a keen opera singer and the daughter of the head chef of King’s College. (Ancestry.co.uk suggests that Stanley already had a wife, Vera Rothkugel, in South Africa) Skewes pops up in the Turing timeline as a useful illustration of the mathematical culture at Cambridge in the 1930s: they used to row together in the King’s boat.  Years later Skewes was at pains, when having to communicate a slightly delicate point about the two of them working on the same area, to remind Turing of the connection. Stanley seems to have taught at the University of Cape Town until at least the 1970s: he wrote a reference for the young JM Coetzee.

Ingham himself was a mathematician rather in the mould of his contemporary Max Newman: a grammar school boy, son of a boot machine operator, for whom a Trinity scholarship and then high Tripos results were the making of a career. As Burkill wrote ‘In the early 1920’s young men who had escaped or survived the war found a market, favourable to both buyers and sellers, in appointments at Cambridge or Oxford and other Universities. G. H. Hardy had a large say in the placing of pure mathematicians.’ In 1930 Frank Ramsey had become a genius by dying early and Ingham came back from Leeds to take Ramsey’s old job at King’s where he stayed a Fellow for the rest of his life: he would probably have been Turing’s undergraduate supervisor. Norbert Wiener, who would later parlay a brilliance with Fourier transforms into a bestseller via the creation of cybernetics, and rarely missed a chance to make everything about himself, gave a rare acknowledgement of Ingham as an inspiration. I don’t know why Ingham’s papers ended up in Trinity rather than King’s but I suspect it reflects Ingham’s opinion of where the prestige lay in Cambridge mathematics.

Ena Skewes, second left, at the International Congress of Mathematicians in 1932. Mary Cartwright, later one of the first chaos theorists, is at the far righr. From Wikipedia