TURING (ALAN)


Autograph letter signed ("A.M. Turing"), to Lionel March, discussing linear and group algebras ("...A 'linear algebra' is a technical term for a space of vectors... To be a linear algebra as well as the addition of vectors and multiplication by scalars there must be multiplication of the algebra-elements together, and the distributive and associative laws must hold... What this all boils down to is that there are certain real coefficients... The distributive laws are then automatically satisfied, but for associativity it is necessary that [demonstrations follows]... In quite a lot of these systems each l/i l/j is another 'base element' e.g. l/k. In that case the base elements themselves form what is called a 'finite group', e.g. the six l/1 l/2 l/3 l/4 l/5 l/6 with multiplication table below would form a 'finite group'...When the base elements have this sort of multiplication table the algebra is called a 'group algebra'. Yours was a little different. Your base elements when multiplied together do not give another base element but +/- another base element. I was suggesting you should take the case where you allow any real factor, not just +/- 1. for instance the table [illustrated]... The problem I was suggesting you might try was to find all such 'group algebras with factors with six base elements..."); included in the lot is March's school mathematical notebook and his typed 'Rebmun' thesis (see below) 3 pages, slight dust-staining and weak at folds, 4to, "The Computing Laboratory/ Manchester" (2)
|'DISTRIBUTIVE AND ASSOCIATIVE LAWS MUST HOLD' – ALAN TURING WRITES FROM 'THE COMPUTING LABORATORY, MANCHESTER', TO A YOUNG MATHEMATICAL PRODIGY. Lionel March, the recipient, was at the time at school and working on complex numbers and, as secretary of the science club, had delivered a paper on 'n' dimensional numbers. This was sent to the Daily Express science correspondent, Chapman Pincher, who ran the following story: 'Lionel March, an 18-year-old schoolboy, has astonished university dons by thinking out an entirely new kind of mathematics... While doodling one evening three months ago he suddenly realised he had stumbled on what seemed to be a new kind of algebra. It was so new he had to invent a name for it. So he called it "Rebmun," which is "number" spelled backwards... Certain that his mathematical reasoning was sound, Lionel typed a complicated 16-page thesis. First it went to Dr Frank Roberts, mathematician and electronics expert at University College, London. He pronounced it to be an outstanding contribution to mathematical theory, which should be sent immediately to a higher authority. The thesis then reached Dr Alan Turing, chief mathematician of the "electronic brain" laboratory at Manchester University. Dr Turing was equally impressed. He knew that some top-flight mathematicians were thinking along similar lines' (Express, 24 March 1953). March himself was to recall: 'Typically, in the course of a three-page letter, [Turing] posed a problem for me... this was before I knew who he was and before the world knew who he was. He was in Manchester, that's when they developed "our" computer, with many people from Cambridge, and there had been a time when I'd been told I should go to Manchester because of the stellar group. But I didn't know about it, and at the same time there was a great enthusiasm to get people into Oxbridge, and Magdalene was experimenting with taking a working class student... I didn't even understand the problem he posed! It hit the headlines, me doing this piece of mathematics, but though it was glorious it was completely useless, except for the idea of extending mathematics into three or four dimensions' (interview in Cambridge Business, Issue 26, Nov/Dec 2013). In March's opinion, it was Turing who used his influence to help secure him a place at Magdalene College, Cambridge, from which he was to graduate with a first.He was afterwards to enjoy a distinguished career in architecture and the arts, being especially remembered for his work with Sir Leslie Martin: 'In 1967 Martin established the department's Centre for Land Use and Built Form Studies (renamed the Martin Centre in 1973) and initiated a programme of research on fundamental architectural issues. Most notably, in his work with Lionel March, he developed a strong theoretical basis for urban design—applying geometrical principles to the issue of ground coverage and building form. Martin and March summarized this work in their comparison between the pavilion form and its anti-form, the court, and demonstrated how it was possible to achieve high housing densities while at the same time providing useful space at ground level and avoiding the use of high buildings. This work flew in the face of conventional wisdom at a time when the Ministry of Housing was, through its tall building subsidy, positively encouraging the construction of local authority housing towers' (Peter Carolin, 'Sir Leslie Martin', ODNB).March's career took in many other fields and aspirations, including a pioneering exhibition of serial art at the ICA in 1962. In the words of one obituary: 'Lionel March was a scholar and artist. He inspired generations of students and colleagues to combine the formal and the creative in planning and design. His contributions to theory and practice ranged from mathematics to painting, from computation to stage set design, from architectural history to architectural practice at its most daring; a modern Alberti. His career at Cambridge in the Department of Architecture, in Canada at the Department of Systems Design Waterloo University, in Milton Keynes at the Open University, in London at the Royal College of Art and in Los Angeles at UCLA, was remarkable for his individual achievements, the research groups he established but most of all for his outstanding generosity in sharing ideas. Talking with Lionel made people think differently. His students and colleagues loved him for this generosity while university administrators were often exasperated by his mercurial mischievousness. His eye for the winner, in supporting new talent and new ideas in Design, was unrivalled' (Chris Earl, for the Open University, 27 March 2018).