TURING (ALAN) Autograph letter signed ("Yours Alan") to Alfred William Beuttell ("Dear Mr Beuttell"), returning his notes on the Monte-Carlo system, Cambridge, 2 February [19]33

This lot has been removed from the website, please contact customer services for more information

Lot 115
TURING (ALAN)
Autograph letter signed ("Yours Alan") to Alfred William Beuttell, sending a four-page analysis of the Monte-Carlo betting system and offering a solution to a technical lighting problem, Cambridge, 2 February [19]33

Sold for £ 94,000 (US$ 114,122) inc. premium
TURING (ALAN)
Autograph letter signed ("Yours Alan") to Alfred William Beuttell ("Dear Mr Beuttell"), returning his notes on the Monte-Carlo system "...with a few notes on what I imagine is the explanation of its success...", going on to say "...I remember your telling me a few months ago that a method for calculating the illumination level on the working plane in a room was rather badly needed. Of course one could not expect to get a simple & accurate formula for anything so complicated...", followed by detailed explanations illustrated by an equation ("...It is illuminated by a uniform point source of candle power I placed at the centre... I am sure there is no need for me to say how one would apply it in practice... I just thought this one might be of use to you..."), sending "...Regards to everyone, and please don't feel there is any need to answer these ravings of mine..."; together with the above-mentioned four-page analysis of the Monte-Carlo system headed "Gambling System", concluding "...The general effect is when that for short runs one most probably wins or else once loses an unexpectedly large sum. As the length of the run is increased the chances of winning becomes more remote & is negligible for 100,000 spins...", 7 pages in all on King's College headed paper, light dust staining, creased at folds, rust stain from old paperclip, 8vo (178 x 134mm.), Cambridge, 2 February [19]33

Footnotes

  • 'PLEASE DON'T FEEL THERE IS ANY NEED TO ANSWER THESE RAVINGS OF MINE': ALAN TURING'S ANALYSIS OF THE MONTE-CARLO GAMBLING SYSTEM & WORK ON A NEW METHOD OF LIGHTING.

    Turing's analysis of the Monte-Carlo Gambling System is couched in the language of mathematics and equations but put simply, by working out the probability of winning at increasing increments of 150, 1,520, 4,560 and 30,400 spins he proved mathematically that the longer you play, the probability of losing money increases – "...for short runs one most probably wins or else one loses an unexpectedly large sum. As the length of run is increased the chances of winning becomes more remote...", he confirms.

    The recipient of our letter, Alfred William Beuttell (1880-1965) was the father of Turing's schoolfriend Victor Beuttell (see the following lot). After leaving Sherborne, the boys remained close and Turing spent much time with the Beuttell family. Alfred had made his fortune by inventing and patenting the Linolite electric strip reflector lamp (better known now as the striplight) in 1901, his first important contract being a system of continuous lighting for the Coronation of Edward VII, manufactured by the Edison and Swan Electric Company with whom he had a long association.

    Buoyed by his company's success pre-war he enjoyed the life of a wealthy bachelor – flying (he met Bleriot and watched the Wright brothers), motor racing and sailing. He spent several months at Monte Carlo operating with some success his own gambling system. Stories of having lived for a month on his winnings piqued the young Turing's interest whilst staying with the family over Christmas 1932 after the death of Victor's mother in November: '...He showed Alan his gambling system, which Alan took back to Cambridge and studied. On 2 February 1933 he wrote back with the result of his analysis, which was that the system yielded an expected gain of exactly zero, and that accordingly Mr Beuttell's winning had been entirely due to luck and not to skill...' (Hodges, A., Alan Turing: The Enigma, 2014, p.89). Our letter is hitherto unpublished, but his biographer Andrew Hodges mentions it with reference to a letter Turing wrote to his friend Norman Routledge in 1953 mentioning the odds of being arrested for homosexuality: '...Alan Turing used logarithms of betting odds as the key to the work he had done for the 'racket' of cryptography, and his sustained fascination with probability is illustrated by that reference [in Routledge's letter] to a one-in-ten chance of being caught. In his 1953 stoic humour there is a link with innocent Anti-War undergraduate days of twenty years earlier when he analysed Alfred Beuttell's Monte Carlo gambling system...' (Hodges, p.xxxi). Whilst his analysis here was a light-hearted exercise, Turing's work on probability had wider implications, and his research paper, The Applications of Probability to Cryptology, in which he applied vigorous probability analysis to a wide range of cryptoanalytic problems, was key to the decryption work undertaken at Bletchley Park.

    Turing also helped Beuttell in his pioneering work in the scientific measurement of illumination. In 1927 Beuttell had taken out patents on a new invention, the 'K-ray Lighting System', designed to allow uniform illumination of pictures of posters within a glass box and in Turing he found the perfect person to find the right formula for the curvature of the glass. Turing '...suddenly produced the formula, without being able to explain it, which agreed with Alfred Beuttell's calculation. But Alan went further, and pointed out the complication which arose through the thickness of the glass, which would cause a second reflection on the front surface. This made necessary a change in the curve of the K-ray System which was soon put into application for exterior hanging signs, the first contract being with J. Lyons and Co., Ltd, the catering chain... it always delighted Alan that a mathematical formula could actually work in the physical world. He had always liked practical demonstrations, even though he was not good at them...' (Hodges, p.73-4). By the early 1930's Beuttell's work as a specialist lighting consultant brought him large projects such as the illumination of the Freemason's new headquarters in London, which Turing also advised on. Our letter provides a formula for the illumination of the floor of a hemispheric room lit from its centre, a problem which they had previously discussed ("...I just thought this one might be of use to you..."). During the Second World War, the Linolite company became the main supplier of hose clips for the de-icing systems of bomber aircraft but reverted back their main activity in 1945. The company remained in Malmesbury until its closure in 1993.

    A photograph of Alfred Beuttell at the time this letter was written and a copy of his biography The Man Who Made Linolite is included in the lot.

    Provenance: Alfred Beuttell (1880-1965); Victor Beuttell (1915-1993); and thence by descent.
Contacts
TURING (ALAN) Autograph letter signed ("Yours Alan") to Alfred William Beuttell ("Dear Mr Beuttell"), returning his notes on the Monte-Carlo system, Cambridge, 2 February [19]33
Auction information

This auction is now finished. If you are interested in consigning in future auctions, please contact the specialist department. If you have queries about lots purchased in this auction, please contact customer services.

Buyers' Obligations

ALL BIDDERS MUST AGREE THAT THEY HAVE READ AND UNDERSTOOD BONHAMS' CONDITIONS OF SALE AND AGREE TO BE BOUND BY THEM, AND AGREE TO PAY THE BUYER'S PREMIUM AND ANY OTHER CHARGES MENTIONED IN THE NOTICE TO BIDDERS. THIS AFFECTS THE BIDDERS LEGAL RIGHTS.

If you have any complaints or questions about the Conditions of Sale, please contact your nearest customer services team.

Buyers' Premium and Charges

For all Sales categories, buyer's premium excluding Cars, Motorbikes, Wine, Whisky and Coin & Medal sales, will be as follows:

Buyer's Premium Rates
27.5% on the first £20,000 of the hammer price;
26% of the hammer price of amounts in excess of £20,000 up to and including £700,000;
20% of the hammer price of amounts in excess of £700,000 up to and including £4,500,000;
and 14.5% of the hammer price of any amounts in excess of £4,500,000.

VAT at the current rate of 20% will be added to the Buyer's Premium and charges excluding Artists Resale Right.

Payment Notices

For payment information please refer to the sale catalogue.

Shipping Notices

For information and estimates on domestic and international shipping as well as export licences please contact Bonhams Shipping Department.

App