A scientific paper written by Alan Turing, the brilliant computer scientist who cracked the Enigma code during the Second World War and bolstered Britain’s war efforts, was recently declassified by the British government and uploaded to the arXiv pre-print server. The paper’s entitled ‘The Applications of Probability to Cryptography’. It has Turing bringing to bear a style of reasoning that is absent in today’s statistics-heavy technical literature. It is both didactic and meticulous, and provides great insight into how Turing explored the cryptographic problems he was confronted with.
When the whole evidence about some event is taken into account it may be extremely difficult to estimate the probability of the event, even very approximately, and it may be better to form an estimate based on a part of the evidence, so that the probability may be more easily calculated. This happens in cryptography in a very obvious way. The whole evidence when we are trying to solve a cipher is the complete traffic, and the events in question are the different possible keys, and functions of the keys. Unless the traffic is very small indeed the theoretical answer to the problem “What are the probabilities of the various keys? ” will be of the form “ The key . . . has a probability differing almost imperceptibly from 1 (certainty) and the other keys are virtually impossible”. But a direct attempt to determine these probabilities would obviously not be a practical method.
Here and there, he also admits he’s making guesses – some quite in the air and others not so much – of the sort that are inadmissible in the modern era of scientific publishing, where demands on researchers to be exact have driven many to fabricate results and fake conclusions. At one point, Turing writes, “This judgement is not entirely a guess; some rather insecure mathematical reasoning has gone into it”, prompting the popular statistician Andrew Gelman to quip on his blog: “He’s so goddamn reasonable. He’s everything I aspire to.”
The paper was uploaded to arXiv on May 18 together with another called ‘The Statistics of Repetitions’, both accompanied by editor’s notes that focused on what it was like to prepare manuscripts “at a time when typographical errors were corrected by hand, and mathematical expression handwritten into spaces left in the text”. The papers can be found here and here.
Alan Turing’s claims to fame are many, ranging from deciphering the Enigma code used by the Nazis for encrypted communication, to defining the hypothetical Turing machine that’s influential in studies of computing, to predicting oscillating chemical reactions that were observed about a decade later. He was also gay at a time when homosexuality was a crime in the UK, and was chemically castrated when he refused to be sent to prison for fear he’d have to discontinue his work. He died of cyanide poisoning in 1954, barely 42 years old. In 2009, then British Prime Minister Gordon Brown issued an apology for the way Turing had been treated in his lifetime. Queen Elizabeth II pardoned him posthumously in 2013.
Most recently, he was brought to life in the blockbuster movie ‘The Imitation Game’ (2014), where he was played by Benedict Cumberbatch.