Intuition and ingenuity: Alan Turing’s work and impact

Don't blame Alan Turing
Don’t blame Alan Turing

Legend has it that Apple’s rainbow-coloured logo showing the apple with a bite out of it is in homage to Alan Turing “the father of modern computing”. Turing died of cyanide poisoning on 7 June 1954, two years after being convicted of homosexuality and accepting chemical castration instead of prison. A half-eaten apple was found next to him, and one theory is that he’d laced it with cyanide, his own homage to the wicked queen in Snow White, his favourite Disney cartoon. Another theory is that he died accidentally after inhaling cyanide fumes from apparatus he had in his bedroom for electroplating spoons. A third explanation is that he really did commit suicide, but set up the apparatus so his mother would think it was an accident. The coroner didn’t test the apple for cyanide, so we’ll never know for sure.

If there are doubts about Turing’s death, his life is fairly well-known, or at least some aspects of it. His most noteworthy exploit for the general public was helping to break the code of the Enigma machines the Germans used to communicate with their submarines during the Second World War. If you’d like to get some idea of how he did it, take a look at the excerpts from the “Enigma Paper” in Alan Turing, His Work and Impact, just published by Elsevier. Cryptography is the second of four parts of this thousand-page overview presenting Turing’s most significant works from the four-volume Collected Works along with comment, analysis and anecdote from leading scholars. The other three parts are on Turing’s contributions to computability, artificial intelligence, and biology.

That simple naming of the parts already gives you some idea of the breadth of Turing’s influence, and we could also add economics. I actually got the Elsevier book thanks to Professor K. Vela Velupillai who wrote for us about Turing’s economics here.  That article described the foundations of computable economics, while here at the OECD the project on new approaches to economic challenges was being launched. “New Approaches” revisits some of the fundamental assumptions about the functioning of the economy, and the implications for policy. It also addresses how to extend the capabilities of existing tools for structural analysis and analysing trends over the long term to factor in key linkages and feedback – for example between growth, inequality, and the environment.

Vela cites Turing’s Precept, an idea that should be kept in mind by economic theorists, analysts and policy makers everywhere: “the inadequacy of reason unsupported by common sense”. There’s a corollary to that in how you present the reasoning, best summed up by the German mathematician David Hilbert at the 1900 conference of the International Congress of Mathematicians in Paris. Presenting a paper on 23 unsolved problems that would help set the research agenda for mathematics in the new century, Hilbert quoted an old French mathematician as saying: “A mathematical theory is not to be considered complete until you have made it so clear that you can explain it to the first man whom you meet on the street”. And Turing himself claimed that “No mathematical method can be useful for any problem if it involves much calculation.”

Gregory Chaitin recalls Hilbert’s remark when he presents Turing’s “Solvable and unsolvable problems”, that ends with Turing’s Precept. In this “lovely paper” Turing explains the notion of computability and proves the unsolvability of a decision problem without using any mathematical formalism. His “models” are two puzzles that were popular at the time: a picture made up of a number of movable squares set in a frame, with one square missing so you can move the squares around to form the image; and two pieces of intertwined wire you can separate without bending or breaking them.

That said, much of what’s presented is for specialists and you’d need a good grounding in mathematics to follow it. But there’s still plenty even for a non-mathematician like me, some of it surprisingly moving, for example when Bernard Richards describes how he presented his and Turing’s work on morphogenesis to Turing’s mother shortly after his death. Some of it is intriguing – why does the UK government still refuse to declassify the two 1946 papers “Report on the applications of probability to cryptography” and “Paper on statistics of repetitions”? But no matter how well you know the life and work of Turing, you’ll learn something from this book.

By the way, that Apple story at the beginning is only a legend. Rob Janoff who designed the logo explained that he was asked to come up with something simpler than the (hideous) picture of Newton sitting under an apple tree that was the company’s first logo, and the bite was just to show that it was an apple, not a cherry or a tomato. The gay-friendly rainbow was to advertise the colour graphics capabilities of Apple’s computers. On British TV show QI XL, Stephen Fry recalled asking  his friend Steve Jobs about the Turing story “It isn’t true, but God we wish it were!” was Jobs reply.

Useful links

Models used in the OECD Economics Department

Patrick Love

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