The Man Who Knew Too Much: Alan Turing and the Invention of the Computer
  April 11, 2011

You probably say "Turing Test" without thinking overmuch about the source of the expression - or its inventor.

We live in a world greatly informed by the insights and perspectives of Alan Turing. The world where he lived, though, was unsympathetic to much of his person, and ultimately hostile to the point of death.

That's a summary of litterateur David Leavitt's biography The Man Who Knew Too Much (MWKTM). He's right, and he makes a strong argument, but it's certainly different from the one I would have made.

Turing machine, Turing test, Turing puzzles

That's the potential value of the latest in Norton's 300-page slender Great Discoveries (my favorite: the Obsessive Genius of Marie Curie) series, of course: It presents an important intellectual pioneer in a light few readers would see without its help. Most of us know to mumble about "Turing machines" as a sort of landmark in computing theory to which we can anchor our squabbles about on-line syntax, and a fraction recognize that he contributed multiple critical ideas to mathematics and computing. Was every step of his professional path as determined by his homosexuality as Leavitt believes? My training in mathematics rejects the notion, but Leavitt presents Turing's theory with enough precision and appreciation to earn credibility for his psychoanalysis.

Consider Turing's intellect first: He solved one of the great questions of 20th century mathematics, Hilbert's Entscheidungsproblem". To the extent that any solution or invention can ever be considered in isolation, and understanding that lambda-calculus inventor Alonzo Church independently solved the decision problem almost simultaneously, Turing's "On Computable Numbers ..." was a remarkable, almost singular, achievement. He was a leader in the crucial war-time cryptography work of the British military (although Leavitt misses an opportunity to honor Turing's range, in underemphasizing the statistical ingenuity of his anti-Enigma achievements). He contributed significantly to the ferment of ideas that resulted in the first working digital computers in the United Kingdom, he left us with a "Turing test" well-enough grounded in theory to become a cultural icon, and he worked competently if replaceably in biomorphogenesis, group theory, analysis, speech encryption, number theory, and other domains.

He was always a bit of an outsider, though, and died under mysterious and certainly troubled circumstances. Leavitt teaches that many of Turing's computing expressions resulted from his homosexuality. The famous "Turing test", for example, is the sort of scenario best crystallized by a man who had spent his whole life trying to act like a ("normal") man.

Leavitt's a novelist, and his narrative certainly is readable and even compelling. He's a conscientious academic, and supplies a satisfying wealth of useful references so that an interested reader can research specific points for himself. His mathematical descriptions are almost entirely accurate, to the point that he supplies, if anything, too much detail about the encoding of Turing machines. Ultimately, though, any reader of MWKTM will want to know if it's true, that is, if Turing's sexuality set the terms of his mathematics in the way Leavitt believes.

Scholar as human

I certainly don't know. Paul Halmos, one of the greatest mathematical expositors ever, wrote his academic autobiography without ever naming either of his two wives. Conventional mathematical culture inculcates that this reticence isn't pathologic or deceptive, but an essential aspect of good style: a discovery or proof or analysis is clearer the less it is bound to individual psychology.

Even when we accept this archimedean heritage, it's legitimate to wonder how personality shapes productivity. Leavitt only intrigues, and doesn't convince. He leaves me thinking Turing's creativity is as undecidable as the circumstances of his death or the diagonalized non-computables of his '36 paper. Turing was well-educated at Cambridge, an enthusiastic athlete, indifferent to material status, fond of early Disney movies and author G. K. Chesterton (one of whose books was titled, The Man Who Knew Too Much), surprised by manners in the USA, cordial with those around him, and independent. An aggressive diagnostician might look for Asperger's Syndrome in his nonconformities. And he was homosexual. As best I can tell, it was all of Turing that went into his scientific achievements, and we can only understand him personally as a whole, too. While I close MWKTM thinking Leavitt overdid one dimension, I thank the author for weaving together the threads he assembled for this biography.

Finally, is there any application of MWKTM to the mundane daily practice of readers? Only tenuous ones, I think: it's entertaining to speculate how much different the evolution of computing might have been had associative memory and language syntax been emphasized at the start over the von Neumann architecture. Lisp arrived only a couple of years after Turing died, by which time he'd largely abandoned electronics anyway. Perhaps his contribution to computing was already over. For me, Turing's biography just reinforces the importance of listening carefully to all the contributors to a project: people with quite different mental habits or styles, like Turing and the other computing pioneers, sometimes produce work that alloys wonderfully.

This article, originally written for unixreview, is reprinted by permission of the author. The original can be found on Cameron Laird's site.