Book Review: Alan Turing: The Enigma, by Andrew Hodges

Alan Turing: The Enigma by Andrew Hodges is the definitive biography of this brilliant, fascinating and complex man.

It isn't possible to fully recap a 500 page book in a diary, and I highly recommend this book to anyone interested in the history of logic and mathematics or cryptanalysis or computers, because Turing made fundamental contributions to all three. The book also deals with Turing's homosexuality, and the role it played in his life and death.

In logic/mathematics the most fundamental contribution Turing made was his paper On Computable Numbers. This gave a solution to the Entscheidungsproblem that David Hilbert had posed in 1928, and extended the results of Kurt Godel's Incompleteness Theorems. Per Mathworld, the problem is

Does there exist an algorithm for deciding whether or not a specific mathematical assertion does or does not have a proof?

For elementary number theory, Turing showed that the answer is "no". So, not only are some true theorems of a formal system unprovable (Godel) but there is no algorithmic way to know whether any specific theorem is among the provable ones.

In cryptanalysis, Turing was probably the person most responsible for breaking the German Enigma codes in WW II.

And both of these tied in to Turing's long fascination with computing and computers. He developed the idea of what became known as a Turing machine, which consists of an infinite string of tape, and a device for making (and erasing) marks on squares of that tape, according to certain rules. He proved that this machine was equivalent to any computer. The work on codes could not have been completed without computers.

Indeed, while the computer was not invented by any one person, and while ideas similar to the computer had been thought up by people before Turing, if one had to answer the question "Who invented the computer?" with a single name, Turing's would be high on the list. Turing also came up with what became known as the Turing Test, which exists in various versions, but essentially involves a test of whether a computer is "thinking" by having an interrogator ask questions of the computer and trying to determine if it is a computer or a person answering the questions.

In addition to being a genius, Turing was gay. For most of his life, this caused him relatively little problem (with relative being, well.... relative). He attended King's College, Cambridge, which was probably the place in England that was most tolerant of homosexuals. Turing also seems to have had few romantic relationships. But homosexuality was illegal in England at the time, and, in the period after WW II, England (partly by American demand) got increasingly concerned with homosexuality, especially when it involved people who had access (as Turing did) to secret information. Turing had sex with another man, thus breaking that law; he pleaded guilty. He was given the choice of jail or "treatment" with hormones to "cure" his homosexuality. He chose the latter.

A year after treatment ended, Turing killed himself by eating an apple he had dipped in cyanide.