If it seems a long time since I last posted on books, that's because this biography is thoroughly researched and rather stolid. The chapters are 50+ pages long, which makes it rather awkward to put down, but it's also often rather heavy to keep going in places, particularly in the early chapters on Turing's ancestry and childhood.
Ironically, the sections on the Enigma machine itself are surprisingly accessible. Though the Enigma system itself had some flaws (such as the impossibility of generating the same letter for the ciphertext as the plaintext), most of the cracks that allowed the work at Bletchley Park to be so successful stemmed from the way the German authorities used the Enigma, careless and arrogant in its perceived impregnability. Hodges also points out that some parts of the German system, where more care was taken in the use of the Enigma, were never broken.
Though Turing's war work takes up an appropriately large section of the book, this section is also the part of the book that is least about Turing, and more about a team of people. Beforehand, the book relates Turing's unpromising childhood and schooling, surprise scholarship to Cambridge, and the seminal paper Computable Numbers, which disproved one of Hilbert's conjectures regarding the solvability of problems.
The later chapters focus on Turing's interest in the development of mechanised computing, later to become electronic computing, and its relation, if any, to thinking and intelligence; and also on mathematical patterns in biological structures. The story of the ACE project at the National Physical Laboratory presents a prescient picture of the British Government's approach to IT projects. Amusingly, in a talk at the London Mathematical Society in 1947, Turing predicted: "The masters [i.e. intellectuals] are liable to get replaced because as soon as any technique becomes at all stereotyped it becomes possible to devise a system of intruction tables which will enable the electronic computer to do it for itself. It may happen however that the masters will refuse to do this. They may be unwilling to let their jobs be stolen from them in this way. In that case they would surroung the whole of their work with mystery and make excuses, couched in well chosen gibberish, whnever any dangerous suggestions were made. I think that a reaction of this kind is a very real danger." It seems to me that the only part of this paragraph that could be challenged today is whether the gibberish is well-chosen.
Turing's sexuality weaves a discreet and intermittent thread through most of the book, but gains prominence in the final chapters. In 1952 he was arrested, charged and convicted of gross indecency, following a sordidly stereotypical experience leading to a burglary in his house and a whiff of blackmail. Turing escaped a prison sentence at the expense of a year of hormone treatment. From this time until his death in 1954 he made a number of overseas trips, where the British authorities could not prevent or prosecute any further sexual activity, though Hodges suggests that American intelligence services would have had kittens if they knew about it in the Cold War climate and the era of Burgess and Maclean. There's ample scope for conspiracy theorists: the coroner ruled that Turing committed suicide by eating a poisoned apple, yet the apple was never tested for cyanide. Hodges suggests that Turing may have wanted to provide an option for his mother to believe the death was accidental, as she was always fretting about his chemical experiments. The possibility that his mind was disturbed as a result of the hormone treatment, which had ceased a year previously, seems unlikely. It appears that Turing was always one for dealing with events in a matter-of-fact way, and if he decided his time was over, that would be that.
[Postscript] Perhaps it was no coincidence that Hodges decided to call the final chapter in the book On The Beach. It does carry a certain echo reminiscent of Aschenbach in Death in Venice. Said's On Late Style didn't discurse into whether scientists have a late style, but I think that an argument could certainly be made in Turing's case, with his quasi-polymath exploration of applied yet somehow very pure mathematics. See also, perhaps, Schrödinger's What Is Life?