Alan Turing edited by Christof Teuscher, Springer Verlag, 拢46/$69.95, ISBN 3540200207 Reviewed by Mike Holderness
ON 7 June 1954 Alan Mathison Turing took a bite from an apple laced with potassium cyanide. You should mark the 50th anniversary of his death, and a fitting way would be to finish this Festschrift that came out of a 2002 celebration of the 90th anniversary of his birth. You may have to start soon, however, because, like Turing, the book is difficult.
In 1936 Turing published arguably the deepest result in mathematics or logic to date. Loosely, it is that there is no such thing as a mathematical checker of mathematical theorems. In order to achieve this feat of meta-mathematics he needed to define 鈥渃alculate鈥�, and his answer was the theoretical underpinning for computers and of computability.
Advertisement
What is not so well known 鈥� and is discussed in detail here 鈥� is that he also founded the study of neural networks. Moreover, he laid the foundations for our understanding of how genes can control growth and structure.
Other contributions range from memoirs filling in details of his time breaking military codes at Bletchley Park in the 1940s to speculations about 鈥渉ypercomputing鈥� 鈥� calculating that which he proved to be incalculable. Alarmingly, some of the latter seem to depend on mediaeval-style appeals to authority: specifically that in his 1939 PhD Turing discussed an 鈥渙racle machine鈥�. Re-reading that, this is clearly mathematical sarcasm. The more entertaining contributions involve programs that require infinite memory and dropping computers into carefully chosen black holes.
What, asks biographer Andrew Hodges, would Turing have done had he lived longer? He would have continued investigating the intersection of mathematics and biology 鈥� and quite likely extended this into evolution, inventing chaos and fractals in a moment of boredom on the way. Then imagine him in 1967, when his sexuality was finally decriminalised in the UK鈥�