Douglas R. Hofstadter

1979

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This is a book that's either loved or hated. It has a cult following amongst mathematicians and computer scientists: Hofstadter himself is a respected computer scientist with an interest in biological modelling.

The "plot", such as there is, revolves around explaining Godel's incompleteness theorem: the idea that any formal mathematical system has inherent limitations and inconsistencies. Godel incompleteness is to mathematics what Turing computability is to computing: a bound on ambition, a constraint that prevents some problems from being explored. The former perhaps has less significance to everyday life than the latter, but still remains one of the cornerstone discoveries of 20th century science.

Hofstadter also zones in on the familiar discussions about art and mathematics, the appeal that recursive, self-reflecting art works (like those of Escher and Bach) have to the mathematically inclined. The weaving of these themes within the book is quite astonishing, and at times illuminating. However, it does mean that this is not a book one can dip into: it requires concerted and prolonged effort, which it only partially repays.

The scope is both impressive wide and restrictively narrow, with the reader emerging with an understanding of a problem whose everyday relevance can be questioned, but also with an exposure to a wide range of aesthetic and scientific problems that he might otherwise never consider.

3/5. Finished 11 November 2012.

(Originally published on Goodreads.)