##Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter

Rating: ★★★★★

I pretty much had to be impressed by this one. Not only does Hofstadter painstakingly build up your understanding in order to communicate the operation of Gödel's incompleteness theorem, with its intuition and implications, but he does so while drawing together a range of isomorphisms from across music, art, biology, particle physics, computer science, the human mind, and his own book itself. Not only is it edifying, not only is it wide-ranging, but it is playful, too, with the self-referential Dialogues illustrating their own topics in their structures. I could complain about Hofstadter sounding somewhat too impressed with his own cleverness at times, but, well, it is fabulously clever.

The edition I read was the 20th anniversary edition, released in time for the millennium. There is something dreadfully appropriate about that, because at times GEB feels like it is a book of the 21st century, rather than the 20th. This is a book which is at core about self-reference, and the implications of contradiction for artificial intelligence. In many ways its cross-references, its dialogue and its central fascinations all seem so... Internet. But at other times, the fact that the book is nearly 40 years old does leap out at you. In Hofstadter's time, Fermat's Last Theorem was still unsolved and Kasparov had yet to be beaten by Deep Blue. Hofstadter's speculations about the future of AI are extremely amusing to read now, with the benefit of hindsight.

Hofstadter's central speculative points about the relationship of self-reference to consciousness are well-taken, and I think survive disentanglement from the now outdated form of symbolic AI which Hofstadter seems to have been aligned with at the time. And of course, there are other attempts to explain Gödel to popular audiences, and no doubt ones which do not take such an all-encompassing approach to the subject, but for sheer ambition and evident reflection, GEB has to be considered a significant, even canonical work.