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What I'm trying to say is: this was interesting but holy moly I just don't want to think about it.
Gödel, Escher, Bach impacted my thinking in ways that no other book has. I won't try and produce the comprehensive summary that others have so bravely provided, but there are a few things I must say about this remarkable book.
The concepts presented in Gödel, Escher, Bach have such universal application-- I find myself referring back to it frequently as I make more and more connections between self-reference, isomorphisms, chaos, etc. and their real-world applications. Even if that were not the case, the ideas themselves really do enrich my thinking. I am a composer, and GEB provided an essential link between compelling, logical form, and whimsical, self-referential substance (this is the technique that Bach liked to use).
The book makes for difficult, rigorous reading-- I put it down on my first try only to pick it up again two years later-- but be brave, knowing that the benefits are well worth the effort.
(To get a taste of the ideas behind GEB, take a look at Nomic and 1000 Blank White Cards-- two of my favorite games!)
As such, had it been edited down to a smaller volume, perhaps one that's trimmed by 30 - 50%, I think it would have been a stronger work overall. I believe this is what Hofstadter did in his later refinement of these ideas in I am a Strange Loop, and I am eager to check out that book to see if, perhaps, it leaves me with fewer annoyances than this one did.
if num == 0:
return
hanoi(start, aux, finish, num - 1)
print("Moved from {0} to {1}".format(start, finish))
hanoi(aux, finish, start, num - 1)