Godel, Escher, Bach: An Eternal Golden Braid" by Douglas Hofstadter
I first read started reading this book shortly after its publication in the early 1980s. I gave up. I started it again in the 2000s. I gave up. In 2016 I started and finished it.
In 20 chapters Hofstadter attempts to teach the elements of Typographical Theory and therefore to (a) explain Godel's Incompleteness Theorem (b) lay down some rules for developing Artificial Intelligence. Along the way he tries to explore the concept of Strange Loops, recursive propositions that are self referential and paradoxical, such as "This statement is false". In order to help the general reader get anywhere near these difficult ideas he uses the art of Escher, which is full of self-reference and paradox, and the structure of a musical fugue such as those developed by Bach. He also intersperses every heavyweight chapter with a diversion, such as a dialogue between Achilles and a Tortoise (also involving a Crab, an Anteater and the Author) or the Jabberwocky in three languages.
Well I really enjoyed the diversions, which gave me some basic understanding of Hofstadter's arguments, and I enjoyed a lot of the more heavyweight stuff, although I skipped quite a lot too and there were bits that I frankly didn't understand.
A lot of the music stuff was really interesting and I learned about fugues, hemiolas, canons, organ points, strettos and fermatas.
He made a lot of interesting points such as that "Intelligence loves patterns and baulks at randomness. For most people, the randomness in Cage's music requires much explanation ... whereas with much of Bach, words are superfluous.In that sense Bach's music is more self-contained than Cage's music." (p 175)
A brilliant attempt to make a really hard subject accessible which nearly worked for me and no doubt has enlightened many cleverer than myself.
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