This is a book of brilliant insights separated by hundreds of pages of tangents.
It touches on a ridiculous number of topics: number theory, music theory, fugues, art, physics, linguistics, literature, cognition, calculus, logic, programming, recursion, molecular biology, Zen, and much more. Many of these are used as the basis for understanding cognition, knowledge and AI; some make for superb analogies to make it easier to understand these complicated topics; unfortunately, Hofstadter sometimes goes into way too much detail on these tangential topics, and occasionally, it just feels like he's showing off his (undeniably impressive) intellect.
It's a shame, because all of this extra material makes the book much harder to get through and actively distracts from some of the gems hidden within. If a good editor had chopped out ~300 pages, the book would've been perfect. As it is, it's only worth reading if you're willing to put in a ton of effort to get to some of the delightful parts.
My absolute favorite is the analogy that compares the human mind to a colony of ants; this is the absolute closest I've come to a vague understanding of how an intelligence could emerge from a bunch of simple, unintelligent parts. If you are skimming the book, make sure not to skip that chapter :)
Some great quotes:
“Hofstadter's Law: It always takes longer than you expect, even when you take into account Hofstadter's Law”
Tesler's Theorem: "AI is whatever hasn't been done yet".
“How gullible are you? Is your gullibility located in some "gullibility center" in your brain? Could a neurosurgeon reach in and perform some delicate operation to lower your gullibility, otherwise leaving you alone? If you believe this, you are pretty gullible, and should perhaps consider such an operation.”
“The paraphrase of Gödel's Theorem says that for any record player, there are records which it cannot play because they will cause its indirect self-destruction.”
"Relying on words to lead you to the truth is like relying on an incomplete formal system to lead you to the truth. A formal system will give you some truths, but as we shall soon see, a formal system, no matter how powerful—cannot lead to all truths."
"What is sacrificed is, of course, strict accuracy; what is gained is, I hope, a little insight."
"The naive assumption that all knowledge should be coded into passive pieces of data is actually contradicted by the most fundamental fact about computer design: that is, how to add, subtract, multiply, and so on is not coded into pieces of data stored in memory; it is, in fact, represented nowhere in memory, but rather in the wiring patterns of the hardware."
"When a human forgets, it most likely means that a high-level pointer has been lost - not that any information has been deleted or destroyed."
"It is amazing how deep this problem with the word 'the' is. It is probably safe to say that writing a program which can fully understand the top five words of English - 'the', 'of', 'and', 'a', and 'to' - would be equivalent to solving the entire problem of AI, and hence tantamount to knowing what intelligence and consciousness are."
"Perhaps the greatest contradiction in our lives, the hardest to handle, is the knowledge 'There was a time when I was not alive, and there will come a time when I am not alive.'"
"By the way, in passing, it is interesting to note that all results essentially dependent on the fusion of subject and object have been limitative results. In addition ot the limitative Theorems, there is Heisenberg's uncertainty principle, which says that measuring one quantity renders impossible the simultaneous measurement of a related quantity. I don't know why all those results are limitative."