[jerf]

It's a combination of two things: An extended musing on the nature of Godel's Incompleteness theorem, including its practical and philosophical consequences, and a series of things as jacoblyles explains in his comment.

It's an arty/fun book, I don't think it's bad, but the "mystery" you perceive at the heart of it is simply Godel's theorem, which, to be fair, like many other aspects of computer science does indeed have more application than the immediate, raw application of the proof. I suggest spending some time with one of the more formal explanations of Godel's theorem, one that is really careful to explain how the self-referential statement is really constructed.

[presidentender]

I get Goedel's theorem, I'd like to think. I get strange loops, and how Hofstadter would have a field day with our criticism of xkcd and of xkcd's critics. I just know there's still more.

[jerf]

Is there more? Well, yes. I did just try to summarize the book in about 20 words.

Are you about 90% of the way through? Yes. The book is written in a style to make it have the trappings of more depth than it actually has. I actually enjoy it that way and do not mean it as a criticism. (I also enjoyed the Illuminatus! trilogy, which is self-consciously written with somewhat similar motives.) Don't undersell yourself.

[presidentender]

It's a Dunning-Kruger trap, carefully laid in pretty prose to catch people like me. I'll never be confident that I've "finished" it. As a consequence, I'll always think Hofstadter is smarter than I am. There's evidence beyond the scope of GEB to support that, of course.

[jerf]

What a beautiful way of putting it!

I happened upon the book in my life precisely when it would hold the least mystery, the second year of my graduate studies in computer science. It was fun but by that point in the category of "intellectual fluff" rather than "ow my brain". While I'm sure I have not discovered every last quirky little connection in it, every last pun or every last hidden pattern, I'm also pretty sure I didn't miss any of the main points.

But he's still smarter than me. I can read that book, I could never have written that book.

[scrame]

True, but to say the book is just Godels theorem is underselling it. At its most clinical it is a survey of various sciences, at its essence it is an intuitive theory. The importance of Godels theorem is that an intuitive notion can be proven true in a mathematical framework, as opposed to the piles of bullshit pseudoscience new-age stuff saying Heisenburgs uncertainty principle makes everything subjective.