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Comment by afthonos | Hacker News Reader

I read it cover to cover out of a sense of obligation but came away very disappointed. The Achilles-Turtle-Random Other Creature allegories got very tiresome, and the content took a very long time to get to the point. For anyone interested in the proof, I recommend Gödel’s Proof by Nagel instead. It covers the same material in about a tenth the space.

(GEB has other philosophical discourses that are interesting, if only as an example of how people can very reasonably mispredict the future. In Hofstader’s case, he posited that chess would only be played at a human level by an AGI.)

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Absolutely agree. GEB constantly tries to prove the cleverness of the author, complete with winks and nudges. It stacks so many unintuitive analogies on top of each other that I spent most of the time trying to recall which real-world concepts they all mapped to.

Also, the book is about 98% Gödel and 2% Escher and Bach. Any time it steps outside its wheelhouse of math and into the realm of philosophy or art, you get the distinct sense that it has no idea what it's talking about.

Do yourself a favor and just take discrete math 1 and read a few Wikipedia articles instead.

Do yourself a favor and just take discrete math 1 and read a few Wikipedia articles instead.

+100, exactly. I have some familiarity with mathematical logic, and with Bach (though admittedly I'm less familiar with Escher) and I found GEB to be unintuitive at best, and misleading at worst.

To be honest, there may not be anything really magic about Goedel's incompleteness theorem once you grasp the core concept, which is: If you encode all proofs into a formal language, you can make a statement that is true but unprovable. (Which is, effectively: "This statement has no proof"). Most of Goedel's work on the incompleteness theorem was on the systematization of proofs, which can be tedious to work through.

I found at the time Godel's completeness theorem to be more interesting. Though I never got into model theory or more advanced mathematical logic so, grain of salt.

I agree that it's way over-long and rambling, but it was my introduction to the topic. Where it really shines is his interesting and controversial thesis that connects Godel's proof with the Church-Turing thesis and other things to form a theory of consciousness as pattern and make the claim that a sufficiently powerful AI is as sentient and meaningful a consciousness as we are.

I read Godel's Proof after though, and I agree that it is a far clearer introduction to Godel's theorems.

Chaitin [2007] presented the following analysis:

Godel's proof of inferential undecidability [incompleteness] was too superficial. It didn't get at the real heart of what was going on. It was more tantalizing than anything else. It was not a good reason for something so devastating and fundamental. It was too clever by half. It was too superficial. [It was based on the clever construction] I'm unprovable. So what? This doesn't give any insight how serious the problem is.

If you still have the energy or interest, try I Am A Strange Loop, he wrote in a number of years after and it seemed more approachable

thank you...I just bought it via amazon

The New Turing Omnibus has a good chapter on the Incompleteness Theorem; it covers the basics in 5 or 6 pages, if memory serves.

I found 'Gödel’s Proof' fascinating—surprisingly more so than GEB, which I'd anticipated loving for years before dipping into it (I didn't finish, but the primary reason was loss of interest). It was one of the first things I came across that gave me the sense of something like 'mathematical system architecture'.

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