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I’m fairly certain that this isn’t covered at all in that book.

You are correct, it is not, and the book is not relevant in any way to the article, aside from both containing references to the work of Gödel.

Presumably it would take you five years to figure that out though, by which point you may have discovered new interests.

Not directly, but it is closely related. It still is likely to interest most who were interested by this article

Seconded. There's a whole MIT course on it: https://www.youtube.com/watch?v=lWZ2Bz0tS-s

I liked that book but remembered it being more about incompleteness theorem and cognition than time / space physics.