I knew the book would be interesting when the prologue of the book starts out where the author is looking back 20 years ago when he wrote the book and tries to describe the book. He rambles for a few dozen pages and still doesn't seem to describe it. I think what makes this book hard to describe is that it uses multiple different angles to try and find the point of intelligence or identity. It relies heavily on math but adds in doses of music, art, psychology, and quirky dialogues, in order to describe the idea that self-reference, which breaks many formal systems.
I always lie.
So, is that statement true or false? It is a valid statement in terms of structure, but its inherent meaning in not valid. It can then be put in terms of math where if you create a system where there are a series of functions. Each function is defined by a unique mathematical definition.
f1(x) = x
f2(x) = x * 2
f3(x) = log x
f4(x) = (x + 1) / (x ^2)
Then you create another function g(x) = fx(x). So g(1) = 1; g(2) = 4; etc. But in theory g(x) would exist in the set of function, but because there is no way to write this self-reference.
So how does self-reference apply to intelligence? It is the ability to step outside of a well-defined system and have the symbols necessary to describe the situation.
I do recommend this book to computer scientists and just folks looking for a quirky math book.