Sunday, November 23, 2008

Godel, Escher, Bach book review

Godel, Escher, Bach: An Eternal Golden Braid

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.

3 comments:

The Really Sarcastic Weasel said...

"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."

I'm reading the post carefully, because I might be interested in the book, but I have no idea what the above sentence means. How tired were you when you wrote it?

One way to interpret the sentence has the book making some interesting commentary about a fundamental limitation of mathematics. The other way of interpreting that sentence has the book making a far less interesting conflation of limitations inherent in that particular style of notation for functions, with a fundamental limitation of mathematics.

(Brought to you by the letters "bessesse")

Reverend0 said...

Not so tired as much as hard to communicate some of principles without writing a chapter.

What I was trying to convey is that math doesn't really have the limitation as much as the language used to set our proofs and communicate the concepts of math are limited. Really that is the basic idea of that sentence (describe a set of sets).

I did find it interesting. I would be willing to send it to you if you email me your address.

The Really Sarcastic Weasel said...

I'd send my address, but I wouldn't have time to read it. I haven't read much of anything that's not a text book or technical paper in way too long (poor me).

btw, I have the newest version of Numerical Recipes in my Amazon Wish List, now your widget seems insistent that I buy a book or two on Python. I'm creeped out by the fact that I do indeed want to learn Python.