Godel, Escher, Bach: An Eternal Golden Braid [Hardcover]

At the absolute very least it gives the most lucid account of Godel's Theorem that I have read. Contrary to what many popular authors would have you believe this is neither the most important nor the most profound theorem of logic but it is a deep and interesting one and to have such a result so accessible in a form that is not watered down is a remarkable achievement. Along the way it gives an introduction to logic and formal systems - important branches of modern mathematics. This material alone is enough to make the book a very worthwhile read.

Much of the kind of game playing that goes on in proving Godel's result stems from the same kind of playfulness behind some aspects of the music of Bach and the images of Escher. It would seem that similar ideas that at first seem only mathematical or only artistic can actually find their expression in many different ways. This is also an important insight that makes the book worthwhile.

(And by the way - anyone who criticises this book as being just another religious cult book had better make note of this - to damn the book is to damn (or fail to understand) a large chunk of modern thought including much of mathematics.)

Elsewhere there is a mass of thought provoking material on Zen, ants, psychology, translation, meaning, representation and computers all of which has prompted many readers to think about these topics in a far broader way. In fact giving this book to someone is a good way to smuggle ideas about non-technical subjects into the thought of someone who would normally only read more technically oriented books - and vice versa!

On the other hand I find much of the book's discussion of artificial inteligence a little dated. The book was written in what was probably the heyday of classical artificial intelligence research. Today we see that this research programme produced far less fruit than many expected and much of Hofstadter's discussion doesn't always hold up. I don't think that any kind of magic threshold is going to be crossed on the day we design an artifical system able to reason about itself - by time we reach that point far more amazing thresholds will already have been crossed and self-representation will just be the icing on the cake. So I don't feel that much of the discussion on self-representation is as important or as profound as Hofstadter may originally have thought. Nonetheless there are lessons to be learnt even in this part of the book.

Unfortunately I now have to use that oft repeated cliche: 'Unfortunately I now have to use that oft repeated cliche: "This book changed my life!"'. It opened up my mind to the many varied uses for formal systems and self-reference. This isn't just abstraction - it is something I have to deal with in my ordinary everyday work solving problems and designing systems with computers. And more importantly it made me realise how much of a crossover there is between science and art - after all they are both the product of human minds!

(And to the review reviewers at amazon.com: the first sentence of the last paragraph wasn't a typo but maybe you need to read the book to see what I mean! (But you can leave this paragraph in if you like (oh dear - too much self-reference can drive one mad. Maybe Godel, Escher, Bach needs a health warning - (hmmm...now how many closing brackets do I need to balance the opening ones...1...2...3...4))))