This is the kind of book that inspires awe: for its physical dimension and for the specificity of the thematic, and it’s easy to grasp this even by browsing it.
The whole text is about the concept of “undecidability”, or how lots of disciplines (and also the reality) are based on the idea of different levels that do not communicate among them: it’s impossible to go from one level to the others.
This concept is expressed – in math – by one of Gödel’s theorem:
Any effectively generated formal system capable of expressing elementary arithmetic cannot be both consistent and complete. In particular, for any consistent, effectively generated formal theory that proves certain basic arithmetic truths, there is an arithmetical statement that is true, but not provable in the system. ( from Wikipedia)
but it’s also present in other fields, from biology to informatics and the Artificial Intelligence theories, but also in art, as Escher’s drawings demonstrates, with their tendency to an unreal tri-dimensionality, the ultimate desire to get out from the painting itself.
The author has a deep knowledge on different fields, and he is able to integrate them in a single book; one example of his skill are the brilliant dialogues between Achilles and the Tortoise, structured as musical canons (taken from Bach works) and introducing the main theme of the chapter that follows.
I think it’s quite hard to understand everything the book could offer, maybe this could be possible only having a profound knowledge in different fields; I dealt better with the scientific themes (but I skipped some derivations), and worse with the musical ones (I listened and liked Bach, but I’m not able to associate a dialogue to a specific musical canon). I’m however sure that the main ideas will stick to the reader.
In the end it’s a good book, very interesting but one must be sure to want reading it, because it’s not an easy read.
* Gödel, Escher, Bach: An Eternal Golden Braid by Douglas R. Hofstadter ★★★☆☆½
*I read this book in italian