Earlier this year I came across a book called "Proust and the Squid" which I reviewed a few posts ago. That book started me on the thread of Gödel and his incompleteness theorem, and I read a book on that "Incompleteness: The Proof and Paradox of Kurt Gödel", which lead me to "Gödel, Escher, Bach: An Eternal Golden Braid".
I highly recommend this book to anyone interested in mathematics and AI. Hofstadter covers a wide range of topics, and he's very good at explaining things, using diagrams, Socratic dialogue, and exercises for the reader. He describes in great detail, and from first principles, a number theory he calls Typographical Number Theory, and with that and other devices he explains Incompleteness theorem. In addition there are great swathes of information about how genetics works at the cell level, knowledge representation, in particular hierarchical. Also, of course, there's plenty of information about Bach (and Fugues) and Escher from the title. In regards to the rest of the post, this book is interesting because it's really about the mind. About how it emerges from simple low level processes, and how at the highest level (our own stream of consciousness), we don't need to know about neurons firing and so on because we're essentially the software running on the hardware.
As an aside I found it both fascinating and sad that Bach's last composition included his name as possibly the last four notes he wrote: BACH (I know there's no H in the musical scale, but in German there is).
This is a book you could spend a lot of your life obsessing over, as it is filled with mystery's and difficult exercises for the reader. But even if you just rush through it like I did, enjoying some parts and being utterly baffled by others, you will find much to enjoy I am sure.
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