Hofstadter, Douglas. Gödel, Escher, Bach: an Eternal Golden Braid. New York: Basic Books, 1999.
This book is an excellent and fun, if lengthy, romp through art (visual, literary, and musical), mathematics, logic, provability and computability, linguistics, cognitive science and artificial intelligence, and more. Hofstadter cleverly explores a myriad of amazing connections between all these fields. And while he ends up drawing no substantive conclusions about his final hypothesis of emergent intelligence, the journey is no less exciting.
I disagree with Hofstadter’s opinion of the nature of intelligence. But I thoroughly enjoyed this book for a number of reasons. First, despite its imposing size, it is accessible; Hofstadter presents mathematical proofs in an easily understood way, using examples, analogies, and much explanatory prose. Second, despite its imposing size, it is delightfully fun; this book is brimming with humor, wit, cleverness, and exciting coincidences. Lastly, it is an excellent introduction to a broad variety of topics.
I first read this book in eighth grade and deeply enjoyed it. In part this book served as my introduction to the exciting fields of logic, mathematics, and computer science.