Godel, Escher, Bach: an Eternal Golden Braid by Douglas Hofstadter
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This book is a marvel of playful synthesis telling a compelling story about computers and intelligence through math, linguistics, music, and visual art. The author builds up his argument through analogy, carefully piece by piece wandering through fugues, set theory, formal logic, syntax, Zen Buddhism, and number theory with a light enough touch that even people with no background in the subjects can follow along. If that sounds like an ungodly mess to you, the miracle is that it comes together beautifully providing a pointed, deep exploration on what it means to think and be human.
Because the book was originally published in 1979, some of the discussion of then current topics in computing is rather dated, although its surprising how much of what he observed still holds true more than 40 years later. I suspect that's in large part because, like many early computer scientists, he was a bit of a polymath, and focused his argument on ground truths in mathematics, language, and logic that haven't changed very much despite the ensuing sea changes in software design.
The book first came to my attention in high school in the 90's, and I sincerely wish I had read it then, not only because it would have been more "current," but also because I was much fresher on higher math. I think I would have enjoyed it on a slightly more sophisticated level had I read it 20 or 25 years ago. That is to say, while the book is relatively easy on a lay reader, there are a few more rigorous sections where I was just kind of nodding along without really being able to follow the argument, and I suspect, once upon a time, I might have been able to actually hang on.
But timing gripes and laments for my lost youth aside, the book is superlative, edifying, and amusing. It's a Pulitzer-prize-winning time capsule from an era when computer science was fresher and the approaches were much less fully formed: there was still plenty of room for talented amateurs from diverse backgrounds to poke around and discover things, and everything had yet to be commodified. In short, the book is an elegant meditation on the nature of intelligence (whether artificial or natural) from a gentler, more human age of computing, and can still be read with significant profit today.