Thursday, August 2, 2007
Rudy Rucker's Infinity and the Mind - a Review
This is a long overdue review.
I encountered Infinity and the Mind several years ago, wanting to learn a bit more about infinity (duh). Having long been a fan of Rudy Rucker's fiction, I was actually surprised to find out he also wrote non-fiction.
I think Infinity and the Mind is a great book by a phenomenally entertaining and insightful author. It served as a jumping-off point for me, into Cantor, Dedekind, Russell, and re-awakened my long-latent interest in all things mathematical. And I liked it so much the first time that I just re-read it.
The book is entertaining, enlightening, soulful (classic Rucker), and smart. I give it an uncountably infinite, Big-Omega stars out of 0, which probably doesn't make it any more than it was, but as a programmer, dividing by zero is the one way to ensure that infinity stays infinite.
If you're looking for a synopsis, here's my quick take.
The first chapter is all about infinity: history, philosophy, mathematics, and paradoxes. He closes this and every chapter with thoughtful and entertaining puzzles about the topic at hand.
Chapter two, all about numbers. It was because of this chapter that I bought John H. Conway's Book of Numbers, knowing already it was a fun topic. He doesn't stop with finite, though- he gives a very impressive overview of cardinality, and continues the continuum far beyond what I'd previously thought about.
Chapter three, the paradoxes. True to his style in other (fiction) books, he approaches paradox head-on. By the end of this chapter, he presages Gödel, but we're not there yet. Chapter three was my favorite of the book.
I don't like the name of chapter four, but I like the chapter. The question, "Might a machine have a soul?" is quickly interrupted by a glorious description of Gödel's proof. I can't provide spoilers, because Rucker doesn't answer the question, which I love.
Chapter five, the one and the many. I love this question. Is there thing-ness, or is everything the same thing? What gives an object its thing-ness. Rucker's approach is deferential, and like the last chapter, he doesn't give us an easy answer, but unlike the last chapter, he does give us an answer. Read it yourself to find out.
The last two sections of the book are "excursions." One led by Cantor and one by Gödel. You might be able to guess what they're about.
Did I mention I love this book?
I encountered Infinity and the Mind several years ago, wanting to learn a bit more about infinity (duh). Having long been a fan of Rudy Rucker's fiction, I was actually surprised to find out he also wrote non-fiction.
I think Infinity and the Mind is a great book by a phenomenally entertaining and insightful author. It served as a jumping-off point for me, into Cantor, Dedekind, Russell, and re-awakened my long-latent interest in all things mathematical. And I liked it so much the first time that I just re-read it.
The book is entertaining, enlightening, soulful (classic Rucker), and smart. I give it an uncountably infinite, Big-Omega stars out of 0, which probably doesn't make it any more than it was, but as a programmer, dividing by zero is the one way to ensure that infinity stays infinite.
If you're looking for a synopsis, here's my quick take.
The first chapter is all about infinity: history, philosophy, mathematics, and paradoxes. He closes this and every chapter with thoughtful and entertaining puzzles about the topic at hand.
Chapter two, all about numbers. It was because of this chapter that I bought John H. Conway's Book of Numbers, knowing already it was a fun topic. He doesn't stop with finite, though- he gives a very impressive overview of cardinality, and continues the continuum far beyond what I'd previously thought about.
Chapter three, the paradoxes. True to his style in other (fiction) books, he approaches paradox head-on. By the end of this chapter, he presages Gödel, but we're not there yet. Chapter three was my favorite of the book.
I don't like the name of chapter four, but I like the chapter. The question, "Might a machine have a soul?" is quickly interrupted by a glorious description of Gödel's proof. I can't provide spoilers, because Rucker doesn't answer the question, which I love.
Chapter five, the one and the many. I love this question. Is there thing-ness, or is everything the same thing? What gives an object its thing-ness. Rucker's approach is deferential, and like the last chapter, he doesn't give us an easy answer, but unlike the last chapter, he does give us an answer. Read it yourself to find out.
The last two sections of the book are "excursions." One led by Cantor and one by Gödel. You might be able to guess what they're about.
Did I mention I love this book?
// posted by David @ 9:21 AM 
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