by Rudy Rucker
Reviewed by Michael J. Mehl
(Though this is apparently long out of print, I found this copy at Borders.)
To misquote Douglas Adams and Ronald Reagan, "Infinity is Big. Really Big. How Big? Well, if you stacked a trillion dollar bills up in a pile, it might stretch from here to the moon, but it would be further from infinity than the Cubs are from a World Series."
It's a scary subject. In my youth, I remember avoiding church on the first Sunday in Advent, because our pastor had a tendancy to dwell on the last days, which sounded scary, and Eternal Life, which is really scary. I mean, we're talking forever here.
Anyway, it probably takes a combination science fiction writer, mathematician, and theologian to really discuss infinity, and Rucker qualifies on the first two counts and takes a stab at the third.
Infinity is really a study in paradoxes. There are exactly as many positive even integers as there are integers, for example, even though the first set is a subset of the second. Rucker presents a large (though finite) set of the paradoxes. There are Zeno's paradoxes, of course, which have to do with dividing space into an infinite number of parts. Others include the liar's paradox ("This sentence is not true," or, more simply, "I am lying"), made famous by SF writer Eric Frank Russell and at least one Star Trek episode; another is the '.99999999.... = 1' "paradox", which we've argued here before (and is really a Zeno offshoot). One I hadn't heard of is the Berry Paradox (what is "The least integer not nameable in fewer than nineteen syllables"?), which gets us into the semantics of naming numbers. The whole ediface is capped of by Godel's theorem, which basically says that no finite system of axioms can ever be complete.
Rucker trots out all of this stuff, including examples from his science fiction, but the book didn't work for me. Part of the problem is the depth of the math. Rucker presents a fairly formal development of the cardinality of infinite numbers, for example, and a very detailed outline of Godel's theorem. It might be possible for the intellegent layman to understand all of this, but I wouldn't have expected to find it in a book on the popular science shelf. The other problem is the theological one. Rucker wants to identify 'absolute infinity' with God, at least symbolically. I find this a hard concept to swallow.
If you want my recommendation, buy this book if you want an mathematical and philosophical overview of Infinity and the problems humans have in dealing with it. If you're looking for something on the order of one of Asimov's books, this isn't it.
Author: Rudy Rucker Title: Infinity and the Mind Publisher: Bantam Books, 1983 ISBN: ISBN 0-553-23433-1 List Price: $5.95
Bantam Doubleday Dell Online
© 1996 by Michael J. Mehl
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