06.30.06
Weird!
Two Philosophies of Mathematical Weirdness
Two Philosophies of Mathematical Weirdness
Jaron Lanier
Meta Math! The Quest for Omega. Gregory Chaitin. xiv + 220 pp. Pantheon Books, 2005. $26.The Lifebox, the Seashell, and the Soul: What Gnarly Computation Taught Me about Ultimate Reality, the Meaning of Life, and How to Be Happy. Rudy Rucker. x + 564 pp. Thunder’s Mouth Press, 2005. $35.
A strange thing happened to the philosophy of mathematics in the past century or so: Math-ematics increasingly revealed truths about itself that utterly confounded the expectations of philosophers. In other words, math got weird.
A century ago, math was thought to be an orderly Platonic phenomenon, imperious in its perfection. The first prominent onset of weirdness came in 1931, when Kurt Gödel showed that important systems of mathematical ideas could never be completed. In order to get his result, he indexed mathematical ideas in a way that was somewhat analogous to the way the Web is now indexed by services such as Google. That computational framework began to give mathematicians a completely new perspective.
Since Gödel, developments in mathematics