The Unreasonable Effectiveness of Mathematics

Last month trail running comrade Caren Jew asked me, in the middle of a pleasant excursion on Massanutten Mountain, "What's the connection between math and the real world?" It's a wonderful, deep, unanswerable question. I gave as good an answer as I could — not a very good one — but my attempt to discuss the issue reminded me of physicist Eugene Wigner's 1960 essay The Unreasonable Effectiveness of Mathematics in the Natural Sciences, a classic lecture that I had heard of but never actually read. When I got home I looked it up, and was delighted. Wigner begins his musings with a parable:

There is a story about two friends, who were classmates in high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. "How can you know that?" was his query. "And what is this symbol here?" "Oh," said the statistician, "this is pi." "What is that?" "The ratio of the circumference of the circle to its diameter." "Well, now you are pushing your joke too far," said the classmate, "surely the population has nothing to do with the circumference of the circle."

Wigner then goes on to discuss, in enchanting style, the mysterious-magical power of mathematics to describe phenomena in the physical world — a true blessing to science. Wigner concludes:

Let me end on a more cheerful note. The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.

^z - 2008-02-17

(correlates: MoralToPhysical, Mr. Know-It-All, PsychoGeography, ...)