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A Sidebar in Jonathan Witt’s “The Gods Must Be Tidy”
The one thing I’ve noticed that most knocks my students out of their secure evolutionism is a question on the status of mathematical objects. I ask them, “Have you ever seen a circle?” They respond that they have, poor unsuspecting students. “You mean you’ve seen a set of points of no dimension, equidistant from a given point, on a plane of infinitesimal thinness?” Well, no, now that I put it that way, they’ve never seen one of those.
“So you’ve never seen a circle?”
“Um, no, I guess not.”
“In fact, you could never see a circle, because circles are not material objects.”
“I guess not.”
“But you know things about circles.”
“How can I know things about circles, if I’ve never seen one?”
“Good question. But you do: You know that the ratio of the circumference to the diameter is a number called pi.”
“Well, actually the number is the limit of any number of infinite series. But would you say that pi exists, and that people discovered what it was, or that pi didn’t exist until someone invented it, and that, if there were no human beings, there would be no such thing as pi? Be careful: pi shows up in equations dealing with electrical current, number theory, the probabilities of coin tosses, you name it. Was pi discovered, or was it only invented?”
At this point they are trapped. They will say what any mathematician without a philosophical ax to grind will say. They will say what Archimedes said when he discovered the law of displacement of fluid. They will say that pi was discovered.
“Then pi exists?”
“But pi is not material.”
“Then at least one immaterial object exists, namely pi.”
“How can an immaterial object evolve?”
I think pi was there in the beginning, when the sons of morning sang for joy!
Anthony Esolen is Professor of English at Providence College in Providence, Rhode Island, and the author of The Ironies of Faith (ISI Books), The Politically Incorrect Guide to Western Civilization (Regnery), and Ten Ways to Destroy the Imagination of Your Child (ISI Books). He has also translated Tasso's Gerusalemme liberata (Johns Hopkins Press) and Dante's The Divine Comedy (Random House). He is a senior editor of Touchstone.