MIKE KERRIGAN: God and Math at Dinner: My son explains why some infinities are bigger than others.
In “Orthodoxy,” his masterpiece of Christian apologetics, G.K. Chesterton observed something interesting about bards and rationalists: “The poet only asks to get his head into the heavens. It is the logician who seeks to get the heavens into his head. And it is his head that splits.”
I shared this observation with my eldest son, Joe, early in his college career, when he told me he’d declared math as a major. Chesterton’s warning wasn’t against using logic, only embracing it to the exclusion of all else. The topic came up again recently over dinner when Joe, now a senior, explained something counterintuitive to his old man.
He said that between integers—say, 1 and 2—there are infinitely many real numbers, like 1.1 and 1.265. Such thinking scared me straight into law school at his age, yet somehow I grasped it now, if only conceptually. “Like the Incarnation,” I offered. An instance of the Creator, while remaining fully God and fully man, entering into his creation: the infinite bounded by the finite.
“I suppose,” Joe answered, checking my catechism against his set theory. Then he said something even trippier. Although whole numbers can be listed out to infinity, the hypothetical list of real numbers is necessarily larger than the hypothetical list of whole numbers. Not all infinities are equal.
Infinity and infinity-plus? Had that notion entered my mind in college, I’d have reclined in darkness with a cold compress on my head. I didn’t get the underlying math but, thinking I understood the broader concept, parried with another analogy: “Like higher and lower degrees of heavenly perfection.”
Long ago I’d accepted how a shotgun shack in heaven’s outermost borough was good enough for a sinner like me. Joe concurred, and when he did, I was relieved. To Chesterton, the madman “is not the man who has lost his reason” but “the man who has lost everything except his reason.” Our conversation assured me that Joe had ample stores of wonder. He was simply seeing God in the math, as I see the math in God.
It was a delightful dinner between a father and his son. And when the check came, perhaps proud of the numerical proficiency I’d shown, Joe graciously let me pay.
I’ve never known a mathematician offer to split up a restaurant check.