Why I drink whisky from a Klein bottle

Two mathematicians are sitting in a bar, arguing about what degree of mathematical literacy one could expect from the average person. In a conspiratorial whisper, the optimistic mathematician instructs his waitress: “When my friend (A) comes back from the bathroom, I’m going to ask you a question, to which I want you to respond, ‘one-third x cubed.’” Sure enough, the friend returns, (no doubt after computing the base to his own natural log) and the mathematician bets that their waitress will be able to vindicate the average man by providing a correct answer to a proposed integral. He then calls the waitress and asks “What is the integral of x squared?” The waitress responds “one-third x cubed,” and, while walking away, turns back with a smile and adds “plus a constant!”

I confess to feeling twitches of this old joke whenever I have occasion to overhear my quantitatively inclined social science colleagues talk shop. Indeed, there has been something of a mathematical gold-rush in most social science fields, which is sometimes characterized by a prickly penis envy that roughly corresponds to how well one’s discipline is able to approximate the numerical rigors of the “hard” sciences. What is truly astonishing is the speed with which even the most flaccid competitors are catching up. Anyone who is familiar with the great Tom Lehrer (mathematician, satirist, alleged inventor of the “Jello shot”) might have heard rumors of “fanatics, in their attics, learning mathematics all for sociology … ”

To what should we attribute this astonishing, and by now decades-long surge in quantophilia? Surely mathematics reliably imposes at least some minimum standard of cognitive ability. This cannot, however, be the primary answer. There are many disciplines that impose the same kind of quality control, perhaps even more so than many of the math-crazed social sciences—in my whole life, I have met just one profoundly stupid classicist. Besides, the idea of standards in the meaningful sense is loathsome to our enlightened, radically egalitarian tastes. The spectacle of social policy types testifies to how ingenious we have become with our euphemisms. With sigmas and chi squareds proudly in tow, they cannot seem to grasp the idea that half of any group of people is below average. Only the most Pollyannaish polynomials survive the cut. I once heard a math activist, completely enamored with “persuasion by equation,” argue that all positive integers are special, because even the least special of special numbers is still special.

But I digress. The reason for the enormous and increasing influence of mathematical methods is, quite simply, that they work. Mathematics corresponds to the physical world in such a way that its models are accurate enough to send us safely to the moon, and make accurate predictions about the fate of an electron travelling at a certain velocity and angular momentum toward another particle. Whether or not we want to extend these success stories to the social sciences is another story. Economics, the most quantitatively developed of the social sciences, is looking highly questionable these days. The point is rather that the will toward quantification, whether justified or not, owes its attractions to motives of a vulgar, utilitarian variety.

It is only the “pure” mathematician who is able and inclined to defend mathematics from a more lofty and aesthetic perspective. Perhaps the most famous instance of this is G.H. Hardy’s 1941 memoir, “A Mathematician’s Apology,” which positively relishes in the “uselessness” of what he calls “real mathematics.” He argues that the kind of mathematics responsible for these achievements is “elementary” and ugly, and not the sort of thing any truly gifted mind would waste its time thinking about. Beauty and seriousness shines through most of all in number theory, and Hardy gives a number of examples of accessible proofs that illustrate this claim. My own pick would be Euler’s Identity. Go ahead and look it up.… I challenge you not to be enchanted. Hardy’s gloats with touching anachronism that, in addition to its inherent beauty, no area of “real” pure mathematics can be put to destructive use in wartime—a claim soundly refuted by the modern science of cryptography. In a modest refutation of my own, I habitually drink my whiskey out of a Klein bottle.

Where does this leave the social sciences? A cynic might suggest that they possess all of the uselessness traditionally attributed to pure mathematics together with the mathematical inelegance of engineering. I close with one of the best limericks I’ve written on this sad possibility:

When the cops discover your stash

And yur payoffs decidedly clash