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4. Euclid Alone Has Looked on Beauty Bare (1)

I am poor at mathematics and hate the subject but love it too much to leave it alone.  I am more fascinated by the questions the system raises than the answers it gives us.  Mathematics can play a major role in our view of the world.  The hubris of mathematicians may plainly be seen in those who think that the final explanation of existence will be a mathematical formula, attainable and perhaps even soon to be discovered.  In one of my novels, a character asks of another whether he would marry a complete mathematical model of a beloved woman.  One supposes that something vital and real in the woman would be missing from a mathematical model of her, no matter how perfect and complete the defining math.  Cleopatra was something more than a rigid relationship among variables, which is a way of saying that Nature is not a subset of Mathematics.  Nevertheless, we cannot dismiss entirely the possibility that a complete model of a human actually is that human.  Our knowledge of nature comes from a verifying science that always leaves room for doubt and never escapes from degrees of probability rather than absolute certainty.

Abusive use of mathematics occurs in the soft sciences that investigate complexities that cannot be reduced to controlled experiments.  Usually, the abuse takes the form of claiming valid inferences about biological, environmental, or social phenomena but without data from controlled experiments that make precise predictions about expected outcomes.  Because I have spent thousands of hours pursuing economic questions, I will illustrate the malpractice in that context.  Economists sometimes call their trade the Queen of the Social Sciences because it is so highly mathematized.  That chutzpah covers a major case of pseudo physics.

Usually it surprises the novice to find that economists are as mathematical as physicists, in some ways more so.  Anyone even slightly familiar with the forays since the 1970s into string theory may doubt that economists reach similar mathematical altitudes.  I have in mind, however, the peculiar fact that the passion of the physicist is directed toward nature itself.  Economists instead often suffer tools gladly.  In most undergraduate texts, we would notice only as elementary algebra, some forays into marginals, or perhaps some calculus footnotes.  Beyond these first encounters, economic theories reside in a thicket of mathematics, much of it thorny.  Further, the profession itself, as seen in its journals and awards, operates through its mathematicians at surprising levels of abstraction and formalism.  The dominant and dominating economists wield mathematics like a scepter.  Even the profession’s policy pundits must either pass a mathematical litmus test in the journals or be looked down upon.

Why the mathematical Mandarins?  Let me tell you a story.  Once I was taking a French literature class in which our session always followed a physics lecture in the same room.  One morning the physicist was running late.  After we had filed in, suddenly he set to, erasing the blackboard equations furiously as though in great alarm.  Then that gentleman, who spoke French comme une vache, turned to us with a grin and explained that he had not wanted to frighten us.  So saying, he airily left the room, leaving us humble folk to turn our attention to Molière.

Thereby hangs at least half the tale of modern economics. Even so, thought experiments are reasonable activity.  These do contain insights, sometimes deep ones.  Therefore, unlike Whitman, we do not abandon the learned astronomer in his lecture hall to go out into the mystical moist night air and look up in perfect silence at the stars.  Our caveat concerning even the best of pure structures is that they can be critically misleading if taken physically.  The profession’s scholasticism has numerous devices imprecisely similar to the point particles (of zero dimensions) in particle physics, which is an idealization that has its uses but has led to absurdities.  It is “imprecisely similar” because, in physics, theory is either heading for the laboratory or else heading out the door.  Among economists, pure theory is the man who came to dinner.

            Setting aside the abuses of mathematics, what can we do with it when we use it validly?  What does it tell us about love, about our minds and our emotions, about suicide, about hatreds and other passions or about the celebrated quiet desperation of most lives?  Nothing.  Nothing at all.  It helps us to keep our airplanes flying, our ships afloat.  It enhances our control of the environment around us and is part of our cunning and even of our safety.  It whispers to us prophetically, like Cassandra herself, of the cogs and wheels in the great machine around us.  It tells us nothing of the ghost in the machine.  As a romantic, I find the greatest thing about mathematics, the priceless gift that it give us, comes from the radiant beauty that lurks like a whispering angel among the equations and topologies.  It holds within itself the most beautiful things mere humans ever encounter.  Euclid alone has looked on beauty bare and heard her massive sandal set on stone.

1 See Edna St. Vincient Millay’s sonnet Euclid Alone.