Paul Zorn on Communicating Mathematics II: Mathematics in Literature

Paul Zorn, St. Olaf College

Part I: Introduction

Part II: Mathematics in Literature

Before we get to the harder stuff, please indulge me in some random thoughts, from a defrocked English major, on mathematics and mathematicians in literature.

Mathematics, mathematicians, and literature have non-empty intersection, as we all know. One might cite Flatland, various works of Lewis Carroll and John Updike, and Jorge Luis Borges‘s Library of Babel, which contains every possible book that can be written with the available font of symbols. (That’s infinitely many books, but at least it’s countable.)

Mathematics plays interesting roles in all of these, but in general the authors aim less to communicate mathematics as such than to use mathematics to point to ideas outside of mathematics.

Sometimes we mathematicians face an uphill PR battle with the literati. Here’s Jonathan Swift, in Gulliver’s Travels (1726) about the cloud island of Laputa, whose inhabitants were obsessed with mathematics and music. Warning: Swift wasn’t up to modern standards of gender equity.

The knowledge I had in mathematics, gave me great assistance in acquiring their phraseology, which depended much upon that science, and music; and in the latter I was not unskilled. Their ideas are perpetually conversant in lines and figures. If they would, for example, praise the beauty of a woman, or any other animal, they describe it by rhombs, circles, parallelograms, ellipses, and other geometrical terms, or by words of art drawn from music, needless here to repeat. I observed in the king’s kitchen all sorts of mathematical and musical instruments, after the figures of which they cut up the joints that were served to his majesty’s table.

Their houses are very ill built, the walls bevelled, without one right angle in any apartment; and this defect arises from the contempt they bear to practical geometry, which they despise as vulgar and mechanic; those instructions they give being too refined for the intellects of their workmen, which occasions perpetual mistakes. And although they are dexterous enough upon a piece of paper, in the management of the rule, the pencil, and the divider, yet in the common actions and behavior of life, I have not seen a more clumsy, awkward, and unhandy people, nor so slow and perplexed in their conceptions upon all other subjects, except mathematics and music. They are very bad reasonless, and vehemently given to opposition, unless when they happen to be of the right opinion, which is seldom their case. . . .

The women of the island have abundance of vivacity: they, contemn their husbands, and are exceedingly fond of strangers, whereof there is always a considerable number from the continent below. . . . Among these the ladies choose their gallants: but the vexation is, that they act with too much ease and security; for the husband is always so rapt in speculation, that the mistress and lover may proceed to the greatest familiarities before his face, if he be but provided with paper and implements.

In John Updike’s Roger’s Version, to cite another literary example, a computer science graduate student called Dale is keen on cellular automata and fractals, but less for their own sake than as evidence, he hopes, for the presence of God. And, yes, as material for an interdisciplinary research grant from the Harvard Divinity School. It doesn’t work out well for Dale, by the way. Read the book to find out why.

On the other hand, some mathematical writers try literary styles, with more or less success depending on one’s point of view. Here, for instance, is David Berlinski, in his quite good book A Tour of the Calculus, setting the stage for Galileo’s law of falling bodies:

Now imagine a gorgeous tower, its parapet jewel-encrusted, the dreamy Peruvian hills in the background, lacy clouds above. And on this tower an Italian dandy, dressed in silks puffed at the wrists and at his thighs, is fingering a large and lavish rose and rufous stone, a fabulous ruby or garnet, something luscious and lustrous. He dangles an elegant forearm over the parapet, holding the ruby in his upturned palm, and then slowly and with vast sensual deliberation rotates his wrist so that the precious stone, its cut facets catching the golden Tuscan light, slides from his polished palm and winking colored fire slips off into space.

That style’s a bit rich for some tastes, but Berlinski has a good point to make: Galileo’s law (and, by extension, the calculus) is universal. It applies regardless of the Tuscan light, the puffed silks, the cut facets, and every other accident.

Sometimes the author lets his vivid imagery overpower the mathematics, at least to my ear. Distinguishing between lines and curves, he writes:

But curvature at a point would seem to tremble on the same margin of incoherence as speed at an instant. The moving finger meanders over the rounded shoulder and stops, creating a pressure dimple in the molded flesh, but the hand having stopped, the sense of curvature conveyed by the caress disappears as well, the indented point being simply what it is, a way station along a sensuous arc; it is the whole of that shoulder that conveys to the voluptuary the conviction that he is getting anywhere at all.

The lesson of love is not to linger too long at a point, the same lesson, curiously enough, taught by the calculus.

What were we talking about again? This, too, is not exactly my taste, but one has to admire an author who can segue so smoothly between genres, from mathematical exposition to bodice-ripper.

Still other literary works are even more fundamentally mathematical. Here’s a work that never seems to end.

Nor, for that matter, does it ever really begin. How’s that for a new literary genre, or is it a new literary genus? The author, Barry Cipra, is among the speakers at the session on mathematical communication.

Part III: What Is Mathematics?
Part IV: Mathematical Language: Learning from Barbie
Part V: Rule Books and Tour Guides: Two Live Questions
Part VI: Lessons from History
Part VII: Valuing Communication

What is Math Comm

MAA Mathematical Communication (mathcomm.org) is a developing collection of resources for engaging students in writing and speaking about mathematics. The site originated in the MIT Department of Mathematics and was expanded through support from an NSF grant.