# Of Words and Variables

This article was written by Gregory Thole, a graduate student in mathematics at Boston College. If you’d like to write for Math-Blog.com as well, please email us at [email protected].

And what was he?
Forsooth, a great arithmetician.
-Shakespeare Othello, I.i

Perhaps it should not be surprising, considering the vast libraries of published works, that mathematics should appear topically in works of fiction, but anyone who has sat through an introductory course in algebra can understand the difficulty that an author might have in captivating a reader if the subject is predominantly mathematical. This is not to say that casual readers should hold Jean-Pierre Serre up to the same literary standards of William Shakespeare, but that fiction can involve mathematics in complex and beautiful ways.

Mathematics is a rich ground for metaphor: the first scene of Tom Stoppard’s Arcadia is an excellent example of the intertwining of such unusual topics of conversation. In the very first scene, our young protagonist Thomasina is trying get her tutor, Septimus, to explain sexuality to her, whereas Septimus would rather encourage her studies:

Septimus: Carnal embrace is sexual congress, which is the insertion of the male genital organ into the female genital organ for purposes of procreation and pleasure. Fermat’s Last Theorem, by contrast, asserts that when x,y and z are whole numbers each raised to power of n, the sum of the first two can never equal the third when n is greater than 2.
(Pause)
Thomasina: Eurghhh!
Septimus: Nevertheless, that is the theorem.
Thomasina: It is disgusting and incomprehensible. Now when I am grown to practice it myself I shall never do so without thinking of you. (3)

Thomasina grunts out of mathematical frustration or coital pleasure, or perhaps both. And what precisely will she be doing when thinking of Septimus? This early comparison of algebraic theory with sexual self-discovery alters the tone of every mathematical reference uttered through the rest of the play, and double-entendres arise from otherwise innocent mathematical statements. Arcadia is laced with math, most prominently geometry and chaos theory. From carnal embrace to architecture, math is among the primary metaphors for examining the impermanence of forms and the struggle to find meaning in a world of background static.

While sex and death are compelling, authors also use math not as a metaphor for other things but as itself: a philosophical tool with which to pry off the lid of the universe. Neal Stephenson has written a number of historical fiction (or arguably science fiction) novels whose primary or secondary characters are mathematicians. The Baroque Cycle is a compendium of three novels centered around the dispute between Newton and Leibniz. In Quicksilver, the first book in the cycle, a character muses on the significance of conic forms (ie tracing the intersection of a cone and a plane) and gravitation:

Comets passed freely through space, their trajectories shaped only by (still mysterious) interactions with the Sun. If they moved on conic sections, it was no accident. A comet following a precise hyperbolic trajectory through the æther was a completely different thing from Daniel’s just happening to trace a roughly hyperbolic course through the English countryside. If comets and planets moved along conic sections, it had to be some kind of necessary truth, an intrinsic feature of the universe. It did mean something. What exactly? (676)

Daniel ponders an old question: is nature written according to the rules of Euclidean Geometry, or is geometry just the illusion of patterns in the fog? Newton’s “On the Motion of Bodies in Orbit” appears to answer the question, and in so doing open a window to the mind of God. The influence of mathematics on metaphysics has a tremendous effect on religious, and therefore political, thinking at the time. In this way mathematics drives a thousand plot lines spinning off from its philosophical implications.

But the subjects need not always be as weighty as the Universal Law of Gravitation. Math can appear within a sense of whimsy and joy in the beauty of solving puzzles and word games. Lewis Carroll’s Alice’s Adventures in Wonderland is full of subtle math jokes woven into the fabric of his fantastic tale. At the Mad Tea Party, when the Hatter wants another cup of tea, he has the whole party move around the table in a kind of infinite sequence. When Alice asks what happens when all the places are used up, the March Hare asks for a change of subject. In Through the Looking Glass, the chess queens grill Alice on her arithmetical skill:

“And you do Addition?” the White Queen asked. “What’s one and one and one and one and one and one and one and one and one and one?”
“I don’t know,” said Alice. “I lost count.”
“She can’t do Addition,” the Red Queen interrupted. “Can you do Subtraction? Take nine from eight.”
“Nine from eight I can’t, you know,” Alice replied very readily: “but – “
“She can’t do Subtraction,” said the White Queen. (222)

These are the joyous little jokes that make the Alice’s Adventures in Wonderland and Through the Looking Glass so endearing. In addition to writing children’s stories, Lewis Carroll was a mathematician; word games and clever exchanges such as these are the result of a mathematical attention to the precise meanings of words. Many excellent articles have been written on the logical puzzles hidden in his works.

Thus, contrary to the common perception that mathematics and literature occupy opposite ends on the spectrum of human thought, one can see how well the two disciplines may interweave. This is but a sampling, there is much more math to be found in fiction than just the few examples above. Whether heavy-handed or light-hearted, explicit or metaphorical, math appears in all sorts of ways throughout literary works. If you have but the patience to look into it and see, mathematics can be a light to brighten the many worlds you might visit.

#### References

1. Carroll, Lewis. Alice’s Adventures in Wonderland & Through the Looking Glass. New York: Penguin Putnam, 2000.
2. Stephenson, Neal. Quicksilver. New York: HarperCollins, 2003.
3. Stoppard, Tom. Arcadia. New York: Faber and Faber, 1993.