A Brief Collection of Math Metaphors in Literature

This list goes against everything I’ve been taught about good writing.

Good writing, they say, is vivid and sensory. It involves punchy verbs, concrete nouns, and long descriptions of rain.

Mathematics is not sensory. It is not concrete. And it is not much good for describing rain.

Instead, math is a library of concepts: shelf after shelf of abstract relations between x and y. Mathematical ideas are like pencil drawings of spider webs, airy and ethereal schematics of something that was pretty airy and ethereal to begin with.

And that’s what makes mathematical metaphors so perfect.

The essence of novels is context. They show us people embedded in whole worlds, everything existing in relation to everything else. Mathematics gives us precise and evocative language for those relations, indeed, for all relations. For that reason alone, math is a powerful source of metaphors for purveyors (and perpetrators) of fine literature.

Here, then, is a brief collection of mathematical metaphors I’ve come across, along with why I love them.

“A Sort of Semantic Geometry”

"We speak a kind of esoteric, family language, a sort of semantic geometry in which the shortest distance between any two points is a fullish circle." -J.D. Salinger, Franny and Zooey

Why I love it: The narrator is describing his family’s intricate dynamics. Unable to speak plainly, they couch everything in intellectual games. So of course he couches this sentiment in an intellectual game.

“Everything Doubling Back Over Itself”

"We talked all night. Everything felt so intense and coiled and Mobius strip-like, all those drinks and drugs and hormones making everything constantly double back over itself." -Anne Lamott, Traveling Mercies

Why I love it: The Mobius strip is the kind of mind-blowing, trippy object you might first encounter in college. It makes a fitting image for a late-night dorm conversation.

“The Revolutions of an Irregular Solid”

"In short, woman was a problem which, since Mr. Brooke's mind felt blank before it, could be hardly less complicated than the revolutions of an irregular solid." -George Eliot, Middlemarch

Why I love it: Mr. Brooke is so bad at understanding women that it extends even his choice of analogy; he treats “woman” as a kind of computational challenge. “Irregular” is an especially delicious choice of term: as if, to Mr. Brooke, there is something irregular about the workings of women, as if their minds are off-center objects, rotating oddly. (Thanks to my pal James Butler for showing me this one.)

“This Is An Averaging Gun.”

He took [the gun] from his shoulder and held it for me to see. "It's a combination gun. Look, two triggers. This"—he tapped the broad-gauge tube—"a shotgun. It spreads possibilities." He made an extending cone with his hands. "And this?" The other. "This rifle's a long-range single shot."

He showed me how he'd aim with it.

"You can shoot one, the other, or both. The rifle shoots right down the very center of the spread. Like an average. A range and its mean. This is an averaging gun."

-China Mieville, This Census Taker

Why I Love It: This metaphor baffles and frightens me, just like this book baffled and frightened me. It’s a good image for the book itself: both a scattershot spray and a work of highly targeted precision, aiming at something in the distance I can’t quite discern.

“Caves Like Nothing She Had Ever Seen”

"The caves were like nothing she had ever seen. There were many of them, hundreds, some tiny, no more than bubbles in the rock, some big as the doors of hangars. They made a lacework of circles interlocking and overlapping in the wall of rock, patterns, traceries. The edges of the entrances were fretted with clusters of lesser circles, silvery stone shining against black shadow, like soap-suds, like foam, like the edges of Mandelbrot figures." -Ursula Le Guin, The Telling

Why I love it: The description keeps probing and reaching for a further image, an additional refinement; what better place to come to rest than a fractal, which contains infinite further layers of probing and refinement? (Though Le Guin mentions the Mandelbrot set, the imagery reminds me more of an Apollonian gasket: circles between circles between circles.)

“If We Can Only Keep the Pendulum Vertical”

"Indulgence leads to misbehavior, which angers the nanny and prompts her to deliver punishment more severe than is warranted. The nanny then feels regret, and subsequently overcompensates with further indulgence. It is an inverted pendulum, prone to oscillations of ever-increasing magnitude. If we can only keep the pendulum vertical, there is no need for subsequent correction." -Ted Chiang, "Dacey's Patent Automatic Nanny," Exhalation

Why I love it: The narrator, overly analytical, thinks of the relationship between his son and the nanny as a kind of dynamical system that keeps falling out of its equilibrium. The system instead swings between overindulgence and severity. The mechanical description belies that his own cold aloofness is the real problem.

“As Intangible as an Equation”

"Emergencies in space can be as obvious as an explosion or as intangible as an equation, but their obviousness has nothing to do with how dangerous they are." -Kim Stanley Robinson, Red Mars

Why I love it: This metaphor threatens to stop being a metaphor at all, and become literal. After all, space travel is made possible by our work with equations. The effect, I find, is to blur the line between symbol and symbolized, between the mathematical model and the world it describes. It paints outer space as a kind of abstract void, which we traverse like voyagers through Plato’s realm of forms, navigating around ideas and concepts that can somehow kill us. 

“A self-defining object of one surface only.”

"In itself, a dictionary is like a Mobius strip, a self-defining object of one surface only, collecting and explaining without claiming a narrative third dimension.... It is the readers who... recognize in a dictionary one or several of many books: an anthology, a hierarchical catalogue, a philological thesaurus, a parallel memory, a writing and reading tool. A dictionary is all these things, though not all perhaps at the same time." -Albert Manguel, Packing My Library

Why I Love It: In Manguel’s vision, the dictionary is like a mathematical abstraction: a self-sufficient, logically circular object, awaiting humans to interpret and assign meaning to it. Thus, it’s not just the specific image of the Mobius strip that sells the passage, but the inherited flavor of mathematics itself.

Anyway, that’s what I’ve got for now. To be expanded as others catch my eye!

EDIT 11/1/2023: Note on others to include…

From Joseph Torres on Facebook: in Paradiso, Canto 33, Lines 133-141, Dante uses the problem of squaring the circle as an analogy for the challenge of trying to describe the Trinity.

Raymond Queneau‘s short story “Destiny” describes how a person changes: “But a day comes when conversion fulfills him. A new integration reveals some new function.” A nice double bit of wordplay: “integration” can be read as “a way of organizing the parts of one’s soul,” while “function” can be read as “purpose of way of existing in the world.”

12 thoughts on “A Brief Collection of Math Metaphors in Literature

  1. Check out _The Mountain and the Valley_ by Ernest Buckler. I took a Canadian fiction class in university once and we covered this book. The lecturer (poet Christian Bok! Check out his _Eunoia_) started off by drawing the unit circle and the sine wave on the board, causing consternation among all the English majors in the class, who had expected never to have to deal with this stuff again. But he pointed out that Buckler was a mathematician who often expressed himself in mathematical terms. Anyway, the protagonist’s fortunes follow the trajectory of a sine wave during the story: up, back down, way down, then back up to even. And the book starts and ends with the same image, a literary device called circularity, and of course the sine wave and unit circle are two ways of expressing the same thing. I thought it was the greatest lecture I’d ever had.

    1. Ooh, that sounds fabulous — and I’ve actually read Eunoia! A very impressive display of latter-day Oulipo wizardry. Anyway, I’ll check out Buckler!

  2. For many more math metaphors, check out Sarah Hart’s new book “Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature“.

  3. Now I understand why I love your blog. I, a poet who got 6 per cent in her final high school maths exam. (You can guess my age and nationality by that word “maths.”)

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