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”
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”
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”
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.”
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”
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.)
EDIT 1/3/2024: Le Guin invokes the Mandelbrot set — more fittingly and chillingly — in her essay “The Critics, the Monsters, and the Fantasists.” Her thesis is that fantasy literature puts us into imaginative contact with a pre-industrial time, before humans became alienated from the land, the sea, the sky, the animal, the Other. She contrasts this with our dreary present reality:
The monstrous homogenization of our world has now almost destroyed the map, any map, by making every place on it exactly like every other place, and leaving no blanks. No unknown lands. A hamburger joint and a coffee shop in every block, repeated forever. No Others; nothing unfamiliar. As in the Mandelbrot fractal set, the enormously large and the infinitesimally small are exactly the same, and the same leads always to the same again; there is no other; there is no escape, because there is nowhere else.
Cheek by Jowl, p. 40
“If We Can Only Keep the Pendulum Vertical”
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”
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.”
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.”
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Published
October 30, 2023January 3, 2024
