Striving For Harmony

Using geometrical concepts to strengthen the structure of a work

A poster in the back of my high school math classroom announced Math Is Everywhere. The words were displayed across a flowering shaft of lavender, the feather of a bird’s wing, and the interior of a seashell. Mapped into the center was the Pythagorean theorem: the square of a right triangle’s hypotenuse is equal to the sum of the squares of its other two sides. The Greek philosopher Pythagoras swam in math, leading devotees to believe in the “harmony of the spheres,” a relation of the vibrations and distance of celestial bodies from earth to string length-ratios. This idea, that numerical ratios are present in both math and music, was taken by Johannes Kepler and further extended into geometry. I often think about that poster because it reminds me of the kind of harmony creative nonfiction writers strive to achieve.

We use mosaic, fragment, and lyric (among other terms) to describe work that departs from traditional, continuous expository form. Conceptions of the ways these forms treat fragmented text vary, and some, like the lyric, might even be described as shape-less. Yet they all share similar craft elements that often cohere into a form, much like the parts of a geometrical figure.

Some writers focus on this final effect as they begin working on a piece, but regardless of whether these choices are planned out in advance or emerge organically over the course of writing, I’ve found it important, above all, to remember that the final goal—especially in works pieced together from parts—is the kind of euphony Pythagoras found in the triangle. That image, along with a few guiding questions derived from geometrical concepts, can help writers explore gaps and puzzles, or even determine a shape altogether. Here are a few questions I’ve found useful, along with some examples from works which take up different kinds of structures.

What are the various angles?

In geometry, a shape’s sides determine the size and position of its angles. In a piece of writing, material can be positioned to create refractive and reflective elements. Joan Wickersham’s memoir, The Suicide Index, attempts to bring order to the experience of her father’s death. Each index subentry, such as “day after,” “where I am now,” and “life summarized in an attempt to illuminate,” falls under the main heading, “Suicide.” Some subentries are further split into additional sub-subentries—the subheading “intrafamilial relationships reexamined in light of,” for example, also includes the sub-subentries “Munich” and “my grandmother.” The result is a composition of forty-eight locators that engage one another in myriad ways and invite the reader into complex levels of interpretation. In the sub-subentry “his” under the subentry “attitude toward,” we learn that Wickersham’s father disapproved of the suicides of family friends, and in “readings in the literature of,” she quotes other writers’ takes on suicide, including Plato and Flaubert. The effect is kaleidoscopic, putting her father’s suicide into conversation with thinkers, his own views, and her upside-down experience of the aftermath. “So you keep going back to the beginning,” Wickersham writes. “Or to a beginning, anyhow. The fiendish thing about this particular maze is that there are so many different beginnings, and an infinite number of possible places to end.”

In an interview with Solstice, Wickersham explains she didn’t plan for the unification of the work as she wrote but instead let the parts guide her. She remarks, “I decided to just do it in pieces and not worry about how the pieces were going to fit together for then.” Eventually, the index emerged. “If I’d started with the index,” she says, “the book wouldn’t have the organic structure that I hope it does.” The creative writing insight here is that considering the number of angles and their sizes’ effects on one another at some point in the process—either at the outset or along the way—can serve to elevate the harmony of a piece.

What are the sides composed of?

Just as sides give form to a geometrical shape, decisions about what concepts will be engaged in the text through imagery, symbology, or motifs can fortify the overall effect of a piece of writing. This may come by way of explicit allusions or repetitions of objects and ideas, but even when these are more subtle, it can be important to consider what they are and how they are held together.

Multimodal works or pieces drawing from several types of sources are excellent models of this. Theresa Hak Kyung Cha’s Dictee, for example, is structured as nine chapters titled after the Greek Muses, one of which she has replaced and reimagined. In these chapters—described variously by critics as autobiography, history, collage, essay, poetry, and even film—Cha blends stories of real and mythical women with images, documents, maps, and other ephemera to relate the stories of historical and familial female figures. Even the text itself is hybrid. In “Erato / Love Poetry,” for example, the text includes shot angles of the written scene: “Camera pans left, and remains still at the profile of another woman seated. Camera pans back to the right, she turns her head to the front. The screen fades to white.” The chapter includes passages from St. Thérèse of Lisieux’s Story of a Soul and is bookended by images of St. Thérèse and Maria Falconetti’s cinematic portrayal of Joan of Arc. As in the case of other chapters’ muses, these elements’ connections to Erato, the goddess of erotic poems, are never made clear, but each piece creates sides exploring language, memory, resistance, inheritance, colonization, and history (among other concepts). Photographs go uncaptioned, text is written in varied languages, including French, English, Chinese, and Korean, blank space appears across pages—the result is a sort of prism.

The fragmentary composition at once isolates and deconstructs the individual concepts. At the same time, a unified form emerges where the text’s ideas are put into conversation. Cha even considers the fragments themselves, writing, “To extract each fragment by each fragment from the word from the image another word another image the reply that will not repeat history in oblivion.” Cha’s work has been interpreted through a myriad of lenses but serves as a sophisticated example of how powerful putting together the sides in a piece of writing can be.

What is at the center?

A triangle’s center is found by drawing a line from each vertex to the midpoint of its opposite side. Similarly, in an effective piece of writing, the intersections of various craft techniques can contribute to an overall equilibrium. This harmony can result from a particular part’s compression or reduction in emphasis, or even another’s expansion. Alternatively, a part might serve as a repeating refrain throughout a piece, or carry additional weight compared to others. At the center of Valeria Luiselli’s Tell Me How It Ends: An Essay in Forty Questions is the idea of story itself. Drawn from the intake questionnaire Luiselli uses as an interpreter for unaccompanied children in a federal immigration court in New York City, the forty questions unfold across the book. Referenced both explicitly and implicitly is the concept of beginning, middle, and end, which she treats in varied measures. Luiselli constructs this nucleus in a number of ways: through imagery of murky borders and their starts and ends; by explicating on the children’s journey-narratives at key moments; and through accounts of her own experience with obtaining a green card, a narrative thread woven through the book. There is also the ongoing dialogue with her own daughter, who consistently inquires about the children’s fates. As Luiselli weaves each protocol question into the text, she constructs and dismantles timelines, using the messy, complicated, and nonlinear arc of events to portray the complications of defining what a story even is. She writes in the opening, “The problem with trying to tell their story is that it has no beginning, no middle, and no end.”

While the center of a work might be the driving force behind the act of writing itself, it may also surface as parts come together, morph, and grow. Luiselli continuously gestures toward beginnings, middles, and endings by drawing attention to them in both expansive and staccato fashion. A triangle’s center is its balancing point, and for the purposes of creative nonfiction, considering the nucleus of a piece and the ways it can be intersected from different entry points (such as imagery, plot, and dialogue, among others) can help a piece achieve a more harmonious form. 

Geometry is driven by principles. In writing, rules are much less absolute, and a rigid adherence to rule-following can limit creativity. In writing essays and long-form pieces, we must sometimes take productive detours, scrapping and rearranging parts in service to the final harmony of a piece. As Theodor Adorno noted, the essay, “does not permit its domain to be prescribed. Instead of achieving something scientifically, or creating something artistically, the effort of the essay reflects a childlike freedom that catches fire, without scruple, on what others have already done.” Childlike freedom in writing is good.

In writing, we must sometimes take productive detours, scrap & rearrange parts in service to the final harmony of a piece.

And yet, even as very young children, we learn that inventing rules can help a game commence (even if we frequently abandon or revise them once we’ve begun playing).

If Pythagoras was looking for anything, it was beauty. Plato wrote in the Timaeus, “The best bond is one that effects the closest unity between itself and the terms it is combining; and this is best done by a continued geometrical proportion.” Considering the intersections of math and writing at any phase of the creative process can help situate us to leverage voice in ways that complement and enhance an overarching, harmonious vision. As in the Pythagorean theorem, all the vectors work separately and together. Using the insights derived from the equation—or any one we feel suits us—can help invite constraints and create openings that ultimately reify the parts of our work in the same way that a triangle so perfectly holds itself together.

About the Author

Kristin Keane

Kristin Keane is the author of the novella Luminaries and a memoir about grief and time travel, An Encyclopedia of Bending Time. Her writing and research have appeared in the Washington Post, New England Review, TriQuarterly, Electric Literature, Catapult, Reading Research Quarterly, American Educator, and elsewhere.

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