Authors / Fiction / Go Figure

GO FIGURE: The Hyperbola Stories – Part 1

by Susan Sechrist

“Go Figure” is a regular feature at Bloom that highlights and celebrates the interdependence and integration of math and literature, and that will “chip away at the cult of youth that surrounds mathematical and scientific thinking.”  Read the inaugural feature here.


My notebook from February 4, 2020 is littered with pencil sketches of Cartesian coordinate systems, parabolas, and hyperbolas. There are also a smattering of disembodied words surrounding the hastily drawn and lopsided figures:

“mapping meaning”
“glitch pedagogy”
“democratizing the tools”
“do-it-yourself narrative”
“sociocultural and material coherence”

These notes were from a meeting with my friend and colleague, fellow PhD student Rachel Horst, whom I first met in a philosophy of science class that focused on historical contingency and Support Independent Bookstores - Visit IndieBound.orgcounterfactual analysis. One of the areas we studied was how authors use contingency and alternative history in narrative. Alternative histories are big business in literature and film – think of The Man in the High Castle, The Plot Against America, The Boleyn King, etc. They are often speculations about what would have happened if the bad guy won the war or a pivotal, childless monarch had an heir, though there are many other compelling treatments of branching time and untrod paths. One of the best examples is Jorge Luis Borges’ The Garden of Forking Paths – on its surface, a World War I spy story, but in its twists and turns, an elaborate many-worlds scenario where multiple, incompatible outcomes coexist. Rachel and I immediately bonded over this story’s strangely surprising yet inevitable iterations, reflections, and echoes. From talking about Borges, Rachel and I forked off into the directions our own work was taking. Rachel’s fascinating research is focused on how storytelling can be used as a way to shape our futures and how narrative inquiry can help us think creatively about the many intractable social, environmental, and political problems we currently face. We are both bloomers, having shifted gears to juggle professional careers and family while writing and studying in mid-life.

Rachel is a consummate academic and creative thinker. I admire her research chops immensely; her ability to distill a complex article into something more connective and generative is like watching someone unravel an already beautifully knitted sweater into a kinked pile of yarn only to reweave something truly unexpected out of it. Over a few weeks of coffees and beers, we decided to collaborate on a writing project together, something that continued our interest in contingency and the hyperbolic. We would each write a short story inspired by my most recent (and enduring) mathematical crush – the rectangular hyperbola and its hidden lemniscate. Go Figure readers will recognize it from my feature on Janna Levin’s A Madman Dreams of Turing Machines.


This mathematical figure features twin hyperbolic curves, mapped back to back and never intersecting. The inverse of the hyperbola is the lemniscate, the familiar figure-eight symbol for infinity. Three points along the x-axis define the lemniscate: the focus of each hyperbola and zero, the origin of the graph. (Visit this Wikipedia entry on the Lemniscate of Bernoulli for a mesmerizing animated gif that clearly derives the relationship between the hyperbola and the lemniscate.)

As we played with the mathematical figure, Rachel also found the lemniscate’s algebraic equation:

She used the variables and their relationship to each other to shape her story, about two divorced women with children moving into a large house together. My story was about a woman seeing a therapist for her maladaptive daydreaming disorder, trying to integrate her hidden, internal self with a more socially acceptable and functional form.


By mid-March, the province of British Columbia had responded swiftly and resolutely to the emerging COVID-19 pandemic. My husband and I were both working and studying from our apartment in Vancouver. Our local markets were denuded of eggs, toilet paper, and beer. Then, in April, my mother-in-law died suddenly. The Canadian border was closed to travelers to and from the United States due to the virus – we wouldn’t be able to travel to Connecticut. We grieved from afar, making arrangements on the phone and via Zoom for a future funeral when the family could gather safely. It was a surreal and sad and lonely experience. My ability to concentrate on much of anything plummeted.

Then I got an email from Rachel – our collaborative writing project, which we titled The Hyperbola Stories, was accepted for presentation at a virtual conference. Rachel suggested we incorporate COVID and quarantine and heartache into our emerging narratives and allow the unease and discomfort and loss to shape the weird collaborative bubble that we were designing.


An excerpt from Remarkable Curves, by Rachel Horst

They moved into the house one vacant and capacious afternoon near the end of winter. Through the uncovered windows they could see wide swathes of a bleached and dull blue sky that was like construction paper left out in the sun too long. All the doors in the house were open when they arrived, as were some of the windows, and they wondered what spirits or smells the previous tenants were airing out for them. The hallways felt impartial and bland and the children ran through them, shrieking and laughing and filling up the house, ahead of their things, with the promise of hilarity. The mothers had already discussed the geometry of the house ahead of time, over glasses of Merlot at a suburban restaurant nearby. It was a chain restaurant that served artichoke dip in ceramic boats and wine in enormous, long-stemmed glasses with cups as big as grapefruits. They had planned out the gridwork of their shared existence and how they would navigate the kitchen, one of the many pivot points around which, they agreed, people became a family.

They would share groceries and household duties and alternate the cooking between them with the sort of amiable flexibility that would be indicative of their household. Alexis would prepare Kai’s lunch in the evening, Wynn would prepare Nic’s in the morning – that way they wouldn’t be competing for counterspace. Alexis and her daughter Kai, who was six years old, would take the two eastern rooms with access to the bathroom and a view of the neighbour’s nasty monkey tree, the scaly branches of which hung low over the fence and into their yard. Wynn and her son Nic, who was four and a half, would take the two western rooms.


After we read each other’s stories, we strategized on what it meant to collaboratively “hyperbolize” them further. I have lots of notes on this, too – how does one take the tangent or derivative of a sentence? How does a paragraph flow like the curve of a figure on a graph? What is the area under that literary curve? I wanted my decisions to be empirically and mathematically sound, not just arbitrary or simply interpretative. We decided to let that process take organic form – each of us would decide what it meant to be iterative and reflective, like the lemniscate, and divergent like the hyperbolic curves. We would each decide how those approaches overlapped or intersected, if at all.

I decided to do a text analysis of Rachel’s Remarkable Curves, to find the most frequently used words. These words became the forks in the road of the story, the variables that shaped its first iteration. What would happen if I took a different path, if I used the inverse of a pivotal word? What even is the inverse of a word? Its antonym? I played with changing words and bending phrases and experimenting with form to reshape the story, while trying to retain the overarching plot or defining grid – two families coming together to share the same space.

[A digressive note on text analysis – it sounds deconstructionist and cold and decidedly uncreative and anti-literary, but these techniques, refined by digital humanities researchers like Lauren Klein, Sara Ahmed, Bethany Nowviskie and others, address the disturbingly deep furrows in our thinking that can emerge in our stories. Granted, distant reading or computational linguistics is typically used to analyze very large literary systems – whole subgenres of literature or at least, whole novels, not a single short story. These data that emerge from this analysis can be illustrative of what’s there and what’s not there. What’s not there is often the language, ideas, and concerns of the marginalized. Or, those marginalized ideas and characters are often there in the story but treated as so commonplace or unimportant as to be invisible or incorporeal. This, of course, includes marginalized peoples – women, people of color, indigenous people, people without economic power – but it can include the differently-animate – other living creatures; or the inanimate – the ecologies and environments and phenomena of the universe seen only as exploitable human resources.]

I did a simple word frequency analysis of each paragraph in Rachel’s story (using Voyant Tools – it’s free online) and developed a graphical representation that would help me reset the initial conditions of her complex system. It felt surprisingly like turning a lovely woven object over and over in my hands looking for where its crenellated folds parted, where the embedded loops intersected or where the contour lines connected along the unseen rise and fall of its topographic map.

Here’s the graphical representation of the word frequency in the excerpt from Remarkable Curves that I included above:

The large words in the graphic, like “house” and “windows” and “rooms,” are the ones that appear more frequently than the smaller ones, like “chain” and “artichoke” and “big.” Their orientation and color in the graphic is arbitrary, but I also used these features of the image to create my own interpretation of Rachel’s paragraph. I used this mix of order and random chance to create my own view of what I sensed was the plot of her story – the foreshadowing of complication that can emerge from comfort, community, and domesticity:

From the bathroom emerges a bleached smell; the previous tenants airing the place out, killing the virus. The place is vacant except for the ceramic branches of some unfinished construction project, an amateur attempt at a fountain or planter? Alexis can’t tell. Wynn is obsessed with the counterspace in the kitchen and the chain of poorly painted blue frames around the living room windows. She says, “these look like those square glasses my mother used to wear in the 70s.” This won’t be home, but it is a good house. It can be their household together.

I did this throughout the entire story, creating a new text that experimented with the literary and material objects that defined Rachel’s fictional world, the intentions of her characters and the trajectory of the plot. What I created felt new yet related, genetically connected but differentiated. It was an intriguing and empowering experience as a reader – to actually get into the text and change its initial conditions. As a result of this experimentation, this counterfactual process – what happens if I do this instead of that – the text ceased to be an edifice and instead became a living system. And the DNA of that living system is built into the original story, like the lemniscate is built into the hyperbola; like the contingent is built into the historical.

My rattled, unfocused, distracted mind was suddenly enraptured by the metaphoric and mathematic connections: my reflection of Rachel’s story was more than a new spin around the curves of the beautiful, predictable lemniscate. There was something inherently divergent in that persistent, stable form. A change in the balance of what is written and what it marginalized and what is outright hidden. Once that balance is shifted, the text takes its own breath; the expected features of a botanical are altered by a chromosome that mutates, or a storm strengthens or weakens with a minor meteorological shift in wind. I started thinking about grander metaphors the more I dabbled in the story. Dare I dream cosmologically? Can a story be like a star destined to an afterlife as a supernova or a black hole, decided by a mote of charge or heat?

Or, it could be the quarantine anxiety talking.

In Part 2, I’ll share an excerpt of my story and Rachel’s take on it, and we’ll have more conversation about the hyperbolizing process, as well as what startled us when we started putting components of each hyperbolized story into yet another, more intricate fiction. It’s not as Frankenstein-y as you might think. We’ll also celebrate authors like Borges, Ted Chiang, Rivka Galchen, Ian Williams (a bloomer), Ursula K. Le Guin, Jane Austen and others who inspired each of us to engage in literature as readers, authors, researchers, and experimenters.

Bloom Post End

Susan Sechrist is a freelance technical writer and PhD student at the University of British Columbia, striving to better integrate her creative and mathematical sides. She published her first short story, the mathematically-themed “A Desirable Middle,” both in Bloom and the Journal for Humanistic Mathematics.

Feature photo courtesy of Susan Sechrist.

One thought on “GO FIGURE: The Hyperbola Stories – Part 1

  1. Pingback: GO FIGURE: The Hyperbola Stories – Part 2 Half Measures | Bloom

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