Points and Planes: On “Hypatia on St. Katherine”

Kelly Krumrie

You might not yet have read “Hypatia on St. Katherine.” I do wonder how important that is for what I’m writing about now. The details of these two women are available on the internet; my story is a narrative based on recorded history. On the page, the story is landscape-formatted and has two columns. The column on the right is a condensed account of Hypatia, the earliest recorded female mathematician who was murdered by Christians around 415 ce. It is written in the first person. The column on the left is a condensed account of St. Katherine of Alexandria, a Christian murdered by pagans around 305 ce. It is written in the third person, but from the point of view of Hypatia—she’s telling the story. Last, there is a short list of texts I used and language I borrowed. But this is just a description of the story’s matter and medium.

In July of 2018, I facilitated a mathematics workshop for teachers, and we talked a lot about coordinate planes (x-y axes). How could the teachers make the planes real for the students? How are these positions not abstractions? We mapped out a field, sketched a garden in it. We read stories on the history of cartography. Examples of how to layer meaning there. A few days later, I read about grids in James Elkins’ Six Stories from the End of Representation:

Grids and sets of parallel lines take pictures out of lived experience and place them in a realm where visual phenomena are parceled out in discrete pieces… An empty gridded surface, like a sheet of graph paper, is a way of announcing that something is going to happen: an object is going to be measured, or an image is going to be transferred from one scale to another, or a form is going to be drawn and studied… [X-Y graphs are] radical abstractions from reality. They are not expected to correspond with normal habits of viewing or criteria of realism. The objects in them are detached from real-world settings: they are distorted and transfixed by the gridlines, ready for sustained analytic attention.[i]

These stories are flat and not, representations and objects, myth and fact: Hypatia was a real person whose work is known only through references in others’ writing. Her contemporaries wrote to and about her; her father thanked her in one of his texts. Katherine’s story came about centuries after her death with no evidence of her having lived at all. Yet she is venerated and immortalized. One explored mathematics, the other god. They were in the same place at the same time, both martyred, both vague enough to merge:

The objects are both visible (in the sense that they are unambiguously recorded) and invisible (in the sense that there is almost nothing to see).[ii]

I am imagining this piece printed on tracing paper or transparencies. The section on Katherine, the section on Hypatia, and a bibliography (not the bibliography already there but one much expanded, an editable, ongoing collection of resources that led to and lead back to this compression of information and thinking) would each be printed on separate pages.[iii] The bibliography would be last, and when the other two pages lie on top of it, the text is visible but kind of unreadable—it darkens the layers. Katherine and Hypatia—I am not sure who would come first. Lines on top of each other, simultaneous, dynamic, but inherently two dimensional, always paper. This object might be impossible or virtual: a flickering between two women, a reference list creeping longer.

Though I am imagining these pages lying flat and occupying two-dimensional space (think of multiple graphs on the same plane), each line, or even words within lines or notes in the bibliography… all is coordinate. A coordinate is a point on the plane, and by definition has no dimension at all. A coordinate is a representation of information. What if that information is myth? God? A lost equation that even if found I couldn’t understand? How do we connect the coordinate to the world?

To be a martyr you must have a body. These two women, points of data, map to one body. Polar narratives, satellite fact.

Stories and biographies “[are ways] of announcing that something is going to happen”—on the page but also immeasurably beyond it.[iv] Here, in this kind of written representation, we’re not only connecting words to words and sentences to sentences, points into lines—a shape we can see and measure—

(Reading and writing are like measurement: how we use or interpret language and concepts according to understood criteria, in this case recorded history, as one would measure the length of an object against a ruler.)

—but reaching out into the z-axis (the third dimension), coming off the page and into our various spheres, references, and resources. This is how, perhaps, the coordinate becomes real: when the paper must reach out to a / the world. [v]

Some information is not quite tangible until assembled, like we can’t interpret the data without organizing it in a particular way, using “sustained analytic attention,” the internet, or a dictionary, a pencil in hand noting that an astrolabe is—

centrifugal force is—

was it tiles or shells that killed her


[i] Elkins, James.Six Stories from the End of Representation: Images in Painting, Photography, Astronomy, Microscopy, Particle Physics, and Quantum Mechanics,1980-2000. Stanford University Press, 2008, p. 66.
[ii] ibid., p. 111, on the visual records of distant galaxies
[iii] The idea of the transparent flap bibliography came up in a fiction workshop this spring for some of my other work—so the idea is not mine.
[iv] Consider Hypatia’s relationship to her ostraka.
[v] If you’re interested, another text that has generated some of my thinking here is Angus Fletcher’s The Topological Imagination: Spheres, Edges, and Islands (Harvard University Press, 2016).

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Kelly Krumrie is a PhD student in Creative Writing at the University of Denver, and she has an MFA from the University of San Francisco. She often writes about children, houses, plants, and math. Her work is forthcoming from or appears in SHARKPACK AnnualBurning House PressSleepingfishShirley MagazineYour Impossible Voice, and elsewhere.