Sestinas and Set Theory, Oh My!

The philosopher Martin Heidegger describes poetry in his book, Poetry, Language, and Thought, as “the saying of the unconcealedness of what is” and the “intimate unity of being with language and word.”

The Stanford Encyclopedia of Philosophy discusses set theory as such: “[t]he axioms of set theory imply the existence of a set-theoretic universe so rich that all mathematical objects can be construed as sets. Also, the formal language of pure set theory allows to formalize all mathematical notions and arguments.”

From these two definitions, we can see that math and poetry are not a polarized as one might think. Both are tools of organizing and arguing for a version of reality. An interesting thing happens when you apply set theory to a very specific poetic form — the sestina.

Sestinas are thirty-nine line poems comprised of six sestets and an envoi. The major key of a sestina are its six determined end words that shift position through out the poem. Below is an example of a sestina by Elizabeth Bishop —

September rain falls on the house.
In the failing light, the old grandmother
sits in the kitchen with the child
beside the Little Marvel Stove,
reading the jokes from the almanac,
laughing and talking to hide her tears.

She thinks that her equinoctial tears
and the rain that beats on the roof of the house
were both foretold by the almanac,
but only known to a grandmother.
The iron kettle sings on the stove.
She cuts some bread and says to the child,

It’s time for tea now; but the child
is watching the teakettle’s small hard tears
dance like mad on the hot black stove,
the way the rain must dance on the house.
Tidying up, the old grandmother
hangs up the clever almanac

on its string. Birdlike, the almanac
hovers half open above the child,
hovers above the old grandmother
and her teacup full of dark brown tears.
She shivers and says she thinks the house
feels chilly, and puts more wood in the stove.

It was to be, says the Marvel Stove.
I know what I know, says the almanac.
With crayons the child draws a rigid house
and a winding pathway. Then the child
puts in a man with buttons like tears
and shows it proudly to the grandmother.

But secretly, while the grandmother
busies herself about the stove,
the little moons fall down like tears
from between the pages of the almanac
into the flower bed the child
has carefully placed in the front of the house.

Time to plant tears, says the almanac.
The grandmother sings to the marvelous stove
and the child draws another inscrutable house.

Now, If we were to render this poem into set theory there are a few things we need to discuss first. There are two ways to talk about sets, extensional and intensional. Extensional sets are sets in which the members of the set are only listed. Intensional sets are sets in which the members of the set are described. With most sets, there frequently exists a separate power set. A power set is a set in which all the members of the original set are represented.

Here’s the fun part—below is an extensional set representation of Elizabeth Bishop’s end words from Sestina —

S1 = {house, grandmother, child, stove, almanac, tears}

S2 = {tears, house, almanac, grandmother, stove, child}

S3 = {child, tears, stove, house, grandmother, almanac}

S4 = {almanac, child, grandmother, tears, house stove}

S5 = {stove, almanac, house, child, tears, grandmother}

S6 = {grandmother, stove, tears, almanac, child, house}

E1 = {almanac, stove, house}

S1 (stanza one) becomes the power set and the poem, written out in its entirety, becomes the intensional set. As seen in traditional mathematical set theory, extensional sets often times come across as bland and random—it is not until extensional sets are translated into their intentional versions that the set gains any interest or meaning. The same is happening here with the sestina. Bishop’s end words rendered as a plain list could have a variety of correlations and meanings; it is not until the end words are placed in stanzas and reordered throughout the poem that we get Bishop’s own personal argument for the connection between those words.

Although math and poetry seem like two practices that would be rival sports teams in some sort of tangent universe, they both work towards achieving the same goal—organizing and creating meaning of objects and experiences in a seemingly random chaotic world. Or at least, that is my two cents. Thanks for reading!


Tali Cohen is an MFA candidate at Virginia Tech. She likes thinking about outer space, soy milk in her coffee, and hopes to one day be able to do a cartwheel.

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