To Look on Beauty Bare: Mathematics as Metaphor in Poetry

Year: 2024 Authors: Shanna Dobson; E.R. Lutken

Core claim

Mathematics can shape poetic structure and language as a rich metaphorical resource adaptable to classroom writing exercises.

Topics

math metaphor, poetry workshop, constraint-based writing, pattern poetry

Domains

Fibonacci sequence, symmetry, calculus metaphors, category theory, poetry, literary form, concrete poetry, creative writing

Methods

workshop exercises, guided composition, example analysis, template-based writing

Media

poems, text templates, structured verse, sample metaphors

Paper text

The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.

Bridges 2024 Conference Proceedings

To Look on Beauty Bare: Mathematics as Metaphor in Poetry

Shanna Dobson¹ and E.R. Lutken²

¹Department of Mathematics, University of California, Riverside, USA; Shanna.Dobson@email.ucr.edu ²Saint Joseph, Louisiana, USA; erlutken@email.com

Abstract

Mathematics is an excellent source of metaphor in poetry. Its capacity to express difficult ideas succinctly can be employed in the structure or language of a poem. In this workshop, participants will be introduced to several examples of mathematics as metaphor in these different capacities. Participants will first explore structure as metaphor, then write poems with two different structural patterns. They will write poems using the constraint of the Fibonacci Sequence, and secondly, poems reflected around a vertical axis. In the third exercise, sample poems with mathematical metaphors within the text will be discussed. Then participants will create poems with metaphors of their own choosing. These exercises can easily be adapted for use in the classroom.

Introduction

Metaphors have been employed throughout recorded history to stretch the mind and to elucidate phenomena that defy simple explanation. Mathematics with its precision and, perhaps surprisingly, with its subject matter (abstract ideas such as infinity, absence, multiple dimensions, etc.) provides a rich source of metaphors for poets. As referred to in the title, Edna St. Vincent Millay’s sonnet “Euclid alone has looked on beauty bare” [10] is an elegant illustration of math as metaphor.

In the first two exercises of this workshop, we will review examples of metaphor in the structure of poems, then write poems involving such structures. In the third exercise, we will describe metaphors in the text of poems. A list of additional possible mathematical metaphors will be provided, and participants will choose a metaphor and write a poem.

Metaphor in Structure

Metaphor can be conveyed by the appearance of the poem on the page, sometimes referred to as concrete or pattern poetry. In ancient times, spiritual poems were sometimes written in the shape of altars. Perhaps one of the most well-known early modern shape poems is George Herbert’s “Easter Wings” [6], its shape suggesting both hourglasses and wings, emphasizing the themes of death and resurrection.

For a mathematical example, the poem “Measured Illusion” [7, p.19] has a form which suggests a (rotated) logarithmic curve for $\ln (\mathfrak{n})$ , but the stepwise lines also echo the graph of the series $\mathrm{n}\to \infty$ , $[1+1/2+1/3+\dots +1/\mathrm{n}]$ . The epigraph for the poem is the equation for the Euler-Mascheroni constant:

harmonic series, Etch A Sketch trace along the logarithmic line an endless staircase cascading down the smoothed channel cobbled road of clear-cut stories worn down to history

581

beads mapped on unspooling strand of mind

dubstep popping, swan-lake dance apace

step and thread exactly separated

by one bare number, carried

119 billion places so far

we know it and don’t;

rational, irrational

transcendental

algebraic?

but we

know

it is

real

0.57721566490153286060651209008240243104215933593992…

Exercise 1

For a quick warm up exercise, we will write “Fib” poems which involve a theme of growth. The Fibonacci numbers in mathematics 1;1;2;3;5;8…are based on a sequence of sums, and thus a specific pattern of growth. Poems using this sequence may be made of syllables, words or phrases as units. The syllabic version was first mentioned in a blog by Gregory Pincus [11]. Some examples can be seen in the Bridges Collection of Fib poems which appeared in the Journal of Humanistic Mathematics in 2022 [5], and a thorough explanation can be found in the Journal of Mathematics and the Arts [3]. Poems can use the Fib structure simply as a form, but in our exercise, we’ll write Fib poems specifically with growth as the underlying theme. That could mean any kind of growth: population, knowledge, despair. Here’s a (not very serious) rabbit poem invented for this paper, titled “Rabbit Fib” by E. R Lutken:

It

takes

at least

two rabbits

to get things going

then they quickly get out of hand

Exercise 2

In the poem “Reflection” (by E. R. Lutken, previously unpublished) phrases are reflected over a vertical axis. This does not produce a real mirror image, since each word is considered as an entity, but does function as if each word were given a set of coordinates. The poem can be read straight across, or down the right and left halves, and has completely different, yet somehow similar perspectives with each reading — the phrasing bringing unusual meanings to each reflected line:

staring into mirrors

angle of incidence=

angle of reflection

clear silver looking glass

invisible wisps of blinks

mirrors into staring

= incidence of angle

reflection of angle

glass looking silver clear

blinks of wisps invisible

To Look on Beauty Bare: Mathematics as Metaphor in Poetry

For this exercise, we will construct reflected poems of a minimum of four lines with at least three or four words in each phrase, and (of course) three or four words in the reflected phrase. In order to write these, we’ll take a close look at the individual words, especially the prepositions and participles in the lines of the sample poem. A list of some common prepositions that might be helpful to draw from in constructing phrases is provided here:

aboard, about, across, after, against, along, amid, among, around, as, at, before, behind, below, beneath, beside, between, beyond, by, down, during, except, for, from, in, inside, instead, into, like, near, of, off, on, onto, outside, over, past, round, since, then, through, throughout, to, toward(s), under, underneath, unlike, until, unto, up, upon, with, within, without.

Below is a template with some example reflective words, more rabbits, and more spaces to try a few words for practice:

Figure 1: Template for reflected poem with sample words.

Metaphor in Language

Metaphors within text can create vivid imagery and enhance creative thinking. In this section, we explore such metaphors in several examples from various areas of mathematics, in order to give some idea of the many possibilities of mathematical metaphors. Reference to the metaphor can be a brief mention as in Millay’s poem cited above, or can pervade every line.

Poems Inspired by Arithmetic Operations

The first poem below “Arithmetic” [7, p.77] simply uses subtraction as metaphor in the last lines.

One cupcake bite, I’m back in first grade: chalkboard dust, spelling apple and you, counting by tens, selling lemonade, three take-away one, the struggle to tie shoes. Mid-east wars have been going solid since, a seventeen-year count of money and lives. I should know but can’t remember much more than black hair, his laugh, piggy-back rides. Statisticians seem to agree near six trillion dollars, but casualties are another story, from one hundred thousand to a million depending on who’s taking inventory. And every one who died must have left someone lost, blank, wondering about the subtraction.

Poems inspired by Algebra

The second poem “Ars Parabola” [7, p.52] requires more of a stretch for the mind. The poem uses the graph of a parabola to elucidate the art of poetry. Aspects of the graph as they relate to rhyme, meter, sound, and meaning in this detailed metaphor are woven throughout the poem.

Can’t say what a poem is or not but graph it and the plot might trace that perfect spot for one whose vertex taps the sun: abscissa makes a run from rhyme to none and metric time devolves from frozen symmetry. Equal distance of free line and focal point defines sure sense, logic’s stare obscured as symbols play in pure sound’s bright flare. White-hot words ignite a sharp savor, the bite, the risk, an ordinate of bliss.

Poems Inspired by Topology

In this third poem, the metaphor is only named in the title, “Borromean Rings”[8]. The mathematical term represents three simple closed curves linked topologically, which cannot be separated, but all come apart when one is cut. This metaphor echoes interpersonal relationships, and is the foundation of the poem.

misty April pall masses of craneflies attended the service

To Look on Beauty Bare: Mathematics as Metaphor in Poetry

of her interrupted arc even the interred might wash away in a record rain when the river scours banks leaving gray cypress logs paddlefish carcasses splintered hulls of boats strewn across low sandbars

after half a century he and I suddenly unable to speak nothing alive but separate circuits burning in thought no defense for watery dissolution

without her interwoven grace only the husks of two selves remain – tongues and hearts just more flotsam sloughed into an unforgiving river

Poems inspired by Category Theory

The final poem “Diamond” [2] by Shanna Dobson uses concepts from category theory to explore the relation of the self to the external world in contemporary poetry. Specifically, the poem utilizes the powerful categorical concepts of universal property and terminality, and a categorical construction called a diamond [12, 1, 9]. A categorical diamond resembles a mineralogical diamond in a particular way. The categorical diamond has interior points that resemble mineralogical impurities, in that they cannot be observed directly. While mineralogical impurities appear as sparkling reflections on the many sides of the diamond, in the categorical diamond, the impurities appear as profinitely many copies of the interior point. Recall, a profinite set is a compact, totally disconnected Hausdorff space. In the poem, Dobson composes a dialogue in powerful confessional style that shifts perspective from the inside to the outside of her categorical/mineralogical diamond.

If I was your diamond, What would profinite see?

I know, sweet Kierkegaard, Reflections only to me

Total internal reflection Makes aporia sparkle

Great concession Categorical Marble

Your diamond is a darkling Unhallowed Sparkling

Dark energy must have Diamonds Adamantem Lions

I hear total internal reflection Red functorial subreption

As Topos Tigers dream of Looking-glass ice-cream

Does no one else see the Black rainbow?

I dare you to compose anything here And hope for anything but what was always here.

Clarion Universal You could not see 4th Dimensional me Profinetely.

Dobson and Lutken

Exercise 3

The participants will be given time to write a poem with a mathematical metaphor. They may use one from the examples above, or from the listed suggestions below (accompanied by some examples mentioned from various authors for further reading), or from their own imaginations.

Particular numbers, such as 0 as void, 1 as unity

Example poems, “Sine Qua Non” by A. E. Stallings [13, p.11], “The Invention of Mathematics” by Amy Uyematsu [14, pp. 30-33]

Imaginary numbers representing the nebulous or inscrutable

Example poem “imaginary territory” by E. R. Lutken [7, p. 36]

Negative numbers echoing mystery, debt, or absence

Example poem “The First Negative” by Sarah Glaz [4, p.17]

Order of operations: order representing time

Example poem “Antecedents” [7, p.38]

Integral calculus as the summation of small details over time, derivatives as instants in time

Example poem “Sonnets from the Calculus” [7, p.84]

Proofs as inspiration

Example poem “Like a Mathematical Proof” by Sarah Glaz [4, p. 47]

Game Theory as conflict

Example Poem “The Truel” [7 p.71]

References

[1] S. Dobson. “A Comprehensive Review of Diamonds and their Use in the Langlands Program.” PhilArchive, 2023. https://philarchive.org/archive/SHAACR-5.

[2] S. Dobson. “Diamond.” Women in MathArt: Research, Creativity, and Teaching. Springer Nature, 2024.

[3] S. Glaz. “Poems Structured by Integer Sequences.” Journal of Mathematics and the Arts 10. 2016.

[4] S. Glaz. Ode to Numbers. Antrim House, 2017.

[5] S. Glaz (curator). “Poetry in the Glade: Bridges 2021 Fib Collection.” Journal of Humanistic Mathematics Volume 12 Issue 1, 2022.

[6] G. Herbert. The Complete Poetry. Penguin Classics. 2015.

[7] E. Lutken. Manifold: Poetry of Mathematics. 3: A Taos Press, 2021.

[8] E. Lutken. “Borromean Rings.” Crosswinds Poetry Journal Volume IX. 2023.

[9] S. Mac Lane. Categories for the Working Mathematician. Graduate Texts in Mathematics, Springer, 2000.

[10] E. St. Vincent Millay. Collected Poems. Harper Perennial Modern Classics, 2011.

[11] G. Pincus. blog entry April 2006. Poetry Foundation. https://www.poetryfoundation.org/articles/68971/1-1-2-3-5-8-fun.

[12] P. Scholze, and J. Weinstein, Berkeley Lectures on P-adic Geometry. Princeton University Press, Annals of Mathematics Studies 207, 2020.

[13] A. Stallings. Hapax. TriQuarterly Books, Northwestern University Press, 2006.

[14] A. Uyematsu. Stone Bow Prayer. Copper Canyon Press, 2005.