Poetry and mathematics

• SUMMARY: Rhyme schemes and meter in poetry can be mathematically analyzed and some new forms of poetry are based on mathematical priniciples.

A popular sentiment is that mathematics and poetry lie on opposite ends of some spectrum. However, both are the works of pure intellect and they share many similarities. Whether considering rhyme, rhythm, or visual layout, effective poetry is rich with patterns that may be analyzed with a mathematical eye. At the same time, succinct mathematics has often been compared to poetry. In the modern era, the connections have become explicit, as mathematics has been co-opted by poets to create new poems, while poetry has been analyzed (and occasionally written) by mathematicians.

Meter and Rhyme

Poetic meter is a formalized version of rhythm. When considering rhythm in spoken language, one can focus on syllable stresses, pitch, tone, or morae. Mora (plural morae) is a term used by linguists to denote an individual unit of sound; a long syllable (such as “math”) consists of two morae, while a short syllable consists of a single mora. A poetic cadence of length n is a pattern of long and short syllables whose total number of morae is n. Cadences play an especially important role in Indian and Japanese poetry, as well as in modern free verse.

Traditional English meter, however, is usually based on stressed syllables (denoted —) versus unstressed syllables (denoted ˘). The most well-known English meters are iambic pentameter and dactylic hexameter, used extensively by William Shakespeare and Henry Wadsworth Longfellow, respectively. In each of these meters, the first word denotes the metrical foot, and the second word denotes the number of feet per line. A metrical foot is a particular pattern of stressed and unstressed syllables. It usually consists of two, three, or four syllables. For example, an iamb consists of an unstressed syllable followed by a stressed syllable. So a line of iambic pentameter is 2×5=10 syllables in length, and the pattern is ˘—˘—˘—˘—. A dactyl consists of stressed syllable followed by two unstressed syllables. A line of dactylic hexameter is 3×6=18 syllables, and the pattern is —˘˘—˘˘—˘˘—˘˘—˘˘—˘˘. Simple counting shows that there are four possible disyllabic feet (pyrrhus is ˘˘, iamb is ˘—, trochee is —˘, and spondee is ——), eight possible trisyllabic feet, and 16 possible tetrasyllabic feet.

There are further formal devices used by poets, often with the aim of producing euphony, which is beautiful sound combinations: assonance (the same sound repeating within a line), alliteration (multiple words beginning with the same consonant), or specific rhyme schemes. Two examples of rhyme schemes are ababcdcdefefgg for a Shakespearean sonnet and abbaabbacdecde for an Italian sonnet. The initial lines of Shakespeare’s “Sonnet 30”:

When to the sessions of sweet silent thought

I summon up remembrance of things past,

I sigh the lack of many a thing I sought,

And with old woes new wail my dear time’s waste:

illustrate alliteration and an “abab” rhyme in iambic pentameter—though “past/waste” is only a near rhyme.

Classical Poetic Traditions and Forms

History is rich with individuals such as Omar Khayyám, who excelled in poetry and mathematics separately without drawing a strong connection between the two. However, in at least one culture, the two disciplines were intimately interwoven. In the Indian Vedic civilization, poetic chants and hymns were utilized to pass down a vast body of knowledge. A portion of this knowledge was mathematical, including theorems in arithmetic and geometry. The method of transmission was mathematical: a single text would be recited in up to 11 different ways. Each way emphasized a different poetic approach, such as applying devices of euphony, pausing every other word, or repeating groups of words forward, backward, and in even more complicated permutations. This method is reminiscent of the error-correcting codes employed in twenty-first century CD audio discs. Just as a scratched CD will often still play seamlessly, the redundancy of the Vedic poetic chants allowed for an uncorrupted oral transmission year after year.

A poetic form offers the writer a set of constraints to which the work has to conform. There are many such prescribed forms, some very strict, and others quite open. Perhaps the best-known forms are the sonnet, ode, and haiku. The traditional Japanese haiku, for instance, comprises three lines of 5, 7, and 5 morae, respectively. In English, the syllable is used as counter instead of the mora. Similarly, nursery rhymes, which are considered short poems, often have strong mathematical ties, using rhyme and pattern to create memorable lines.

A sestina is a 39-line poem consisting of six 6-line stanzas followed by a 3-line envoy. The six words ending the lines in the first stanza must end the lines in each of the subsequent stanzas, but in a fixed new order. The permutation of the words may be denoted

This notation indicates that the word ending the first line must end the second line of the next stanza, the word ending the second line must next end the fourth line, and so forth. This permutation is then repeated from one stanza to the next. Mathematicians Anton Geraschenko and Richard Dore have investigated a generalized notion of a sestina to an (n-line-per-stanza) n-tina where n can be any whole number. They prove that if the n-tina is to be interesting—in the sense that the pattern does not repeat before the poem ends—then 2n+1 must be a prime number.

Modern Directions

In the modern era, poetry is more often read on a page than spoken aloud, and the two-dimensional geometry of the text is visible. For example, a poem in traditional meter naturally takes on a ragged-on-the-right rectangular shape. The diamond shape of a diamante poem, introduced in 1969 by Iris Tiedt, naturally results from the prescribed construction of its seven lines: one noun, two adjectives, three gerunds, four nouns, three gerunds, two adjectives, and one noun. When poetry purposefully forms a recognizable shape it is called “shape poetry,” “griphi,” “carmen figuratum,” or “concrete poetry.” The idea of a shape poem is nothing new: around 300 B.C.E. the Greek poet Simias of Rhodes wrote Pteryges, Oon, and Pelekys (Wings, Egg, and Hatchet, respectively) poems whose shape mirrored their subject. Recently, shape poetry has flourished: Lewis Carroll gave a mouse’s tail; Guillaume Apollinaire, the Eiffel Tower; E.E. Cummings, a snowflake; John Hollander, a swan with reflection; and Mary Ellen Solt, a forsythia bush. In the 1990s, Eduardo Kac moved poetry into the third dimension with his holopoetry: poetry that floats above a surface as a hologram and takes different meanings when viewed from different angles.

The group Ouvroir de Littérature Potentielle (Workshop of Potential Literature), or Oulipo for short, originated in 1960 with 10 writers, mathematicians, and philosophers. The group has the twin goals of elucidating old and creating new rigid forms for potential literature. A prototypical example of their oeuvre may be seen in Raymond Queneau’s Cent Mille Milliards de poèmes (One Hundred Thousand Billion Poems). This work appears at first glance to consist of 10 sonnets. However, it also includes the instruction that the reader should consider all poems that may be formed by choosing a first line from among the 10 given, then a second line, and so forth. At each stage, the reader has 10 lines from which to choose, and there are 14 lines, so this work encompasses 10¹⁴=100,000,000,000,000 complete sonnets.

Many forms of poetry have emerged that are very consciously mathematical. The “pioem” is a poem whose words are of length determined by the digits of π in order: 3, 1, 4, 1, 5, 9,… . The number of words in a pioem is not predetermined; it may be as long or short as the author desires. The “Fib” is a poetry form that, like the haiku, prescribes the number of syllables to appear in each line. This prescription is based upon the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13,… in which each number is the sum of the previous two numbers. Interestingly, the Fibonacci sequence not only gives a form for poetry, but also arises in the mathematical study of poetic cadence. If Cn denotes the number of poetic cadences of length n, Indian polymath Acarya Hemacandra showed

Cn = Cn−1 + Cn−2.

This equation, known as a recurrence relation, generates the Fibonacci sequence. Hemacandra’s observance was about 50 years prior to Leonardo of Pisa’s 1202 treatise Liber Abaci, from which the Fibonacci sequence derives its name.

Bibliography

Birken, Marcia, and Anne Coon. Discovering Patterns in Mathematics and Poetry. Rodopi, 2008.

Filliozat, Pierra-Sylvain. “Ancient Sanskrit Mathematics: An Oral Tradition and a Written Literature.” History of Science, History of Text, edited by Karine Chemla, Kluwer Academic, 2004.

Fussel, Paul. Poetic Meter & Poetic Form. Random House, 1965.

Hart, Sarah. “The Patterns of Poetry: On the Mathematical and Poetic Value of Numbers.” Lit Hub, 12 Apr. 2023, lithub.com/the-patterns-of-poetry-on-the-mathematical-and-poetic-value-of-numbers/. Accessed 11 Oct. 2024.

Lamb, Evelyn. “How Poetry and Math Intersect.” Smithsonian Magazine, 24 Apr. 2018, www.smithsonianmag.com/science-nature/how-poetry-and-math-intersect-180968869/. Accessed 11 Oct. 2024.

Robson, Ernest, and Jet Wimp, editors. Against Infinity: An Anthology of Contemporary Mathematical Poetry. Primary Press, 1979.

Wolosky, Shira. The Art of Poetry: How to Read a Poem. Oxford UP, 2001.