Mathematical forms in poetry 3 – Reflection Symmetry

My granddaughter was making Christmas angels. She folded a piece of card in two, drew half an angel shape on one side, cut it out and opened the fold. Lo! – a perfect, complete angel!

My granddaughter’s angel is a neat example of reflection symmetry; one half of the shape is a mirror image of the other. This is a characteristic of many naturally occurring phenomena: a bird on the wing, the reflection of snow-dusted mountains in the still water of a loch, the hexagonal form of a snowflake. Our own bodies have approximate reflection symmetry.

Symmetry has featured in poetry since early times. The tradition of pattern poetry (also known as shaped or concrete poetry), in which the structure and layout of a poem generate a specific visual effect, extends back at least to ancient Greece. Simmias of Rhodes, who flourished around 300 BCE, is the earliest known poet to have composed pattern poems. Surviving examples of his work take as their form and subject an axe, an egg and a pair of wings, all displaying reflection symmetry. 

The English poet George Herbert (1593 – 1633) likely drew inspiration from Simmias when he composed his celebrated pattern poem ‘Easter Wings’. The poem was originally published sideways, on facing pages to give the appearance of a pair of wings.

The use of reflection symmetry is not confined to pattern poetry. William Blake’s ‘The Tyger’, for example, consists of six four-line stanzas, each with a rhyme scheme of AABB. Structurally, therefore, the first three stanzas are a mirror image of the remaining three, and the idea of symmetry was certainly present in Blake’s mind:

Tyger Tyger, burning bright
In the forests of the night;
What immortal hand or eye,
Could frame thy fearful symmetry?
 

These four opening lines are repeated almost verbatim in the concluding stanza apart from a single deviation – ‘What immortal hand or eye,/ Dare frame thy fearful symmetry?’ – leaving us to ponder the nature of creation and the intent of the Creator.

Contemporary poets have used reflection symmetry in rich and innovative ways. The British poet Julia Copus has devised a poetic form in which the second half of a poem is, line by line, a mirror image of the first. She calls it a specular poem (from speculum, the Latin word for mirror). Adroit variations in the punctuation allow for smooth transitions from line to line and subtle shifts of meaning, as in Copus’s poignant ‘The Back Seat of My Mother’s Car’, where a car window acts as an agent of reflection.

In mathematics (and other disciplines), the t-axis on a graph represents time.  This charming poem by Sarah Glaz, from her collection Ode to Numbers, is reflective in both form and content:

Pedro Poitevin’s ‘Antimatter’, which has some similarities in appearance with Glaz’s poem, takes as its theme annihilation processes between sub-atomic particles and their corresponding antiparticles. Note how, on either side of the central caesura, Poitevin uses words that are mirror images of each other, to connote the particle-antiparticle pairing.

‘Antimatter’ can be found in the anthology Science Poems, published by Penteract Press.

Reflections, another anthology from Penteract Press, showcases a variety of forms of reflection symmetry. Among them are several brilliantly crafted palindromes: poems that, letter by letter, read the same forwards and backwards (recall the SATOR square that I discussed in my earlier blog post on Square Poems). Here’s one by Anthony Etherin, who is a master of the palindrome and other forms of constrained poetry. The turning point of the poem is the s in ‘the fourth line.

Ever since I first learned about Pascal’s Triangle in high school, I’ve been entranced by its elegant reflection symmetry and multifarious patterns (not to mention its range of mathematical applications!). A couple of years ago I wrote a poem, Autumn Sunrise, in which the letter count for each word is based on the triangle’s structure. Taking inspiration from my granddaughter’s seasonal craft activities I’ve written another Pascal’s Triangle poem to reflect the time of year (here the hyphens are included in the word letter count).

Wishing you a peaceful, happy and healthy conclusion to 2020 and a good start to the New Year.

Note: ‘Reflection About the t-Axis’ by Sarah Glaz, ‘Antimatter’ by Pedro Poitevin and ‘Volcano’ by Anthony Etherin are all reproduced here by kind permission of the poets.

References and Further Reading

Birken, Marcia and Coon, Anne C. (2008) Discovering Patterns in Mathematics and Poetry, Amsterdam, Rodopi.

Copus, Julia (1995) The Shuttered Eye, Bloodaxe Books

Etherin, Anthony (2019) Stray Arts (and Other Inventions), Penteract Press

Etherin, Anthony and Daneri, Clara (eds) (2020) Science Poems, Penteract Press

Etherin, Anthony and Daneri, Clara (eds) (2019) Reflections, Penteract Press

Glaz, Sarah (2017) Ode to Numbers, Connecticut, Antrim House

Glaz, Sarah and Growney, JoAnne (eds) (2008) Strange Attractors, Wellesley, A.K. Peters 

Pavlović, B. and Trinajstić, N. (!986) ‘On Symmetry and Asymmetry in Literature’, in Comp. & Maths. with Appls. Vol. 12B, Nos. 1/2, pp. 197-227. Available online at https://core.ac.uk/download/pdf/82028216.pdf

Posted on the 21st December 2020

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