Mathematical forms in poetry 3 – Reflection Symmetry

Reflection symmetry, where one half of a shape is a mirror image of the other, 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 300 BC when Simmias of Rhodes composed poems in shapes that displayed 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.

Palindromes are poems that, letter by letter, read the same forwards and backwards (the SATOR square is an example of a palindrome). WAR ENDS WAR, by Anthony Etherin, consists of two sonnets that are not only palindromes but also perfect anagrams of each other.

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.

There are many striking uses of reflection symmetry in The Fib Review, such as Colin Bell’s ‘Cultivation’ and Tyson West’s bilateral poem ‘Equis Homo’ in Issue #39 Summer 2021.

Marian’s book From Fibs to Fractals: exploring mathematical forms in poetry, will be published by Beir Bua Press later this year.

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

Updated on 20th August 2021. This is a summary of my former blog post on Reflection Symmetry.

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