var _gaq = _gaq || []; _gaq.push(['_setAccount', 'UA-39795839-1']); _gaq.push(['_setDomainName', 'mathophilia.com']); _gaq.push(['_trackPageview']);

(function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })();

Dear readers,

Today is World Poetry Day, and I would like to draw some parallels between poetry and mathematics. It’s certainly true that they are quite different, but the connections are much more significant than one might expect. I will describe some of them, drawing on my experience as a reader and (former) writer of poetry.

The most superficial connection is in the fact that both poetry and mathematics are abstract arts. While the kind of abstraction is different between the two, it is nevertheless impossible to appreciate either one without a proper understanding of the abstraction (though arguably, poetry is more accessible to those without a special training than mathematics). Both poetry and mathematics illuminate a certain part of our experience – poetry, of the real world, and mathematics, of the conceptual world it describes. Just like a good poem can provide insights into particular situations, a good work of mathematics (this can be a model, a theorem, or an analysis) can provide insights into particular areas it is examining. Of course, I’m using “good” in a subjective way, which illustrates another similarity between poetry and mathematics – their beauty is subjective, and repeated exposure leads one to develop a particular taste for the kind of poems, and the kind of mathematics, that one enjoys the most. For instance, I tend to enjoy form poetry with a regular rhythmic structure and containing unusual imagery; similarly, I tend to enjoy mathematical models and methods with a small number of tunable parameters, explicitly stated assumptions and that can be examined analytically rather than exclusively with numerical simulations.

This leads me to the next point – both poetry and mathematics deal with patterns. While a lot of contemporary poetry is written in free verse, historically, most poetry has been written using pre-defined patterns, or forms, such as the sonnet, the villanelle, the rondeau, or, in the East, the haiku, the ghazal, the rubai (plural: rubaiyat), and so on. Each of these forms imposes particular restrictions on one of the following poetic “parameters”: length (number of lines per stanza and in total); rhyming pattern (which lines line with which other ones); meter (which syllables bear stress and which do not); and number of syllables in each line (such as the 5-7-5 pattern of the haiku). One of my poems included in an embarrassing treatise on writing poetry addressed to my friends that I put together 10 years ago (incidentally, while taking breaks from studying abstract algebra), made use of 3 of these restrictions. The entire poem had 6 stanzas, each stanza had 6 lines, and each line had 6 syllables. Mathematics can not only suggest other interesting forms, but can also be used to count the number of possibilities. For instance, the number of possible rhyming patterns of a certain length is counted by the Bell numbers, while the number of possible non-crossing rhyming patterns (eg. excluding ABAB) is counted by the Catalan numbers, mentioned in one of my earlier posts.

But, just as poetry can inspire a mathematical analysis of structure, mathematical concepts have also inspired numerous poems. There is an entire blog dedicated to poems inspired by mathematics. I’m a big fan of using mathematical ideas in poetry, and still recall bits and pieces of a love poem I wrote in undergrad starting with the words “You are not isomorphic to any other”. But, of course, the unrivaled champion of mathematical poetry is, in my opinion, “The finite simple group of order 2” from this post.

Despite these various connections, there has only been one person to my knowledge who has made a significant contribution to both mathematics and poetry – the great Persian philosopher of the 11^{th} century Omar Khayyam. He did a lot of fundamental work in algebra, discovering what we now call Pascal’s triangle, and proposing a systematic method for solving cubic equations by finding intersections of conic sections: parabolas, hyperbolas, ellipses and circles. In addition to this and other mathematical accomplishments, he is most well-known as a poet for his rubaiyat (quatrains), which are very concise yet profound. Here is one of my favorites (original here), translated by Edward Whinfield:

Of mosque and prayer and fast preach not to me,

Rather go drink, were it on charity!

Yea, drink, Khayyam, your dust will soon be made

A jug, or pitcher, or a cup, may be!

On that note, I hope you all enjoy the official beginning of spring as well as World Poetry Day!

Pingback: Mathematics and Theater – a Tale of Two Plays | Mathophilia, or the Love of Math