How Pascal's Triangle Explains Poetry

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Taking apart poetry with mathematics? Sacrilege! Or is it? Genetics professor Steve Jones shows how the two ancient disciplines can get along in The Telegraph. Certainly poetry uses patterns in its rhyme schemes, and poets such as Robert Frost have famously not just accepted but celebrated the place of rules in verse. But the math-poetry relationship goes far beyond a mere appreciation of an iamb or an ABAB structure, he explains. The arranging of long and short syllables, crucial even to Sanskrit poets "as early as 200 BC," has a hidden bit of numerical beauty:

A syllable is short, with one beat, or long, with two. In how many ways can a metre of four syllables be constructed? Four shorts or four longs have just one pattern for each, while for three shorts and a long, or three longs and a short, there are four (SSSL, SSLS, SLSS, and LSSS, for example). For two of each kind of syllable, there are six possibilities. Do the sum for metres of one, two, three, four and more and a mathematical pattern emerges. It is Pascal's Triangle, the pyramid of numbers in which the series in the next line is given by adding together adjacent pairs in the line above to generate 1, 1 1, 1 2 1, 1 3 3 1, 1 4 6 4 1, and so on.

As in a great poem, hidden within that elegant structure are deeper truths that touch on apparently unrelated things; on fractal patterns, on the theory of numbers, on primes, and of complexities too deep to be accessible to mere mortals untrained in the mathematical art. One useful property is that Pascal makes it possible to ask in how many ways it is possible to arrange a group of objects, be they footballers in a league, or lines in a poem.

[Hat tip: Arts and Letters Daily]

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