### unlock the mathematical secrets of verse

#### Science and poetry were once closer than they are now, writes Steve Jones in response to National Poetry Day.

By Steve Jones

Lord Byron, a rather better poet than Erasmus Darwin and a fan of Newton. Photo: GETTY

Thursday is National Poetry Day, a fact that once would have been of much interest to scientists. In the 1700s several poems appeared that passed on a scientific message. The best known is The Loves of the Plants, by Erasmus Darwin, who in 1791 set out in verse an account of the sexual habits of the vegetable world. He used heroic couplets, in which the rhyme pattern is AA, BB, CC and so on (for the sensitive plant, for example, he wrote that "Weak with nice sense the chaste Mimosa stands,/ From each rude touch withdraws her timid hands;/ Oft as light clouds o’erpass the summer glade,/ Alarm’d she trembles at the moving shade"). Byron, a rather better poet, liked the form ABABABCC and in his epic Don Juan even manages to squeeze in a mention of Newton ("And this is the sole mortal who could grapple/ Since Adam, with a fall or with an apple.")

Overblown as Erasmus Darwin’s verses might seem nowadays, the point of poetry was pattern; to use a strict structure of rhythm and rhyme as a framework for words of passion or pedantry that would become fixed in a reader’s brain. Robert Frost put it neatly when he wrote that "Poetry without rules is like tennis without a net".

Poetry, in other words, is mathematics. It is close to a particular branch of the subject known as combinatorics, the study of permutations – of how one can arrange particular groups of objects, numbers or letters according to stated laws. As early as 200 BC, writers on Sanskrit poetry asked how many ways it is possible to arrange various sets of long and short syllables, the building blocks of Sanskrit verse. 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.