The essence of poetry is ambiguity. A good poem can be read many times; each time you read it, some new facet or shade of meaning presents itself to you.
By contrast, the essence of written mathematics is clarity. The writing must say exactly what the author means, and explain it clearly.
So probably there is no deep connection between these two subjects. (And yet I can’t help thinking that there must be more to it…)
In fact there is one place where mathematics and poetry meet. Consider cryptic crosswords: a good clue certainly should have poetry about it, but the answer should be completely precise. There is nothing more irritating to a crossword solver than an inexact clue or one with superfluous words.
More generally, the kind of poetry with very strict rules often appeals to mathematicians. The sonnets, triolets, villanelles, and so on of yesteryear are not as popular as they were, but mathematicians are attracted to forms like the limerick, the haiku,…
Double dactyl, or “Higgledy-piggledy”, is a verse form. It is described in a nice Wikipedia entry which gives lots of examples, all of them biographical; and indeed, this seems to be a defining feature …
I was able to make use of the result of his creativity on one occasion. Here is a picture of me leading the audience in a recitation of a higgledy-piggledy on the Sims conjecture, at a conference for Cheryl Praeger’s birthday (she was one of the team who proved it).
But I want to talk about an experiment I did a few years ago on an older form, the sonnet. I had been given the Wordsworth Book of Sonnets as a present. Contrary to what you might think, this is not a book of sonnets by the Lake poet; but a book of sonnets by many hands, published by a company called Wordsworth, who specialise in cheap editions of out-of-copyright material. The book was edited by Linda Marsh and published in 1995.
There are rules for sonnets, but all the great poets who have used the form break these rules. Roughly speaking,
- there are fourteen lines, each an iambic pentameter;
- the lines split as 8+6, with a development of subject-matter or tone from the 8 to the 6;
- the rhyme scheme is ABBA ABBA CDEDEC (though the scheme for the last six lines is quite variable).
Hopkins wrote many sonnets, and used the rules very creatively; his sonnets may be shorter (one famous one is 10 1/2 lines, split as 6+4 1/2) or longer; extra feet are often added to a line.
Anyway, I decided I could regard the entries in the Index of First Lines in the book as an acceptable selection of sonnet lines (that is, breaking the rules to the degree that great poets thought appropriate). Now it was a case of dividing them up according to rhyme, and selecting lines with an eye to the sense. As you might expect, I had to watch the rhyme very consciously, and meanwhile something unconscious happened with the meaning; I think the overall effect is not too bad. Here it is.
Earth has not anything to show more fair!
Now sleeps the crimson petal, now the white;
In the long, sleepless watches of the night,
All Nature seems at work. Slugs leave their lair,
Keen fitful gusts are whispering here and there,
The azured vault, the crystal circles bright.
O soft embalmer of the still midnight,
What has this bugbear Death that’s worth our care?
Beauty, sweet Love, is like the morning dew.
There is a silence where hath been no sound;
It is the season of the sweet wild rose.
Lord, With what care has thou begirt us round!
When I consider every thing that grows,
I seek but one thing – to make sure of You.
Somehow there is a progression, from night to morning, and from a rather material view of nature to one which is more spiritual (I think).
For the record, the lines are the first lines of sonnets by Wordsworth, Tennyson, Longfellow, Coleridge, Keats, King James I, Keats, Walsh, Daniel, Hood, Meredith, Herbert, Shakespeare, and Mary Queen of Scots. Poetry was clearly a right royal occupation once!
P.S. It occurs to me that, as Martin Gardner once advocated, I have reversed Lewis Carroll’s maxim “Take care of the sense, and the sounds will take care of themselves”.
P.P.S. Ivar Ekeland, in The Broken Dice, and other Mathematical Tales of Chance, (University of Chicago Press, Chicago, 1993), says:
The formalism and rigor of skaldic poetry is in no way inferior to that of modern mathematics, and anyone who is able to weave kjenninger while respecting the rules of alliteration will also be able to derive theorems from one another following the rules of logic. In both cases, creativity is a bonus; it adds meaning and beauty and distinguishes the artist from the laborer.