The makars of patterns?

A few weeks ago I discovered a new distraction, the Journal of Humanistic Mathematics. At the time it had only reached its first issue, but it’s an idea that deserves to prosper. What struck me particularly was that this issue contained three poems plus an article titled “Is (Some) Mathematics Poetry?” I admit I was more impressed by the poems than by the article, which strays a little too close for my taste to the definition of poetry as stuff that doesn’t quite reach to the margins, but the combination chimed with a plaintive little passage I’d rediscovered recently:

How happy the lot of the mathematician! He is judged solely by his peers, and the standard is so high that no colleague or rival can ever win a reputation he does not deserve. No cashier writes a letter to the press complaining about the incomprehensibility of Modern Mathematics and comparing it unfavourably with the good old days when mathematicians were content to paper irregularly shaped rooms and fill bathtubs without closing the waste pipe.

(W. H. Auden, Selected Essays, 1964, chapter 2.)

Of course, Auden was writing before a more militant generation of cashiers subjected mathematics to the impact agenda, but I think the point of the plaint remains clear. This in turn recalled a couple of rather more famous quotations:

Oppenheimer, they tell me you are writing poetry. I do not see how a man can work on the frontiers of physics and write poetry at the same time. They are in opposition. In science you want to say something that nobody knew before, in words which everyone can understand. In poetry you are bound to say… something that everybody knows already in words that nobody can understand.

(Paul Dirac, attrib. in various versions.)

A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas… In poetry… [t]he poverty of the ideas seems hardly to affect the beauty of the verbal pattern. A mathematician, on the other hand, has no material to work with but ideas, and so his patterns are likely to last longer, since ideas wear less with time than words.

(G. H. Hardy, A Mathematician’s Apology, 1940.)

For anyone who, like me, has at least a reader’s interest in both poetry and mathematics, statements like these inevitably niggle at the edges of the mind. Maths and poetry can sometimes seem like a couple of distant cousins who are no longer on speaking terms, but whose family resemblance sometimes strikes strangers far more strongly than it does either of them. Both are perceived as the aristocrats among their immediate neighbours; to put it more cynically, each has a certain snob-value which results from the perception that it is purer or more distilled than other forms of language or of thought. It’s perhaps because of this that in our present culture, they’re probably the most widely despised of the major art forms — I don’t know whether the proportion of people who “just don’t get poetry” is greater than the proportion who “were never any good at maths at school”, but few people seem ashamed of admitting that either art is a blank to them. (Compare the likely social responses to “I just don’t get music” or “I was never any good at reading at school”.)

Less depressingly, the aesthetics of both arts depend on setting up mutually supportive conceptual and formal patterns; both prize economy of expression and in both there is an interplay between what is to be said and the language in which it is being said. And each, much to the frustration of the critic, resists translation into prose far more vigorously than it seems it should. I suspect that further parallels could be drawn at the risk of stretching credibility beyond its tensile strength, but I think these few at least are fairly defensible.

And yet, as the famous apocryphal statement by Dirac illustrates, there’s a gulf of mutual suspicion between the mathematicians and the poets. The last major mathematical figure I can think of to have made serious attempts to establish himself as a poet was the ebulliently polymathic William Rowan Hamilton, who earned himself a courteous squishing by Wordsworth for his pains:

You send me showers of verses which I receive with much pleasure, as do we all; yet have we fears that this employment may seduce you from the path of Science which you seem destined to tread with so much honour to yourself and profit to others. Again and again I must repeat, that the composition of verse is infinitely more of an art than men are prepared to believe, and absolute success in it depends upon innumerable minutiae, which it grieves me you should stoop to acquire a knowledge of.

(Wordsworth to Hamilton, 1831; see Tomalin (2009) and refs therein.)

(This treatment looks even more tactful if one compares it with Wordsworth’s handling of, say, the young Keats, and if one bears in mind the less than spectacular quality of Hamilton’s poetry.) Since Hamilton, the wedge that the Romantic era hammered between science and art seems to have forced maths and poetry further and further apart — even though mathematics has always been at best an anomaly when considered as a member of the sciences.

Trying to take a longer perspective for a moment, perhaps mathematics is such an anomaly because it represents the subset of the old liberal arts that modern science has both made part of its own toolkit and yet has permitted to retain a separate identity. No natural scientist is likely to deny the occasional usefulness of arithmetic, geometry or logic (if that can be considered a part of maths) in his or her own discipline, and one can comfortably describe oneself as an applied mathematician working in geology, or physics, or genetics — that is, as an expert in the mathematical art who puts this expertise at the service of the science in question. The same natural scientist almost certainly relies on the arts of grammar and rhetoric, but is liable to regard the former as almost trivial and to feel uncomfortable about admitting the latter. And try to imagine someone describing themselves as an applied grammarian working in genetics; or a conference attended by working scientists with the title “Rhetorical Biology”; or a compulsory first-year university course called “RG101: Rhetoric and Grammar for Physicists”. (It doesn’t seem like such a bad idea, put like that.)

So how might we get these estranged family members talking sensibly again? I don’t know, though I suspect it has to be at some deeper level than that of developing algorithmic notations to classify poetic forms, or finding a metaphysical conceit in a mathematical entity. I’m not denying the merit of either, and the latter certainly offers sufficiently omnivorous poets some genuine opportunities. (If borrowing mathematical concepts was good enough for John Donne, it ought to be good enough for the rest of us, whatever Dryden may have thought — and personally I suspect that Donne had forgotten more about the successful deployment of “amorous verses” than Dryden ever knew.)

Maybe there’s some way for us to start learning each other’s real aesthetics again. How many poets have ever genuinely been struck by the beauty of a completely comprehended proof; how many mathematicians have ever tried to take apart, say, a tightly written sonnet and realised how strongly the external and internal rhymes, the scansion and the syntax knit the thing together? We’d have to lose some bad habits first, like using “poetry” as synecdoche for anything elegant and “mathematical” as shorthand for inhuman or numerical, but perhaps it could be done.

Perhaps another way in might be to recognise some odd parallels between the working methods of the poet and the mathematician — or at least between those of some poets and some mathematicians. Both poets and mathematicians often seem to operate a kind of “working mythology” or “working mysticism”: a vaguely held faith that, although not terribly defensible philosophically, provides a basis for actually producing maths or poetry. In the case of mathematicians, this working mysticism notoriously takes the form of a naive confidence in the independent reality of mathematical entities, generally described as “mathematical platonism”. In the case of poets, who tend to be less naive and more evasive on the subject, this mysticism often takes the form of a faith in the independent power of language to disclose truths.

To illustrate this faith, here’s Seamus Heaney on George Herbert:

such antithetical pairings… are functions of the poet’s mind as it moves across the frontier of writing, out of homilies and apologetics into poetry, upon the impulses and reflexes of awakened language.

(The Redress of Poetry, 1995, chapter 1; emphasis mine.)

And again, on Philip Larkin’s Aubade:

when a poem rhymes, when a form generates itself, when a metre provokes consciousness into new postures… [w]hen a rhyme surprises and extends the fixed relations between words… [w]hen language does more than enough, as it does in all achieved poetry…

(ibid, chapter 8).

Less reverently, but I think expressing the same thought, Auden:

The poet is the father of his poem; its mother is a language: one could list poems as race horses are listed — out of L by P… [a poet’s] attitude is that of the old lady, quoted by E. M. Forster — ‘How can I know what I think until I see what I say?’.

(Selected Essays, 1964, chapter 2.)

And, less reverently still and doing his best to give the game away, Don Paterson:

most poets work to a stricter or a looser formal template… then go nose blows rose chose Montrose suppose Atholl Brose comatose for days on end until… they hit the right combination of music and sense… Rhyme… can trick a logic from the shadows where one would not have otherwise existed. This is one of the great poetic mysteries…

(101 Sonnets: from Shakespeare to Heaney, 1999, introduction).

What I think unifies these is that, no matter how exactly it’s expressed, the poet is working with the grain of the language, letting its accidents guide not just the music but the sense of the poem and trusting that somehow the pattern of thought that emerges will be more coherent or richer than might have been achieved by thinking first and then capturing the thought in words. This seems to me rather similar to the way that a good mathematical notation does half the thinking for us, leaving the brain to noodle around and pick out the productive or the surprising directions and connections that emerge:

By relieving the brain of all unnecessary work, a good notation sets it free to concentrate on more advanced problems, and, in effect, increases the mental power of the race.

(Alfred North Whitehead, An Introduction to Mathematics, 1911.)

In each case, what’s going on seems almost like an inversion of  linguistic relativity: the language is being relied on to shape thought, but in the hope that this will paradoxically lead to a result that is more universal rather than less. Seen like this, is the faith we mathematicians place in the reliability and adequacy of our formal language really more defensible than the faith the poets place in their natural language? In each case, all that justifies this faith is that for millennia it seems to have worked out all right.

This productive mysticism has to be contrasted both with the apparently mystical nature that poets sometimes see in the outputs of mathematics and with the obfuscation — too often met in school — that presents poems as an outpouring of “feeling” separate from and superior to thought. It’s far too easy to treat mathematics as a source for numerological ramblings: there’s a sad example in the essay by Don Paterson that I quoted above, in which the Fibonacci sequence and modular arithmetic are used to try to prove that the fourteen lines of the sonnet are actually thirteen are actually one. (I don’t quite get it. However, a poet’s numerological speculations don’t have to make sense in order to provide a valuable intellectual stimulus, any more than Yeats’s mystical explorations had to correspond to the real universe in order to provoke great poetry, or non-dissipative motion had to be possible in order to justify analytical mechanics.) Even when a poet isn’t side-tracked into numerology, they can find themselves confronted by the sheer ice wall of one of the advanced and unmotivated concepts that have strayed into popular understanding:

Those mystical mathematicians
don’t help either. I listen
to their fifth dimensions, I try
to pick up a piece of bent light —

(Norman MacCaig, It’s hopeless, 1969)

Equally, it’s far too easy to get or give the impression that poetry is, in Dirac’s terms, saying “something that everybody knows already in words that nobody can understand”: intruding a completely personal and idiosyncratic form of expression into a universal experience. When poetry is being taught to teenagers in school, maybe the best way in is through the terminology of self-expression and by encouraging them to try writing in the freest of verse. When it is being presented to mathematicians, or to people who think like mathematicians, it might be more productive to revert to an older tradition and display a poem as a made thing, formed by thought wrestling with the tight restrictions of a language and a set of rules — the product of an intellectual discipline.

I’m by no means suggesting that there’s a meaningful correspondence between a poem and a piece of mathematics, or that it’s worth anybody’s while trying to produce some kind of hybrid of the two art forms. (They’re both too proud for that: until I see evidence to the contrary I’ll continue to suspect that a maths–poem would be a chimera with the strengths of neither and the weaknesses of both.) Beyond mutual respect, maybe the best I can hope for is that one day we might start to think it natural that the average poetry reader could appreciate the basics of a mathematical proof, or the average mathematician take time out to admire a sonnet. Or, more puckishly, that the same animating spirit might continually distract the lovers of each art form with the other:

On sighting mathematicians it should unhook the algebra from their minds and replace it with poetry; on sighting poets it should unhook the poetry from their minds and replace it with algebra.

(Brian Patten, Prosepoem Towards a Definition of Itself, in The Mersey Sound, 1967)

This might make it harder to get work done, but it might also be quite fun.

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