Poetry and Maths

(Benoit Mandelbrot, 1924 – 2010)

Benoit Mandelbrot first started thinking about complexity when he was contemplating, as a young researcher, the length of coastline of Britain. The answer, he realised, depended on how closely you looked. Measure the sweep of a bay, and it might be a mile long; include the ins and outs of the craggy inlets of that bay and you might get a length of two miles; zoom into each indentation of each tiny irregularity that you might feel when you run your fingers over the surface of the rock, and how long might that measure? So, how long is that coastline? In an interview with the New York Times earlier this year, Mandelbrot said that the question was an impossible one. "The length of the coastline, in a sense, is infinite."

I first heard of Benoit Mandelbrot in the pages of a book. Arthur C. Clarke’s The Ghost from the Grand Banks has a character, a nine year old maths genius called Ada who becomes obsessed with the beauty and complexity of the Mandelbrot Set. The M-Set is basically an equation: Z = z² + c. Well, I got my O level maths, so I can see that it’s in the language of maths, but it means little to me. I need a translation. And the translation comes when someone plots that equation on a graph. And what you get, is this:

And the thing about this, is when you zoom in on any part of it, what seems at first smooth becomes more and more complex, and eventually that complexity starts repeating itself. Think of a cauliflower – a kind of blobby brain shape. But it’s made up of little florets that are miniature versions of the whole. And when you look at the florets, they are made up of even tinier little mini-florets. Now if you keep zooming in on the M-set, you will find those complex Mandlebrotian florets budding off the line of the equation, for ever and ever and ever.  In Clarke’s book, Ada explains:

‘The boundary of the M-Set is fuzzy – it contains infinite detail: you can go in anywhere you like, and magnify as much as you please – and you’ll always discover something new and expected – look!’

The image expanded: they were diving into the cleft between the main cardiod and its tangent circle. It was […] very much like watching a zip-fastener being pulled open – except that the teeth of the zipper had the most extraordinary shapes.

First they looked like baby elephants waving tiny trunks,. then the trunks became tentacles. then the tentacles sprouted eyes. Then, as the image continued to expand, the eyes opened up into whirlpools of infinite depth… […] Flotillas of seahorses sailed by in stately procession. At the screen’s exact centre, a tiny black dot appeared, expanded, began to show a haunting familiarity – and seconds later revealed itself as an exact replica of the original Set.

I’m a words person, not a numbers person. But it seems to me that Mandelbrot’s investigation of the complexity of apparent smoothness, its fractal nature, can be seen as analogous with poetry. Take a ‘simple’ poem by Charles Simic:

Evening Chess

The Black Queen raised high

In my father’s angry hand.

Two lines. Not even a sentence in grammatical terms, since there is no verb. But if we start zooming in on the poem, we find all sorts of complexity. Sonic complexity, with the repeated, stabbing short vowels (black/angry/hand) and the long threatening vowels (high/my). Then there is contextual and connotational complexity: zoom out and think about what a game of chess might signify: a quiet civilised evening pastime, or a ritualised battle? Semantic and syntactic complexity: the word ‘black’ is placed by both sonic and grammatical echoing, in apposition with ‘angry’ – calling up to me, simply through those relationships, the image of a face darkening in rage. And of course you can look inside the meanings of individual words and find more complexity. The word ‘father’ has so many connotations: the OED has thirteen main definitions of the noun, all of which, by the nature of language, are underlying in some way its use in this poem.  I could, like the Mandelbrot set, go on for ever!

Mandelbrot died yesterday. And that’s given me the push I needed to start this long-planned blog. Coastlines, language, maths, poetry, life: they’re all fascinating in their complexity and their simplicity. This blog will be my ‘little room’, for zooming out, and zooming in.