A poem I wrote about learning to count in infants school ends like this:
Those bright buttons of colour we placed on our tongues, to taste the smoothness the thinness of 1.
We were taught using coloured plastic counters, which we placed on spotted boards, the spots being arranged in patterns like those on dominoes. The poem is about all the other things we did with the counters, for example playing tiddlywinks, but also about how we learnt to count through the visual recognition of different patterns. When I had finished the poem, I wondered if pattern was somehow fundamental to mathematics, and for the first time in my life found myself going to the mathematics section of the public library. I quickly found out that pattern was indeed mathematically important, and borrowed books on all aspects of the subject: numbers in nature and the Fibonacci series; Chaos Theory; the Butterfly Effect; prime numbers; the mathematics of ancient civilizations such as the Maya, the Inca, the Chinese, the Greek; mathematics and astronomy; Gematria (a type of number mysticism)…
So began a very unlikely journey of discovery — unlikely because I was never very good at maths at school and until that moment hadn’t had the slightest interest in the subject. Yet now I felt a growing fascination for anything to do with numbers. I began to think of them as living entities with distinct personalities and behaviours, and personified some in poems: the number eleven became a boy of that awkward age, not a child anymore and not yet a teenager, still growing into his new long trousers. I even invented a new number ‘throur’ to come after three and before four, to help children to learn to count. Similarly, geometric shapes took on a life of their own and I found myself imagining a square who longed to be something else — a rhombus, a parallelogram, a circle, an ellipse… My wife began to question my sanity when she saw that I had covered pages and pages with columns of twin primes (pairs of numbers which are only divisible by themselves and 1 and which are separated by only one other number, for example 17 and 19) and had pinned them above my desk. This was in the hope that I, a poet, might do what no mathematician in history had been able to do and discover a mathematical pattern to their occurrence.
I began to demonstrate the remarkable qualities of the Möbius strip to my daughters at the dinner table. I set them a challenge (the winner to get a pound) to find a quick way to add all the numbers between 1 and 100 inclusive. My youngest daughter, who has always had a very logical mind, came up with the answer in next to no time (1+100 = 101; 2+99 = 101; 3+98 = 101 etc. so to add all the numbers you just multiply 101 x 50 = 5,050).
In short, I became a bit obsessed. I think I would have found the idea of writing poetry about mathematics too daunting if I hadn’t had the shining example of Edwin Morgan, many of whose poems addressed aspects of science and even science fiction. His work showed me that poetry can address anything, from the Loch Ness Monster to space travel. I took courage from that and forged ahead.
My research took me to some unlikely places, which often involved specialised vocabulary, which I tried to integrate into the poetry. Mathematical theories, I discovered, could be ‘provable’, ‘unprovable’ or ‘undecidable’ (neither provable nor unprovable). I read about triskaidekaphobia (the fear of the number 13) and came across the ancient Chinese name for the 13th month: ‘Lord of Distress’. I was intrigued to find out how the Incas developed a method of recording numerical information which did not require writing, but instead involved coloured strings called quipu, knotted to represent numbers. Each colour used had several meanings – including abstract concepts, such as peace or war – as well as signifying more concrete things such as the number of livestock in a particular village or its human population. In addition to colour-coding, another way of distinguishing the strings was to make some strings subsidiary, tied to the middle of a main string rather than being tied to the main horizontal cord.
Since the Incas had no written records, the quipu played a major role in the administration of the Inca empire. ‘The Inca emperor appointed quipucamayocs, keepers of the knots, to each town. Larger towns might have up to thirty quipucamayocs who were essentially government statisticians, keeping official records of the population, the produce of the town and its animals and weapons.’ This information was sent annually to the capital Cuzco via an official delivery service consisting of relay runners called chasqui, who passed the quipu on to the next runner at specially constructed staging posts, sometimes covering vast distances. I imagined being such a runner, entrusted to deliver the quipu. Enthralled by the words ‘quipu’, ‘chasqui’ and ‘quipucamayoc’ as well as the whole idea of long-distance runners laden with knots, I had to write a poem about it. Similarly, I wondered about the Roman who first came up with the Roman counting system and Roman numerals, using only seven letters: I, V, X, L, C, D & M. The system lacked a zero, and zero and the history of zero became a research topic for me all of its own and was, eventually, the title of my book.
I also became fascinated by mathematicians and their biographies. I wondered why, in geometry at school when they taught us about the 3-4-5 triangle, they hadn’t also taught us a little more about Pythagoras. His belief, for example, that we should not eat beans because of the bean’s resemblance to a human foetus, or his assertion that earthquakes were caused by the restlessness of the dead, or the fact that he didn’t actually discover the 3-4-5 rule but found it when travelling in Babylonia, where people for centuries had used it to demarcate fields when the floodwater of the Nile had receded. His genius was to recognise its universality. Pythagoras was famous in ancient Greece. So much so, that various legends sprung up about him, some of which are thought to foreshadow the miracles of Christ. For example, it was rumoured that he could walk on water, because he had been sighted on two different islands at the same time. Such anecdotal material might have made geometry a little more colourful for us.
I read about many other mathematicians, such as August Ferdinand Möbius, imagining him in Paris in 1858, at the very moment he discovered his famous strip; Sophie Germain, who had to impersonate a man in order to gain a place in the École Polytechnique, and whose research into elasticity became crucial to the construction of the Eiffel Tower; Alan Turing, whose work at Bletchley Park during the war did so much to break the codes used in German communications and who is generally held to be the father of the modern computer; and John Napier, whose ivory ‘bones’, carved with numbers in a patterned concatenation, constituted a sophisticated calculator for the times. Napier’s times, incidentally, were highly superstitious and his practices often appeared strange to his servants, so that rumours circulated that he was in league with the powers of darkness. (According to Mark Napier, one of his descendants, he deliberately played upon such beliefs by walking out at night wearing his nightgown and cap and carrying a cock which he had covered in soot).
I also fell in love with Mary Somerville, who grew up in Burntisland and attended Miss Primrose’s boarding school for girls. Her father feared that the abstract thought involved in mathematics might injure her tender frame. When she left the school she said that she felt ‘like a wild animal escaped from a cage’. Then there were the endless parties and concerts and balls expected of young ladies of the time, – though her shyness made playing the piano in front of others an ordeal – but the Scottish painter Naysmith was employed to be her painting tutor, and he noted her interest in plotting perspective and the vanishing point. Her parents did not think it appropriate for her to pursue her interest in mathematics, and even had the servants confiscate her candle when she went to bed at night in order to curtail her late night studies. She overcame this obstacle by memorising formulae so that she could continue to work on mathematical problems in her head in the dark. She studied the stars, and found that something was causing a perturbation in the orbit of Uranus, which subsequently led to the discovery of the planet Neptune.
I came to realise that mathematicians are all too human, and not so very different from artists – using their intuition to discover a proof before they can actually demonstrate it – and that mathematics underpins everything in our lives. You can’t have a table and chair without mathematics, you can’t have music… you can’t, even, have poetry.
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Brian McCabe speaks with Geoff Hattersley about why mathematicians are a bit like artists, how something being funny doesn’t mean it’s light, and the process of imaginatively recreating the worldview of a child.