Thinking in Numbers: How Maths Illuminates Our Lives (15 page)

I wonder what Garrido makes of our deficient hands, all of us counting to the tune of ten? Does he pity us as the Romans pitied their thumbless veterans? He calls his condition a blessing; it is clear that he would not wish to be any other way.

Some believe that we should all learn to count like Garrido. A society, formed in the mid-1900s, advocates replacing the decimal system with a ‘dozenal’ one, since twelve divides more easily than ten. Leaving aside itself and one, the number twelve can be divided into four factors: two, three, four and six, compared with the factors of ten: two and five. In England and America the Society still militates for the return of Roman fractions (among other measures), judging their abandonment a gross error.

Like the Esperantists and the simplified spellers that came before them, the Society’s members dream of a highly rational world comprising pairs, trios, quarters and sextets, a world innocent of messy fractions. Theirs is the charm of the hopeless cause.

An English queen with eleven fingers, a Cuban man with twelve toes – such stories still incite our wonder and with it our vague sense that something has gone awry.

Montaigne, typically generous, remedies this view. He recalls once encountering a family who exhibited ‘a monstrous child’ in return for strangers’ coins. The infant had multiple arms and legs, the remains of what we now call a conjoined twin. In the infinite imagination of its Creator, Montaigne supposes, the child is simply one of a kind, ‘unknown to man’. He concludes that, ‘Whatever falls out contrary to custom we say is contrary to nature, but nothing, whatever it be, is contrary to her. Let, therefore, this universal and natural reason expel the error and astonishment that novelty brings along with it.’

The Admirable Number Pi

To believe the poet Wislawa Szymborska, I am one in two thousand. The 1996 Nobel laureate offers this statistic in her poem ‘Some Like Poetry’ to quantify the ‘some’. Actually I think she is a tad too pessimistic – I am hardly as rare a reader as that. But I can see her point. Many people consider poetry to be all clouds and buttercups, without purchase on the real world. They are right and they are wrong. Clouds and buttercups exist in poetry, but they are there only because storms and flowers populate the real world too. Truth is, a good poem can be about anything.

Including numbers. Mathematics, several of Szymborska’s verses show, lends itself to poetry. Both are economical with meaning; both can create entire worlds within the space of a few short lines. In ‘A Large Number’, she laments feeling at a loss with numbers many zeroes long, while her ‘Contribution to Statistics’
notes that ‘out of every hundred people, those who always know better: fifty-two’ but also, ‘worthy of empathy: ninety-nine’. And then there is ‘The Admirable Number Pi’, my favourite poem. It – the poem, and the number – begins: three point one four one.

Once, in my teens, I confided my admiration for this number to a classmate. Ruxandra was her name. Like the poet’s, her name came from behind the Iron Curtain. Her parents hailed from Bucharest. I knew nothing of Eastern Europe, but that did not matter: Ruxandra liked me. She liked that I was quite different from the other boys. We spent breaks between lessons in the school library, swapping ideas about the future and homework tips. Happily for me, her strongest subject was maths.

In an access of curiosity, I asked about her favourite number. Her reply was slow; she seemed not to understand my question. ‘Numbers are numbers,’ she said.

Was there no difference at all for her between the numbers 333, say, and fourteen? There was not.

And what about the number pi, I persisted; this almost magical number that we learned about in class. Did she not find it beautiful?

Beautiful? Her face shrank with incomprehension.

Ruxandra was the daughter of an engineer.

The engineer and the mathematician have a completely different understanding of the number pi. In the eyes of an engineer, pi is simply a value of measurement between three and four, albeit fiddlier than either of these whole numbers. For his calculations he will often bypass it completely, preferring a handy approximation like 22/7 or 355/113. Precision never demands of him anything beyond a third or fourth decimal place (3.141 or 3.1416, with rounding). Word of other digits past the third or fourth decimal does not interest him; as far as he is concerned, it is as though they do not exist.

Mathematicians know the number pi differently, more intimately. What is pi to them? It is the length of a circle’s round line (its circumference) divided by the straight length (its diameter) that splits the circle into perfect halves. It is an essential response to the question, ‘What is a circle?’ But this response – when expressed in digits – is infinite: the number has no last digit, and therefore no last-but-one digit, no antepenultimate digit, no third-from-last digit, and so on. One could never write down all its digits, even on a piece of paper as big as the Milky Way. No fraction can properly express pi: every earthly calculation produces only deficient circles, pathetic ellipses, shoddy replicas of the ideal thing. The circle that pi describes is perfect, belonging exclusively to the realm of the imagination.

Moreover, mathematicians tell us, the digits in this number follow no periodic or predictable pattern: just when we might anticipate a six in the sequence, it continues instead with a two or zero or seven; after a series of consecutive nines, it can as easily remain long-winded with another nine (or two more nines or three) as switch erratically between the other digits. It exceeds our apprehension.

Circles, perfect circles, thus enumerated, consist of every possible run of digits. Somewhere in pi, perhaps trillions and trillions of digits deep, a hundred successive fives rub shoulders; elsewhere occur a thousand alternating zeroes and ones. Inconceivably far inside the random-looking morass of digits, having computed them for a time far longer than that which separates us from the big bang, the sequence 123456789 . . . repeats 123,456,789 times in a row. If only we could venture far enough along, we would find the number’s opening hundred, thousand, million, billion digits immaculately repeated, as though at any instant the whole vast array were to begin all over again. And yet, it never does. There is only one number pi, unrepeatable, indivisible.

Long after my schooldays ended, pi’s beauty stayed with me. The digits insinuated themselves into my mind. Those digits seemed to speak of endless possibility, illimitable adventure. At odd moments I would find myself murmuring them, a gentle reminder. Of course, I could not possess it – this number, its beauty, and its immensity. Perhaps, in fact, it possessed me. One day, I began to see what this number, transformed by me, and I by it, could turn into. It was then that I decided to commit a multitude of its digits to heart.

This was easier than it sounds, since big things are often more unusual, more exciting to the attention, and hence more memorable, than small ones. For example, a short word like
pen
or
song
is quickly read (or heard), and as quickly forgotten, whereas
hippopotamus
slows our eye (or ear) just enough to leave a deeper impression. Scenes and personalities from long novels return to me with far greater insistence and fidelity, I find, than those that originated in short tales. The same goes for numbers. A common number like thirty-one risks confusion with its common neighbours, like thirty and thirty-two, but not 31,415 whose scope invites curious, careful inspection. Lengthier, more intricate digit sequences yield patterns and rhythms. Not 31, or 314, or 3141, but 3
1
4
1
5 sings.

I should say that I have always had what others call ‘a good memory’. By this, they mean that I can be dependably relied upon to recall telephone numbers, and dates of birthdays and anniversaries, and the sorts of facts and figures that crowd books and television shows. To have such a memory is a blessing, I know, and has always stood me in good stead. Exams at school held no fear for me; the kinds of knowledge imparted by my teachers seemed especially amenable to my powers of recollection. Ask me for the third person subjunctive of the French verb ‘être’, for instance, or better still the story of how Marie Antoinette lost her head, and I could tell you. Piece of cake.

Pi’s digits henceforth became the object of my study. Printed out on crisp, letter-sized sheets of paper, a thousand digits to a page, I gazed on them as a painter gazes on a favourite landscape. The painter’s eye receives a near infinite number of light particles to interpret, which he sifts by intuitive meaning and personal taste. His brush begins in one part of the canvas, only to make a sudden dash to the other side. A mountain’s outline slowly emerges with the tiny, patient accumulation of paint. In a similar fashion, I waited for each sequence in the digits to move me – for some attractive feature, or pleasing coincidence of ‘bright’ (like 1 or 5) and ‘dark’ (like 6 or 9) digits, for example, to catch my eye. Sometimes it would happen quickly, at other times I would have to plough thirty or forty digits deep to find some sense before working backwards. From the hundreds, then thousands, of individual digits, precisely rendered and carefully weighed, a numerical landscape gradually emerged.

A painter exhibits his artwork. What was I to do? After three months of preparation, I took the number to a museum, the sprawling digits tucked inside my head. My aim: to set a European Record for the recitation of pi to the greatest number of digits.

March is the month of spring showers, and school holidays, and spick and span windows. It is also the month when people the world over celebrate ‘Pi Day’, on 14 March. So on that day, in 2004, I travelled north from London to the city of Oxford. Members of staff at the university’s Museum for the History of Science were waiting for me. Journalists too. An article in
The
Times
, complete with my photo, announced the upcoming recitation.

The museum lies in the city centre, in the world’s most ancient surviving purpose-built museum building, the Old Ashmolean. Iconic stone heads, wearing stone beards, peer down at visitors as they pass through the gates. The walls are thick, the colour of sand. Approaching the building, a snap of photographers appear as if from nowhere, holding cameras, like masks, up to their faces. The piercing flashes momentarily petrify my expression. I stop and raise my features into a smile. A minute later they are gone.

The record attempt’s organisers have occupied the museum building. Television camera wires snake the length of the floor. Posters requesting donations (the event is raising money for an epilepsy charity, at my request, since I suffered from seizures as a young child) dress the walls. A table and chair, I see on entering, have already been set out for me on one side of the hall. Before it, a longer table awaits the mathematicians who will verify my accuracy. But there is still an hour before the recitation is due to start, and I find only a trio of men talking together. One has a full head of wiry hair, one has a multi-coloured tie, and one has neither hair nor tie. The third steps briskly forward and introduces himself as the main organiser. I shake hands with the museum’s curator and his assistant. Their faces show mild puzzlement, curiosity and nerves. Shortly afterwards, reporters arrive to hold the microphones and man the television cameras. They film the display cases containing astrolabes, compasses and mathematical manuscripts.

Someone asks about the blackboard that hangs high on the wall opposite us. Albert Einstein used it during a lecture, the curator explains, on 16 May 1931. What about the chalky equations? They show the physicist’s calculations for the age of the universe, replies the curator. According to Einstein, the universe is about ten, or perhaps one hundred, thousand million years old.

Footfalls increase on the museum’s stone steps as the hour approaches. The mathematicians duly arrive, seven strong, and take their seats. Men, women and children keep coming; it is soon standing room only. The air in the hall grows thick with hushed talk.

At last, the organiser calls everyone to silence. All eyes are on me; nobody moves. I sip a mouthful of water and hear my voice begin. ‘Three point one four one five nine two six five three five eight nine seven nine three two three eight four . . .’

My audience are only the second or third generation able to hear the number pi beyond the first few tens or hundreds of decimal places. For millennia it existed only in a breathful of digits. Archimedes knew pi to only three correct places; Newton, almost twenty centuries later, managed sixteen. Only in 1949 did computer scientists discover pi’s thousandth digit (following the decimal point): nine.

It takes about ten minutes, at a rate of one or two digits per second, for me to reach this nine. I do not know how long exactly; an electronic clock records the seconds, minutes, hours of the recitation for the public to watch, but I cannot see it from my chair. I stop reciting to sip water and catch my breath. The pause feels palpable. Dolorous even. I feel completely, oppressively alone.

The rules for the recitation are strict. I cannot step away from the desk, except to use the bathroom, and then always accompanied by a member of the museum’s staff. No one may talk to me, not even to cheer me on. I can stop reciting momentarily to eat fruit or a piece of chocolate, or drink, but only at pre-agreed intervals a thousand digits apart. Cameras record my every sound and gesture.

‘Three eight zero nine five two five seven two zero one zero six five four . . .’

An occasional cough or sneeze from the audience punctuates the flow of digits. I do not mind. I meditate on the colours and shapes and textures of my inner landscape. Calmness gains on me; my anxiety falls away.

Most of the spectators know nothing of Archimedes’s polygons, have no idea that the ten digits they have just heard will eventually repeat an infinite number of times, have never thought of themselves as being in any way susceptible to maths. But they listen attentively. The concentration in my voice seems to communicate itself to them. Faces, young and old, round and oval, all wear delicate frowns. Listening to the digits, they hear their dress sizes, their birthdays, their computer pass codes. They hear excerpts – both shorter and longer – from a friend’s, or parent’s, or lover’s telephone number. Some lean forward in expectation. Patterns coalesce, and as quickly disperse, in their minds.