What’s the best number?

Katherine Rundell 13

I love 13 because I love superstitions; they are proof of how the human heart leaks. I love our desire to lay our human anxieties down at the feet of black cats, broken mirrors and ladders; it speaks to something unwieldy and bloody-minded in us.

Fear of the number 13, triskaidekaphobia, goes deep; most sources date it from the Last Supper, and from Judas, the 13th man to take his place at the table. The crucifixion is a story of such passion and guts that it’s unsurprising that the resonance of it attached to every detail, and, just as the crucifixion is about alchemising the dark, so there is hope as well as dread in 13.

There is, too, a Norse myth about a lavish dinner party at Valhalla, attended by 12 gods. Loki arrives, an uninvited 13th and, jealous of the universally loved Balder the Beautiful, coaxes Hoder, the blind god of darkness, into shooting him with a dart tipped with mistletoe. The Earth turns dark, and the whole world mourns. Odin puts Balder, his son, on a pyre, and whispers in his ear, and pushes him out to sea. It is one of the great depictions of ancient grief, and the number 13 reminds us not to play with sharp things like love. Nobody knows what it is that Odin whispered.

The superstition is everywhere; the architecture of justice took on the power of the number and made it 13 steps leading up to the gallows to be hanged. There are 13 witches to a coven, and I know an entirely sane family who won’t sit down 13 at dinner. If necessary, an extra place is set and a teddy bear sits up at table. It’s here, though, that you come up against the limits of superstition: the bear isn’t offered any soup or wine.

Robert Douglas-Fairhurst 42

I don’t usually pay much attention to my birthday. Another click on the meter; another candle to add to a cake already bristling like a porcupine. But I was convinced that my 42nd birthday would be different. I awoke with a spring in my step and a song in my heart.

My favourite childhood reading was Douglas Adams’s “The Hitchhiker’s Guide to the Galaxy”, in which the mega-computer Deep Thought, after seven and a half million years of brooding calculation, intones with “infinite majesty and calm” that the answer to “Life, the Universe and Everything” is “42”. Clearly in some obscure corner of my subconscious I’d been hoping for a similar revelation.

Adams claimed that his choice did not have any special mystical significance. “It was a joke,” he said. “Binary representations, base 13, Tibetan monks are all complete nonsense. I sat at my desk, stared into the garden and thought 42 will do. I typed it out. End of story.” Actually there are several other stories that might explain why this particular number popped into his head. In “Romeo and Juliet”, Friar Laurence offers Juliet a drug to put her into a death-like sleep for “two and forty hours”, like a miniature version of Deep Thought’s mega-coma. The Gutenberg Bible had 42 lines per page. Lewis Carroll chose to have 42 illustrations for “Alice’s Adventures in Wonderland”, and Alice is told that “Rule 42” is that all persons more than a mile high must leave the courtroom.

In fact, wherever you look, this is a number that seems to promise some kind of order underlying life’s usual randomness and flux. There are 42 laws of cricket, 42 possible triangulations of a heptagon, and after Thomas Cranmer’s doctrinal fiddling there were 42 Articles in the Church of England. The atomic number of molybdenum, the angle of light required to produce a rainbow, the number of minutes it would take to fall straight through the Earth – all 42. And how many characters does the phrase “the Answer to Life, the Universe and Everything is” contain, including the comma? You’ve guessed it.

Julian Barnes 200,000,000,000

When Lenin arrived at the Finland station in April 1917, among the crowds – according to family legend, at least – was the ten-year-old Dmitri Shostakovich. The future composer came from the liberal St Petersburg intelligentsia; he had an Old Bolshevik uncle – exiled during the 1905 revolution – who enthused him with the heroic ideas that would shape Russia’s future. Little Dmitri would proudly wear a scarlet ribbon on his coat. His first compositions, before his official Opus One, were a “Funeral March for the Victims of the Revolution” and a “Hymn to Liberty”.

Then, very quickly, the revolution turned sour, paranoid and carnivorous. In 1926, five years into Lenin’s New Economic Policy, Shostakovich wrote to a friend that, yes, indeed, “Heaven on Earth will come – in 200,000,000,000 years.” It is a figure that sticks in the mind – in mine anyway. So when politicians of whichever party promise us that a new Britain can be forged in five, ten, or at the longest 20 years; when Steven Pinker assures us that the world is getting less not more violent; when American gun-lobbyists assert that people, not guns, kill others; when Donald Trump is held to be a plausible presidential candidate; when any quick-fix idealist or religious dreamer suggests that utopia could be just around the corner – on such occasions, I repeat to myself that, yes, indeed, Heaven on Earth will come in 200,000,000,000 years. But I don’t think we should get too impatient, or over-hopeful about it arriving any sooner.

Mark Vanhoenacker 747

One summer day in the cockpit of a Boeing 747, sailing high over navy-dark Arctic waters en route from London to Los Angeles, a fellow pilot told me that as a child she dreamed not of flying, but of flying the 747.

I wasn’t surprised. Like her, I fell early and hard for this aeroplane: its silvery wings, the iconic bump in the forward fuselage (an echo, surely, of its lead designer’s boyhood obsession with great birds), and the palindromic majesty of those three digits, which, when I was young, summed up everything I found most interesting about flying and the world.

For many air and armchair travellers, too, it remains the only airliner that comes easily to mind: a numerical shorthand for a physical form, a technological legend, and above all a certain sensibility about the sky and the planet it encircles. In “Amelia”, Joni Mitchell sings of “the strange pillows of my wanderlust” and dreams of “747s, over geometric farms”. No need to specify the manufacturer, in what’s now several generations of songs and stories that reference this aeroplane; the number flies well enough on its own.

A few years ago I flew to Hong Kong with a captain who – like the 747 itself now – is nearing retirement. I will probably fly another airliner, but he will not. In the cockpit we spoke quietly, and at the pace that long night flights slow to naturally. The four engines turned steadily through each mile’s new air, while the snow-dusted deserts of north-west China slowly conjured themselves from the darkness. Nearly everyone on board was asleep and I wondered, as I often do at such moments, about the nearest other conversation to us, somewhere on the awakening planet below.

Over the Gobi Desert he told me something I have not heard from any other colleague. In a career of more than three decades, the only airliner he had flown was the 747. Almost no one will have been carried so far by it, almost no one will have spent so many hours looking out from its grand array of flight-deck windows at the stars and the turning world. This well-numbered plane was his life’s work, and a pilot, he and I agreed, could not be luckier.

Marcus du Sautoy 17

The Indian mathematician Srinivasa Ramanujan was reputed to know every number as his own personal friend. Each number had its own particular characteristics and traits. Although I can’t claim such intimate and infinite knowledge as Ramanujan, if I had to choose a best number like a best friend I would plump for 17 for its wonderfully multi-faceted character.

First off, 17 is a prime number. These indivisible numbers, infinite in number, are the atoms of mathematics. Yet understanding a pattern that makes sense of this tribe of numbers is one of the greatest unsolved problems of the discipline.

Nature, too, likes 17. It is the key to the evolutionary survival of a species of cicada in North America that only appears every 17 years. It seems that the indivisibility of 17 helps the cicada to avoid a predator that also appeared periodically in the forest.

This asynchronicity is also central to the opening movement of Messiaen’s “Quartet for the End of Time”, which features a piano part that consists of a 17-note rhythmic sequence that combines with a 29-note harmonic sequence to create an incredible feeling of never ending time.

A polygon with 17 sides is one of only five known prime-sided shapes that has the property that it can be perfectly constructed by using just a straight edge and compass. It was the discovery of the construction of the 17-sided polygon using this simple equipment that launched the mathematical career of one of the giants of 19th-century mathematics, Carl Friedrich Gauss.

One of my favourite destinations across the world is the Alhambra in Granada, whose walls are a celebration of symmetry. Using the work of the young French revolutionary Evariste Galois mathematicians have revealed that, despite the seemingly infinite variety of forms in the Alhambra, there are only 17 different symmetrical games that the artists can create.

But ultimately the reason 17 is my best number is that it is the number I sport on the back of my shirt every time I play football for my Sunday league team, Recreativo Hackney.

Helen Joyce Infinity

I remember my first mathematical thought. I was thinking about big numbers: a thousand, a million, a billion, a trillion…and it occurred to me that there could never be a biggest number, because however far up you went, you could always add one. It was intoxicating. I don’t know what age I was; perhaps six. Forty years on, with a PhD in mathematics, I still find beauty in that thought. It’s so simple, yet profound. You can explain it to a small child, but it is highly abstract. That, for me, is what mathematics is all about.

The idea that you can always go higher is what mathematicians mean by “infinity”. At least, it’s what they meant until one of my favourite mathematicians, the German Georg Cantor (1845-1918), asked himself whether all infinite collections were the same size – or whether, in some sense, some infinities could be bigger than others. Since the Greeks we’ve known that not all numbers can be expressed as fractions (pi, the ratio of a circle’s circumference to its diameter, is one example; the Greeks’ frantic attempts to write it as a fraction are the origin of the expression “squaring the circle”).

Cantor showed that though the number of fractions is infinite, the collection of “real” numbers (all the fractions, plus numbers like pi that naturally arise when you do geometry or solve quite straightforward equations) is much, much bigger. He found a clever way to “count” fractions – there is a way to line them all up without leaving any out (though you’ll never get to the end of the list). But if you try to make a list of real numbers, he proved that you were bound to leave most of them out. We now say that the real numbers are “uncountable”.

Mathematicians now know that there are infinitely many infinities, spiralling outwards and upwards to – well, infinity. Thinking about this gives me the same feeling, of touching eternity, that some people get when they contemplate the ocean or the night sky. It’s a more sophisticated version of the feeling I had as a small child, but not qualitatively different. And it’s available to everyone.■

Images: Magnum, Corbis, Panos