Writing by Numbers

“There is a divinity in odd numbers”, wrote William Shakespeare, “either in nativity, chance or death”. Whether or not you accept that some numbers have supernatural properties, undeniably in numbers of every kind there is art.

Numbers have always provided inspiration in all forms of human creativity, including the art of storytelling. The importance of numbers in literature has been reinforced by the publication of two high-profile debut Australian novels, Steven Toltz’s A Fraction of the Whole and Toni Jordan’s Addition.

Toltz’s book is a raucous, sprawling saga about the men in an Australian family with a peculiar gift for numeracy, while Jordan’s relatively sedate domestic novel is about a woman with a compulsion to order her world by counting everything around her.

A greater contrast between two first novels would be hard to imagine, yet for that reason alone A Fraction of the Whole and Addition affirm that numbers are as vital to writing as they are to every other part of human activity, whether we are fully aware of it or not.

Indeed in neurological terms our ability to think numerically without even realising it may be as innate as our capacity for creativity. According to French cognitive scientist Stanislas Dehaene, our brains are hardwired to produce a “number sense”, which, like artistic ability, is natural to us but must be nurtured intelligently in order for us to realise its full potential.

Toltz and Jordan are not the first Australian authors to have pursued mathematical themes—Tom Petsinis’ novel The French Mathematician is a fictionalised biography of the neglected nineteenth-century genius Evariste Galois.

There is no shortage of novels, plays, movies and television shows depicting mathematicians. Tom Stoppard’s play Arcadia portrays the life of a thirteen-year-old female genius who in nineteenth-century England fails to solve Fermat’s last theorem but does anticipate modern chaos theory. At the other end of the scale, in the crime drama Numb3rs a streetwise Los Angeles policeman solves crimes with the help of his unworldly mathematician brother.

Perhaps the most famous living mathematician is John Nash. In the Oscar-winning film A Beautiful Mind, Nash is played by Russell Crowe. In a memorable scene at a student bar, Crowe’s character presents game theory—for which the real Nash won his Nobel Prize—to some of the other male students as a useful strategy for picking up women.

It is a classic Hollywood set piece, presenting complex ideas to a mass audience in a way that is either magical or crass, or both. Nash advises his drinking buddies never to go for the most attractive woman in the room. “If we all go for the blonde and block each other, not a single one of us is going to get her,” he explains. “So then we go for her friends, but they will all give us the cold shoulder because no one likes to be second choice. But what if none of us goes for the blonde? We won’t get in each other’s way and we won’t insult the other girls. It’s the only way to win. It’s the only way we all get laid.”

Game theory may or may not work as a seduction technique, but in storytelling mathematics does provide ways of shaping narrative outcomes and may even supply dialogue. One example everyone knows is Alice in Wonderland, which on the surface is a whimsical children’s story but apparently is packed with maths.

The book was written by Oxford mathematician Charles Dodgson, using the pen name Lewis Carroll. Among the many allusions to mathematical principles is an example of an inverse relationship in logic and semantics given in conversation between the Mad Hatter and the March Hare: “Why, you might just as well say that ‘I see what I eat’ is the same thing as ‘I eat what I see’!”

Other novelists who have incorporated mathematics into their work include Tolstoy, Dostoevsky and Austen. According to Austen biographer Park Honan, the title of Austen’s novel Emma alludes jokingly to an eccentric mathematical formula intended by its creator, eighteenth-century philosopher Francis Hutcheson, to “prove” that a person’s true virtue cannot exceed their ability to act benevolently. Hutcheson’s ratio measuring virtue is M/A, where A is perfect virtue and M is attained virtue. Emma’s quest is to turn M < A into the perfection of M = A.

At the most basic level in storytelling, numbers can dictate the choice of plot. At the beginning of Western literature there were two master plots represented by the Iliad and the Odyssey. The former—the tale of the siege of Troy—was static, while the latter—the tale of the return voyage by Ulysses to Troy after the fall of the city—involved movement. Stories thus either stood still or they moved.

Thousands of years later there are no more than seven basic story plots, according to English author Christopher Booker. The seven plots are: overcoming the monster, rags to riches, the quest, voyage and return, comedy, tragedy, rebirth. One or other of these is present in everything from Shakespeare to Star Wars.

What’s more, Booker argues, there are essentially two ways of ending a story:

“Through all the millions of stories thrown up by the human imagination just two endings have outweighed all the others. In fact we might almost say that, for a story to resolve in a way which really seems final and complete, it can only do so in one of two ways. Either it ends with a man and a woman united in love. Or it ends in death.”

Other literary applications of numbers have to do with the choice and arrangement of individual words. The rules of metre—which dictate the construction and arrangement of lines of verse—are indispensable to the writing of poetry, or at least they used to be.

In the eighteenth century, when poets were expected to conform strictly to metrical standards, Alexander Pope complained of the absurdity of critics evaluating verse purely by applying certain units of measurement. “But most by numbers judge a poet’s song, / And smooth or rough with them is right or wrong”.

Nowadays some readers might feel that the absence of metrical standards in so-called free verse diminishes poetry as a form of artistic expression. Literary critics, meanwhile, have not lost their love of numbers. In the early 1970s there was a flowering in numerological criticism, which sought to derive complex patterns from literary texts.

At around this time, a young South African academic by the name of J.M. Coetzee, who several decades later was to win the Nobel Prize for Literature, completed a doctoral dissertation based on a computer-generated stylistic analysis of the works of Samuel Beckett. For his part, Beckett once referred to literary critics dismissively as “certified recountants”.

The flow of ideas between numbers and literature does not travel in just one direction and indeed it may not be possible to understand numbers themselves without some form of narrative. British mathematician Ian Stewart argues that storytelling plays a vital role in the creation of successful mathematical proofs and encourages mathematicians to think in terms of narrative. “Like any good story, a proof has a beginning and an end, and a story line that gets from one to the other without any logical holes appearing.”

There are other ways in which mathematics helps us to understand storytelling, and vice versa. In Once upon a Number, American mathematician John Allan Paulos looks at the hidden mathematical logic of stories. He contends that storytelling preceded the modern theory of probability, since “mere acceptance of an idea of alternative possibilities and open-endedness essential to storytelling almost entails a notion of probability; some scenarios will be judged more likely than others”.

But there can also be a disjunction between numbers and stories, which we sense in stories that do not conform to our intuition as to probability. Ideally the best stories achieve a kind of aesthetic harmony between anticipation and the unexpected. When there is too much coincidence in a story we consider it implausible, and when there is too little cause and effect the story seems chaotic and meaningless.

All art must be both objective and subjective, and for it to work those elements remain in balance. Too much subjectivity is bad for art, and can lead us to lose our sense of reason and proportion, as can the misreading of statistics. But some stories have such a powerful grip on our imagination that they defy rational analysis.

As Canadian author Dan Gardner explains in Risk: The Science and Politics of Fear, we can exaggerate the importance of statistics to the point where events that are highly unlikely or not even causally related can nevertheless induce a state of actual panic. He even suggests that the power of storytelling itself can make us misinterpret the figures in a subjective way.

This is why, for example, we tend to think that shark attacks are much more common than they are in reality, a fear partly fuelled by the enormous and enduring cultural impact of the movie Jaws. Gardner points out that the likelihood of being eaten by a shark is less than that of being killed by poorly wired Christmas lights, though of course no one is going to make a blockbuster movie based on the latter scenario.