Thinking in Numbers: How Maths Illuminates Our Lives (22 page)

Naturally,the share will vary from person to person. Money is fickle, always changing owners. That different people have dissimilar wealth is not surprising. What surprises is the scale and constancy of the divide. The economist and mathematician Vilfredo Pareto, who first observed (at the end of the nineteenth century) that twenty per cent of Italians owned eighty per cent of the nation’s wealth, found nearly identical results when he studied the historical data from many other parts of Europe. The distribution of wealth in Paris since 1292, he discovered, had hardly moved at all. Later researchers confirmed these findings.

Because most men and women, for want of resources, remain at the bottom, the elite, for want of competition, remain at the top. The poorest expend all their energies simply to keep body and soul together. I think of Degas’s painting of the two peasant women ironing: one is anonymous, hunched over her iron; the other yawns candidly, her mouth the shape of an ‘O’. The yawn distorts her features, undoing the individuality of her face.

The Spartan Lycurgus, we saw, made money as big as men; imagine, an instant, men as big as their money. Picture the difference between a miller and a millionaire. The man who mills grain owns perhaps no more than one-thousandth of the rich man’s fortune: the millionaire, his advantage converted into height, would be a thousand times as tall. To him, the miller would appear no bigger than an ant. With whom will the giant do business? Only with someone big and strong enough to carry his employer’s burden. Likewise this someone, smaller than the millionaire on whom he is dependent, but still far greater in size than the grain-running ant, to whom will he entrust his dealings? To his peers. They, in turn, will do the same. Good manners and compromise characterise the bulk of these transactions, but hardly anyone thinks to condescend to those with whom they have next to nothing in common. Our lowly ant friend is simply nowhere in sight.

Every man and woman, at whichever point along the scale, prefers to look up, not down. Even the miller gives a hand to his equal or his superior, rather than to someone far below him, for fear of conceding his rank to the worse-off man. With the wealthier, he is generous; with the poorer, he is mean. He has little, but the little he has goes purely to keeping up his minor station.

Comparisons are somewhat facile, of course. Beside a billionaire, even the millionaire is poor. The world’s hundredth-richest person has but one dollar for every eight in the pocket of the world’s richest man.

Whether the economy expands or whether it shrinks, the obsession with ‘keeping up one’s station’ remains. The inequality this obsession feeds off is a precocious learner: the more of it there is, the faster it will grow. Take the hypothetical egalitarian society, for example, where forty-five per cent of the population own fifty-five per cent of its wealth. In such a society, around twenty per cent (forty-five per cent of the forty-five per cent) of citizens own about thirty per cent (fifty-five per cent of the fifty-five per cent) of the total resources. By the same logic, a sixth (fifty-five per cent of the thirty per cent) of the society’s goods belongs to one citizen in every eleven (forty-five per cent of twenty per cent).

The contrast between this theoretical society and most of our modern cities – those that obey Pareto’s 80–20 principle – is striking. Wealth in these places can propagate far more ruthlessly, dramatically: the accounts of as few as four individuals in every hundred (twenty per cent of twenty per cent) will bloat with as much as two-thirds (eighty per cent of eighty per cent) of all the available income. And of these four men made of money, the very richest might have up to one half (eighty per cent of the two-thirds) all to himself.

Human beings and their self-interest are inseparable, but inequality needs a society to invent it. The creation of any vast and ambitious social project demands an unequal allocation of resources in order to achieve its goals. Without substantial inequality, as John Maynard Keynes pointed out, Europe’s railways – a ‘monument to posterity’ – would never have been constructed. Tolstoy, for one, hated the railways precisely because they represented this inequality, going even so far as to throw his best-loved character under a murderous train. It is true that most of the men who laid the rails never had the opportunity to ride them. Why then did they agree to do so? The railwaymen chose to cooperate with the wealthy, Keynes argued, on the tacit understanding that what they produced together, using the money of one side, the labour of the other, would ultimately serve the nation as a whole, and the principle of ‘progress’. World war, however, would subsequently smash this fragile alliance between the classes, by shaking the faith of both in the future. The bludgeoning of bombs and the gutting of gunfire disclosed to all ‘the possibility of consumption . . . and the vanity of abstinence.’

When Keynes spoke of the value of inequality he did not mean unbridled inequality. He meant an inequality that was consensual and that served a collective purpose. The selfish motive of making money, he admitted, helped to produce goods and services that benefit many. The same motive could also turn certain ‘dangerous human proclivities’ – cruelty, self-aggrandisement and the tyrannical pursuit of power – to more harmless pursuits. But, he was not at all complacent.

It is not necessary for the stimulation of these activities and the satisfaction of these proclivities that the game should be played for such high stakes as at present. Much lower stakes will serve the purpose equally well, as soon as the players are accustomed to them. The task of transmuting human nature must not be confused with the task of managing it.

How we lower those stakes is a question I leave to our politicians. I will not hold my breath. There is no easy solution – none analogous to a politician’s promise. Money’s abstractness is complex, evasive. It turns our world upside down. For instance, a farmer’s cow calves more prodigiously than other cattle – this is normal, part of nature. What, though, should we think of houses that beget more houses? Like many of those born poor my father never had the chance to own the roof above his head, whereas the proprietor of four houses will likely wind up with six, or twelve, or twenty.

All of which brings us to the question that Tolstoy posed his readers in the short story ‘How much land does a man need?’ Pahom, the greedy peasant, kills himself in the endless pursuit of more and more acres.

‘They are poor in the midst of riches,’ Seneca observed of some of ancient Greece’s wealthiest – and greediest – men, ‘which is the worst kind of poverty.’

A Model Mother

Not long ago, my mother’s age reached double mine. Two lives when compared with my young man’s span – half of her that I cannot see.

My mother has always been a mystery to me. We have had my lifetime to get to know one another, but it still feels nowhere near long enough. Her behaviour eludes me; it outpaces my powers of comprehension. Try as I might, I cannot figure her out.

Her face has not changed much with the years. She often wears an expression that flits between smugness and fright. The same stubborn creases, made by steady clenching, around the mouth; the same defiant twinkle in her eyes. She smiles fitfully, unexpectedly, as if bestowing a favour. Beneath the fine greying hair and wrinkles, I can still find myself in her gaze.

Memories. Take the kitchen of my childhood for example, where my mother would spend the lion’s share of her day. I remember her prowling the linoleum, biro and notepaper in hand, alive to every sound and suspicious of the slightest incursion. She was compiling a list of groceries to buy. She poked her nose into cupboards and the fridge, looking for the tins of beans and the bottles of milk and the packets of cheese and sliced bread bought only a day or two before. Thin air had taken their place.

‘The children eat us out of house and home,’ she complained to my father.

My father assumed a posture of resignation.

We kids knew which of our parents held command. Or, at least, we thought we did. At other times my mother would suddenly come over all shy and prone to blushing. My father could hardly draw a word out of her.

Then there were the Christmas presents. Year-round she would ferret out bargains at local car-boot sales, sequestering the toys and games in closets or under beds until Santa’s sleigh arrived. Of course, we always knew where to find them, but in the spirit of the season we turned a blind eye. It was never easy: buried treasure seemed to lie in every nook and cranny of every room. Why then, many Decembers later, under piles of old clothes, did we bring unopened presents to the surface? Had she simply mislaid them, forgotten their location? Could it really be that the buying of them had meant more to her than the offering?

A mathematician would say, ‘graph the data.’ That is how mathematicians speak. And it is true enough: puzzling occurrences usually require the long view – and a firm grasp of context. Early on in my childhood, I decided that if only I could assemble enough of my recollections, and settle on some parameters for their analysis, it might be possible to make a predictive model of my mother’s behaviour.

It was around the time that I began to look like her, once the primary school blackboard became a blur. Our myopia, it could be said, brought us closer together. ‘A mummy’s boy,’ my father sometimes called me. None of my brothers earned this epithet. Spending more and more time in her company, I felt the puzzle of her presence intensely.

Back then, a thigh thinner, she was always on the go. I took to mapping her movements. Saturday mornings my mother would return from the local library, carrying a couple of romantic paperbacks in her arms, smelling faintly of must. In the space in the living room before the television, I would sit for what seemed like hours half-listening to the yellow rustling of the pages that originated from the settee. Every other Sunday, robed in her best dress, she would take us – my brother, sister, and I – to the neighbour’s on the corner to drink tea and trade gossip. Midweek, she would venture out to do the rounds of second-hand shops, returning with bags fattened on goods that nobody seemed to need.

Perhaps she noticed me tracking her and wished to catch me out, or perhaps she simply grew bored with her own repetition, but for whatever reason she would sometimes decide to mix it all up. Come Saturday, the living room would contain the same atmosphere. But now, dog-eared biographies exhaled the musty smell. Without warning, the front door would stay shut for the Lord’s Day of rest; we took tea with the neighbour an evening after school instead. Even her favourite shops suddenly became good only for returning things.

One afternoon she took me with her to return a pair of shoes. Approaching the shop, I compared the imaginary mother in my head with the real thing. The imaginary mother would choose a male shop assistant (my mother, I knew, hated to haggle with other women). She would complain that the shoes pinched her young son’s toes, and when the man lifted the offending footwear from its container, she would add that the leather scuffed immediately. To the request for a receipt (which she always lost), her voice would rise in volume, detailing all the children’s feet that she had to keep dry and warm. The man would then nod patiently before offering an exchange.

Unfortunately, on this occasion my real mother bore no resemblance to her model.

A young woman with tight bound hair assisted all the customers. My mother’s voice as she handed over the shoebox sounded weak, her words unacquainted with one another. ‘I’m sorry to hear it,’ the woman interrupted, as though offering her condolences, ‘I’m sorry to hear it, but there really is nothing that I can do.’

I confidently expected my mother to put up a fight. But she promptly slumped into one of the seats intended for the trying-on of shoes, with only a long sigh for a rejoinder. The shop assistant reiterated that a refund was quite out of the question. My mother looked down at the floor and merely sighed again. Eventually, when my mother showed no signs of relenting, the young woman said, ‘Please leave’ and then, ‘Please leave, or I will have to call the police.’ My mother sagged even deeper into her seat and crossed her legs.

My ten-year-old self was filled with apprehension. My imaginary mother would never have behaved like that! It took a long time for me to understand my real mother’s sit-in. Of course, she knew all too well what she was doing. She knew that the young lady had conceived her own version of my imaginary mother. On that day, in that shop, my mother in her flesh and blood defied them both.

At last, driven to exasperation, the woman pulled something small and shiny from her pocket. ‘Do not breathe a word of this to anyone,’ she said, before sketching a long gash along one of the shoes with the blade of her penknife. ‘This way we get a refund from the manufacturer for damaged goods.’

In fact, it did not bother me as much as you might think when the actions of my mother and her imaginary doppelganger failed to coincide. I slowly came to understand how limited and clumsy an approximation was my model of her, how many variables I had not accounted for (whose existence I had not even guessed), and how large and liberating a role chance played in all our affairs. Besides, each variation between the imaginary and the real provided me with new clues. This variation, I hoped, growing larger or smaller by turns, would act as a sort of compass toward a greater understanding of my mother’s true nature.

On those rare occasions when my mother became her model’s mimic, the eerie sense of déjà vu nauseated me. I worried that it suggested some dark cunning within me, or, worse, deterioration in the liberty of my mother’s will. Besides, how could I even be sure that my success showed real merit? Perhaps it could be put down to nothing more than luck: even a stopped watch gives the correct time twice a day.

Possibly, my inability to understand my mother is the result of an anterior uncertainty, that is: what should a mother’s behaviour look like? I am not talking about an ideal mother – I do not believe, alas, in such creatures – but rather the most common and distinguishing maternal qualities. A baseline, if you will.