Thinking in Numbers: How Maths Illuminates Our Lives (18 page)

We find this view studded throughout the pages of
War and Peace
, in those portions
that resemble the tight and intense arguments of a pamphleteer. It so happens that they are the same parts that most modern readers tend, perhaps understandably, to skip. But this less diligent reader misses a crucial bedrock of Tolstoy’s work.

The movement of humanity, arising as it does from innumerable arbitrary human wills, is continuous. To understand the laws of this continuous movement is the aim of history . . . only by taking infinitesimally small units for observation . . . and attaining to the art of integrating them (that is, finding the sum of these infinitesimals) can we hope to arrive at the laws of history.

Calculus, which Tolstoy defined as ‘a modern branch of mathematics having achieved the art of dealing with the infinitely small,’ offered him a vocabulary in which to voice his disagreement with many historians. He denounced their lamentable tendency to simplify. The experts stumble onto a battlefield, into a parliament or a public square and demand, ‘Where is he? Where is he?’ ‘Where is who?’ ‘The hero of course! The leader, the creator, the great man!’ And having found him, they promptly ignore all his peers and troops and advisors. They close their eyes and abstract their Napoleon from the mud and the smoke and the masses on either side, and marvel at how such a figure could possibly have prevailed in so many battles and commanded the destiny of an entire continent. ‘There was an eye to see in this man,’ wrote Thomas Carlyle about Napoleon in 1840, ‘a soul to dare and do. He rose naturally to be the King. All men saw that he was such.’

But Tolstoy saw differently. ‘Kings are the slaves of history,’ he declared, ‘the unconscious swarmlike life of mankind uses every moment of a king’s life as an instrument for its purposes.’ Kings and commanders and presidents did not interest Tolstoy. History, his history, looks elsewhere: it is the study of infinitely incremental, imperceptible change from one state of being (peace) to another (war).

The decisions of exceptional men could explain all of history’s great events said the experts. For the novelist, this belief was evidence of their failure to grasp the reality of an incremental change brought about by the multitude’s infinitely small actions. Out of a need to theorise, to locate ‘causes’, the historian privileges one series of events and examines it apart from all the others. Why, all of a sudden, had Napoleonic France and Tsarist Russia rushed to war? What drove millions of men, men who licked their plates and read stories to their sons and worried about their looks, to suddenly thieve and crush and slaughter one another? Napoleon overreached, a victim of his own pride and mania, says one expert. He let himself go, growing fat and moody. With successive battle victories under his belt, he fell inevitably to thinking himself invincible. No, no, says another historian, you forget how weak and high-strung was the Tsar Alexander. Such weakness certainly invited a military strike. The longstanding economic embargoes in Europe, suggests a third, led to strained relations between the different peoples. A fourth points out that hundreds of thousands of soldiers obtained gainful employment. Napoleon himself, near the end of his life, is said to have put the war down to the intrigues of the British.

Naturally, not all these ‘causes’ can be right, and some are even mutually contradictory. Either Napoleon’s decision to invade Russia was impetuous and instinctive, or else it was carefully calculated (against Russian weakness) and deliberate (to keep his forces busy). Either Russian weakness impelled the attention of France’s army, or else Napoleon’s mania invented such weakness for its own purpose. Either the war resulted from French initiative, or from British interference.

A Briton who lives in France, I see how each nation selects its own causes, and edits them convincingly into its own version of history. In Britain, Napoleon’s name is synonymous with tyranny and a small comic man’s delusions of grandeur. In France,
au contraire
, he is a revolutionary who stood up for the new Republic against the hostile monarchies of Europe. The puffed-up Napoleon with ‘small white hands’, as depicted by Tolstoy, is of course a Napoleon from the Russian perspective.

This third Napoleon, as conceived by Tolstoy, had at least one cardinal virtue: he knew to keep out of the way of his soldiers, not to tread on anyone’s boots, to give a fair impersonation of someone who is in command. It is the soldiers who shoot, and stab, and cough, and groan and bleed. They constituted the vast majority of the French emperor’s army, but they issued not a single command. The commands came from the officers above the soldiers, who took them in turn from the generals above the officers, who took them from the commander-in-chief above the generals. The most important commands always come from those who participate least in the physical action. Consequently, most of these commands, thousands of them, not corresponding to conditions ‘on the ground’ at the moment and in the place that they finally filtered down to the troops, were never executed. They did not coincide with the reality of circumstances that remained beyond the chief’s control. As far as Tolstoy is concerned, then, to say that Napoleon invaded Russia is only to say that a few of his commands, out of the thousands that came to nothing, coincided with certain broader events between the peoples of France and Russia in the year of 1812.

What were these broader events ‘on the ground’? As the novel’s calculus analogy suggests, they were innumerable, infinitesimal. At a given moment, in a given place, the wishes and desires and intentions of hundreds and thousands of people temporarily coalesced. Tolstoy illustrates such a moment in the life of a backwoods Russian region.

In the vicinity of Bogucharovo were large villages belonging to the crown or to owners whose serfs . . . could work where they pleased . . . In the lives of the peasantry of those parts the mysterious undercurrents in the life of the Russian people, the causes and meaning of which are so baffling to contemporaries, were more clearly and strongly noticeable than among others. One instance, which had occurred some twenty years before, was a movement among the peasants to emigrate to some unknown ‘warm rivers.’ Hundreds of peasants . . . suddenly began selling their cattle and moving in whole families toward the southeast. As birds migrate to somewhere beyond the sea, so these men with their wives and children streamed to the southeast, to parts where none of them had ever been. They set off in caravans, bought their freedom one by one or ran away, and drove or walked toward the ‘warm rivers.’ Many of them were punished, some sent to Siberia, many died of cold and hunger on the road, many returned of their own accord, and the movement died down of itself just as it had sprung up, without apparent reason. But such undercurrents still existed among the people and gathered new forces ready to manifest themselves just as strangely, unexpectedly, and at the same time simply, naturally, and forcibly. Now in 1812, to anyone living in close touch with these people it was apparent that these undercurrents were acting strongly and nearing an eruption.

Contemporary historians, to believe Tolstoy, took no notice of these ‘undercurrents’ in the life of a people. They failed to see the ocean of history for the waves. Aware only of the tides they called ‘causes’, they ignored the vast depths from which these ripples emerge. A man called Napoleon has an impetuous character; six months later Moscow is under siege. The historian looks at these two situations and asserts a link: namely, that hundreds of thousands of Muscovites fled their homes, and whole battalions of soldiers lost their lives, because of the impetuousness of this single man called Napoleon. Or, the historian notices that in, say, Liverpool and London there occurred local riots caused by a shortage of bread and that within a year Russian troop masses were fending off the French. Entire theories, each more elaborate and ingenious than the next, are spun in order to thread the rowdy fisticuffs in these English cities with the subsequent slashing and burning and murdering at Borodino.

I have, admittedly, offered only gross approximations of these historical theories, and of course they are often far more complex, discerning many separate causes – one cause after another – of a war. The temperament of a man called Napoleon is only one cause, they say, and the bread shortage in a city like Liverpool another. Often they will find a third, and perhaps a fourth or fifth cause to supplement the first and second. All the same, Tolstoy’s chief objection remains. Historians tend by their very nature to adopt a flawed approach, he argued, because a mass conflict can no more be reduced to a handful of causes than can a ship’s course be reduced to a few waves. Between a French port and a Russian port lie innumerable points in the sea: why label the fifteen thousand four hundred and third point, say, or the seventy-one thousand nine hundred and sixty-eighth point, as being ultimately responsible for the ship’s arrival?

An equivalent mistake would be to inquire of an age-beaten man, in which hour of your life was the blow delivered? Which blow? Why, the blow that loosened your teeth, and broke your bones, and thrashed your skin. Of course, there is no sense in such a question. The flow of time erodes patiently, continuously. What then could our elderly man say by way of a reply? He might recall that during a particularly hot summer night in 1968 he rolled out of bed and broke a shin. Perhaps he would smell once more the harsh carbolic soap with which, as a child growing up in the 1940s, he scrubbed his face. A game with his grandson in 1997 might come to his mind, in which a hard rubber ball accidentally struck his jaw. But none of these events, not less in combination, could truly help us to understand the elderly man’s present condition.

Change appears to us mysterious because it is invisible. It is impossible to see a tree grow tall or a man grow old, except with the precarious imagination of hindsight. A tree is small, and later it is tall. A man is young, and later he is old. A people are at peace, and later they are at war. In each case, the intermediate states are at once infinitely many and infinitely complex, which is why they exceed our finite perceptions.

Even a dramatic change can thus be accomplished without our knowledge. A friend once related to me the following illustrative tale. An American friend of my friend inherited a house in southern Europe. This house contained many fine pieces of furniture and works of art. Every summer, the American flew to Europe and lived for several months in the house among these objects. She sat on the same cushions, walked past the same paintings and heard the same ticking of the grandfather clock. The house’s upkeep she entrusted to a small and loyal staff, so that its rooms were always cleaned and polished and in good repair whenever she came through the door. And then one day, several summers following her inheritance, the American’s kid sister came to stay. The sister felt excited; she had heard many good things about the house and was longing to see it. But this feeling quickly gave way first to curiosity, then to confusion and finally to astonishment. A distinguished-looking chair in the hall, upon closer inspection, revealed itself to be cheap and rickety. Removed from its frame, the painting that hung above the fireplace flapped poster-thin. The marble-coloured statuette in the guest bedroom gave off the unmistakeable whiff of plastic. Fakes! Frantically, the sisters raced from room to room, until the whole place was left upside down. Every chair, every vase, every painting, virtually everything in the house – over one hundred items – unbeknownst to the American, had been meticulously replaced. Little by little, piece by piece, a wily member of staff had stolen the house away from under her nose.

Sometimes, revolutions turn over a country in the same way that the American’s staff member turned over her house. Imperceptibly, dissidence grows across a land long before the dictator calls out his tanks. And as recent events in the Arab world remind us, nobody predicts a revolution before it happens and nobody controls it once it is under way. ‘Why war and revolution occur we do not know,’ affirms Tolstoy. ‘We only know that to produce the one or the other action, people combine in a certain formation in which they all take part.’ Hearing the sudden drumbeat of shoes, the roar of voices, the upturned faces – flushed with anger – the almighty, most wise and beneficent ruler does not comprehend. In his incomprehension, he asks the same question that many of his fellow dictators end up asking themselves: from where did they come? All these people with their fists and their voices. He shakes his head in disbelief. And yet, the answer is simple because only one answer is possible. Simply put, the people were always there: on the streets, in the mosques, in the bazaars. Only now, this distributed mass of people suddenly and noisily combines. Only now does the man without work, and the woman without dignity, and the teenager without anything to eat make themselves seen and heard.

What is the power that moves peoples? Not the power of rulers, says Tolstoy, or for that matter the power of ideas. It is ineffable, invisible.

History seems to assume that this force is self-evident and known to everyone. But in spite of every desire to regard it as known, anyone reading many historical works cannot help doubting whether this force, so variously understood by the historians themselves, is really quite well known to everybody.

This force is the Human Life in which every person – from the lowly peasant Karataev to the Emperor Napoleon – participates. It is the ‘hidden warmth’ of patriotism experienced by the Muscovites when suddenly confronted with the dramatic threat of foreign invasion. It is the ‘chemical decomposition’ of the fleeing mass of French soldiers once their goal (the head-on confrontation in Moscow with an appointed ‘enemy’) becomes unattainable. It is the ‘force of habit’, during a salon conversation, which makes Prince Vasili Kuragin say ‘things he did not even wish to be believed.’

Rather than assign various degrees of responsibility to this cause or that, Tolstoy proposes that historians pay far greater attention to this force. Moscow’s conflagration, which the historians variously explain as a defensive tactic of the Russians (the so-called policy of ‘scorched earth’) or the wild vengeance of the invading French, becomes explicable in other terms.