Читать книгу The Tyranny of Numbers: Why Counting Can’t Make Us Happy - David Boyle - Страница 12

To really get down to the business of measuring life, two important ideas about numbers were still needed – a concept of zero and a concept of negative numbers. But to emerge into common use, both had to run the gauntlet of the old battle lines about numbers drawn across medieval Europe. Then there were the adherents of the old ways of the abacus, whose computations were not written down, and whose ritual movements as they made their calculations were inspired by the old wisdom of Pythagoras. The new computations were all written down. They had no mystery. There was something open and almost democratic about them, and they needed no priests to interpret them. Calculation was no longer a mysterious art carried out by skilled initiates.

And the big difference between them now was zero. Its arrival in Europe was thanks to a monk, Raoul de Laon – a particularly skilful exponent of the art of the abacus – who used a character he called sipos to show an empty column. The word came from the Arabic sifr, meaning ‘empty’, the origin of the word ‘cypher’. Either way, the old abacus could be put away in the medieval equivalent of the loft.

Inventing zero turns numbers into an idea, according to the child psychologist Jean Piaget. It’s a difficult idea too: up to the age of six and a half, a quarter of all children write 0+0+0 = 3. But once people had begun to grasp it, they tended to regard zeros with suspicion. Division by zero meant infinity and infinity meant God, yet there it was bandied around the least important trade calculations for fish or sheep for everyone to see. Even more potent were the objections of the Italian bankers, who were afraid this little symbol would lead to fraud. It can, after all, multiply other figures by ten at one slip of the pen.

So zero was among the Arabic numbers banned in 1229. But the enormous increase in trade because of the crusades and the activities of the Hanseatic League meant that something of the kind was needed. Italian merchants increasingly used zero as an underground sign for ‘free trade’. Bootleggers and smugglers embraced the idea with enthusiasm. Like the V sign across the continent under Nazi tyranny, zero became a symbol of numerical freedom, a kind of medieval counterculture.

What normally happens with countercultures is that they get adopted by everyone, and that’s exactly what happened here. Soon everyone was using zero quite openly and adding and subtracting happily using a pen and ink. Soon the abacus had died out so much that it became a source of fascination. One of Napoleon’s generals was given one in Russia when he was a prisoner-of-war, and he was so astonished that he brought it back with him to Paris to show the emperor. Don’t let’s dismiss the abacus completely, though. In occupied Japan in 1945, the US army organized a competition between their automatic calculator and skilled Japanese abacus-users. The abacus turned out to be both quicker and more accurate for every computation except multiplication.

The people of Western Europe resisted negative numbers for much longer. They called them ‘absurd numbers’, believing they were futile and satanic concepts, corresponding to nothing real in the world. Now, of course, our lives are dominated by them, because the debts they represent correspond to positive numbers at the bank. Debt opened the way to negatives via the world-shattering invention of double-entry book-keeping. This may not have been the brainchild of a friend of Leonardo da Vinci, a Milanese maths teacher called Fra Luca Pacioli, but it was Pacioli’s destiny to popularize it. The writer James Buchan described his method as a ‘machine for calculating the world’. It was one of the ‘loveliest inventions of the human spirit’, according to Goethe. It could work out, at any moment, when your complex deals were profitable, allowing you to compare one deal with another.

Pacioli was a Franciscan who knew all about profit. He had special dispensation from the Pope (a friend of his) to own property. ‘The end and object of every businessman is to make a lawful and satisfactory profit so that he may sustain himself,’ he wrote. ‘Therefore he should begin with the name of God.’ Pacioli and his followers duly wrote the name of God at the beginning of every ledger. Before Pacioli, traders tended to give any fractions to the bank. After Pacioli they could record them. They could grasp at a glance where they stood while their cargoes were on the high seas, or while they waited two years or more for them to be fabricated into something else. They could make them stand still to be counted.

A Neo-Platonist, fascinated by Pythagoras and his ideas of divine proportion, Pacioli filled his book with other stuff like military tactics, architecture and theology. He chose a potent moment to publish it: the year after Columbus arrived back from discovering America. But despite his Pythagorean roots, Pacioli provided the foundations for a more complex idea of profit and loss, of assets and liabilities, making all of them clearly measurable. His critics feared he had abolished quality altogether. All that you could put down in the double entries were quantities – numbers of sheep, amounts of wool: there was no column for qualities like good or bad. The numbers had taken over, simplifying and calculating the world in their own way.

‘If you cannot be a good accountant, you will grope your way forward like a blind man and may meet great losses,’ said Pacioli, the first accountant. He explained that it was all a matter of taking a piece of paper, listing all the debit totals on one side and all the credit totals on the other. If they add up and there’s a profit – the result is happiness, he said, sounding like a Renaissance Mr Micawber. If not, you have to find out where the mistake is – as millions of frustrated amateur accountants have been doing ever since.

Within three centuries, accountants had developed into the professionals you called in after bankruptcy, a kind of undertakers for the business world, which is why the Companies Act of 1862 which regulated such matters became known as ‘the accountant’s friend’. ‘The whole affairs in bankruptcy have been handed over to an ignorant set of men called accountants, which was one of the greatest abuses ever introduced into law,’ said Mr Justice Quinn during a bankruptcy case in 1875. By 1790, the Post Office directory for London lists one accountant. By 1840 there were 107 of them and by 1845 – right in the middle of the railway boom – there were 210, ready to assist cleaning up the mess in the financial collapse the following year. Maybe they were even responsible for the rash of suicides in London in 1846; maybe they helped prevent more. We shall never know. Either way, it was just the beginning for the accountants. By the turn of the century there were over 6,000 in England and Wales. Now there are 109,000, but – as far as I know – no counting horses left at all.