by David Boyle
Renaissance humanity was putting some distance between themselves and the animals, or so they believed. Anyone still dragging their feet really was holding back history. Some dyed-in-the-wool conservatives insisted that people know pretty well when it was day and night, and when the seasons change, without the aid of the new counting devices. But anyone who thinks that, said the Protestant reformer Philip Melanchthon, deserves to have someone ‘shit a turd’ in his hat. The new world of number-crunchers had arrived.
III
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.
IV
Pacioli and his spiritual descendants have helped to create the modern world with its obsession with counting, and the strange idea that once you have counted the money, you have counted everything. There is a hard-headed myth that numbers are serious and words are not – that counting things is a rigorous business for a serious man’s world. ‘When you can measure what you are speaking of and express it in terms of numbers, you know something about it,’ said the scientist Lord Kelvin. ‘When you cannot express it in terms of numbers your knowledge of it is of a meagre kind.’
Armed with this attitude, Lord Kelvin dismissed radio as pointless, aeroplanes as impossible and X-rays as a hoax, so we might wonder if he was right. But is my knowledge really of a meagre kind? Can I express something about myself in numbers? If Lord Kelvin’s successors managed to express my entire genetic code in numbers, would they know me better than I do myself when I can do no such thing? Well, in some ways, maybe they can – but I doubt it. Any more than the Nazis could know anything about the victims in concentration c
amps by branding a unique number on their arms.
We are more than branded now. We are in a world obsessed with numbers, from National Insurance and interest rates to buses, from bank balances and bar codes to the cacophony of statistics forced on us by journalists, politicians and marketeers. They seem to agree with Lord Kelvin that it provides us with a kind of exactitude. Actually it is exact about some of the least interesting things, but silent on wider and increasingly important truths.
We have to count. I’ve used piles of statistics in this book. Not counting is like saying that numbers are evil, which is even more pointless than saying that money is evil. We need to be able to count, even if the results aren’t very accurate. ‘Without number, we can understand nothing and know nothing,’ said the philosopher Philolaus in the fifth century BC, and he was right. But 25 centuries after Philolaus, the French philosopher Alain Badiou put the other point of view, and he was right too: ‘what arises from an event in perfect truth can never be counted’. Both Philolaus and Badiou are right. The more we rely on numbers to understand problems or measure aspects of human life, the more it slips through our fingers and we find ourselves clinging to something less than we wanted. Because every person, every thing, every event is actually unique and unmeasurable.
This is the paradox. If we don’t count something, it gets ignored. If we do count it, it gets perverted. We need to count yet the counters are taking over our lives. ‘The measurable has conquered almost the entire field of the sciences and has discredited every branch in which it is not valid,’ said the French poet Paul Valery. ‘The applied sciences are almost completely dominated by measurement. Life itself, which is already half enslaved, circumscribed, streamlined, or reduced to a state of subjection, has great difficulty in defending itself against the tyranny of timetables, statistics, quantitative measurements and precision instruments, a whole development that goes on reducing life’s diversity, diminishing its uncertainty, improving the functioning of the whole, making its course surer, longer and more mechanical.’
There was a time when numbers had significance beyond just ‘how many’, but we have lost the ancient understanding of numbers as beautiful and meaning something beyond themselves – the discredited and forgotten wisdom of Augustine and Pythagoras. We snigger patronizingly when we read St Thomas Aquinas’s solemn injunction that 144,000 would be saved at the end of time. Though probably the last thing he meant was that literally 144,000 people would make it to heaven. To Aquinas, a thousand meant perfection, and the 144 is the number of the apostles multiplied by itself. ‘I speak in parables of eternal wisdom, my honoured sir,’ he might have said, like a character in Andrew Sinclair’s novel Gog. ‘I leave statistics to plumbers.’
The old way of looking at numbers means nothing to us now. The historian of the medieval mind Alfred Crosby called it the ‘venerable model’. ‘We sniff and cluck at its mistakes – that the earth is the centre of the universe, for instance – but our real problem with the Venerable Model is that it is dramatic, even melodramatic, and teleological: God and Purpose loom over all,’ he wrote. ‘We want (or think we want) explanations of reality leeched of emotion, as bloodless as distilled water.’
Bloodless one-dimensional messing can dismiss a horse so sensitive that it can read the faintest human gestures, just because it doesn’t meet our narrow definition of intelligence.
Bizarre measurement No. 2
Momme
(Unit of mass in Japan used for measuring the size of pearls. 1 momme = 10 fun.)
* * *
Amount of time the average American spends going through junk mail in a lifetime: 8 months
Amount spent by Americans every year breaking into broken automatic car locks: $400 million
Chapter 2
Historical Interlude 1: Legislator for the World
Nature has placed Mankind under the governance of two sovereign masters, pain and pleasure. It is in them alone to point out what we ought to do, as much as what we shall do.
Jeremy Bentham
There is nothing which has yet been contrived by man, by which so much happiness is produced as by a good tavern or inn.
Samuel Johnson, 21 March 1776
I
It was one of the strangest funerals ever held. Three days after his death on 6 June 1832, the body of the great utilitarian philosopher Jeremy Bentham (dressed in a nightshirt) was unveiled to his friends and admirers, gathered together at the Webb Street School of Anatomy in London. It was a stormy early evening, and the grisly occasion was lit by flashes of lightning from the skylight above, as Bentham’s young doctor Thomas Southwood Smith began a speech which included a demonstration of dissection on his old friend.
Among the faithful were some of the great figures of reform from the immediate past and future, the radical tailor Francis Place and the future sanitation reformer Edwin Chadwick in the shadows. In their minds, we might imagine, was a sense of enormous achievement – two days before, the Great Reform Act, which had been the focus of all their hopes, had been given Royal Assent. There might also have been the occasional less welcome echo from Mary Shelley’s Gothic novel Frankenstein, published 14 years before, as Southwood Smith’s scalpel glinted in the candlelight – with all its warning for the Godless who meddle with the untouchable moments of birth and death.
They might also have been wondering whether this was the right way of remembering their hero. Dissection was then regarded as such an appalling end that it was handed out as an extra punishment for the murderers who normally found themselves cut open in this room. Southwood Smith the former preacher managed to keep his voice steady, but his face was as white as the corpse’s. Bentham’s funeral guests would have reassured themselves that they were carrying out the details of his will, and that they were men of the new age of science, and could put aside those old-fashioned notions of superstition, emotion and shame.
Could those things be measured in Bentham’s new political morality of ‘utility’? The facts – yes, the rigorously logical facts – were that it was more ‘useful’ to dissect the philosopher’s body than it was to bury it. And as Bentham had written himself, if you were going to have statues or portraits of him, it was more ‘useful’ to use the real thing, rather than let it go to waste in a coffin in the earth.
When Smith finished his work of cleaning and embalming, Bentham’s body was to be an ‘Auto-Icon’, a modern monument and a more exact replica of the man than any artist could possibly achieve. It would be dressed in his own clothes, with his walking stick (which he used to call Dapple, after Sancho Panza’s mule) firmly in his hands. It would remain in a glass case in University College, London, which he had done so much to turn into the reality of bricks and mortar.
The plan didn’t go quite as expected. Despite Bentham’s best endeavours to study the head-shrinking methods of primitive tribes, his own head shrivelled ghoulishly and extremely fast. A few years later, the college decided to replace it with a waxwork. The original was placed between his legs, from where it has occasionally been stolen. And there Bentham’s Auto-Icon remains, wheeled gravely into important college meetings, and still on display to the professors and students of London University and anybody else who wanders in, together with some very un-Benthamite rumours about ghosts.
It was a fittingly scientific end to the life of the man who gave us the philosophical school of utilitarianism. Because it was Bentham who told us that what is good and right is what most promotes human happiness – not necessarily what it says in law or the Bible. And it was Bentham who launched the world’s politicians on an increasingly determined set of calculations, so they can know what this ‘good’ is in any given situation.
The daily outpouring of figures and statistics that now so dominates our conversations began partly with Bentham, but he was also a symptom of his time. At the beginning of his life, as he stood with his father at the age of 12 to watch the coronation procession of George III, London was dirty, foul-smelling and dangerously
brutal, with one congested bridge over the river. By the end there were eight bridges over the Thames and the streets were lit by gaslight, and steam trains – ‘self-moving receptacles’, as he described them – were beginning to change the shape of cities. What’s more, his native land had experienced no less than 30 years of census returns and was about to start the compulsory registration of births, marriages and deaths. The number-crunchers had arrived. Some people even predicted it at the time. ‘The age of chivalry is gone,’ moaned Edmund Burke in the House of Commons. ‘That of sophisters, economists and calculators has succeeded, and the glory of Europe is extinguished for ever.’ And if one person could be blamed for that, you could probably waggle the finger at Jeremy Bentham.
Now almost two centuries have gone by since his death, you would have thought it might be possible to get more perspective on the man who did so much to create this aspect of the modern world. But that still seems impossible. Bentham, for all his mild manners and gentle unemotional ways, has inspired passionate feelings of distaste ever since. Thomas Carlyle described Bentham’s contribution as a ‘pig philosophy’. Karl Marx went even further, describing Bentham as ‘the insipid, pedantic leather-tongued waste of the commonplace bourgeois intelligence of the nineteenth century’. Trotsky was immediately converted by reading his works at the age of 17, but later condemned Bentham’s ideas as ‘a philosophy of social cookbook recipes’. The humourless Nietzsche was even moved to verse to describe him: