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The Tyranny of Numbers: Why Counting CanвЂ™t Make Us Happy
David Boyle

Never before have we attempted to measure as much as we do today. Why are we so obsessed with numbers? What can they really tell us?Too often we try to quantify what canвЂ™t actually be measured. We count people, but not individuals. We count exam results rather than intelligence, benefit claimants instead of poverty. The government has set itself 10,000 new targets. Politicians pack their speeches with skewed statistics: crime rates are either rising or falling depending on who is doing the counting.We are in a world in which everything designed only to be measured. If it canвЂ™t be measured it can be ignored.But the big problem is what numbers donвЂ™t tell you. They wonвЂ™t interpret. They wonвЂ™t inspire, and they wonвЂ™t tell you precisely what causes what.In this passionately argued and thought-provoking book, David Boyle examines our obsession with numbers. He reminds us of the danger of taking numbers so seriously at the expense of what is non-measurable, non-calculable: intuition, creativity, imagination, happinessвЂ¦Counting is a vital human skill. Yardsticks are a vital tool. As long as we remember how limiting they are if we cling to them too closely.Americans who claim to have been abducted by aliens = 3.7 millionAverage time spent by British people in traffic jams every year = 11 daysNumber of Americans shot by children under six between 1983 and 1993 = 138, 490

THE TYRANNY OF NUMBERS

Why Counting CanвЂ™t Make Us Happy

David Boyle

Contents

Cover (#udca9dee7-93c8-565f-bbe6-f290fbb55cf0)

Title Page (#u3026d26e-0b5b-5103-9e7a-826e6d84230e)

Dedication (#ulink_d20694fb-4b81-55e2-891f-baedcc623005)

Introduction: Still Life with Numbers (#u84be7350-40ad-57c2-9abe-c5724dab957e)

Chapter 1: A Short History of Counting (#u7c2af22a-e531-59c4-ada9-9da21cefbd72)

Chapter 2: Historical Interlude 1: Legislator for the World (#uc6d10461-cff0-599a-a939-963090da295a)

Chapter 3: Elusive Happiness (#uafed602b-37d1-5be2-a8ac-2ef32d48a046)

Chapter 4: Historical Interlude 2: Commissioner of Fact (#litres_trial_promo)

Chapter 5: The Feelgood Factor (#litres_trial_promo)

Chapter 6: Historical Interlude 3: Social Copernicus (#litres_trial_promo)

Chapter 7: The New Auditors (#litres_trial_promo)

Chapter 8: Historical Interlude 4: National Accountant (#litres_trial_promo)

Chapter 9: The New Indicators (#litres_trial_promo)

Chapter 10: Historical Interlude 5: The Price of Everything (#litres_trial_promo)

Chapter 11: The Bottom Line is the Bottom Line (#litres_trial_promo)

Postscript (#litres_trial_promo)

Keep Reading (#litres_trial_promo)

Index (#litres_trial_promo)

Acknowledgements (#litres_trial_promo)

About the Author (#litres_trial_promo)

Also by the Author (#litres_trial_promo)

Copyright (#litres_trial_promo)

About the Publisher (#litres_trial_promo)

Dedication (#ulink_6a70494b-c3f5-5aee-afb4-4eeed503d10a)

For Joanna, Ben, Agatha and Frances

Introduction (#ulink_71173a14-9e16-573a-ab90-a27c61ca49a1)

Still Life with Numbers

The renowned cosmologist Professor Bignumska, lecturing on the future of the universe, had stated that in a billion years according to her calculations, the earth would fall into the sun in a fiery death. In the back of the auditorium a tremulous voice piped up. вЂ?Excuse me Professor, but h-how long did you say it would be?вЂ™ Professor Bignumska calmly replied, вЂ?About a billion years.вЂ™ A sigh of relief was heard. вЂ?Whew! For a minute there, I thought you said a million years.вЂ™

Douglas Hofstadter,Scientific American, May 1982

There are no such things as still lifes.

Erica Jong

I

Mary Poppins was the first film I ever saw. I was six years, four months old вЂ“ letвЂ™s measure it precisely. I remember trotting as fast as I could beside my father along Whitehall, past the Treasury and the other palaces of national calculation, to the Haymarket. I remember the strange red torches and the national anthem at the end. ThatвЂ™s how it was in those more deferential and innocent days before the hippies. And I remember being completely blown away by the experience, the songs of Julie Andrews and the idea that life should be a little more magical than it was.

Within weeks I knew most of the lyrics by heart, though I barely understood the words. Maybe, in retrospect, I was also a little influenced by Mary PoppinsвЂ™ ridicule of George Banks вЂ“ Hollywood has recycled the name George Banks for pompous boobies ever since вЂ“ and his fascination for the kind of order brought by numbers. вЂ?They must feel the thrill of totting up a balance book,вЂ™ she sings to poor deluded George about his children:

вЂ¦ A thousand cyphers neatly in a row.

When gazing at a graph that shows the profits up,

their little cup of joy should overflow.

The irony is lost on him вЂ“ as it was on me. And though Hollywood is still busily promoting the idea of magic, you would never catch them in this post-Thatcherite age making fun of profits or ridiculing the vital importance of calculation вЂ“ still less the idea of cyphers neatly in a row. ItвЂ™s just too important to us all these days.

So I came away from the cinema determined to make sure I flung my tuppence away on some little old bird woman, rather than marvelling at the strange alchemy of compound interest if I put it in the bank. I was not going to be a George Banks. Yet here I am, 35 years later, with my pension and life insurance, living in a world completely overwhelmed by numbers and calculation.

ItвЂ™s the same for nearly all of us. There are personal calculations to be made each day, about investments, journey times, bank machines and credit cards. There are professional figures at work, in the form of targets, statistics, workforce percentages and profit forecasts. As consumers, we are counted and aggregated according to every purchase we make. Every time we are exposed to the media, there is a positive flood of statistics controlling and interpreting the world, developing each truth, simplifying each problem. вЂ?Being a man is unhealthy,вЂ™ said the front page of the Evening Standard recently, adding вЂ“ like every similar newspaper article about statistics вЂ“ the word: вЂ?official.вЂ™ As if we had been wondering about the truth all these years and, thanks to the counters, we now know. As if the figures are so detached that there is no arguing with them.

But of course we keep arguing. Just as the government keeps arguing despite its battery of benchmarks, quality indicators and league tables, as it struggles to hold back chaos like King Canute in front of the waves. We take our collective pulses 24 hours a day with the use of statistics. We understand life that way, though somehow the more figures we use, the great truths still seem to slip through our fingers. Despite all that calculating, and all that numerical control, we feel as ignorant as ever.

Mary Poppins might have been talking about me when she said that вЂ?sometimes a person we love, through no fault of his own, canвЂ™t see past the end of his noseвЂ™. She meant George Banks, of course, but I feel just as myopic myself. Life never keeps still long enough to measure anything important.

If you are said to be вЂ?calculatingвЂ™, people could mean one of two things about you вЂ“ both related and equally repellent. It could mean that you are constantly comparing what is best for you in any given situation. This is not a compliment. It implies something cold, fish-like and completely self-interested. But it could also mean you are someone who counts too much, someone who measures things but canвЂ™t see the reality behind them.

There is something equally clinical about that, but disinterested rather than self-interested. A calculating person, in this sense, is someone for whom the world past the end of their nose is a foreign country. And although we have become exactly that with all our counting, and increasingly so, it can send a shiver down the spine when you come across extreme examples. Like the eighteenth-century prodigy Jedediah Buxton, in his first trip to the theatre to see a performance of ShakespeareвЂ™s Richard III. Asked later whether heвЂ™d enjoyed it, all he could say was that there were 5,202 steps during the dances and 12,445 words spoken by the actors. Nothing about what the words said, about the winter of our discontent made glorious summer; nothing about the evil hunchback king.

Today, Buxton would probably be described as autistic. It is particularly horrifying to hear that his numbers turned out to be exactly right.

The story is funny now as then, but it is also faintly disturbing, and I have been wondering why this is. It could be that we see Jedediah Buxton as a fearsome symbol of the modern age, counting everything but seeing the significance of nothing. But I think it is deeper than that. There is something inhuman about it вЂ“ not so much the ability to count, but the failure to be moved. We shiver, I think, at anybody with no emotions вЂ“ as if they were completely amoral, like Dr Strangelove. We shrink from white-coated doctors too like cold calculating machines. Even doctors should be slightly fallible.

Even so, we encounter these вЂ?calculatingвЂ™ machines almost every day. ItвЂ™s hard not to turn on the news without audibly tripping over one of them. Like the academic who refuses to pass judgement on any problem, however urgent, because there hasnвЂ™t been enough research. Or the politician who is so obsessed with the polling figures that he can no longer trust his gut instincts. Or the social scientist who has laboriously proved with the use of statistics something which anybody else with an ounce of common sense knew already вЂ“ that the death of a parent can scar a child for life, or that alcoholics have an unusually high depression rate. ItвЂ™s official, they say. Like the University of Michigan study which revealed that children who donвЂ™t take exercise and eat junk food tend to be fatter. Or the recent research which showed that areas of high unemployment tend to have fewer jobs.

Then there are the familiar people who muddle up the numbers with the truth. Or, even worse, those who think you can change the truth just by changing the statistics. DonвЂ™t forget those dismal agriculture ministers who urged the public to listen to the scientists over the safety of BSE beef (and really believed it) even though they were quietly suppressing the research of anybody who argued that it might not be safe to eat.

These are modern monsters, but none of us can completely escape the accusation. WeвЂ™re all tied up with figures, even if they are just cricket averages and lottery numbers.

Romantics and leftists traditionally say this is a bad thing. Romantics think that it reduces the individual to mere figures. Leftists think itвЂ™s a kind of tyranny. They are both wrong in the sense that we do need to be able to count вЂ“ but they are right too. The strange thing is that ratcheting up the calculations has often been done for excellent humanitarian reasons, driven by impeccably radical reformers. Of course in the history of the tyranny of numbers over life there are crazed scientists and Nazis with branding irons who stalk through the pages. This is no scientific history of counting, and there is no account of the great statistical pioneers like Herbert Spencer or Karl Pearson. Nor does it cover the byways of scientific research or IQ вЂ“ or the people who really believed you could control individuals by counting them.

But counting was also a way of improving the world. Maybe they wanted to prove the existence of great inequality or disease, like Edwin Chadwick. Maybe they wanted to find a way of aggregating the national accounts to defeat Hitler, like John Maynard Keynes. Or maybe they wanted to force politicians to worry about peopleвЂ™s happiness, like Jeremy Bentham. All the historic interludes IвЂ™ve chosen in this book fall into that category. They are people who вЂ“ for the best of motives вЂ“ brought forth the flood of numbers and calculations into the non-scientific parts of our lives.

It still is a way of improving the world. Are your schools not performing as well as they should? Then measure their results. Are you worried about the performance of a local council, a company, a great institution, a hospital? Send in the auditors, set some standards as benchmarks. You donвЂ™t trust the professionals? Summarize their decisions in number form, send in the cost-benefit experts and keep your beady eye on them. It is the modern way. Numbers вЂ“ like money вЂ“ drive out the mysterious power of elites, the clubbable atmosphere of the professions, the we-know-best patronizing attitudes of those thick-set people with glasses and firm handshakes who used to lord it over our lives. We can control them if we can reduce their complex professionalism to numbers.

The trouble is that the numbers have proliferated, and itвЂ™s sometimes hard to breathe вЂ“ still less tell the difference between one statistic and another. It is difficult enough to remember your car registration number, PIN number, home, work and mobile phone numbers all at the same time. ItвЂ™s almost enough to make you coldly calculating.

II

If you want to watch people who go further than that вЂ“ people who try to measure things which can probably never be measured вЂ“ then come with me for a moment to the closing minutes of a libel action at the Law Courts in the Strand, London. The jury has decided that when a national newspaper described a respectable lady as a prostitute вЂ“ when she was no such thing вЂ“ they had clearly вЂ?lowered her in the estimation of right thinking people,вЂ™ which is one legal definition of libel. But what kind of damages should she be given?

The amount awarded is a decision for the jury, and the judge is not allowed to even hint at a figure. He cannot suggest to them that the average pay-out might be ВЈ10,000 or ВЈ500,000. His half-moon spectacles perched on the end of his nose, he turns to the jury box. вЂ?Imagine if you will,вЂ™ he says, вЂ?a small flat in Battersea. Or perhaps a semi-detached in Maida Vale. Or maybe a penthouse apartment in Mayfair вЂ¦вЂ™

And so he goes on. Did the humiliation the woman received deserve the flat, the house or the penthouse? Or something else? How could you start to measure such things? But the jury played safe and plumped for the house, and who can say whether they were right or not? вЂ?If this is justice, IвЂ™m a banana,вЂ™ said the editor of Private Eye famously with damages of ВЈ600,000 awarded against him in the same court. Damages are notoriously difficult to judge, but sometimes you still have to try.

Libel damages are just one example among many. What makes this such a peculiar moment in the history of measurement is that in almost every area of public life, qualities like happiness, competence or loyalty are being picked over by hordes of radical accountants and politicians, visionary entrepreneurs and planners вЂ“ desperately trying to find ways of being more effective in a competitive world.

Despite the proliferation of measurements, somehow the numbers are still not providing an effective lever. Why? Because, so often, you canвЂ™t measure whatвЂ™s really important. But itвЂ™s all very well to say it is impossible: decisions still have to be made вЂ“ and if you donвЂ™t count whatвЂ™s really important, it gets ignored. It doesnвЂ™t count. There are only so many resources, so doctors must compare the quality of life of a 70-year-old with heart failure against a suicidal teenager with a long history of depression. Planners have to compare the pleasure and disruption brought by a new 18-screen cinema with the contentment of keeping the site as a park. Investors have to compare a notoriously polluting oil company with a dodgy record in human rights with a tremendously successful Internet company with three employees and no profits.

ItвЂ™s impossible of course, but they have to try, because otherwise the wrong decision will be made or their rivals will steal an advantage. So they find themselves isolating something which can be counted. Then they measure, measure, measure, knowing that what they measure is alive and will not keep still, and suspecting that maybe вЂ“ however much they count вЂ“ they will not capture the essence of the question they are asking. Things have to keep static if youвЂ™re going to count them: thatвЂ™s probably why the first statisticians were known as вЂ?statistsвЂ™. But real life isnвЂ™t still.

How, for example, can businesses measure what they are worth, when value is increasingly ephemeral вЂ“ encompassing things which go way beyond traditional balance sheets? How can we measure our national or local success when our measuring rods are so inadequate, and yet so important to our politicians? Yet without measuring rods, it is hard to know whether we are making any progress.

But if politicians have a difficult time, it is nothing to what is happening in the business world, as managers struggle to find ways of measuring customer loyalty, brand reputation or staff morale. And as they do so, Internet companies which have never made a profit and which sell intangible products, rush past them up the Wall Street indices. When the balance sheets of a company like Microsoft show assets worth only 6 per cent of its stock market value, they need to find an answer.

ItвЂ™s all a bit like a computer game. What really matters canвЂ™t be counted, but itвЂ™s a much worse situation than that. If you make the attempt but measure the wrong thing, it isnвЂ™t just wasted effort. It can destroy everything youвЂ™ve worked for. Like the school league tables that make teachers concentrate on getting borderline pupils through at the expense of their weaker classmates. Or the hospital waiting lists that fell because only quick simple problems were treated. ItвЂ™s a familiar story, just as unemployment statistics bear no relation to the number of people who actually want to work. It all comes down to definitions: governments prefer to count people claiming benefits rather than unemployed people. To count things, you first have to define them in measurable ways, and magically the system can manipulate the figures by narrowing the definition.

This amounts to a kind of crisis. We need answers, but we also know that what is most important to our lives simply canвЂ™t be pinned down like a still life. We canвЂ™t measure happiness directly, any more than we can measure God or measure life, but we can measure some of its symptoms, and some of the symptoms of its absence. Which is why a city like Seattle started measuring success by the number of vegetarian restaurants, or why Strathclyde started measuring success by the number of golden eagles. It is why schools are trying to measure their pupilsвЂ™ self-esteem, why investors are measuring the ethics of their investments вЂ“ and why companies like Toys РЇ Us and Shell are pouring resources into measuring the knowledge and contentment of staff, communities and stakeholders.

A century and a half ago, the followers of the philosopher Jeremy Bentham were dashing around the country in their stagecoaches to measure everything they possibly could вЂ“ from the health of slum inhabitants to the religious feelings of children вЂ“ coming home with tables of figures with which to challenge the world. Now there is a new generation of iconoclasts who are determined to solve the measurement problem. You donвЂ™t see them at work. They are safely behind their calculators or drawing up tables of comparison in just the same way. This book is about them, because вЂ“ like scientists reaching into the unknown вЂ“ they may change our lives for ever.

III

What we canвЂ™t do is leave things as they are вЂ“ all of those numbers are making us misunderstand things. They make us ignorant of the world past the ends of our noses, measuring things means defining them and reducing them. Still life is dead life. In fact, in Italian, still life is вЂ?natura mortaвЂ™. We lose some of the magic in it. Every time a new set of statistics comes out, I canвЂ™t help feeling that some of the richness and mystery of life gets extinguished. Just as individual stories of passion and betrayal get hidden by the marriage statistics, or the whole meaning of the Holocaust gets lost in the number 6,000,000. There is a sort of deadening effect, a distancing from human emotion and reality. Not much, but just enough for it to matter вЂ“ like Jedediah Buxton trying to understand ShakespeareвЂ™s masterpieces by counting the words.

Magic is about breaking out of categories, words and definitions, and I should declare an interest вЂ“ I want a bit more of it. Measuring things takes away the childish sense of wonder where things are really possible. A serious-looking man with a white coat and clipboard вЂ“ one of those disinterested people who counts a lot but feels little вЂ“ will have to put me right, and tell me off for filling peopleвЂ™s minds with airy-fairy nonsense.

But donвЂ™t blame me. I was plummeted into this frame of mind as a teenager when I came across a poem by D. J. Enright called вЂ?Blue UmbrellasвЂ™, which in a few short lines summed up the poverty of definitions:

The thing that makes a blue umbrella with its tail вЂ“

How do you call it? You ask. Poorly and pale

Comes my answer. For all I can call it is peacock.

Now that you go to school, you will learn how we call all sorts of things;

How we mar great works by our mean recital.

You will learn, for instance, that Head Monster is not the gentlemanвЂ™s accepted title;

The blue-tailed eccentrics will be merely peacocks; the dead bird will no longer doze

Off till tomorrowвЂ™s lark, for the letter has killed him

The dictionary is opening, the gay umbrellas close.

Bizarre measurement No. 1

Guz

(Middle Eastern measurement of variable length. One Guz = 27 inches in Bombay, 37 inches in Bengal, 25 inches in Arabia and 41 inches in Iran.)

Americans who claim to have been abducted by aliens: 3.7 million

Speed of London traffic in 1900: 12 mph

Speed of London traffic in 1996: 12 mph

Average time US patients are allowed to speak before being interrupted by their doctors: 18 seconds

Chapter 1 A Short History of Counting (#ulink_24d2d955-05d9-57d1-b563-8c3c52452b00)

Know then thyself, presume not God to scan,

The proper study of mankind is man.

Alexander Pope

I have often admired the mystical way of Pythagoras, and the

secret magic of numbers

Sir Thomas Browne,Religio Medici

I

It was 12 September 1904. The Kaiser was on the throne, the Dreadnought was less than a few rivets on the ground and Freud was in his Vienna consulting rooms, thinking the unthinkable. In Berlin, the unthinkable seemed to be becoming real.

As many as 13 of the cityвЂ™s greatest scientific minds were convinced. The leading psychologists, veterinary surgeons, physiologists вЂ“ even the director of the Berlin Zoo вЂ“ had come away from the demonstration shaking their heads, worrying slightly for their professional reputations. Yet they had just signed the paper: the horse they had spent the day watching was not responding to signals from its owner when it demonstrated its considerable mathematical powers. Clever Hans, in other words, was officially not a circus act. He really was clever.

Clever Hans sounds like the title of a Grimm fairy tale or one of FreudвЂ™s more spectacular patients. Actually he was a horse belonging to a retired maths teacher called Wilhelm von Ostein, who believed passionately in its ability to do complicated multiplication and division вЂ“ even fractions вЂ“ tapping out the answer with its hoof and manipulating sets of numbers up to six decimal places. WhatвЂ™s more, by converting his answers into numbers, Hans could also read, spell and identify musical tones. Zeros he communicated with a shake of the head.

Wearing a hard black hat over his streaming white hair and beard, von Ostein exhibited Hans in a northern suburb of the city every day at noon. He refused to take money for the show, rewarding Hans with a pile of bread and carrots for answering the questions of the daily audience who gathered around.

A leading biologist had become fascinated with the Hans phenomenon, and had invited the 13 eminent scientists вЂ“ the so-called Hans Commission вЂ“ to defend him and von Ostein from ridicule in the press. The commission recommended further study by a rising young psychologist, Oskar Pfungst. In the six weeks that followed, Pfungst had been severely bitten by Hans, von Ostein had withdrawn his horse in a rage, and (with a sigh of relief) modern science had cracked the mystery of the counting horse.

First of all, Pfungst noticed that Hans got excited if he could not see the questioner, and made strenuous efforts to see round his blindfold so that he could. They also found that the horse lost the arithmetical plot if he was asked questions that the questioners didnвЂ™t know the answer to themselves. Clearly he must be responding to some kind of unconscious signal from the person asking the questions. When the implications of the blindfold experiment sank in, von Ostein exploded with fury at Hans, but the following day he had regained his ardent belief and took the horse away.

It was too late. PfungstвЂ™s report became a legend in experimental psychology. He argued, completely convincingly, that Hans was able to pick up the slight incline of the questionersвЂ™ heads when they had finished asking the question and expected the answer to be tapped out. When Hans had reached the right number of taps, he was able to notice the tiny relaxation, the minute straightening up or raised eyebrow with which the questioners betrayed themselves, and he stopped tapping. Hans also tapped faster when he knew it was a long answer (a practice that added to his intellectual reputation) and this too, said Pfungst, he was able to deduce from tiny changes of facial expression.

PfungstвЂ™s own reputation was made, modern science had been vindicated вЂ“ animals could not count. Von Ostein died a few months later. History does not relate what happened to Hans, but IвЂ™m not hopeful.

It was, of course, the dawn of the century of numbers. A hundred years later, we prove our humanity every time we open our newspapers with the mass of statistics on offer. Numbers are our servants, the tools of human domination. For centuries, counting was accepted as one of the key differences between human beings and animals. вЂ?Brutes cannot number, weigh and measure,вЂ™ said the great pioneer of quantification, the fifteenth-century cardinal Nicholas of Cusa. The arrival of a mathematical horse was a serious challenge to the numerical world view.

But 1904 was not just the year of Rolls-Royce and the entente cordiale, it was a moment of fantasy and wish-fulfilment. Peter Pan was on stage for the first time, British troops were taking the mysterious Tibetan city of Lhasa, and there was an absolute rash of вЂ?cleverвЂ™ animals on offer, each one challenging the accepted view of numeracy as exclusively human. There was the English bulldog Kepler, owned by Sir William Huggins, which barked out its numerical answers. There was Clever Rosa, the so-called Mare of Berlin, and doyenne of the local music-hall stage. There was the clever dog of Utrecht, the reading pig of London, all forerunners of Babe in their own way. Pfungst despatched many of their reputations, but he was too old later to investigate Lady, the talking and for-tune-telling horse of Virginia.

Lady managed to count and tell fortunes by flipping up letters on a special chart. PfungstвЂ™s biographer told the story of a colleague of his who had visited Lady to ask where his missing dog had gone. The horse spelled out the word DEAD. Actually, the dog turned up alive and well a few days later, and following Pfungst he gave his opinion вЂ“ having studied Hans in such detail вЂ“ that Lady had probably been able to sense the manвЂ™s conviction that the dog was dead.

So we can all breathe a sigh of relief вЂ“ animals canвЂ™t count; numbers are safely human. But a century later, I still want to shake them all and say: вЂ?Hang on a minute!вЂ™ Here was a horse that was apparently able to read minds and spell correctly, never mind counting.

The accepted order of things is not absolutely safe, but we will never be able to set the clock back long enough to find out. Lady and Hans have long since gone to the knackers, and modern science is blind to strange phenomena like that. But the issue of counting and who is entitled to do so is still with us. Numbers have been in constant use for the past 6,000 years, but we have never quite resolved what they are. Are they intellectual tools for humans, invented by us for our own use? Or are they fantastical concepts, pre-existing in the universe before Adam, which we had to discover along with America and the laws of thermodynamics? Which came first: man or numbers? Are they available for any species to use or just an aspect of mankind? Are they real or human?

The consensus moves backwards and forwards through the centuries, and always with political implications. If numbers are a mysterious aspect of the universe put there by God, we tend to become subject to control and manipulation by accountant-priests. If they are a method by which humanity can control chaos, they become part of the tools of a technocratic scientific elite. The modern world is firmly in the second camp. We have rejected rule by priests in favour of rule by science. Measuring is something humans have invented for themselves, and animals вЂ“ by definition вЂ“ canвЂ™t hack it. They might be able to spell or pick up astonishingly subtle body language, but it is important for our world view that they canвЂ™t count.

The other view вЂ“ that numbers have meaning in their own right вЂ“ was represented by the Greek philosopher Pythagoras, in the sixth century BC, who was the great believer in the natural God-given beauty of numbers. For Pythagoras, numbers corresponded to a natural harmony in the universe, as bound up with the music of the spheres as they are with calculations. Music and beauty were underpinned by numbers. The story goes that Pythagoras listened to a blacksmith hammering away and heard the musical notes made by the anvil. He realized that they were generated by different lengths of hammer, and that there were perfect ratios of halves, thirds and quarters which generated perfect chords. They were the secret harmonies generated by the real numbers in nature. Another legend says that he learned about such things from the wisest people among the Egyptians and Phoenicians, and spent 12 years studying with the Magi after being taken captive and imprisoned in Babylon.

Numbers existed even before the universe itself, according to Pythagoras. But even that was too mild for St Augustine of Hippo, who declared that six was such a perfect number that it would be so even if the world didnвЂ™t exist at all. вЂ?We cannot escape the feeling,вЂ™ said the mathematician Heinrich Hertz, вЂ?that these mathematical formulae have an independent existence and an intelligence of their own, that they are wiser than we are, wiser even than their discoverers, that we get more out of them than was originally put into them.вЂ™

Numbers rule the universe, said Pythagoras and his followers. Anything less like irrational numbers was вЂ?unutterableвЂ™ and initiates were sworn to secrecy about them. According to his follower Proclos, the first people who mentioned such possibilities all died in a shipwreck. вЂ?The unutterable and the formless must needs be concealed,вЂ™ he said. вЂ?And those who uncovered and touched this image of life were instantly destroyed and shall remain forever exposed to the play of the eternal waves.вЂ™

It was irrational numbers that eventually did for Pythagoras. When his descendants opened up a whole new world of paradoxes, irrationality, bizarre computations, negative numbers, square roots, then nothing ever seemed the same again. And although technocrats might breathe a sigh of relief about this evidence of the modern rationality breaking through, we may also have lost something from that sense of pre-existing perfection.

II

The tyranny of numbers over life began with the simple counting of things with marks on wood. You find notched reindeer antlers from 15000 BC, well before Britain separated itself from continental Europe. These methods lasted into modern times, and were known in the English medieval treasury as вЂ?tally sticksвЂ™. Tally sticks were finally abandoned by the British civil service as a method of keeping track of public spending as late as 1783. After that, the old ones hung around for a generation or so, piled into the Court of Star Chamber until they needed the room. Someone then had the bright idea of burning them in the furnace that was used to heat the House of Lords. The result was that the furnace set light to the panelling and led to the conflagration in 1834 which burned down the Palace of Westminster, and led to the world-famous monstrosity that we know today, complete with Big Ben and mock Gothic.

A few more of these dangerous items were found during repairs to Westminster Abbey in 1909, and they were put safely into a museum, where they could do less damage.

Notches probably came before language. Prehistoric people probably used words like вЂ?oneвЂ™, вЂ?twoвЂ™, вЂ?threeвЂ™ and вЂ?manyвЂ™ for anything more complicated. In fact, sometimes вЂ?threeвЂ™ might mean вЂ?manyвЂ™. Take the French, for example: вЂ?troisвЂ™ (three) and вЂ?tresвЂ™ (very). Or the Latin: вЂ?tresвЂ™ (three) and вЂ?transвЂ™ (beyond). A tribe of cave dwellers was discovered in the Philippines in 1972 who couldnвЂ™t answer the question вЂ?How many people are there in your tribe?вЂ™ But they could write down a list of all 24. But then counting is a philosophical problem, because you have to categorize. You have to be able to see the similarity in things and their differences, and decide which are important, before you can count them. You have to be able to do Venn diagrams in your head. вЂ?It must have required many ages to discover that a brace of pheasants and a couple of days were other instances of the number two,вЂ™ said the philosopher Bertrand Russell. But once you have grasped that concept, there are so many other categories you have to create before you can count how many people there are in your tribe. Do you count children? Do you count foreigners who happen to live with you? Do you count people who look completely different from everybody else? Counting means definition and control. To count something, you have to name it and define it. It is no coincidence that it was the ancient Sumerian civilization, the first real empire, which developed the idea of writing down numbers for the first time. They had to if they were going to manage an imperial culture of herds, crops and people. Yet any definition you make simply has to be a compromise with the truth. And the easier it is to count, the more the words give way to figures, the more counting simplifies things which are not simple. Because although you can count sheep until you are blue in the face, actually no two sheep are the same.

The old world did not need precision. If ChristвЂ™s resurrection was important, it wasnвЂ™t terribly vital to know what the actual date was. Instead Europeans used numbers for effect вЂ“ King Arthur was described as killing tens of thousands in battles all by himself. Modern politicians are the last remaining profession which does this, claiming unwieldy figures which they have achieved personally, and pretending a spurious accuracy by borrowing the language of statistics, when actually they are using the numbers for impact like a medieval chronicler. Nor were the numbers they used much good for calculation. Nowadays Roman numerals only exist for things which powerful people want to look permanent вЂ“ like television programmes or the US World Series вЂ“ but which are actually very impermanent indeed.

The new world needed accuracy and simplicity for its commerce. Although they were briefly banned by an edict at Florence in 1229, the new Arabic numbers вЂ“ brought back from the Middle East by the crusaders вЂ“ began to be spread by the new mercantile classes. These were the literate and numerate people вЂ“ with their quill pens tracing the exchange of vast sums вЂ“ plotting the despatch of fleets for kings, managing the processing of wool with the new counting boards.

And soon everybody was counting with the same precision. King JohnвЂ™s Archbishop of Canterbury, Stephen Langton, had already organized a system of chapters and verses for the Bible, all numbered and meticulously indexed, which by the following century used the new Arabic numerals. Soon the new numbers were being used to measure much more elusive things. By 1245, Gossoin of Metz worked out that if Adam had set off the moment he was created, walking at the rate of 25 miles a day, he would still have to walk for another 713 years if he was going to reach the stars. The great alchemist Roger Bacon, who tried to measure the exact arc of a rainbow from his laboratory above OxfordвЂ™s Folly Bridge, calculated shortly afterwards that someone walking 20 miles a day would take 14 years, seven months and just over 29 days to get to the moon.

ItвЂ™s a wonderful thought, somehow akin to Peter PanвЂ™s famous directions for flying to Never Never Land, вЂ?turn right and straight on till morningвЂ™. But it was a different time then, when space was measured in the area that could be ploughed in a day and when time was dominated by the unavoidable changes between day and night. There were 12 hours in the medieval day, and 12 hours in the night too, but without proper tools for measuring time, these were expanded and compressed to make sure the 12 hours fitted into the light and the dark. An hour in the summer was much longer than an hour in the winter, and actually referred to the вЂ?hoursвЂ™ when prayers should be said.

Nobody knows who invented clocks, though legend has it that it was the mysterious Gerbert of Aurillac, another medieval monk who spent some time in Spain learning from the wisdom of the Arabs, and who, as Sylvester II, was the Pope who saw in the last millennium. He was said to be so good at maths that contemporaries believed he was in league with the Devil. It was not for 250 years that clocks arrived in the mass market, but once they had, you could not argue with their accuracy. From the 1270s, they dominated European townscapes, insisting that hours were all the same length and that trading times and working times should be strictly regulated. Counting in public is, after all, a controlling force, as the people of Amiens discovered in 1335 when the mayor regulated their working and eating time with a bell, attached to a clock.

Clocks had bells before they had faces, and were machines of neat precision, as you can see by the fourteenth-century one still working in the nave of Salisbury Cathedral, with its careful black cogs swinging backwards and forwards, the very model of the new medieval exactitude. Soon every big city was imposing heavy taxes on themselves to afford the clock machinery, adding mechanical hymns, Magi bouncing in and out and вЂ“ like the one in Strasbourg in 1352 вЂ“ a mechanical cockerel which crowed and waggled its wings.

Where would they stop, these medieval calculators? Scholars at Merton College, Oxford in the fourteenth century thought about how you can measure not just size, taste, motion, heat, colour, but also qualities like virtue and grace. But then these were the days when even temperature had to be quantified without the use of a thermometer, which had yet to be invented. They must have been heady days, when the whole of quality вЂ“ the whole of arts and perception вЂ“ seemed to be collapsing neatly into science.

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 вЂ?shit a turdвЂ™ 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 вЂ“ 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 вЂ“ a particularly skilful exponent of the art of the abacus вЂ“ who used a character he called sipos to show an empty column. The word came from the Arabic sifr, meaning вЂ?emptyвЂ™, the origin of the word вЂ?cypherвЂ™. 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. ItвЂ™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 вЂ?free tradeвЂ™. 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 thatвЂ™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 NapoleonвЂ™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. DonвЂ™t letвЂ™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 вЂ?absurd numbersвЂ™, 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 PacioliвЂ™s destiny to popularize it. The writer James Buchan described his method as a вЂ?machine for calculating the worldвЂ™. It was one of the вЂ?loveliest inventions of the human spiritвЂ™, 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. вЂ?The end and object of every businessman is to make a lawful and satisfactory profit so that he may sustain himself,вЂ™ he wrote. вЂ?Therefore he should begin with the name of God.вЂ™ 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 вЂ“ 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.

вЂ?If you cannot be a good accountant, you will grope your way forward like a blind man and may meet great losses,вЂ™ 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 thereвЂ™s a profit вЂ“ the result is happiness, he said, sounding like a Renaissance Mr Micawber. If not, you have to find out where the mistake is вЂ“ 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 вЂ?the accountantвЂ™s friendвЂ™. вЂ?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,вЂ™ 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 вЂ“ right in the middle of the railway boom вЂ“ 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 вЂ“ as far as I know вЂ“ 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 вЂ“ that counting things is a rigorous business for a serious manвЂ™s world. вЂ?When you can measure what you are speaking of and express it in terms of numbers, you know something about it,вЂ™ said the scientist Lord Kelvin. вЂ?When you cannot express it in terms of numbers your knowledge of it is of a meagre kind.вЂ™

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 KelvinвЂ™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 вЂ“ but I doubt it. Any more than the Nazis could know anything about the victims in concentration camps 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. IвЂ™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 arenвЂ™t very accurate. вЂ?Without number, we can understand nothing and know nothing,вЂ™ 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: вЂ?what arises from an event in perfect truth can never be countedвЂ™. 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 donвЂ™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. вЂ?The measurable has conquered almost the entire field of the sciences and has discredited every branch in which it is not valid,вЂ™ said the French poet Paul Valery. вЂ?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 lifeвЂ™s diversity, diminishing its uncertainty, improving the functioning of the whole, making its course surer, longer and more mechanical.вЂ™

There was a time when numbers had significance beyond just вЂ?how manyвЂ™, but we have lost the ancient understanding of numbers as beautiful and meaning something beyond themselves вЂ“ the discredited and forgotten wisdom of Augustine and Pythagoras. We snigger patronizingly when we read St Thomas AquinasвЂ™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. вЂ?I speak in parables of eternal wisdom, my honoured sir,вЂ™ he might have said, like a character in Andrew SinclairвЂ™s novel Gog. вЂ?I leave statistics to plumbers.вЂ™

The old way of looking at numbers means nothing to us now. The historian of the medieval mind Alfred Crosby called it the вЂ?venerable modelвЂ™. вЂ?We sniff and cluck at its mistakes вЂ“ that the earth is the centre of the universe, for instance вЂ“ but our real problem with the Venerable Model is that it is dramatic, even melodramatic, and teleological: God and Purpose loom over all,вЂ™ he wrote. вЂ?We want (or think we want) explanations of reality leeched of emotion, as bloodless as distilled water.вЂ™

Bloodless one-dimensional messing can dismiss a horse so sensitive that it can read the faintest human gestures, just because it doesnвЂ™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 (#ulink_f3736518-f9d8-533e-934b-236972ba2cb2)

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 BenthamвЂ™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 вЂ“ 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 ShelleyвЂ™s Gothic novel Frankenstein, published 14 years before, as Southwood SmithвЂ™s scalpel glinted in the candlelight вЂ“ 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 corpseвЂ™s. BenthamвЂ™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 BenthamвЂ™s new political morality of вЂ?utilityвЂ™? The facts вЂ“ yes, the rigorously logical facts вЂ“ were that it was more вЂ?usefulвЂ™ to dissect the philosopherвЂ™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 вЂ?usefulвЂ™ 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, BenthamвЂ™s body was to be an вЂ?Auto-IconвЂ™, 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 PanzaвЂ™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 didnвЂ™t go quite as expected. Despite BenthamвЂ™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 BenthamвЂ™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 вЂ“ not necessarily what it says in law or the Bible. And it was Bentham who launched the worldвЂ™s politicians on an increasingly determined set of calculations, so they can know what this вЂ?goodвЂ™ 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 вЂ“ вЂ?self-moving receptaclesвЂ™, as he described them вЂ“ were beginning to change the shape of cities. WhatвЂ™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. вЂ?The age of chivalry is gone,вЂ™ moaned Edmund Burke in the House of Commons. вЂ?That of sophisters, economists and calculators has succeeded, and the glory of Europe is extinguished for ever.вЂ™ 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 BenthamвЂ™s contribution as a вЂ?pig philosophyвЂ™. Karl Marx went even further, describing Bentham as вЂ?the insipid, pedantic leather-tongued waste of the commonplace bourgeois intelligence of the nineteenth centuryвЂ™. Trotsky was immediately converted by reading his works at the age of 17, but later condemned BenthamвЂ™s ideas as вЂ?a philosophy of social cookbook recipesвЂ™. The humourless Nietzsche was even moved to verse to describe him:

Soul of washrag, face of poker,

Overwhelmingly mediocre.

Looking at Jeremy BenthamвЂ™s face now, in the glass case, it does seem a little on the poker side. Even his clothes seem ludicrous, as if they have been borrowed from a Disney cartoon, and donвЂ™t seem nearly dangerous enough to inspire such hatred. Nor do the stories of the old boy jogging from his home in Westminster to Fleet Street well into his 70s, about his ancient cat (whom he called the Reverend Dr John Langhorn) and his determined early-morning walks round the garden.

His works are impenetrable and his autobiography was bolwderized and put into an unreadable third person by his incompetent assistant John Bowring, so it is hard to get a sense of the man. The overwhelming impression is that here was a mild, vain, fastidious, pedantic, irritating obsessive, who never really lived a full life вЂ“ hardly loved and barely lost вЂ“ but who brought about a revolution which is still such an important part of our lives that he remains as ambiguous as ever.

II

Jeremy Bentham was born on 15 February 1748, the son of a successful City of London lawyer who provided him with such a miserable, monotonous and gloomy childhood that he put the attainment of happiness at the centre of his philosophy. His mother died when he was ten, and life with JeremyвЂ™s overbearing and demanding father meant no games and little fun. No other children were ever asked to the house.

Instead of embracing the law as his father intended, Bentham used his small allowance to spend his time reading the works of the philosophers David Hume and Claude Adrien HelvГ©tius. In them he found the basis for his philosophy вЂ“ that you could estimate happiness from a number of different pleasures and that public вЂ?utilityвЂ™ was the basis of all human virtue. Reading HelvГ©tius during the 1770s, and walking a little way behind his family вЂ“ you can picture their exasperation at this gauche and bookish adolescent trailing along after them вЂ“ he asked himself: вЂ?Have I a genius for anything?вЂ™

Adolescents ask themselves this question often. But to Bentham, the answer came like the Angel Gabriel appearing to Mary. He took the clue from the book he was reading, where HelvГ©tius gave his opinion that legislation was the most important of earthly pursuits, an opinion widely approved by legislators the world over. вЂ?And have I indeed a genius for legislation?вЂ™ said the young Jeremy to himself. вЂ?I gave myself the answer, fearfully and tremblingly вЂ“ Yes.вЂ™

Enthusiastically, and already packing his mind with this sense of historic mission, he devoured as many of the works of moral and political philosophy as he could get his hands on. Tom Paine was starting to think up his Rights of Man, there was simmering discontent in the American colonies, and ideas were dangerous world-shifting things. Bentham flung himself in. But it was when he travelled back to Oxford to vote as a university MA in the 1768 parliamentary election, that he had his real breakthrough. He was rummaging through the small library in HarperвЂ™s Coffee House, when he came across the pamphlet by the chemist Joseph Priestley, which included the phrase вЂ?the greatest happiness of the greatest numberвЂ™. Bentham let out a sharp вЂ?Eureka!вЂ™ and dashed out to make it his own.

It remains the phrase for which Bentham is best known. Priestley never used it again вЂ“ he didnвЂ™t need it, said Bentham вЂ“ so he adapted it as the centre of his philosophy. And there it is, in the first page of the first work he ever published, A Fragment on Government: вЂ?It is the greatest happiness of the greatest number that is the measure of right and wrong.вЂ™

Before Bentham (or so he believed) the laws of England and the morality on which they were based were a hopeless jumble of superstition, tradition, contradiction and privilege. After Bentham there would be a clear logical reason for laws, and governments would know automatically what to do. It would no longer be a matter of balancing distrust of the people with fear, as Gladstone said later, but a simple piece of arithmetic. Government action, all action in fact, should be based on what would make most people happiest.

For the rest of his life, Bentham devoted most of his intellectual effort to working out how his Greatest Happiness Principle might become clear in practice. Borrowing the popular thinking of the time which classified diseases or the Linnean classification of plants and animals into families, he set about classifying pleasures to meet the strict demands of his legislative theory. By the end of his life, Bentham had defined 14 broad kinds of pleasure and sent a generation of followers and enthusiasts away to measure them.

вЂ?I wish I could return in six or seven centuries time,вЂ™ he was fond of remarking, вЂ?so that I can see the effects of my work.вЂ™ вЂ?Alas! His name will hardly live so long,вЂ™ wrote the essayist William Hazlitt, putting his finger on the whole problem with utilitarianism in one neat sentence: вЂ?There are some tastes that are sweet in the mouth and bitter in the belly, and there is a similar contradiction and anomaly in the mind and heart of man.вЂ™

But in spite of this put-down, Bentham has managed to remain famous for over a century and a half. For a long time, it didnвЂ™t seem as if he would even achieve this. He was much better known abroad. Hazlitt was also right when he said that BenthamвЂ™s fame was in inverse proportion to the distance from his house in Westminster. When the traveller and writer George Borrow found himself arrested in Spain, he was released from prison on the grounds that he shared a nationality with the man his captor called вЂ?The Grand BenthamвЂ™. And when Bentham visited Paris towards the end of his life (an honorary French citizen after the Revolution) the lawyers at the courts of justice rose to receive him.

вЂ?The case is, though I have neither time nor room to give you particulars,вЂ™ he wrote in 1810, вЂ?that now at length, when I am just ready to drop into the grave, my fame has spread itself all over the civilized world.вЂ™

III

So what kind of man was the legislator for the world, the philosopher who thought you could calculate human happiness? Not a very worldly one. You know instinctively that anyone who calls his morning walks something as pompous as вЂ?antejentacular circumgyrationsвЂ™ is likely to be pretty cut off from life. This after all was someone with sufficient mental space to have a pet name, not just to call his walking stick, but for his teapot (Dick) вЂ“ and who probably never talked to women at all, except for his cook and housemaid. He was never once drunk, and fell in love briefly twice вЂ“ but without obvious effect. He proposed to Caroline Fox in 1805. They never met again, but when he was 80, he wrote her a nostalgic letter saying that not a single day had gone by since then without his thinking of her.

He surrounded himself with luxuries of bread, fruit and tea, but he never read literature. He covered his walls with Hogarth prints, and happily wandered round and round his garden in Queen Square Place, Westminster, scrupulously dressed with his straw hat on his head.

He loved animals more than people. It somehow makes him a little more human and endearing to think of him encouraging mice to play in his office while he struggled to classify human experience (though it was difficult to manage their relationship with his beloved cats). But it hardly seems like the description of a man so fired with life that he could settle down and measure the unmeasurable passions. His putative ward and interpreter John Stuart Mill certainly thought so, and he knew him: вЂ?He had neither internal experience, nor external,вЂ™ Mill said of Bentham. вЂ?He never knew prosperity and adversity, passion nor satiety; he never had even the experiences which sickness gives вЂ¦ He knew no dejection, no heaviness of heart. He never felt life a sore and a weary burthen. He was a boy to the last.вЂ™

He pottered about his writing, enthusiastically starting gigantic projects of classification, the first chapter of which would turn out to be so voluminous that he would have to concentrate on that and abandon the rest. It was a pattern that continued for the rest of his life. He began by writing a long critique of the distinguished jurist William Blackstone, part of which came out in 1776, as A Fragment on Government. The rest was expanded and expanded and abandoned because it was out of control. Next there was the Treatise on Punishments. Only the introduction was ever near to being finished. The rest had once again expanded beyond control and had to be turned into a study on laws in general. And so on and so on, collating, noting in margins, packed with expletive and rage, then putting the papers aside never to be looked at again.

Luckily, according to the historian Leslie Stephen, he вЂ?formed disciples ardent enough to put together these scattered documents as the disciples of Mahomet put together the KoranвЂ™. Even so, it was hardly enough to make him a bestseller. One reviewer in his lifetime described his style as вЂ?the Sanskrit of modern legislationвЂ™ and those were the days when nobody could understand Sanskrit. вЂ?He has parenthesis within parenthesis, like a set of pillboxes,вЂ™ wrote his erstwhile secretary Walter Coulson. вЂ?And out of this habit have grown redundancies which become tiresome to the modern reader.вЂ™

Nor did the Fragment have the desired effect. He published it anonymously, and it was immediately pirated in Dublin, so that the first 500 copies were sold without any profit to him, but it did attract some interest as people in political circles wondered who the author was. Unfortunately for Bentham, he confided his authorship to his father to prove he was achieving something in his career. But his father was extremely indiscreet, and as soon as people knew the pamphlet had been written by a nobody, the sales collapsed.

It was the Panopticon that changed BenthamвЂ™s life. This was his invention of an efficient, modern prison, build in the shape of a flower, with the prison keeper at the centre able to watch over all the prisoners at once. The governor would run the new institutions as profit-making concerns, which would use the prisoners as motive power for a range of inventions that would make a profit and at the same time вЂ?grind the rogues honestвЂ™.

To Bentham the idea was a masterpiece of enlightenment. Because the new prison governors relied for their profit on the prisonersвЂ™ health, it was in their interest to keep them healthy and well-fed. It was never built, so we shall never know whether the prisoners would actually have thanked him вЂ“ as Bentham believed they would. But since he was intending to work them 14 hours a day with another hour on the treadmill for exercise, itвЂ™s hard to believe their gratitude would have been overwhelming.

For the next 20 years, Bentham barraged the government with his plans, and with some effect. They even bought a site for it on Millbank, where the Tate Gallery stands today, but the final signature was frustratingly difficult to obtain. Bentham was so certain the money would come through that he sank at least ВЈ10,000 into the project as early as 1796, and he soon found himself on the verge of imprisonment for debt. Day after day he wandered the Treasury corridors, writing letters, his hopes rising when William Pitt was replaced as Prime Minister by Henry Addington, only to be dashed again. вЂ?Mr AddingtonвЂ™s hope is what Mr PittвЂ™s hope was,вЂ™ he wrote in despair, вЂ?to see me die broken-hearted, like a rat in a hole.вЂ™

He asked everyone he could for help. вЂ?Never was any one worse used than Bentham,вЂ™ wrote the anti-slavery campaigner William Wilberforce. вЂ?I have seen the tears run down the cheeks of that strong-minded man, through the vexation at the pressing importunity of creditors and the insolence of official underlings.вЂ™

In the meantime, he turned himself into a Professor Branestawm of crazy ideas. He tried to interest the Treasury in currency schemes (always a sign of mild instability) and speaking tubes. He suggested the idea of a train of carts drawn at speed between London and Edinburgh. He told the Americans they should build a canal across Panama, and suggested to the city authorities that they should freeze large quantities of vegetables so that there could be fresh peas available at Christmastime. Not content with that, he linked up with Peter Mark Roget, later to write the first Thesaurus вЂ“ a Benthamite project of classification if ever there was one вЂ“ to invent what he called a frigidarium to keep food cold. He told the Bank of England how they could create an unforgeable banknote. He wrote widely in favour of votes for women and proposed, in unpublished writings, that homosexuality should be legalized, at a time when you could be hanged for sodomy. вЂ?How a voluntary act of this sort by two individuals can be said to have any thing to do with the safety of them or any other individual whatever, is somewhat difficult to be conceived,вЂ™ he wrote.

Absolutely none of these ideas was taken up. He had more luck with inventing new words. вЂ?InternationalвЂ™ is one of his. So is вЂ?codifyвЂ™ and вЂ?maximizeвЂ™. He had less success renaming astronomy as вЂ?uranoscopic physiurgicsвЂ™. Still less renaming biology as вЂ?epigeoscopic physiurgicsвЂ™. And his letters urging the government to rename the country вЂ?BrithiberniaвЂ™ remained in the ministerвЂ™s in-trays. His attempts to reshape the cabinet also had to wait more than a century. He suggested that there should be twelve ministers: including one for education; one for вЂ?the preservation of the national healthвЂ™; one for вЂ?indigence reliefвЂ™; one for вЂ?preventive serviceвЂ™ (to stop accidents) and an вЂ?interior communication ministerвЂ™ (transport). In fact he died the year before the government first voted any money to education at all.

The hopelessly old-fashioned shape of the government was probably why the Panopticon stayed stubbornly unbuilt. That is certainly what Bentham thought, even when a parliamentary committee took pity on him in 1813 and voted him ВЈ23,000 in damages, with which he paid off his debts. The Panopticon story is important here because it made him realize that the whole of government needed reform. If Lord Spencer could hold up the project for a generation, simply because it was near his London landholdings, then the whole system was corrupt. He needed a method of government to calculate right from wrong, rather than letting it fall to whoever happened to have the ear of the prime minister of the day. If the system of government could not see that it was in the general interest to adopt his plan, then how could you construct a system of government that would automatically want to improve human happiness?

вЂ?All government is in itself one vast evil,вЂ™ said the frustrated philosopher, and set about doing something about it. So, with a sigh of relief, he went back to writing his impenetrable prose. And in 1802, it all came right. The Swiss publisher Pierre Dumont at last managed to get him to agree to publishing some of his work. By the time Dumont had finished with it, it was even easy to read and was attracting attention in Paris, Moscow and Madrid. This was the TraitГ©s de LГ©gislation Civile et PГ©nale. It included crucial parts of BenthamвЂ™s Introduction to the Principles of Morals and Legislation, and it was the first of many.

He soon found that although he had a good deal more influence abroad than he did in London, he still had little power. By the time he had sent out his constitutional code to the revolutionary governments of Spain and Portugal, both had succumbed to counter-revolution. He sent it in nine instalments to the provisional government in Greece, with much the same effect. His ideas were welcomed at first by Rivadavia in Argentina and Bolivar in Columbia, though it wasnвЂ™t long before Bolivar was busily banning his works from the universities. His letter bombardment of Sir Robert Peel seemed to leave Peel pretty cold. And the Duke of Wellington did not respond to his promise that his name would be as great as AlexanderвЂ™s if he took his advice on law reform. He had more success in Italy because Cavour remained a fan. The Tsar Alexander even sent him a ring, which he returned with the seal unbroken. And thanks to Lord Macaulay, he did have an influence in shaping the new laws of India. So he was increasingly optimistic. In a calculation reminiscent of those by his medieval forebears, he predicted that his code would finally be adopted in every country in the world in the year 2825, presumably exactly a thousand years since he made the prediction. It was a letter from Guatemala that same year which gave him the title which stuck: вЂ?legislador del mundoвЂ™ вЂ“ the legislator for the world.

The idea of measuring happiness was central to almost everything he wrote. But when he began to consider exactly how the formula would work вЂ“ something his followers had to tackle after his death вЂ“ he fell back on the moderate thought that any kind of calculation was better than none. вЂ?In every rational and candid eye, unspeakable will be the advantage it will have over every form of precision being ever attained because none is ever so much as aimed at,вЂ™ he wrote. All you needed was the formula, and that meant calculating the pleasures and pains against their intensity, duration, certainty, rapidity, fecundity, purity and extensiveness. Simple!

From the start he realized that this principle, whatever it was called, depended on being able to measure the way people felt. вЂ?Value of a lot of pleasure or pain, how to be measuredвЂ™, was the title of chapter 4 of his Introduction to the Principles of Morals and Legislation. He imagined that this was a simple proposition: вЂ?who is there that does not calculate?вЂ™ he asked airily, but the complete absence of any official figures made him think again. Where was the raw data? He asked the Bank of England how much paper money was in circulation. They didnвЂ™t know. Neither had the Foundling Hospital any idea about the cost of living for paupers.

In a sudden burst of enthusiasm for figures, he persuaded the great agricultural reformer Arthur Young to use his Annals of Agriculture to send out a questionnaire about rural poverty. Young even wrote an encouraging introduction to it. Unfortunately, BenthamвЂ™s enthusiasm got the better of him, and the questionnaire included no less than 3,000 questions. Not surprisingly, only a handful of answers ever arrived back at Queen Square Place.

And even if they had poured in, how could you compare these different pleasures and pains? You couldnвЂ™t count the number of people affected by them and you certainly couldnвЂ™t compare how much they were feeling them. What if slaves were happy вЂ“ did that make slavery right? This was a difficult question for Bentham, who was a lifelong critic of slavery. And how do you compare the one person who gets a great deal of pleasure from building a multi-screen cinema on a well-known beauty spot with the thousands of people who are mildly inconvenienced? ItвЂ™s still an absolutely impossible question to answer satisfactorily.

Luckily for the utilitarians, there was an answer to some of these practical problems in the new вЂ?scienceвЂ™ of economics. You can measure it all with money, what Bentham called the вЂ?only common measure in the nature of thingsвЂ™. Using money means you can find the zero point between pleasure and pain, he said. So Bentham plunged himself into all things economic, getting to know the pioneer economist David Ricardo and seeing the new economists as the intellectual force which would put his movement into practice.

Towards the end of his life he worried that people would think only the majority mattered if he used the phrase вЂ?the greatest numberвЂ™. He also worried that people would think only money had any value вЂ“ вЂ?a vulgar errorвЂ™ he said. By 1831, just a few months before his death, he had carefully reformulated what he meant: the optimal goal is вЂ?provision of an equal quantity of happiness for everyoneвЂ™. But that makes the calculations even more difficult to manage. Especially these days, when the happiest people in the world were shown to be the Mexicans (the poorest) and the most miserable are known to be the Americans (the richest).

What about beauty? If you convert morality into a pseudoscience, how do you recognize the great benefits of creativity? What about spirituality? Bentham had three pianos and loved music, but it was Cardinal Newman who pointed out that he had вЂ?not a spark of poetry in himвЂ™. This was confirmed in a letter the philosopher wrote to Lord Holland. The difference between poetry and prose, he explained, is that вЂ“ with poetry, the lines donвЂ™t reach the margin.

This was the stick with which his critics have beaten him ever since. But he seems to have agreed with them with his great defence of the game of shove-halfpenny: вЂ?Prejudice apart, the game of push-pin is of equal value with the arts and sciences of music and poetry.вЂ™ Fripperies, fripperies.

IV

When Bentham died, on 6 June 1832, he was surrounded by 70,000 pieces of un-indexed paper. It was left to his adoring disciples to do something with them, the first task of the political utilitarians before they got down to measuring the world. And foremost among them was James Mill, one of those frighteningly dour and driven Scots pioneers who had driven the reputation of the country in the eighteenth century. From the time he met him in 1808, Mill was walking from his home in Pentonville to have supper with Bentham every evening. By 1810, the whole Mill family had moved into John MiltonвЂ™s draughty old house, which happened to be in BenthamвЂ™s garden, but he soon discovered this was so unhealthy, he moved back out to Stoke Newington. It was over the question of whether he could accept BenthamвЂ™s subsidy of his rent that the two eventually fell out. Mill needed someone to hero worship, and he found it in Bentham. Bentham needed followers and a driven mind to organize them. It was a perfect match. Rigid and stern though he was, Mill signed his letters to Bentham as вЂ?your most faithful and fervent discipleвЂ™.

Soon the patterns of BenthamвЂ™s days were set. Dictating as he powered round the garden early in the morning, вЂ“ вЂ?vibrating in my ditchвЂ™, as he put it. There were very occasional meetings with visitors during the day. Then dinner was served progressively later to allow for more work, as Mill, Bowring and Chadwick ministered to his needs. At the end of the day there was an hour-long ritual, after which he tied on his night cap, gave his watch to his secretary, who then read to him, and after a strange ritual with his window, he leapt into a special sleeping bag of his own design.

It was a disturbing time, and as well as parliamentary reform, the talk was of education. Mill and Francis Place even started a school, which collapsed by 1816, only to be replaced by plans to build another one in BenthamвЂ™s back garden. David Ricardo even donated ВЈ200 to build it, but Bentham began to realize what having his home overlooked constantly by schoolboys might mean, and the scheme was abandoned. Meanwhile, Mill was trying another educational experiment of his own вЂ“ on his eldest son. His history of India, dry and stern, had appeared in 1817 and as a result he was made Assistant to the Examiner of Indian Correspondence, with a hefty salary of ВЈ800. By 1830, he had risen to the rank of Examiner. By then he had been using every spare moment from writing the book to concentrate on John Stuart MillвЂ™s education.

And so began a strange intensive indoctrination, which involved starting to learn ancient Greek at the age of three, with gruelling studies from 6 to 9 am and from 10 am to 1 pm every day. There were no holidays. There was no birching, but his fatherвЂ™s sarcasm was almost as unpleasant. There was to be no mixing with other children вЂ“ the young John wasnвЂ™t even allowed to go to church. What he learned in the morning, he was expected to pass on to his eight brothers and sisters in the afternoon.

John could not exactly love his father tenderly, he said later in his Autobiography. He described him as вЂ?the most impatient of menвЂ™, and we can imagine what that simple sentence conceals. For the rest of his life, he confessed that his conscience spoke with his fatherвЂ™s voice. But he certainly gave him a 25-year head start over his contemporaries, which must have helped him slip into the role of the great Liberal philosopher of the Victorian age. The only area of human knowledge that he was kept in ignorance of was Utilitarianism: this he had to choose for himself, his father decided. Mill Senior neednвЂ™t have worried. When he introduced the idea to his 16-year-old son in a series of вЂ?lecturesвЂ™ as they walked along, demanding an essay on the subject the next morning which would be re-written and re-written again, John Stuart was so enthusiastic that he formed his own Utilitarian Society. James MillвЂ™s friends and allies looked on in astonishment. There was no doubt that John was a prodigy, said Francis Place, but he would probably end up вЂ?morose and selfishвЂ™. Unfortunately, he was right.

In 1820, just before he left for a life-broadening trip to Paris, James Mill took his son for a grave walk in Hyde Park, and told him that his education would single him out, and this should not be a source of pride. It was because of his fatherвЂ™s efforts and nothing to do with him. In fact, it would be disgraceful if he didnвЂ™t know more than everybody else in those circumstances.

It is hard to warm to Mill senior, or any of the unemotional utilitarians. Bentham said that his sympathy for the many sprang out of his hatred for the few. James Mill despised passionate emotions, describing them as a kind of madness. He showed almost no feelings at all вЂ“ except for one: he was quite unable to hide how much he disliked his wife. He вЂ?had scarcely any belief in pleasureвЂ™, according to his son. вЂ?He would sometimes say that if life was made what it might be, by good government and good education, it would be worth having: but he never spoke with anything like enthusiasm even for that possibility.вЂ™

James Mill lived only a few years longer than Bentham. The dust he inhaled in his regular journeys to his country cottage in Mickleham gave him a serious lung haemorrhage in 1835, and he died on 23 June the following year, leaving it to his son John as the second generation to carry the baton for Utilitarianism. It was John who gave the movement its name: he found it in a novel called Annals of the Parish about a Scottish clergyman who warns his parishioners not to abandon God and become вЂ?utilitariansвЂ™.

At 20 John Stuart Mill вЂ“ regarded by both his father and Bentham as their spiritual heir вЂ“ set to with a will to finish BenthamвЂ™s Rationale of Evidence for publication. вЂ?Mr Bentham had begun his treatise three times at considerable intervals, each time in a different manner, and each time without reference to the preceding,вЂ™ he wrote. He spent months unpicking his crabbed handwriting, chopping his sentences up into manageable parts, and finally sending five volumes off to the printers. The following year he had a nervous breakdown or a вЂ?mental convulsionвЂ™ as the Victorians put it. The breakdown took the form of a series of doubts about the whole Bentham legacy.

вЂ?Suppose that all your objects in life were realised; that all the changes in institutions and opinions which you are looking forward to, could be completely effected at this very instant: would this be a great joy and happiness to you?вЂ™ And an irrepressible self-consciousness distinctly answered, вЂ?No!вЂ™ At this my heart sank within me: the whole foundation on which my life was constructed fell down. All my happiness was to have been found in the continual pursuit of this end. The end had ceased to charm, and how could there ever be any interest in the means? I seemed to have nothing left to live for.

It was an important question and it seemed to fly in the face of everything that Bentham stood for, just as the harsh unemotional education that he had received at the hands of his father seemed completely inadequate to deal with it. If the question couldnвЂ™t be answered, how could any calculation of pleasure come to any conclusion? Life seemed complex beyond anything Bentham could have imagined.

For much of the year, Mill could hardly work at all. Music was a relief, and so were the poems of William Wordsworth, who he was convinced had experienced something similar himself. But, still in the grip of Bentham, Mill worried about music. If there were only a limited number of notes, wouldnвЂ™t the music run out? Can you calculate the potential number of pieces of music in the world? Experience shows that it is too complicated to count, just as you canвЂ™t count the combination of possible poems by the 26 letters of the alphabet. But these are the fears of a Utilitarian who has looked into the abyss.

He never fully recovered. A decade later he had another collapse, and for the rest of his life he suffered from a nervous twitching over one eye.

With antecedents like Bentham and Mill, it is touching to think of John Stuart struggling to find some kind of emotional meaning. He found it by coming out of his reclusion to dine twice a week with Harriet Taylor, the intelligent wife of a wholesale druggist. Mr Taylor seems to have been generous enough to overlook whatever was going on between them. His family roundly condemned him for the relationship and he retired from the world completely, finding that any reference to her by anybody else made him overexcited.

Instead he wrote a book about logic, then his magnum opus Political Economy. And when HarrietвЂ™s husband died in 1849, he married her. When she died in Avignon of congestion of the lungs, he was absolutely devastated, and bought a house there so he could spend half his time near his wifeвЂ™s grave. вЂ?The highest poetry, philosophy, oratory, and art seemed trivial by the side of her,вЂ™ he said. At last love had come to the Utilitarians. She probably enabled him to humanize the Utilitarian gospel. She certainly inspired him to write The Subjugation of Women in 1869, and his lifelong support for votes for women.

In 1865, he was persuaded back into public life to stand for Parliament for the Liberal Party. He agreed, on condition that he didnвЂ™t have to canvass, spend any money or answer any questions about religion. His disarming honesty seemed to win him support. вЂ?Did you declare that the English working classes, though differing from some other countries in being ashamed of lying, were yet вЂњgenerally liarsвЂќ?вЂ™ asked a hostile questioner during a public meeting.

вЂ?I did,вЂ™ he replied, to tremendous applause, and found himself elected with an enormous majority. And there he sat until he lost his seat to W. H. Smith the newsagent in 1868, small and slight with his eyebrow twitching, his weak voice hard to hear above the hubbub. Sometimes he would lose his drift during a speech and stand in complete silence for a moment, but his fellow parliamentarians listened with respect. It was Mill who first dubbed the Conservatives the вЂ?stupid partyвЂ™. On 5 May 1873, he walked 15 miles in a botanical expedition near Avignon, and died unexpectedly three days later. He was, in a real sense, the last of the line.

V

вЂ?All emotions were abhorrent to his cold, precise but admirably balanced mind,вЂ™ wrote Sir Arthur Conan Doyle, introducing the great detective Sherlock Holmes to the public just over half a century after BenthamвЂ™s death. You can point to other figures, from Victor Frankenstein to the Duke of Wellington, who provided role models for human beings as calculating machines вЂ“ WellingtonвЂ™s dispatch from the battle of Waterloo was so modestly written that the American ambassador reported back home that he had lost. But it was Bentham the вЂ?reasoning machineвЂ™ who tried to strip morality and government of its emotional and traditional baggage, who made Sherlock Holmes possible, with his detailed knowledge of inks and papers.

вЂ?He was, I take it, the most perfect reasoning and observing machine that the world has seen вЂ¦вЂ™ went on Conan Doyle on the opening page of his first Sherlock Holmes story, вЂ?A Scandal in BohemiaвЂ™. вЂ?He never spoke of the softer passions, save with a gibe or a sneer вЂ¦ For the trained reasoner to admit such intrusions into his delicate and finely adjusted temperament was to introduce a distracting factor which might throw a doubt upon all his mental results.вЂ™

Holmes could use his delicate and unemotional brain to see through the complex fogs of London to the truth, just as Bentham wanted to be able to do with the confusing mists of government. Whether you can actually get to any truth coldly and calculatingly, certainly any truth worth having, is an issue we still donвЂ™t know the answer to. The twentieth century has rehearsed the arguments backwards and forwards, balancing the respective claims of the so-called Two Cultures, and probably the twenty-first century will as well. Can science find meaning? Can scientists make any kind of progress without leaps of imagination? We still donвЂ™t agree, but we do now live in BenthamвЂ™s world. He didnвЂ™t have the necessary figures to make his calculations; we are drowning in them. He could not see some of the moral consequences of his ideas; we have some of the more unpleasant Utilitarian creeds of the century etched on our hearts. But he made the rules.

Yet his creed was softened by John Stuart Mill, who rescued utilitarianism for the modern world, so much so that it is now the Western worldвЂ™s dominant moral creed, among government ministers just as it is among everyone else. He also recognized that Bentham may have been вЂ?a mere reasoning machineвЂ™ and said the same could have been said of himself for two or three years before he learned to appreciate the value of emotions вЂ“ though there are still precious few of those in his Autobiography. MillвЂ™s repeated depressions showed him also that happiness must not be the conscious purpose of life, or paradoxically, it would slip through your fingers. Bentham would never have understood.

Bizarre measurement No. 3

Gry

(A very small linear measurement proposed in England in 1813 that was intended to make all measurements decimal. 1 gry = 0.008333 of an inch. вЂ?GryвЂ™ means literally вЂ?speck of dirt under the fingernailвЂ™.)

Number of times every year that hackers infiltrate the PentagonвЂ™s computer system: 160,000

Average time people spend watching TV in the UK every day:

3 hours 35 minutes

Chapter 3 Elusive Happiness (#ulink_8ac04a82-f1ee-5df5-b564-b9f4f47fa280)

I said to my soul, be still, and wait without hope, For hope would be hope for the wrong thing; wait without love For love would be love of the wrong thing; there is yet faith

T. S. Eliot, вЂ?East CokerвЂ™

A scientist may explore the Universe, but when he comes home at night, he doesnвЂ™t understand his wife any better.

Simon Jenkins,The Times, December 1999

I

But suppose you get everything you want, wondered John Stuart Mill at the start of his first nervous breakdown and his rejection of BenthamвЂ™s puritanical legacy: вЂ?Would this be a great joy and happiness to you?вЂ™ And the irrepressible self-consciousness distinctly answered, вЂ?No!вЂ™

MillвЂ™s irrepressible self-consciousness definitely got it right. The human psyche is too complex and far too fleeting to be pinned down in quite that way. You can carry out BenthamвЂ™s calculations of happiness with incredible accuracy, you can measure what you want precisely, but somehow the psyche slips away and sets up shop somewhere else. Or as Gershwin put it: вЂ?After you get what you want, you donвЂ™t want itвЂ™. While Mill was locking himself into his bedroom, Samuel Taylor Coleridge was coming to similar conclusions: вЂ?But what happiness?вЂ™ he said to the Benthamites with a rhetorical flourish. вЂ?Your mode of happiness would make me miserable.вЂ™ Mill was having his collapse 30 years before Freud was even a flicker in his fatherвЂ™s eye, and the idea that human beings might secretly want something different from what they think they want was untested and unfamiliar. Yet Mill instinctively knew that measuring happiness was just too blunt an instrument.

Generations later we make the same kind of discoveries ourselves over and over again. But we tend to solve the problem by measuring ever more ephemeral aspects of life, constantly bumping up against the central paradox of the whole problem, which is that the most important things are just not measurable. The difficulty comes because they can almost be counted. And often we believe we have to try just so that we can get a handle on the problem. And so it is that politicians canвЂ™t measure poverty, so they measure the number of benefit claimants instead. Or they canвЂ™t measure intelligence, so they measure exam results. Doctors measure blood cells rather than health, and people all over the world measure money rather than love. They might sometimes imply almost the same thing, but often they have little to do with each other.

Anything can be counted, say the management consultants McKinsey & Co., and anything you can count you can manage. ThatвЂ™s the modern way. But the truth is, even scientific measurement has its difficulties. Chaos theory showed that very tiny fluctuations in complex systems have very big consequences. Or as the gurus of chaos theory put it: the flapping of a butterflyвЂ™s wings over China can affect the weather patterns in the UK. The same turned out to be true for other complex systems, from the behaviour of human populations to the behaviour of share prices, from epidemics to cotton prices.

The man who, more than anybody else, undermined the old idea that measurements were facts was a Lithuanian Jew, born in Warsaw before the war, the son of a clothing wholesaler who found himself working for IBMвЂ™s research wing in the USA. Benoit Mandelbrot is probably the best known of all the pioneers of chaos because of the extraordinary patterns, known as fractals, that he introduced by running the rules of chaos through IBMвЂ™s computers. And he got there with a simple question that makes the kind of statistical facts the Victorians so enjoyed seem quite ridiculous. The question was: вЂ?How long is the coastline of Britain?вЂ™

On the face of it, this seems easy enough. You can find the answer in encyclopaedias. But then you think about it some more and you wonder whether to include the bays, or just to take a line from rock to rock. And having included the bays, what about the sub-bays inside each bay? And do you go all the way round each peninsula however small? And having decided all that, and realizing that no answer is going to be definitive, what about going round each pebble on the beach? In fact the smaller you go, to the atomic level and beyond, the more detail you could measure. The coastline of Britain is different each time you count it and different for everyone who tries.

There was a time when accountants were able to deal with this kind of uncountable world better than they are now. In the early days of the American accountancy profession, they were urged to avoid numbers. вЂ?Use figures as little as you can,вЂ™ said the grand old man of American accounting James Anyon, who came from Lancashire. вЂ?Remember your client doesnвЂ™t like or want them, he wants brains. Think and act upon facts, truths and principles and regard figures only as things to express these, and so proceeding you are likely to become a great accountant and a credit to one of the truest and finest professions in the land.вЂ™

Anyon had arrived in the USA in 1886, to look after the firm of Barrow, Wade, Guthrie and Co вЂ“ set up three years before by an English accountant who realized that there was a completely vacant gap in the accountancy market in New York City. Unfortunately, the day he arrived, he was threatened with violence by the very large chief assistant, who had been secretly trying to take the enterprise over. The case ended up in the Supreme Court. Anyon survived the ordeal and 30 years later, he was giving advice to young people starting out in what was still a new profession. вЂ?The well trained and experienced accountant of today вЂ¦ is not a man of figures,вЂ™ he explained again.

But AnyonвЂ™s successors ignored his advice, and for a very familiar reason. The public, the politicians and their business clients wanted control. They wanted pseudo-scientific precision, and were deeply disturbed to discover that accountancy was not the exact science they thought it was. Every few years, there was the traditional revelation of a major fraud or gigantic crash, and a shocked public could not accept that accounts might ever be drawn up in different ways. How could two accountants come to different conclusions? How could some companies keep a very different secret set of accounts?

This issue was brought up by Pacioli himself, who said that even in his day some people kept two sets of books: one for customers and one for suppliers. In the First World War, Lloyd George once remarked that the War Office kept three sets of casualty figures, one to delude the cabinet, one to delude the public and one to delude itself. Anyone reading the public accounts of some companies will realize this practice has life in it yet. But as the centuries passed, it has become more and more of an issue, and accountants have been on the front line of solving the resulting confusions. The Western world is now awash with consultants and accountants who will accept a large fee to come into your organization, measure the way you work, test your assumptions and your profits, or lack of them, measure the mood of your employees and customers, and tell the public.

The National Audit Office and the Audit Commission arrived in the world in the early 1980s and set to with a vengeance. The British Standards Institute organized a standard of quality, then called BS5750, which auditors could measure accountantsвЂ™ achievements by. Environmental quality standards followed, and the whole range now available across the world, US, European, global standards, and auditors behind each one вЂ“ measuring, measuring, measuring. By 1992, environmental consultancy alone was worth $200 billion. Counting things is a lucrative business. Which is one of the reasons the private sector auditing firms, like Arthur Andersen, PricewaterhouseCoopers and KPMG entered such a boom period in the 1980s. By 1987, they were creaming off as many as one in ten university graduates. It is one of the paradoxes of the modern world that the failure of auditors is expected to be solved by employing more auditors. And the trouble with auditors of any kind (accountants or academics) is that they are applying numerical rules to very complex situations. They wear suits and ties and have been examined to within an inch of their lives about their understanding of the professional rules. But their knowledge of life outside the mental laboratory may not be very complete. Sometimes itвЂ™s extremely sketchy. And when Western consultants arrive in developing countries with their clipboards, like so many Accidental Tourists, it can do a great deal of damage.

Just how much damage can be done by faulty figures has been revealed in an extraordinary exposГ© by the development economist Robert Chambers. The number-crunchers he described like innocents abroad, deluded by local elders in distant villages. Sometimes deliberately. As a result of what may have been an elderly insect-damaged cob, consultants convinced themselves during the 1970s that African farmers were losing up to 40 per cent of their harvest every year. The real figure was around 10 per cent, yet American aid planners diverted up to $19 million a year by the early 1980s into building vast grain silos across Africa to tackle a problem that didnвЂ™t exist.

Then there was the UN Food and Agriculture OrganizationвЂ™s notorious questionnaires in the early 1980s, which completely ignored mixed farms in developing countries. They only asked about the main crop, anything else was too complicated. As a result, production rates in developing countries seemed so low that multinationals believed they needed genetically-manipulated seeds to help cut famine. But then, as Emerson said, people only see what they want to see. ThatвЂ™s the trouble with questionnaires.

вЂ?Professional methods and values set a trap,вЂ™ says Chambers in his book Whose Reality Counts?:

Status, promotion and power come less from direct contact with the confusing complexity of people, families, communities, livelihoods and farming systems, and more from isolation which permits safe and sophisticated analysis of statistics вЂ¦ The methods of modern science then serve to simplify and reframe reality in standard categories, applied from a distance вЂ¦ Those who manipulate these units are empowered and the subjects of analysis disempowered: counting promotes the counter and demotes the counted.

Auditors deal in universal norms, methods of counting, targets, standards вЂ“ especially in disciplines like psychology and economics that try to improve their standing by measuring. This is how economics transformed itself into econometrics, psychology transformed itself into behavioural science, and both gained status вЂ“ but all too often lost their grip on reality. Sociologists tackled their perceived lack of вЂ?scientificвЂ™ respectability by organizing bigger and bigger questionnaires to confirm what people knew in their heart of hearts anyway. Even anthropologists, who need a strong dose of interpretation provided by the wisdom, understanding and imagination of a researcher on the ground, began to lose themselves in matrices and figures. Scientists have to simplify in order to separate out the aspect of truth they want to study вЂ“ and itвЂ™s the same with any other discipline that uses figures.

Often itвЂ™s only the figures that matter, even when everybody knows they are a little dodgy. One paper on this phenomenon by the economist Gerry Gill вЂ“ called вЂ?OK the dataвЂ™s lousy but itвЂ™s all weвЂ™ve gotвЂ™ вЂ“ was a quote by an unnamed American economics professor explaining his findings at an academic conference. Which is fine, of course, unless the data is wrong вЂ“ because peopleвЂ™s lives may depend on it. вЂ?Yet professionals, especially economists and consultants tight for time, have a strongly felt need for statistics,вЂ™ says Chambers. вЂ?At worst, they grub around and grab what numbers they can, feed them into their computers, and print out not just numbers but more and more elegant graphs, bar-charts, pie diagrams and three-dimensional wonders of the graphic myth with which to adorn their reports and justify their plans and proposals.вЂ™

Chambers found that there were twenty-two different erosion studies in one catchment area in Sri Lanka, but the figures on how much erosion was going on varied by as much as 8,000-fold. The lowest had been collected by a research institute wanting to show how safe their land management was. The highest came from a Third World development agency showing how much soil erosion was damaging the environment. The scary part is that all the figures were probably correct, but the one thing they failed to provide was objective information. For that you need interpretation, quality, imagination.

вЂ?In power and influence, counting counts,вЂ™ he wrote. вЂ?Quantification brings credibility. But figures and tables can deceive, and numbers construct their own realities. What can be measured and manipulated statistically is then not only seen as real; it comes to be seen as the only or the whole reality.вЂ™ Then he ended up with a neat little verse that summed it all up:

Economists have come to feel

What canвЂ™t be measured, isnвЂ™t real.

The truth is always an amount

Count numbers, only numbers count.

But the distinctions really get blurred when politicians start using numbers. Waiting lists up 40,000, LabourвЂ™s ВЈ1000 tax bombshell, fertility down to 1.7, 22 Tory tax rises вЂ“ elections are increasingly a clash between competing statistics. ItвЂ™s the same all over the world. Figures have a kind of spurious objectivity, and politicians wield them like weapons, swinging them about their heads as they ride into battle. They want to show they have a grasp of the details, and there is something apparently hard-nosed about quoting figures. It sounds tough and unanswerable.

But most of the time, the figures also sound meaningless. The public donвЂ™t take them in, and they simply serve as a kind of aggressive decoration to their argument. But, as politicians and pressure groups know very well, a shocking figure can every so often grasp the publicвЂ™s imagination. In the UK, the best-known election policy for the 1992 general election вЂ“ repeated in the 1997 election вЂ“ was the Liberal Democrat pledge to put 1p on income tax for education. It sounded clear and costed, but it was the perfect example of a number being used for symbolic effect. It implied real commitment and risk: the 1p meant almost nothing. вЂ?If relying on numbers didnвЂ™t work,вЂ™ said Andrew Dilnot of the Institute of Fiscal Studies in a recent BBC programme, вЂ?then in the end a whole range of successful number-free politicians would appear.вЂ™

They havenвЂ™t appeared yet. The problem for politicians is that they have to use figures to raise public consciousness, but find that the public doesnвЂ™t trust them вЂ“ and the resulting cacophony of figures tends to drown out the few that are important. The disputes of political debate have to be measurable, but they get hung up about measurements that only vaguely relate to the real world.

Take rising prices. You canвЂ™t see them or smell them, so you need some kind of index to give you a handle on what is a real phenomenon. You canвЂ™t hold them still while you get out your ruler, yet the ersatz inflation figures have assumed a tremendous political importance. We think inflation is an objective measure of rising prices, when actually it is a measurement based on a random basket of goods which has changed from generation to generation. In the 1940s, it included the current price of wireless sets, bicycles and custard powder. In the 1950s, rabbits and candles were dropped in favour of brown bread and washing machines. The 1970s added yoghurt and duvets, the 1980s added oven-ready meals and videotapes, and the 1990s microwave ovens and camcorders. ItвЂ™s a fascinating measure of our changing society, but it isnвЂ™t an objective way of measuring rising prices over a long period of time.

II

вЂ?Oh the sad condition of mankind,вЂ™ moaned the great Belgian pioneer of statistics, Adolphe Quetelet. вЂ?We can say in advance how many individuals will sully their hands with the blood of their neighbours, how many of them will commit forgeries, and how many will turn poisoners with almost the same precision as we can predict the number of births and deaths. Society contains within it the germ of all the crimes that will be committed.вЂ™

ItвЂ™s a frightening thought, just as it was frightening for QueteletвЂ™s contemporaries to hear him say it in the 1830s. But he and his contemporaries had been astonished by how regular the suicide statistics were. Year after year, you seemed to be able to predict how many there would be. There were the occasional bumper years, like 1846, 1929 and other economic crash periods, but generally speaking it was there. People didnвЂ™t seem to be able to help themselves. Amidst a constant number of individuals, the same number would take it into their heads to murder as much as get married. Statistics were powerful.

Quetelet was among the most influential of the statisticians trying to solve the confusion of politics by ushering in a nice clean, unambiguous world, urging that we count things like the weather, the flowering of plants and suicide rates in exactly the same way. вЂ?Statistics should be the dryest of all reading,вЂ™ BenthamвЂ™s young disciple William Farr wrote to Florence Nightingale, explaining that they could predict with some certainty that, of the children he had registered as having been born in 1841, 9,000 would still be alive in 1921.

To help the process along, Quetelet invented the dryest of all people вЂ“ the monstrous intellectual creation, lвЂ™homme moyen or Average Man. Mr A. Man is seriously boring: he has exactly average physical attributes, an average life, an average propensity to commit crime, and an average rather unwieldy number of children вЂ“ which used to be expressed as the clichГ© 2.4. But Average Man only exists in the statistical laboratory, measured at constant room temperature by professional men with clipboards and white coats. The whole business of relying on numbers too much goes horribly wrong simply because Mr Average is the Man Who Never Was вЂ“ counted by people who know a very great deal about their profession or science but precious little about what they are counting. The Man Who Never Was measured by the Men Who DonвЂ™t Exist. ItвЂ™s the first and most important paradox of the whole business of counting:

Counting paradox 1: You can count people, but you canвЂ™t count individuals

Average Man belongs to the Industrial Revolution and the Age of the Masses, but we just donвЂ™t believe most of that Marxist stuff any more. It belongs in the twentieth-century world of mass production, where people were transformed into cogs in giant machines, as pioneered by the great American industrialist Henry Ford вЂ“ the man who offered his customers вЂ?any colour you like as long as itвЂ™s blackвЂ™. Mass production and Average Man had no space for individuality. Figures reduce their complexity, but the truth is complicated.

Now, of course, you can almost have your car tailor-made. You can mass-produce jeans using robots to designs which perfectly match the peculiarities of individual bodies on the other side of the world. The days have gone when clothes issued by the military didnвЂ™t fit, when you struggled to keep up with the speed of the production line, with your tasks individually timed for Average Person by the time and motion experts. And we can see more clearly how difficult it is to categorize these widely different individuals who make up the human race. But in the hands of a bureaucratic state, people who donвЂ™t conform to the norm get hounded and imprisoned. Or, these days, social workers visit them and remove their children.

And after all that, when you get to know Mr Average, you find he has a bizarre taste in underwear, he has extraordinary dreams about flying through galaxies, and a hidden collection of Abba records. He wasnвЂ™t average at all. Counting him in with other people ignores the real picture.

Counting paradox 2: If you count the wrong thing, you go backwards

Because it is so hard to measure what is really important, governments and institutions pin down something else. They have to. But the consequences of pinning down the wrong thing are severe: all your resources will be focussed on achieving something you didnвЂ™t mean to.

Take school league tables, for example. When the Thatcher government latched onto the idea of forcing schools to compete with each other by measuring the progress of children at three comparable moments of their lives, they were intending to raise standards. They probably have done in a narrow way. The trouble was that schools concentrated on the test results to improve their position on the tables, which was anyway pretty meaningless. That meant excluding pupils who may drag down the results, concentrating on the D grade pupils вЂ“ the only ones who could make a difference in exam result league tables вЂ“ to the detriment of the others. It meant concentrating on subject areas the school could compete in, never mind whether they were the subjects the children needed. And worst of all, it meant squeezing the curriculum to produce children that can read and write but are, according to National Association of Head Teachers general secretary David Hart, вЂ?unfit philistinesвЂ™.

Then there was the business of using hospital waiting lists as a way of measuring the success of the health service. Tony BlairвЂ™s new government made an вЂ?interim promiseвЂ™, which then hung around their neck like an albatross, to reduce waiting lists by 100,000. They did push the lists down, though painfully slowly. But the result was the emergence of new secret waiting lists for people just to get in to see the hospital consultant, before they were even allowed near a real waiting list. Quick simple easy operations were also speeded up to get the numbers down, at the expense of the difficult ones. And when the hospital league tables of deaths came out in 1999, consultants warned it would make administrators shy of taking on difficult complicated cases.

Governments and pressure groups latch onto the wrong solutions and then busily measure progress towards them. They thought that shifting to diesel fuel for cars would clean up polluted air and measured progress towards achieving it. Result: air full of carcinogenic particulate matter. They thought more homework for primary school children was the solution to underachievement and measured progress towards it. Result: miserable dysfunctional kids.

It has all the makings of a fairy tale. If you choose the wrong measure, you sometimes get the opposite of what you wanted. And any measure has to be a generalization that canвЂ™t do justice to the individuals that are included.

Counting paradox 3: Numbers replace trust, but make measuring even more untrustworthy

When farmers and merchants didnвЂ™t trust each other to provide the right amount of wheat, they used the standard local barrel stuck to the wall of the town hall, which would measure the agreed local bushel. When we donвЂ™t trust our corporations, politicians or professionals now, we send in the auditors вЂ“ and we break down peopleвЂ™s jobs into measurable units so that we can see what they are doing and check it. If doctors hide behind their professional masks, then we measure the number of deaths per number of patients, their treatment record and their success rate, and we hold them accountable. When politicians look out of control, we measure their voting records and their popularity ratings вЂ“ just as the TV commentators break down a sporting performance into opportunities, misses, aces, broken services and much else besides.

It wasnвЂ™t always like that. Previous generations realized that we lose some information every time we do this вЂ“ information the numbers canвЂ™t provide. They realized, like James Anyon, that we could never measure what a doctor does so well that we could do it for them. They still have experience that slips through the measurement, so we still have to accept the word of the professionals to get to the truth. The British establishment used to be quite happy to accept the word of the professionals if they were вЂ?trustworthy gentlemen of good characterвЂ™. But from the outside, that trust looked like a cosy nepotistic conspiracy. And probably it was.

It was this kind of political problem which led to the growth of cost-benefit analysis. This was originally used by French officials to work out what tolls to charge for new bridges or railways, but it was taken up with a vengeance in twentieth-century America as a way of deciding which flood control measures to build. After their Flood Control Act of 1936, there would be no more federal money for expensive flood control measures unless the benefits outweighed the costs. Only then would the public be able to see clearly that there was no favouritism for some farmers rather than others. It was all going to be clear, objective, nonpolitical and based on counting.

Even so, the professionals clung to their mystery as long as they could, just as doctors fought the idea of scientific instruments that would make the measurements public and might lead people to question their diagnoses вЂ“ the stethoscope was acceptable because they were the only ones who could listen to it. Even the US Army Corps of Engineers вЂ“ in charge of the flood control analysis вЂ“ tried to keep the mystery alive. вЂ?It is calculated according to rather a complex formula,вЂ™ a Corps official told a Senate committee in 1954. вЂ?I wonвЂ™t worry you with the details of that formula.вЂ™ It couldnвЂ™t last. The more they were faced with angry questioning, the more their calculations had to be public.

But how far do you go? Do you, as they did for some flood control schemes, work out how many seagulls would live in the new reservoir, and how many grasshoppers they would eat, and what the grain was worth which the grasshoppers would have eaten? Do you work out what these values might be in future years? Do you value property when no two estate agents can name the same price? вЂ?I would not say it was a guess,вЂ™ one of their officials told the US Senate about property values. вЂ?It is an estimate.вЂ™ And after all that, it is economists who persuaded the US Secretary of the Interior, Bruce Babbitt, to start demolishing the dams their predecessors laboriously calculated.

So hereвЂ™s the paradox. Numbers are democratic. We use them to peer into the mysterious worlds of professionals, to take back some kind of control. They are the tools of opposition to arrogant rulers. Yet in another sense they are not democratic at all. Politicians like to pretend that numbers take the decisions out of their hands. вЂ?Listen to the scientists,вЂ™ they say about BSE or genetically-modified food. вЂ?ItвЂ™s not us taking the decisions, itвЂ™s the facts.вЂ™ We are submitting these delicate problems to the men in white coats who will apply general rules about individual peculiarities. It is, in other words, a shift from one kind of professional to another, in the name of democracy вЂ“ from teachers and doctors to accountants, auditors and number-crunchers. And they have their own secretive rituals that exclude outsiders like a computer instruction manual.

But when it comes to auditing the rest of us in our ordinary jobs, auditing undermines as much trust as it creates вЂ“ because people have to defend themselves against the auditors. Their lives вЂ“ usually their working lives вЂ“ are at stake, and their managers will wonder later why the figures they spent so much to collect are so bizarrely inaccurate. And as we all trust the companies and institutions less, we trust the auditors less too.

Counting paradox 4: When numbers fail, we get more numbers

Because counting and measuring are seen as the antidote to distrust, then any auditing failure must need more auditing. ThatвЂ™s what society demanded the moment the Bank of Credit and Commerce International had collapsed and Robert Maxwell had fallen off his yacht into the Bay of Biscay. Nobody ever blames the system вЂ“ they just blame the auditors. Had they been too friendly with the fraudsters? Had they taken their eyes off the ball? Send in the auditors to audit the auditors.

If the targets fail, you get more targets. Take the example of a large manufacturer that centralizes its customer care to one Europe-wide call centre. After a while, they find that the customers are not getting the kind of care they were used to before. What does the company do, given that it canвЂ™t measure what it really needs to вЂ“ the humanity and helpfulness of their service to customers? They set more targets вЂ“ speed answering the telephone, number of calls per operator per day. They measure their achievements against these targets and wonder why customers donвЂ™t get any happier. вЂ?People do what you count, not necessarily what counts,вЂ™ said the business psychologist John Seddon.

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