The Tiger That Isn't

by Andrew Dilnot

  Another way of thinking about this is to say that your debts would be too big only if you could not repay them. But how many news reports of UK debt also report UK wealth? Quite absurdly, it almost never gets a mention, even though it would be one of everyone's first considerations. We have taken to calling this the Enron School of Reporting. The energy firm Enron, readers may recall, trumpeted its assets, but conveniently neglected to talk about its debts, and went spectacularly bust. News reporting about the public's financial state is often the other way round, blazing with headlines about debt, but neglecting to mention wealth or income. So trust what is known to be true for the individual, take the calculation anyone would make personally, and apply it to the national picture. This shows (see chart) that personal wealth has been increasing over recent years steadily and substantially. In 1987 the total personal wealth of all the households in the UK added up to about four times as much as the annual income of the whole country. By 2005 wealth was six times as great as annual national income. Not poorer, but prodigiously richer, is the story of the last twenty or so years. This wealth is held in houses, pensions, shares, bank and building society accounts, and it is held very unequally, with the rich holding most of the wealth, as well as most of the debt. Some of the increase reflects house-price growth, some increases in share prices, but there is no denying that as the economy has grown, and incomes with it, so have savings and wealth. Debt has been rising, but wealth has been rising much more quickly.

  Figure 2 Wealth and debt in the UK

  Even if we look at the category of debt said to be running most seriously out of control – unsecured personal debt (which includes credit cards) – we find that as a proportion of what we have available to spend – household disposable income – this debt has remained steady for the last five years (before which it did go up – a bit). Once more, it is unequally distributed and more of a problem for some than others, but for precisely those reasons it makes no sense to use the total number as if it says anything whatsoever about those in direst financial straits.

  How can we know from personal experience that the debt number may not be as monstrous as it looks? By thinking about our own life cycle and our own borrowing. We are happier to borrow more as we grow richer, and often do, but it tends to become less rather than more of a problem. With that much clear, it is easy to see that rising debt might well indicate rising wealth in the population as a whole. Essentially, we use the same method as before, we share out the number where it belongs, rather than according to what makes a good story. So we should share it mostly among the rich, far less among the poor. Just for good measure, £1 trillion of debt shared out across the population is a little less than £17,000 per person, compared to wealth, on average, of over £100,000.

  It is not only debt in the UK that can more usefully be put into human proportions. In the summer of 2005 at the Gleneagles summit – held during the UK's presidency of the G8 group of countries – the Chancellor of the Exchequer Gordon Brown announced that $50bn of developing country debt would be written off. It sounds generous, and is important for developing countries, but how generous does it look from inside the G8? Is it a big number for us?

  Fifty billion dollars was the stock of outstanding debt. By writing if off, what the G8 countries actually gave up were the annual repayments they would have received, often at preferential interest rates, equal to about $1.5bn a year. This was the real cost, substantially lower than the headline figure. Convert $1.5bn into pounds, and it seems smaller still, at around £800m at the then prevailing exchange rates. £800m a year still sounds a lot, but remember the exhortation to make numbers personal. The population of the G8, conveniently, is around 800 million. So the Gleneagles deal will cost each person living in the G8 about £1 a year. Even that is an exaggeration, since much of the money will come out of government aid budgets that would have gone up anyway, but will now be diverted to pay for the Gleneagles deal, leaving the best estimate of how much more Gleneagles will cost each of us than had it never happened, at close to zero.

  Let's look, finally, at the other end of the scale, to a number in single figures, a tiny number: six. You will be honing your scepticism by now, reluctant to take anyone's word or commit to an opinion, and wanting to know more of the context. That is as it should be. The six we have in mind is the celebrated six degrees of separation said to exist between any two people on the planet. So, is six a small number?

  The idea was first proposed – according to Wikipedia – in 1922 in a short story titled 'Chains' by a Hungarian writer, Karinthy Frigyes. But it was an American sociologist, Stanley Milgram, who became most closely associated with the suggestion when, in 1967, he claimed to have demonstrated empirically that six steps was generally more than enough to connect any two people in the United States. He called this 'the small world phenomenon'.

  Milgram recruited nearly 300 volunteers whom he called 'starters', asking each to send a gold-embossed passport-like package to a stranger, usually, but not always, in another city. They could use any intermediary they knew on first-name terms, who would then try to find another who could do the same, each time moving closer to the target. All they had to go on was the recipient's name, home town, occupation, and a few descriptive personal details, but no address. Milgram reported that 80 per cent of packages reached their target in no more than four steps and almost all in fewer than six.

  The story became legendary. Then, in 2001, Judith Kleinfeld, a psychologist at the University of Alaska, became interested in the phenomenon and went to study Milgram's research notes. What she found, she says, was disconcerting: first, that an initial unreported study had a success rate of less than 5 per cent. Then, that in the main study more than 70 per cent of packages had never reached their intended destination, a failure rate that raises doubts, she says, about the whole claim. 'It might be true,' she told us, 'but would you say that the packages arrived in fewer than six steps when 70 per cent never arrived at all?' Furthermore, in criticism that bears more closely on our question, she notes that senders and recipients were of the same social class and above-average incomes, and all likely to be well connected.

  So six may or may not be the right number, and the central claim in the experiment has never been satisfactorily replicated, but would it, if true, nevertheless be a small number? The point that connections are easier among similar people is a clue, and a prompt. This encourages us to think that not only the number of steps, but also the size of the steps matters. And if each step is giant, six will amount to an impossible magnitude.

  Other studies, including more by Milgram himself, according to Judith Kleinfeld's summary of his personal archives, found that where the packages crossed racial differences, the completion rate was 13 per cent, rising to 30 per cent in a study of starters and targets living in the same urban area. When, in another study, the step was from a low-income starter to a high-income target, the completion rate appears to have been zero. Connections were not nearly so easy across unexceptional social strata.

  And as Judith Kleinfeld herself points out: 'A mother on welfare might be connected to the President of the United States by a chain of fewer than six degrees: her caseworker might be on first name terms with her department head, who may know the Mayor of Chicago, who may know the President of the United States. But does this mean anything from the perspective of the welfare mother? … We are used to thinking of “six” as a small number, but in terms of spinning social worlds, in a practical sense, “six” may be a large number indeed.'

  'Six' is usually small; a billion is usually large. But easy assumptions will not do when it comes to assessing size. We need to check them with relevant human proportion. Six steps to the President sounds quick, but let people try to take them. They can be an ocean apart and represent a world of difference. A billion pounds across the UK can be loose change, 32p each per week. We need to think, just a little, and to make sure the number has been properly converted to a human scale that recognises human
experience. Only then, but to powerful effect, can we use that personal benchmark. The best prompt to thinking is to ask the question that at least checks our presumptions, simple-headed though it may sound: 'Is that a big number?'

  3

  Chance: The Tiger That Isn't

  We think we know what chance looks like, expecting the numbers she wears to be a mess, haphazard, jumbled. Not so, for chance has a genius for disguise and fools us time and again. Frequently and entirely by accident, she appears in numbers that seem significant, orderly, coordinated, or slip into a pattern. People feel an overwhelming temptation to find meaning in these spectral hints that there is more to what they see than chance alone, like zealous detectives over-alert to explanation, and to dismiss with scorn the real probability: 'it couldn't happen by chance!'

  Sometimes, though more seldom than we think, we are right. Often, we are suckered, and the apparent order is no order, the meaning no meaning, it merely resembles one. The upshot is that discovery after insight after revelation, all claiming to be dressed in the compelling evidence of numbers, will in fact have no such respectability. It was chance that draped them with illusion. Experience offers us innumerable examples. We should take them to heart. In numbers, always suspect that sly hand.

  Who was it, furtive, destructive, vengeful in the darkness? At around midnight on bonfire night – 5 November 2003 – on the outskirts of the village of Wishaw in the West Midlands, someone had crime in mind, convinced the cause was just.

  Whoever it was – and no one has ever been charged – he, she, or they came with rope and haulage equipment. A few minutes later, on the narrow stretch between a riding stables and a field, the 10-year-old, 23-metre-tall mobile-phone mast on the outskirts of the village was first quietly unbolted, then brought crashing down. The signal from the mast ceased at 12.30 a.m. precisely. Police found no witnesses.

  By morning, protestors had surrounded the upended mast and refused to allow T Mobile, its owners, to take it away or replace it. A solicitor representing the protestors told the landowners they would not be permitted access because that meant crossing someone else's property. The protest quickly became a round-the-clock vigil with both sides paying private security companies to patrol the boundary.

  The villagers' earnest objection had a despairing motivation. Since the mast had gone up, among the twenty house-holds within 500 metres, there had been nine cases of cancer. In their hearts, the reason seemed obvious. They were, they believed then and still believe now, a cancer cluster. How could such a thing happen by chance? How could so many cases in one place be explained except through the malign effect of powerful signals from that mast?

  The villagers of Wishaw might be right. The mast has not been replaced and the strength of local feeling makes that unlikely, not now, perhaps not ever. And if there were a sudden increase in crime in Wishaw such that nine out of twenty households were burgled, they would probably be right to suspect a single cause. When two things happen at the same time, they are often related.

  But not always, and if the villagers are wrong, the reason has to do with the strange ways of chance in large and complex systems. If they are wrong, it is most likely explained as a result of their inability – an inability most of us share – to accept that apparently unusual events happening simultaneously do not necessarily share the same cause, and that unusual patterns of numbers in life, including the incidence of illness, are not at all unusual, not necessarily due to some guiding force or single obvious culprit, but callously routine, normal and sadly to be expected.

  To see why, stand on the carpet – but choose one with a pile that is not too deep (you might in any case want a vacuum cleaner to hand) – take a bag of rice, pull the top of the packet wide open … and chuck the contents straight into the air. Your aim is to eject the whole lot skyward in one jolt. Let the rice rain down.

  What you have done is create a chance distribution of rice grains over the carpet. Observe the way the rice is scattered. One thing the grains have probably not done is fall evenly. There are thin patches here, thicker ones there and, every so often, a much larger and distinct pile of rice: it has clustered.

  Wherever cases of cancer bunch, people demand an explanation. With rice, they would see exactly the same sort of pattern, but does it need an explanation? Imagine each grain of rice as a cancer case falling across the country. The example shows that clustering, as the result of chance alone, is to be expected. The truly weird result would be if the rice had spread itself in a smooth, regular layer. Similarly, the genuinely odd pattern of illness would be an even distribution of cases across the population.

  We asked a computer to create a random pattern of dots for the next chart, similar to the rice effect. Imagine that it covers a partial map of the UK and shows cases of a particular cancer.

  Figure 3 Scattergram – how random things cluster

  One area, the small square to the right (let's call it Ipswich), we might be tempted to describe as a cluster. The other, the rectangle, with no cases at all, might tempt us to speculate on some protective essence in the local water. The chart shows that such patterns can, and do, appear by chance.

  It also illustrates a tendency known as the Texas Sharp-shooter Fallacy. The alleged sharpshooter takes numerous shots at a barn (actually, he's a terrible shot, that's why it's a fallacy) then draws his bull's-eye afterwards, around the holes that cluster.

  These analogies draw no moral equivalence between cancer and rice patterns, or pot shots, and people who have cancer have an entirely reasonable desire to know why. But the places in which cancer occurs will sometimes be clustered simply by obeying the same rules of chance as falling rice. They will not spread themselves uniformly across the country. They will also cluster, there will be some patches where cases are relatively few and far between and others with what seem worrying concentrations. Sometimes, though rarely, the worry will point to a shared local cause. More often the explanation lies in the often complicated and myriad causes of disease, mingled with the complicated and myriad influences on where we choose to live, combined with accidents of timing, all in a collision of endless possibilities which, somehow, just like the endless collisions of those rice grains in a maze of motion, come together in one place at one time to produce a cluster.

  One confusion to overcome is the belief that the rice falls merely by chance whereas illness always has a cause. This is a false distinction. 'Chance' does not mean without cause – the position of the rice has cause all right; the cause of air currents, the force of your hand, the initial position of each grain in the packet, and it might be theoretically possible (though not in practice) to calculate the causes that lead some grains to cluster. Cancer in this respect – and only in this respect – is usually no different. For all the appearance of meaning, there is normally nothing but happenstance.

  Think about the rice example for a moment beforehand and there is no problem predicting the outcome. Seeing the same effect on people is what makes it disconcerting. This is an odd double standard: everyone knows things will, now and then, arrive in a bunch – it happens all the time – but in the event they feel put out; these happenings are inevitable, we know, yet such inevitabilities are labelled 'mysterious', the normal is called 'suspicious', and the predictable 'perverse'. Chance is an odd case where we must keep these instincts in check, and instead use past experience as a guide to what chance can do. We have seen surprising patterns before, often. We should believe our eyes and expect such patterns again, often.

  People typically underestimate both the likely size of clusters and their frequency, as two quick experiments show. Shuffle a standard pack of fifty-two playing cards. Turn them from the top of the deck into two piles, red and black. How many would you expect in the longest run of one colour or the other? The typical guess is about three. In fact, at least one run of five or six, of either red or black, is likely.

  You can test expectations by asking a class of schoolchildren (say thirty people) to ca
ll in turn the result of an imaginary toss of a coin, repeated thirty times. What do they think will happen? Rob Eastaway, an author of popular maths books, uses this trick in talks to schools, and says children typically feel a run of three of the same side will do before it's time to change. In fact, a run of five or more will be common. There will also be more runs of three or four than the children expect. Even though they know not to expect a uniform alternation between heads and tails on all thirty tosses, they still badly underestimate the power of chance to create something surprising.

  But this is so surprising that we couldn't resist testing it. Here are the real results of thirty tosses of a coin repeated three times (h = heads, t = tails). All clusters of four or more are in bold, and the longest are given in brackets.

  1: h t t h t t h h t h h t t t t t t h h h h t h h t t t h h h

  (6 tails in a row, 4 heads in a row)

  2: t t t t h t t h h t h t h h h h t t t h h h t h h t h h t h

  (4 tails in a row, 4 heads in a row)

  3: t h t t t t t h t t t h h t t t t t t h h h t t h t h h t t

  (5 tails in a row, 6 tails in a row)

  There was nothing obviously dodgy about the coin either: in the first test it fell 15 heads and 15 tails, in the second 16–14, in the third 10–20, and the sequences are genuinely random.

  So even in short runs there can be big clusters. The cruel conclusion applied to illness is that even if it were certain that phone masts had no effect whatsoever on health, even if they were all switched off permanently, we would still expect to find places like Wishaw with striking concentrations of cancers, purely by chance. This is hard to swallow: nine cases in twenty households – it must mean something. That thought encourages another: how can so much suffering be the result of chance alone? Who wouldn't bridle at an unfeeling universe acting at whim, where pure bad luck struck in such insane concentration? To submit to that fate would lay us open to intense vulnerability, and we can't have that.