What there is out there, more often than not, is thick mushy peas, through which someone with a bad back on a tight schedule has to wade – and then try to tell us how many peas there are.
The table below shows that when the Census Bureau distributed forms asking people how old they were, there appeared to be about 106,000 centenarians in the US in 1970.
Figure 1 Counts and preferred estimates of centenarians, 1950–90
Or possibly not. The Bureau believes there were probably, in truth, not 106,000, but fewer than 5,000. That is, the count was roughly twenty-two times the estimated reality. Look into the detail of the 1990 Census returns, to take another example, and you find cases where entire families were coded (by circling a date) as born in the 1800s.
The chart also shows that between 1960 and 1980, the counted number of centenarians first leapt to more than ten times the number of a decade earlier, then fell by more than two thirds. Proof of a sudden boom and bust in living longer? Unlikely. Rather it shows persistent but erratic over-counting, which is believed to continue to some extent to this day (the true 1990 number is estimated to be about 29,000, though some statistical commentators think it more likely to be about 22,000).
The raw data shows, in short, a mess, but a mess that reflects life – errors in filling in forms, confusion, poor eyesight, wobbly writing, even a little wishful thinking and hope for celebrity.
So this is not meant as a criticism of the Bureau. Rather, it is a reflection of all of us, more confusing and indistinct than the ordinary notion of counting suggests. The Census Bureau describes the count of people at older ages as 'hounded' by problems, including: 'Lack of birth records … low literacy levels … functional and/or cognitive disability … individuals who deliberately misreport their age for a variety of reasons, as well as those who mistakenly report an incorrect age in surveys'.
The Bureau, of course, did not stop the effort of counting as soon as the computer had totted up the figures for centenarians as they appeared on returned census forms. This was the point at which the investigation began. They looked at the forms again to check their consistency. They compared the data with Social Security Administration files. They looked at Medicare enrolment files and samples of death certificates. They concluded that the United States would need to have a complete registration system for 100 years before it was likely that the true number of centenarians could be known. Even then, we should not expect precision.
All this is at the relatively simple end of counting, where definitions are clear, the subjects have a real presence and everyone knows what they are looking for. Whether you are aged 100 or more ought to be a matter of simple fact. But if the simple, well-defined facts are not always easy to come by, think what happens in government statistics aiming to capture changes in the lives of millions of people, prices and decisions. Take the number out of work. When do we call someone unemployed? Must they be entirely unemployed or can they do some work and still qualify? How much? An hour a week, or two, or ten? Do they have to look actively for work or just be without it? If they do have to look, how hard? What if they work a bit, but they are not paid, as volunteers? Mrs Thatcher's Conservative governments notoriously changed the definition of 'unemployed' twenty-three times (or was it twenty-six? Historical accounts are inconsistent).
Numbers, pure and precise in abstract, lose precision in the real world. It is as if they are two different substances. In maths they seem hard, pristine and bright, neatly defined around the edges. In life, we do better to think of something murkier and softer. It is the difference in one sense between diamonds and mushy peas; hard to believe it is a difference we forget or neglect. Too often counting becomes an exercise in suppressing life's imprecision.
So in that real world of soft edges, let's return to our survey of youth offending and the plight of Yob UK. What was the definition used to identify 1 in 4 teenage boys as serious or prolific offenders? The largest category of offence by far was assault, and judged serious if it caused injury. Here is how it was defined by a survey question:
Have you ever used force or violence on someone on purpose, for example by scratching, hitting, kicking or throwing things, which you think injured them in some way?
And then, deliciously:
Please include your family and people you know as well as strangers.
Fifty-eight per cent of assaults turn out to have been 'pushing' or 'grabbing'. Thirty-six per cent were against siblings. So anyone who pushes a brother or sister six times leaving them no worse for wear is counted a 'prolific offender'. Push little brother or sister even once and bruise an arm and you are a 'serious offender', since the offence led to injury. Or, as the press put it, you are a yob, bracketed with drug dealers, burglars, murderers and every other extremity of juvenile psychopath.
Each time we count something, we define it; we say the things we count are sufficiently the same to be lumped together. But most of the important things we want to count are messy, like people, behaving in odd ways, subtly and not so subtly different. They do not stand still, they change, their circumstances vary hugely. So how do we nail them down in one category under one set of numbers? Using what definitions? Until this context is clear, how can it even be said what has actually been counted?
Behaviours that seem clear-cut and therefore easily countable at the extremes often blur into one another somewhere along a line of severity. Sister-shovers and knife-wielding maniacs differ, so why are they lumped together in the reporting of this survey? In determining a definition of what to count, the researchers looked to the law, whose long arm can indeed be brought to bear on pushing, shoving etc.; can be, but normally isn't. The wise copper on the beat who decides that the brothers with grazed elbows from No. 42 are squabbling kids, not criminals fit for prosecution, is making a human judgement with which formal definition struggles. Definition does not like discretion and so tempts us to count rigidly, as teacher taught, in this case by saying that behaviour is either illegal or not. But this fancifully optimistic classification, insisting on false clarity, serves only to produce a deceptive number. It is astonishing how often the '1 in 4' headline comes along for one social phenomenon or another. It is invariably far tidier than it ought to be, often to the point of absurdity. The paradox of this kind of neatness is that it obscures; it is a false clarity leading to a warped perspective, and an occupational hazard of paying insufficiently inquiring attention to the news, in numbers above all.
Some of the crime identified by the survey was certainly brutal but, given the definitions, what were the headline numbers from the survey really counting? Was there clear statistical evidence of Yob UK? Or did the survey rather reveal a remarkably bovine placidity in Britain's sons and brothers? After all, 75 per cent of all teenage boys claimed not to have pushed, grabbed, scratched or kicked as many as six times in the past year (what, not even in the school dinner queue?), nor to have done any of these things once in a way that caused even the mildest scrape. According to these definitions, the authors of this book must make their confession: both were serious or prolific offenders in their youth. Reader, your writers were yobs. But perhaps you were too?
We make no argument about whether the behaviour of Britain's youth is better or worse than it used to be. We note examples of appalling behaviour like everyone else. We do argue that the 1 in 4 statistic – reported in a way that implied things were getting worse – was no evidence for it, being no evidence of anything very much. Numbers, claiming with confidence to have counted something breathtaking, mug our attention on every corner. This survey told us much of interest, if we could be bothered to read it properly, but the summary statistic, '1 in 4', counted for nothing.
It wouldn't sell, but a more accurate tabloid headline might have read: 'One in four boys, depending how they interpret our question, admits getting up to something or other that isn't nice, a bit thoughtless maybe, and is sometimes truly vicious and nasty; more than that, we can't really say on the evidence available to
us.'
Let us assume the details are usually worked out properly, that we agree whether we mean sheep only or sheep and lambs, and we say so in advance, and we've decided on a clear way of telling the difference, and that what reports of the survey meant to say was that if you look at enough boys you will find a range from brutal criminal thug, through bully, all the way to occasionally unthinking or slightly boisterous lad, now and then, in the dinner queue, maybe. Less dramatic, less novel, and oh, all right, you knew it already; but at least that would be a little more accurate. Sticking a number onto trends in juvenile behaviour gives an air of false precision, an image of diamond fact, and in this case forces life into categories too narrow to contain it. Picture that offending more properly as a vast vat of mushy peas, think again about what single number can represent it, and see this massively difficult measurement for what it is. The fault here is not with numbers and the inevitable way that they must bully reality into some semblance of orderliness. It is with people, and their tendency to ignore the fact that this compromise took place, while leaping to big conclusions.
Is this a mere tabloid extravagance? Not at all: it is common-place, in policymaking circles as in the media.
When, amidst fears of a pensions crisis, the government-appointed Turner Commission published a preliminary report in 2005 on the dry business of pension reform, it said 40 per cent of the population was heading for 'inadequate' provision in retirement. With luck, your definitional muscles will now be flexing: what do they mean by 'inadequate'?
In reaching that 40 per cent figure – a shocking one – the Commission had said each to their own resources: either you have a pension or you don't, a hard-and-fast definition like the interpretation in the yob survey of the law on assault, in or out but nothing in between, covered or not, according to your own and only your own finances.
But perhaps you married young, perhaps you never had a paid job, perhaps your partner earned or still earns a sum equal to the GDP of a small state, perhaps you had been together for forty years, living in a château. All things considered, you might expect a comfortable sunset to life. But if you were fool enough in the Commission's eyes to have no savings or pension in your own name – shame on you – you were counted as lacking adequate provision for retirement.
This was a figure that mattered greatly to policymakers, since it seemed to suggest on an epic scale an irrational population in denial about the possibility of old age. Marriage – hardly an unreasonable detail – was one of many definitional question marks over that assessment. Soon afterwards another report, an independent one, recalculated the number it believed to be without adequate pensions, this time taking marriage into account. It came up with 11 per cent with inadequate savings instead of 40 per cent. In later reports by the Pensions Commission itself, the 40 per cent claim disappeared.
For the time being, we can establish a simple rule: if it has been counted, it has been defined, and that will almost always have meant using force to squeeze reality into boxes that don't fit. This is ancient knowledge, eternally neglected. In Book I of Aristotle's Nichomachean Ethics he writes, 'It is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits.' But not more, and that is the critical point. Always think of the limitations. Always ask: are the definitions diamond hard or mushy pea? Either way, am I content with the units they define? In short: 1, 2, 3 of what? And are there really 4, 5 and 6 of the same?
2
Size: It's Personal
Simplify numbers and they become clear; clarify numbers and you stand apart with rare authority. So begin in the simplest way possible, with a question whose wide-eyed innocence defies belief:
'Is that a big number?'
Do not be put off by its apparent naivety. The question is no joke. It may sound trivial, but it captures the most underrated and entrenched problem with the way numbers are produced and consumed. Zeros on the end of a number are often flaunted with bravado, to impress or alarm, but on their own mean nothing. Political animals especially fear the size question, since their dirty secret is that they seldom know the answer. A keen sense of proportion is the first skill – and the one most bizarrely neglected – for all those interested in any measure of what's going on.
Fortunately, everyone already possesses the perfect unit of human proportion: their own self.
Daniel Adderley is aged nearly 67. He is lucky to be alive, according to the Daily Telegraph: the past two years living near Dorking have been more risky for him than for soldiers on the front line in Afghanistan.
Not that Dorking is a death trap, simply that in November 2005 a front-page story in the Telegraph reported government plans to raise the age of retirement for men from 65 to 67. If enacted, the paper said, one in five who would formerly have survived long enough to collect a pension would now die before receiving a penny. Hundreds of thousands would be denied by two cruel years.
1 in 5. Is that a big number?
In 1997 the Labour government said it would spend an extra £300m over five years to create a million new childcare places.
£300m. Is that a big number?
In 2006 the National Health Service was found to be heading for a budget deficit of nearly £1bn.
£1 billion. Is that a big number?
The answer to the first question is yes, 1 in 5 men aged 65 would be a catastrophic number to die in two years, a number to strike terror into every 65-year-old, a number so grotesquely enormous that someone at the Telegraph should surely have asked themselves: could it be true? Perhaps, if the plague returned, otherwise it doesn't take much thinking to see that the report was ridiculous. It is a simple sort of thinking even smart journalists often do not do.
According to National Statistics (www.statistics.gov.uk), about 4 per cent of 65-year-old men die in the following two years, not 20 per cent. About 20 per cent of those born do indeed die before they reach the age of 67, but not between the ages of 65 and 67. Misreading a number in a table, as the journalists seem to have done, is forgivable; failure to ask whether the figure makes the sort of sense they could see every day with their own eyes, is less so. For the report to be correct, more than 100,000 more 65- and 66-year-old men than usual would have to die every two years. They would be turning up their toes all over the golf course. All things considered, we think Daniel might make his 68th birthday.
Next, Labour's £300m for childcare. Here, no one involved in the public argument, neither media nor politicians, seemed to doubt its vastness. The only terms in which the opposition challenged the policy were over the wisdom of blowing so much public money on a meddlesome idea.
So is £300m to provide a million places a big number? Share it out and it equals £300 per place. Divide it by five to find its worth in any one year (remember, it was spread over five years), and you are left with £60 per year. Spread that across 52 weeks of the year and it leaves £1.15 per week. Could you find childcare for £1.15 a week? In parts of rural China, maybe.
Britain's entire political and media classes discussed the policy as if you could. But by 'create' the government must have meant something other than 'pay for' (though we wonder if it minded being misunderstood), something perhaps along the lines of 'throw in a small sum in order to persuade other people to pay for …' And yet the coverage oozed a sense of bonanza. Does the public debate really not know what 'big' is? Apparently not, nor does it seem to care that it doesn't know. When we asked the head of one of Britain's largest news organisations why journalists had not spotted the absurdity, he acknowledged there was an absurdity to spot, but said he wasn't sure that was their job. For the rest of us, to outshine all this is preposterously easy. For a start, next time someone uses a number, do not assume they have asked themselves even the simplest question. Can such an absurdly simple question be the key to numbers and the policies reliant on them? Often, it can.
The third example, the £1bn NHS deficit, was roundly condemned as a mark of crisis and mi
smanagement, perhaps the beginning of the end for the last great throw of taxpayers' money to prove that a state system worked. But, was it a big number?
The projected deficit had fallen to about £800m at the time of writing, or about 1 per cent of the health service budget. But if that makes the NHS bad, what of the rest of government? The average Treasury error when forecasting the government budget deficit one year ahead is 2 per cent of total government spending. In other words, the NHS, in one of its darkest hours, performed about twice as well against its budgetary target as the government as a whole. There are few large businesses that would think hitting a financial target to within 1 per cent anything other than management of magical precision. They would laugh at the thought of drastic remedial action over so small a sum, knowing that to achieve better would require luck or a clairvoyant. NHS spending is equivalent to about £1,600 per head, per year (in 2007), of which 1 per cent is £16, or less than the cost of one visit to a GP (about £18). No doubt there was mismanagement in the NHS in 2006 and, within the total deficit, there were big variations between the individual NHS trusts, but given the immense size of that organisation, was it of crisis proportions, dooming the entirety? It is often true that the most important question to ask about a number – and you would be amazed how infrequently people do – is the simplest.
The Tiger That Isn't Page 2