Each time a reporter or politician turns emphatic and earnest, propped up on the rock of hard numbers like the bar of the local, telling of thousands, or millions, or billions of this or that, spent, done, cut, lost, up, down, affected, improved, added, saved … it is worth asking, in all innocence: 'and is that a big number?'
In this chapter, six will be big and a trillion won't, without resorting to astronomy for our examples, but taking them from ordinary human experience. The human scale is what is often forgotten when size gets out of hand, and yet this is the surest tool for making numbers meaningful. Nor is there anything the least bit difficult about it. For it is also a scale with which we all come personally equipped.
For example, we asked people to tell us from a list of multiple-choice answers roughly how much the government spent on the health service in the UK that year (2005). The options ranged from £7 million to £7 trillion; so did people's answers. Since being wrong meant under- or overestimating the true figure by a factor of at least 10 and up to 10,000, it is depressing how wrong many were. The correct figure at that time was about £70 billion (70,000,000,000).
Some people find anything with an '-illion' on the end incomprehensible; you sense the mental fuses blowing at anything above the size of a typical annual salary or the more everyday mortgage. A total NHS budget of £7m is about the price of a large house in certain exclusive parts of London (and so somewhat unlikely to stretch to a new hospital), or equivalent to health spending per head of about 12p a year. How much healthcare could you buy for 12p a year? A total NHS budget of £7 trillion would have been more than six times as big as the whole economy, or about £120,000 of NHS spending a year for every single member of the population. When we told people that their guess of £7m implied annual health spending per head of about 12p, some opted instead for a radical increase to … £70m (or £1.20p per head). How many trips to the GP would that pay for? How many heart transplants? These people have forgotten how big they are. Put aside economics, all that is needed here is a sense each of us already has, if only we would use it: a sense of our own proportions.
Millions, billions … if they all sound like the same thing, a big blurred thing on the evening news, it is perhaps because they lack a sense of relative size that works on a human scale. So one useful trick is to imagine those numbers instead as seconds. A million seconds is about 11.5 days. A billion seconds is nearly 32 years.
If £300m can be pitifully small, and 1 in 5 outrageously big, how do we know what's big and what's small? (One of these is a number and the other a ratio, but both measure quantity.)
The first point to get out of the way is that the amount of zeros on the end of a number gets us nowhere; that much will be painfully obvious to many, even if some choose for their own reasons to ignore it. Immunity to being impressed by the words billion or million is a precondition for making sense of numbers in public argument. In politics and economics, almost all numbers come trailing zeros for the simple reason that there is a teeming mass of us and oodles of money in the economy of an entire country that produces more than £1,000,000,000,000 annually, as the UK does, with a population of 60,000,000 people. Plentiful zeros come with the territory. Our default position should be that no number, not a single one of them, regardless of its bluster, is either big or small until we know more about it. A recent much-hyped announcement to spend – gosh – £10m 'to boost singing and music education' in primary schools needs at least this much context: that there are around 10 million schoolchildren, roughly half of them in primary schools. So, £10m for 5 million children, per child, the boost would pay for what, exactly?
All this suggests an easy solution, already hinted at: that the best way to see through a number is to share it out and make it properly our own. Throwing away the mental shortcut – 'lots of zeros = big' – forces us to do a small calculation: divide the big number by all the people it is supposed to affect. Often that makes it strangely humble and manageable, cutting it to a size, after all, that would mean something to any individual, so that anyone can ask: 'Is it still big if I look at my share of it?'
Well, could you buy childcare for £1.15 a week? That is a judgement you can easily make. Will £300m pay for a million extra childcare places for five years? That sounds harder, though it is much the same question. Making the hard question easy is not remotely technically difficult; it is a matter mainly of having the confidence or imagination to do it.
Maybe on hearing numbers relating to the whole nation, some fail to make the personal adjustment properly: here's little me on average earnings and there's £300m. But it is not all yours. To make a number personal, it has to be converted to a personal scale, not simply compared with the typical bank balance. The mistake is a little like watching the teacher arrive with a bumper bag of sweets for the class and failing to realise that it means only one each. Yet being taken in by a number with a bit of swagger is a mistake that is often made. The largest pie can still be too small if each person's share is a crumb.
A convenient number to help in this sort of calculation is 3.12 billion (3,120,000,000), which is the UK population (60,000,000), multiplied by 52, the number of weeks in a year. This is about how much the government needs to spend in a year to equal £1 per person per week in the United Kingdom. Divide any public spending announcement by 3.12 billion to see its weekly worth if shared out between us.
Some readers will be aghast that any of this needs saying, but the need is transparent and those in authority most often to blame. Part of our contention is that salvation from much of the nonsense out there is often straightforward, sometimes laughably so, and the simpler the remedy the more scandalous the need. Of course, not all cases are so routine, not all numbers need sharing equally, for example, often being aimed more at some than others. That's another simple but important principle to which we will return. For now it serves to emphasise the point that we can make more sense of a number if we first share it out where it is due.
None of this is to encourage cynicism, it is about how to know better. And it is worth saying that innumeracy is not the same as dishonesty. Numbers do mislead because people try to pull the wool over our eyes, sure enough, but also because they are themselves muddled, or so eager for evidence for their cause that they forgo plausibility. Maybe the Daily Telegraph journalists, writing about dying pensioners, were so taken with the notion that Blair and company were beastly to old folk who had slaved for an honest crust, that they allowed this apparently satisfying notion to make mush of their numeracy.
This tendency of big brains to become addled over size is why the peddlers of numbers often know less about them than their audience, namely, not much; and why questions are always legitimate, however simple. Size matters. It is odd trying to persuade people to give it more attention, but this is attention of a neglected kind, where, instead of simply bowing to a number with apparent size and attitude, we insist on a human-scale tape measure.
Size is especially neglected in the special case when mixed with fear. Here, there is often no need even to claim any great magnitude; the simple existence of danger is enough, in any quantity.
To see this, and the kind of brainstorm that talks of toxicity or poison as if it means invariably fatal by the micron, think of an impact to the head. If delivered by a kiss to your child's brow, it is seldom harmful; if by a falling girder from the rooftop, it is probably as serious as harm can be. It is clear that impacts to the head have variable consequences depending, well, on the force of the impact, and that below a certain threshold, they do no harm whatsoever. Readers of this book asked to endure an impact to the head would, we hope, not be alone in asking, 'How hard?'
This humdrum principle – that harm depends on how much of a given danger people are exposed to, and that at low levels it often implies no harm at all – is one that everyone applies unthinkingly umpteen times a day. Except to toxicity. Food and environmental health scares are a paranoia-laced anomaly, often reported and, presumably, often read w
ith no sense of proportion whatsoever, headlined with statements the equivalent of 'Impact to head fatal, says study'.
Let's labour the metaphor to bring out its relevance. An impact to the head has variable consequences, depending on the dose. So what happens to this elementary principle when, as happened in 2005, someone tells us that cooked potatoes contain a toxic substance called acrylamide?
Acrylamide is used industrially – and also produced by a combination of sugars and amino acids during cooking – and known at some doses to cause cancer in animals and nerve damage in humans. The scare originated in Sweden in 1997 after cows drinking water heavily polluted with industrial acrylamide were found staggering around as if with BSE. Further Swedish research, the results of which were announced in 2002, found acrylamide in a wide variety of cooked foods.
On average, people are reckoned to consume less than 1 microgram of acrylamide per kilogram of body weight per day (though studies vary). That is 1/1000th of the dose associated with a small increase in cancer in rats. Some will consume more, though in almost all epidemiological studies they have seemed to get no more cancer than anyone else.
Salt is often added to potatoes, particularly chips or crisps, liberally. It is both essential for survival and also so toxic it can kill a baby with smaller quantities than may be contained in a salt cellar. About 3,750 milligrams per kilo of body weight is the accepted lethal dose (LD) for salt (the quantity that has been found to kill 50 per cent of rats in a test group, known as the LD50). For a 3kg baby, that equals about 11 grams, or a little more than two teaspoons. Does anyone report that two teaspoons of salt sprinkled on your chips flirts with death? What is said, for a variety of health reasons, is that we should keep a casual eye on the quantity we consume. Be sensible, is the unexcitable advice. Even a bit of arsenic in the diet is apparently essential for good health.
So why such absolutism about the quantities of acrylamide? Maybe the dual advantages of health paranoia and never having heard of the stuff before made panic more inviting. Had journalists thought about the numbers involved, it might have kept fear in proportion: that quantity of acrylamide equivalent to that associated with a small increased risk of cancer in rats turned out, according to one estimate, to require consumption of about 30kg of cooked potatoes (about a third to a half of the typical human body weight) every day for years.
When the headline reveals toxicity, the wise reader, aware that most things are toxic at some dose, asks, 'In what proportions?' Water keeps you alive, unless, as thirsty consumers of the drug ecstasy are often told, you drink too much, when it can cause hyponaetraemia (water-poisoning). Leah Betts, a schoolgirl, died after taking ecstasy then drinking 14 pints of water in 90 minutes.
That is why all toxicologists learn the same mantra from the first textbook, that toxicity is in the dose. This does not mean all claims of a risk from toxicity can be ridiculed, simply that we should encourage the same test we apply elsewhere, the test of relevant human proportion. Keep asking the wonderful question, with yourself in mind: how big is it?
There are exceptions. Peanut allergies for example can be fatal at such small doses that it would be unhelpful to say the sufferer must quibble over the quantity. Otherwise, though treated like one, 'toxic' is not necessarily a synonym for 'panic!'
Another case where size receives less than its due is the reporting of genetics. Here, headlines typically tell us that researchers have discovered 'the gene for' or 'genetic basis of' or 'gene linked with'. The tendency is to talk of these genes as if they revealed the secret one-way sign of life. At the very least, we assume that genes must give us the heaviest of hints.
With some conditions – cystic fibrosis is an example – this is an apt characterisation of the truth. If you have the genetic mutation, you have cystic fibrosis; if you don't, you don't. It is a real example of 100 per cent genetic determinism.
But it is not typical. More commonly, all that the discovery of 'the gene for' really tells us is that a gene is present in more of the people who have a condition than in those who don't.
For example, if you had to guess how many people with multiple sclerosis have 'the gene for' MS, you might be tempted to answer 'all of them', else how could they have the condition? In fact, a study identifying the genes for MS (two culprits were found) showed that one of these genes is present in 87 per cent of people who have MS. But 13 per cent of those who have MS do not have the 'MS gene'.
Asked how many have 'the gene for MS' but do not have the condition, you might reason that the gene is a predisposition, not a sure thing, and so a lucky few will avoid MS despite having the gene for it. In fact, that same study found the gene in 85 per cent of people who never develop MS.
The other 'gene for' MS is present in 78.1 per cent of those who have MS, and 75 per cent of those who don't. These differences are real, as far as researchers can tell, but tiny. For any individual, the chance of developing multiple sclerosis is almost unaltered whether they have the genes or not, namely, extremely small in both cases. MS is thought to have a prevalence of between about 100 and 120 per 100,000 in England and Wales, about 168 in Northern Ireland and 190 per 100,000 in Scotland. It is a rare illness and its prevalence is only minutely increased among those who have the genes 'for' it.
Restless leg syndrome is another recently identified 'gene for'. Three studies in three countries found that a gene seemed to be in part responsible. How big a part? One study found that it was present in 83 per cent of sufferers and 76 per cent of non-sufferers. The other study said 76 per cent and 68 per cent respectively. The third, 77 per cent and 65 per cent. Again, the differences are smaller than we might expect. That is, the gene plays a part, though probably only a small one. As one critic said, it might be more true to say that the gene has something to do with something else to do with something related to restless leg syndrome.
It is a similar story with asthma. A recently discovered 'gene for' asthma is present in about 62 per cent of sufferers and about 52 per cent of the asymptomatic population. For any individual, having the gene makes little difference to the chance of having asthma.
Some genes are more influential. With some conditions, a group of genes is implicated, each one having a tiny effect on the probabilities, but cumulatively making a more appreciable difference. But reading breathless reports of new genetic discoveries, how many have a sense of the proportions involved? How many, we wonder, have a sense that proportion is a relevant consideration? Playing nature against nurture is a great game. Biology, however, is not often black or white. It should be easy to convey a sense of the shades of grey.
By now, you might be all but convinced of the merit of our coy little question, convinced that size matters but is often untested, and that long lines of zeros tell us nothing. So let's measure that assurance with a real monster of a number: £1,000,000,000,000 – or one trillion pounds, as we now call such a quantity of zeros, in accordance with international economic convention. Imagine this was what British people owed, the total of their debts. Do not be intimidated by the apparent size, go ahead and ask: Is that a big number?
Most newspapers thought so, when we reached that figure in 2006, and some splashed it across the front page. The answer is that it is highly debatable whether debts of £1 trillion today are large or not. It was the highest figure ever, true, since surpassed, but we can also say with supreme confidence that it will be surpassed again, and again, since records are all but inevitable in a growing economy. The reporting implied surprise; but the combination of inflation and a growing economy means that the total number of pounds in Britain rises by about 5 per cent a year. This doubles the number of pounds in the economy every fifteen years. When there are so many more pounds of everything, is it any surprise there are also more pounds of debt?
So put aside the manufactured sense of shock at this number and try pitching at it one of our innocent little questions: how is it shared out? Not evenly, is the unsurprising answer. Nor is it the prototypical shopaholic
with a dozen maxed-out credit cards who accounts for any but a tiny part of the trillion. It is, in fact, the rich who owe overwhelmingly the biggest proportion of the debt, and always have, often in mortgages taken out to pay for houses that are growing in value, which means they also have increasing assets to repay their debts if they have to.
To see the oddity of talking about debt in the tone often employed, apply it to your own debts and see how you fare. First, how much did you owe aged 15? Four pounds and twenty pence – to your brother – how prudent. How much when of working age? What? It went up? Presumably this left you much worse off, at the beginning of a long and shocking slide into middle-aged profligacy, perhaps. And if you subsequently took out a mortgage, why, your debts probably reached a record! This must have been, obviously, the most miserable, destitute moment of your life, as you pined for the financial circumstances of a 15-year-old once more.
This is – probably – not the best way to characterise debt, even if it is in that hallowed media tradition of treating any increase in debt as proof of impending doom. Larger debt is mostly a reflection of larger borrowing power, linked to a rising ability to sustain higher repayments. This is the typical personal experience and it makes the national picture eminently predictable.
Debt is a corrosive problem for those who cannot afford it, and there do genuinely seem to be more people in that position, but this has precious little to do with the trillion pounds, most of which is a sign not of penury, but wealth. Whilst it is true that debts at the extreme can become a serious problem for governments, companies or individuals, it is also true that they can be a sign of robust economic good health.
The Tiger That Isn't Page 3