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 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.

In November 2005 a front-page story in The Daily Telegraph reported government plans to raise the age of retirement for men from 65 to 67. If enacted, the newspaper said, 1 in 5 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.

One in 5. Is that a big number?

The answer is yes, 1 in 5 men aged 65 is 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. But it is a simple sort of thinking that 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.

£300 million. Is that a big number?

In 1997, the new Government said that it would spend an extra £300 million over five years to create a million new childcare places. 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 £300 million 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 a week. Could you find childcare for £1.15 a week? In parts of rural China, maybe: but Britain’s entire political and media classes discussed the policy as if you could.

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 that 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.

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: is that a big number?

© Michael Blastland and Andrew Dilnot 2007

How to count

Take the laughably simple example of three sheep in a field.

What do we want to count? Sheep. How many are there? Three. But one is a lamb. Does that still count as a sheep? Or is it half a sheep?

Also, one is a pregnant ewe in advanced labour. Is that one sheep, or two, or one and a half?

So what is the total? Depending how the units are defined, the total could be 2, 2.5, 3, 3.5 or 4. For a small number, that’s quite a spread; one answer is twice the size of another, and counting to four just became ridiculous.

The lesson is: before you start counting, you must define exactly what it is you’re counting.

From The Tiger That Isn’t: Seeing Through a World of Numbers, Profile, £12.99.
Available from Times BooksFirst for £11.69, inc p&p. 0870 1608080

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