The problem with people being numb to big numbers

I have a confession to make: I hate big numbers. Or rather, I hate it when big numbers are used to impress or bamboozle rather than to make sense of the world. The annual budget speech by the UK’s chancellor, for instance, always involves a dizzying parade of large price tags. This year’s included an extra £63 million (€71.5 million) to be spent on leisure centres, £5 billion over two years for defence, £200 million for potholes and £10 million over two years for suicide prevention, to name just a few.

It’s important in any democracy for people to know how public money is spent. But I suspect the only thing most people hear on such occasions is: “Big number, big number, big number, big number.”

I’m not the first to worry about this. In a piece titled On Number Numbness in the 1980s, the scholar Douglas Hofstadter asked (in a sentence I wish I’d thought of): “Are we growing ever number to ever-growing numbers?” He took a stern approach, saying there was “no excuse for not being able to understand – or even relate to – numbers whose purpose is to summarise in a few symbols some salient aspects of... huge realities”.

He was perhaps a little harsh. As neuroscientists Lindsey Hasak and Elizabeth Toomarian have put it, “the human brain just isn’t built to comprehend such large numbers”. In one research study, many participants placed a million about halfway between 1,000 and a billion on a number line. Even people who know better can struggle to really conceptualise the vastness between a million and a billion.

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Keith Fray, the Financial Times’s head of editorial statistics, used to have a few sentences printed out by his desk that have always stuck with me: a million seconds is about 12 days; a billion seconds is about 32 years; a trillion seconds is about 32,000 years.

Sometimes five is a big number, and sometimes 300 million is a tiny one – it all depends on the context

Who benefits when the public discourse is polluted with big numbers that many struggle to understand? Politicians often drop them into interviews or announcements in the hope they will sound significant to journalists or the public, even if they are actually quite paltry sums in context. Businesses and lobby groups sometimes do the same. “The economic contribution of flexible working is a huge £37 billion,” says one press release in my inbox. “Foreign professionals add £210 billion boost to the UK economy,” says another.

There is no reason to submit helplessly to this guff. One strategy is to make big numbers smaller so they become more meaningful to the public and easier to compare. A study published last year found that non-experts were better able to discriminate between the price tags of different government programmes when the numbers were divided by the size of the population to give amounts per head. The researchers concluded this “relatively simple change to how information is presented ameliorates misunderstandings, thereby improving the potential for participatory democracy”.

If UK chancellor Jeremy Hunt had divided the spending promises in his budget speech by the population (about 67 million in the UK), he would have announced about an extra 94p per person on leisure centres, £74.63 on defence, £2.99 on potholes and 15p on preventing suicides.

If some people would find these figures more meaningful – or at least easier to compare with one another – the Office for Budget Responsibility could publish a table of rescaled policy announcements on budget day. Some judgments would have to be made. Sometimes it might make more sense to divide by the number of households, or the number of beneficiaries of a certain policy. But that’s no reason not to make the effort.

The other imperative is to add more numbers. One big number rarely means anything in isolation. What is the increase in defence spending as a proportion of how much we already spend? What is the contribution of flexible working as a percentage of the overall economy? As Sir Andrew Dilnot, former chairman of the UK Statistics Authority, told me, “sometimes five is a big number, and sometimes 300 million is a tiny one” – it all depends on the context.

Accenture announced recently it would cut 19,000 jobs. That sounds like a lot, I thought when I heard. Then I read the company had 738,000 staff, and had hired more than 230,000 since mid-2020. It is still 19,000 people losing their jobs. But the other numbers help to make sense of the story.

There’s no getting away from big numbers in today’s world, but the public doesn’t have to remain numb to them. Compress them, crunch them, compare them, and the feeling should soon come rushing back. That, perhaps, is what politicians are afraid of. – Copyright The Financial Times Limited 2023