Why are big numbers so scary?

Occasionally I try to impart some elements of good science storytelling to people, and one of the points I make (based entirely on Garrett Hardin) is the big difference between literacy and numeracy. Literacy understands full well that the difference between a million and a billion is one letter. And that a billion is bigger than a million. But how much bigger? My example is simple enough. If a million seconds is 11 days (which it is, give or take), how long is a billion seconds?

It's especially worrying when the big numbers refer to big money. US Senator Everett Dirksen was clearly onto something when he said, "a billion here, a billion there ... pretty soon you're talking about real money". ¹

So I was pleased that my friend Dag had linked to a recent blog post by Philip Greenspun, in which he divided the US budget numbers by a billion to come up with a homely little homily:

We have a family that is spending $38,200 per year. The family’s income is $21,700 per year. The family adds $16,500 in credit card debt every year in order to pay its bills. After a long and difficult debate among family members, keeping in mind that it was not going to be possible to borrow $16,500 every year forever, the parents and children agreed that a $380/year premium cable subscription could be terminated. So now the family will have to borrow only $16,120 per year.

And that's supposed to bring new understanding -- just by removing the same number of zeroes from all the numbers?

The BBC's More or Less pulled a similar trick in the run-up to last year's election in the UK, but rather than dividing by a big number, they divided by the number of households in the UK, revealing just how much each UK resident owed. Naturally I can't find the details now, but at the time I found it much more illuminating -- and scarier -- than the overall numbers, and suspect I would have even if those numbers had been deflated a billionfold.

Oh, about 32 years, by the way.