Humans are terrible with big numbers. The financial meltdown has reminded us that even highly numerate people can't really feel, in their bones, the vast difference between a million, a billion and a trillion: it's still shocking to be reminded that 1m seconds pass in less than 12 days, whereas 1tn seconds is equivalent to around 32,000 years. (To put it another way: if you'd spent £1m a day since Jesus was born, you still would not have spent £1tn.) Trying to be helpful, commentators will explain that, say, the £850bn spent to bail out Britain's banks would, in the form of £1 coins, stretch several times "to the moon and back". But this is worse than useless, because the distance from Earth to the moon is exactly the kind of big number we struggle to visualise. All I know is that it's a very long way, like Ullapool, except probably even farther.

As any charity fundraising expert will tell you, one consequence of this is the phenomenon known as "scope insensitivity": we're troubled by the thought of a starving child, but we're definitely not 1,000 times more troubled by the thought of 1,000 starving children. One famous study asked people how much they'd be willing to pay to save 2,000 birds from dying in oil ponds; the average answer was about £49. And 20,000 or 200,000? The answers were £48 and £53, respectively.

What's going on here, some psycho­ logists argue, is the "purchase of moral satisfaction": instead of trying to picture the scale of the problem and donate accordingly, people just name the price required to achieve the fuzzy feeling of having done their bit. "The level of spending needed to purchase a warm glow depends on personality and financial situation," writes Eliezer Yudkowsky, at the blog Less Wrong. "But it certainly has nothing to do with the number of birds." In a different kind of example, people were willing to pay much more to save the lives of 4,500 Rwandan refugees in a camp of 11,000 than in a camp of 250,000: what counted, apparently, wasn't the number of lives saved, but the sense of having "made a big difference" by saving almost half the camp.

I wonder if all this points to a more pervasive eccentricity – the way we habitually confuse how some effortful act feels with the effect it actually has. Climate change is a case in point: scrupulously recycling household waste takes enough effort that it feels like a major contribution, perhaps big enough to justify a yearly long-haul flight, when in reality this is absurdly faulty reasoning.

But the effect reaches beyond altruism. Personal finance gurus love to champion what one of them calls "the Latte Factor", the notion that by forgoing some small daily luxury, you can stash away a small fortune. Yet, of course, the best way to save money is to forgo big purchases; and if the effort of denying yourself a latte every day makes a new plasma- screen TV seem a reasonable reward, you'll eliminate your savings at a stroke. Come to think of it, isn't the whole world of work designed to encourage us in the mistaken idea that a 12-hour day is more effective than a three-hour day? Yet all we can really say for sure is that it's more effortful – rewarding us with the sense, whether smug or self-pitying, of having put in a good day's work. There are probably millions more examples. Or billions. Or thousands – you know, some really big number like that.

oliver.burkeman@theguardian.com