I’m a bit of a math geek by nature, so I use large numbers all the time. Just by squinting a bit and thinking, I was able to estimate the size of the sun within a factor of 2 the other day… Not that this is especially useful. But I’m comfortable with the way numbers stack and interact and modify each other.

But I still don’t understand large numbers.

Here’s the clue. When we talk about large numbers, we say things like “well, picture this…”. We use analogies. We say things like “if you stacked that many dollar bills, they’d reach the moon”.

All of these tools to “help us understand” are in fact admissions that we don’t.

If the only understanding I can have of a number is an analogy, a representation, then I don’t understand it. Can you imagine someone trying to explain five that way? “Imagine that this many people, lying end-to-end, are about as long as your driveway.” “A stack of bills this tall would fold easily in your pocket and be forgotten until you found them in the dryer.” We don’t need that, because we *know* what “five” is. We can experience five things all-at-once. We can see a group of things and just know that there’s about five of them. By ten, most people are having a hard time.

Even the indirect experience of counting wears out. I counted to a thousand once, but all I know is that it took a very long time (at least to the mind of a four-year-old). Even a hundred is too many; I have to group it into clumps, patterns, to understand it. Ten I might have a handle on, so it’s very easy to group things in tens. I’m thirty-one years old. That’s just over three tens of years, and I was there the whole time, but I honestly don’t think I entirely have a grasp on thirty-one itself.

Trying to comprehend large numbers is both futile and very, very, useful. We can never quite get that same familiarity and intimate understanding of them that we do with the small numbers, but we can get enough of a feel for them to recognize obviously wrong guesses.

Sometimes. I once worked out that there ought to be “oh, at least a trillion, maybe more” cells in a human body, and rejected it as obviously silly; wasn’t a trillion one of those stupidly large numbers they use in analogies? Actually, it looks as though the number probably is around ten trillion - with perhaps another hundred trillion microbes living in us. Wow. I’m not sure which is scarier; being outnumbered by the micobes, or finding out that I was roughly correct on a biology question.

### Comments [archived]

From: ariel

Date: 2003-07-02 00:35:06 -0500

I think one can grasp more numbers (probably 100) in 10 by 10 grid… i.e. a multiplication table… you can still see everything and see that they are in tens and still have overall understanding that there are 100 items before you.

From: Mikis

Date: 2003-10-01 10:17:11 -0500

Good Article. If anyone is interested in this sort of thing, you should read “Innumeracy”. Its a great book that talks about people that just don’t understand numbers. There is alot of great examples in there that everyone can relate to.