Numerical literacy: It happens to other people.


Categories: GeekStuff

This article about Zimbabwe’s old currency contains a thing of beauty:

Scientists and physicists estimate the number of atoms in the universe at 10 to the power of 80 — 10 followed by 80 zeros.

During the worst of Zimbabwe’s economic meltdown and hyperinflation, Zimbabwe’s highest money denominations were logged at 10 to the power of 25 — 10 followed by 25 zeros — or the equivalent of nearly one third of the number of atoms estimated in the universe.

Now, to fully appreciate this, you have to understand that the mathematical genius writing this had just been commenting on how people had expressed concern for the effect on mathematical ability and basic numeracy of the money. But a writer who presumably comes from a more stable part of the universe can’t even get things right within a factor of a few hundred trillions of trillions.

This is a pretty stunning failure to understand the basics of how our number system works.

Here’s a puzzler for the author, one “Angus Shaw”: Given your theory that a one with 25 zeroes after it is “nearly one third” of a one with 80 zeroes after it, let’s try an experiment.

You give me a thousand dollars. I give you three tens. Since a one with one zero after it is a third as much as a one with three zeroes after it, then a one with one zero after it, three times should be just as much as a one with three zeroes after it, right? And because I am such a generous guy, heck, I’ll give you FOUR tens in exchange for your thousand dollars, meaning you get ten times as much money as you give! I will happily do this as often as you’d like. I am just that nice.

Edited to add: Looks like Angus Shaw and the AP don’t understand how journalism works. When you edit a piece after it’s gone live, you identify the edit. You don’t try to pretend you didn’t screw up. A little integrity goes a long way, folks.

Edited again: To clarify, the key thing here is not that we need an exact, detailed, change log (though since you can generate those with software with perfect reliability and zero effort, it would be a nice thing to do), but that if you edit something with no indication that any edit occurred, it makes it look suspiciously like you’re trying to hide that you screwed up. In particular, consider that there’s now no way for someone reading my post, and the linked article, to tell whether or not I’m misquoting the article, and if they see the article first, with no indication that it was edited, they might assume I’m just confused.

Comments [archived]

From: Paul
Date: 2011-01-03 11:44:23 -0600

Hi Peter,

I was astonished to see the numbers as well and did a quick search to find the origins of the error. Thanks for your post.

I like the analogy you use to explain the error, but I think that you would arouse some suspicions with your offer of 4 ten dollar notes (which you said would equal ten times $1,000) as you misinterpreted the mathematical system that Angus has developed. He divided the exponents to come up with the one third value, thus $10 is one third of $1,000. Your offer of four $10 notes is therefore only one and one third times his $1,000. You indicated that four $10 notes would be ten times $1,000. That interpretation creates a new mathematical system that is a hybrid between what goes on in his universe and ours. He still might find your offer generous, but you might arouse suspicion.