Numerical Ignorance

The general public is numerically ignorant; they don't understand the simplest mathematical, numerical, or statistical principles. And they're lazy; they don't even care to. This is such a truism that even the Barbie™ doll once complained that math is hard.

Unfortunately, the media seem to be just as bad as the public, so those few of the public that actually want to understand don't have much of a chance. It's virtually impossible to find a news item in a major newspaper, magazine, or television news broadcast concerning any aspect of science that doesn't contain gross mathematical errors.

Here are corrections to a few of the most common errors.

Things Can't Be X times smaller than Other Things

Six is, indeed, twice as large as three. However, three is not twice as small as six — it can be one-half times as large as six, or it can be one-half as big as six, but there's simply no validity to "so many times smaller than". You won't generally see this error made in a way quite this blatantly stupid, but you'll see things like thirty times smaller than a human hair all the time.

If you need to do this type of comparison, say one-thirtieth the diameter of a human hair instead. But keep the next point in mind …

Be Careful About Size Comparisons In Multiple Dimensions

A cube one metre on a side filled with pure water masses one tonne. How much does a cube twice as big mass? It depends.

Similarly, though a plot of land 100 metres on a side has an area of one hectare, a plot of land 200 metres on a side has an area of four hectares. A square two-hectare plot of land would measure 141.4 metres on a side. It would not be clear which of these would be intended by a phrase like a plot of land twice as large.

Comparsions like twice as big are never particularly clear when more than one dimension is involved. State what you actually mean (precisely!) instead: twice as massive, twice as long, half as thick.

Low-probability Events Happen All The Time

People assume, for some reason, that low-probability events do not happen. That isn't the case, of course — events that don't happen are zero-probability, not low-probability. Low-probability events happen all the time, especially when dealing with large sample sizes. If a mathematician means something won't happen, he'll tell you it's a zero-probability event.

Comparison: winning the lottery is a low-probability event. However, lots of people buy lottery tickets, so almost every week, someone wins the lottery. Don't assume that a one in 1.2 million chance means it isn't something that happens every day.

The Probability of Something That Has Already Happened Is 1.0

I flipped a coin nine times and got nine heads in a row. I've only got a one-in-1024 chance of flipping another head!

No. Every time you flip, you've got a one-in-two chance of flipping "heads". But the last nine heads have already happened, and therefore have a probability of 1.0. The probability of the tenth "heads" is therefore one-in-two, the same as always. This is sometimes stated as "Lady Luck has no memory".