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 thanOther Things
- Be Careful About Size Comparisons In Multiple Dimensions
- Low-probability Events Happen All The Time
- The Probability of Something That Has Already Happened Is 1.0
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?
If you mean a cube two metres on a side, the second cube masses eight tonnes.
If you wanted a cube that masses two tonnes, you need a cube that measures 1.2599 metres on a side.
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.
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".