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 - 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?
It depends.
-
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
.
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".
