This post on the nominal illusion, in which the units of measure we use affect our psychological perception of a quantity, reminded me of something else interesting about the way we perceive units.
When I was in college, my roommate told me about a skiing trip he’d been on, where the snow was “a yard deep.” He’s European, so naturally he was thinking “a meter deep” and converting it for my American ears. To any native speaker of American English, of course, that sounds all wrong: we would say “three feet deep.” The question is why?
As far as I can tell, the answer is that yards are units of horizontal measure, not vertical measure. It’s a bit funny that we have units of length that are only used in certain directions, but once you start looking out for them, there are actually a bunch of them. Miles are horizontal (the exceptions are “the mile-high city” and “the mile-high club,” but I think that in both cases the “incorrect” unit is being deliberately used to make the phrase sound funny or memorable). In aviation, feet are vertical. In the ocean, fathoms are vertical and leagues are horizontal (before saying that “20,000 Leagues Under the Sea” proves this wrong, check out what the title actually means: it’s not how far down they went; it’s how far across.)
Of course, in our everyday lives, we experience horizontal distances quite differently from vertical distances, so maybe we shouldn’t be too surprised that there are different units of measure for them.
There’s a nice analogy here to the theory of relativity. In relativity, we learn to think about spacetime, as opposed to thinking of space and time separately. In doing this, it’s much easier to use a system of units in which distance and time are equivalent (and the speed of light has the value 1). Maybe some day in the future, when we’re all zipping around at close to the speed of light in our personal spacecraft, we’ll all have a strong intuitive grasp of relativity. It’ll seem perfectly natural to us to use the same units for distance and time, and the fact that people used to use different units for the two will seem quaint and archaic, like fathoms and leagues.
Update: I thought of one more exception to the statement that miles are horizontal: the Byrds song “Eight Miles High.” But I think that’s in the same category as the others. Anyway, they were a bunch of hippie stoners, so who cares what they think?