While I procrastinate in writing about more important things...

Physicists (one of which I am not) are quite concerned about units and dimensions and use dimensional analysis for a variety of purposes. And if the units in an equation don't match in all terms and across the equals sign, you've erred.

But sometimes this can lead to confusion. For example, torque (exerting a force about an axis) is measured in dimensions of [force]*[length]. It could be pound feet or newton meters or, for the matter of that, dyne centimeters or ton furlongs. But work and energy are also measured in such units. A joule is a newton meter.

Thus, in thinking about my fuel economy as a U.S. resident, I'm accustomed to thinking of miles/gallon but in countries who've adopted the SI (metric) system, people make a very sensible inversion of this and, rather than distance/volume, they use volume/distance, typically liters/100 kilometers. While this isn't an SI unit, it is metric.

But it's also a volume divided by a length or [length]^3/[length] which is [length]^2 or an area. So I converted my 50 m.p.g. to an area to note that my fuel economy is 4.704*10*10^(-8) m^2 or 0.04704 mm^2. Next time someone asks about my fuel economy, I'm going to say "a bit over 47 thousandths of a square millimeter."

It's not surprising to note that Randall Munroe*, of xkcd fame, has beat me to it. I will state, for the record, that I noted his post after composing all but this portion of this one.



*This is the first time I've noticed a photo of Munroe. It always amazes me how little resemblance there is between what I picture someone to look like in my mind and what they actually look like when I see them or their photo. And I always picture them.