I found this thing... I thought I'd share it.

From the alt text of a recent XKCD:

“Feynman recounted another good one upperclassmen would use on freshmen physics students: When you look at words in a mirror, how come they’re reversed left to right but not top to bottom? What’s special about the horizontal axis?”

Took me a minute of existential-crisis style wondering, but I figured it out and then felt dumb afterwards.

Good one Feynman.

It’s what happens when you discover something verifiably, irrefutably true - which has no use whatsoever. Well, at least at the point of discovery. Pure science has a tendency to become Applied Science in the long run.

So in reading this article by the internet-famous author of webcomic xkcd I came up to a point where it points out that unit cancellation is weird. This is illustrated with the example of fuel economy. It is expressed as miles (or kilometers) per gallon (or litre). Which means it’s distance over distance cubed. So the actual unit of fuel efficiency is distance squared. It’s an area.

At first this doesn’t make any sense, why would MPG be an area? Here’s where the magic happens:

Ok, so what’s the physical interpretation of that number? Is there one?

It turns out there is! If you took all the gas you burned on a trip and stretched it out into a thin tube along your route, 0.1 square millimeters would be the cross-sectional area of that tube.

I now have a visual model of what fuel efficiency means. Imagine all automobiles dragging behind them a chord of varying thickness…

Like a modern sedan on the highway with a thin thread you can barely see.

A moped with an invisible spidersilk strand blowing in the wind.

A Hummer dragging behind it a mooring line…

Then there’s some real fuel-hogs, like rockets. I don’t think there’s ropes as thick as what they’d be trailing - but they have to go vertically and that’s some bad fuel economy. At least until they reach escape velocity.

This is all apropos of absolutely nothing, but I really have no other outlet for weird things I find by myself at work.

Pure science, folks.