That’s interesting. Obviously, you’d put a center dot to disambiguate millihertz from meter-hertz, but I can’t recall ever having learned a rule about that. So some combinations of units are inherently ambiguous?
I can’t tell which unit is more cursed: millihertz or meter hertz. Surely, anything that could be measured in millihertz is more natural to measure as a period, or as revolutions per minute or something, right?
EDIT: Also, TIL about dpt. Thanks!
A dioptre (British spelling) or diopter (American spelling), symbol dpt, is a unit of measurement with dimension of reciprocal length, equivalent to one reciprocal metre, 1 dpt = 1 m^−1.
Speed is metre hertz rather than metre per hertz. Metres per hertz would measure absement, which is a measure of how far away something is from a start point and for how long. So being twice as far away for half the time would be the same amount of absement.
This is actually pretty important to being able to solve engineering problems in the real world. Invariably, every little sub industry has its own cursed unit system. And dimensional analysis is great for solving real problems on its own.
And if you get to a high enough physics level, they start setting hbar = c = 1 or G = c = 1, and you never have to worry about it again.
I’m the mean time, it’s worthwhile to learn the trick to do this stuff fast-ish.