I wish static typing were as uncontentious as units of measure.
I wouldn't say that UOM are uncontentious, things can get dicey around reference units and precision for instance, or the combinatorial explosion of composite units.
Right, but if you told your professor you sometimes represent distance in Volts (to make your calculations simpler) you'd get some funny looks.
You could even double-down on it: "Have there been any studies that prove that using units of measure helps you get the right answer?"
Funnily enough, there are some applications for converting mechanics problems to analogous electricity problems to leverage circuit simulation software such as PSPICE to help solve things like transcendental equations.
Yes, but the mapping doesn't change the relationship between the units of measure, which is the actual meaning as far as the type system is concerned. It's just a change of names.
Sure, I wasn't meaning to detract from the comment above, just to point out what I thought was an interesting related fact.