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this post was submitted on 26 Aug 2023
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Showerthoughts
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This is one of two "warts" that I know of in SI. They wanted a coherent set of units, coherent meaning that no nuisance constants are required to convert between dimensions in the set. The system at the time was gram-centimeter-second. To expand things to all dimensions I suppose it was simpler to use the larger units, like J = kg m^2 / s^2 rather than trying to make a new unit for energy, etc. You'd think they'd have just come up with a new name for mass units and defined it as 1 kg, something like 1 prot = 1 kg, then all of the coherent units would be ones without prefixes. Someone must have really being going to bat for the word "gram" though, because now we have this pretty stupid rule that the coherent units are all of the ones without prefixes, except mass, which has the coherent unit of kg. And then also, prefixes are used to scale the coherent units by appending the appropriate letter to the coherent unit symbol, except for mass, for which g is treated as the coherent unit, even though it's not.
It's not the worst thing, but it's pretty stupid to explain.
until you realize, that "second" is also not the base unit. it's not at obvious because it isn't metric, but second is just the second subdivision of an hour (the first being the minute)
There are no longer any base units as of the 2019 SI redefinition, but prior to that the second was the base unit for time. Hour and minute we're defined based on that. And now even though a second isn't a base unit, hour and minute are still defined based on the second, not the other way around. It's been that way for several decades now. Maybe you're thinking of some no-longer-used system.
Okay I'll bite. What's the other "wart"?
The mole is defined based on the gram and not the kilogram, even though the kilogram is the coherent unit of mass. I don't have an example, but it probably results in a bit of extra math somewhere. Again, who knows why. Apparently the mole has had conflicting definitions in the past, and one of them was based on the kilogram, so it seems like this would have been easy to do. Again, the gram is involved - maybe the two things are related?
Apparently, the SI base units have been redefined, and the link between moles and kg was severed in 2019?
I was vaguely aware of this shake-up after reading someplace that the kg had a new definition in terms of fundamental physical constants rather than the old one based on an official standard kg. This was basically a block of metal sitting in a lab someplace in France. But TIL other base unit definitions were also tweaked at that time.
Their definitions are no longer related, but their sizes are still roughly the same relative to each other. I mean that the unit for amount of substance is based on 12 grams of C, instead of 12 kg of C, despite the kilogram being the unit for mass. Some fields used to use that unit and called it a kg-mole, but that notation would be pretty confusing and you would want to have a different name. https://en.m.wikipedia.org/wiki/Mole_(unit)
I think the 2019 redefinition is really neat. They changed the system so that constants are defined instead of measured, in a way that makes estimates more precise. It's worth reading about if you're interested in the stuff.