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by lomnakkus
3712 days ago
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This is interesting because there's actually a unit-agnostic way of doing units more generally... it's "dimensional" rather than unit-based. So regardless of the base units you'll do "length" (which works for all three axes: length, depth, breadth) and "mass" (which works for kg, pounds, whatever) and "acceleration", "force", etc. Obviously this is slightly more lax and perhaps error-prone than your standard m/s or m/(s^2), etc., but it's one of the lamentably few things computers can do well! EDIT: ... and I should elaborate: In some sub-fields of Physics they usually go even further and just re-normalize everything to units of 1, so that e.g. the speed of light is c is 1. At that point it's really just about convenience since sqrt(1) = 1, and 1^x = 1, etc. (Lorentz Transformation.) |
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For example, if I am looking for a force and I get an answer of 1000 lbs, then dimensional analysis tells me that at least I got a force; but, if my intuition tells me only that the actual force is on the order of magnitude of 1000 N, then I don't know whether my actual answer is way too big, way too small, or about right, unless I know how to convert between Newtons and pounds.
Incidentally, while "units of 1" make correct calculations easy, I think that they are a bad idea precisely because they subvert unit checking; it's hard to know just by looking that 1 + 1 is 1 speed of light + 1 light-year, and hence dimensionally inconsistent.
(Even keeping all SI units can miss some important distinctions; for example, nothing about their SI units (inverse time) allows us to distinguish angular frequency (https://en.wikipedia.org/wiki/Angular_frequency) from temporal frequency (https://en.wikipedia.org/wiki/Frequency), and yet much woe accrues to he or she who does not distinguish radians/time from cycles/time!)