Tuesday, October 12, 2021

[qmhokobr] units for humans

we devise a system of units such that the base units of time, space, and mass are "human sized" (very subjective), and some quantities important to the human experience are nice powers of 10.  the three quantities, constants, that we have chosen to be nice are the length of a day, the acceleration of gravity on earth, and the density of water.

time = 1e-5 day = 0.864 s (about 70 bpm, a heartbeat)

length = 0.1 gravity (1e-5 day)^2 = 1e-11 gravity day^2 = 0.7320625 m

mass = 1e-3 waterdensity (1e-11 gravity day^2)^3 = 1e-36 waterdensity gravity^3 day^6 = 0.39232364 kg

day = 86400 s = 100000 time

waterdensity = 1000 kg/m^3 = 1000 mass / length^3

gravity = 9.80665 m/s^2 = 10 length / time^2

to do: names for the new units.

comparing with the metric system: dividing a day into 2 and 12 and 60 is understandable, arguably superior to 10.  but dividing consistently would have been nicer.  choosing the standard unit of mass based on the density of water was a good idea, replicated here.  the choice of the meter, one ten-millionth of the distance from the north pole to the equator, was a terrible idea.  it might be useful for specialists in geodesy but no one else.  even they would have likely preferred a standard unit which makes the radius (not circumference) of the earth a nice round number.

on one hand, because the defining quantities are inherently imprecise (gravity varies by location, length of day changes, water density depends on isotopes), these units are not intended for high precision.  on the other hand, because we've defined them in terms of SI, they have as much precision as SI.

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