3 ms·
> all angles are without a unit. Dimensionless, sure, but what do you mean here? Radians and degrees are units, are they not?
by dahart 2mo ago
> all angles are without a unit.
Dimensionless, sure, but what do you mean here? Radians and degrees are units, are they not?
- thyristan 2mo agoIn a very awkward way: rad is m/m, which is 1...
- ant6n 2mo agoPerhaps in the physics sense, but in computer science we do have the notion of types which does allow us to model the difference between an angle and other numerics.
- aidenn0 2mo agoIt is only equal to 1 by convention. If we instead considered the ratio of the diameter to the arc-length then rad would be 1/2.
- simiones 2mo agoDimensions and units are separate things, though. For example, 1 minute and 1 second are different units of the same time dimension. Similarly, 1 rad and 1 degree are both dimensionless, but they are both different units.
- thyristan 2mo agoTheoretically, you can define systems of measurement where a lot of seemingly separate things fall on the same units and dimensions. There are "natural units" in physics where you take the fundamental nature of particles and relativity into account and make some convenient choices for some physical constants such as the speed of light c := 1. Then the speed becomes dimensionless, length and time have the same unit and dimension (a length of 1eV is a time period of 1eV), and almost all units are simply derived from a measurement of energy (electron volt, not as basic as people would like, but useful enough). https://en.wikipedia.org/wiki/Natural_units https://en.wikipedia.org/wiki/Natural_units
- dahart 2mo ago> Then the speed becomes dimensionless, length and time have the same unit and dimension Uh, that is not what the article you linked is saying. Natural units don’t make speed dimensionless, nor allow you to use the same unit for length and time. Natural units remove the conversion constants, not the units or dimensions.
- deleted 2mo ago[deleted]
- dahart 2mo agoThat’s the awkward argument for being dimensionless. But we know we have units of angle because we have scale factors to convert between them.