wrote:

I understand perfectly well. If you are moving to the East with speed 10 (in some units) your velocity is v = 10; but if you are going West at speed 10 your velocity is v = -10. If you 5 units to the right of the origin your coordinate is x = 5, but if you are 5 units to the left it is c = -5. That is how physicists use these concepts; mathematicians do so as well.

Nonsense.

Well, some bodies have fewer than 6 degrees of freedom, while others have more than 6. They can have as many as 8 degrees, but if counting the three "position" coordinates (which the OP did not want to do).

No, it is well-documented dynamics. For example, when studying the specific heats of dilute gasses by statistical thermodynamics, we need to worry about these thing; and if we count correctly, we get perfect agreement with experiment. That matters, because physics is an experimental science, after all.

No, it is not just fun mathematics; it is known to anybody who has taken undergraduate statistical mechanics or undergraduate classical mechanics. People who go to the library and read appropriate textbooks know about these things.

R.G. Vickson

I understand perfectly well. If you are moving to the East with speed 10 (in some units) your velocity is v = 10; but if you are going West at speed 10 your velocity is v = -10. If you 5 units to the right of the origin your coordinate is x = 5, but if you are 5 units to the left it is c = -5. That is how physicists use these concepts; mathematicians do so as well.

Nonsense.

Well, some bodies have fewer than 6 degrees of freedom, while others have more than 6. They can have as many as 8 degrees, but if counting the three "position" coordinates (which the OP did not want to do).

No, it is well-documented dynamics. For example, when studying the specific heats of dilute gasses by statistical thermodynamics, we need to worry about these thing; and if we count correctly, we get perfect agreement with experiment. That matters, because physics is an experimental science, after all.

No, it is not just fun mathematics; it is known to anybody who has taken undergraduate statistical mechanics or undergraduate classical mechanics. People who go to the library and read appropriate textbooks know about these things.

R.G. Vickson