"John Phillips" wrote
There are also spaces where the units (or more accurately, the dimensions) are not the same in all directions, so any vectors in those spaces will have mixed units in any coordinate system. A commonly used one is called "phase space" and it includes the position and momentum variables for a system all in the same space. Thinking of them together turns out to be quite important in some applications, so the example can be quite meaningful for some people.
Discussion of the area of mathematical spaces beyond the everyday one brings up an important point regarding PQS and attempts to make it more *generic* re unit systems, but I cant explain it well. Neverthless I will try: The everyday system of units as exemplified by the SI and is about the human scale is relatively stable AFAIKS. Moving further from what might be called the human scale things become less and less certain. I conjecture that as one moves to other more esoteric unit systems then things are less well understood, even by physicists and mathematicians, and that would make working on a units library designed to encompass those systems much more difficult. Is not much of maths and physics a search to find models of those systems? An important aim of PQS is to provide a standardised means of dealing with units. It is only advisable IMO to standardise things that are stable, but the further one goes into maths and physics the less stable things become, so my guess is that any standardised units library would be less satisfactory there. Does that make sense? regards Andy Little