Andy Little wrote:
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?
Actually, I think your understanding of the pieces for generic unit systems is better than you realize. From a physicists point of view, there are just a few choices that need to be made to create a unit system. First is a choice of dimensions. What types of things are you going to measure, and how do they relate to each other. For example, the SI system chooses to measure length, time and mass as independent dimensions. This gives compound units for things like force, velocity and acceleration. Relativistic units make the choice that velocities should be unitless, so to make that happen, the units for length and time must be the same. This is not what our daily intuition would have us expect, but it is consistent with the theoretic decription that unifies length and time. Energy units (The system used in almost all particle physics.) goes further and decides that everything should be measured in different powers of energy. Once the dimensional choices are made, choices of preferred scale need to be made. SI units differ from cgs units and even Imperial units mostly because different scale choices were made. The scale choice for Relativistic units is that the speed of light should be exactly 1, and everything other than that should be SI based. In Energy units, the scale choice is an amount of energy called an Electron Volt (The amount of energy it takes to move one electron across a potential difference of one volt.). In this system, both the speed of light and plank's constant are exactly 1. To my understanding of what you have written, it already supports one specific choice of dimensional quantities (The choice made by the SI units.), and I think it could support other choices with minimal effort, since the choices can be phrased in terms of those made by the SI system. Given that choice of dimensional quantities, it supports scaling between different unit systems. At the moment, I think it does that scaling automagically when the values are compiled and does actual computations in SI units (Please correct me if this understanding is wrong.). I would prefer for unit conversions to only happen when explicitly requested, and for mixed unit expressions without requested conversions that match the units to produce errors. So, there are a few differences between more generic systems and what you have done, but if I understand what you have done so far, they are not as big as you seem to think they are. John
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
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