From: John Phillips (phillips_at_[hidden])
Date: 2006-06-13 13:43:48
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
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.
> 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?
> Andy Little
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