Rijgersberg, Hajo wrote: (01)
> A dimension is not represented by a product of powers of base units, but
> by product of base *dimensions*. (02)
Exactly! I hope the working group understands this point. It is very
important. (03)
> And - although less clear to me but as
> far as I can see - systems of units can have different base dimensions. (04)
Yes. That is why the VIM describes a system of units as _selecting_
'base quantities', i.e., "base dimensions" in Hajo's terms. The VIM
does not suggest that any particular set of "base dimensions" is
"natural"; it just says that SI selected a particular set. The one
requirement on the set of base dimensions seems to be: Every dimension
can be represented by a product of base dimensions. (Philosophically,
that may be difficult to ensure; what we really have as a basis for that
assertion is modern physics, and we already know there are some
contradictions.) (05)
> Furthermore, let me emphasize that a dimension only *has* expressions in
> terms of base dimensions of systems of units. It *is* not such an
> expression as such. Many dimensions exist that have the same expressions
> in terms of other dimenions. (06)
I agree that the dimension is not the same thing as its representation
in base dimensions. That the relationship is not 1-to-1 may be a
serious problem, because it leads to difficulties in the identification
of individuals. What property distinguishes one dimension from another?
How can we tell whether (= D1 D2) or (NOT (= D1 D2))? Do we simply
use the unique naming hypothesis, i.e., if the spellings are different
they are different unless someone tells us they are the same? (07)
-Ed (08)
> However, presently in OUM many dimensions are merged, but they still
> *have* expressions in terms of base dimensions of systems of units.
> Depending on the outcome of the discussion I am willing to distinguish
> these dimensions again, like used to be the case in previuos versions of
> OUM. It is an interesting on-going issue and discussion.
>
> Regards, Hajo (09)
--
Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 301-975-3528
Gaithersburg, MD 20899-8263 FAX: +1 301-975-4694 (010)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (011)
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