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Re: [uom-ontology-std] retitled: magnitude of a quantity

To: uom-ontology-std <uom-ontology-std@xxxxxxxxxxxxxxxx>
From: Ed Barkmeyer <edbark@xxxxxxxx>
Date: Thu, 16 Jul 2009 11:43:25 -0400
Message-id: <4A5F4A9D.4080202@xxxxxxxx>
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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