On Jul 16, 2009, at 10:43 AM, Ed Barkmeyer wrote: (01)
> Rijgersberg, Hajo wrote:
>
>> A dimension is not represented by a product of powers of base
>> units, but
>> by product of base *dimensions*.
>
> Exactly! I hope the working group understands this point. It is very
> important.
>
>> And - although less clear to me but as
>> far as I can see - systems of units can have different base
>> dimensions.
>
> 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.)
>
>> 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.
>
> 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? (02)
Blech. That is a *default* UNA, which is doubly barbaric. These sets
are not going to get exhorbitantly large. Let us stay in classical
logic and list the inequalities explicitly. I hereby offer the CLIF
definition of the useful variadic relation AllDifferent: (03)
(forall (x)(AllDifferent x))
(forall (x y ...)(iff (AllDifferent x y ...)(and (not (= x y))
(AllDifferent x ...)(AllDifferent y ...)) )) (04)
AllDifferent is true of any sequence of arguments none of which co-
refer. (05)
Pat (06)
>
> -Ed
>
>> 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
>
> --
> 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
>
> "The opinions expressed above do not reflect consensus of NIST,
> and have not been reviewed by any Government authority."
>
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> (07)
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