(My comment at the bottom just amounts to a +1 on this perspective.) (01)
On Aug 14, 2009, at 2:48 PM, Ed Barkmeyer wrote: (02)
>> So, if you propose to enlarge the set of Base Units, where do you
>> stop?
> With the Base Quantity "count"/"ones". It is the only measurement
> quantity in common use that is not derivable from the SI Base
> Quantities.
>> There is an arbitrarily large number of dimensionless
>> quantities of different Kinds.
> Yes. There is an arbitrarily large number of Derived Quantities, some
> of which are "dimensionless" in your terms, but have very clear
> derivation expressions in terms of base quantities and perhaps other
> derived quantities. The "base quantity" "ones" isn't derived. It
> doesn't have any such expression that conveys anything about its
> meaning.
>> You may have your favorites, but what
>> distinguishes them from someone else's favorites? The SI has chosen
>> to leave the
>> Base Units bounded in number and the mapping "Kind" loosely
>> defined, I presume
>> so that users may choose to make such distinctions as they deem
>> necessary by
>> defining as many Kinds as they want.
>>
> Of course. The expectation is that new derived quantities will
> arise as
> scientific and engineering disciplines expand.
>
> The fundamental problem with your approach is that no derived quantity
> is "dimensionless" in the sense of lacking a relationship to any base
> quantity. The fact that your symbol algebra discards relationships
> without apparent harm to the calculations doesn't mean that you have
> discovered a meaningful simplification of the Derived Quantity
> concept.
> At the level of defining the Kind of Quantity, the simplification
> (reduction to lowest terms) LOSES meaning. And at that level, the
> loss
> of meaning is loss of knowledge. Energy is not the same thing as
> Torque, and if you simplify the derivation expressions for the
> Quantity,
> you can't distinguish them. If you simplify the unit arithmetic you
> get
> mathematically correct results, which will be physically correct
> results
> only if you interpret the mathematical results correctly. That is the
> difference. (03)
I can't say I understand the subtleties of abelian groups and the
like, but Ingvar's point and this wrap-up seem so eminently reasonable
that I sincerely hope the final ontology provides a way to represent
them, whether or not SI, VIM, or any other system does so. (04)
John (05)
---------------
John Graybeal
Marine Metadata Interoperability Project: http://marinemetadata.org
graybeal@xxxxxxxxxxxxxxxxxx (06)
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