Dear Ingvar, (01)
I, however, do not advocate a theory different from the SI.
I have no problem with the Quantity Dimension "one" (or "dimensionless"). (02)
The quantity "angle" is physically measurable, has the natural unit radian, and
is naturally dimensionless. There's nothing unnatural about the so-called
dimensionless Quantity Dimension. (03)
Multiplication and division are well defined arithmetic operations and their
application to the physical theory of units and quantities in the SI is
consistent with their usual mathematical meaning. I see no reason to make a
distinction if there is no substantive difference. What new mathematics is
required to re-define multiplication and division? It is true that the theory
of
units and quantities is a "physical theory" which is distinct from a
mathematical theory. Were it to fail as a theory, it would only mean that we
would have to apply a different formalism. Pragmatically, I find this unlikely. (04)
Are you proposing that your theory be incorporated in an UoM ontology in
preference to the long-standing, internationally agreed upon SI? (05)
Regards,
Joe C.
ingvar_johansson wrote:
> Joe Collins wrote:
>
>> There is an inherent mathematical structure to the SI units and dimensions
>> beyond scale which are defined in the SI.
>>
>> The Base Quantities, length, mass, time, electric current, temperature,
>> amount
>> of substance, and luminous intensity, whose dimensions, L, M, T, I, Θ, N,
>> J,
>> form a generating set, using the operations of multiplication and
>> multiplicative
>> inverse, for the Quantity Dimensions.
>
> In my paper "Two Changes in the International System of Units?", which I
> mentioned in my former mail, I argue that it is important not to conflate
> *metrological* multiplication and division of dimensions with
> *arithmetical* multiplication and division. If one does, one ends up in
> proposing (as VIM and the SI system do) the dimension 'dimension one'.
>
> Ingvar
--
_______________________________
Joseph B. Collins, Ph.D.
Code 5583, Adv. Info. Tech.
Naval Research Laboratory
Washington, DC 20375
(202) 404-7041
(202) 767-1122 (fax)
B34, R221C
_______________________________ (06)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/
Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx
Config/Unsubscribe: http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/
Shared Files: http://ontolog.cim3.net/file/work/UoM/
Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard (07)
|