Ingvar wrote:
> Joe Collins wrote:
>
>
>> I, however, do not advocate a theory different from the SI.
>> I have no problem with the Quantity Dimension "one" (or "dimensionless").
>>
>
> To be 'dimensionless' or to have the 'dimension one' is not exactly the
> same thing, even though the SI system and VIM now and then write as if
> they were the same.
>
>
Ingvar is correct. The Quantity Dimension "one" is a 'kind of quantity'
that is "count". The quantity of eggs in a box of one dozen eggs is 12
"ones" (or "count" or "each"). The quantity kind of that quantity is
"one" (or "count"). (I prefer calling the kind of quantity "count" and
the unit "one", but business also uses "count" and "each" for the unit.) (01)
There is no such thing as a "dimensionless" unit, from the ontological
point of view. All that means is that in the derivation of the unit,
the referent quantity kinds appear equally in the numerator and
denominator of the relationship expression. But the referents in both
places are part of the unit definition. They are among its "dimensions".
>> 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.
>>
>
> There is nothing wrong with the practical use of radian, but in my (and
> some others) opinion, its dimension is 'plane angle', neither 'dimension
> one' nor 'dimensionless'.
>
Exactly! Its quantity kind is 'plane angle'. 'plane angle' and 'count'
are different kinds of quantity. Its "dimensions" are length/length
(arc length/radius). And that is different from mass/mass or
energy/energy.
>> Are you proposing that your theory be incorporated in an UoM ontology in
>> preference to the long-standing, internationally agreed upon SI?
>>
>
> No, by no means! Of course an UoM ontology should be consistent with the
> SI system. In the paper I have mentioned, I am arguing for changes in the
> SI system.
>
>
Now that is a different matter. Our task is to capture the ontological
concepts and to document the SI system as is as a population of those
concepts. We will also want to capture the English system and probably
others. (02)
But the SI system does not say that radians are "dimensionless" in the
sense of having "kind of quantity" = "ones". It says that "radian" has
the kind of quantity "plane angle". Radian, when represented as the
product of powers of the base units, has only 0 exponents, which is what
the vernacular of scientists and engineers means by "dimensionless", and
what the SI and VIM documents mean by "dimensionless". If you represent
it as powers of the base units in the numerator and denominator
separately (which is not the model that SI uses, but closer to the model
that the ontology will want), you don't get only 0 exponents. So please
don't confuse "dimensions" and "dimensionless" in the notational space
with "kind of quantity" in the concept space. The notational space
("dimensional algebra") is convenient to the mathematics, but we are
talking here about the interpretation of the mathematics. The same
mathematics can have multiple interpretations; in the uom ontology, it
is necessary to get the right one. (03)
-Ed (04)
--
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 (05)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (06)
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