Dear all, (01)
Sorry for my late reply on the mail below; due to holidays with my
famlily at that time I have not been able to read all emails then,
unfortunately. Now I have finally got the time to read and, in some
cases, answer older emails. Pleas excuse me for any inconvenience and
hopefully the discussion is appreciated after all. (02)
My next remark can also be seen in relation to earlier remarks I made
about "kinds". (03)
I certainly do think that kinds should be in UoM. However, in an
ontology (language) we do not define seperate concepts for that (such as
"quantity kind"). "Kind" is inherent to classification; so we define a
class ("quantity"), which represents the quantity kind. (04)
We have to dare and define subclasses of "quantity", such as (|_ means
subclass): (05)
Quantity
|_ Length
|_ Diameter
|_ Circumference
|_ Wavelength
|_ Moment of force
|_ Ednergy
|_ Heat
|_ Kinetic energy
|_ Potential energy (06)
etc. (07)
The good thing about the view above is that, to my mind, it integrates
the different views on quantities and kinds that we have. In the view
above, we still do have quantity kinds, but it is inherent to
classification now. (08)
Best regards, Hajo (09)
-----Original Message-----
From: uom-ontology-std-bounces@xxxxxxxxxxxxxxxx
[mailto:uom-ontology-std-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Joe
Collins
Sent: 21 July 2009 16:58
To: uom-ontology-std
Subject: Re: [uom-ontology-std] retitled: Units of an angle (010)
"Quantity dimension" has a very precise meaning in SI, as does
"quantity", "derived quantity" and other terms. There are many examples
of dimensionless derived quantities (with a quantity dimension of one),
and of products of those dimensionless derived quantities with other
non-dimensionless derived quantities. You may find the SI nomenclature
arcane, but it is very precise. (011)
The SI indicates a property of derived quantities, "kind", which is to
be used for distinguishing between derived quantities having the same
quantity dimension. Its meaning is not fully developed in the SI, rather
it is left to others, such as yourself, to do so. To be consistent with
SI nomenclature, I urge you to use the concept of "kind". (012)
If you are interested in units and their meanings, I strongly recommend
purchasing and reading INTERNATIONAL STANDARD ISO/DIS 80000-1,
"Quantities and units" if you haven't already. It is the first, and most
complete source I have read for international metrology standards. I
suggest this because it seems it would clear up much of the lack of
knowledge and misconceptions often exchanged about quantities, units,
physical dimensions.
It does cost money, but I urge you to overcome, as I did, the cheapness
instilled by "free" information elsewhere. (013)
Regards,
Joe C. (014)
Patrick Cassidy wrote:
> I would like to pursue the issue of the unit of measure of an angle,
> since it also relates to other "ratio'-like quantities that may be
> used as measures. The gist of this note is that I would not like the
> 'dimension' of an angle to be considered as null, or 1, or
> dimensionless, but as something that means 'angular measure'. For an
> ontology that is intended to represent meanings, I am very leery of
> oversimplifications that work fine in restricted contexts but may
prove confusing in missed contexts.
>
> The last note from Ingvar Johansson had this portion of a discussion:
>
> [John Sowa] > > I also like that analysis. But it has to be extended
> to angles,
>>> since we have to support multiple functions that map angles to
>>> numbers: degree and radian.
> [IJ] > I agree, and in a sense so do also the metrologists that (as I
> said in
>> an earlier mail) I criticize. In my opinion, one should say that
>> radian is a unit of the derived dimension length/length, but the SI
>> system and VIM says that it is a dimensionless unit or a unit of
dimension-one.
>> However, everyone agrees that angles can be measured by (or mapped
>> on)
> scales
>> whose magnitudes are 'x degree' or 'x radian'.
>>
>> I think, by the way, that it is misleading to say that "angles are
>> mapped to numbers"; angles are mapped to magnitudes of a scale.
>>
> Although an angle in radians can be expressed as a ratio of linear
> measures, the linear measures themselves do not measure arbitrary
> straight lines, but are quite specific regions of some imaginary
> circle. I think it is a misleading oversimplification, when taking
> ratios of things that are not themselves pure numbers, to ignore the
> meanings of the measures that are being divided. A similar issue has
> arisen in the past about how to express things like "weight percent"
> which, if one ignores the objects that are represented by the
> numerator and denominator, can appear to be a dimensionless number
> (grams/grams). Such ratios have an actual conceptual "dimension"
> though the SI and VIM committees may have found it possible to ignore
> the meanings in the case of radians, knowing that the dimensions will
> likely be interpreted properly in applications. One way to recognize
> the problem is to note that if one wants to represent a weight ratio,
it is possible to use micrograms per gram or grams per gram, and the
"dimensions"
> will appear to cancel out in either case, leaving a "dimensionless"
> number, though the resulting numbers differ greatly depending on what
> units are chosen for the numerator.
> I would suggest that we promiscuously include all quantifiable
"units"
> that carry meaning in any application, and not take as "dimensionless"
any
> measures that are in fact distinguishable in their intended meaning.
A
> weight ratio does *not* have the same dimension as an angle, though
> one can oversimplify either to some dimensionless number.
>
> In this view, a 'radian' is a unit of measure, as is a
> 'degree-of-angle', and if the dimension is represented separately from (015)
> the unit of measure, the dimension in either case would be 'angular
> measure'. The dimension of a weight ratio is the ordered pair of
> objects or types of objects whose weights are being divided (weight
> ratios might better be treated in a different way, but if they were
> treated as measures with a unit, that would be my preference for the
unit).
>
> It may be possible to consider certain ratios as the 'base unit' as (016)
> in the case of a radian, where the subtended arc length and radius are (017)
> the defining measures being divided. In the case of weight ratio,
> grams-of-X/grams-of-Y might be the base unit for each X/Y pair.
> Measures that are related to other ratio measures by some constant
> number, such as angle degrees or micrograms/gram, would then be
> related to the base unit as "prefix"-unit is to other base units,
> where "prefix" may be micro, kilo, etc. or a special non-SI prefix.
>
> Pat
>
> Patrick Cassidy
> MICRA, Inc.
> 908-561-3416
> cell: 908-565-4053
> cassidy@xxxxxxxxx
>
>
>
>
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> (018)
--
_______________________________
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
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