Joe,
Thanks for the reference to some relevant material.
I second John Graybeal's suggestion, more specifically: Would it be
possible for you to quote the paragraphs of that standard that specify the
distinctions between 'quantity dimension' and 'kind' and 'unit of measure',
rather than have us all spend money to buy a document most of which will not
be informative with regard to the issues we are discussing? Do paraphrase
if you think that direct quote would violate copyright. Every constructive
suggestion is welcome in a discussion of this kind, and describing details
that one considers important tends to be more helpful than a suggestion to
read some document, especially one that is not trivially inexpensive. (52
euros). I (and I suspect others) would be willing to cough up the dough if
there were some confidence that the product had essential content that was
not duplicated in other, free documents. There are already a reasonable
number of free units classifications that seem to provide an adequate basis
for an ontology.
The issues in developing an ontology focus in the conceptual
distinctions, and the labels that are used for the concepts of interest are
of minor importance, only requiring some care not to label concepts
misleadingly. Terms such as 'dimension' and 'kind' are used in multiple
senses, so whatever concepts are identified as useful for an ontology of
units, we should make an effort to find unambiguous labels that are
satisfactory to most.
The substantive question in this particular thread relates to the
distinction between 'kind' (in the ISO terminology you quote) and
'dimension', and whether representations of those distinctions can be used
effectively. I have never seen the term 'kind' used in that sense in the
technical literature I am familiar with. If you have examples of the use of
that concept, in some practical application outside the standards document
itself, that could be very helpful in making decisions on what to include in
the units ontology, and it may move some of us to actually buy the standard. (01)
Pat (02)
Patrick Cassidy
MICRA, Inc.
908-561-3416
cell: 908-565-4053
cassidy@xxxxxxxxx (03)
> -----Original Message-----
> From: uom-ontology-std-bounces@xxxxxxxxxxxxxxxx [mailto:uom-ontology-
> std-bounces@xxxxxxxxxxxxxxxx] On Behalf Of Joe Collins
> Sent: Tuesday, July 21, 2009 10:58 AM
> To: uom-ontology-std
> Subject: Re: [uom-ontology-std] retitled: Units of an angle
>
> "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.
>
> 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".
>
> 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.
>
> Regards,
> Joe C.
>
> 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 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 in
> > the case of a radian, where the subtended arc length and radius are
> 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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> >
> >
> >
>
> --
> _______________________________
> 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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