First I'd like to thank Patrick and Gunther for their great recent
posts that have cleared up a lot of my own confusion about those
existing documents, and even suggested a way forward. (01)
It sounds like the 'kind' that Joe refers to is analogous to the
'family' that Patrick refers to, I hope to see more about that
alignment. (02)
And I am just about convinced to purchase ISO 80000-1. Unfortunately,
like ITU's Metric objects and attributes spec [1], which was
recommended to me yesterday, its minor cost will guarantee only a
subset of the population will read it; most will rely on the expertise
of others to read and interpret the contents. (And that split will
grow larger as the 'free information' model/mentality increasingly
takes over.) Further, if we did read it and said "That's the right
way to do it!", would we be able to legally model the ontology on it?
Without passing judgment on those concerns, it does seem that non-free
information will always suffer 'in the marketplace of ideas'. (03)
More to the point, if there is some way to legally and appropriately
summarize the key points of each of these for this discussion, it may
benefit the discussion considerably. At a minimum, understanding
whether the material there conflicts with the expressions here will be
helpful. (04)
John (05)
[1] http://www.itu.int/rec/T-REC-X.739/en (06)
On Jul 21, 2009, at 7:58 AM, Joe Collins wrote: (07)
> "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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> (08)
John (09)
--------------
John Graybeal <mailto:graybeal@xxxxxxxxx> -- 831-775-1956
Monterey Bay Aquarium Research Institute
Marine Metadata Interoperability Project: http://marinemetadata.org (010)
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