Pat Hayes wrote:
> On Aug 5, 2009, at 8:39 AM, Joe Collins wrote:
>
>
>> Comments referring to the UML model:
>>
>> A given "particular quantity" is composed of a number and a reference.
>>
>> The "particular quantity" you refer to is what SI/VIM simply calls a
>> "quantity",
>> (not to be confused with "derived quantity" or "base quantity")
>> defining it as
>> the "property of a phenomenon, body, or substance, where the
>> property has a
>> magnitude that can be expressed by means of a number and a reference".
>>
>
> I think this is not what is meant, if I understand the 'trope'
> language. Take a concrete case, a measurement of length in meters and
> two identical sticks A and B, with exactly the same length. There is
> one property here, called "length", which applies to both sticks and
> produces the same value in each case, say 3.1 meters. So: two sticks,
> one property, one length value of that property. As I understand the
> intention of the UML model, however, there would be two particular
> quantities: the particular length of A and the particular length of B,
> which are distinct, but have the same number and reference values
> (respectively 3.1 and meter).
>
>
Agree. This is the model I understand as well. Bear in mind that the
VIM is primarily about making measurements of quantities. So the two
sticks A and B will necessarily be different measurements (different
measurement actions). VIM 'particular quantities' are the individual
occurrences: 'the length of A' is a different 'particular quantity'
from 'the length of B'. Both properties are instances of the (VIM)
'kind of quantity' "length", which makes them comparable. When we say
that the length of stick A and the length of stick B are the same, the
VIM would say that the 'magnitudes' are the same; magnitude is the
abstraction of the particular property that is comparable. That
magnitude is expressed by a 'quantity value', consisting of a number and
a measurement unit, such as "3.1 metres" or "10 feet".
> (This illustrates why formalisms are so much more use than words, by
> the way, when fixing this stuff. Words are ontologically floppy. For
> another example, when you say, above, that something is "composed of"
> a number and a reference, do you mean that it is literally the pair of
> those things? Or that those are defining properties of it? Or simply
> that those are properties of it? These would all give different
> formalizations in an ontology.)
>
>
Exactly. We keep discussing models like David's because different
people have different understandings of the terms and their definitions
are "sloppy".
>> "Quantity value" is most generally a number and a reference to a
>> measurement
>> procedure. In the usual case where the quantity value is a
>> (multiplicative)
>> product of a number and a measurement unit, the measurement unit
>> refers to a
>> part of the measurement apparatus (the essential part).
>>
I have several problems with this. (01)
First, quantity value is defined to be a number and a reference to a
measurement _unit_. A measurement unit is a "reference magnitude" or
"reference quantity". It is a reproduceable amount of some kind of
quantity that can be used as a basis for comparison. It is defined by a
particular quantity. The measurement procedure for reproducing the
reference quantity changes with technology and with the accuracy
requirement for the intended uses of the reference. (02)
Second, the measurement unit has nothing to do with the measurement
apparatus. All but one of the SI reference units are defined in terms
of an invariant physical phenomenon that can be measured in any
laboratory with appropriate equipment. Moreover, the "best known
procedures" (in terms of "smallest uncertainty") and the corresponding
equipment have changed several times over the last 40 years, but those
changes don't change the units. Changes in the apparatus produce changes
(hopefully improvements) in the "uncertainty" of the measurement of the
phenomenon. (03)
Third, when the number part of the quantity value does not express a
ratio of magnitudes (a "(multiplicative) product"), the concept
expressed by the quantity value does not have the meaning stated in the
VIM. The two things that cause the most confusion are time and
temperature. (Elapsed) time is measured in ratio to the second;
time-of-day is an entirely different concept, controlled by a different
set of standards and references -- it is not a 'quantity' in the VIM
sense. The quantity in a Celsius temperature measurement is a ratio of
differences, plus an offset.
>> For example, in SI, the unit "kilogram" is a reference to the
>> physical artifact
>> stored by BIPM in Sevres, France.
Correct. This is the only SI unit for which there is still a reference
artifact. And that is true only because we can still measure the mass
of that artifact with less uncertainty than we can count a usefully
massive collection of molecules/atoms/particles. (NIST and its
international sisters have been trying for over 40 years.)
>> The measurement instrument, in
>> this case a
>> weighing scale, is calibrated in terms of the reference. The
>> kilogram standard
>> is the essential part of the measurement apparatus. The numbers that
>> the
>> weighing scale gives for masses are the "numbers" referred to in the
>> definition
>> of "quantity".
>>
>>
The U.S. reference kilogram was made from the International Reference
kilogram by polishing a slightly overweight copy of the artifact and
comparing the magnitude on a very precise analytical balance. There was
no 'scale' of the kind described here involved. The reference kilogram,
however, is used to "calibrate" other mass measurement devices, i.e.
determine the exact behavior of the device that corresponds to "1 kg"
under certain well-defined environment conditions. Those are 'scales'
of the kind Joe describes.
>> n.b. - if you change any essential part of a measurement apparatus,
>> like the
>> unit, you change the numerical value.
>>
>>
more of the same confusion. If you change the unit, you change the
number, yes. If you change the apparatus, you have to recalibrate:
relate its (modified) physical behaviors to the intended measurements
and estimate the uncertainties in its measurements (the degree of
unpredictability v. repeatability in its behaviors).
>> When the quantities are expressible in terms of units, you generally
>> can
>> multiply and divide the quantities, and commonly add or subtract
>> them. In the
>> case of VIM example 7, Rockwell C hardness, forget about that.
>> Hardness values
>> can only be ordered - products, ratios, sums, and differences are
>> not valid.
>>
>>
The Hardness scale is an ordering of magnitudes, consisting of a set of
reference measurement units. The number part of the quantity value does
not have a meaning as a number, other than to identify relative position. (04)
IMO, "hardness" is a kind of quantity, but it won't bother me if our
'units of measure ontology' does not support the Rockwell scale. I
would prefer a cleaner ontology that properly supports numeric measures
and uncertainty over bizarre concepts with useless axioms that are
designed to support both SI and the Rockwell scale.
>> I believe that the VIM definition for "quantity" is most appropriate
>> to your
>> "particular quantity".
>>
Correct.
>> The notion of "generic quantity" includes what SI/VIM calls "derived
>> quantity",
>> "base quantity" and "quantity dimension", but a "generic quantity"
>> never has a
>> numerical value.
>>
>>
This is VIM 'kind of quantity'. 'base quantity' and 'derived quantity'
(e.g., 'length' and 'velocity') are subtypes of 'kind of quantity'.
>> Perhaps a more succinct way of saying it is that a "generic
>> quantity" is the
>> *name* of a property
>>
>
> No, don't say that. Names are lexical entities, not things like
> quantities.
>
>
I agree with Pat on this. (05)
'generic quantity' is a _subtype_ of 'particular quantity' -- its
instances are mutually comparable. Every _instance_ of VIM 'kind of
quantity' is a _subtype_ of '(particular) quantity'. That is what makes
the model hard to grok. (06)
(UML "powerset" is the same general idea, but it is defined as the
converse: every modeled subtype of X is an instance of the "powerset" of
X. And I'm not comfortable with that as the 'kind of quantity' model,
partly because the UML powerset is closed while our notion is open, but
more because I'm not sure that the converse is true.)
>> and a "specific quantity" is the *value* of the property
>> for a specific object.
>>
It is "value" as long as you don't confuse it with "quantity value". I
prefer to say it is a "magnitude", an "amount" (of the quantity kind).
Put another way, having the same 'specific quantity' of mass is what
makes the two sides of a scale/balance balance, regardless of what
number and unit you assign to that mass. It's rather like a French cake
recipe: You put in 3 eggs and an amount of flour that is twice the
weight of the eggs. How many grams that is is not a concern. (07)
-Ed (08)
--
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 (09)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (010)
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