Ed Barkmeyer wrote:
> 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". (01)
I agree with this except for the possible implication that "the VIM is
primarily
about making measurements of quantities" is an unnecessarily narrow perspective.
The length of an object only has (physical) meaning when arrived at via a
measurement process. (02)
++++snip++++ (03)
>>> "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.
> First, quantity value is defined to be a number and a reference to a
> measurement _unit_. (04)
Not only that: (05)
"A reference can be a measurement unit, a measurement procedure, a reference
material, or a combination of such." (ISO/DIS 80000-1) (06)
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.
>
> Second, the measurement unit has nothing to do with the measurement
> apparatus. (07)
In the case of the kilogram, the standard, which defines the unit, is an
essential part of the apparatus. You cannot weigh something without it (or one
of its "replicas"). (08)
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. (09)
It is true that names of the units have not changed, but their definitions have.
The only reason this does not present problems is because the newer definitions
support greater precision and are made to be backwardly compatible with old
standards.
I do not think of the kilogram artifact as somehow a "less valid" standard,
though I agree it is certainly less convenient to distribute and does not
provide opportunity for improvement in precision. (010)
>
> 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.) (011)
I don't think the kilogram is "theoretically inferior" to other unit standards.
It is inferior with respect to convenience.
Take the second.
"The second is the duration of 9 192 631 770 periods of the radiation
corresponding to the transition between the two hyperfine levels of
the ground state of the cesium 133 atom." (012)
To measure time you need some cesium 133. Physical theory holds that all cesium
133 atoms are sufficiently similar that any subset may be used. The principal
difference between using an arbitrary collection of cesium 133 atoms to define
a
standard quantity of time and using the kilogram artifact in defining a
standard
quantity of mass is that the kilogram is hard to distribute reliably. Yes, the
kilogram gets "dirty", limiting precision, but the cesium can never be cool
enough. (013)
>>> 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. (014)
Very precise, yes, but is not an analytical balance still a weighing scale?
While not of identical design, many labs use scales that are design variations
of the beam balance with mass standard. (015)
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. (016)
If the reference kilogram is used to calibrate a mass measurement device, is it
not then an essential part of the measurement apparatus? I do not think it
needs
to be permanently attached to be an essential part of the apparatus. (017)
>>> 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. (018)
Sorry. I was equating the reference standard to the unit - a bit of conflation. (019)
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.
> 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. (020)
I agree that supporting SI is most important. (021)
>>> 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. (022)
(out of time for today) (023)
Joe C.
--
_______________________________
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
_______________________________ (024)
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