If I follow this, it can be summarized in a very simple way. The basic
idea is a measure of difference between quantities: the amount by
which one is greater than the other. If this is additive - i.e. if the
difference between A and C is the sum of the differences between A and
B and between B and C, for all A B C - then it makes sense to speak of
multiplication of differences by numbers. If there is also a zero
quantity, then we can define an 'absolute' quantity measure as the
difference between the quantity and zero. The zero is a physical zero
when it is impossible to have a quantity less than it. In this case,
the multiplication factor of the absolute quantity is physically
meaningful, as well as that of the difference. So it makes sense to
say that a temperature difference is twice as large as another, even
using the Fahrenheit scale; but it is only meaningful to say that one
temperature simpliciter is twice that of another when using the Kelvin
scale. This picture seems to apply to temperature, mass, money and
time quite uniformly. Time has no physical zero, unlike the others.
Rockwell hardness has a physical zero but it is not additive, which is
an interesting case. (Another similar example might be the Erdos
number, considered as a scale of mathematical influence.) (01)
Pat H (02)
On Aug 13, 2009, at 5:32 PM, Ed Barkmeyer wrote: (03)
> John F. Sowa wrote:
>> Ed,
>>
>> I agree with Ingvar that there is a fundamental difference between
>> time and temperature: There is a fundamental zero point for
>> temperature, but none for space or time. In that sense, temperature
>> should be compared to mass, which also has a fundamental 0.
>>
>> EB> The absolute zero of time is presumably the Big Bang...
>>
>> As far as we know, there are no physical laws that depend on
>> the time interval between now and the Big Bang. The time of
>> the Big Bang was estimated on the basis of laws that have no
>> fundamental dependence on a zero point for time.
>>
>> But there are many laws that depend on a zero point for temperature:
>> For a gas, pressure times volume is proportional to temperature,
>> as measured from absolute zero.
>>
>> Boltzmann's law states that the amount of energy radiated by an
>> object is proportional to T^4, also measured from absolute zero.
>>
>> The relevance for UoM is that 0 is fundamental for some units,
>> but arbitrary for others.
>>
>> John
>>
>>
> Thank you, John. This is a much clearer description of the issue.
> (You
> didn't use undefined and badly defined terms from a vocabulary not in
> common use.) And I agree that this is an issue for the ontology.
>
> To be very careful about the last statement, 0 is fundamental for some
> quantity kinds -- the magnitudes are always "absolute" in some sense
> --
> while it is arbitrary for others -- the magnitudes are always
> "relative"
> in some sense. I think that is what you meant. That would make
> "temperature difference" a different 'kind of quantity' from
> "temperature", even though they both use the "same?" units.
>
> And then the question is: are the units really the same? Apparently
> not. I model "measurement unit" as a subtype of "quantity magnitude"
> (Q3), so as to talk about ratios. Each measurement unit IS a specific
> magnitude. If the units of absolute measure and difference measure
> are
> the same, the measurement unit would be always relative in some sense
> and always absolute in some sense. So they can't be the same unit.
> The
> result of subtracting two absolute quantities is not an absolute
> quantity, but we use the "same" units!
>
> The model I have in my head works the other way around. The unit is
> always a relative magnitude. It acquires an absolute interpretation
> when the quantity _scale_ has a fixed 0. The quantity kinds are still
> distinct and the scales and magnitudes for absolute quantity kinds
> have
> fixed 0s, while the scales for relative quantity kinds don't. (For a
> relative quantity kind, the zero magnitude always means "no
> difference"
> in that "dimension".) That allows 45°K to mean "a temperature
> difference of 45 degrees" when the scale is for temperature difference
> and "the temperature whose difference is 45 degrees from zero
> absolute"
> when the scale is for temperature. The unit -- the Kelvin degree --
> is
> always a temperature difference (the degree is defined as a specific
> fraction of the difference between two particular temperatures), but
> the
> quantity value that uses it may have a more complex interpretation.
> And
> what I think I am saying is that there is a difference in the
> concepts:
> 'quantity value expresses relative magnitude' and 'quantity value
> expresses absolute magnitude'. In that way, the definition of the
> unit
> doesn't change, but the relation that denotes the use of the unit
> changes.
>
> I trust you understand that the above is my first draft at engineering
> the understanding I suddenly acquired by reading your email (and
> integrating it with what David did). I understand that the primary
> meaning of a temperature value is not a temperature difference, but
> ontologically I want to reverse the chicken and egg for temperature so
> that all units are eggs.
>
> Thanks,
> -Ed
>
> --
> 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
>
> "The opinions expressed above do not reflect consensus of NIST,
> and have not been reviewed by any Government authority."
>
>
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