Ingvar, (01)
you wrote:
> I will not try to put forward a definition that fits an UoM ontology. Why?
> First, since I don't know what kind of definitions are required; second,
> since I will not take part in such a project. I have just tried to make
> this forum aware an already existing notion of 'interval scale', and
> explain it as good as I can. Why? Because I thought it was relevant to
> your enterprise. Here come my last comments on interval scales.
>
>
All the issues you raise around the term "interval scale" are certainly
relevant. Time and temperature are known to be problematic. What I was
hoping for was that you had a clear razor. The problem for both of us
is that we don't know how to write the definition.
> (Comment to what follows after my mail.) Time durations have an absolute
> zero, since if you make a time interval smaller and smaller you approach a
> zero duration. But if you take a temperature interval and make it smaller
> and smaller you do not approach a zero temperature.
Ah. But a time duration is a difference between points in time. The
limit of a decreasing sequence of time intervals, measured in seconds,
is 0 duration, which means that there is no difference in time between
the beginning and end of the interval. In a similar way, if I have a
decreasing sequence of temperature intervals, measured in Celsius
degrees, the limit is 0 temperature difference, which means that the
temperatures at the beginning and end of the interval are the same. The
problem is that we ALSO measure 'absolute temperature' in Celsius
degrees, and that is not the same thing as temperature difference. Now
we are talking about intervals of which the first point is the origin,
and the meaning of 0 is "no difference from the origin", the absolute
temperature that is 0 Celsius. In the same way, the 0 value of the
"interval time scale" TAI means "no difference from the origin" (which I
think is midnight on 20 May 1876 at the Greenwich Meridian). These
scales have the same "quantity values" as expressions, but they have
different meanings -- one expresses difference in temperature from an
arbitrary starting point, and the other expresses difference in
temperature from a fixed starting point. (02)
At that rate, the definition of "interval scale" is "ratio scale that
expresses magnitudes of difference in quantity from a fixed reference
point". And that matches exactly the mathematical formulation q =
number*unit + reference, as the "interpretation" of the "quantity value"
on the interval scale. (And I think this is the model that Mark Linehan
finally adopted for the OMG date/time vocabulary project.) One could
also say that an "interval scale" is derived from a "ratio scale" by
fixing (defining) the origin of all measurements. For the measuring
tape example, this would be the equivalent of gluing the zero end of the
measuring tape to a specific immovable object in 3-D space -- the scale
can now only measure distance from that object.
> This has to do with
> the distinction between extensive and intensive magnitudes. Time is an
> extensive magnitude, but temperature is an intensive.
>
I simply don't understand this. But I think you are comparing "time" as
"duration" (time difference) with "temperature" as "absolute
temperature". And yes, those are different. But "time difference" and
"temperature difference" are both "intensive?" (many intervals can have
that measure), while "time" and "temperature" on the bank sign are both
"extensive?" (refers to a particular interval). (03)
Enjoy your holiday! (04)
Best regards,
-Ed (05)
--
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 (06)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (07)
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