After this mail I will take a time out from this discussion. (01)
Ed B wrote: (02)
> I have yet to see a definition of "interval scale" from either David or
> Ingvar. (03)
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. (04)
> So "interval scales" are not 'quantity value scales' (as
> defined by the VIM clause that Ingvar used to correct my earlier email)? (05)
I regard them as quantity-value scales. (06)
(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. This has to do with
the distinction between extensive and intensive magnitudes. Time is an
extensive magnitude, but temperature is an intensive. (07)
all the very best,
Ingvar (08)
> The measurement unit that is 'degree Celsius' and the measurement unit
> that is 'degree Kelvin' are the same magnitude. Temperature difference
> can be measured in either with the same "ratio scale". Absolute
> temperature is a different concept, and it is all about how we define
> the scale origin "0" with respect to points on the (putative) 'absolute
> temperature axis'. And we are apparently saying that "amounts of
> temperature difference" and "points on the absolute temperature axis"
> are both "magnitudes" of the quantity kind "temperature". But they are
> different things. Are "interval scales" scales that measure
> "magnitudes" on the "absolute <quantity> axis"?
>
> This concept seems to apply to time as well. The second is defined as a
> measure of difference in time (duration, elapsed time). But
> International Atomic Time (TAI) identifies points on the "absolute time
> axis" by their difference from a chosen 0 point. Are TAI times also
> "magnitudes"? The absolute zero of time is presumably the Big Bang, but
> with respect to absolute time, our current measurement technology is
> more like 19th century temperature measurement. So our absolute time
> scale is based on an arbitrary reference point, like Celsius choice of
> the freezing temperature of water.
>
> It is easy to think of "length" as being the difference between points
> in a 1-D space, and thus being parallel to 'temperature difference' and
> 'time difference'. But there is no 'absolute length axis' whose points
> have any meaning. And it is not clear to me that mass and substance and
> light intensity are differences at all.
>
> We agree that there is a difference between "interval scales" and "ratio
> scales", and it can be represented mathematically by m = unit * number +
> offset. But what is the definition? And how do we deal with different
> kinds of magnitudes of the same quantity kind? Those are the ontology
> questions.
>
> -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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> (09)
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