Dear David, (01)
>
> We are still seeking a definition of the term "scale".
>
> In your e-mail you have used "scale" as a synonym for "kind of
> quantity",
> because both temperature and mass are kinds of quantity. (02)
MW: But there can be more than one scale for a kind of quantity, so that
would not work... (03)
>
> I have proposed that a scale be defined as a function from a kind
> of
> quantity to a "set of elements with axioms", such as the real
> numbers. To be
> a valid scale there would have to be constraints upon the nature of
> this
> function. I have no strong opinion as to whether the term scale
> should be
> applied to this function, or to its inverse, or to both. (04)
MW: I would have thought that a minimum requirement was that it was
isomorphic to the magnitudes of the kind of quantity. (05)
>
> I don't think that my proposal has consensus, but I am not clear
> about
> further proposals. (06)
MW: Another obvious question is the relationship between a scale and a
unit of measure. They are not the same thing, but just how are they
related? (07)
Regards (08)
Matthew West
Information Junction
Tel: +44 560 302 3685
Mobile: +44 750 3385279
matthew.west@xxxxxxxxxxxxxxxxxxxxxxxxx
http://www.informationjunction.co.uk/
http://www.matthew-west.org.uk/ (09)
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>
> Best regards,
> David
>
> At 09:37 14/08/2009 -0400, you wrote:
> >Dear Matthew and David,
> >
> >DL> Hence we have two different instances of kind of quantity, for
> > > which the same unit is used. Pressure is a quantity for which
> zero
> > > is well defined, and there is no problem in regarding the bar,
> psi
> > > or Pa as firstly a magnitude of absolute pressure. If it is
> assumed
> > > that there is an addition operator for the kind of quantity
> absolute
> > > pressure, then the same unit can be used for the kind of
> quantity
> > > gauge pressure. This assumption is usually unstated but I
> believe
> > > that it is necessary for the use of the same unit for both
> kinds
> > > of quantity.
> >
> >If you have a scale with an absolute zero, such as temperature
> >or mass, you can still talk about intervals, such as adding
> >an extra 10 degrees of temperature or 10 grams of mass.
> >
> >But for interval measures, such as time and space, there is
> >no absolute zero, and only intervals are meaningful. The
> >choice of "zero" is an arbitrary convenience.
> >
> >John
> >
> >
> >
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> >
>
> ============================================================
> David Leal
> CAESAR Systems Limited
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