John F. Sowa wrote:
> 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.
>
>
This is imprecise, and what is omitted from the above is critical. An
absolute zero _alone_ tells you nothing about "intervals". As Pat
pointed out, you have to have some notion of "increment" (Matthew's
+1). It doesn't mean anything to "add an extra 10 degrees" if "10
degrees" only means an absolute temperature. What you are assuming is
that the absolute meaning of "10 degrees" is 10 unit amounts of
temperature change from absolute zero, where the "unit amount of
temperature change" from 10 degrees to 20 degrees is the same as the
"unit amount of temperature change" from 0 to 10 degrees. There are
scales that have absolute zero but do not have that property. (01)
And I am a bit concerned about how the model applies to something like
signal strength or sound intensity, where the absolute values on the
scale are proportional to the logarithm of the power ratios. The
meaning of a "20 dB boost" is that the output power is 100 times the
input power. But the perceived difference at the receiver is, in
theory, nearly linear.
> 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.
>
That is true, and a very important point. But what David was saying is
that the increment is still meaningful when you move the reference point
to something other than the absolute 0. (02)
-Ed (03)
--
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 (04)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (05)
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