David Leal wrote:
>>> There are at least two ideas of what the members of "1.3 kg" are,
>>> including:
>>> a) the members are mass tropes of different individual quantities
>>> of matter;
>>> b) the members are different individual quantities of matter. (01)
I wrote:
>> I don't know what David's (b) means. I would have said the members
>> of the equivalence class designated "1.3kg" are either:
>> a) 'mass tropes' of different individual things, or
>> b) measurements of the 'mass tropes' of individual things.
>> (02)
Matthew West wrote:
> MW: I would say neither of these, but the individual things themselves.
> The measurements are of these.
>
> E.g. My lump of cheese is a member of the 1.3Kg equivalence class.
> (03)
This may be true of 'mass', but it doesn't generalize. The person Ed
Barkmeyer is not a member of the 180cm equivalence class. The height of
EdBarkmeyer is a member of the 180cm class. But the waist size of
EdBarkmeyer is a member of a different class (predictions of one of my
former students notwithstanding). In a similar way, the existence of a
thing may be a member of one duration class, while some other property
is a member of a different duration class. (04)
> MW: <snip> I think it is important to
> distinguish two concepts:
>
> 1. The mass something has,
> 2. A measurement of the mass something has.
> (05)
I think this is exactly the same pair as David's (a) and (b) above, with
the substitution of "something" for
"individual quantity of matter", and my (a) and (b) above is the same,
with a slightly different substitution. It seems to me that we are all
in violent agreement, except that we can't agree on the spelling of
"some thing". (06)
> We should not be choosing to be interested in one or the other, but
> both.
> (07)
This is in fact exactly the point. The VIM says we cannot know the
first; we can only know the second. But, as Pat points out, this
doesn't mean that the first doesn't exist and cannot be idealized.
Whatever we do in this regard must be consistent. The way in which we
intend to use the "equivalence class" notion to define magnitudes
supposes ideal and exact quantities, independent of measurements. (08)
OTOH, the typical business and scientific usage is about measurements
with respect to a scale that has a "granularity" -- it makes discrete
distinctions and assigns "quantity value" names only to the discrete
intervals, which are "equivalence classes" of a somewhat different
kind. Matt's lump of cheese has a mass of 1.3kg on a scale in which the
next choice is 1.35kg or 1.4kg and finer distinctions are meaningless.
The reason they are meaningless is all about measurement, uncertainty
and tolerance. It is not useful to state that the mass of the cheese is
exactly 1.31415926536 kg, because the scale isn't nearly that good and
it won't change the price. (09)
So I agree we need to think about both, but we need to see the use cases
and requirements to decide how much of this to axiomatize. (010)
-Ed (011)
--
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 (012)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (013)
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