David Leal wrote:
> Dear All,
>
> I fear that reaching an understanding of what mass is, is going to be
>difficult.
> (01)
I want to leave the "understanding of what mass is" to the SI people.
For our purposes, mass is a kind of quantity that is one of the "base
quantities" of the SI system. Whatever the SI definition is, we replicate. (02)
> There seems to be agreement that there is an object denoted "1.3 kg". In
> Ed's synthesis, this is:
> - an equivalence class of members of Q1 ("particular quantity");
> - a member of Q3 ("magnitude of quantity").
>
> 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.
> (03)
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. (04)
> To me approach (b) seems simpler. Using this approach, "1.3 kg" is merely a
> class of individual quantities of matter which is defined by a single
> necessary and sufficient condition - equilibrium with the 1 kg in Paris
> using a 1:1.3 ratio balance (or some practical equivalent).
> (05)
The problem with this is twofold:
- There are no "individual quantities of matter". There are individual
material things/phenomena that have a "mass" property.
- The "practical equivalent" is exactly where the measurement concept
and notions of uncertainty and tolerance come in.
So David' description of 'approach (b)' crosses exactly the two notions
I distinguish above. (06)
I am coming to the conclusion that "1.3 kg" is an equivalence class of
measurements that is defined in part by some specification of the
tolerable variance in those measurements. Put another way, the ratio of
the measurements to the reference kilogram in Paris is 1.3 to the
accuracy that we decided to express them (which includes both the
uncertainty in the measurement and the practical tolerance). Scientific
measures have no notion of tolerance, but they express uncertainty;
business measures tend to assume that the uncertainty is very small
relative to the tolerance. In both cases, the "1.3 kg" is a 'nominal
value' that denotes a classification of the measurements. (07)
I must say that I also find this model cumbersome and scary (because I
lack the intuition to formulate the axioms). So, like the Cowardly
Lion, "there's just one thing I want you to do -- talk me out of it." :-) (08)
> Similarly for length
> --------------------
> There is a similar discussion for length (and maybe for all quantities). Two
> ideas of what the members of "1.3 m" are, include:
> a) the members are length tropes of different individual physical objects;
>
yes. (09)
> b) the members are point pairs.
> (010)
This is some formal geometric characterization, and I don't want to mix
'quantities' with geometry, just because 'length' and 'angle' are
quantity kinds. But in fact, this may just mask a 'measurement' concept. (011)
> With approach (a), the length of my_table is a member of "1.3 m". With
> approach (b), my_point_pair is a member of "1.3 m". There may be a separate
> statement that the points in my_point_pair are at opposite ends of my_table.
> (012)
What makes you think your table has "points"? It has "length", which is
how much space it occupies in one dimension. In one view, you get
"points" when you make a geometric model of the table (which is not the
table). In another view, you get the "points" when you introduce the
measuring device and locate it in space relative to the table, which
gives rise to "points of coincidence" -- places where the two bodies touch. (013)
Either way, it is not clear how this kind of conceptualization would
generalize to a model for quantities that aren't spatial in nature. In
fact, we do the reverse -- we introduce scales, which have an
intellectual model that is spatial displacement, and use them as the
model for organizing measurements. (014)
> A question for the ontology experts
> -----------------------------------
> Can we agree a definition of the object Q3 ("magnitude of quantity"), whilst
> at the same time having different understandings of Q1 ("particular
>quantity")?
> (015)
Do we have different understandings of 'particular quantity'? It seems
to me that the problem is what Q3 is.
Surely "1.3 kg" is an "expression of" (a name for) an instance of Q3.
But we apparently don't agree on what the Q3 is. And this is the crux
of the ontology, because a 'measurement unit' is either a 'particular
quantity' (which I doubt) or a Q3. (016)
-Ed (017)
--
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 (018)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (019)
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