On Sep 24, 2009, at 6:02 PM, Ed Barkmeyer wrote: (01)
> 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.
>
> 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.
>>>
>
> 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.
>>
>
> This may be true of 'mass', but it doesn't generalize. The person Ed
> Barkmeyer is not a member of the 180cm equivalence class. (02)
Thats because 180 cm isn't a meaningful quantity applied to you,
without further specification. It would like saying that you don't
have a voltage, which is true but not very interesting. But as soon as
you specify a meaningful length class (height, waist size) then the
analogy with mass works just fine. And you are a member of an
equivalence class of volumes, for example. (03)
> 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.
>
>> MW: <snip> I think it is important to
>> distinguish two concepts:
>>
>> 1. The mass something has,
>> 2. A measurement of the mass something has.
>>
>
> 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".
>
>> We should not be choosing to be interested in one or the other, but
>> both.
>>
>
> 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.
>
> 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. (04)
Actually its worse, they aren't equivalence classes (because being
within tolerance isn't transitive) hence things like the barber
paradox. This whole topic of tolerances and error ranges and degrees
of granularity is a tar-pit of conceptual problems. AFAIK, *nobody*
has given a satisfactory general account of this whole area. I suggest
that we don't even try, but just describe some clear cases that are
widely useful and thoroughly analyzed, such as engineering tolerance
intervals and the idea of 'to n places of decimals'. But lets not for
example try to axiomatize the idea of acuity, or an account of a
vernier scale. (05)
BTW, I was recently helping a professional framer, and noticed that he
specifies measurements to the nearest sixteenth of an inch, but
sometimes qualifies them with 'fat' or 'thin'. The interest being that
these increments are below the granularity of the scale, but still
meaningful. (06)
> 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. (07)
Right. (08)
> 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)
Right. But still, it makes sense to say that there exists a real
number which is the *actual* mass of the cheese in kilograms. It might
even be a genuinely irrational number with no finite specification. (010)
Pat (011)
>
> 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.
>
> -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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