Joe Collins wrote:
> Dear Ingvar,
>
> Assume you have a beam.
>
> The beam has a length, l, a volume, V, a surface area, A, and a second moment
>of
> area, I.
>
> The properties l, V/A, and sqrt(sqrt(I)) all have quantity dimension of
>length.
> Are they all of the same kind?
>
> How do you know? By what process does one decide? (01)
This is exactly my point. Thanks Joe for giving such rich set of
fresh examples. (02)
And this is the heart of the answers to the other related issues
here: (03)
>> Gunther S (to Pat H): “so we agree that 1 N.m = 1 N.m when we talk about
>> units and there is no such thing as "N.m moment of force" as a unit?
>> There is of course the Quantity moment of force 1 N.m, but the unit is
>> still N.m without knowing anything about torque vs. energy.”
>>
>> IJ-comment: Every real unit presupposes a scale for a kind-of-quantity; a
>> unit with no reference at all to a scale or quantity is meaningless. What
>> I have proposed to call a ‘nominal unit’, is a unit that necessarily
>> refers to other units, i.e., to real units with scales for
>> kinds-of-quantities.
>> ---
>>
>> Gunther S: “The VIM speaks about Quantities and measurement and a little
>> bit about Units. The SI speaks a lot about Units. I don't think that
>> either one argues that Units contain the detail of the Quantities.”
>>
>> IJ-comment: I think you are wrong. VIM’s definition 1.9 says: measurement
>> unit = real scalar quantity, defined and adopted by convention, with which
>> any OTHER QUANTITY OF THE SAME KIND CAN BE COMPARED. Definition 1.10 says:
>> base unit = measurement unit that is adopted by convention FOR A BASE
>> QUANTITY. The SI brochure says (p. 103): The terms quantity and unit are
>> defined in VIM. That is (at least in my interpretation), both VIM and the
>> SI are stating the view that ‘Units presuppose the detail of the
>> Quantities’. Or in my words, once again: every real unit presupposes a
>> scale for a kind-of-quantity. (04)
I am not doubting that in a system of quantities and units, every
base unit is tied to one base kind of quantity. And in that respect,
all of Joe C's examples are of kind of quantity "length". But it
is length at a very high level of abstraction where kind of quantity
is 1:1 related to dimension. They are all in dimension L, and their
base kind of quantity is "length" but we would be hard pressed to
be happy calling the quantity "surface areic volume" (V/A) a "length". (05)
This is where IMO the VIM and SI have not completely succeeded to
formally lay out the problem space. We use "quantity" and "kind
of quantity" is if we understood what it means, but they didn't
really define those very well. (06)
I believe that "kind of quantity" for VIM and SI is often this very
high-level kind where everything measured in 1 m is a "length".
They use the term "quantity" to mean the more specific quantitative
property universal, but still "quantity" is used as universal. Notably
the VIM isn't very good in applying "universal" and "particular"
systematically and so "quantity" is still ambiguous and therefore
"kind of quantity" is ambiguous too. (07)
regards,
-Gunther (08)
--
Gunther Schadow, M.D., Ph.D. gschadow@xxxxxxxxxxxxxxx
Associate Professor Indiana University School of Informatics
Regenstrief Institute, Inc. Indiana University School of Medicine
tel:1(317)423-5521 http://aurora.regenstrief.org (09)
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