Dear Ingvar, (01)
Assume you have a beam. (02)
The beam has a length, l, a volume, V, a surface area, A, and a second moment
of
area, I. (03)
The properties l, V/A, and sqrt(sqrt(I)) all have quantity dimension of length.
Are they all of the same kind? (04)
How do you know? By what process does one decide? (05)
R/jbc (06)
ingvar_johansson wrote:
> Dear all,
>
> Here are some answers and comments to some parts of some of yesterday’s
> mails (taken in temporal order)
> ---
> Gunther S: ”Nowhere in my practical experience of working with units in
> the sciences do I ever see a qualification of units.”
>
> IJ-answer: I firmly believe you, but I think this absence of
> qualifications is due to the fact that in each practical case the context
> automatically creates a qualification as background knowledge. But general
> metrology can have no such pre-given context qualifications.
> ---
>
> Joe C: “I would not agree that "many units are unambiguously tied only to
> one kind-of-quantity".”
>
> IJ-answer: Depends on what we mean by ‘many’. Surely, all the six base
> property quantities of the SI are (but not ‘amount of substance’).
> ---
>
> Matthew W: “Could you give me a unit (or two) that you think only applies
> to one kind-of-quantity, and I'll see if I can identify another?
>
> IJ-answer: m (length), kg (mass), and t (duration).
> ---
>
> 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.
> ---
>
> Best,
> Ingvar
>
>
>
>
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> (07)
--
_______________________________
Joseph B. Collins, Ph.D.
Code 5583, Adv. Info. Tech.
Naval Research Laboratory
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