Dear David, (01)
> It is good that we are understanding each other - it is a necessary first
> step to reaching agreement :). (02)
Agreed. I Think so too. (03)
> Unit and magnitude/measure
> --------------------------
> A difficulty with your taxonomy is that metre and 1.3 metre are unrelated
> concepts. (04)
No, "1.3 metre" refers to "metre" in its property "unit of measure". (05)
> A member of Q3, such as 1.3 metre, is an equivalence class which contains
> ALL members of Q1 that are equal. The definition of "the metre", as a unit,
> seems to be the definition of just such an equivalence class. Hence in the
> diagram, it is assumed that "1.0 metre exactly" and "the metre" are the same
> equivalence class which is a member of Q3. This approach has the advantage
> of simplicity, therefore to reject it requires an arguement that "the
> metre", as defined by the BIPM, is not a member of Q3. (06)
I admit that I have difficulties in following this. I think this may be related
to the confusion about measure/magnitude and quantity. (07)
> I agree that "length - as class of magnitude" and Q4 are largely
> mathematical constructs. Nonetheless the set of all length magnitudes {1.0
> metre, 1.1 metre, 1.2 metre, etc. } is a useful one. The statement that
> 'each can be expressed as a real number times "the metre"' is not a trivial
> one and therefore it implies something about the object "length - as class
> of magnitude". (08)
In fact, here you are saying that a quantity can have a value, that it "can be
expressed as a real number times "the metre"", in this specific case (of the
metre). Well, what is this, this real number times a unit of measure? A
measure/magnitude. Read further below. (09)
> Property of a magnitude/measure
> -------------------------------
> It is probably not correct to say that a magnitude/measure has a "unit of
> measure" property. Any length magnitude/measure can be expressed using any
> "unit of measure", so we can equally say that 1.3 metre has a "unit of
> measure" of "the inch".
>
> A better way of looking at it is to regard the (number, reference) pair as a
> whole as the property. Hence using your notation, we have:
>
> > |_ 1.3 metre
> > - expressed as: (1.3, metre)
> > - expressed as: (51.181102, inch) (010)
Again, the (number, reference) pair you refer to *is* the measure/magnitude.
How 1.3 meter can also be expressed in different ways, for example in terms of
the inch, is not relevant here. This can be derived (which is also safer from a
maintenance point of view) from the definition of inch in terms of metre.
(*That* should be in the ontology: how a unit of measure is defined in terms of
other units of measure, or (standard) quantities, but that seems to be already
another discussion.) (011)
So let's model this (number, reference) pair, call it measure/magnitude, or Q3,
and assign the properties "numerical value" and "unit of measure": (012)
Measure/magnitude (Q3)
- numerical value: Float
- unit of measure: Unit of measure (013)
where "Measure/magnitude (Q3)", "Unit of measure" and "Float" are classes, and
"numerical value" and "unit of measure" are properties. (Where noted that in
many languages, "Float" is not a class but a datatype.) (014)
Best regards, Hajo (015)
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