>
> PH>Dimensional analysis? Writing general code to convert between units?
>>
>> I would say that 'meter' denotes a function from lengths to
>> numbers, and one meter is the length, such that the value of
>> that function when applied to it, >is the number 1:
>>
>>(the (x) (= (meter x) 1) )
>>
>>And by the way, (= meter metre) (01)
John Sowa wrote:
> I like that analysis -- especially because it does not introduce
> any ontological notions that are not already present in logic
> and elementary math. (02)
Dear John, what is the purpose of the definition? Is it to find a purely
logical-mathematical counterpart to what metrologists and scientists
working with scales are talking about, or is it to find a way to construct
a computer ontology of units of measure? If it is the latter, I don't
understand how this can be done only with notions that are "already
present in logic and elementary math." Mathematical natural science cannot
possibly be reduced to logic and mathematics; mathematical physics is not
mathematics, it is mathematics applied in physics. (03)
> IJ> To have the value 1 is also to have a value. On the other
>> hand, a value without a unit is just a pure mathematical
>> number. I think Graybeal's distinction should be replaced by
>> the following:
>> 0) Base units
>> 1) Values of base units.
>
> I also like that analysis. But it has to be extended to angles,
> since we have to support multiple functions that map angles to
> numbers: degree and radian. (04)
I agree, and in a sense so do also the metrologists that (as I said in an
earlier mail) I criticize. In my opinion, one should say that radian is a
unit of the derived dimension length/length, but the SI system and VIM
says that it is a dimensionless unit or a unit of dimension-one. However,
everyone agrees that angles can be measured by (or mapped on) scales whose
magnitudes are 'x degree' or 'x radian'. (05)
I think, by the way, that it is misleading to say that "angles are mapped
to numbers"; angles are mapped to magnitudes of a scale. (06)
Ingvar J (07)
>
> John Sowa
> (08)
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