Dear Pat, (01)
I agree except for one thing - a scale is not a set of items/symbols in
itself, but a mapping from a set of "magnitudes of quantity" to a set of
items/symbols. Hence re-expressing the consensus in these terms we have: (02)
scale: a mapping f from Q (set of magnitudes of quantity) to S (set of
symbols - commonly numbers), such that: (03)
f(q1) = f(q2) if and only if q1 = q2 (04)
ordinal scale: a scale where both Q and S are ordered, such that: (05)
f(q1) > f(q2) if and only if q1 > q2 (06)
ratio scale: a scale where ratios can be defined for both Q and S, such that: (07)
r.f(q1) = f(q2) if and only if r.q1 = q2 (08)
Best regards,
David (09)
At 11:20 11/08/2009 -0500, you wrote:
>
>On Aug 11, 2009, at 5:51 AM, ingvar_johansson wrote:
>
>> John Sowa wrote,
>>
>>> It is true that the latest and greatest science and technology was
>>> necessary to define the units of measure to the current degree of
>>> precision. However, we must remember that the same words were
>>> used for those units in the 19th century. The values used then
>>> differ from the current values by much less than 1%.
>>
>>> The UoM ontology should be little more than a compendium of the
>>> values of the units and the relations among them. The details
>>> of how they were derived is not necessary for using them.
>>
>> Not contesting what John here says, I would like to add that I think
>> that
>> it is good for UoM ontology constructors to be aware of the
>> following four
>> facts:
>>
>> 1. Ratio scales, interval scales, and ordinal scales require different
>> formalisms.
>
>Surely not. We plan to produce an ontology all written in one formalism.
>
>Let me test my understanding of these terms.
>A scale is a set of items used to represent measurements.
>An ordinal scale is a scale with a total order on its elements.
>An interval scale is a scale with a difference function from pairs of
>scale items to ... (what? Real numbers? Some other scale? Could there
>be an interval scale in which differences were restricted to natural
>numbers, for example?).
>A ratio scale is a scale which has a zero element and a multiplication
>operation by rational numbers.
>
>(My source for this is
http://www.stat.sfu.ca/~cschwarz/Stat-301/Handouts/node5.html
>, by the way, found through google)
>
>>
>> 2. Out of every ratio scale an interval scale can be constructed,
>> and out
>> of every interval scale an ordinal scale can be constructed, but not
>> conversely.
>>
>> 3. In the late nineteenth century, physics was able to replace the
>> existing interval scales for temperature with a ratio scale for
>> temperature (the Kelvin scale).
>>
>> 4. There is no axiom or theorem to the effect that science can turn
>> all
>> ordinal scales into interval scales, and all interval scales into
>> ratio
>> scales.
>
>Right, all those make perfect sense.
>
>Pat
>
>
>
>>
>> Ingvar J
>>
>>
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