On Aug 11, 2009, at 12:44 PM, David Leal wrote: (01)
> Dear Pat,
>
> 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. (02)
Well then let us use a different name for that set of items/symbols,
which is the thing I am wanting to describe for the moment, although I
would rather not specify its metaphysical nature. What name would you
suggest? (Scale value?) I will go on using 'scale' until this group
comes to a different consensus. (03)
> Hence re-expressing the consensus in these terms we have:
>
> scale: a mapping f from Q (set of magnitudes of quantity) to S (set of
> symbols - commonly numbers), such that:
>
> f(q1) = f(q2) if and only if q1 = q2 (04)
Iff is surely too strong. And if true, this makes the two sets S and Q
exactly equivalent, so why are we talking about two of them? (05)
>
> ordinal scale: a scale where both Q and S are ordered, such that:
>
> f(q1) > f(q2) if and only if q1 > q2 (06)
Whoa. if S is a set of symbols, there is no natural order, so what is
the ordering being used? And we would need to use two different order
relationships for S and for Q. (Can we extend the scale mapping to the
orders themselves, and write f(q1) f(<) f(Q2) ? (07)
>
> ratio scale: a scale where ratios can be defined for both Q and S,
> such that:
>
> r.f(q1) = f(q2) if and only if r.q1 = q2 (08)
What is r here? Any real number? What does it mean to multiply a
number and a symbol? And do we really want to say that multiplication
can be done directly to a magnitude? (09)
In this formulation, the (sets of) magnitudes and symbols are so
similar that it hardly seems worth distinguishing them. They would be
isomorphic, considered as mathematical categories. One could for
example swap them without changing anything. Surely this cannot be
right. (010)
Pat (011)
>
> Best regards,
> David
>
> 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
>>>
>>>
>>> _________________________________________________________________
>>> Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/
>>> Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx
>>> Config/Unsubscribe:
> http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/
>>> Shared Files: http://ontolog.cim3.net/file/work/UoM/
>>> Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard
>>>
>>>
>>
>> ------------------------------------------------------------
>> IHMC (850)434 8903 or (650)494
>> 3973
>> 40 South Alcaniz St. (850)202 4416 office
>> Pensacola (850)202 4440 fax
>> FL 32502 (850)291 0667 mobile
>> phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes
>>
>>
>>
>>
>>
>>
>> _________________________________________________________________
>> Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/
>> Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx
>> Config/Unsubscribe:
> http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/
>> Shared Files: http://ontolog.cim3.net/file/work/UoM/
>> Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard
>>
>>
>>
>
> ============================================================
> David Leal
> CAESAR Systems Limited
> registered office: 29 Somertrees Avenue, Lee, London SE12 0BS
> registered in England no. 2422371
> tel: +44 (0)20 8857 1095
> mob: +44 (0)77 0702 6926
> e-mail: david.leal@xxxxxxxxxxxxxxxxxxx
> web site: http://www.caesarsystems.co.uk
> ============================================================
>
>
>
> _________________________________________________________________
> Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/
> Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx
> Config/Unsubscribe: http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/
> Shared Files: http://ontolog.cim3.net/file/work/UoM/
> Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard
>
> (012)
------------------------------------------------------------
IHMC (850)434 8903 or (650)494 3973
40 South Alcaniz St. (850)202 4416 office
Pensacola (850)202 4440 fax
FL 32502 (850)291 0667 mobile
phayesAT-SIGNihmc.us http://www.ihmc.us/users/phayes (013)
_________________________________________________________________
Message Archives: http://ontolog.cim3.net/forum/uom-ontology-std/
Subscribe: mailto:uom-ontology-std-join@xxxxxxxxxxxxxxxx
Config/Unsubscribe: http://ontolog.cim3.net/mailman/listinfo/uom-ontology-std/
Shared Files: http://ontolog.cim3.net/file/work/UoM/
Wiki: http://ontolog.cim3.net/cgi-bin/wiki.pl?UoM_Ontology_Standard (014)
|