Dear All, (01)
The "Moving Forward on the UoM Standard" events are timely because there
seems to be a consensus around "Ed's synthesys" - i.e. the interpretation of
the terms "quantity" and "kind of quantity" as Q1, Q2, Q3, Q4 (which are
summarised at the bottom of Ed's e-mail of Fri, 14 Aug 2009 15:45:38-0400,
and documented on the Wiki). (02)
We do not yet have a similar consensus on "scale". An exchange of e-mails,
largely involving Ed, Ingvar and me, reached a fuzzy concensus that it is
mapping in some direction between a "kind of quantity" and something
(perhaps a set of numbers or quantity values). To go further we need to discuss:
1) which type of "kind of quantity" - Q2 kind of quantity (as class of
particular quantity) or Q4 kind of quantity (as class of magnitude);
2) which direction;
3) whether a "kind of quantity" is mapped to a set of numbers or set of
quantity values, where a quantity value is a (number, reference) pair. (03)
My suggestions are as follows: (04)
1) A scale mapping should involve Q4 rather than Q2. This is because a
mapping involving Q2 maps particular quantities whereas a mapping involving
Q4 maps their equivalence classes. A mapping for Q2 can be easily derived
from a mapping for Q4. (05)
2) If we define a mapping from set A to set B as the triple (A, B, {some
(a,b), where a in A and b in B}), then a mapping completely defines its
inverse. However, many properties of a mapping cannot be derived from the
properties of its inverse. "Scale" can be defined as a mapping in one
direction, and "inverse scale" as a mapping in the other. I have no
respectable reason for prefering one direction over the other. (06)
I have a sordid reason for prefering a scale to be defined with the kind of
quantity as its domain - it gives a neat representation in RDF. Hence an
anonymous node that is the boiling point of water is in N3 [:celsius "100"] . (07)
3) Mappings with sets of quantity values and with sets of numbers both
exist. Hence we can define a mapping celsius-qv, such that: (08)
celsius-qv(my temperature) = (234, celsius) or celsius-qv((234,
celsius)) = my temperature (according to choice of direction - see (2) above) (09)
and a mapping celsius-n, such that: (010)
celsius-n(my temperature) = 234 or celsius-n(234) = my temperature
(according to choice of direction - see (2) above) (011)
I suggest that we should give both mappings names and call one "quantity
value scale" and the other "numeric scale". One can be derived from the other. (012)
Best regards,
David (013)
============================================================
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
============================================================ (014)
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