Indiscrete variables, spectrum values and topic map occurences

Patrick Durusau posed the following issue on the Topic Maps mailing list:

The more interesting case arises with location information,
such as Right Ascension/Declination in astronomy, longitude and
latitude in GIS systems (and targeting systems), where finding all the
occurrences that share a point on a particular axis could well be important.

Note that I don’t think making coordinates topics would solve the
problem as given the fine grained nature of coordinate systems there
would be a proliferation of topics for any relatively sophisticated
system of coordinates. Not to mention that coordinates are commonly
thought to be characteristics of objects/locations and not subjects in
their own right.

Is there some conceptual reason for this treatment of occurrences in
the data model?

This is my take:

On the contrary, I think there is a compelling argument that such treatment should be explicitly excluded: they are indiscrete (or analogue) variables and can never be defined with a discrete value: in taxonomy work, it the phenomenon of spectrum values: as you say, it depends on the granularity to which you are prepared to take a particular classification.

There is also a principle of economy to be considered: in a vary random or unevenly distributed set of values, the “discrimination” offered may vary wildly: whereas for one part of the spectrum, values of 21,22, 23 might be enough to discriminate between different occurrences; at another part you might need values as fine as 1.113, 1.114, 1.115, etc.

You can never know in advance how to model indiscrete values in a discrete manner…and it indeed makes assertions about equivalence well nigh impossible; do two people with ages of “23”, “23 years and 1 day”, and “22 years 11months and 27 days” all have the same age?

Would/Could it be useful to know whether the concept – however formulated – of scope helps here: can we state that we are interested in “documents with version numbers between 1 and 3”; or “items in the night sky between RA/DEC coordinates xy and x’y’ ” ? It seems that all the debate about facets/scope has looked (correctly) at the issue of an “axis” of interest, but not this problem of discrete and indiscrete values/ranges.

All the best…
Peter

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