RE: SUO: RE: A proposed SUO content outline
Pat,
Pat Hayes wrote
>
>John Velman wrote:
>>I've snipped most of the following, and left only the snippet I want to
>>comment on
>>just now.
>>
>>It seems to me that it is fundamental that things don't have locations.
>>They only
>>have locations _relative_ to other things.
>
>Why do you think so? This idea doesn't conform to normal geographical
I guess this highlights two different senses of "where" (a "where" function
was proposed in the part of previous message that I edited out.) Or
perhaps to my use of the word "location" (the context that I didn't snip
out refered to a function from things to their locations).
Why do I think so? Because of many years of starting an analysis with
words to the effect: "Assume a coordinate frame with origin at the center
of the earth, X axis oriented positively toward the vernal equinox..", or
"Coordinates are given relative to the Clarke Ellipsoid of 1866 ". In
other words, specifying the locations of things relative to some agreed
upon identifiable stamdard (although only specified with the precision
necessary for the purpose).
On the other hand, your reference to geographical intuition is a clue to
another sense, I guess. "Where is Taksim Square?" "In Istanbul." I'm
not so sure, however, that it is possible to specify where something is
_except_ in terms of its spacial relationship to something else, either
explicitly or implicitly. ("Where is Istanbul? On the Bosphorus. Where
is the Bosphorus? Between the Black Sea and the Sea of Maramara, a long
ways from California.") Perhaps my geographic intuition has been spoiled
over the years. Or perhaps I'm still missing your point.
>intuition, it isn't supported by Newtonian physics and it isn't even
>strictly true in General Relativity. I believe the only person who
>seriously believed this was Ernst Mach.
This is also a puzzle. As far as I recall, Mach claimed that inertial
properties of matter were due to the distribution of mass in the universe
(roughly speaking). Inertial properties have to do with accelerations, not
with absolute locations. Both the mass distribution in the universe, and
accelerations of individual bodies are properties concerning relative
locations. Of course Newton thought space was absolute in the sense of
inertial properties of matter. But I don't think his spinning bucket
experiment has anything to do with locations per se. If you have a
reference otherwise, I'd be most grateful.
As I recall, general relativity implies frame dragging, and some other
things that go a little way toward Mach's principle, but not all the way.
I also recall that Einstein relied extensively on simultaneity (as John
Sowa's http://www.bestweb.net/~sowa/ontology/causal.htm reminded us).
This clearly depends on a relationship between two events in space-time.
Perhaps I'm looking at things in a totally different way than you
are, but I can't see how one can talk about the location of one thing
without at least implicitly referring it to another thing (or event, in 4
D).
>
>> (This harks back to John
>>Sowa's list
>>of coordinate systems or coordinate free alternatives of a day or so
>back.)
>>
>>There is a function underlying _where_ that is a binary function, for
>>example,
>> separation(x,y).
>>
>>(Sorry, I can read some KIF but can't write it yet.).
>>
>>Then there would be functions from whatever is in the range of
>_separation_
>> to the real numbers, so we would have, for example,
>> miles(separation(me,home))= 15.
>>
>>It isn't too far from here to being able to define coordinate frames.
>>I'll try
>>to put some rigor behind this as an exercise for myself.
>
>You might check out recent work by the Leeds group at
>http://www.comp.leeds.ac.uk/spacenet/publications.html#2000
>
I'm most grateful for this reference.
Lots to read!
> especially
>
> Bennett, B, Cohn, AG, Torrini, P and Hazarika, SM, A Foundation for
>Region-Based Qualitative Geometry, Proceedings of 14th European
>Conference on Artificial Intelligence (ECAI-2000), pp 204-208. Aug 20
>- Aug 25, 2000, Berlin, Germany.
>
>Pat Hayes
Best,
John Velman