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).
Ah, yes: but reference to a coordinate frame precisely ISNT reference
to another "thing". Is it? (If you think so, then I simply
misunderstood you, and withdraw my comment. )
>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.
I was thinking precisely of the use of coordinate frames, rather than
dead-reckoning locations from 'landmarks, as being counter to your
claim.
> >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).
Right, so location is defined by reference to *things* (with mass,
and rather a lot of them, but things for all that.) Mach believed
that there would be no inertia in an empty universe, contra Newton
(for whom absolute location was simply a property of space).
> Inertial properties have to do with accelerations, not
>with absolute locations.
But in Newtonian mechanics, acceleration is defined to be the second
temporal derivative of (absolute) location. A single particle in an
otherwise empty universe can still be accelerated, which is *why* it
will feel inertia. So empty space has to be 'real', which indeed
Newton admitted was very puzzling.
>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.
I believe Newton himself used it as an argument for the absolute
nature of space, did he not? I think the argument is in Principia, in
fact, but I don't have the page reference. The distinction between
space as location and space as the vessel for inertial properties is
(I think) a more modern reconstruction; but I may be out of my
historical depth here.
>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.
GR refers gravity to essentially geometric properties of
spati(otempor)al coordinates rather than to relative locations of
other material things. That was widely cited as its chief beauty over
Newtonian 'action at a distance', I gather. There is no action at a
distance in GR; things just go along minimum-action paths, determined
locally by the locally curved spacetime.
>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.
Those are used in his intuitive account of special relativity, which
is indeed wonderfully convincing. But the point there is really only
to infer the equations of the coordiante transformations. Once those
are determined, there is no need to then refer all measurements to
other events or other 'things': space-time itself has a geometry.
(However, as Ive emphasised before, space-time with the Minkowski
metric is a very different beast from the nice orthogonal Newtonian
4-d spacetime that Matthew West and I like to use for ontological
reasoning. I really don't think we should base a practical ontology
on Minkowski space; I don't want to have to be always thinking about
Lorentz contractions.)
>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).
Well, look at Einstein's equations.
Pat Hayes
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