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[ontolog-forum] Kinds of 4-d (Was: Thing and Class)

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>, "Pat Hayes" <phayes@xxxxxxx>
From: "Christopher Spottiswoode" <cms@xxxxxxxxxxxxx>
Date: Wed, 10 Sep 2008 14:29:44 +0200
Message-id: <74FE458289DA415CA1735E45D6D81EA1@Dev>
Pat,    (01)

Here you were responding to John S:    (02)

>>  The word 'here' and 'now' are indexical terms that are 
>> always tied to a particular observer or speaker.  In 
>> discussions of relativity in 4-d spaces, it is common to talk 
>> about a different 'here' and 'now' for each observer.
> Relativistic 4-d (Minkowski space) is a whole other ball of 
> wax, not at all like the 4-d that Matthew and I are talking 
> about.
> But it seems clear that you and I agree on the essentials, so 
> I won't go on and on about it :-)    (03)

I am not trying to address the original issue of this thread (in 
which, having chosen "entity" and "type" for my project at least 
15 years ago, I have already wholeheartedly supported John's 
position).  Nor do I want to "go on and on" on what might or 
might not really separate you and Matthew from John.  But I am 
worried about that "whole other ball of wax", and far from 
wanting to belabour it until it becomes a tar-ball instead, I 
still have difficulty in seeing what real issues - as against 
formal issues - make the two kinds of 4-d so different.    (04)

I suspect that a strong majority on this list is reasonably 
acquainted with relativistic 4-d.  We are aware that the speed 
of light and light-cones, while obviously key to relativity in 
physics, are only a relatively small part of the mathematical 
view of relativity, with issues such points-of-view, reference 
frames, transformations and covariance predominating.  On the 
other hand, surely many of us have seen a bill of materials with 
time dimensions offered as a prime example of where n-ary 
relationships are rather handy.  So I suspect that I am also 
speaking for a number of others on this list...    (05)

As for myself, on the other hand, I have a further interest in 
this matter.  For over 30 years already I have been using a 
notion of "relativistic realtime" to explain one of the key 
generalizations in MACK (or rather, in a predecessor now fully 
absorbed into MACK).  But from a formal point of view I see that 
whole scene as a mere extension or generalization of the key 
abstract lessons of physical relativity.  So despite your 
various past attempts at explaining your view of 4-d, I still 
cannot grasp just why it is inevitably a "whole other ball of 
wax"!  In the MACK world the 4-d view of data seems to me to be 
perfectly coherent with 4-d in physics.    (06)

(... though, true, the difficulty of presenting it as such - 
along with a great many other matters - is certainly one reason 
why I still haven't posted my long-promised "5th instalment" of 
my "MACK basics" series of posts to this list!  (Did you notice 
how I had in a small way started broaching the whole subject in 
my "4th instalment"?  (That was from this paragraph in it: 
http://ontolog.cim3.net/forum/ontolog-forum/2008-04/msg00109.html#nid027.)))    (07)

I apologize in advance for any mental block I may have in seeing 
the problem you see, but I really hope you can try to clear it. 
(I am also hoping that any such efforts on your part would help 
me in better pitching the matters of my 5th instalment to this 
audience, so please don't ask me to set out my position first! 
My question relates to the problem _you_ see.)    (08)

TIA!    (09)

Christopher    (010)

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