On Jan 12, 2009, at 10:08 AM, Olken, Frank wrote: Pat Hayes and Pat Cassidy, These statements are only true for "Newtonian" conceptualizations of time. Relativistic models of "space-time" require the specification of both spatial and temporal locations.
Sure, but one still needs to discuss the topology of the time-line used in talking about space-time. BTW, the "4-D" models being mentioned here are usually Newtonian; one gets relativistic space-time by using a different metric on the same underlying topology. But until one gets into measurement issues (which very few of these temporal ontologies do), the difference isn't apparent. Relativistic temporal models arise in astronomy, astrophysics, high energy physics. In a purely computer science context see the classic paper by Leslie Lamport on Time, Clocks, and the Ordering of Events in a Distributed System, Communications of the ACM, vol. 21, no. 7, p. 558-565, July 1978
Yes, great paper. I know John Sowa has also pointed out that relativistic reasoning also applies in what one might call social-communication space, where the "speed of light" is much slower than in physics, but one still gets phenomena like the 'light cone'.
Pat Frank Olken
On Jan 11, 2009, at 10:18 AM, Pat Hayes wrote:
When you say “Those various temporal theories can all be expressed in terms of three concepts: time-point, time-interval and duration.” , what do you mean by that? Is being “expressed in terms of” used only for necessary and sufficient definitions?
No, I mean only that each theory uses only those three terms, or can be reformulated using only those (or in some cases only two of them.) Of course, since the theories have different axioms, they assign somewhat different meanings to them.
Thinking more, this isn't really accurate. They all use only these three classes, but they also use various different relations, such as the timepoint and subinterval orderings and the various relations between points and intervals. So perhaps the typical number of concepts is more like six or seven than two or three.
PatH
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