I wrote: (01)
>> With my NIST hat firmly on, I would say that in John's parenthetical
>> addendum he hit on a critical issue. Most identifications of "points in
>> time" are inaccurate, and the stated precision probably isn't the
>> intended accuracy. (02)
Pat wrote: (03)
> All true and important. Nevertheless, it is also important to
> distinguish having points in ones ontology from claiming to be able to
> locate points numerically with absolute precision. These are not the
> same issue. One can embrace the former without claiming the latter. (04)
Absolutely. It is meaningful to talk about time points and time
intervals in *an ontology*, where the presumption is that the users
share the meanings of the individuals, however exact or fuzzy that may be. (05)
> Indeed, one can show rigorously that under certain reasonable
> assumptions about intervals (basically, that they can satisfy a coherent
> notion of 'meeting' one another, or being adjacent without any gaps or
> overlapping), that pointlike entities must exist. This is not to say
> that one can pin one of them down with a finite representation: but it
> does mean that would be foolish to deny that they are real things; and,
> moreover, it demonstrates that to assume that they exist will not
> produce any contradictions or difficulties. (06)
That is, one can have a kind of "topology" for a given "time dimension".
Yes. And it has useful meaning, and one can reason validly from it. (07)
> And such assumptions are
> extremely useful, to put it mildly. We say things like, see you at noon;
> we don't say, see you in the fuzzy interval 11:5912:01. (08)
Indeed, as long as I do not use the corresponding ontology to decide
that 11:59 is "before" noon. (09)
> I would also point out that very discussion about timereferences being
> approximate itself presumes that there is a finergrained "real" time
> available for the approximate times to fail to coincide in. (010)
But it is this presumed finegrained reference time model to which the
idea of converting timestamps with different "granularities" appeals.
Because we have UTC time for a reference time model for terrestrial
events, and this model technically goes to very high accuracy (into the
picosecond range), there is a finegrained "real" time model to which
all scientifically established times can be referenced. Further, there
are arithmetic relationships among times pegged to UTC, and use of those
relationships as definitions of the more generalized temporal
relationships is logically consistent with the generalized temporal
relationship models. Similarly, many scientific and engineering
processes peg events to a Tzero, which is not itself pegged to UTC, but
is simply the origin of a time axis whose intercepts are labeled using
the same scientific system of reckoning elapsed time. (011)
The problem is that most statements about time are *not* scientifically
accurate, and they do *not* have a welldefined mapping to the UTC
reference model. Further, even though many of these other time models
involve numbers for time representation, it is not clear that the
arithmetic relationships among those numbers are consistent with the
intended temporal model. That was my point. (012)
You can state a fact base that explicitly defines the relationships
among specific instances. This requires you to enumerate the
identifiable instances in your time model. So "11:30 is before noon"
can be a fact while "11:55 is before noon" is not, and in fact, 11:55
need not be a time instance in your model! But if you try to state the
fact base as a set of numeric "rules", you must be very careful not to
lose intended fuzziness in interpretation. That is, the numeric
representations give rise to a useful analogy for the time reasoning
process, but they are not exactly the intended time model. And when you
convert between granularities with some mathematical algorithm, you know
you are distorting one of the time models involved, and maybe both, by
forcing them both into a reference model that is consistent with the
arithmetic. (013)
11:30 on 21 January is clearly "on 21 January", but whether 23:59 on 21
January by my watch is really "on 21 January" by Matt West's definition
of the interval depends on the accuracy of my watch and his definition
(many banks see any time after 16:00 on 21 January, by their clock, as
22 January). Sometimes it makes a difference whether the event occurred
"on 21 January" or "on 22 January", and sometimes it doesn't (it almost
always matters to the banks). (014)
> If we were
> really at the universal discrete limit of Plank time, notions of
> approximation become paradoxical. (015)
Sure. Models of subatomic time and models of galactic time are entirely
different creatures. "There there be dragons." (016)
Ed (017)

Edward J. Barkmeyer Email: edbark@xxxxxxxx
National Institute of Standards & Technology
Manufacturing Systems Integration Division
100 Bureau Drive, Stop 8263 Tel: +1 3019753528
Gaithersburg, MD 208998263 FAX: +1 3019754694 (018)
"The opinions expressed above do not reflect consensus of NIST,
and have not been reviewed by any Government authority." (019)
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