At 12:02 PM -0500 1/22/08, Ed Barkmeyer wrote:
John Sowa wrote:
>> There are so many hard problems, it's hard to say which are
harder.
>> But the idea of taking the least significant digit as the
criterion
>> for implicit granularity is fairly common for experimental
data
>> (unless some explicit margin of error is stated).
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.
<big snip>
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. 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 point-like 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. 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 11:59-12:01.
I would also point out that very discussion about time-references
being approximate itself presumes that there is a finer-grained
"real" time available for the approximate times to fail to
coincide in. If we were really at the universal discrete limit of
Plank time, notions of approximation become paradoxical.
Pat
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