Hmmm, if the time corresponding to these
infinitesimal transitions is, say "epsilon"(>0) seconds,
and the distance traversed by these transitions,
is "delta" inches, then to be completely
non-paradoxical, observe that
delta = 0.765(inches/sec)*epsilon(sec)
(assuming constant speed)
.. further, note that this relationship holds
for even an "infinite" number of transitions
. no paradox here
.. the main problem
I see is the application of mathematics
consistent with both "real" and "complex"
numbers to expressions containing "unreal" numbers
"Infinity " may well be a reality,
but it isn't a "real number"
.
My good buddy George Cantor gave of his
sanity so that we who remain could be free
from the confusion surrounding this
land where some say "here there be dragons"
.
("alas poor George, we hardly knew ye
")
>forever, which is obviously not the case. If, on the other hand, the
>transitions happen instantaneously, you have a seeming paradox, where
>one infinity tries to cancel out the other, leaving you with however
>long it took you to move the glass, say, 0.765 seconds. Obviously,
>something is wrong here as well.
>A paradox is nature's way of telling us one of three things:
>1) Our initial assumptions were erroneous
>or
>2) Our assumptions were sound but out analysis was faulty
>or
>3) Both.
well, ok
but I suppose there could be more possibilities
such as the communication of non-verbal ideations