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Charlie wrote:
> There can be no mathematical solution to Zeno's paradoxes because the
> paradoxes are about physical reality.
I disagree.
How can paradoxes be about physical reality when we continue observing
world in motion and don't perceive any paradox? Achilles (equivalent)
is certainly outrunning turtle in physical reality so where is the
paradox in physical reality?
Paradox is in the description of that reality, in the logic used.
> Most mathematical solutions to Zeno's paradoxes casually assume a
> Newtonian -Euclidean view of physical reality, which are scale
> invariant.
>
> But reality is NOT scale invariant and the world would be very
> different if it were.
How does the scale enter the picture exactly? While I'm not disagreeing
with your statements about the scale invariance your argument (so far)
is like proving that Moon is made of cheese by mentioning that complex
molecules do exist in inter(stellar)(galactic) space.
> Among other things, Zeno is merely pointing out our natural discomfort
> with the idea of continued halving.
I see no particular discomfor in here?! Yes, if we set up a computer to
do this continued halving (and summing it all) and if we assume that
computer will do it by maintaining precision, storing intermediate
results in ever-growing registers, such computer will consume the mass
of the whole Universe (assumed finite) and still won't be even
beginning to get close to the solution.
It is probably not comfortable that not even the most powerful
computers can do what abstract taking of the limit does in
few-neuron-seconds spent in non-physical abstract space of mathematical
thinking.
> A modern quantum solution to Zeno's paradoxes is still
> discomforting..
I'm not aware there is any quantum solution short of generic babble
about particles not being localized in any precise location. Which is
IMHO like proving that God is an alchocolic because there are alcochol
molecules all over the vast expanses of our physical Universe.
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