Re: Hamilton's Rule is Xeno's Paradox ( was Re: Underestimating 'r')


<EKurtz99@xxxxxxx> wrote in message news:dj4np4$3ej$1@xxxxxxxxxxxxxxxxxxxxxx
> John Edser wrote:
> In Xeno's Paradox the algebraic constant "time" has
>> been deleted as an oversimplification. This reduces the mathematics to
>> become entirely, just a relative proposition within which the hare can
>> never
>> actually catch up to the tortoise.
>
> Of course it doesn't, you idiot. Zeno thought he had found a paradox
> because he did not know how to compute the limit of a convergent sum.
> Neither do you, of course. However, he has an excuse - he lived 2,500
> years ago. What's yours?
>
> (to compound the problem, you are confusing one of Aesop's fables - The
> Hare and The Tortoise - with Aristotle's version of Zeno's paradox (or
> one of them) - Achilles and the Tortoise)
>

John,

I appreciate your thinking, but not your resort to personal attack.

The issue is this: that Zeno's paradox of the arrow remained a paradox even
after Newton and Leibniz.
Newton's realization that we could think of an arrow's trajectory in terms
of what he termed "fluxions,"
did not resolve the paradox. It merely found a work-around, by way of our
manipulating (mathematically) the relationships between functions and
factors (an over-simplification, but representative). It also relied upon
'rounding.' Motion can be expressed only irrationally, unless one rounds,
just as Pi can only be expressed irrationally. Motion and non-motion can
not be equated rationally because they are mutually exclusive. (For that
matter nothing in the cosmos can be defined as not-in-motion EXCEPT insofar
as it may be arbitrarily assigned to be the only non-moving point in the
cosmos (or all cosmoses, the singleness or plurality of which we cannot be
certain).

At the quantum level, the paradox at the Newtonian level is potentially
resolved in the Newtonian sense, but translates into still ANOTHER paradox,
since here it is found to move in fits and starts, not stopping and
starting, exactly, but ceasing to exist at one quantum moment and then
reappearing at the next one, which is 6.626 x 10 to the minus 34 power,
perhaps, away (Planck's constant).

For purposes of computation, we can round as much as we like, measuring in
feet per second, or inches per second, or whatever... but these are only
rounded approximations until, and unless, we get down to the ticks of the
clock in the arrow's frame of reference. And EVEN THAT varies from one
frame of reference to the next (due to the expansions and contractions of
time, through which photons and arrows may pass).

Fortunately, for crude predictions, such as determining for purposes of
building an aircraft engine -- even to tolerances of a mere one-to-five
thousandths of an inch, we still have to round... because Pi can NEVER be
resolved into a real number fraction, nor a terminal decimal equivalent).
Take a micrometer and hone our engine parts to "close enough," and there we
settle upon imperfection.

I am not judging whether you have a point worth making here. I am only
speaking to the issue of whether it is accurate to say a person is stupid or
wrong for not translating the paradoxes of motion and time into a round
figure and calling that a resolution of them.






.

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