Space minus Time & A Limitation on Fractals

[RascalPuff]

"Xeno's Paradox": revisited

Zeno’s Paradox: Reprise.
The premise for Zeno’s ancient paradox is that if and when a finitely extended straight line - A - B - continues to be divided in half, you never get to the other end.

You keep dividing yer spatial halves in half and you just don’t get to B from A.

OK.

Meanwhile, in the real world, you can arrive at B from A when you simply move from A to B.

Departures from A and arrivals at B happen all the time.

What Zeno’s Paradox omits, is time. Chronology.
The guy is talking exclusively about flash-frozen space, without factoring in time - where it’s synonymous with motion...

Moreover, there was no way for Zeno to know that he would eventually arrive not only at the atom of Democritus; but then encountering the electrons, neutrons and protons of Thompson, Chadwick and Rutherford, and finally, Max Planck’s photon, which, until further notice, is furthermore indivisible.

That is, Zeno probly wouldn’t be able to hack and bisect the Planck length any further. (Although 'string theorists' might take issue, with the application of esoteric mathematics.)

He will have arrived at B from A.

There is a possibility that Zeno (‘Xeno’) deliberately cooked the books on his proffered ‘paradox’, just for the recreation of presenting what is in fact a resolvable riddle, though, it’s unlikely that in his own time, the riddle would unravel, not only with the included factor of time, but also the limitations of dividing Planck’s quantum (1900 AD vintaged) photon.

Webster's 'fractal': An irregular curve or shape that repeats itself on any scale in which it is examined.

Whereas, the subatomically descending fractal is limited by Planck length and sub-quantum measurements - it encounters a limitation of a scale upon which it may repeat itself.


(Ran into this in an old notebook and thought to share it with other rocket scientists. Anyone care to add or subtract anything to or from this?)

[mkirkpatrick]

Thanks RP for the thread starter,may I be bold and suggest that you look up a chap called Dan Winter,you can Google his name,he has been writing and teaching about fractals for years,he also
occasionally posts on this forum,you may find what he has to say of some interest to you.

warmest regards michael.

[dleviwing]

Zeno's argument is a fallacious one; it's due to erroneous use of the math and only fools are impressed by it!
No such thing as a paradox in nature; they only exist in thought!