Dose anyone know how Newton solved Zeno's paradox?

Question

those guys in mathmatics arent being very helpful.

Answer 1

Kant's, Hume's and Hegel's solutions to the paradoxes have been very stimulating to subsequent thinkers, but ultimately have not been accepted. There is now general agreement among mathematicians, physicists and philosophers of science on what revisions are necessary in order to escape the contradictions discovered by Zeno's fruitful paradoxes. The concepts of space, time, and motion have to be radically changed, and so do the mathematical concepts of line, number, measure, and sum of a series. Zeno's integers have to be replaced by the contemporary notion of real numbers. The new one-dimensional continuum, the standard model of the real numbers under their natural (less-than) order, is a radically different line than what Zeno was imagining. The new line is now the basis for the scientist's notion of distance in space and duration through time. The line is no longer a sum of points, as Zeno supposed, but a set-theoretic union of a non-denumerably infinite number of unit sets of points. Only in this way can we make sense of higher dimensional objects such as the one-dimensional line and the two-dimensional plane being composed of zero-dimensional points, for, as Zeno knew, a simple sum of even an infinity of zeros would never total more than zero. The points in a line are so densely packed that no point is next to any other point. Between any two there is a third, all the way "down." The infinity of points in the line is much larger than any infinity Zeno could have imagined. The non-denumerable infinity of real numbers (and thus of points in space and of events in time) is much larger than the merely denumerable infinity of integers. Also, the sum of an infinite series of numbers can now have a finite sum, unlike in Zeno's day. With all these changes, mathematicians and scientists can say that all of Zeno's arguments are based on what are now false assumptions and that no Zeno-like paradoxes can be created within modern math and science. Achilles catches his tortoise, the flying arrow moves, and it's possible to pass an infinite number of places in a finite time, without contradiction. And one need not accept that a person can perform an infinite number of actions in a finite time, if actions have first points and last points, or beginnings and endings and next actions.

No single person can be credited with having shown how to solve Zeno's paradoxes. There have been essential contributions starting from the calculus of Newton and Leibniz and ending at the beginning of the twentieth century with the mathematical advances of Cauchy, Weierstrass, Dedekind, Cantor, Einstein, and Lebesque. Philosophically, the single greatest contribution was to replace a reliance on what humans can imagine with a reliance on creating logically consistent mathematical concepts that can promote quantitative science.

http://www.kuro5hin.org/story/2005/1/5/111446/4154

http://plato.stanford.edu/entries/paradox-zeno/

http://www.eurekalert.org/pub_releases/2003-07/icc-gwi072703.php

http://philsci-archive.pitt.edu/archive/00001197/02/Zeno_s_Paradoxes_-_A_Timely_Solution.pdf

http://www.iep.utm.edu/t/time.htm

http://www.cs.auckland.ac.nz/CDMTCS//researchreports/089walter.pdf

Answer 2

It's based on a faulty assumption.

the idea that a body moves in 1/2 discrete increments was the problem. It's false, and was also based on chosing one arbitrary place in space (the destination). Choose a place on the far side of the destination to measure from, and the paradox no longer holds.

Answer 3

Yes, I do.