Mathematics

What is Xenos Paradox



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Xeno's paradox presents us with the question of how motion can occur. If an arrow is always in it's own space in flight, how can it ever get beyond itself and get anywhere? How can the tortoise ever cross the finish line if each area it crosses has an infinite number of tiny little spaces ahead forever subdivisible? Xeno of Elea asked that sort of thing in ancient Greece. Relative motion was an answer to such inquires, as well as conditional motion, and the inability of relevant objects to make the required infinitely tinier steps themselves required to shrink down into puny-space and not get anywhere.

Motion is entirely relative; rate of change is contrasted from one body to others. Some things can cross the space of an atomic nucleus while others only deem it worthy to attend big functions such as are associated with planets, galaxies and larger than atomic or nuclear force size objects. We cannot be entirely certain why some things like bosuns don't leap out of puny-space and cross finish lines like a rabbit otter, yet they don't, but instead cohere in appropriate clump-forms such as comprise larger wave-particle forms enabling molecules and even mammals to exist. Xeno's paradoxical ideas are all mind instead of in the empirical world. His paradoxes were made by misunderstanding Newton and Leibniz's infinitesimal calculus, and his friend Euclid wouldn't give him a clue about how to calculate the motion of objects across large and tiny spaces in space-time accurately-perhaps he should have known.

We can thank Plato for providing the philosophical ideas of realism and the realm of forms that do not require direct observation and calculation of spaces both infinitely small and infinitely vast; why can't the Universe just get its hyper-expansion over after all and reach eternity right away instead of requiring six billion more years just to get where it is now after the first seven billion or so? That is such a paradox that we cannot immediately require a comprehensive and complete answer.

If W.V.O. Quine's Ontological Relativism can be an epistemological guideline for sorting out language paradoxes and their relation to the 'empirical' world perhaps we can say that Xeno's paradoxes required a translation into a different language of science for a satisfying explanation, and so it is with so many present cosmological questions. Cosmological question regarding the motion of the plenum/universe and of it's occupancy of a space other than itself were known to be raised as early as the 7th century B.C. pre-Socratic philosopher Parmenides. M-String theorists making many extra spatial dimensions represented in math matrices present Eleatic paradoxes worthy perhaps of Xeno if they are considered as real Universes at least in theory. It is the theoretical naturef the Eleatic paradoxes that made it difficult for Xeno to answer them. Pragmatic observations would have presented a different mechanics too him with obvious answers and a better theoretical criteria for forming judgments-perhaps.

The analytic-synthetic distinction that seemed to be a fallacy of the empirical philosophical formalization of logical relationships between words and objects wasn't a problem for Xeno. Xeno believed the rational question regarding mechanics and motion were natural and directly valid as evaluative verbal criteria. We know that there are more than 230 crystal formations, that Democritus was on the right track generally, and that the ability of a human mind to form abstract questions regarding nature does not invariably present the right questions to ask or answers to pursue.



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