An effort to solve Zeno's motion Paradoxes

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SUMMARY

Zeno's motion paradoxes can be resolved by substituting finite-sized points for geometric points, eliminating the notion of infinite divisibility in space. The discussion highlights four key paradoxes: the stadion paradox, arrow paradox, dichotomy paradox, and Achilles paradox, each demonstrating the complexities of discrete versus continuous interpretations of space and time. Participants agree that Zeno's assumptions about the atomic nature of time and the continuous nature of space lead to contradictions, ultimately asserting that if spacetime is continuous, the paradoxes dissolve. The conclusion emphasizes that "paradox" signifies a challenging concept rather than an impossibility.

PREREQUISITES
  • Understanding of Zeno's paradoxes and their implications.
  • Familiarity with concepts of discrete versus continuous space and time.
  • Basic knowledge of mathematical series, particularly infinite series.
  • Awareness of philosophical implications in physics, particularly in relation to spacetime theories.
NEXT STEPS
  • Explore the mathematical foundations of infinite series and convergence.
  • Research the implications of discrete versus continuous models in physics.
  • Study the historical context and interpretations of Zeno's paradoxes in philosophy.
  • Investigate modern theories of spacetime, including quantum mechanics and relativity.
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Philosophers, physicists, mathematicians, and students interested in the foundations of motion, the nature of time and space, and the implications of Zeno's paradoxes in contemporary physics.

  • #91
Hmm, do you know the 'The Jewel Net of Indra'?
 
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  • #92
Originally posted by UltraPi1
You might find this a little nutso, but I think the whole purpose of the universe is to count (create) the finite empty spaces of an infinite space. This process is ongoing and will take forever to complete. Keep in mind that I consider existence to be purely conceptual. There are no physical entities. They only come across to you as being that way.
So your existence is a hodge podge of conceptually discrete empty spaces, and each space acts in accordance with our known physical (conceptual) laws.
Nothing, well written, in a philosophy forum, should be considered "nutso", especailly not the expression, simply, of idea/concepts/and/or/thoughts...so don't worry bout that..

It begs metaphysical, inasmuch as, resolving the Idea of 'Infinite', with existence, requires understanding(s) like; "In an infinity, the center can be everywhere!" as 'material existence' and 'Infinite' seem incompatable otherwise...but Xenos is a play 'tween Theory of math (language of math) and perception(s) of reality...

In a singular 'empty space' you could count to x ? Infinity? (absurdity) the number of "empty spaces" (non-existant) you could find, in there, then, A'la Xeno, when you think you have gotten them all, halve the space that that amount of numbers 'occupies', and keep counting!

(has the absurdity become clear to you, in that example?)
 

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