Theoretical analysis reveals that discrete state-space frameworks resolve classical paradoxes of motion, indicating that continuous space-time models create physical impossibilities.
Description:This paper reevaluates Zeno of Elea’s classical paradoxes of motion—the Dichotomy, Achilles and the Tortoise, and the Arrow in Flight—not as historical curiosities or semantic puzzles, but as valid demonstrations that continuous space-time manifolds (R⁴) lead to logical impossibilities. The work argues that nineteenth-century calculus limits and infinite series convergence (Cauchy, Weierstrass) bypassed Zeno’s arguments via mathematical abstraction rather than resolving the physical step-execution mechanism. By transitioning from a continuous coordinate paradigm to a native discrete state-space matrix framework, the paper shows how Zeno's paradoxes naturally dissolve, offering a fresh perspective on the metaphysics of motion and physical reality.
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Sagar Kapadia (2026) studied this question.
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