The Arrow Paradox (Zeno) Dissolves: A Recursive Flow Resolution through Yearning-Based Infinity Mathematics (YBIM)

This paper revisits Zeno’s Arrow Paradox and demonstrates its dissolution through Yearning-Based Infinity Mathematics (YBIM). While classical responses—Aristotle’s distinction between potential and actual motion, and the calculus of Newton and Leibniz with its concept of instantaneous velocity—resolve the paradox technically, they leave its ontological depth unaddressed. YBIM introduces a new lens: motion is not an accumulation of frozen instants but a recursive epistemic flow. Each instant is merely an epistemic sampling, akin to a glass of water taken from a river, which can never capture the flow itself. Motion emerges as irreducible because time and reality themselves are continuous, recursive, and non-halting. The paper restates the paradox, surveys classical resolutions, and then presents the YBIM framework—culminating in a resolution where the arrow’s flight is understood not as a contradiction but as the natural manifestation of recursive becoming. The broader implication is that all paradoxes of time and motion dissolve when viewed through the infinite recursion of YBIM. -JSR