Extracting a Paradox by the Roots

Abstract

Zeno's paradoxes are explained as being the result of inappropriate combination of discrete and continuous mathematical systems. It is proposed that the source of this confusion lies in the course of development of the number system, which was originally created to model discrete elements of experience and only later, by the invention of standards of measurement, expanded to continuous entities, leading to subtle contradictions when applied to time, space and motion. Analysis of these contradictions furthers our understanding of the relationships between number systems and the physical world.