Extracting a Paradox by the Roots

TL;DR

This paper analyzes Zeno's paradoxes as arising from historical development of number systems, highlighting contradictions when applying discrete and continuous models to physical concepts like time and space.

Contribution

It offers a historical and mathematical analysis explaining the origins of paradoxes through the evolution of number systems and their application to physical phenomena.

Findings

Number system development caused the paradoxes.

Contradictions emerge when discrete and continuous models are combined.

Understanding these contradictions clarifies the relationship between mathematics and physical reality.

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.