TITLE:
Zeno’s Paradoxes and Lie Tzu’s Dichotomic Wisdom Explained with Alpha Beta (αβ) Asymptotic Nonlinear Math (Including One Example on Second Order Nonlinear Phenomena)
AUTHORS:
Ralph W. Lai, Melisa W. Lai-Becker, Evgenios Agathokleous
KEYWORDS:
Dichotomy, Asymptotic Concave and Convex Curve, Upper and Bottom As-ymptote, Cumulative and Demulative Numbers (Opposite to Cumulative Numbers), Coefficient of Determination, Skewed Bell, Sigmoid Curve
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.11 No.5,
May
6,
2023
ABSTRACT: Zeno’s paradoxes are a set of philosophical problems that were first introduced by the ancient Greek philosopher Zeno of Elea. Here is the first attempt to use asymptotic approach and nonlinear concepts to address the paradoxes. Among the paradoxes, two of the most famous ones are Zeno’s Room Walk and Zeno’s Achilles. Lie Tsu’s pole halving dichotomy is also discussed in relation to these paradoxes. These paradoxes are first-order nonlinear phenomena, and we expressed them with the concepts of linear and nonlinear variables. In the new nonlinear concepts, variables are classified as either linear or nonlinear. Changes in linear variables are simple changes, while changes in nonlinear variables are nonlinear changes relative to their asymptotes. Continuous asymptotic curves are used to describe and derive the equations for expressing the relationship between two variables. For example, in Zeno’s Room Walk, the equations and curves for a person to walk from the initial wall towards the other wall are different from the equations and curves for a person to walk from the other wall towards the initial wall. One walk has a convex asymptotic curve with a nonlinear equation having two asymptotes, while the other walk has a concave asymptotic curve with a nonlinear equation having a finite starting number and a bottom asymptote. Interestingly, they have the same straight-line expression in a proportionality graph. The Appendix of this discussion includes an example of a second-order nonlinear phenomenon.