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 th...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. .展开更多
Analyses of astrophysics and electrostatic separation data were illustrated with the Asymptotic Curve Based and Proportionality Oriented (ACP) nonlinear math for relating two physical variables. The fundamental physic...Analyses of astrophysics and electrostatic separation data were illustrated with the Asymptotic Curve Based and Proportionality Oriented (ACP) nonlinear math for relating two physical variables. The fundamental physical law asserts that the nonlinear change of continuous variable Y is proportional to the nonlinear change in continuous variable X. Mathematically, this is expressed as dα{Y, Yu, Yb} = −Kdβ{X, Xu, Xb}, with Yu, Yb, Xu, and Xb representing the upper and baseline asymptotes of Y and X. Y is the continuous cumulative numbers of the elementary y and X is the continuous cumulative numbers of elementary x. K is the proportionality constant or equally is the rate constant.展开更多
文摘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. .
文摘Analyses of astrophysics and electrostatic separation data were illustrated with the Asymptotic Curve Based and Proportionality Oriented (ACP) nonlinear math for relating two physical variables. The fundamental physical law asserts that the nonlinear change of continuous variable Y is proportional to the nonlinear change in continuous variable X. Mathematically, this is expressed as dα{Y, Yu, Yb} = −Kdβ{X, Xu, Xb}, with Yu, Yb, Xu, and Xb representing the upper and baseline asymptotes of Y and X. Y is the continuous cumulative numbers of the elementary y and X is the continuous cumulative numbers of elementary x. K is the proportionality constant or equally is the rate constant.
