Zeno of Elea

Zeno of Elea introduced his Dichotomy Paradox as a way to demonstrate the illusion of movement with the concept of infinities. To travel from point A to point B one would have to cross the half way point C, but before that point could be crossed point D halfway between A and C would have to be crossed. This process would go on for an infinite number of divisions. Since there were an infinite number of points a person could not cover all of the point and therefore would not reach point B or even be able to have any movement at all. This concept can be viewed from a different perspective through the Regressive version. “Any step may be divided conceptually into a first half and a second half. Before taking a full step, the runner must take a 1/2 step, but before that he must take a 1/4 step, but before that a 1/8 step, and so forth ad infinitum, so Achilles will never get going.” (Dowden) This concept brought up the idea that all motion was an illusion.

This paradox is more of a philosophical concept instead of a mathematical concept. Calculus defined movement so that paradox’s such as this one could be explained using whole numbers. “The resolution of the paradox awaited calculus and the proof that infinite geometric series such as (i=1)^(infty)(1/2)^i=1 can converge.” (Field) With this concept we know that all fractions have to equal to 1. So with Zeno’s scale all the fractions of 1 or point A to B, will eventually have to equal 1 and define motion. With this understanding movement can be defined and is not an illusion. While Zeno presented an interesting philosophical idea of infinity it is not an accurate method to describe movement. I can’t agree with Zeno that motion is an illusion since we can measure the distance traveled from point A to point B and determine the distance traveled over time.

References:

Dowden, B. (n.d.). Internet Encyclopedia of Philosophy. Retrieved April 14, 2015, from http://www.iep.utm.edu/zeno-par/#SSH3aii

Field, Paul and...