Zeno’s paradox suggests that all movement is impossible because that which is moving must reach the midpoint before the end. The end of things, according to Zeno, is infinite. I find this theory to be particularly difficult to wrap my brain around. According to Aristotle, his argument “falsely assumes that it is impossible to traverse or come into contact with an infinite number of things individually in a finite time.”
Using the example of Achilles and the tortoise, Zeno states that the slowest as it runs will never be overtaken by the quickest. In the time it takes the quicker to travel the distance to where the slowest had departed, the slowest would also have been traveling at a constant speed all the while, therefore separating himself further from the quickest. The two will continue on and on this way, therefore, it is virtually impossible for the quickest to catch up to the slowest because the deficit between them will keep shrinking infinitely, thus, this distance between them will never end.
This example, similar in nature to the childhood fable with which I am familiar, “The Tortoise and The Hare,” is one that resonates with me yet puzzles me at the same time. I find it difficult to grasp how seemingly clear cut and finite things, such as distance or time, are actually infinite in and of themselves. The quicker runner should be able to outrun the slower, because he is faster by nature. But, given the head start of the slower, Zeno claims that the distance separating them will never be traversed traveling at constant speeds in a finite span of time.