Abyss & Apex : Fourth Quarter 2005 : Zeno’s Duet – Introduction

Reductio ad absurdum…

What were the odds that we would receive two good (but very different) stories invoking Zeno of Elea (490-430 BC), the teacher of Socrates, a man called “the father of dialectical reasoning” by Aristotle? Zeno’s paradoxes overturned the whole structure of mathematics, for he argued that all human knowledge is based on unprovable hypotheses, on split infinities — and applied that thinking to mathematics. His greatest contribution to science was to replace what human imagination thought of as truth with logically consistent mathematical concepts. And to Zeno, despite the information of his senses, math proved that motion was an illusion, an impossibility.

He was rumored to have been put to death for conspiring against the tyrant Nearchus, and various versions of his heroism under torture are given. But heroism is motion, and motion is impossible because it is infinitely divisible, just like the flight of an arrow. The arrow, at any one point, is always at rest. A paradox.

What is the relationship between cause and effect? Two space-suited figures float “toward” each other in an infinite vacuum: which one is stationary, and which is moving? Two people are in conflict. Who is set upon whom? Are you looking at it from the viewpoint of one person, the other … or from outside of time?

Arguments from absurdities. They’re all a matter of perspective. .

Wendy S. Delmater
Associate Editor

  





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