Good and Evil

[bennyboy]

It should serve as a warning for trusting an abstract argument too much and not paying attention to counter-evidence that is readily available.  The error of Zeno's reasoning is explained in Calculus, but even without the explanation, it should be clear enough that he made a mistake somewhere, even if one does not know what the mistake is.

As taught to me, the explanation in calculus was that the sequence {1/2, 3/4, ... (2^n - 1)/2^n} has a limit point at 1. None of the sequence's elements themselves are equal to 1; there's apparently no motion involved with constructing limits in calculus, a form of math as stationary as geometry, which can nonetheless describe rates of change. I wonder if Zeno's mistake was to assume that a thing is "real" only if it admits of formulation with a finite number of discrete steps. Natural language, which has a finite vocabulary and grammar, forces us to do the latter for everything we want to describe.

Yeah, it's obvious to us now that even though each division takes time, it's less time. So an infinitely short distance will take infinitely short time.