I got into an argument with a friend who says logic and reason alone cannot determine the truth, and that we need emotions too. He says that Zeno’s Paradox is proof of the shortcomings of math/physics in determining the nature of reality. Is he right about this? I thought math/physics are the holy grails for understanding the nature of the universe.
In: Physics
Zeno’s paradox doesn’t take the time required to cover the distances into account. Zeno assumes that Achilles takes just as long to cover each half-measure as he did to cover the previous full-measure. From that perspective, *of course* he never catches the tortoise. He’s slowing down the closer he gets to it.
If Achilles runs at a constant speed, the problem resolves itself. He covers each half-measure in half the time. Both the distance *and* the time it takes to cover that distance are going to zero.
Zeno’s premise is that it is impossible to perform an infinite number of tasks in finite time. That’s obviously true when each task requires the same amount of time, but what about when the time required to perform the task is proportional to the size of the task? As the size of the tasks becomes infinitesimal, so too does the time required to perform them.
Zeno takes a finite distance and divides it into infinitely many, non-overlapping segments. The sum of these segments, by construction, must be the original distance. In particular, the sum is a *finite* distance. Does it not stand to reason that we could do the same with time, that the sum of infinitely many, non-overlapping time segments can, at least in some cases, be finite?
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