Divergence - Zeno's Paradox of Achilles and the Tortoise

Zeno of Elea is famous for coming up with some philosophical problems. His is chiefly known for three of them and this blog post will focus on one of those three. As you might have guessed, that one will be that of Achilles and the Tortoise.

The problem runs as such: Suppose that Achilles and a tortoise have a race. For the sake of simplicity, suppose that Achilles runs at twice the speed as the tortoise (thus making him the faster of the two). Further suppose that Achilles gives the tortoise a head start, and for the sake of simplicity, suppose that this head start means starting at half the distance to the finish line.

Thus, when the race begins, Achilles must travel to where the tortoise started, which is half the overall distance to the goal. However, by the time Achilles gets there, the tortoise will have moved away and traveled a quarter of the overall distance to the goal. So now Achilles must travel a quarter of the overall distance to the goal to arrive at where the tortoise just was, but by the time he gets there, the tortoise will have moved away and traveled an eighth of the overall distance to the goal. So now Achilles must travel an eight of the overall distance to the goal to arrive at where the tortoise just was, but by the time he gets there, the tortoise will have moved away and traveled a sixteenth of the overall distance to the goal. And this goes on ad infinitum.

What logic dictates is that Achilles must never reach the tortoise, as Achilles must first reach a place that the tortoise has already been and will then have some distance to go. And yet we know that he not only must reach the tortoise, but also that, given how we have constructed this problem, the two must reach the finish line at the same time. That's how reality works.

Weird, right?

Now you're asking "RQK why are you talking about this?" Well, I mention it because it's something I want you all to ponder as the story continues.

Comments

[terrycloth]

So she got that far and then *didn't* invent calculus?