Some would say that the paradox of Zeno is just a piece of sophistry, intended to keep young people with overactive minds busy for a while. I disagree with this, and would propose that Zeno was just way ahead of his time. So far ahead of his time, in fact, that he did not know what he was describing.
I assume you're all familiar with the paradox in question. Achilles and a tortoise are about to have a race by foot, and to make things fair the tortoise is given a head start by a certain amount of distance. Running happens. When Achilles has made it to the point where the tortoise started out, the tortoise has moved that much closer to the finishing line. And as Achilles makes up for this distance, the tortoise has moved even further, and is thus still in the lead, leaving Achilles to catch up yet again - and so forth and so on.
The gist of it is that Achilles never catches up with the tortoise. Rather, they seem to get stuck in an ancient version of a time warp, lost forever in a race against time.
This is somewhat confusing. And the reason this is confusing is that it actually isn't about young men or tortoises, but about Youtube.
I imagine you've all been there, trying to watch a video which is slightly bigger than your bandwidth. The thing you have to do is to wait just long enough for the video to buffer enough so that the "never catching up" paradox applies. The video is bigger than your bandwidth can manage, true, but with enough buffer you can still watch it without having to pause. As you watch the buffered part, more is put into the buffer, and as you watch that part, more is put into the buffer - and so on, until the video ends.
The reason the Ancients had such a hard time with this is, as you might imagine, that they didn't have Youtube or online videos back then. Achilles and the tortoise are stuck in this eternal time loop not because of its paradoxical nature, but because of Zeno being two thousand years ahead of himself!
Now, some might argue that Youtube is just a piece of sophistry intended to keep young people with overactive minds busy for a while. I'm not so sure about that, though.
Thought error, January 8, 2012