Occasional Tales

And jump and turn and twirl and kick. Another of Zeno’s paradoxes today. I have no idea what the paradox is, but the book has pictures. The top line of dancers moves to its left. The middle line of dancers stays where it is. The bottom line of dancers moves to its right. They all end up aligned with each other. It might be some sort of paradox about relative motion or something to do with Zeno’s paradox about space and continuous vs. discrete space. According to the book, the top line will’ve passed twice as many members of the bottom line (and vice versa , I assume) as it will’ve passed of the inert middle line of dancers. I think I can see what Zeno’s getting at. It seems to be like a question I’ve had about spinning disks. The further from the centre a point on a disk is, the faster it goes to complete a circuit. But that means that at the very centre of the disk, there’s no movement at all. But in that case, the points on the edge of the disk are the same distance from the point of...

Is that Calculus I see peeking through the curtain? Today we look at one of Zeno’s Paradoxes. This is the one about Achilles and the tortoise, and why the former, πόδας ὠκύς though he was, could never catch the tortoise. Of course, the problem is idealised, but I like it to my record of games of Freecell. At the moment, I win about 75% of them, but, of course, even if I never lose another game of Freecell in my life, the number will only approach 100%, but never actually reach it. In other words, the goal of 100% always remains in front of me just as the tortoise, at least as a mathematical construct, remains ahead of Achilles. Zeno, according to the book, considered the problem of continuity vs. discretion in matters of time and space. If time is continuous, there can be no present; if it’s a series of infinitely small, discrete moments, then it can only ever be present and unchanging. Space could be similarly described. At least with regard to time, I’ve long wondered whether we exp...