The Xeno Arrow Paradox

I think I'm becoming a nerd. Believe it or not, I found yesterday's tutorial on Media Audiences rather interesting. Having said that, I won't be in the least surprised that I might have moved up the Nerd-O-Meter from "Dude with Nerdy Tendencies" to "Nerd with Social Life". Give me two more months and I'll be upgraded to "Nerd with remnants of Social Life", and finally by the end of this semester, I'll just be a full-fledged "Nerd". Still, there is a glimmer of hope, because the most interesting part of the tutorial had little relation to the actual topic at hand.

Our tutor talked about the Paradox of Xeno's Arrow. Now Xeno was this Greek philosopher-mathematician who probably, like every one else during those days, had too much sodding free time on their hands. In order to properly expound this theory, I would require the use of diagrams.


Fig 1.1

Okay, let's introduce you to our two friends (Fig 1.1). Seeing as how this theory was conceptualized during the Greeco-Roman era, we shall use names more suited for that timeframe.


Fig 1.2

So we have Hephaistos the archer and Leto the um... other guy. So they're standing on this little grassy plain on a nice sunny day, minding their own business. Don't ask how they got there and why they're staring at each other like that. This is hypothetical. So everything is cool until Leto the um... other guy gives Hephaistos the archer the Finger (Fig 1.2).


Fig 1.3

Hephaistos the archer naturally gets angry. And back in those days where feudalism was more openly received and less questioned, it was perfectly okay for Hephaistos the archer to shoot Leto the other guy in the head (Fig 1.3). Very commonplace incident in ancient Greece; the people learn that Hephaistos the archer is one violent bugger so keep away from him, the people learn that Leto the other guy is dead - wouldn't you know, that son of a bitch still owes us fifty denarii! - and then they go on drinking their beers. Nothing specially, really.

But here's where Xeno comes in; it gets a tad mathematical now, so if your standard of Additional Mathematics plateaus at problems like "If I have two apples, how many apples do I have?" (Fig 1.4) then I'd suggest not going further until you've rectified that. Now Xeno theorizes that before the arrow can reach Point B from Point A, it has to pass the midpoint M (Fig 1.5).


Fig 1.4


Fig 1.5

Sounds okay so far? Now as if that weren't enough, Xeno goes on to say that before the arrow reaches M, it has to first reach the midpoint between A and M, Midpoint N (Fig 1.6).


Fig 1.6

Now that's just fine and dandy. Sure, it makes sense. Before you get to the midpoint, you need to get the midpoint of the midpoint. Whatever. End of story right? Wrong-O, because Xeno now says that in order for the arrow to reach N, it has to first reach the midpoint between A and N, Midpoint O (Fig 1.7).


Fig 1.7

Yes, you've guessed it, in between A and O, there is another midpoint in which the arrow must first traverse, in between which, there is yet another midpoint. So Xeno theorizes that since there is no finite number of the divisions of midpoints (i.e. any number can be divided by half, no matter how small), there will be no end to the midpoints that the stupid arrow must first reach. And therefore, if you fire an arrow, the arrow will never reach point B (Fig 1.8).


Fig 1.8

And that is the paradox of Xeno's Arrow. Really interesting if you think about it, that this Greek Xeno actually had the audacity to come up with such a bold theory that defies the laws of Physics. Either he must have been a mathematical genius, or he just wanted to find a way to deter people from constantly shooting arrows at him.

So if you're at a rave party and are called upon to make small talk, show them that you too could be a nerd/geek/wanker (delete wherever appropriate, if deletion is appropriate to begin with) and share with them the Xeno's Arrow Paradox. It sure beats constantly commenting on how huge that chick's rack is at any rate. Besides, it's also a great time to show the girls some of your pseudo-intelligence (Fig 1.9)


Fig 1.9

And so ends my lengthy discourse of the Xeno's Arrow Paradox. For what it's worth, I have a funny feeling that Xeno might have at one point realized that there was a serious flaw in his little theory. But as it turned out, I don't think he was around for too long to find out what it was (Fig 1.10)


Fig 1.10

THE END!