MacCruiskeen wrote:brainpanhandler wrote:And why can't I subdivide a Planck length? Who says it makes "no physical sense"? I mean if Zeno's suction cup dart is one planck length from my forehead doesn't it have to travel half a planck length before it reaches it's target?
And then it would have to travel half
that remaining distance (i.e., 1/4 Planck length) and then half
that (i.e., 1/8 Planck length), and so on ad infinitum. In other words, neither Zeno's nor anyone else's arrow can ever reach your forehead. Which is reassuring, but dangerously so, because of course arrows have often, in fact, reached foreheads.
Not that I understand this myself! It is all highly weird.
The Modernity of Zeno’s Paradoxes
The form in which that paradox was first introduced to me was (roughly speaking): "In order for an arrow to reach its target, it has to travel half the distance, then half the remaining distance, then half the remaining distance (and so on). Therefore it never gets there. Why don't you go think about that for a while?" I was bored, and had been pestering and interrupting my mother, who was in the middle of doing something, I don't remember what. I was probably about...ten or eleven, maybe? Within a year or so of that. She meant well.
And it really didn't strike me as kind of an odd way to accommodate a child's natural need for something of an attention-and-time-occupying nature, either, at the time. That was just business as usual in my world. As I understood the general set-up, it was just the natural order of things for me often to be asked to clear some random intellectual hurdle for no very apparent reason, and it was then my job to do so. And that was just that. Besides which, in this particular case, I actually was interested by the question. Because, you know, it's interesting.
So I went away and though about it. After a while, it occurred to me that the reason the arrow did hit the target in reality was that it would naturally do so while traveling half the remaining distance of half the remaining distance of half the remaining distance (and so on) between the point from which it had been shot and a tree (or whatever) standing two feet (or whatever) behind the target.
So. I was just totally beside myself with excitement about having come up with that solution. It had been presented to me as an ancient Greek paradox, and I sort of vaguely pictured having my picture on the front page of the newspaper and...I don't know, getting to ride on a float covered with roses or something like that. For being the ordinary little wise child who had
solved the riddle that had been frustrating the minds of untold numbers of profoundly learned (yet kinda jolly and probably German-accented men with studies full of leather bound volumes and possibly one or two pipe racks) of enormous erudition for lo these many millennia.
I felt that I had a game show appearances in my future, basically. And I was just thrilled to death about that. For as long as it took me to race to my mother's side and tell her what the what was. Whereupon she said something to the effect of: "Why, yes, that was the solution proposed by so-and-so, some monk" -- or saint or philosopher or whatever, I don't really recall -- "in the ninth century, AD, who stated it as So-and-So's Proposition, to wit: Infinity is unattainable. However, at least theoretically, anything short of infinity can be attained."
I decided then and there that I was never ever again even going to bother wasting one single extra second's thought on any serious academic matter beyond whatever bare minimum might be required of me by circumstance while I was still in school for the rest of my life. A resolution to which I've remained true from that day to this. I wasn't so much disappointed as I was mad pissed off. Because I just couldn't believe that the life of the mind had gone and seduced, betrayed and generally fucked around with my heart like that. I regarded it as an outrage greater than any innocent and well-intentioned person could or should be expected to tolerate, and felt deep silent umbrage.
And I'm really not so sure I wasn't justified in that feeling, to be honest. I mean, there was probably some emotional stuff that I wasn't really yet in conscious touch with mixed in there, too, I readily concede. But deep thought actually is a very demanding pastime, and oftener a punishing one than it is rewarding, I was at least right about that much.
Oh. And also. I've never thought about it again or looked into the matter further. So I could definitely be wrong. But that's the solution to Zeno's Paradox, as I understand it. FWIW. Oo, it makes me
so mad even just thinking about it, still. I mean, the nerve of that philosophy stuff. It's not the boss of me.
by 23 » Sat Jan 30, 2010 11:33 pm 
