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 Posted: Sun Nov 05, 2006 5:57 am
Okay, I remember reading somewhere, that not matter how fast you are, you can never win a race.
What it said was 'A turtle racing a runner. The turtle would win because for each part you run, you would have to go half that distance, half that distance half that distance and so forth. So although the runner is faster, it never makes the finish.' or something like that. What do you think about that?
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Posted: Sun Nov 05, 2006 8:23 am
That is interesting...do you think you could find the source? I'd like to share that with a couple of my friends and my philosophy instructor. I am not quite sure what to think about it myself, but I will have to think upon it a bit...
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Posted: Mon Nov 06, 2006 4:33 pm
confused confused ... Is this some sort of a math problem... like if you must run 1mt, then 50cm (half the distance), then 25 cm, then 12,5...and so and so.... so you never get the goal after all....??
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Posted: Tue Nov 07, 2006 5:26 pm
That is what it sounds like...but then, wouldn't neither racer win? Because they would both have to stick to those perameters..
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Posted: Thu Nov 09, 2006 3:30 am
What they said was, since the runner was going so fast, He was in effect, going almost nowhere. Because however far you go you must always cover half the distance, therefor the runner would never be able to beat the turtle.
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Posted: Mon Nov 13, 2006 5:32 pm
For some reason, I've always heard this where the runner is Achilleus. No idea why.
But yeah, it's math. The distance between point A and point B is essentially infinite. For A I'll use 0, and for B 1.
To get from 0 to 1, you must cover half the distance, and then half that, etc.
So we have this.
0 <-- START
1/2
3/4
7/8
15/16
So the only true finish would be where 1 = x-1/x. I tested that once. It ain't a pretty graph.
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Posted: Thu Nov 16, 2006 7:09 am
Really the only use this fraction concept has is when teaching pre-calc students about the concept of limits. It isn't that you don't ever reach the finish in a real-world sittuation. It's a metaphor for a mathematical concept.
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Posted: Thu Nov 16, 2006 3:16 pm
Oh, I know that, Star. I was just clarifying.
And yeah, if that were true in real life, we'd never have reached the end of the equation. 3nodding
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Posted: Mon Jan 22, 2007 12:13 pm
It is one of Zeno's (presocratic philosopher) paradoxes against motion. If we divide the race into an infinite number of discrete tasks then Achilles can never catch up with the tortoise as long as the tortoise has a head start because by the time Acilles covers one "unit" of space the totoise has already moved on. However Zeno ignores the difference between potentiality and actuality so he may be correct that space is infinitely divisable but this does not mean that space is infinitely divided.
other paradoxes by Zeno = the runner who can't start the race and the motionless moving arrow, it is all to do with ancient atomic theories - if anyone is interested pm me i am a little rusty but i can give a basic explanation.
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Posted: Mon Jan 22, 2007 6:13 pm
Doesn't work in the real world though, so can be comfortably disregarded.
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Posted: Sat Feb 03, 2007 11:22 am
You can win "a" race, but not if the race consists of going according to the pattern you mentioned: first step is half the distance left, then half that distance, etc. It's kind of like the idea that a circle has infinite lines of symmetry. But since most races are not structured with the "half distance" rule, you can eventually pass the distance of the racetrack in a smaller amount of time than the turtle.
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