Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.
Physics education research, electronic materials, and the musings of Christopher Moore, Ph.D.
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A tortoise and a hare are racing. The tortoise is given a hundred metre head start on the (obviously much speedier) hare. When the tortoise touches the hundred metre line, the hare starts off, thinking to himself that he himself needs to get to the hundred metre line; but when he gets there the tortoise is slightly ahead (a hundred and one metres, say). So the rabbit, as he zooms past the hundred metre line, thinks to himself that now he needs to get to the hundred-and-one metre line. But when he gets there, the tortoise is slightly ahead still! This continues on infinitely, with the hare catching up to where the tortoise *was* only to find him slightly ahead.
Therefore, the hare must go through an infinite number of distances before he can overtake the tortoise. Thus, while common sense and common experience would hold that the rabbit can catch the tortoise, according to the above argument, he cannot. Solve the paradox.
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Ooooh, that's a really good one, Bishop. I wonder if someone will try and answer it.
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The hare has been training really hard for this race, focusing on making his legs stronger. So after months of doing squats and jumping as high and fast as he can, he has super powerful legs. What he doesn't realize is that rabbits move by hopping, so while they travel the same distance horizontally, the rabbit, as a result of his erratic locomotion, must cover more distance than the tortoise if you include the space he must travel through the air as he hops!
Silly, I know, but a good guess I think! 
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It's easy. Yes, the hare must make infinite number of distances, but who said that it cannot be done in finite time? Mathematicaly it means that the sum of these time periods is finite. Nothing more.
Paradox of "Achiles and tortuise" was a paradox, because greeks couldn's imagine an infinite sum. So it goes.
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I conclude that you need a better hare - since the tortoise is obviously in the lead, you only need to aim ahead of the thing, yes? So, get a hare that isn't so damned clever!
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I should ask, is this taken from the discworld novels by Terry Pratchet?
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isn't this Zeno's paradox?
Where you move through an infinite amount of infinitely small distances in finite time.
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Nicholas wrote:
isn't this Zeno's paradox?
Where you move through an infinite amount of infinitely small distances in finite time.
Yes. This is one of Zeno's paradoxes.
http://en.wikipedia.org/wiki/Zeno%27s_paradoxes
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if i were the tortoise,i would aim ahead cos there is no way to catch up to the tortoise this way.i wonder if there really is a rabbit that can measure such small distances in a race 
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coolcat94 wrote:
if i were the tortoise,i would aim ahead cos there is no way to catch up to the tortoise this way.i wonder if there really is a rabbit that can measure such small distances in a race
sorry i meant "if i was the hare,i would aim....."
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