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# How would you explain this paradox? Tweet

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1. How would you explain this paradox?

The Achilles would obviously overtake the Tortoise but how would you solve the paradox?
2. Re: How would you explain this paradox?
Because Achilles runs faster - he doesn't just move a few millimetres when he takes a stride

Edit: The top comment on the video (on Youtube) pretty much sums up the nature of the paradox. He keeps moving closer and closer and closer to the tortoise until he passes the tortoise.
Last edited by Giant; 25-06-2012 at 22:54.
3. Re: How would you explain this paradox?
I know this doesn't answer your question but the guy who is narrating sounds like David Mitchell.
4. Re: How would you explain this paradox?
(Original post by SneakyDoug)
I know this doesn't answer your question but the guy who is narrating sounds like David Mitchell.
I'm pretty sure it IS David Mitchell!

Maybe because in a second the tortoise effectively doesn't move a single step whereas Achilles does? I'm still not answering the paradox really though, as you could still put the same question to two continuously steadily moving forces.
5. Re: How would you explain this paradox?
(Original post by SneakyDoug)
I know this doesn't answer your question but the guy who is narrating sounds like David Mitchell.
I just presumed it was David Mitchell, who is the narrator?
6. Re: How would you explain this paradox?
The paradox requires an infinite number of available points to be occupied between Achilles and the tortoise. Since there isn't an infinite precision in the placement of atoms, the gap becomes smaller and smaller, until the distance between Achilles and the tortoise is actually zero.
7. Re: How would you explain this paradox?

Just model both of them as particles with constant acceleration (zero), a different starting distance, and different speeds In such an instance there is a critical distance value where the position of both particles are equal.
8. Re: How would you explain this paradox?
Because although the distance reduces to 0, so does the time so in a finite length of time, a finite distance will have been travelled.
9. Re: How would you explain this paradox?
The conclusion that he will "never" catch the tortoise uses an implicit assumption, that infinitely many events cannot happen in a finite amount of time. This is wrong.

The "catching up series" is just one example of an infinite set of events that can happen in finite time. A more trivial example is: {t = 0.9, t = 0.99, t = 0.999, t = 0.9999, ...}

(Assuming no quanta, of course, as with quanta, there really are only a finite number of steps.)
10. Re: How would you explain this paradox?
If that happened, it would only be up to a certain distance and they could never reach the end of the track.
11. Re: How would you explain this paradox?
they don't keep a constant velocity.
12. Re: How would you explain this paradox?
Basically you're saying that the distance between Achilles and the tortoise gets "exponentially smaller", which is fine in Mathematics but obviously doesn't occur in the real world (which the video pretty much states; there's no paradox here).
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