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60-second adventures in thought - Achilles and the tortoise (1/6)

60-second adventures in thought - Achilles and the tortoise (1/6)

Surely Achilles, being so much faster, can easily overtake a tortoise? Not if you follow a perfectly reasonable line of logic. From a series on paradoxes by the Open University, short and entertaining enough for the YouTube attention span. Voiced by comedian David Mitchell. Open University philosophy videos: http://tiny.cc/n0spp

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Guest: Richard (3765 days ago)
The paradox is simply resolved by calculus, and the concept of a limit. As the distance-increments get smaller, the time intervals get correspondingly shorter; dividing one by the other gives a constant speed, even as the time-interval, delta-t, becomes infinitesimally small.
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The paradox is simply resolved by calculus, and the concept of a limit. As the distance-increments get smaller, the time intervals get correspondingly shorter; dividing one by the other gives a constant speed, even as the time-interval, delta-t, becomes infinitesimally small.
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Guest: (3765 days ago)
We still get the paradox that at any given instant there is no motion. And I don't think I would consider differential calculus "simple." It took 2000 years from Zeno and a lot of maths geniuses to get to the point where Newton or Leibniz was able to invent it!
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We still get the paradox that at any given instant there is no motion. And I don't think I would consider differential calculus "simple." It took 2000 years from Zeno and a lot of maths geniuses to get to the point where Newton or Leibniz was able to invent it!
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Guest: Kamikaze (3762 days ago)
Latest comment: This "paradox" always seemed trivial to me, as it's obvious that as the distances get smaller and smaller, so do the time intervals. The paradox depends on dividing the distance into infinitely small incremements, then applying a finite time increment to each increment. The only difficulty I saw from this was how to express it mathematically, which is what took mathematicians centuries to develop. They needed Calculus to do it.
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Latest comment: This "paradox" always seemed trivial to me, as it's obvious that as the distances get smaller and smaller, so do the time intervals. The paradox depends on dividing the distance into infinitely small incremements, then applying a finite time increment to each increment. The only difficulty I saw from this was how to express it mathematically, which is what took mathematicians centuries to develop. They needed Calculus to do it.
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Guest: (3765 days ago)
Mortgages are worked out on finite series, not infinite series. Perhaps that was after the point where Mitchell started being funny.
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Mortgages are worked out on finite series, not infinite series. Perhaps that was after the point where Mitchell started being funny.
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60-second adventures in thought - Achilles and the tortoise (1/6)
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