Achilles and the Tortoise - 60-Second Adventures in Thought (1/6)

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Ancient mathematical trickery proves that a mighty hero cannot overtake a tortoise.

(Part 1 of 6)
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[OUlearn]

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[harnaik singh]

Could he just .... run past it ? ... i dont think i get it

[24willa]

my calc teacher talked about this today...

[Sardonac]

Neither, since it doesn't seem to be for you.

[William Letzkus]

Excellent site for learning about paradox!!! Dr. Why

[kingkrazy0wns]

The Achilles and the tortoise paradox is not a literal problem to be solved. Rather, it is a thought experiment. If we apply modern physics as you suggested, then yes, the solution is quite obvious - Achilles beats the tortoise in the race. Zeno and the other Greek philosophers knew this as well, but they approached the problem from a different, metaphysical angle in order to provoke discussion and create a seemingly logical paradox.

[cyclopwarriorgunman]

The problem with this is that neither time nor acceleration is considered. When we take time in to account, we can see that if the tortoise is given a 100 meters headstart and, hypothetically, travels this time in 100 seconds, but Achilles can run the same distance in 10 seconds, then it is quite clear that after some 120 seconds Achilles has run 200 meters, but the tortoise only 120 meters. This paradox is created by nothing but a faulty method I recon.

[Half Life Fanboy]

If both had the same speed the distance would never change between them...

[Don Clue]

The paradox is that you can split a finite number into an infinite amount of points. e.g Achilles is running round a race track of length 400m. But as you know, before he passes the 400m mark, he must pass the 200m mark; before he passes the 200m mark he must pass the 100m mark, and before this the 50m mark, 25m mark and so on. it gets to the point where before the 1/10000 mark he must pass the 1/20000 mark and as there is no maximum limit for the denominator, this continues ad infinitum

[Don Clue]

no. before you run 1m you must first pass the 1/4m point. So taking this into account:- Achilles is 10x faster than the tortoise. The tortoise has a 2m headstart. Achilles passes the 2m mark, but now the tortoise is 2/10m ahead of this point. Now achilles must pass this 2m+2/10m point before, say, he passes 2.3m, and he must pass 2.3m before he passes 2.4m. So to progress he must now pass the 2.3 m mark, but the tortoise will have moved on and be at 2.31 metres, and so on. Hope you understand