View Full Version : The Achilles and tortoise paradox

Pyroworld

03-18-2016, 04:29 PM

In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise. Achilles allows the tortoise a head start of 100 feet. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 feet, bringing him to the tortoise’s starting point. During this time, the tortoise has run a much shorter distance, say, 10 feet. It will then take Achilles some further time to run that distance, by which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been, he can never overtake the tortoise. Of course, simple experience tells us that Achilles will be able to overtake the tortoise, which is why this is a paradox.

Try to figure this one out, ladies and gentlemen.

Lionex01

03-18-2016, 04:31 PM

I don't get the paradox, simple physics disproves it.

Pyroworld

03-18-2016, 04:33 PM

I don't get the paradox, simple physics disproves it.

Then answer it.

Lionex01

03-18-2016, 04:35 PM

Then answer it.

What is the question which I have to answer?

Pyroworld

03-18-2016, 04:42 PM

What is the question which I have to answer?

Does Achilles overtake the tortoise or not?

Lionex01

03-18-2016, 04:44 PM

Does Achilles overtake the tortoise or not?

Yes he does

|ThyLuigi|

03-18-2016, 05:21 PM

I've heard of the paradox, but he does overtake the tortoise eventually.

Explanation: 100 + 10 + 1 + 1/10 + 1/100 + 1/1000 + 1/10000 + ... = 1111/9.

Pyroworld

03-18-2016, 06:07 PM

more answers?:o

abt79

03-18-2016, 06:16 PM

Achilles would have to slow down gradually in order to stay behind the tortoise as you described

In theory, a "point" is infinitely small to the point where it doesn't exist in reality, so yes there are infinite points between any two points, but still Achilles will pass infinite points and the tortoise.

Luminesce

03-18-2016, 07:07 PM

In the paradox.

The solution would be to add up all the points, and the time it took to traverse them.

Creating a finite value, instead of an infinite number of points.

Although the paradox can be seen in 2 perspectives.

And one wouldnt require an answer, achilles just surpasses the tortoise in the 2nd perspective.

LolDawn

03-18-2016, 07:29 PM

Neither. Achilles belongs in the foot and the tortoise belongs in the sea.

|ThyLuigi|

03-18-2016, 07:46 PM

Okay, so Achilles will catch up to the Tortoise after 111 1/9 paces. I looked in The Little Book of Mathematical Principles, Theories, & Things. It's the explanation that satisfies mathematicians.

JOSHIE63

03-18-2016, 11:38 PM

It is too late in the day to think…

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