Achilles and the tortoise

[sorgoth]

I read about this in a book about philosophy (Story of Philosophy, great book, its not a boring read, suprisingly.)

For those of you who don't know the thing, its an argument that a wrong answer can be achieved by using perfectly good reason the whole way.

"There is a race on old Greece between Achilles, the fastest man on town and a tortoise (the fastest of his kind). But as Achilles is 12 times as fast, it is of course fair to let the tortoise have a head start of 12 stadion. Who will win? Achilles of course, we all think, but Zenon will teach us better: Achilles won't win the race as he won't even reach the tortoise!

When Achilles has reached the point where the tortoise started, it would have moved by 1/12 stadion, And when Achilles reaches that point, the tortoise will have moved to 1/144 station and so on.
"

You see, when people say it's impossible, the are thinking of achilles and the tortoise as points, which of course they can't be. So, achilles WOULD touch the tortoise, as he is(of course)larger than a point, and would eventually touch the tortoise. ...I think I've just solved a paradox. Any problems with my logic?

[Skeptical Greg]

This is a problem of misdirection...

The poser suggests that the problem is:
When Achilles has reached the point where the tortoise started, it would have moved by 1/12 stadion, And when Achilles reaches that point, the tortoise will have moved to 1/144 station and so on.When the real problem is:

" What is wrong with the problem as presented? "

[kourama]

What is the tortoises motivation to run at full speed? Why would he maintain that speed? What if achilles trips over a stone?

Are we talking math or philosophy here?

Originally posted by sorgoth

You see, when people say it's impossible, the are thinking of achilles and the tortoise as points, which of course they can't be. So, achilles WOULD touch the tortoise, as he is(of course)larger than a point, and would eventually touch the tortoise. ...I think I've just solved a paradox. Any problems with my logic?

Other than the fact that it's incorrect, not a thing. :D

This is simply Zeno's paradox. The fallacy lies in the fact that an infinite series of numbers 1/2 + 1/4 + 1/16 etc. DOES add up to a finite number. Therefore Achilles can catch up to and pass the turtle.

[whitefork]

Sorgoth is that Will Durant's Story of Philosophy? I'd check out Modern Science and Zeno's Paradoxes by Adolph Grunbaum, if you can find it anywhere.

The paradoxes are still pretty fresh after all these years, insofar as they are the subject of spirited debate as to what they really mean.

[c4ts]

Originally posted by sorgoth
I read about this in a book about philosophy (Story of Philosophy, great book, its not a boring read, suprisingly.)

For those of you who don't know the thing, its an argument that a wrong answer can be achieved by using perfectly good reason the whole way.

"There is a race on old Greece between Achilles, the fastest man on town and a tortoise (the fastest of his kind). But as Achilles is 12 times as fast, it is of course fair to let the tortoise have a head start of 12 stadion. Who will win? Achilles of course, we all think, but Zenon will teach us better: Achilles won't win the race as he won't even reach the tortoise!

When Achilles has reached the point where the tortoise started, it would have moved by 1/12 stadion, And when Achilles reaches that point, the tortoise will have moved to 1/144 station and so on.
"

You see, when people say it's impossible, the are thinking of achilles and the tortoise as points, which of course they can't be. So, achilles WOULD touch the tortoise, as he is(of course)larger than a point, and would eventually touch the tortoise. ...I think I've just solved a paradox. Any problems with my logic?

Eventually, the turtle will fall face first into horse dung and Achilles will pass him.