You can't catch a turtle

[Modeps]

Before you can overtake the turtle, you must first run to point A, where the turtle started. But then the turtle has crawled to point B. Now you must run to point B. But the turtle has gone to point C, etc. You are stuck in a situation in which you get closer and closer to the turtle, but never catch him.

 

[HardcoreRobot]

this is only the case if his speed > yours, or you are taking a longer path

 

[bunker]

Skip a point, step on the bastard and smush him, run back to the point you need then catch up.

What's the problem?

 

[Demon-Xanth]

You must run really slowly.

 

[notfred]

An infinite number of distances that converge toward zero fast enough can add up to a finite distance. Take calculus.

 

[Modeps]

Lets say it takes you a second to run a meter, and it takes the turtle 10 seconds to run a meter... If the turtle starts out one meter in front of you, in the second that you take to get to him, he will have already moved .1 meter... so you have to move to 1.1m to catch him, it takes you .1s to get to that spot, but in the time that it took you to get there, the turtle will have traveled another .01m, so you have to go there.... etc etc.

 

[MisterJackson]

What you don't know (and Bugs didn't either) is that he's got an f'ing jet pack secretly hidden in his shell, and a million clones of himself so he appears "everywhere at once".

 

[jagec]

Originally posted by: Modeps
Speed really has nothing to do with it.
Lets say it takes you a second to run a meter, and it takes the turtle 10 seconds to run a meter... If the turtle starts out one meter in front of you, in the second that you take to get to him, he will have already moved .1 meter... so you have to move to 1.1m to catch him, it takes you .1s to get to that spot, but in the time that it took you to get there, the turtle will have traveled another .01m, so you have to go there.... etc etc.

the integral of that function will give you a discreet answer. As notfred said, take calculus.

 

[Kyteland]

http://mathworld.wolfram.com/ZenosParadoxes.html

 

[notfred]

Originally posted by: Modeps
Lets say it takes you a second to run a meter, and it takes the turtle 10 seconds to run a meter... If the turtle starts out one meter in front of you, in the second that you take to get to him, he will have already moved .1 meter... so you have to move to 1.1m to catch him, it takes you .1s to get to that spot, but in the time that it took you to get there, the turtle will have traveled another .01m, so you have to go there.... etc etc.

Yes, and as you add up all those times that get increasingly smaller, even though there are an infinite number of them, they'll add up to a finite value, which is the amount of time it takes to pass the turtle.

Take calculus.

 

[eigen]

calculus > turtle

It is a geometric series.IIRC

 

[HardcoreRobot]

they said it better

 

[Gibson486]

Originally posted by: jagec

Originally posted by: Modeps
Speed really has nothing to do with it.
Lets say it takes you a second to run a meter, and it takes the turtle 10 seconds to run a meter... If the turtle starts out one meter in front of you, in the second that you take to get to him, he will have already moved .1 meter... so you have to move to 1.1m to catch him, it takes you .1s to get to that spot, but in the time that it took you to get there, the turtle will have traveled another .01m, so you have to go there.... etc etc.

the integral of that function will give you a discreet answer. As notfred said, take calculus.

what function are you actually talking about?

 

[jagec]

Originally posted by: Gibson486

Originally posted by: jagec

Originally posted by: Modeps
Speed really has nothing to do with it.
Lets say it takes you a second to run a meter, and it takes the turtle 10 seconds to run a meter... If the turtle starts out one meter in front of you, in the second that you take to get to him, he will have already moved .1 meter... so you have to move to 1.1m to catch him, it takes you .1s to get to that spot, but in the time that it took you to get there, the turtle will have traveled another .01m, so you have to go there.... etc etc.

the integral of that function will give you a discreet answer. As notfred said, take calculus.

what function are you actually talking about?

Off the top of my head, I believe it would be the initial distance between them, minus the difference in speeds times the time, integrated from 0 to infinity.

 

[Gibson486]

Originally posted by: jagec

Originally posted by: Gibson486

Originally posted by: jagec

Originally posted by: Modeps
Speed really has nothing to do with it.
Lets say it takes you a second to run a meter, and it takes the turtle 10 seconds to run a meter... If the turtle starts out one meter in front of you, in the second that you take to get to him, he will have already moved .1 meter... so you have to move to 1.1m to catch him, it takes you .1s to get to that spot, but in the time that it took you to get there, the turtle will have traveled another .01m, so you have to go there.... etc etc.

the integral of that function will give you a discreet answer. As notfred said, take calculus.

what function are you actually talking about?

Off the top of my head, I believe it would be the initial distance between them, minus the difference in speeds times the time, integrated from 0 to infinity.

n/m, notfred expained it......

 

[FrustratedUser]

Originally posted by: Modeps
Lets say it takes you a second to run a meter, and it takes the turtle 10 seconds to run a meter... If the turtle starts out one meter in front of you, in the second that you take to get to him, he will have already moved .1 meter... so you have to move to 1.1m to catch him, it takes you .1s to get to that spot, but in the time that it took you to get there, the turtle will have traveled another .01m, so you have to go there.... etc etc.

I just picked up one the other day. j00 = wr0ng!