Achilles and the Tortoise in one of Zeno’s paradoxes. It appears to demonstrate that even the fastest of runners, Achilles, could not catch the slowest of creatures, the tortoise, if the tortoise were given a head start.

To get from one place to another takes time. If the distance between the two is very small, or the speed of travel is very fast, then it may take a very short amount of time, but it will take some time nevertheless. It is impossible to move from one point to another instantaneously.

To catch someone, you need to cross the distance between you and them, you need to move from where you are to where they are. If there is any distance between you at all, then this will take time.

Suppose that the person that you are trying to catch is moving away from you, then in the time that it takes you to get from where you are to where they are, they will have moved on. If you begin at point A, and they begin at point B, then by the time you reach point B they will be at point C. The person that you are trying to catch will no longer be at the point that you have reached.

To catch them, then, you will need to reach the point that they are now at, you will have to get from point B to point C. Doing so, though, will again take time. Point C is at a distance from point B, and so by the time you have reached point C, your target will have reached point D. This process can be repeated ad infinitum, without you ever catching your target.

Zeno illustrated this with the example of Achilles and the tortoise. If, in a race, the tortoise, who moves slowly, is given a head-start on Achilles, then no matter how quickly Achilles runs he will never catch the tortoise.

[Edited on 7/12/2005 by Mega X.exe]

[Edited on 7/12/2005 by Mega X.exe]

Yeah, this one doesn\'t fit together. Unless the tortoise was the smallest distance possible away from the finish when Achilles started and Achilles could not teleport, and also that the tortoise was in anyway moving, it is possible for Achilles to win. Let\'s say, Achilles can travel at the fastest rate imaginable, but short of teleportation. If the tortoise moves at a rate of 1 peg per [x amount of time], and there are 2 pegs between him and the finish line, it is still possible that as he could be beaten if Achilles ran the entire race course as the tortoise walked the first peg. So therefore, unless the situation matches the first situation I gave, I don\'t think this theory holds true.

Yeah, this doesn\'t make sense to me either. The passage seemed to be trying to prove that a faster object can\'t catch a slower object if the slower had a head start, right? But then the topic seems to have them moving at the same speed (Faster reaches B when slower reaches C), which would mean that they had to be moving at the exact same rate. So their wouldn\'t be a faster or a slower...

The tortoise, being one point ahead of Achilles and all points being the same distance apart, could still be caught if Achilles was only twice as fast, right?