Paradoxes
In the paradox of Achilles and the Tortoise, Achilles is in a footrace with the tortoise (because now tortoises can communicate with humans?). Achilles allows the tortoise a head start of 100 meters, for example. 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 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, say, 10 meters. 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....
(Okay, so you want to get to a door to go somewhere, yeah?) But before you can get to it, you have to walk halfway to the door, then go back, and walk halfway plus half of the halfway, and then you have to go back and walk halfway, plus half of the half(a quarter), plus half of the half of the half (one eight) and so on... You can never reach the door, just get infinitely close...
In the arrow paradox (also known as the fletcher's paradox), Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that in any one (durationless) instant of time, the arrow is neither moving to where it is, nor to where it is not.[13] It cannot move to where it is not, because no time elapses for it to move there; it cannot move to where it is, because it is already there. In other words, at every instant of time there is no motion occurring. If everything is motionless at every instant, and time is entirely composed of instants, then motion is impossible. (So every time we move, we don't move? God, this is getting confusing)
