Look at the comments on this paper.
Zeno of Elea, born approximately 490-485 BC, was a follower of Parmenides, said to be his favorite. He published a book on philosophical puzzles and paradoxes, which is a defense of Parmenides' theory of oneness (Kirk, Raven, Schofield, p. 248) According to Aristotle, Zeno was the first to use dialectic, the method of interrogation and analysis used later by Socrates. His method was to challenge a person's beliefs by reducing them to absurdity or showing that they conflicted with other beliefs.
Zeno is most well-known for his four paradoxes of motion, which argue against the possibility of motion as we see it. The Dichotomy, otherwise known as the Stadium, argues that a runner going from point A to point B will never be able to reach his goal because he must traverse an infinite distance. Similarly, the paradox of Achilles and the Tortoise shows that the faster Achilles can never catch up to the slower tortoise as long as the tortoise has had a head start of a certain distance, because Achilles can only reach as far as the last place the tortoise has been. These two paradoxes refute the assumption that space and time are infinitely divisible.
The second pair of paradoxes, the Arrow and the Moving Rows, show that space and time cannot consist of indivisible minima, and that motion cannot be made up of immobilities. His discussion of the Arrow concludes that an object is at rest throughout its entire movement. The paradox of the moving rows describes a different aspect of movement, arguing that if two objects moving through equal spaces in equal times pass each other in opposite directions, they will pass each other in the same space in half the time.
Each of Zeno's paradoxes can be explained in some way by more modern concepts of thought and motion, and they have been further explained and analysed from Aristotle's time to the modern day. (See SA article Nov. 1994) Mathematicians explain the Stadium and Achilles and the Tortoise in terms of a geometric progression converging to zero. The points in this type of sequence (for example, 1/2, 1/4, 1/8, ...) get infinitely smaller, but never actually reach the zero point. The sum of these numbers still gives us the total distance travelled, which is equal to one unit. Similarly, the sum of the sequence 1+1/2 +1/4+1/8... becomes 2. In reality, we can say that time is also infinitely divisible and can be measured in whole-second increments as above, so it is possible for the runner to reach his goal and for Achilles to catch up to the tortoise.
Physicists explain the Arrow paradox in terms of instantaneous velocity. An object when seen at a particular instant, as in a photograph, appears to be standing still, yet its entire motion is made up of a series of these instantaneous photos. We can explain this by saying the object is still moving, even when it appears to be at rest, it is just moving at a rate that is too small for us to perceive.
The Moving Rows paradox (now here's the winner) was a puzzle when seen by Zeno, but does not seem as complicated to us if we think of all motion as being relative. While Zeno measured each row's movement as an absolute quantity which appeared to defy the laws of time and movement, we can see that the objects in row B logically move past the moving row C in half the time it takes to pass the standing row A. Zeno's method of argument influenced later thought and led to a more analytical approach to the world as perceived through the senses. His use of dialectic as an approach to science has received much discussion from Plato to Pericles to modern students and analysts.