Could someone please help me with Zeno's dichotomy paradox?

Question

I just started philosophy and our teacher gave us Zeno's dichotomy paradox, where he states that movement is an illusion. Could someone please explain to me in simple terms why it is incorrect?

Answer 1

The best explanation that I could give based on my learning is this... Zeno's Dichotomy Paradox was Zeno's way of attempting to explain that motion is an illiusion based on the idea that one could never actually traverse a "set" distance. This is because the individual must first travel half the distance and in order to travel half the distance he must first travel two quarters of the distance and so on. Until, the person is actually travelling such small distances that he is not moving at all. The reason that his idea must be flawed is because if an observer watches a person walking the person does, in fact, travel from point A to point B. Therefore, motion is a reality.

Answer 2

Zeno gives the example of Achilles racing against the turtle. The turtle is 1 000 meters ahead of Achilles and at each step, Achilles is overtaking one half of the distance separating him from the turtle.
So at the first step, the turtle is 500 meters ahead, 250 at the second, 125 at the third, etc... But one can see Achilles will never catch up to the turtle.
This is wrong because in reality, Achilles' speed would have to be diminishing for that to happen. Newtonian physics will show this doesn't work. The turtle is 1 000 meters ahead and moves at 1 meter a second. Achilles moves at 100 meters a second. So at the first second, Achilles is at 100 meters, while the turtle is at 1 001. At the second, its 200 meters, against 1 002, etc... So you can then see the distance separating them diminishes constantly, and not by a fraction. Achilles will overtake the turtle in the 11th second, when he's traveled 1 100 meters and the turtle is at point 1 011.
This sophism of Zeno is based on the idea of 'dividing the distance by half'. If you make a chart of the distance traveled in Newtonian terms, you will find Achilles' speed is actually diminishing as you go along. (From 500, to 250, to 125, etc...)

Answer 3

Draw two lines 12 inches from one another. draw a line half way between that - at 6 inches. Another at 3. Another at 1.5 inches. What the idea is is that you have to get to the halfway point before you can move through space. Therefore you cannot move. Can be applied to time as well.

Answer 4

Refer to http://en.wikipedia.org/wiki/Zeno's_paradox

It is bound to be helpful.