Zeno

I interviewed the famous Zeno of Elea and talked to him about his life and mathematical achievements. He told me about his paradoxes. The interview follows this paragraph.

Drew: So Zeno, if I may call you Zeno, where were you born and when?

Zeno: Well Drew, I was born in the Greek Colony of Elea which is situated in southern Italy. I was born in about the year 495 B.C.

Drew: So Zeno, did you have any real teachers or did you come up with your paradoxes on your own?

Zeno: Actually, my first teacher was Parmenides, who was a philosopher. And with him I traveled to Athens where I met Socrates and eventually got into Plato's book Parmenides. Actually apart from what many think I am not a mathematician but a philosopher and logician.

Drew: Then I guess we will have to change our column title, huh. Well back to math, what do you think is your best stumper for mathematicians?

Zeno: Well, I would have to say that The Achilles is the best stumper.

Drew: And how exactly does that go?

Zeno: Well if you start a tortoise ahead of Achilles in a race, then Achilles will never get ahead of the tortoise.

Drew: How is that possible? Isn't Achilles the fastest runner?

Zeno: It's very possible. Achilles first has to make it to where the tortoise starts. By that time, the tortoise will have moved forward a little, and then Achilles will have to reach the spot where the tortoise just made it to. Then it will just keep happening over and over again.

Drew: So Zeno, How did people react to your theories and paradoxes?

Zeno: Well even up to today people are trying to figure out ways to counter my paradoxes.

Drew: Wow! I guess it really does make sense. Do you have any other examples of that?

Zeno: Yes, actually I do. If you want to cross a room, you have to get to half the distance of the room. Then to get to that distance you half to go half of that, which would be one quarter of the distance. If you keep halving the distance you have to go you never get anywhere. So in numbers this looks like; 1/2 + 1/4 + 1/8 + 1/16 + 1/32 + 1/64 + 1/128 + 1/256.......... and this goes on and on infinitely. But if you add all the numbers up, you don't get one, and so you have not gone all the way. Therefore, is it that we can't move or that we never reach our destination?

Drew: Do you realize what you just said, 'We cannot ever reach our destination?' Then how did you get here for this interview?

Zeno: I didn't say it made sense but if you do the problem logically then you come to a conclusion that tells us we cannot move.

Drew: Wow, you are a really smart guy, and it does all make sense but it stumps me. Thanks for coming to have this interview with me. I still don't know how you got here since we can't move. But it was nice talking with you.

Later that week Zeno was tortured for conspiracy against the ruler of Elea. (That's how it is written that he died).