Just like
Vincent Van Gogh and Emily Dickenson, Zeno of Elea and his paradoxes were appreciated
after his death. In fact, many mathematicians today are picking up where he
left off. Zeno proposed the idea that you can divide the finite distance
between two points infinitely. He was the first person in history to shed light
on the problem with infinity (Dowden).
His most
famous example was that of a race between a tortoise and the legendary warrior Achilles.
Zeno claimed that you can continue halving the distance between the tortoise
and Achilles, causing Achilles never to reach the tortoise, because he must
cross half of the distance, and then half of that distance, and so on, ad infinitum.
However, this
paradox does not pass the test of our daily experience. Following Zeno’s logic,
there would be no such thing as motion, because to get somewhere, a car would
have to cross infinite halves of halves of halves. However, in our world, cars do make it to their destinations, and the
faster the car can move, the sooner it will reach its goal. This car example fits our common sense, even
though we may not be able to mathematically explain how the car traveled
through infinity – that is, the infinite number of points between the departure
and the destination.
If you think
that those ideas are wild, then check out these crazy stories written about
him. Not much is known about his life. It is assumed that he was born around
490 BCE, in a city called Elea in southern Italy. He was the student of Parmenides, and Plato
stated that Zeno’s paradoxes all came from his teacher’s ideas. Parmenides
emphasized the distinction between appearance and reality, and he believed that
our perception of reality is deceptive and does not report what is real
(Dowden).
Plato also
claimed that Zeno was caught aiding the rebellion against the tyrant of Elea.
Zeno was eventually arrested, and when questioned about his supplying weapons
to the opposition, he tricked the tyrant into getting closer to him, whereupon
he bit him and wouldn’t let go until he was stabbed (Dowden). After reading all
these crazy rumors, do you wonder about Plato’s credibility in reporting Zeno’s
life?
Dowden,
Bradley. "Internet Encyclopedia of Philosophy." Zeno’s
Paradoxes []. N.p., 7 June 2009. Web. 25 Nov. 2013.
<http://www.iep.utm.edu/zeno-par/>.
Hiba, your example of the car and zeno's paradox definitely fits the contradiction we experience in trying to resolve these paradoxes. And this makes it more difficult trying to understand infinity from the rationalistic point of view because it makes no sense. Though i have been able to appreciate infinity better especially with respect to these paradoxes from a rationalistic point of view, empiricism helps my senses better.
ReplyDeleteThat's right Tessy, I remember in psychology we learnt that our rationale (common sense) is very strong. It sometimes lets our guard down when our inner intuition senses danger. I know we are not talking danger here but our rational thinking is very strong. In class, each time we seem to grasp Zeno's paradox (i.e, mathematically) someone mentions how the pictures we view in class don't make sense, and then the confusion starts again.
DeleteHiba,
ReplyDeleteYou mentioned, “This car example fits our common sense, even though we may not be able to mathematically explain how the car traveled through infinity – that is, the infinite number of points between the departure and the destination.” However, calculating the speed, velocity, and acceleration (physics) is possible. If we measure the amount of time/ steps it takes from one point within infinity to another, then we can measure how the car got from one place to another. Of course the speed of the car could vary.
Sara,
ReplyDeleteWhen it comes to the car, you are right, we can explain the distance from A to B. However, we cannot count all the infinite points in between, which is where Zeno went wrong.
Imagine we have a number line with points 1 to 2; if a normal person is crossing the line, they will simply take a huge step from 1 to 2.
However, when Zeno is crossing the gap, he will say that we have to step on every little tick mark between 1 to 2. In this case, it makes sense that Achilles will not be able to catch up to the tortoise: he's too busy trying to step on all the infinite points.
That was what I was talking about: we may not know how many infinite tick marks there are between point A and B, or when we crossed over them. or how we did it, but we do know that it's possible to make it to the other side.