Thread: Zeno's stadium paradox
09-12-2004, 09:37 PM #1
Zeno's stadium paradox
Another thread reminded me of this.....I'm sure most of you have heard this, but just in case you forgot...
It is impossible to traverse a stadium because before you cover the whole stadium, you must cover the half; and before you cover the half, you must cover the quarter; before the quarter, the eighth; etc. etc. to infinity. Therefore, to traverse a stadium is to traverse an infinite number of halves in a finite time. The same argument may be applied to any spatial interval.
Another way to look at it is this.
say im in a square room with my back against a wall and I want to get to the wall on the other side of the room. First, I half to walk half way there, then half way again from that point, then half way from that point...So I will never get to the other wall. Things that make you go hmmmm......
09-12-2004, 09:43 PM #2
well he knew little about calculus it seems. as he approaches more half of halfs etc. the time it takes him to traverse that half goes to zero. of course, i think calc came a little after his time...but i dunno for sure
09-12-2004, 09:53 PM #3
09-12-2004, 10:04 PM #4say im in a square room with my back against a wall and I want to get to the wall on the other side of the room.
i also dont see the point in this post. yea, you cant ever reach a destination if you always travel half the distance.
Last edited by Psychotron; 09-12-2004 at 10:06 PM.
09-12-2004, 10:14 PM #5
the point is straight forward. Logically, you would never reach the wall. by observation, you know that you do reach the wall. hence the paradox.
09-12-2004, 10:24 PM #6
This problem is a common sense fallacy and was proven so after the invention of Calculus.
09-13-2004, 05:56 AM #7Originally Posted by symatech
09-13-2004, 08:26 AM #8
I'll reiterate. The key is the infinite number of iterations.
Originally Posted by chicamahomicoOriginally Posted by Psychotron
09-13-2004, 11:32 AM #9
This boils down to time intervals and convergent and divergent series:
1/1 + 1/2 + 1/4 + 1/8 + 1/16 .... converges at 2
1/1 + 1/2 + 1/3 + 1/4 + 1/5 .... diverges to infinity
The first series represents the intervals travelled while crossing the stadium. Therefore we know he's traveling a finite distance. Assume he's traveling at a constant speed. Finite distance / constant speed = finite amount of time
No calculus needed (in the explanation).
09-13-2004, 11:38 AM #10
but it doesnt answer the question. finite distance\constant speed perhaps equals a finite amount of time but it doesnt explain how he is able to cross the infinite number of halfs.
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