i just finished an excellent book - the emperor's children - and in the book is the mention of something called Zeno's Paradox - so i looked into exactly what it was.
Basically - it means we will never reach our goal - the finish line - the end - we will always be halfway there.
it claims if you throw, say a ball - towards a wall (i chose a ball because it rhymes. with wall) - the closest it will ever get is halfway there. so if it is ten feet it will turn into 5 then 2.5 then 1.25 then .625 then .3125 and it will continue to only be half way there - forever.
it says we will never meet our destination.
what do you think of this claim of Zeno's Paradox? do you think this is true? will we ever get there? and then what is our destination? what is there?
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Zeno was this really old guy who lived in ancient Greece and taught math. Basically he came up with thousands of paradoxes just like this one for his students. The point of the paradox is that it is not true. That's the basis. And Zeno came up with them to force his students to prove why they were wrong. So the whole story isn't true and it takes a bunch of mathematical and logical principles to prove it.
The destination thing is really more of an opinion. I think we can ultimately reach our destination, goals, etc. just that once we get there it's not always what we imagined it to be.
I kind of agree with anna. i believe that everything happens for a reason. i believe that every decision that we make, no matter what choice it is, will take us to this ultimate destination in one form or another. say that we were destined to marry a certain person. if we were to marry a different person, ultimately, that marriage will fail, no matter how many years go by. but we will eventually be lead to the right person. so those are my two cents.
A paradox is not by definition false. A paradox is a demonstration of a theory that can be proven neither true nor false.
Mr. Reck - so what do you think about the paradox? do you think it is true?
I think the very prospect of infinity is a terrifying one. It makes each and every one of us both miniscule and repetitious. If infinity exists, then you and I and everyone exist many times over without end. If the universe is truly without boundaries, this is the ramification. Zeno's paradox suggests almost the inverse, that instead of an outward infinity, the universe's infinities are in its deconstruction from what we can see to the smallest (and maybe the smallest doesn't really exist if the paradox holds true) particle. Scary stuff. If anyone's interested in infinity, definitely read Jorge Luis Borges!
I think Zeno's paradox is true for most things except when the situation can be measured. Like throwing the ball against the wall. It will reach the full 10 feet if it is thrown with enough force. However, if it isn't, it will fall short of the ten feet but not necessarily half way.
Another example in which Zeno's paradox is wrong when applied to measured situations is on road trips. On road trips, there are the start and destination points. Once someone gets to the destination, that's it. They reached their goal. The traveler didn't go halfway on the road trip and say, "No I can't make it." The trip was a measured distance and so the traveler could reach the goal.
But as I said before, Zeno's paradox is true under circumstances that can't be measured. Because in those situations, things will always come up to make the finish line so impossible to reach. And if we do reach the finish line we realize that it wasn't the goal we wanted and so we make a new goal. We reached, in a way, halfway of the original goal. But the goals never end; one goal lends itself to another. And so we will never actually reach the goal.
For example, as teenagers, we have goals for our futures, what college we will go to, what career we'll have. And so right now, we're working towards that goal. But is the goal just to become whatever career you want? No, it is to be in that career and to be HAPPY, satisfied with life. But as of now, our career goals are mostly based on the pros of the career, not on the cons. We have a mostly idealized view of the career. And so when we actually "reach" the finish line, we'll realize that the career wasn’t everything we thought it'll be and so we'll make another goal in hopes that achieving the new goal will make us happy. And so, the cycle continues.
Zeno's paradox is true, but only under situations that can’t be physically or mathematically measured.
I don't think Zeno is right. I think that no matter what the destination is, physical, mental, emotional, or whatever, can reach it. We aren't always just going to be half way there.
awww... you guys are so optimistic! ( just had to say that )and i agree - no matter what the destination is - if you work to get there, you will get there. eventually. and maybe recognizing that you are halfway there - as in almost there - can help a person along the way.
I do not really understand this theory. Maybe im being a pessimist but dont we reach the end (death) and doesnt the ball always eventually reach the wall? etc.. This also is true for goals as others say, I believe that anything somoene puts their mid to can be reached.
i think that any destination can be reached. it depends on yourself. we aren't just going to be halfway there...i don't think that's even possible.
I think that Zeno was a jerk that only wanted to mess with our minds and make us question our sanity.
But to add my opinions on his paradox, i think it is incorrect. We will eventually reach the end. Whether its the glorious ending we expected or not, its still were we end. We WILL reach it. And the ball example just goes to prove that or else nobody would want to throw the ball in the first place, 'cause they would never get it back.
1+1=2
There, its not true.
But wait...
1+1=Window
I agree with what Mr. Reck said above. Sometimes I find myself thinking about paradoxes like these and it is scary. Some people theorize that the Big Bang will reverse and the universe will collapse upon itself. What if this cycle of Bang and Collapse continues on and on. What if that cycle was infinite. How obsolete does that make us? What is time? What am I? Jeff said it right, Zeno made me go insane thinking about this.
Zeno's paradox is fascinating in that the logic of his argument (that in order to reach a goal point, you must first reach halfway and will infinitely half the distance instead of reaching it) yet we know its not true. When we release an arrow from a bow, it makes contact with the target.
A way that Zeno's paradox can theoretically loop-holed is this: What if we have a goal, but then we change it to be twice our original goal? The original goal becomes the halfway point of the new goal, therefore by attempting to reach the new goal, we can reach the original goal.
Dana "Sunshine"
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