Zeno of Elea created one of the first and most perduring paradoxes

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In summary, Zeno's paradox is a thought experiment that challenges the idea that time and movement exist, and that it is possible to walk or move from one point to another in a certain amount of time.
  • #1
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Many of you will know that Zeno of Elea created one of the first and most perduring paradoxes of all. If any of you think you have solved it.....you ARE wrong. sorry. But you can try it:

Imagin you want to fo from here to there and th distance is one meter (it works with any distance and directiona and speed), you walk, and get their. but, no. First of all, to get to the other place you have to go thorugh the whole meter, but before the whole meter, you have to cross half of it. Now you are in the middle. Then, you have to go forward, but before crossign the half you have to, you cross the half of that half. Then the half of that half. And the half of that, and that one two... But, no. Because before getting to the half, you have to get to the half of the first half, but before to it's half, and before to it's half, and so on.

So in actual fact, you can't move, so motion does not exist, so time does not exist.

I proved mine, (well, Zeno did) now someone has to disprove.
 
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  • #2
Going halfway each time takes half as much time. You can perform an infinite number of acts in a finite amount of time if the acts are small enough. For example, say you are moving at 1 meter/second. The first half meter takes you half a second; the next quarter meter takes you a quarter second; the next eighth meter takes you an eighth of a second. The sum is the sum of an infinite geometric series with first term 1/2 and ratio 1/2, which is half the sum of an infinite geometric series with first term 1 and ratio 1/2 so it sums to (1/2) * 1/(1-1/2) = 1 second.
 
  • #3
BicycleTree said:
Going halfway each time takes half as much time. You can perform an infinite number of acts in a finite amount of time if the acts are small enough. For example, say you are moving at 1 meter/second. The first half meter takes you half a second; the next quarter meter takes you a quarter second; the next eighth meter takes you an eighth of a second. The sum is the sum of an infinite geometric series with first term 1/2 and ratio 1/2, which is half the sum of an infinite geometric series with first term 1 and ratio 1/2 so it sums to (1/2) * 1/(1-1/2) = 1 second.

what if the time you take in each half is always the same?

actually, there is no time, because you can't move, so you can't use time to disprove it when this disproves time.
 
  • #4
The time is not the same because at a constant speed the amount of time it takes to travel a distance is proportional to the distance.

Your argument is depressingly circular. "There is no time because of my argument; and your argument is wrong because there is no time." Petitio principii.
 
  • #5
Proof by contradiction: my fingers moved in order to type this message!
 
  • #6
Also, the series [tex]\sum_{i=1}^{\infty}\frac{1}{2^i}[/tex] is convergent.
 
  • #7
BicycleTree said:
The time is not the same because at a constant speed the amount of time it takes to travel a distance is proportional to the distance.

Your argument is depressingly circular. "There is no time because of my argument; and your argument is wrong because there is no time." Petitio principii.

what if the speed isn't constant? I never sai dit was...what if the time taken to each half was the same as the last one?
 
  • #8
All this seems to disprove is the usefulness of the concept of quantifiable time and distance in all circumstances.

If time and movement do not exist, could you present an alternative to how someone appears to get from A to B in x seconds?
 
  • #9
matthyaouw said:
All this seems to disprove is the usefulness of the concept of quantifiable time and distance in all circumstances.

If time and movement do not exist, could you present an alternative to how someone appears to get from A to B in x seconds?

that question makes no sense. Becuase time and distance, or better said, dimensions, are what state that A and B exist, and that there is a space (dimension) between them, and that x seconds exist.
 
  • #10
<<<GUILLE>>> said:
what if the speed isn't constant? I never sai dit was...what if the time taken to each half was the same as the last one?
If the time taken to complete each half was the same as the time taken to complete the last one, then the person would be slowing down geometrically and would indeed never reach the door. In most circumstances in the real world, however, the time needed for each succeeding half is about half the time of the previous one because the walker usually moves at about a constant rate.
 
  • #11
BicycleTree said:
If the time taken to complete each half was the same as the time taken to complete the last one, then the person would be slowing down geometrically and would indeed never reach the door. In most circumstances in the real world, however, the time needed for each succeeding half is about half the time of the previous one because the walker usually moves at about a constant rate.

true. But your mathematics used before (upper posts) works if indeed, we move. The fact of all, is that we don't even move, so time can't pass 8or better said, doesn't pass) and there is no dimensional motion.
 
  • #12
Your argument is entirely circular and it is not worth explaining it again to you.
 
  • #13
BicycleTree said:
Your argument is entirely circular and it is not worth explaining it again to you.

life is circular. does that mean it is wrong? no. there are many circular and infinite things in the universe.
 
  • #14
Ive seen a very simular thing but with a dart board and throwing darts at it.
 
  • #15
that is paradigma and your explenation about time and distance are close to nonsense. you cannot say that time does not exist just because you taught (or relatively to you) it doesn't.

while on the other hand, time and distance according to the paradigm does not exist. and using that hypotesis it is true. yet it does not produce a useful theory.
 
  • #16
ArielGenesis said:
that is paradigma and your explenation about time and distance are close to nonsense. you cannot say that time does not exist just because you taught (or relatively to you) it doesn't.

while on the other hand, time and distance according to the paradigm does not exist. and using that hypotesis it is true. yet it does not produce a useful theory.

I know it doesn't, I just posted it because I wanted comments on it, or even solutions to it. I just state that for this paradox dimensions do not exists. but of course they do.
 
  • #17
my assumption is that there is a limit of half ^ n, until it is small enough to be traveled in an instant.
 

Related to Zeno of Elea created one of the first and most perduring paradoxes

1. Who is Zeno of Elea?

Zeno of Elea was a Greek philosopher who lived in the 5th century BCE. He is known for his paradoxes, which were thought experiments used to challenge and question common beliefs and ideas.

2. What is a paradox?

A paradox is a statement or situation that seems to contradict itself or go against common sense, but upon closer examination, may hold some truth or reveal a deeper understanding of a concept.

3. What is the paradox created by Zeno of Elea?

Zeno's most famous paradox, also known as the "Achilles and the Tortoise" paradox, states that in a race between Achilles, the fastest runner in the world, and a tortoise, Achilles will never be able to overtake the tortoise if the tortoise is given a head start, no matter how small. This is because Achilles must first reach the point where the tortoise started, but by the time he reaches that point, the tortoise will have moved ahead, and this process will continue infinitely.

4. How did Zeno's paradox challenge traditional thought?

Zeno's paradox challenged the idea of motion and change, which were believed to be continuous and infinite. His paradox suggested that motion and change were actually made up of infinitely small moments, and therefore, could not truly exist.

5. How has Zeno's paradox influenced modern mathematics and philosophy?

Zeno's paradox has had a significant impact on modern mathematics and philosophy. It has led to the development of the concept of limits, which is essential in calculus and other areas of mathematics. It has also sparked debates and discussions about the nature of time, space, and motion, and continues to inspire new ways of thinking about these concepts today.

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