What Is Zeno’s Dichotomy Paradox? – Colm Kelleher

What is Zeno’s Dichotomy Paradox? – Colm Kelleher

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Can you ever travel from one place to another? Ancient Greek philosopher Zeno of Elea gave a convincing argument that all motion is impossible – but where’s the flaw in his logic? Colm Kelleher illustrates how to resolve Zeno’s Dichotomy Paradox.

Lesson by Colm Kelleher, animation by Buzzco Associates, inc. paradox


This Post Has 31 Comments
  1. This isn't true, if you keep adding half of the remaining distance you won't actually reach the total distance. The more you divide the more closer you will get to the distance, but you will never actually reach that distance. You can thin about this paradox in this way: the equation the video has described goes like this: X= 1/2+1/4+1/8…. So on. Lets say take the value "1/2" Now to reach 1 you have to add another 1/2, but everything to the right of "1/2" added up together doesn't actually equal 1/2. You can use this same logic for any of the number in this equation. So, X will never equal one mile.

  2. But what about this version of the paradox instead:
    Note: the whole goal is to get to 1 no matter what the equations say we are try to use the sum to get towards 1 without skiping it on the infinite terms of the sums.
    If the goal is to get to one by only 1/3 each per term
    But on the calculator if you put the equation as I did above on the calculator then you get only about 1/2.
    How will you ever get to one? another example:
    but on the calculator it says about 1/3
    So what term will it take to get the last one term if it was like this or a example like this…
    sum(1/x^n) = 1/(x-1) if and only if n equals to infinity.
    I found this the other day messing with math my self.
    The only the acceptable conclusion must be the sum(1/2^n)=1
    Dam convergent series.

  3. I have the answer: 1/2 + 1/4 + 1/8 + … + 1/2n = 2n-1/2n approximately 1 and it not infinity

    Explain: because 1/2 = 1 – 1/2 ; 1/4 =1/2 – 1/4 ;1/8 = 1/4 – 1/8 ; ….; and 1/2n = 1/2n-1 – 1/2n

    SO: 1/2 + 1/4 + 1/8 + … + 1/2n= 1 – 1/2 + 1/2 – 1/4 + 1/4 – 1/8+….+ 1/2n-1 – 1/2n

    Shorten the equation so we have the result: 1/2 + 1/4 + 1/8 + … + 1/2n= 1 – 1/2n = 2n-1/2n approximately 1 so the paradox has been solved.

  4. Zeno was on his way to the park to pluck the excellent quality of weed he had been smoking lately.

  5. At the time this may have been a thing but now I feel a measurement can only be to the smallest divisible part. Say a particle, this would argue that it is finite measurement as such an upper limit.

  6. The thing that confuses me is if he walks half of the distance he walked, he will never be able to reach to point zero ( which is finishing the road I mean by zero). He is suppose to reach the number Upsilon because it is not possible to reach zero by dividing 2 like we say in limit.We just use the number Upsilon to say closest value to zero. He shouldn’t be able to reach the point he tries to go since it’s impossible to reach that point right?

  7. Um wow… Good paradox so I thought the answer wasn't infinity. It will be infinity if he had remain walking. But he stops and so does his infinity values to finity right? 😂😂

  8. If you added all these you just get closer and closer to 1 but never actually get there just get even closer

  9. An old man walks into a hair saloon. Asks the hairdresser : what do you have?
    He said.. "Cutting and Shaving "

    The old man replied

    "Give me a plate each…. ! "

  10. Whoe anyone one else notice that if you put this in the square terms like the example it forms fibonacci sequence.

  11. The reason we observe motion in life, there is a limit to the minimum length in universe… in zeno's paradox there is no limit hence the motion cannot be completed. We cannot define measurement with %100 accuracy ever in our physical world, because we dont know the limit, the limit of minimum length in real universe. We have to use axioms and use all numbers on a reference system. Even math is a reference system, there are axioms you blindly accept in order to solve things… now you may ask hey it works in the real world, it does give you an approximate answer on results in fact its the best reference system we got, we have not discovered any other system that gives us more accurate results, probably we dont need more accurate results yet.

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