Zeno's Paradox

Discussion in 'Physics & Math' started by Xenu, Jun 22, 2002.

  1. wesmorris Nerd Overlord - we(s):1 of N Valued Senior Member

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    9,846
    NOOOOOOOOOOO!!!!!!!!!!!!!!!!!!!!!!!!

    Well on second thought, what are you going to call the thread?
     
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  3. Xenu BBS Whore Registered Senior Member

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    Holy smokes, this thread is still going!

    I haven't had time to read all 200 and some posts, but let me touch on what I've glanced over...

    Yes, there are a number of Zeno's Paradoxes. I picked the simplist one so that I could get down to a basic level more quickly.

    I think the whole 0.9999 = 1 issue is very pertinent to the issue, glad to see a new thread about this.

    A number of you are talking about how there is no paradox in the real world, and I'd say you are right, there is no paradox. The paradox is in mathematics trying to define things in the real world.

    Even deeper the paradox resides in mathematics trying to incorporate infinities. It can approximate this by using things called limits, but on a basic math level (such as dividing a line segment) it can't handle without contradiction.

    And no, this problems isn't simple or cut-and-dry rational, just look at how many posts there are between the two threads, something like 400 and some. If all these brilliant minds can't come to a consensus on this, then there's got to be something amiss in the math system.
     
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  5. wesmorris Nerd Overlord - we(s):1 of N Valued Senior Member

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    Irrisistable urge to point out the obvious: Wouldn't the distance measurement between two points lose all meaning at the distance of the width of the atom itself? Wouldn't it become undefined at that point? Hehe.. doesn't eh problem become "the car" at that point? Hell it become that problem at the molecular level eh? (sorry if someone already hit that angle)
    Excellent point. Nice to see it illustrated so convincingly.
     
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  7. StrangeDays Registered Senior Member

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    Personally, I don't see any paradox in the math or the real-world application thereof. I see it as being counterintuitive but not demonstrably paradoxical.
    Sometimes it takes a while for minds to come to a consensus when logic and intuition clash. Take a look at the probability thread, where everyone has their own vision of a solution but we can't seem to communicate it effectively to each other.

    In problems like these, what is needed is someone with enough clarity and language skills to state the solution in a way that causes a light bulb to come on in other people's heads. That's a skill I wish I had.
     
    Last edited: Jun 21, 2003
  8. yayacatfight Registered Senior Member

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    this thread rocks!

    totally agree with Xenu, while we humans struggle to explain everything to our satisfaction, these paradoxes point to where we come up short.

    can anyone recommend any interesting books on the subject? i'd love to read more about infinity, and how it throws a wrench in the math machinery.
     
  9. drnihili Registered Senior Member

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    I'm currently working my way through A. W. Moore The Infinite. It's pretty good.
     
  10. yayacatfight Registered Senior Member

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    thanks, i'll check that out.
     
  11. rabbit Registered Member

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    "But, whether true or false, my opinion is that in the world of knowledge the idea of good appears last of all, and is seen only with an effort; and, when seen, is also inferred to be the universal author of all things beautiful and right, parent of light and of the lord of light in this visible world, and the immediate source of reason and truth in the intellectual; and that this is the power upon which he who would act rationally, either in public or private life must have his eye fixed." - Plato (the real reason the name Zeno survived)

    Has anyone even considered that Zeno may have been correct afterall? All arguments about 1 and .999... aside, I believe that in order for Zeno to have any possible credibility all things would indeed HAVE to be equal to one. In my opinion, this is his central thesis. Therefore, any other observances would have to be nothing more than persistant illusion(s). Obviously, this difficult concept immediately collides with the human concept of individuality and will almost always invoke an incredulous response of disbelief.

    However, please consider that even Einstein insisted that "time" was nothing more than a persistant illusion. If you lived in the past it would appear to you to be the present. Possibly, the idea that everything is so much an individual element is also nothing more than just such an illusion.

    It is commonly accepted among most modern science that this Universe (of which most of us belong) began with an amazing and unexplainable singularity...ONE thing! Is it not also reasonable to conjecture that we may also only be shadows cast in a play of one?
     
  12. HallsofIvy Registered Senior Member

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    Do you have a reference for that? It seems very strange that he would declare that the universe is a "four dimensional space-time continuum" if he believed that time was an illusion.
     
  13. rabbit Registered Member

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    "The distinction between past, present and future is only an illusion, however persistent."

    Albert Einstein l879-l955; letters to Michelangelo Besso, March 1955
     
  14. wesmorris Nerd Overlord - we(s):1 of N Valued Senior Member

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    My translation of his point as a Haiku!:

    The time is right now.

    Look, the time is still right now.

    When is it later?
     
  15. StrangeDays Registered Senior Member

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    "No matter where you go, there you are." - Buckaroo Banzai
    Therefore, space is illusory.
     
  16. drnihili Registered Senior Member

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    Time present and time past
    Are both perhaps present in time future,
    And time future contained in time past.
    If all time is eternally present
    All time is unredeemable.
    What might have been is an abstraction
    Remaining a perpetual possibility
    Only in a world of speculation.
    What might have been and what has been
    Point to one end, which is always present.


    T. S. Eliot
     
  17. rabbit Registered Member

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    Well, I wish that I could subscribe to your notion of a human experience without paradox because that would certainly make it an easier journey to comprehend. Unfortunately, I believe that the human experience is filled with paradox and may in fact be a paradox in itself. I think that we have a startling tendency to just kind of ignore anything that we can't explain (scientific methods included) I have a few simple examples and must admit that they are somewhat abstract but here goes:

    "Matter cannot be created nor destroyed" - Well, that has to be a misnomer doesn't it?

    "What came first the chicken or the egg?"

    I mean, lets all be honest here...Mathematics and Science are obviously falling short of "reality" because of paradox such as Zeno's. But then again, the really hard to face "reality" is that Mathematics and Science are merely the limited observations made by and interpreted by the limited human mind. I think that it is a little bit presumptious for us to consider our minds to contain the ultimate truth while ignoring or creating imaginary rules and numbers to satisfy shortcomings of such limited yet extremely useful tools such as science and mathematics.
     
  18. HallsofIvy Registered Senior Member

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    Zeno's paradoxes were "solved" with the advent of calculus.

    Of course, there are new paradoxes: Russel's paradox lead to a revolution in basic set theory. Paradoxes are one way mathematics advances.
     
  19. HallsofIvy Registered Senior Member

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    That is NOT the same as saying that time is an illusion! Surely Einstein, of all people, understood that.
     
  20. wesmorris Nerd Overlord - we(s):1 of N Valued Senior Member

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    You missed that I was attempting to assert a distinction between objective reality and the subjective experience. I was attempting to say that "while paradox in objective reality is basically disallowed, the subjective experience is chalked full of them". Er, that would be the implication from what I was saying anyway. I basically concur that consciousness itself is a paradox of sorts.
     
  21. wesmorris Nerd Overlord - we(s):1 of N Valued Senior Member

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    I like mine better! Hehe.. who's your narcissistic daddy eh? LOL

    I do like mine better only because it gets to the point a hell of a lot faster.

    Please Register or Log in to view the hidden image!

     
  22. drnihili Registered Senior Member

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    All calculus tells us is when Achilles catches the tortoise. We knew that before calculus. Calculus is irrelevant to the central question of the paradox. "How do you finish a series that has no end?"
     
  23. StrangeDays Registered Senior Member

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    The implication here is that such a thing should take forever. But if you spend an appropriate amount of time on each element of the series, then the total time will be finite rather than infinite.
     

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