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Zenos paradox - Is math real?

  1. May 17, 2007 #1
    Hi,

    I am a total retard at math and have what is probably a naive philosophical question that either has an obvious answer you all know about or has no answer and is right up there with the meaning of life.

    Anyway, as you probably know, Zeno said something like, "Movement is impossible because in order to get from a to b you need to travel half the distance and in order to travel half the distance you need to travel half that distance add infinitum".

    Now, mathmematicins answer this with limits but are limits just an abstract concept or is the physical universe a set of infinite limits? I mean, is math in this case just a simplification in order to deal with this problem but doesnt represent the true physical reality of movement?

    Sorry if that was confusing :P

    Just trying to get my head around what is real and what is just human thought.

    And please no pedantic arguments about how real is real :)

    Thanks for any insight..
     
  2. jcsd
  3. May 17, 2007 #2
    depends on if you define a fundamental stepsize(that is for each movement you make you must at least translate 1 stepsize unit)

    If you do then at that fundamental scale Zeno's statement fails...however if you can take an infinitesimal stepsize then his statement holds.

    and In pure mathematics the concept of infinitesimal is a powerful concept.

    in physics, it is whether you believe that there exists a fundamental set of things.
     
  4. May 17, 2007 #3

    HallsofIvy

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    Would asking you what you mean by "real" be pedantic? Certainly mathematics gives useful answers to such questions as "how fast" or "how far". If that doesn't mean that mathematics "represents true physical reality", then I don't understand your question. What more do you want?
     
  5. May 17, 2007 #4
    Thanks Neurocomp, not sure what you mean by step size. In my mind, it doesnt matter what size the move is you would need to travel half that move making movement impossible.

    The only way i can get around it is that life isnt real. :P

    For example, when i am having a dream in deep sleep, i can see things moving and it seems real at the time. But there are no "things" and the whole thing is just an illusion. So maybe the physical univesre is also just an illusion and from the human perspective we get fooled into thinking there are discrete "things" when the whole things is one big dream :P

    Too off topic for this forum i'm sure but for me, infinite series does not solve zenos paradox but only provides a handy tool for humans to use in their reality approximations.
     
  6. May 17, 2007 #5
    stepsize- it has to move at least a certain amount of distance and cannot be any smaller..hence no infinitesimal but quantized length.

    Or you could think of the velocity part...its gotta make up this length in a certain amount of time.
     
  7. May 17, 2007 #6
    Isn't movement continuous?
     
  8. May 17, 2007 #7
    Thanks again Neuro. I guess step size is another human invention to quantify models but i doubt it is reality.

    And continuous makes no sense outside of human reasoning.

    I guess i'll just die ignorant like everyone else :P
     
  9. May 17, 2007 #8
    An utterly ridiculous assertion. First, sense is part of human reasoning, how can you even talk about sense "outside" human reasoning? Second, it is perfectly sensible in absolute terms: an object that moves from A to B on a straight path will pas through every singular point position between A and B. In other words, time (hence movement) can always be broken down in smaller quantities. Anything else would be admitting that teleportation exists.
     
    Last edited: May 17, 2007
  10. May 17, 2007 #9
    An utterly ridiculous assertion. There are infinite singular point positions between point A and B therefore it would take an infinite amount of time to cross them all. It would go for eternity. Continuous only makes sense in the human mind, just like 3 dimensions when we find it hard if not impossible to visualise a 16 dimensional universe.
     
  11. May 17, 2007 #10
    That is fallacious logic. Look at things this way: for any point between A and B, we could find a certain moment at which the object was at that point. You either accept this, or try to convince me that objects teleport in space. And your comment about dimensions sounds straight out of a sci fi. Dimensions are merely frames of chosen parameters, not some kind of unimaginable alternate realities.
     
  12. May 17, 2007 #11

    Office_Shredder

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    How long does it take to go across a point? Zero time/point.

    You've just introduced zero time/point*infinite points to traverse gives you the time it takes to move from anywhere to anywhere else. Turns out that's really just not useful

    Alternatively, we can accept that measuring the time it takes to moves across a point is kind of useless, and thus we're back to standard continuous movement as we know it today
     
  13. May 17, 2007 #12
    I dont think anyone gets what i am saying.

    I understand the concept of continuous and agree that thinking about the amount of time between time is infinite and the amount of space between to points is infinite and is not useful but i am not talking about being useful, i am talking about how insane the concept of infinite is when clearly day to day reality appears discrete which we in turn label "continuous" out of convenience.

    Bah, forget it..
     
  14. May 17, 2007 #13
    There is nothing mystic about continuity, it's a mathematical concept. Spacetime is assumed to be continuous as the mathematical definition wishes.
     
  15. May 17, 2007 #14
    Exactly, i am not talking about the concept but the actual reality. Humans make models because they are useful but it doesnt shed any light onto the actual, complete exact ultimate reality of existence and makes space and time look completely like creations of the mind. A 2 dimensional creature sees the universe as 2 dimensional, we see it as three because our brains evolved to create our little illusions via our senses but it is not how it is.
     
    Last edited: May 17, 2007
  16. May 17, 2007 #15

    Office_Shredder

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    The universe doesn't look discrete at all!! In fact, only in the past 100 years or so has the concept of the universe being discrete even been a scientifically studyable concept, before that we weren't able to actually see anything that wasn't a continuous process
     
  17. May 17, 2007 #16
    Fair enough but by discrete i meant in terms of movement which is the current topic.

    As in, you can stop time and see the object at point a, then stop time a second later and see the object at point b even though there was an infintite amount of time in that 1 second and an infinite amount of space between point a and b.

    It looks discrete because there is movement but infinity is unexplainable. The continuos concept is purely mathematical and only a model, not the actual thing.
     
  18. May 17, 2007 #17
    But what do you mean the actual thing? Who are you to affirm that?
     
  19. May 17, 2007 #18

    Office_Shredder

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    There isn't an infinite amount of time between 0 and 1, there's just one second. Just because there are infinite points doesn't mean you spend time passing through each one (I already addressed that point in fact)
     
  20. May 17, 2007 #19

    StatusX

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    I never understood why this is a paradox. To go half the distance takes half the time, a quarter takes a quarter the time, and so on, so the total time taken is finite, since 1/2+1/4+... is certainly less than, say, 2.

    Is the problem just in completing an infinite number of "tasks"? If the definition of tasks allows them to be these increasingly smaller movements, then I would say this argument is simply proof that you can in fact complete infinitely many tasks in a finite time, rather than any other conclusion you might reach from it.

    Or is the objection something like "you can't start because what would be your first step?" This is just a restatement of the question "what is the smallest positive number?", which simply has no answer, just like the question "what is the largest positive number?"
     
    Last edited: May 17, 2007
  21. May 17, 2007 #20

    EnumaElish

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    Assuming constant velocity, you are right. But how should one define velocity as Δd ---> 0 and Δt ---> 0? Isn't v = 0/0 at "that point"?

    I think this is a restatement of the OP.

    I believe this is a related but separate paradox.
     
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