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Arrow paradoxon

  1. Jun 19, 2005 #1
    hi folks
    maybe somebody can help out concerning this topic...
    i once heard of an arrow paradoxon, even though i'm not sure whether it really is one.
    it is about movement, just check out the scenario:
    when you shoot an arrow towards an aim you can physically describe its movement from the bow to the aim. when you break up the movement into infinite steps of movement ( like frames of a video stream ) you have x->infinite positions of the arrow, but in each and every 'picture', seen independantly from each other, the arrow does not move. one could say the movement of the arrow is the sum of no-movement.
    this is how it was described but i dont know how to handle it...

    now does the arrow move or not? many spiritual people say that time, movement, or the solid appearence of matter is illusion and itz only interpreted by the brain in such a logical construct that it only appears in such a way we perceive it. point of relativity: the arrow only seems to move when i observe it, related to the arrow, not moving myself. when i move with the same speed and same direction the arrow stands still.
    what is in your opinion movement? in fact, one has to say that everything is in constant movement ( quantum physics ) but what about movement which is directly perceived by living organisms? what is the truth now, in a philosophical point of view? the direct perception or that what lies beyond that?
    when there is no absolute time and no absolute relation point for movement, does it exist anyhow? or only in a way one is creating it for oneself ( indepentant interpretation of reality of different mind)
    please give me your thoughts about that... whether brainstorming or facts, im open for athing ;)
  2. jcsd
  3. Jun 19, 2005 #2


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    But each "picture" does not show reality! The arrow, at each instant in time, does have a speed. Of course, using algebra, speed is defined as [tex]\frac{\Delta x}{\Delta t} or "distance moved in a given time period divided by that time period". At a given instant there is not time period and no distance moved- so you can't use that formula but that doesn't mean there is no speed. Newton developed calculus precisely to be able to find speed (and acceleration) at a given instant.
  4. Jun 19, 2005 #3
    We do actually represent speed as a vector(numerical value as scale and direction) in a still-picture..
  5. Jun 20, 2005 #4
    Everything you have said is too ambiguous to understand. You say that we perceive things like frames of a video camera, yet there is no evidence of this.

    Our minds make sense of millions of signals from our eyes which are sent almost continuously and several times from each optic nerve. Physically we do not see in frames. There is no set frame rate for the mind.

    In terms of memory we take snap shots as you say, which seems to be the closest approximation to how the mind understands changes in terms of frames. However, I am imagining a football being kicked about 30 metres into a goal right now and I am imagining a footballs moving continuously.

    In terms of physics it is possible that the arrows is moving a certain distance one "planck time period" at a time, however this is much too fast for the human mind to perceive.

    The mind seems to understand things continuously, like a curve graph instead of a bar chart.

    You need to elaborate your point.

    Spiritual peope are wrong about reality being an illusion. An illusion is something which appears to have happenned whe in fact it has not, the classic example being a magician making the statue of liberty dissapear. It hasn't dissapeared, it just looks that way. We are not omnipotent so reality is an illusion in the sense that we cannot perceive everything absolutely, but this is pushing the ambiguity of the term illusion to it's limits.

    I don't understand this at all.

    In terms of a person running at the same speed as a football flying above his head, (arrows are too fast) the immediate perception of the person is that he accelerated therefore he is the one who is moving.

    Of further interest is the football. As the football slows down in relation to the ground due to air resistance every atom in the football knows it is accelerating as it is being pushed by the atom behind it and at the surface of the footballs it is experiencing a net force of air resistance which makes it slow down to wind speed, however it does not know whether it is falling or not as each atom is attracted equally by the force of gravity. It seems that something can only be aware of it's acceleration if it goes against some aether like property of the universe which is relative to velocity.

    For instance a passenger in a space ship in deep space (no gravity) is travelling at 9.8m/s^2 (note how I'm communicating properly and so don't have to explain my equation afterwards) will experience the same "pull" down as he would on earth. In each case this property is opposed as on earth the ground prevents the person from falling to the center of gravity of the earth and orbitting it and the passenger in the space ship is accelerating.

    Some people call this the time space continuumand describe it as a flat rubber sheet with mass bodies like planets and stars as being indentations in the rubber sheet which create the effect of gravity. It is better to think of it a loads of arrows which point in the direction that an extremely light particle would accelerate and how fast ift would accelerate if it were placed there, during an extremely short moment in time. This is a 3 dimensional view and much more practical, seeing as there are 3 spacial dimensions and time in this instance is represented by the arrows.
  6. Jun 30, 2005 #5


    Suggest you do a search on 'Zeno's Paradox'. There you'll find the paradox to which you refer and several others like it - all interesting reading !
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