Desription and arguement - el Infinite

Discussion in 'Physics & Math' started by Quantum Quack, Jun 13, 2008.

  1. Quantum Quack Life's a tease... Valued Senior Member

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    Hi this thread is actually devoted to Prince James and how we may be able to paradox the paradox so to speak.

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    It is best described by asking two comparative questions:
    1]
    How many infintesimally thin planes can be fitted into the volume of a 12 inch brick?
    2]
    How many zero thick planes can be fitted into the volume of a 12 inch brick?


    Now by using the words infinitely thin we are granting according to Prince James an ultimately smallest thickness in that infinitely can not reduce to zero. So there fore at it's smallest point it must have thickness.
    So therfore more zero thick planes by an infinite amount will fit into the volume of the 12 inch brick than planes that have thickness even if infinitely thin.
    So therefore zero is the only value that can be legitimately used infinitely with in a given volume where as infinitely small can not be granted the same priviledge as the use becomes irrational or illogical.

    The point being that the use of infinitey in these ways ends up always paradoxical.
    My main arguement to Prince james is that infinitey is an absolute notion and cannot be in any way limited to a given stop point or finish point as in his time segmented arguement using zenos paradox as it's founding.

    So if used commonly and in my opinoin incorrectly an infinite number of infinitely thin planes should fit into our 12 inch bricks volume.

    And the same would apply to zero think planes but I would bet that zero thick planes would be a better use of infinity than infinitely thin. [ because no matter how thin you go an infinitely thin plane will always have thickness where as a zero thick plane does not. Thus infinity poses a paradox when qualified using words like "thin" or "small" or "slow"]

    And thus it is worth debating I think to clarify this issue.
    Care to discuss?
    Could be fun!
     
    Last edited: Jun 13, 2008
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  3. Prince_James Plutarch (Mickey's Dog) Registered Senior Member

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    I'll post the stuff I wrote in the other thread on this here, then ask you a question:

    I do not ascribe to the reality of anything less than 3 spatial dimensions. But theoretically speaking, yes.

    The difference, however, would be that infinitesimally small planes could produce a substantial plane which is non-infinitesimal together. A zero-dimensional plane in the 3rd dimension (a two dimensional plane) could never do so.

    One would be "1 + 1" the other would be "0 + 0".

    Now my question:

    What is 0 * x, where x is any integer?
     
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  5. BenTheMan Dr. of Physics, Prof. of Love Valued Senior Member

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    Clearly this is a question of existence in the mathematical/Platonic sense versus existence in the physical sense, and so it is somewhat akin to arguing about angels on the heads of pins, or whether anyone can actually draw a "perfect circle". The point is, an infinitely thin plane exists in principle, and we can do thought experiments with it, and we can derive equations. The problem is that when we go into the lab to try and BUILD an infinitely thin plane, and do experiments on it, our equations are off by a bit. The bit that they're off by lets us know how good of an approximation we made in getting there.

    James is correct because everything has a physical dimension, because it must be built out of atoms, which have some effective radius (if only due to the fact that they have some charge). So in some sense, there is no such thing as an infinitely thin plane. However, this does not preclude one from considering ideal solids or massless strings---this is what a physicist does, to avoid having to work with complicated equations.

    Another example is to think in four dimensions. When you take a picture, you have a three dimensional slice of the four dimensions we live in. If the picture is infinitely good (i.e. corresponding to an infinite shutter speed in your camera, or something), you have an infinitely thin three dimensional slice of our universe.
     
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  7. QuarkHead Remedial Math Student Valued Senior Member

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    Sorry to be boring, but this is akin to the question "how many real numbers are in the interval \([0,1]\)"? We know that this interval is finite, but we also know it contains infinitely many real numbers.

    This is an issue which crops up repeatedly on discussion fora - the confusion between the notion of an infinite number of elements in a finite interval, and the notion of an interval of infinite extension, say \((-\infty, \infty)\).

    A classic example is the frequent claim that \(\pi\) is infinite. True, it has, as far as one knows, an infinitely non-recurring decimal expansion. But it is most surely an element in the finite real open interval \((3,4)\), and is therefore finite.

    P.S As I have had a couple of beers, let me say this. There is a school of thought, which I discussed with D H in another thread, that says something like this; you say that \(\pi\) exists, but then, say I, unless you can write it out explicitly, digit by digit, then I am not obliged to accept that it exists.

    This is, of course, a characterture of what is known as the "constructivist" view of mathematics. D H finds it repellent; I feel some sympathy with it it - but only some.....
     
    Last edited: Jun 13, 2008
  8. funkstar ratsknuf Valued Senior Member

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    The problem I have with this view is that the same thing can pretty much be said for any infinite structure in mathematics. Considering, say, 1 as a real, you cannot "write it out explicitly, digit by digit" any more than you can with \(\pi\) - even though you have a recurrent pattern, there's no reason that one such recurrent pattern should count as real, and another not. Hell, even for finite structures, most of them will be so incomprehensively cumbersome in their naïve representations that the same impossibility of "writing out" applies.
     
  9. Quantum Quack Life's a tease... Valued Senior Member

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    Actually thinking on pi for the moment.
    Pi is an infinite resolution to an equation. yes?

    In other words pi is simply providing an infinite clarity to a given problem.
    A perfect example of infinite reductionalism....ha IMO
    a bit like comparing a 2 megpix image with a infinite megpix image that happen to have the same dimensions [ height X width ]
     
  10. Quantum Quack Life's a tease... Valued Senior Member

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    The problem that I see is that once you subscribe a value to the thiness of a plane that plane can not longer be used infinitely to fill a given volume.

    So the process fails to work in reverse thus the supposed paradox.

    ie.
    We have a 12 inch long rectangular brick.
    We decide that we can construct an infinitely thin plane.
    How ever the question begs:
    How many infinitely thin planes can fit into a 12 inch brick.

    The answer IMO must be less that infinity.
    So infinity in one direction fails in the other.
    logically the only plane that can fit infinitely into the volume of a 12 inch brick must be zero thick. As soon as you subscribe thickness you no longer can use infinity as infinity is now limited.
     
  11. Quantum Quack Life's a tease... Valued Senior Member

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    re pi:
    an interesting thought:

    A given figure say 8.125 could be said to be absolutely resolved where as pi can not be said to be absolutely resolved.
    Yet it must be... hmmmmm.......

    so is pi a finite resolution afterall....? hmmmmm
     
  12. Quantum Quack Life's a tease... Valued Senior Member

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    I disagree as I tend to think that infinity is an imaginary concept and far from real. So the requirement that it be "physical" is not necessarilly true.
     
  13. Quantum Quack Life's a tease... Valued Senior Member

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    so maybe this sort of discussion has a sort of pi resolution in that it is infinitely unresolvable?!

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    actually all jokes aside I think this has been, will be and is the case...IMO
     
  14. Prince_James Plutarch (Mickey's Dog) Registered Senior Member

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    QH:

    Zero thick would never fit into the brick. 0 * 0 = 0.

    Divide the brick infinitely and you will "eventually" get to infinitely small.
     
  15. Quantum Quack Life's a tease... Valued Senior Member

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    The whole point with infinity is that you can never get to infinitely small because it is an infinite progression without time to an impossible to reach destination. IMO
    it just keeps on getting smaller infinitely
     
  16. Prince_James Plutarch (Mickey's Dog) Registered Senior Member

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    Quantum Heraclitus:

    It is an ideal which can be referenced coherently. Furthermore, we know the answer from analytic means.
     
  17. Quantum Quack Life's a tease... Valued Senior Member

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    Exactly because infinity is an irrational notion. And once you apply a finite boundary or limitation which is excatly what you are doing it is no longer infinity but a finite infinity.
     
  18. Prince_James Plutarch (Mickey's Dog) Registered Senior Member

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    Quantum Heraclitus:

    If it is coherent it is not irrational. Furthermore, it is not irrational in any other way - what about it do you find it irrational?

    I am not giving a "finite limitation". An infinitesimal is beneath every number. Any given number is infinitely far from the infinitesimal.
     
  19. Quantum Quack Life's a tease... Valued Senior Member

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    try:
    How big is an infinitely large sphere?
    How deep is an infinitely deep ocean?
    and apply the same logic to the infintely small and if not why not?
     
  20. Prince_James Plutarch (Mickey's Dog) Registered Senior Member

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    Quantum Heraclitus:

    Infinitely large.

    Infinite deep.

    Infinitely small.
     
  21. Quantum Quack Life's a tease... Valued Senior Member

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    Correction:
    An infinitesimal is INFINITELY beneath every number.
    imo
     
  22. Quantum Quack Life's a tease... Valued Senior Member

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    your infinitesimal segment can be divided infinitely again and again ad-infinitum as thsi is what infinity is...infinite

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    why stop at any given size?
     
  23. Quantum Quack Life's a tease... Valued Senior Member

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    you have a number say
    .0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 and so on and it finishes with a number one at some point. This is still a finite number no matter how many decimal places we talk about.
    an infinite progression cannot finish as that is why it is called an infinte progression
     

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