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What determines the fact that a dimension actually exists?

This entire question is based off the assumption that a Point (0-dimensions) is nonexistent in the fact that no matter how infintesimally close you get to a point, it still does not exist other than the representation that it symoblizes a location.

Considering this assumption, I propose my question. Would the extra dimensions technically be nonexistent as well? If you have a point and stretch it across a direction, you have a line. You get the line, which is 1-dimensional, no matter how close you get to the line, since it's just an infinite number of nonexistences, wouldn't the line itself be nonexistent? The closer you get to the line, you still won't be able to say that the line exists, as the infinite number of points that make it up themselves are nonexistent.

Now this is where it gets a bit interesting. If you get a 1-dimensional line, and stretch it across a new direction, you get a 2-dimensional object, which again is made of infintesimal number of lines that are, according to the previous paragraph, nonexistent. So wouldn't that mean that the 2-dimensional object is nonexistent? Now the argument here would be that since the 2-dimensional object has area, it is existent, due to the fact that it has an infintesimal amount of points within the boundaries of it's 2-dimensional shape. I concur that this would be a valid argument if it weren't for the fact that the question was from a 3-dimensional perspective. We as humans are only capable of experiencing 3 dimensions, but there is nothing that says that there can't be more dimensions! If you looked at the 2-dimensional shape from a 4-dimensional perspective, the object would again, become basically nonexistent, just like the line is nonexistent in our 3-dimensional perspective! This could be said the same for the 3rd dimension, from a 5-dimensional perspective! Is this assumption correct or totally out of the ballpark?

  • Jun 28 2012: First, you seem to be mixing up mathematical concepts with physical concepts, and that can be confusing. So I am going to discuss only physical concepts.

    To the best of my knowledge, all physical objects have three dimensions. If there were two dimensional physical objects, I think we would probably be able to detect them, and we haven't, so I am going with the assumption that they do not exist. That does not completely rule out the possibility that one dimensional objects actually exist. It seems to me that one dimensional objects would be undetectable and would have no effect on us whatsoever, so there is not much point in discussing them as real objects. So all known physical objects have at least three dimensions. (For the purpose of my discussion, I am ignoring time.)

    Could there be more than three dimensions, and we are not aware of them? Yes, as Stewart's video demonstrates. Determining that more dimensions actually exist will require evidence (possibly in the form of a visit by a four dimensional being). To date, we have no such evidence. Theorists who are using 4 or more dimensions to try to explain our universe are trying to use mathematics to make predictions that we can test with experiments that will then provide the evidence for the extra dimensions. Until we have actual evidence of extra dimensions, I am content to accept the obvious notion that we live in a three dimensional universe.

    After reading my own writing, it seems a bit obvious; its certainly not my intention to "speak down to you" or be patronizing. I have gone through the same sort of confusion you seem be experiencing, and more than once. Its good to touch base with the obvious once in a while.
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      Jun 28 2012: I think I read somewhere that scientists were trying to get things to purposefully enter more dimensions by giving them lots of energy. That was actually an idea about the neutrinos which people thought broke lightspeed, "some" said it could have entered another dimension and traveled through it briefly.
      Also I think, that thinking in terms of objects is too macro. As you say 1D things aren't worth looking for, this is why string theory is so played down because we could never really detect them.
      Here's an interesting idea, if we could make something 2d, could it break lightspeed as it's no longer subject to our universal laws? hmm
      • Jun 30 2012: "Here's an interesting idea, if we could make something 2d, could it break lightspeed as it's no longer subject to our universal laws? hmm"

        Wow, you really got me hooked. Off hand, I do not know of any area of physics that deals with 2d objects at all, so to the best of my knowledge, modern physics cannot rule out 2d objects. Perhaps dark matter is 2d. If we could put computer circuits on 2d objects, we could pile up any number of them in no space at all. 2d paint? If a 2d object had no mass, it would be very difficult to move around without losing control of it; the slightest nudge would accelerate it to super light speed. Can you think of any way to definitively determine that 2d objects are impossible?
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          Jun 30 2012: I think I'm limited here by my imagination and middle world sense of dimensions. I can't think of any way you could disprove it, but I also thing we'd have no way to detect it unless someone came up with a great idea.
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    Jun 27 2012: A single bump on my forehead caused by a windowframe was proof to me... ;o)

    A point, a line, an area, those are mathematical constructions and thus free of any physical boundaries. This freedom is quite practical, as it avoids discussions about scale, zoom-levels and so on, which they would rose if they would have a physical expansion. So if you start moving your mathematical point - without physical expansion - along a mathematical line - without physical expansion - do better not expect the result to become any more physical as it was before.

    As you said yourself, your question is based on an assumption - and so it is. Not powerful enough to create new matter out of thin air, yet powerful enogh to create a lot of quite real headache to a lot of pupils arround the world...

    Imaginative we can have as many dimensions we wish at any point we choose in any moment passing by and all of them are as valid as we make them. The only limitation is that we can bump into them if they fold into three only ...

    And honestly, my forehead is thankful for that!

    ;o)
  • Jun 27 2012: What determines the fact that a dimension actually exists?

    Let's see if I can grasp this.

    It is determined by
    the fact that you can draw a non-existing line in it

    What I personally find more interesting is the fact that Rene Descartes theory, that one's conscious existence cannot or is not, debatable, is in fact no longer true, as more and more people are becoming artificially intelligent, mental robots as it were, and thus, consciously, no longer exist.

    But, you can get real close to them and talk to them and they will prove it to you.
  • Jun 27 2012: Your approach isn't one that I've seen or considered before but you're right.

    What you're explaining is a concept which was popularised by someone called Zeno.

    http://en.wikipedia.org/wiki/Zeno%27s_paradoxes

    His flying arrow paradox is especially interesting.

    If you're interested in this sort of thing, you should definitely read about his paradoxes.
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    Jun 26 2012: We actually live in a 4D world, X,Y,Z and time.
    http://www.youtube.com/watch?v=BWyTxCsIXE4 This video explains it well.
    Also there are theories out there that only infinitely small scales, some of the smallest particles could behave as if they were in a 10D world
    • Jun 26 2012: Yes I understand that we live in a 4D world, where Time is the 4th dimension. That is stated in Einsteins theory of relativity, that says the bends and curves in spacetime are what causes the effects gravity. The thing is that even though we live in a 4-D world, we can actually only control our displacement in the 3-dimensions that we are familiar with, but move along the 4th dimension of time at velocities almost that of the speed of light, without control in which direction it goes(hence the saying time only moves forward, never backwards). I have seen that video several times already, but that doesn't talk about the existences of the dimensions themselves, just assumes that the dimensions exist already, and explains how they work. Also, regarding string theory, yes the smallest of particles do live in a 10 dimensional world, with 1 added time dimension to make 11, but most of them are curled up in ways that we cannot see. These are all wonderful aspects of physics that I myself am currently trying to pursue, however that doesn't answer the question that I posed regarding the actual existences of dimensions. What causes the dimensions to exist, if they exist at all? Obviously, we can't say that the world we live in doesn't exist, we can use our 5 senses to determine that, however what if our senses are actually just fooling us, and the dimensions that we humans all enjoy and are familiar with are actually nonexistent? This seems highly unlikely to me, but this question has been bugging me for the longest time, so I would like to at least be proven wrong, with a logical explanation so I can finally put this question to rest.
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        Jun 26 2012: Well I think you mention the answer to your own question there, what creates or makes the dimensions? The body that perceives the dimensions in effect creates the dimensions it resides in. So maybe the universe during the big bang became 4D, but then suppose on the quantum level, that the additional dimensions only exist because of what resides within them, created the dimension within which to live. This could explain why predominantly most things exist in 3D + time, it is the most stable form of dimensions to exist in. Maybe? A good analogy to this is how bugs rely on surface tension of water, it means nothing to us big humans but to a small spider it can float across a still lake just gliding on the meniscus. Different perspective relevant to size? Mabye

        Edit= The curves and bends in space time don't create gravity, gravity creates them is it not? And gravity is caused by a body's affect on the Higgs field.
        • Jun 26 2012: Sorry about that, thanks for the catch on gravity, I was rushing to type out that wall of text.

          Regarding the body that perceives the dimensions, if we take them out, would the dimensions exist, considering the assumption that I made from my original question. And I know that multiple dimensions are curled up in tiny spaces, but what if we were talking about sub-planck length scales? Would those dimensions also technically exist, if there is a higher dimension that would be able to deduce the nonexistence of that dimension considering the original assumption of the nonexistence of a point?
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        Jun 27 2012: Hmm it's very interesting. I would hesitate to talk about sub planck lengths unless there's some maths that could allow for such lengths.
        But you pose a very interesting question, which I think is best presented in the macro, say all of the universe just disappeared, would there still be four dimensions? I think the best answer is that they coincide with each other very well. Maybe the physical structure for a dimension constantly exists but won't actually form until there is something to occupy it.
        Very interesting questions.