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Thread: Random Theory of Dimensional Analysis

  1. #1 Random Theory of Dimensional Analysis 
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    Greetings,

    I often think about Physics(as I love science) and something recently came up regarding dimensions of space(I was having a discussion with my peers). As a result of this discussion, I came to an interesting conclusion regarding dimensions of space that seems to remain consistent so long as a few things remain constant. Here it is:

    1) Take any amount of space that is defined by X number of dimensions.
    2) Next, duplicate the space defined in the first step and set the number of dimensions X parallel to it.

    By doing this, a new "space" is created between the two spaces defined in the two rules. As a result the SPACE BETWEEN SPACES becomes an additional dimension of space so long as the following rule occurs:

    3) Any given point from one of the two spaces must directly correspond to its duplicate point.


    That's it, any thoughts from the community would be great, and if anyone can point me in the direction of similar work I would be highly pleased. Oh, and if anyone finds any discrepancies please point them out!

    Thanks.


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  3. #2  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Mathematically, you've only introduced one new dimension. The X dimensions of the original and the clone are the same and only the new direction used to separate them is a new dimension. But if you're introducing a new dimension, you don't really need the other space to be a clone of the first, only that it takes up X or fewer dimensions.


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  4. #3  
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    I was aware that i am only creating one new dimension, however am I wrong in saying that the same process can be repeated? It seems to.
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  5. #4  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Well, if you start with a single point (zero dimensions), that procedure is basically a way of visualizing what dimension means. Stretch the point out into a line and you've got 1 new dimension. Stretch it again into a square to get two dimensions. Again for a 3D cube. Then a 4D hypercube. Then a 5D hypercube. They're all called hypercubes past that. (If you spin it instead of stretching it, you get hyperspheres. If you just add a single point in some new direction, you get simplexes.) The only real requirement though is that at each step you move in a new direction that can't be expressed as some combination of the directions you've already used.
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  6. #5  
    KJW
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    One can combine the two (or more) spaces by forming a Cartesian product, for which the dimension is the sum of the dimensions of the component spaces.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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