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Thread: dimensions

  1. #1 dimensions 
    Moderator Moderator AlexP's Avatar
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    Is what we're existing in (leaving time alone) just the 3rd dimension, or is it a combination of the first, second, and third?


    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
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  3. #2  
    Forum Ph.D.
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    its not a "third dimension" its 3-dimensional.
    height, width, depth.
    i hope that should explain it for you.

    dimension = size, or length

    you can simply ask: whats the dimensions of this box.
    and thats basically what it is. nothing magical or mystic about dimensions.


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  4. #3  
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    Well if you don't count the 4th dimension which is said to be time, and the theory of the other 7 that are just too thin to see.
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  5. #4  
    Forum Senior anand_kapadia's Avatar
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    I don't think how can we count dimensions since they are mathemetical imagination just as latitudes on the earth.
    You can similarly distingiush a bat who has just other dimension as they can watch waves of frequencies different from us.
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  6. #5  
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    Well you can count them.

    Just like you can count lines of latitude.

    Take the usual 3D idea.

    1. Height
    2. Length
    3. Depth

    There, I have counted them.

    Simple.
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  7. #6  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Counting dimensions is easy. It's just the number of continuous variables/numbers required to express position in the space in question. For example, how many variables do you need to express a position on the Earth's surface? Two, latitude and longitude. Therefore, Earth's surface is two dimensional. How many for an arbitrary point inside a box? Three, height, width, depth. How about for a point somewhere in the solar system at a particular point in history? Four. Using spherical coordinates centered at the sun, they'd be angle (forgot what this one is called), inclination, radius and time (or offset in time). How many are required to describe the position of a string in superstring theory? Ten or eleven depending on which one your talking about (I don't actually know much about any of them). Four of those are height, width, depth and time.

    Just because we can't see something doesn't make it any less real. I've never seen an electron, but I don't doubt its existence. (Maybe the descriptions of its form I've heard though.)

    Edit: Hazz beat me to it.
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  8. #7  
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    Quote Originally Posted by MagiMaster
    Edit: Hazz beat me to it.
    Damn right!
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  9. #8  
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    What about fractal dimensions?

    How do you physically explain something that has a fractal dimension of say 2.5?
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  10. #9  
    Forum Senior anand_kapadia's Avatar
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    Quote Originally Posted by billiards
    What about fractal dimensions?

    How do you physically explain something that has a fractal dimension of say 2.5?
    Is it fractional dimension.
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  11. #10  
    Forum Professor river_rat's Avatar
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    Quote Originally Posted by MagiMaster
    Counting dimensions is easy. It's just the number of continuous variables/numbers required to express position in the space in question. For example, how many variables do you need to express a position on the Earth's surface? Two, latitude and longitude. Therefore, Earth's surface is two dimensional. How many for an arbitrary point inside a box? Three, height, width, depth. How about for a point somewhere in the solar system at a particular point in history? Four. Using spherical coordinates centered at the sun, they'd be angle (forgot what this one is called), inclination, radius and time (or offset in time). How many are required to describe the position of a string in superstring theory? Ten or eleven depending on which one your talking about (I don't actually know much about any of them). Four of those are height, width, depth and time.
    Now there exists a continuous function f:[0, 1] -> [0, 1]<sup>2</sup> that covers [0, 1]<sup>2</sup> (i.e. a continuous curve from the unit interval to the unit square) so by your definition a square is only 1 dimensional as you only need one continuous variable t to give you any point on the square

    The question of dimensionality is much more subtle then this, its actually quite a bastard area in topology!
    As is often the case with technical subjects we are presented with an unfortunate choice: an explanation that is accurate but incomprehensible, or comprehensible but wrong.
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  12. #11  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Maybe I should have said smooth variables, or smooth functions? I know about space filling curves, but I was trying to subtly exclude them.

    As far as fractal dimensions go, I'm not quite sure. I understand how you obtain the dimension and what the point of having it is, but I'm not sure how that translates to normal dimensions. If the fractal dimension is a whole number, it roughly means the object is the same as an object of that many dimensions. For example, the curves river_rat was talking about have fractal dimensions of 2, even though they are all one dimensional functions. I guess, in that way, fractal dimension is a better measure of physical dimensions (?).
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  13. #12  
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    I agree that counting dimensions isn't quite as simple as some have dismissively stated, especially when it comes to fractals. If we leave fractals aside, maybe the number of dimensions of a given space should be described as the maximum number of independent coordinates, rather than a minimum number "required to express position" in that space?

    By the way, the surface of the Earth that I know is not two-dimensional (although its cartographical projection may well be). It's closer to three-dimensional, actually fractal.
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  14. #13  
    Forum Radioactive Isotope MagiMaster's Avatar
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    Yeah, that's certainly more accurate. As for the surface of the Earth, I was thinking more of a slightly smoothed surface (as in, given latitude and longitude to any precision, you'd know where that meant).
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