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Thread: Which is the math models explain the different dimensions ?

  1. #1 Which is the math models explain the different dimensions ? 
    Universe Supervisor dapifo's Avatar
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    Which is the math models explain the different dimensions ?...Euclides, Riemann, ...

    How we could modelize a n-space dimensional ... with different "n" values?... 1D. 2D. 3D, 4D,..., nD....

    Which model could give a logical, balanced, symmetrical, variable and adjustable n-space ?


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  3. #2  
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    First question - the number of dimensions is not determined by the type of geometry. Eucildean, etc. geometry can be defined for any finite n.

    I don't understand your other questions.


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  4. #3  
    Universe Supervisor dapifo's Avatar
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    Quote Originally Posted by mathman View Post
    First question - the number of dimensions is not determined by the type of geometry. Eucildean, etc. geometry can be defined for any finite n.

    I don't understand your other questions.
    OK...I mean if there are any maths model that parametrize the different space dimensions... I thought that Euclides do part of it...

    For example...which maths could modelize the 6D-Calabi-Yau shapes?
    "If everyone is thinking alike, then somebody isn't thinking". George S. Patton
    "Science does not know its debt to imagination". Ralph Waldo Emerson

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  5. #4  
    Moderator Moderator Markus Hanke's Avatar
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    I think what you are after is the area of differential geometry. This is a very complex field though, and one could easily devote a lifetime to studying this.
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    Universe Supervisor dapifo's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    I think what you are after is the area of differential geometry. This is a very complex field though, and one could easily devote a lifetime to studying this.
    Ok...I would look for it (just to have an idea)...thanks
    "If everyone is thinking alike, then somebody isn't thinking". George S. Patton
    "Science does not know its debt to imagination". Ralph Waldo Emerson

    "Why settle with the known models and patterns (but not underlying laws) of Our Universe , if we might understand them better if we could puzzle out them from outside its limits?"
    (The common sense)
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  7. #6  
    ***** Participant Write4U's Avatar
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    Quote Originally Posted by mathman View Post
    First question - the number of dimensions is not determined by the type of geometry. Eucildean, etc. geometry can be defined for any finite n.

    I don't understand your other questions.
    Please clarify - the number of dimensions is not determined by their type of geometry? Is each dimension itself not a geometric construct? Fields, Vectors, Potentials?
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  8. #7  
    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by Write4U View Post
    Please clarify - the number of dimensions is not determined by their type of geometry? Is each dimension itself not a geometric construct? Fields, Vectors, Potentials?
    What he means to say is that you can define any type of geometry ( flat, curved ) in any number of dimensions; e.g. it is just as easy to mathematically describe a 6-sphere in (8+3)-spacetime than it is to describe a circle on a flat plane. Both are mathematically trivial. Same for fields, vectors and potentials - you can define each of these in arbitrary dimensions. What does change though is the physics - (3+1) space-time has a somewhat privileged status, as many laws of physics simply wouldn't work in space-times with a different number of spatial and temporal dimensions. For example, the inverse square law for conservative force fields is true only in three spatial dimensions; change this to, say, five spatial dimensions, and you'd get a very different force law.
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  9. #8  
    Universe Supervisor dapifo's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    .... What does change though is the physics - (3+1) space-time has a somewhat privileged status, as many laws of physics simply wouldn't work in space-times with a different number of spatial and temporal dimensions. For example, the inverse square law for conservative force fields is true only in three spatial dimensions; change this to, say, five spatial dimensions, and you'd get a very different force law.
    Now, Im who do not understand what you mean in this sentence ...(??)
    "If everyone is thinking alike, then somebody isn't thinking". George S. Patton
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    Quote Originally Posted by dapifo View Post
    Now, Im who do not understand what you mean in this sentence ...(??)
    Basically what I am trying to say is that the world as we see it can only be the way it is in a universe with three spatial and one temporal ( macroscopic ) dimensions. If the number of macroscopic dimensions differed in any way, then we most likely would not be here, or at least the universe would be a very different place with different laws of physics.
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    Forum Junior epidecus's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    just as easy to mathematically describe a 6-sphere in (8+3)-spacetime
    Just curious, but do the 6-sphere and/or this 8+3 space-time have any real interest in the physics realm? One particular thing comes to mind, but I'm not sure if this was purely for example.
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  12. #11  
    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by epidecus View Post
    Just curious, but do the 6-sphere and/or this 8+3 space-time have any real interest in the physics realm?
    No, it was just an arbitrary example.
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  13. #12  
    Universe Supervisor dapifo's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by dapifo View Post
    Now, Im who do not understand what you mean in this sentence ...(??)
    Basically what I am trying to say is that the world as we see it can only be the way it is in a universe with three spatial and one temporal ( macroscopic ) dimensions. If the number of macroscopic dimensions differed in any way, then we most likely would not be here, or at least the universe would be a very different place with different laws of physics.
    Markus...what you say now is more clear...but only there is an mistake: As you make refferences to "macroscopic" dimensions...you know that there could be 6D extra space dimensions (Calabi-Yau shapes) rolled at very small dimensions (Planck dimensiion: 10^-35 meters))...but there also could be 1D extra (4+1 D space-time dimensions) at very large dimension (larger than Our Universe: 10^+27 meters).

    So, yes we could be in a 3+1 D Universe between two others Universes with other dimensions (6+3+1 D for smaller & 4+1 D for larger)....then our physics law models are valid only for this range...and other physics law models could be out of these limmits...although the "underlaying laws" could be the same for all of them... and we could define a new TOA wider thn M-Theory that could be valid also for these scales....where we have to take into account the extra dimensions that will be there.

    The dimensions could be a funtion of the space scale (!??)....D (n) = f (n_scale).

    And as you propose...there could be other forces fields...nD Forces Fields...
    "If everyone is thinking alike, then somebody isn't thinking". George S. Patton
    "Science does not know its debt to imagination". Ralph Waldo Emerson

    "Why settle with the known models and patterns (but not underlying laws) of Our Universe , if we might understand them better if we could puzzle out them from outside its limits?"
    (The common sense)
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  14. #13  
    Forum Junior epidecus's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    No, it was just an arbitrary example.
    Okay. Thanks.
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  15. #14  
    Moderator Moderator Markus Hanke's Avatar
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    Quote Originally Posted by dapifo View Post
    Markus...what you say now is more clear...but only there is an mistake: As you make refferences to "macroscopic" dimensions...you know that there could be 6D extra space dimensions (Calabi-Yau shapes) rolled at very small dimensions (Planck dimensiion: 10^-35 meters))...but there also could be 1D extra (4+1 D space-time dimensions) at very large dimension (larger than Our Universe: 10^+27 meters).

    So, yes we could be in a 3+1 D Universe between two others Universes with other dimensions (6+3+1 D for smaller & 4+1 D for larger)....then our physics law models are valid only for this range...and other physics law models could be out of these limmits...although the "underlaying laws" could be the same for all of them... and we could define a new TOA wider thn M-Theory that could be valid also for these scales....where we have to take into account the extra dimensions that will be there.

    The dimensions could be a funtion of the space scale (!??)....D (n) = f (n_scale).

    And as you propose...there could be other forces fields...nD Forces Fields...
    I agree, that is quite possible, and there are various proposals along those very lines, e.g. String theory, brane cosmology, causal dynamical triangulation etc.
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  16. #15  
    Universe Supervisor dapifo's Avatar
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    OK...Thanks..I didnt know about the "causal dynamical triangulation "....but it seams to be very similar to the "fractal cosmology"....
    "If everyone is thinking alike, then somebody isn't thinking". George S. Patton
    "Science does not know its debt to imagination". Ralph Waldo Emerson

    "Why settle with the known models and patterns (but not underlying laws) of Our Universe , if we might understand them better if we could puzzle out them from outside its limits?"
    (The common sense)
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