What are the dimentions exactly?

Discussion in 'Astronomy, Exobiology, & Cosmology' started by Shadow1, Jun 25, 2010.

  1. Dywyddyr Penguinaciously duckalicious. Valued Senior Member

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    Then you're contending from ignorance, or bloody-mindedness.

    What conclusion? To post a definition?

    On a graph, yes.

    Because an axis is not a dimension.

    Wrong. It's because I prefer to be precise.
     
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  3. John99 Banned Banned

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    I will ignore the insults.

    Dyw said: "What conclusion? To post a definition?"

    Look up the word redundant.
     
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  5. Dywyddyr Penguinaciously duckalicious. Valued Senior Member

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    There were no insults.

    Keep trying. I do wish you'd post in English.
    What conclusion are you talking about?
     
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  7. John99 Banned Banned

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    I am saying your usage of Axis and Dimension signifies a redundancy. What was so hard to understand about that?
     
  8. Dywyddyr Penguinaciously duckalicious. Valued Senior Member

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    Because I have already pointed out (as has AlphaNumeric) that "axis" and "dimension" are NOT synonymous and mean different things.
    If they have different meanings how can using both be redundant?
    So the part that was "hard to understand" is why you persist in your inane belief that there is any conflation.
     
  9. AlphaNumeric Fully ionized Registered Senior Member

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    An axis is a vector, the dimensionality of a space signifies the number of axes you'll need at any given point (ignoring singularities).

    A plane \(\mathbb{P}\) is 2 dimensional. This is independent of how you define your coordinates, it simply tells you how many independent coordinates you've got. An axis is a point of direction (aka a vector) within that space, its a choice of what coordinates you write down. The usual Cartesian coordinates of a plane are two parameters (x,y) which signify the displacement a point in the plane has in the direction of two previously stated axis unit vectors, \(\hat{\mathbf{x}}\) and \(\hat{\mathbf{y}}\). Any location in the plane can be written as a vector (though really you shouldn't conflate vectors and locations, only in nice flat spaces can it even be vaguely viable) via \(\mathbf{v} = x \hat{\mathbf{x}} + y \hat{\mathbf{y}}\), ie the set of vectors \(\{ \hat{\mathbf{x}},\hat{\mathbf{y}} \}\) span the plane, \(\mathbb{P} = \langle \hat{\mathbf{x}},\hat{\mathbf{y}} \rangle\) and since they are linearly independent the dimensionality of \(\mathbb{P}\) is two and thus \(\mathbb{P} \sim \mathbb{R}^{2}\).

    You're conflating 'dimension' with 'direction', dimensions really only should refer to the cardinality of a tangent space vector basis, which in turn defines the cardinality of the coordinates of the space itself.

    I get what you're trying to say, lots of people use 'dimension' and 'direction' interchangeably but if you throw out 'dimension' and say 'direction' or 'axis' then you no longer have a word to signify the cardinality of the set of coordinates of a space.
     
  10. John99 Banned Banned

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    Like i said, i only scanned your other posts but will read them through in a while. So if this is repetitive you can just cite the relevant post.

    Regarding your last post.

    I dont know but it seems to me they are similar.

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  11. Shadow1 Valued Senior Member

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    sorry, i abig mistake in here, what i meant by dimention was, another univerce, anyway, i got my answer now, heheheh, i saw some videos

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  12. Emil Valued Senior Member

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    Dimension, and size could mean.

    If you're referring to the geometrical dimensions,where are three that determine the volume.

    If you mean space, I noticed two opinions.

    One says that space has three dimensions and is static.If we add the time it formed a
    space-time system.Here we can study not only the body shape and size but also their movement.With that I agree.

    The other opinion says that space has four dimensions, three geometric and time.
    Here the four dimensions are considered identical and interchangeable between them.
    This theory is more abstract and I do not agree.

    To study the motion of objects,engineering, there are still three dimensions which we call degrees of freedom or degrees of motion.
    In total there are six degrees of movement(freedom) three of translation(linear) and three rotation.


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    Typical industrial robots feature a 6-axis configuration, or six degrees of freedom.


     
    Last edited: Jul 31, 2010
  13. Shadow1 Valued Senior Member

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    yeah i know those things,i studied about when i was in elementary school, anyway, what i meant, is, a parallel univerce, in sci-fi films, they say dimentions, so that's why i used teh wrong words and so maked a topic about anoher thing

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  14. Emil Valued Senior Member

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    Depends on the imagination.

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  15. Doreen Valued Senior Member

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    Dimensions are possible ways something can extend, including not really empty space. I personally generally take into consideration three ways of extending spatially and I extend in each of these ways. I seem to extend in time - at least, memory is doing a nice job of fooling me that I do.

    I may extend in other ways beyond the three spatial ways and the one temporal way, but as of yet I have not come up with practical applications.
     
  16. machiaventa Registered Senior Member

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    Time is relevant to what system you are using to measure it first and only, second it can be affectted by one other thing or force:Gravity.
     

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