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Variance of Variances and Space

  1. Oct 16, 2008 #1
    I think I'll ask it this way. Here goes...

    1 point = zero dimensions.
    2 points = 1, which is line; 3 points, shape; 4 minimum to have volume.

    Somewhere, or rather, when, time applies, most preferably at that case in which dimensionality, quite plainly, is. My question follows a hunch that supposes a possible elegance or symmetry that's beyond me.

    From 1 point to 2 we go from no dimensions to the dimension of difference.
    From 2 points to 3 do we not see a difference of differences, i.e. variance? (Keep in mind that I am accounting for any change in difference here as a kind of point, as well. Time has equal application here, particularly in the establishment of dimension, itself.) If so, then would it follow that a variance of variances comes next? This is where my eyes cross.

    Assuming my train of logic is still on its track (appologies. my first post.), I'll ask my final:

    What then? If we can draw a comparison between variance and time (which is what I'm attempting to do), then would a variance of variances fit in to one of the progressively higher dimensions? Can variance fit into space independent of time, independent of change? (or is this where we get into the concept of multiverses?)
  2. jcsd
  3. Oct 16, 2008 #2
    Those are some good thoughts, but I think a problem might be that viewing any given dimension as time-like - as a form of change, as you say - is somewhat arbitrary. It works conceptually but the universe we perceive doesn't appear to work like that. I think a dimension would need to have an attribute like the arrow of time to feasibly be construed as change / time-like.
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