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3D geometry

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  • mswaney
    Folks, Glad to read so many messages from people like me. Otherwise, I would have no outlet for these strange obsessions of mine. I especially liked the
    Message 1 of 6 , May 14 7:18 AM
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      Folks,

      Glad to read so many messages from people like me. Otherwise, I would have
      no outlet for these strange obsessions of mine. I especially liked the
      Hermes & Mercury stuff, though I haven't had time to digest it yet, my life
      is a poverty of "Have To" and "Don't Have Time". Whine, Snivel, Whimper.

      Anyway, as for the multi-dimensional quandary, from a mathematical point of
      view, dimensions above 3 are no problem. I encourage anyone to experiment
      with multi-dimensional magic squares, cubes, tessaracts, and 5th 6th etc,
      dimensional hypercubes. After you do this, you can see pretty easily that
      time is not an ordinary dimension. All these magic tessaratcs and higher
      dimensional hypercubes exist in the same way as do magic squares and cubes -
      presumably no problem in visualization - well the cubes are kinda hard to
      see all at once - they are usually written down in two-dimensional sections.

      In any case, a 4 dimensional magic hypercube is just like an extended magic
      cube which is just like an extended magic square. And so, mathematically -
      our most trustworthy sense - "extra" spatial dimensions are not anything too
      weird at all.

      However, there is a big difference between spatial dimensions and the
      temporal dimension. That's why we can't measure time in inches. A four
      (spatial) dimension cube - or hypercube - will not have the same properties
      as a three (spatial) dimension cube that also has a temporal dimension.

      But now for some real fun boys and girls, why do we think that there is only
      1 temporal dimension - the "one" we call time?

      It is easy enough to work with as many spatial dimensions as are needed to
      solve the problem at hand. The preferred number for physicists to explain
      the universe is 11. We just make them up as we go along, and it works
      pretty well. But what makes the temporal dimension so unique? If there are
      so many spatial dimensions, then why not as many temporal dimensions as we
      want?

      Mark

      ----- Original Message -----
      From: "johnberger_x" <magician@...>
      To: <sacredlandscapelist@yahoogroups.com>
      Sent: Monday, May 13, 2002 9:54 PM
      Subject: [sl] Re: 3D geometry


      > --- In sacredlandscapelist@y..., "J Vincent Beall" <vincent@d...>
      > wrote:
      > > What do you think that the author of the manual means by visualize
      > the
      > > hypercube? It doesn't seem to me that this is very straightforward.
      >
      > Here's someone who thinks they have it down:
      >
      > http://dogfeathers.com/java/hyprcube.html
      >
      > Forgive me if this is obtuse or naive, or if I am missing something
      > very important in this concept, but the whole concept of the
      > hypercube seems inherently flawed to me.
      >
      > One site I looked at contained the following statement: "Imagine a
      > person who lives in 4 spatial dimensions, watching a hypercube
      > rotate." Well, I live in four (plus) spatial dimensions. The fourth
      > dimension is simply an additional axis, not a wholly independent
      > realm of space and time.
      >
      > So if you accept that the fourth dimension is time, then wouldn't
      > a "hypercube" simply be a cube that exists for a fixed duration which
      > is the temporal equivalent of the length of its physical 3-D sides?
      >
      > So all you have to do is can figure out a way to measure time in
      > inches, and you can make a hypercube, a four-dimensional cube.
      >
      > Alternatively you could program a computer environment in which the
      > time and space units can be more easily converted back and forth from
      > each other, a much easier proposition, especially since you don't
      > have to account for relativity.
      >
      > It just wouldn't be extremely entertaining, I suspect. It would just
      > be an animation of a 3-D cube that exists for a certain duration,
      > then ceases to exist.
      >
      > --John B.
      > http://www.chaosdancer.com
      >
      >
      >
      >
      >
      > Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
      >
      >
    • johnberger_x
      ... experiment ... 6th etc, ... easily that ... I m not sure I see that. Time is a measurable axis on which we move. It s pretty much a dimension, like any
      Message 2 of 6 , May 16 9:41 AM
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        --- In sacredlandscapelist@y..., "mswaney" <mswaney@e...> wrote:
        > view, dimensions above 3 are no problem. I encourage anyone to
        experiment
        > with multi-dimensional magic squares, cubes, tessaracts, and 5th
        6th etc,
        > dimensional hypercubes. After you do this, you can see pretty
        easily that
        > time is not an ordinary dimension.

        I'm not sure I see that. Time is a measurable axis on which we move.
        It's pretty much a dimension, like any other dimension. What's
        interesting and unique are 1) how we perceive time, and 2) the ways
        we move through time.

        > However, there is a big difference between spatial dimensions and
        the
        > temporal dimension. That's why we can't measure time in inches.

        On what do you base that statement? Why isn't time spatial? I am not
        currently able to measure it in inches because I don't know how to
        hold my tape measure. I think if you could figure that out, you could
        not only measure time in inches, but it would be more accurate and
        more relativistically sound than measuring in minutes.

        > pretty well. But what makes the temporal dimension so unique? If
        there are
        > so many spatial dimensions, then why not as many temporal
        dimensions as we want?

        There could well be. My own theory is that some of our higher mental
        and spiritual functions (as we perceive them) occur and can be
        represented as higher-dimensional functions. After all, if knowledge
        or creativity or imagination is quantifiable, it should be able to be
        modeled mathematically.

        You can argue that some or all of this already models into the 4-D
        neurochemical structure of our brains, but it seems to me that
        there's an abstraction to some of these qualities that wants to be
        recognized and may not boil down to a simple chemical formulation.

        -j
      • Barry Carroll
        more power to you in your quest. the only comment i would make is that the use of the platonic solids and any symbolism connected with them is linked to
        Message 3 of 6 , May 20 10:32 PM
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          more power to you in your quest.

          the only comment i would make is that
          the use of the platonic solids
          and any symbolism connected with them
          is linked to various movements and historical periods.

          for some folks the issue is not so much about
          various other kinds of polygons and their potential
          mystical implications as it is about historical detective work.

          for instance, trying to understand how of some of the neoplatonist
          medieval and renaissance scholars, churchmen and builders
          expressed their belief about the
          structure of the cosmos thru their work.
          --or how neoplatonist ideas influenced the art deco and streamline
          design movents of the 1920's and '30's.

          if that is also interesting to you, you may find good reading
          in Mike Bispham's essay on Platonic Atomism in the
          Cathedrals in the essay section of the Sacred Landscape website.
          B.

          At 05:15 PM 5/13/02 +0000, you wrote:
          >I'm looking to go deeper into the the study of symmetry rather than
          >limiting myself to what is already considered "sacred geometry".
          > I know the Platonic Solids and the Archimedean Solids
          >are talked aboutin sacred geometry books. But there is so much more
          >to the study polyhedra. Actually the study of Polytopes would cover
          >polyhedra which are 3-d polytopes, and 2-d polgons, star polygons,
          >and into higher dimensions, like that of a 4-d polychoron.
          >These are things that you must be willing to let go of "sacred
          >geometry" to start to understand.
          > To me all ideas take form and can be descibed numericaly,
          >and geometricaly. It's all part of the same, it's all Sacred
          >Space.
          >
          >
          >
          >
          >
          >
          >Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/
          >
          >
          >
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