Timespatiality

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Timespatiality
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From I (a point 0-D nothingness, emptiness)
to Other (a line 1-D linearity, bivalence)
to I ? Other (a plane 2-D possibly 3-valued)
to Community (a cube 3-D many-valued) to
Cosmos (a hypercube 4D potentially ?-valued)
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For example, the Klein-bottle

• The Klein bottle is an unorientable surface. It
  can be constructed by gluing together the two
  ends of a cylindrical tube by protruding one end
  through the tube and connecting it with the other
  end (while simultaneously inflating the tube at
  this second end). The resulting picture looks
  something like this

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• However, the result is not a true picture of the
  Klein bottle, since it depicts a
  self-intersection which isn't really there (in
  other words, there should be no discontinuity
  the surface should be continuous throughout). The
  Klein bottle, in contrast to its limited
  3-dimensional, can easily be realized in
  4-dimensional space one lifts up the narrow part
  of the tube in the direction of the 4-th
  coordinate axis just as it is about to pass
  through the thick part of the tube, then drops it
  back down into 3-dimensional space inside the
  thick part of the tube.

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However there is no need to go through the mental
contortions of visualizing the Klein bottle in
4-dimensional space, if we adopt the intrinsic
point of view we developed for dealing with the
Möbius strip. We do not attempt to physically
realize the gluing described above, but rather
think of it as an abstract gluing, imagining how
the resulting space would look to a 2-dimensional
crab swimming within the surface of the Klein
bottle. This leads us to the following convenient
model of the Klein bottle
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Or perhaps an illustration of the Klein-bottle
through the Möbius-band
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To construct a Möbius band, take a strip
of paper, and twist one end of it,
Then glue the two ends together, and you have a
band with only one continuous side.
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• To relate this to our previous description of the
  Klein bottle, note that the gluing instructions
  tell us to glue the top and bottom edges of the
  rectangle. The result is a cylindrical tube with
  the left and right edges forming the two circular
  ends of the tube. The gluing instructions then
  tell us to glue the two ends of the tube with a
  twist.
• Note also that in creating the Möbius-band the
  gluing instructions tells to glue all four
  corners of the rectangle into a single point.

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Our friend Ms Triangle, is, when navigating
along the band, Either Outside or Inside, or Both
Inside and Outside, or Neither Inside nor
Outside, however we wish to define her. Or, we
might define her in another manner, as
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The containing-contained-uncontained is from our
view of the strip from a 3-D viewpoint. For the
flatlander, her trajectory is 1-D, whereas we
perceive 2-D surfaces. Her discontinuous point
at Contained 1-D space would not be perceived,
unless she were to make a point-hole in her 2-D
plane in order to construct a Möbius-strip.
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We would have to do the samemake a 2-D hole in
our planar surface in order to construct a
Klein-bottle. But a Hyperspherelander could see
it all from here perspective, like we can see it
all in Flatlanders world from our own
Spherelander perspective.Actually, a
Klein-bottle can be constructed from two
Möbius-bands, on right-handed and the other
left-handed, like this
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In this manner, just as the twist in the 2-D
Möbius-band can be created only within 3-D
space, so also the hole in the Klein-bottle can
be created only within 4-D space.