On Wed, 17 Jan 2007, Jacques Basaldúa wrote:
Any coherent higher dimension model should explain which
of the three circumstances is not met, how and why and
without making any particular dimension different from the
others. Something a lot more complicated than just drawing
"easy conclusions" from analytic geometry.
Of course the "higher" dimensions are way "smaller",
otherwise we would see them :-)
Seriously, string-theory requires higher dimensions with
a very small curvature (they are different from the 3).
And you are correct, it gets very complicated.
The geometrical examples were just meant as an easy to
understand explanation why higher dimension do not
increase the 3-d volume of the universe.
Christoph
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