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stbenge wrote:
> It's good to know that some people are taking the idea of a fourth
> spatial dimension seriously. A lot of people argue that time is the
> "true" 4th dimension, but that idea just doesn't sit well with me, even
> though I don't have a lot of knowledge in this area.
An extra spatial dimension gives you 4D Euclidian space.
Time as an extra dimension gives you a 4D non-Euclidian space, which
turns out to be useful in Einstien's various reletivity theories.
These are two seperate, unrelated geometries.
4D Euclidian space is interesting because it's a straight extension of
3D Euclidian geometry.
And then, as I mentioned, there are other non-Euclidian geometries. For
example, elliptic geometry. In 2D elliptic geometry, a "straight line"
is in fact a line drawn on the surface of a sphere. Since the surface of
a sphere is curved, all these "straight lines" curve around it and
eventually close into circles. (E.g., the Earth's equator is such a
circle.) Thus, in elliptic geometry, *all* lines intersect each other,
and there is no such thing as "parallel" lines.
Somewhat weirder is hyperbolic geometry, where multiple "straight lines"
through a single point do not intersect each other [except at that
point]. You really need to play with this:
http://cs.unm.edu/~joel/NonEuclid/NonEuclid.html
I lost hours in it...
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