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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