Re: [vox] [OT] philosophy class about space and time at UCD

[Peter Jay Salzman <p@diracMAPS.org>]

begin Ryan <ryan@mother.com> 
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> On Tuesday 24 September 2002 11:25 pm, Peter Jay Salzman wrote:
> 
> >    "given any straight line and a point not on it, there exists only one
> >    straight line which passes through the point and never intersects the
> >    first line, no matter how far they're extended"
> >
> > which can be used to prove
> >
> >    "if line A is parallel to line B and line B is parallel to line C
> >     then line A must be parallel to line C".
> >
> > both the postulate and corollary are scrapped in general relativity.
> 
> That goes out the window when you go beyond 2 dimensions. ^_^
> 
> It would be valid in 3 dimentions if you were taking about planes and not 
> lines, and curved space would break *that*.
 
very true.  but that's the common parlance of geometers.  for example,

a "sphere" is a collection of points equidistant from a locus in
whatever dimension you happen to be in.

so in 2 dimensions, a "sphere" would be what we would call a circle.

in 3 dimensions, a "sphere" would be what we call a ball.

in 4 dimensions, a "sphere" would be what we call a hypersphere (it's
   hard, but try to imagine gluing the outsides of two three dimensional
   spheres completely together).

anyway, a plane is a line in 3 dimensions, so everything is cool with
euclid.  :)

pete
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