[Archy (George)]

RE: "Remember this is a thread on General Relativity which involves the geometry of space not the geometry of bodies.
Steven[/quote]"

The thread started with: "Has anyone managed to find a mental trick to assist in visualising a curved space." This is a general question, not one restricted to General Relativity.

Graham had a second line: "My thought experiment is the classic surface of a sphere with a triangle with three 90 degree angles... I find it difficult to change my thinking to 'see' the lines of the triangle as one dimensional and not 2 dimensional in euclidian space. So to my cartesian mind, its not 'really' a triangle."

Later he added: "Say that I'm an ant that lives on this curved sphere.
I walk up to the vertex of the triangle at the north pole and I measure it - I find it to be 90 degrees - right?
I walk to the other two and I measure 90 degrees. Totalling 180 degrees.
Would I perceive that I was upsidedown at the south pole as compared to the north pole? I don't think so, as the space itself is curved, but if I was on a sphere in euclidian space, then I would perceive myself as upsidedown on the south pole."

It was in that context that I commented:
"Although by carefully choosing the origin (0,0,0) position in space can be defined so that there is an up and a down, it is also possible in every case to have a position in 3D or nD space ( where n is two or more) such that there is no up or down, although there will generally be a "higher"or "lower".

In reference to the ant going from the North pole to the South pole, I can't see that the ant's perception will be different to mine. When I travel to the UK I do not see that i am upside down. Do You? "