AstroKing

OK, What about the up/down to give 3D coordinates and the closed loop manifests as the surface of a 4D sphere. This is what I see and observe.

So in a closed universe which has the possibility that travelling far enough across the universe you would end up where you started. The close universe infers curvature and could be described by an extra dimension. Is this dimension just abstract. If this could be verified then how can it be abstract. RE: "It's just a way to express coordinates" you can have a w,x,y,z coordinate system where w is an extra spacial dimension. So what you are saying is the curvature of space would NOT be "w" in a w,x,y,z system where xyz refer to classical three-dimensional space.

I did not mean to imply 2-D space, ignore any 2-D thoughts.

The ants think they are on a 3-D toy globe and are not 2-D ants. The ants think they exist in 3-D. By doing scientific measurements using 3-D tools they show the toy globe to be flat in 3-D space but curved in some higher space. So really the ants think that something is strange and must be living in a higher space but cannot workout where they are. The space has the properties of a globe (eg like our Earth) they can walk around it and come back to the same point. My question is what shape space can be like this?

He is my question: I really wanted to discus 4 (or more) spacial dimensions only and ignore time, I included time in the title to make that clear. Consider an ant living on a toy globe 1 meter in diameter. The ant considers his world flat because he cannot see the whole globe. On his journeys he tries to map the world and discovers that by walking in a straight line he has returned to the same point. The ant now thinks that he lives on a globe. Wanting to map the toy world he struggles with the idea of how to draw a representation of the globe onto a 2-D drawing and comes to the conclusion that to map the toy globe he cannot do it without distortion and sees how to project the globe onto the 2-D map. Meanwhile other ants are happy to think they still live on their flatland. The other ants still prefer their flatland way of thinking and say they can prove it too. The flatland proof is based on 3-D space instruments such as using a gyroscope.Thus two conflicting proofs (globe and flat) which both stand up to best scientific reasoning. The flatland proof is based on 3-D while the globe is measured round in a higher (4-D or more) space. My question is how can the space (toy globe) be modified so that both are still true. I think we are looking at changing the toy globe into maybe a 4-D sphere or torus perhaps? Sorry I have edited my question because my description was wrong. I got confused with the two proofs and separated them one into 3-D the other into 4-D

I have been thinking about this for a while. At present trying to learn quaternions. My question is below regarding ants on toy globe.