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JAM-OTBOC

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What happens if we extend this concept to attempt to diagram the same thing for our three-dimensional universe? Does this imply that our 3-D universe is 'embedded' within a higher dimensional space?

The metric tensor used to describe the motion of an object in the presence of mass makes use of a multi-dimensional Reimannian Space. This (as I understand it) is necessary in order to explain the distortion of our three dimensions according to general relativity due to the presence of mass. Into what does our 3D universe distort according to this law? The two dimensional plane needs our 3D universe in order to deform to show gravitation in that realm. What kind of universe is required to explain the distortion of our 3D universe? Could this be some kind of Hyperspace? If so what are it's properties?