> Hi - - > I'm hoping that at least one of you has a real > familiarity with hyper-surfaces, (which for myself > are mostly interesting as the posited analogs, in > some models, of our physical universe.) Being > very uninformed about hyper-anythings, I ask: > > Assuming for sake of discussion that our universe > were somehow the equivalent of a (say) three-dimen- > sional hyper-surface on a hyper-sphere, would > a given point <in> our universe correspond to a > given point <on> that 3-D hyper-surface?
Yes, why not? You can consider any "manifold" as "embedded" (Whitney/Nash embedding theorems).
> Or might a given point in our universe correspond somehow to a higher > dimensional object,
Yes, that is a possible description, which is also not completely different from the standard procedure of describing states (like electromagnetic fields) to points in space.
> perhaps even a 2-D surface entirely spanning the > hyper- sphere.
This does not make sense to me.
> I'm just wildly grasping at straws here. Thanks.
You're welcome. But note that your question is off-topic here.