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Re: Elementary Query on hypersurfaces
Posted:
Feb 5, 2013 4:31 AM


stargene <stargene@sbcglobal.net> writes:
> Hi   > I'm hoping that at least one of you has a real > familiarity with hypersurfaces, (which for myself > are mostly interesting as the posited analogs, in > some models, of our physical universe.) Being > very uninformed about hyperanythings, I ask: > > Assuming for sake of discussion that our universe > were somehow the equivalent of a (say) threedimen > sional hypersurface on a hypersphere, would > a given point <in> our universe correspond to a > given point <on> that 3D hypersurface?
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 2D 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 offtopic here.



