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Topic: Elementary Query on hypersurfaces
Replies: 3   Last Post: Feb 5, 2013 4:31 AM

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Nicolas Neuss

Posts: 8
Registered: 6/21/11
Re: Elementary Query on hypersurfaces
Posted: Feb 5, 2013 4:31 AM
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stargene <> writes:

> 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.

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