On Thu, Oct 25, 2012 at 1:43 PM, Stephen P. King <stephe...@charter.net> wrote:
> On 10/25/2012 11:52 AM, meekerdb wrote:
>
> On 10/25/2012 4:58 AM, Richard Ruquist wrote:
>
> Stephan,
>
> Since yesterday it occurred to me that you may be thinking of the 10
> or more dimensions of string theory as being orthogonal because they
> were so before the big bang. But the dimensions that
> curled-up/compactified went out of orthogonality during the big bang
> according to Cumrun Vafa. I'll look up that reference if you are
> interested.
>
> According to Vafa 2 dimensions compactified for every single space
> dimension that inflated. In over simplified terms,  2 dimensions
> (actually in strips of some 10,000 Planck lengths) to be compactified
> lined up say in the east-west space dimension so that space in an
> orthogonal direction could expand. So some semblance of orthogonality
> exists in the compactification process, but it is clear that the
> compactified dimensions become embedded in 3D space for inflation to
> occur.
>
>
> It's implicit in the definition of dimensions of a Riemannian manifold that
> there are as many orthogonal directions as dimensions.  Compactified
> dimensions are just small; they're small, not infinite, because they have
> closed topology.  That property is completely independent of having
> orthogonal directions.
>
> Brent
>
> Dear Brent,
>
>     Compactness and orthogonality are not the same quantities. Yes. But my
> point is that the compact structures in string theories (super or not) are
> orthogonal to the dimensions of space-time. Maybe we need all take a
> remedial math class on linear algebra and geometry!

I am still waiting for the explanation of how you know that to be true-
that the compact manifolds are orthogonal to space dimensions.
Richard

>
> --
> Onward!
>
> Stephen
>
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