On Thu, Oct 25, 2012 at 1:43 PM, Stephen P. King <[email protected]> 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 > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to [email protected]. > To unsubscribe from this group, send email to > [email protected]. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
