On 26 Oct 2012, at 14:00, Roger Clough wrote:

Hi Brent, What happens -- or is it even possible -- to collapse the dimensions down to one (which I conjecture might be time), or zero (Platonia or mind).

Yes it is more zero, or zero^zero (one). In my favorite working theory. Bruno

Roger Clough, rclo...@verizon.net 10/26/2012 "Forever is a long time, especially near the end." -Woody Allen ----- Receiving the following content ----- From: meekerdb Receiver: everything-list Time: 2012-10-25, 15:27:47 Subject: Re: Compact dimensions and orthogonality On 10/25/2012 11:47 AM, Richard Ruquist wrote:On Thu, Oct 25, 2012 at 2:23 PM, meekerdb wrote:On 10/25/2012 10:49 AM, Richard Ruquist wrote:On Thu, Oct 25, 2012 at 1:43 PM, Stephen P. King 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 ofthe 10or more dimensions of string theory as being orthogonal becausetheywere so before the big bang. But the dimensions thatcurled-up/compactified went out of orthogonality during the bigbangaccording 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 becompactifiedlined up say in the east-west space dimension so that space in anorthogonal direction could expand. So some semblance oforthogonalityexists in the compactification process, but it is clear that thecompactified dimensions become embedded in 3D space forinflation tooccur.It's implicit in the definition of dimensions of a Riemannianmanifoldthatthere are as many orthogonal directions as dimensions.Compactifieddimensions are just small; they're small, not infinite, becausethey haveclosed topology. That property is completely independent of having orthogonal directions. Brent Dear Brent,Compactness and orthogonality are not the same quantities. Yes.Butmypoint is that the compact structures in string theories (superor not)areorthogonal to the dimensions of space-time. Maybe we need alltake aremedial math class on linear algebra and geometry!I am still waiting for the explanation of how you know that to betrue-that the compact manifolds are orthogonal to space dimensions. RichardIf they weren't orthogonal then a vector on them could berepresented by bya linear combinations of vectors in 3-space - and then theywouldn't providethe additional degrees of freedom to describe particles andfields. They'djust be part of 3-space.They are just part of 3 space once the extra dimensions arecompactified.No, that's incorrect. I don't know much about string theory, but Iwrote my dissertationon Kaluza-Klein and the additional dimensions are still additionaldimensions. KK issimple because there's only one extra dimension and so compactifyingit just means it's acircle, and then (classically) the location around the circle is thephase of theelectromagnetic potential; quantized it's photons. Being compactjust means they'refinite, it doesn't imply they're part of the 3-space. If they werethey couldn't functionto represent particles 'in' 3-space.I do not know about what happens to the extra degrees of freedom.If you lost them then you'd just have 3-space, possibly withdifferent topology, but youcouldn't represent all the particles which was the whole point ofstring theory.Brent--You received this message because you are subscribed to the GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.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 GoogleGroups "Everything List" group.To post to this group, send email to everything-list@googlegroups.com.To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com.For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.

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