Re: Compact dimensions and orthogonality
On Sat, Oct 27, 2012 at 1:56 AM, Stephen P. King stephe...@charter.net wrote: On 10/27/2012 12:07 AM, Richard Ruquist wrote: Stephen, I agree that All of this discussion is below the level of conscious self-awareness, but prefer to think of raw perception as distinguishing what can be from what cannot be, as for example in constructor theory. In my model conscious awareness is an arithmetic emergent due to the incompleteness of discrete, ennumerable compact manifolds. What can or cannot be is at a lower level, perhaps due to discrete arithmetic computations that may be teleological, a nod to Deacon as well as Deutsch. Hi Richard, Umm, interesting. The incompleteness forces consciousness... Please elaborate! Stephan, That is what my paper is all about: http://vixra.org/pdf/1101.0044v1.pdf It appears that your memory is no better than mine. I went into physics because of my poor memory. When I got kicked out, really black-balled due to the Star Wars protest I managed to get into med school at age 55 but my memory failed me and I had to settle for being a doctor of physics. I am going to Hoboken to celebrate my 75th birthday with my son and grandson over this weekend. So I will not be able to get on-line until Sunday night. It's been fun. 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 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 Google Groups 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.
Re: Re: Re: Re: Compact dimensions and orthogonality
Hi Richard Ruquist Yes, the strings themselves are extended, but theoretical strings (string theory itself) are not. Roger Clough, rclo...@verizon.net 10/27/2012 Forever is a long time, especially near the end. -Woody Allen - Receiving the following content - From: Richard Ruquist Receiver: everything-list Time: 2012-10-26, 09:48:32 Subject: Re: Re: Re: Compact dimensions and orthogonality Roger, Your Leibniz monads are not extended, but the monads of string theory are extended yet have most of the important properties of inextension. Richard On Fri, Oct 26, 2012 at 9:08 AM, Roger Clough wrote: Hi Richard Ruquist Thank you, but monads are not extended in space, they are mental and so inextended. Roger Clough, rclo...@verizon.net 10/26/2012 Forever is a long time, especially near the end. -Woody Allen - Receiving the following content - From: Richard Ruquist Receiver: everything-list Time: 2012-10-26, 08:08:44 Subject: Re: Re: Compact dimensions and orthogonality No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. However, the string theory monads that result from compactification have many of the properties that you ascribe to unextended realms. Because of BEC and instant mapping effects, the entire collection of monads in the universe may behave as though the existed at a single point despite being extended. Richard On Fri, Oct 26, 2012 at 7:56 AM, Roger Clough wrote: Hi Richard, Is there some way, such as reducing the dimensions of strings to zero, that one can transverse from the world of extension (the physical world) to that of inextended experience or theory? 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, 14:23:04 Subject: Re: Compact dimensions and orthogonality 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 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 If they weren't orthogonal then a vector on them could be represented by by a linear combinations of vectors in 3-space - and then they wouldn't provide the additional degrees of freedom to describe particles and fields. They'd just be part of 3-space. Brent -- You received this message because you are subscribed to the Google Groups 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 Google Groups 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
Re: Even more compact dimensions Re: Re: Compact dimensions and orthogonality
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 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 If they weren't orthogonal then a vector on them could be represented by by a linear combinations of vectors in 3-space - and then they wouldn't provide the additional degrees of freedom to describe particles and fields. They'd just be part of 3-space. They are just part of 3 space once the extra dimensions are compactified. No, that's incorrect. I don't know much about string theory, but I wrote my dissertation on Kaluza-Klein and the additional dimensions are still additional dimensions. KK is simple because there's only one extra dimension and so compactifying it just means it's a circle, and then (classically) the location around the circle is the phase of the electromagnetic potential; quantized it's photons. Being compact just means they're finite, it doesn't imply they're part of the 3-space. If they were they couldn't function to 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 with different topology, but you couldn't represent all the particles which was the whole point of string theory. Brent -- You received this message because you are subscribed to the Google Groups 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 Google Groups 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 . http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups 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.
Re: Compact dimensions and orthogonality
On Friday, October 26, 2012 11:46:23 PM UTC-4, Stephen Paul King wrote: On 10/26/2012 11:36 PM, Craig Weinberg wrote: All of it ultimately has to be grounded in ordinary conscious experience. Otherwise we have an infinite regress of invisible homunculi translating crystalline manifolds in compactified space into ordinary experiences. At what point does it become necessary for vibrating topological constructs to imagine that they are something other than what they are, and to feel and see rather than merely be informed of relevant data? I am confident that ultimately there can be no reduction of awareness at all. Awareness can assume mathematical forms or physical substance, but neither of those can possibly generate even a single experience on their own. Craig Hi Craig, All of this discussion is below the level of conscious self-awareness. At most there is just raw perception, the basis distinguishing of is from not is. Hi Stephen, I'm not seeing why the problem would be any different any particular level though? If you have experience, then sure, a manifold can possibly have an experience or be experienced by something that can, but if there is no theory for primordial perception in the first place, no amount of topological position indices will generate it. All that Calabi-Yau does is make an interesting shaped body, but the body still has nowhere to put a mind or a self, much less a reason for those things to ever exist. Craig -- Onward! Stephen -- You received this message because you are subscribed to the Google Groups Everything List group. To view this discussion on the web visit https://groups.google.com/d/msg/everything-list/-/5WoF5DHRmucJ. 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.
Re: Compact dimensions and orthogonality
On 27 Oct 2012, at 07:56, Stephen P. King wrote: On 10/27/2012 12:07 AM, Richard Ruquist wrote: Stephen, I agree that All of this discussion is below the level of conscious self-awareness, but prefer to think of raw perception as distinguishing what can be from what cannot be, as for example in constructor theory. In my model conscious awareness is an arithmetic emergent due to the incompleteness of discrete, ennumerable compact manifolds. What can or cannot be is at a lower level, perhaps due to discrete arithmetic computations that may be teleological, a nod to Deacon as well as Deutsch. Hi Richard, Umm, interesting. The incompleteness forces consciousness... Please elaborate! AUDA is the final elaboration of that. At the propositional level. I remind you. G and G* are the logic of incompleteness. Gödel's second theorem is the arithmetical interpretation of Dt - ~BDt, and by Solovay's theorem we get them all. In fine consciousness is something between Dt and Dt V t, Dt V t V Bf, the modal duals of the saured box of the corresponding variants of G. Incompleteness is just the startling fact of the logic of self- reference, which can translated the classical theory of knowledge in the arithmetical or machine languages. Bruno -- 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 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 . http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups 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.
Re: Re: Compact dimensions and orthogonality
Hi Richard, Is there some way, such as reducing the dimensions of strings to zero, that one can transverse from the world of extension (the physical world) to that of inextended experience or theory? 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, 14:23:04 Subject: Re: Compact dimensions and orthogonality 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 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 If they weren't orthogonal then a vector on them could be represented by by a linear combinations of vectors in 3-space - and then they wouldn't provide the additional degrees of freedom to describe particles and fields. They'd just be part of 3-space. Brent -- You received this message because you are subscribed to the Google Groups 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 Google Groups 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.
Even more compact dimensions Re: Re: Compact dimensions and orthogonality
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). 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 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 If they weren't orthogonal then a vector on them could be represented by by a linear combinations of vectors in 3-space - and then they wouldn't provide the additional degrees of freedom to describe particles and fields. They'd just be part of 3-space. They are just part of 3 space once the extra dimensions are compactified. No, that's incorrect. I don't know much about string theory, but I wrote my dissertation on Kaluza-Klein and the additional dimensions are still additional dimensions. KK is simple because there's only one extra dimension and so compactifying it just means it's a circle, and then (classically) the location around the circle is the phase of the electromagnetic potential; quantized it's photons. Being compact just means they're finite, it doesn't imply they're part of the 3-space. If they were they couldn't function to 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 with different topology, but you couldn't represent all the particles which was the whole point of string theory. Brent -- You received this message because you are subscribed to the Google Groups 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 Google Groups 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.
Re: Re: Compact dimensions and orthogonality
No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. However, the string theory monads that result from compactification have many of the properties that you ascribe to unextended realms. Because of BEC and instant mapping effects, the entire collection of monads in the universe may behave as though the existed at a single point despite being extended. Richard On Fri, Oct 26, 2012 at 7:56 AM, Roger Clough rclo...@verizon.net wrote: Hi Richard, Is there some way, such as reducing the dimensions of strings to zero, that one can transverse from the world of extension (the physical world) to that of inextended experience or theory? 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, 14:23:04 Subject: Re: Compact dimensions and orthogonality 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 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 If they weren't orthogonal then a vector on them could be represented by by a linear combinations of vectors in 3-space - and then they wouldn't provide the additional degrees of freedom to describe particles and fields. They'd just be part of 3-space. Brent -- You received this message because you are subscribed to the Google Groups 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 Google Groups 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 Google Groups 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.
Re: Re: Re: Compact dimensions and orthogonality
Hi Richard Ruquist Thank you, but monads are not extended in space, they are mental and so inextended. Roger Clough, rclo...@verizon.net 10/26/2012 Forever is a long time, especially near the end. -Woody Allen - Receiving the following content - From: Richard Ruquist Receiver: everything-list Time: 2012-10-26, 08:08:44 Subject: Re: Re: Compact dimensions and orthogonality No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. However, the string theory monads that result from compactification have many of the properties that you ascribe to unextended realms. Because of BEC and instant mapping effects, the entire collection of monads in the universe may behave as though the existed at a single point despite being extended. Richard On Fri, Oct 26, 2012 at 7:56 AM, Roger Clough wrote: Hi Richard, Is there some way, such as reducing the dimensions of strings to zero, that one can transverse from the world of extension (the physical world) to that of inextended experience or theory? 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, 14:23:04 Subject: Re: Compact dimensions and orthogonality 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 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 If they weren't orthogonal then a vector on them could be represented by by a linear combinations of vectors in 3-space - and then they wouldn't provide the additional degrees of freedom to describe particles and fields. They'd just be part of 3-space. Brent -- You received this message because you are subscribed to the Google Groups 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 Google Groups 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 Google Groups 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 Google Groups 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
Re: Re: Re: Compact dimensions and orthogonality
Roger, Your Leibniz monads are not extended, but the monads of string theory are extended yet have most of the important properties of inextension. Richard On Fri, Oct 26, 2012 at 9:08 AM, Roger Clough rclo...@verizon.net wrote: Hi Richard Ruquist Thank you, but monads are not extended in space, they are mental and so inextended. Roger Clough, rclo...@verizon.net 10/26/2012 Forever is a long time, especially near the end. -Woody Allen - Receiving the following content - From: Richard Ruquist Receiver: everything-list Time: 2012-10-26, 08:08:44 Subject: Re: Re: Compact dimensions and orthogonality No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. However, the string theory monads that result from compactification have many of the properties that you ascribe to unextended realms. Because of BEC and instant mapping effects, the entire collection of monads in the universe may behave as though the existed at a single point despite being extended. Richard On Fri, Oct 26, 2012 at 7:56 AM, Roger Clough wrote: Hi Richard, Is there some way, such as reducing the dimensions of strings to zero, that one can transverse from the world of extension (the physical world) to that of inextended experience or theory? 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, 14:23:04 Subject: Re: Compact dimensions and orthogonality 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 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 If they weren't orthogonal then a vector on them could be represented by by a linear combinations of vectors in 3-space - and then they wouldn't provide the additional degrees of freedom to describe particles and fields. They'd just be part of 3-space. Brent -- You received this message because you are subscribed to the Google Groups 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 Google Groups 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 Google Groups 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 Google Groups Everything List group. To post
Re: Even more compact dimensions Re: Re: Compact dimensions and orthogonality
On 10/26/2012 5:00 AM, 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). I'm not sure what you mean by 'collapse'. Do you mean, Is is possible to invent a theory which has only a one-dimensional Remannian manifold? Sure, but I don't think you can make it agree with physical observations. In my view, these are models we invent to try to understand the world; so we need our model to be understandable. That's one of my objections to a lot of 'everything' theories like Tegmark's; they hypothesize a model that is incomprehensible in order to 'explain' something - it's like God did it and God works in mysterious ways. Brent -- You received this message because you are subscribed to the Google Groups 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.
Re: Compact dimensions and orthogonality
On 10/26/2012 5:08 AM, Richard Ruquist wrote: No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. Do you have a reference that describes this 'embedding'? Brent -- You received this message because you are subscribed to the Google Groups 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.
Re: Compact dimensions and orthogonality
Yes http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory On Fri, Oct 26, 2012 at 3:01 PM, meekerdb meeke...@verizon.net wrote: On 10/26/2012 5:08 AM, Richard Ruquist wrote: No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. Do you have a reference that describes this 'embedding'? Brent -- You received this message because you are subscribed to the Google Groups 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 Google Groups 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.
Re: Compact dimensions and orthogonality
On 10/26/2012 4:31 PM, Richard Ruquist wrote: Yes http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory Hi Richard, Could you cut and paste the specific description that answers Brent's question? On Fri, Oct 26, 2012 at 3:01 PM, meekerdb meeke...@verizon.net wrote: On 10/26/2012 5:08 AM, Richard Ruquist wrote: No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. Do you have a reference that describes this 'embedding'? Brent -- You received this message because you are subscribed to the Google Groups 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. -- 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 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.
Re: Compact dimensions and orthogonality
On 10/26/2012 1:31 PM, Richard Ruquist wrote: Yes http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory A search on embed turns up nothing about embedding in 3-space. Brent On Fri, Oct 26, 2012 at 3:01 PM, meekerdbmeeke...@verizon.net wrote: On 10/26/2012 5:08 AM, Richard Ruquist wrote: No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. Do you have a reference that describes this 'embedding'? Brent -- You received this message because you are subscribed to the Google Groups 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 Google Groups 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.
Re: Compact dimensions and orthogonality
The requested excerpt from http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory: Calabi-Yau manifolds in string theory Superstring theory is a unified theory for all the forces of nature including quantum gravity. In superstring theory, the fundamental building block is an extended object, namely a string, whose vibrations would give rise to the particles encountered in nature. The constraints for the consistency of such a theory are extremely stringent. They require in particular that the theory takes place in a 10-dimensional space-time. To make contact with our 4-dimensional world, it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X . The 6-dimensional space X would be tiny, which would explain why it has not been detected so far at the existing experimental energy levels. Each choice of the internal space X leads to a different effective theory on the 4-dimensional Minkowski space M3,1 , which should be the theory describing our world. The 6d space is tiny indeed, said by Yau in his book The Shape of Inner Space to be 1000 Planck lengths in diameter. The rest of that reference apparently describes a number of possible realizatons of the 6d space that is way beyond my comprehension. So now I am reading http://universe-review.ca/R15-26-CalabiYau.htm, a math review of Yau's book, to get a more definitive answer to our questions. Richard. On Fri, Oct 26, 2012 at 4:48 PM, Stephen P. King stephe...@charter.net wrote: On 10/26/2012 4:31 PM, Richard Ruquist wrote: Yes http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory Hi Richard, Could you cut and paste the specific description that answers Brent's question? On Fri, Oct 26, 2012 at 3:01 PM, meekerdb meeke...@verizon.net wrote: On 10/26/2012 5:08 AM, Richard Ruquist wrote: No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. Do you have a reference that describes this 'embedding'? Brent -- You received this message because you are subscribed to the Google Groups 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. -- 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 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 Google Groups 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.
Re: Compact dimensions and orthogonality
On Fri, Oct 26, 2012 at 6:36 PM, Richard Ruquist yann...@gmail.com wrote: The requested excerpt from http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory: Calabi-Yau manifolds in string theory Superstring theory is a unified theory for all the forces of nature including quantum gravity. In superstring theory, the fundamental building block is an extended object, namely a string, whose vibrations would give rise to the particles encountered in nature. The constraints for the consistency of such a theory are extremely stringent. They require in particular that the theory takes place in a 10-dimensional space-time. To make contact with our 4-dimensional world, it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X . The 6-dimensional space X would be tiny, which would explain why it has not been detected so far at the existing experimental energy levels. Each choice of the internal space X leads to a different effective theory on the 4-dimensional Minkowski space M3,1 , which should be the theory describing our world. The 6d space is tiny indeed, said by Yau in his book The Shape of Inner Space to be 1000 Planck lengths in diameter. The rest of that reference apparently describes a number of possible realizatons of the 6d space that is way beyond my comprehension. So now I am reading http://universe-review.ca/R15-26-CalabiYau.htm, a math review of Yau's book, to get a more definitive answer to our questions. Richard. From http://universe-review.ca/R15-26-CalabiYau.htm Compactification - Since all of us experience only 3 spatial and 1 temporal dimensions, the 10 and 26 extra-dimensions have to be hidden under some schemes. One of the two alternatives is to roll them up into very small size not observable even under a very powerful microscope. The other one is to consider our existence on a 3 brane floating in the bulk of ten spatial dimensions. The first alternative is called compactification. It is more complicated than merely shrinking the size (of the dimensions). Even in the very simple case of a (4+1) toy model, compactification to a small circle of radius R produces particle in the 3-D space with mass = n/R, where n is an integer. It manifests itself as a scalar particle (spin 0) obeying the Klein-Gordon equation. Compactification of the 16 extra-dimensions for the bosonic string, produces the gluon and electroweak gauge fields. Compactification of the remaining 6 extra-dimensions breaks the Heterotic string symmetry down to the point where the hadrons and leptons of more conventional theories are recovered. Viewed from a distance, the symmetry-broken Heterotic strings look just like familiar point particles - but without the infinities and anomalies of the particle approach. In order to maintain conformal invariance (i.e., the world sheet should remain unchanged by relabeling), these 6 extra-dimensions have to curl up in a particular way - a more promising one is the Calabi-Yau manifold (see more in Compactification) as shown in Figure 12, where each point stands for a 3-D space. Figure 12 Calabi-Yau Space The keys words are produces particle in the 3-D space with mass. The picture of the compact manifolds, somewhat like a crystalline structure, did not copy over. More: Calabi-Yau Manifold - As mentioned in the section of Calabi-Yau Manifold for Dummies, all the above-mentioned requirements are satisfied by the Calabi-Yau manifold as if it is made to order for the occasion. By the way, it also correctly reproduce the three generations for the fermions, and is itself a solution of the 6-D field equation in General Relativity (producing the gravitino). The word embedding appears in this reference: Another way to compute g is through embedding the Calabi-Yau manifold in a higher dimensional background space. But so far no one has been able to work out the coupling constant g or mass for any fermion. Anyway, this is one example of the attempts to derive fundamental constants in the 3+1 large dimensions from the 6 dimensional compactified space. Bottomline, I am not satisfied with what I am able to extract from these references anything to satisfy your criticisms, or even my concerns. I am afraid that I have been influenced by the picture of the Compact Manifolds as a periodic structure of 6d particles in 3D space. Richard On Fri, Oct 26, 2012 at 4:48 PM, Stephen P. King stephe...@charter.net wrote: On 10/26/2012 4:31 PM, Richard Ruquist wrote: Yes http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory Hi Richard, Could you cut and paste the specific description that answers Brent's question? On Fri, Oct 26, 2012 at 3:01 PM, meekerdb meeke...@verizon.net wrote: On 10/26/2012 5:08 AM, Richard Ruquist wrote: No Roger, In string theory dimensions are conserved
Re: Compact dimensions and orthogonality
Dear Richard, From the quote below: it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X. This local product operation, represented by the 'x' is the act of adding two manifolds, one of 4 dimensions and one of 6 dimensions for a total of 10 dimensions, thus this yields a very different structure from, for example, a 10d Euclidean manifold. All of the local degrees of freedom are present at every point but the compacted ones are such that any motion (a translational transformation within M^3,1) shifts from one local 6d manifold to another 6d manifold. The 6d compactified manifolds are Planck sized 6d tori 'glued' (using the math of fiber bundles http://mathworld.wolfram.com/FiberBundle.html) to each and every point in the M^3,1 space. It is not correct to think of the compacted manifolds (actually they are tori) as free floating in a 3,1 dimensional (not 4d for technical reasons as the signature of time is not the same as the signature of the spatial dimensions) manifold. i.e. space-time. On 10/26/2012 6:36 PM, Richard Ruquist wrote: The requested excerpt from http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory: Calabi-Yau manifolds in string theory Superstring theory is a unified theory for all the forces of nature including quantum gravity. In superstring theory, the fundamental building block is an extended object, namely a string, whose vibrations would give rise to the particles encountered in nature. The constraints for the consistency of such a theory are extremely stringent. They require in particular that the theory takes place in a 10-dimensional space-time. To make contact with our 4-dimensional world, it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X . The 6-dimensional space X would be tiny, which would explain why it has not been detected so far at the existing experimental energy levels. Each choice of the internal space X leads to a different effective theory on the 4-dimensional Minkowski space M3,1 , which should be the theory describing our world. The 6d space is tiny indeed, said by Yau in his book The Shape of Inner Space to be 1000 Planck lengths in diameter. The rest of that reference apparently describes a number of possible realizatons of the 6d space that is way beyond my comprehension. So now I am reading http://universe-review.ca/R15-26-CalabiYau.htm, a math review of Yau's book, to get a more definitive answer to our questions. Richard. On Fri, Oct 26, 2012 at 4:48 PM, Stephen P. King stephe...@charter.net wrote: On 10/26/2012 4:31 PM, Richard Ruquist wrote: Yes http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory Hi Richard, Could you cut and paste the specific description that answers Brent's question? On Fri, Oct 26, 2012 at 3:01 PM, meekerdb meeke...@verizon.net wrote: On 10/26/2012 5:08 AM, Richard Ruquist wrote: No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. Do you have a reference that describes this 'embedding'? Brent -- 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 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.
Re: Compact dimensions and orthogonality
Dear Richard, You wrote: the picture of the Compact Manifolds as a periodic structure of 6d particles in 3D space. I agree that a crude reading of 10d string theory is consistent with this picture. This picture is built for use in quantum field theories where particles are excitations of the field that are localized at a fixed point in space-time. To do calculations involving GR this picture simply does not work. On 10/26/2012 7:01 PM, Richard Ruquist wrote: On Fri, Oct 26, 2012 at 6:36 PM, Richard Ruquist yann...@gmail.com wrote: The requested excerpt from http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory: Calabi-Yau manifolds in string theory Superstring theory is a unified theory for all the forces of nature including quantum gravity. In superstring theory, the fundamental building block is an extended object, namely a string, whose vibrations would give rise to the particles encountered in nature. The constraints for the consistency of such a theory are extremely stringent. They require in particular that the theory takes place in a 10-dimensional space-time. To make contact with our 4-dimensional world, it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X . The 6-dimensional space X would be tiny, which would explain why it has not been detected so far at the existing experimental energy levels. Each choice of the internal space X leads to a different effective theory on the 4-dimensional Minkowski space M3,1 , which should be the theory describing our world. The 6d space is tiny indeed, said by Yau in his book The Shape of Inner Space to be 1000 Planck lengths in diameter. The rest of that reference apparently describes a number of possible realizatons of the 6d space that is way beyond my comprehension. So now I am reading http://universe-review.ca/R15-26-CalabiYau.htm, a math review of Yau's book, to get a more definitive answer to our questions. Richard. From http://universe-review.ca/R15-26-CalabiYau.htm Compactification - Since all of us experience only 3 spatial and 1 temporal dimensions, the 10 and 26 extra-dimensions have to be hidden under some schemes. One of the two alternatives is to roll them up into very small size not observable even under a very powerful microscope. The other one is to consider our existence on a 3 brane floating in the bulk of ten spatial dimensions. The first alternative is called compactification. It is more complicated than merely shrinking the size (of the dimensions). Even in the very simple case of a (4+1) toy model, compactification to a small circle of radius R produces particle in the 3-D space with mass = n/R, where n is an integer. It manifests itself as a scalar particle (spin 0) obeying the Klein-Gordon equation. Compactification of the 16 extra-dimensions for the bosonic string, produces the gluon and electroweak gauge fields. Compactification of the remaining 6 extra-dimensions breaks the Heterotic string symmetry down to the point where the hadrons and leptons of more conventional theories are recovered. Viewed from a distance, the symmetry-broken Heterotic strings look just like familiar point particles - but without the infinities and anomalies of the particle approach. In order to maintain conformal invariance (i.e., the world sheet should remain unchanged by relabeling), these 6 extra-dimensions have to curl up in a particular way - a more promising one is the Calabi-Yau manifold (see more in Compactification) as shown in Figure 12, where each point stands for a 3-D space. Figure 12 Calabi-Yau Space The keys words are produces particle in the 3-D space with mass. The picture of the compact manifolds, somewhat like a crystalline structure, did not copy over. More: Calabi-Yau Manifold - As mentioned in the section of Calabi-Yau Manifold for Dummies, all the above-mentioned requirements are satisfied by the Calabi-Yau manifold as if it is made to order for the occasion. By the way, it also correctly reproduce the three generations for the fermions, and is itself a solution of the 6-D field equation in General Relativity (producing the gravitino). The word embedding appears in this reference: Another way to compute g is through embedding the Calabi-Yau manifold in a higher dimensional background space. But so far no one has been able to work out the coupling constant g or mass for any fermion. Anyway, this is one example of the attempts to derive fundamental constants in the 3+1 large dimensions from the 6 dimensional compactified space. Bottomline, I am not satisfied with what I am able to extract from these references anything to satisfy your criticisms, or even my concerns. I am afraid that I have been influenced by the picture of the Compact Manifolds as a periodic structure of 6d particles in 3D space. Richard On Fri, Oct 26, 2012 at 4:48 PM, Stephen P. King
Re: Compact dimensions and orthogonality
No one said they were free floating On Fri, Oct 26, 2012 at 7:55 PM, Stephen P. King stephe...@charter.net wrote: Dear Richard, From the quote below: it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X. This local product operation, represented by the 'x' is the act of adding two manifolds, one of 4 dimensions and one of 6 dimensions for a total of 10 dimensions, thus this yields a very different structure from, for example, a 10d Euclidean manifold. All of the local degrees of freedom are present at every point but the compacted ones are such that any motion (a translational transformation within M^3,1) shifts from one local 6d manifold to another 6d manifold. The 6d compactified manifolds are Planck sized 6d tori 'glued' (using the math of fiber bundles) to each and every point in the M^3,1 space. It is not correct to think of the compacted manifolds (actually they are tori) as free floating in a 3,1 dimensional (not 4d for technical reasons as the signature of time is not the same as the signature of the spatial dimensions) manifold. i.e. space-time. On 10/26/2012 6:36 PM, Richard Ruquist wrote: The requested excerpt from http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory: Calabi-Yau manifolds in string theory Superstring theory is a unified theory for all the forces of nature including quantum gravity. In superstring theory, the fundamental building block is an extended object, namely a string, whose vibrations would give rise to the particles encountered in nature. The constraints for the consistency of such a theory are extremely stringent. They require in particular that the theory takes place in a 10-dimensional space-time. To make contact with our 4-dimensional world, it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X . The 6-dimensional space X would be tiny, which would explain why it has not been detected so far at the existing experimental energy levels. Each choice of the internal space X leads to a different effective theory on the 4-dimensional Minkowski space M3,1 , which should be the theory describing our world. The 6d space is tiny indeed, said by Yau in his book The Shape of Inner Space to be 1000 Planck lengths in diameter. The rest of that reference apparently describes a number of possible realizatons of the 6d space that is way beyond my comprehension. So now I am reading http://universe-review.ca/R15-26-CalabiYau.htm, a math review of Yau's book, to get a more definitive answer to our questions. Richard. On Fri, Oct 26, 2012 at 4:48 PM, Stephen P. King stephe...@charter.net wrote: On 10/26/2012 4:31 PM, Richard Ruquist wrote: Yes http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory Hi Richard, Could you cut and paste the specific description that answers Brent's question? On Fri, Oct 26, 2012 at 3:01 PM, meekerdb meeke...@verizon.net wrote: On 10/26/2012 5:08 AM, Richard Ruquist wrote: No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. Do you have a reference that describes this 'embedding'? Brent -- 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 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 Google Groups 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.
Re: Compact dimensions and orthogonality
On 10/26/2012 4:55 PM, Stephen P. King wrote: Dear Richard, From the quote below: it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X. This local product operation, represented by the 'x' is the act of adding two manifolds, one of 4 dimensions and one of 6 dimensions for a total of 10 dimensions, thus this yields a very different structure from, for example, a 10d Euclidean manifold. All of the local degrees of freedom are present at every point but the compacted ones are such that any motion (a translational transformation within M^3,1) shifts from one local 6d manifold to another 6d manifold. The 6d compactified manifolds are Planck sized 6d tori 'glued' (using the math of fiber bundles http://mathworld.wolfram.com/FiberBundle.html) to each and every point in the M^3,1 space. It is not correct to think of the compacted manifolds (actually they are tori) as free floating in a 3,1 dimensional (not 4d for technical reasons as the signature of time is not the same as the signature of the spatial dimensions) manifold. i.e. space-time. They are manifolds - just some more dimensions that happen to be compact. It makes no more sense to talk about them as 'free-floating' than to talk about altitude free floating on lat-long; it's another 'direction', not an object. Brent On 10/26/2012 6:36 PM, Richard Ruquist wrote: The requested excerpt from http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory: Calabi-Yau manifolds in string theory Superstring theory is a unified theory for all the forces of nature including quantum gravity. In superstring theory, the fundamental building block is an extended object, namely a string, whose vibrations would give rise to the particles encountered in nature. The constraints for the consistency of such a theory are extremely stringent. They require in particular that the theory takes place in a 10-dimensional space-time. To make contact with our 4-dimensional world, it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X . The 6-dimensional space X would be tiny, which would explain why it has not been detected so far at the existing experimental energy levels. Each choice of the internal space X leads to a different effective theory on the 4-dimensional Minkowski space M3,1 , which should be the theory describing our world. The 6d space is tiny indeed, said by Yau in his book The Shape of Inner Space to be 1000 Planck lengths in diameter. The rest of that reference apparently describes a number of possible realizatons of the 6d space that is way beyond my comprehension. So now I am reading http://universe-review.ca/R15-26-CalabiYau.htm, a math review of Yau's book, to get a more definitive answer to our questions. Richard. On Fri, Oct 26, 2012 at 4:48 PM, Stephen P. Kingstephe...@charter.net wrote: On 10/26/2012 4:31 PM, Richard Ruquist wrote: Yes http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory Hi Richard, Could you cut and paste the specific description that answers Brent's question? On Fri, Oct 26, 2012 at 3:01 PM, meekerdbmeeke...@verizon.net wrote: On 10/26/2012 5:08 AM, Richard Ruquist wrote: No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. Do you have a reference that describes this 'embedding'? Brent -- 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 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 Google Groups 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.
Re: Compact dimensions and orthogonality
Hi Richard, OK, then where are we in disagreement? On 10/26/2012 8:05 PM, Richard Ruquist wrote: No one said they were free floating On Fri, Oct 26, 2012 at 7:55 PM, Stephen P. King stephe...@charter.net wrote: Dear Richard, From the quote below: it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X. This local product operation, represented by the 'x' is the act of adding two manifolds, one of 4 dimensions and one of 6 dimensions for a total of 10 dimensions, thus this yields a very different structure from, for example, a 10d Euclidean manifold. All of the local degrees of freedom are present at every point but the compacted ones are such that any motion (a translational transformation within M^3,1) shifts from one local 6d manifold to another 6d manifold. The 6d compactified manifolds are Planck sized 6d tori 'glued' (using the math of fiber bundles) to each and every point in the M^3,1 space. It is not correct to think of the compacted manifolds (actually they are tori) as free floating in a 3,1 dimensional (not 4d for technical reasons as the signature of time is not the same as the signature of the spatial dimensions) manifold. i.e. space-time. On 10/26/2012 6:36 PM, Richard Ruquist wrote: The requested excerpt from http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory: Calabi-Yau manifolds in string theory Superstring theory is a unified theory for all the forces of nature including quantum gravity. In superstring theory, the fundamental building block is an extended object, namely a string, whose vibrations would give rise to the particles encountered in nature. The constraints for the consistency of such a theory are extremely stringent. They require in particular that the theory takes place in a 10-dimensional space-time. To make contact with our 4-dimensional world, it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X . The 6-dimensional space X would be tiny, which would explain why it has not been detected so far at the existing experimental energy levels. Each choice of the internal space X leads to a different effective theory on the 4-dimensional Minkowski space M3,1 , which should be the theory describing our world. The 6d space is tiny indeed, said by Yau in his book The Shape of Inner Space to be 1000 Planck lengths in diameter. The rest of that reference apparently describes a number of possible realizatons of the 6d space that is way beyond my comprehension. So now I am reading http://universe-review.ca/R15-26-CalabiYau.htm, a math review of Yau's book, to get a more definitive answer to our questions. Richard. On Fri, Oct 26, 2012 at 4:48 PM, Stephen P. King stephe...@charter.net wrote: On 10/26/2012 4:31 PM, Richard Ruquist wrote: Yes http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory Hi Richard, Could you cut and paste the specific description that answers Brent's question? On Fri, Oct 26, 2012 at 3:01 PM, meekerdb meeke...@verizon.net wrote: On 10/26/2012 5:08 AM, Richard Ruquist wrote: No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. Do you have a reference that describes this 'embedding'? Brent -- 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 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.
Re: Compact dimensions and orthogonality
On 10/26/2012 8:33 PM, meekerdb wrote: On 10/26/2012 4:55 PM, Stephen P. King wrote: Dear Richard, From the quote below: it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X. This local product operation, represented by the 'x' is the act of adding two manifolds, one of 4 dimensions and one of 6 dimensions for a total of 10 dimensions, thus this yields a very different structure from, for example, a 10d Euclidean manifold. All of the local degrees of freedom are present at every point but the compacted ones are such that any motion (a translational transformation within M^3,1) shifts from one local 6d manifold to another 6d manifold. The 6d compactified manifolds are Planck sized 6d tori 'glued' (using the math of fiber bundles http://mathworld.wolfram.com/FiberBundle.html) to each and every point in the M^3,1 space. It is not correct to think of the compacted manifolds (actually they are tori) as free floating in a 3,1 dimensional (not 4d for technical reasons as the signature of time is not the same as the signature of the spatial dimensions) manifold. i.e. space-time. They are manifolds - just some more dimensions that happen to be compact. It makes no more sense to talk about them as 'free-floating' than to talk about altitude free floating on lat-long; it's another 'direction', not an object. Brent I agree! -- 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 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.
Re: Compact dimensions and orthogonality
Well, I admit that you said that. I said they had a rather crystalline structure. And you repeated my remark. If you think they are free floating, then we are in disagreement. Richard On Fri, Oct 26, 2012 at 9:21 PM, Stephen P. King stephe...@charter.net wrote: Hi Richard, OK, then where are we in disagreement? On 10/26/2012 8:05 PM, Richard Ruquist wrote: No one said they were free floating On Fri, Oct 26, 2012 at 7:55 PM, Stephen P. King stephe...@charter.net wrote: Dear Richard, From the quote below: it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X. This local product operation, represented by the 'x' is the act of adding two manifolds, one of 4 dimensions and one of 6 dimensions for a total of 10 dimensions, thus this yields a very different structure from, for example, a 10d Euclidean manifold. All of the local degrees of freedom are present at every point but the compacted ones are such that any motion (a translational transformation within M^3,1) shifts from one local 6d manifold to another 6d manifold. The 6d compactified manifolds are Planck sized 6d tori 'glued' (using the math of fiber bundles) to each and every point in the M^3,1 space. It is not correct to think of the compacted manifolds (actually they are tori) as free floating in a 3,1 dimensional (not 4d for technical reasons as the signature of time is not the same as the signature of the spatial dimensions) manifold. i.e. space-time. On 10/26/2012 6:36 PM, Richard Ruquist wrote: The requested excerpt from http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory: Calabi-Yau manifolds in string theory Superstring theory is a unified theory for all the forces of nature including quantum gravity. In superstring theory, the fundamental building block is an extended object, namely a string, whose vibrations would give rise to the particles encountered in nature. The constraints for the consistency of such a theory are extremely stringent. They require in particular that the theory takes place in a 10-dimensional space-time. To make contact with our 4-dimensional world, it is expected that the 10-dimensional space-time of string theory is locally the product M4×X of a 4-dimensional Minkowski space M3,1 with a 6-dimensional space X . The 6-dimensional space X would be tiny, which would explain why it has not been detected so far at the existing experimental energy levels. Each choice of the internal space X leads to a different effective theory on the 4-dimensional Minkowski space M3,1 , which should be the theory describing our world. The 6d space is tiny indeed, said by Yau in his book The Shape of Inner Space to be 1000 Planck lengths in diameter. The rest of that reference apparently describes a number of possible realizatons of the 6d space that is way beyond my comprehension. So now I am reading http://universe-review.ca/R15-26-CalabiYau.htm, a math review of Yau's book, to get a more definitive answer to our questions. Richard. On Fri, Oct 26, 2012 at 4:48 PM, Stephen P. King stephe...@charter.net wrote: On 10/26/2012 4:31 PM, Richard Ruquist wrote: Yes http://www.scholarpedia.org/article/Calabi-Yau_manifold#Calabi-Yau_manifolds_in_string_theory Hi Richard, Could you cut and paste the specific description that answers Brent's question? On Fri, Oct 26, 2012 at 3:01 PM, meekerdb meeke...@verizon.net wrote: On 10/26/2012 5:08 AM, Richard Ruquist wrote: No Roger, In string theory dimensions are conserved but can undergo extreme modification such as in compactification where formerly orthogonal dimensions become embedded in 3D space in spite of what Brent thinks. Do you have a reference that describes this 'embedding'? Brent -- 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 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 Google Groups 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.
Re: Compact dimensions and orthogonality
On 10/26/2012 9:27 PM, Richard Ruquist wrote: Well, I admit that you said that. I said they had a rather crystalline structure. And you repeated my remark. If you think they are free floating, then we are in disagreement. Richard Hi Richard, They cannot be free floating. On that we agree. -- 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 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.
Re: Compact dimensions and orthogonality
On 10/26/2012 7:35 PM, Stephen P. King wrote: On 10/26/2012 9:27 PM, Richard Ruquist wrote: Well, I admit that you said that. I said they had a rather crystalline structure. And you repeated my remark. If you think they are free floating, then we are in disagreement. Richard Hi Richard, They cannot be free floating. On that we agree. I don't know what it means to say some dimensions are crystalline? Does this just mean periodic? Brent -- You received this message because you are subscribed to the Google Groups 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.
Re: Compact dimensions and orthogonality
All of it ultimately has to be grounded in ordinary conscious experience. Otherwise we have an infinite regress of invisible homunculi translating crystalline manifolds in compactified space into ordinary experiences. At what point does it become necessary for vibrating topological constructs to imagine that they are something other than what they are, and to feel and see rather than merely be informed of relevant data? I am confident that ultimately there can be no reduction of awareness at all. Awareness can assume mathematical forms or physical substance, but neither of those can possibly generate even a single experience on their own. Craig -- You received this message because you are subscribed to the Google Groups Everything List group. To view this discussion on the web visit https://groups.google.com/d/msg/everything-list/-/T2g533kDCJ0J. 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.
Re: Compact dimensions and orthogonality
On 10/26/2012 11:36 PM, Craig Weinberg wrote: All of it ultimately has to be grounded in ordinary conscious experience. Otherwise we have an infinite regress of invisible homunculi translating crystalline manifolds in compactified space into ordinary experiences. At what point does it become necessary for vibrating topological constructs to imagine that they are something other than what they are, and to feel and see rather than merely be informed of relevant data? I am confident that ultimately there can be no reduction of awareness at all. Awareness can assume mathematical forms or physical substance, but neither of those can possibly generate even a single experience on their own. Craig Hi Craig, All of this discussion is below the level of conscious self-awareness. At most there is just raw perception, the basis distinguishing of is from not is. -- 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 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.
Re: Compact dimensions and orthogonality
Stephan, I agree that All of this discussion is below the level of conscious self-awareness, but prefer to think of raw perception as distinguishing what can be from what cannot be, as for example in constructor theory. In my model conscious awareness is an arithmetic emergent due to the incompleteness of discrete, ennumerable compact manifolds. What can or cannot be is at a lower level, perhaps due to discrete arithmetic computations that may be teleological, a nod to Deacon as well as Deutsch. Richard On Fri, Oct 26, 2012 at 11:46 PM, Stephen P. King stephe...@charter.net wrote: On 10/26/2012 11:36 PM, Craig Weinberg wrote: All of it ultimately has to be grounded in ordinary conscious experience. Otherwise we have an infinite regress of invisible homunculi translating crystalline manifolds in compactified space into ordinary experiences. At what point does it become necessary for vibrating topological constructs to imagine that they are something other than what they are, and to feel and see rather than merely be informed of relevant data? I am confident that ultimately there can be no reduction of awareness at all. Awareness can assume mathematical forms or physical substance, but neither of those can possibly generate even a single experience on their own. Craig Hi Craig, All of this discussion is below the level of conscious self-awareness. At most there is just raw perception, the basis distinguishing of is from not is. -- 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 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 Google Groups 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.
Re: Compact dimensions and orthogonality
On 10/26/2012 9:55 PM, Stephen P. King wrote: On 10/26/2012 10:36 PM, meekerdb wrote: On 10/26/2012 7:35 PM, Stephen P. King wrote: On 10/26/2012 9:27 PM, Richard Ruquist wrote: Well, I admit that you said that. I said they had a rather crystalline structure. And you repeated my remark. If you think they are free floating, then we are in disagreement. Richard Hi Richard, They cannot be free floating. On that we agree. I don't know what it means to say some dimensions are crystalline? Does this just mean periodic? Brent -- Hi Brent, Yes, it is periodic, but not just... By just I meant continuous symmetries as opposed to the discrete crystal groups. Brent -- You received this message because you are subscribed to the Google Groups 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.
Re: Compact dimensions and orthogonality
On 10/27/2012 12:07 AM, Richard Ruquist wrote: Stephen, I agree that All of this discussion is below the level of conscious self-awareness, but prefer to think of raw perception as distinguishing what can be from what cannot be, as for example in constructor theory. In my model conscious awareness is an arithmetic emergent due to the incompleteness of discrete, ennumerable compact manifolds. What can or cannot be is at a lower level, perhaps due to discrete arithmetic computations that may be teleological, a nod to Deacon as well as Deutsch. Hi Richard, Umm, interesting. The incompleteness forces consciousness... Please elaborate! -- 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 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.
Re: Compact dimensions and orthogonality
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! -- 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 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.
Re: Compact dimensions and orthogonality
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 -- You received this message because you are subscribed to the Google Groups 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 Google Groups 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.
Re: Compact dimensions and orthogonality
On 10/25/2012 10:49 AM, Richard Ruquist wrote: On Thu, Oct 25, 2012 at 1:43 PM, Stephen P. Kingstephe...@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 If they weren't orthogonal then a vector on them could be represented by by a linear combinations of vectors in 3-space - and then they wouldn't provide the additional degrees of freedom to describe particles and fields. They'd just be part of 3-space. Brent -- You received this message because you are subscribed to the Google Groups 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.
Re: Compact dimensions and orthogonality
On Thu, Oct 25, 2012 at 2:23 PM, meekerdb meeke...@verizon.net wrote: On 10/25/2012 10:49 AM, Richard Ruquist wrote: On Thu, Oct 25, 2012 at 1:43 PM, Stephen P. Kingstephe...@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 If they weren't orthogonal then a vector on them could be represented by by a linear combinations of vectors in 3-space - and then they wouldn't provide the additional degrees of freedom to describe particles and fields. They'd just be part of 3-space. They are just part of 3 space once the extra dimensions are compactified. I do not know about what happens to the extra degrees of freedom. Richard Brent -- You received this message because you are subscribed to the Google Groups 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 Google Groups 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.
Re: Compact dimensions and orthogonality
On 10/25/2012 11:47 AM, Richard Ruquist wrote: On Thu, Oct 25, 2012 at 2:23 PM, meekerdbmeeke...@verizon.net wrote: On 10/25/2012 10:49 AM, Richard Ruquist wrote: On Thu, Oct 25, 2012 at 1:43 PM, Stephen P. Kingstephe...@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 If they weren't orthogonal then a vector on them could be represented by by a linear combinations of vectors in 3-space - and then they wouldn't provide the additional degrees of freedom to describe particles and fields. They'd just be part of 3-space. They are just part of 3 space once the extra dimensions are compactified. No, that's incorrect. I don't know much about string theory, but I wrote my dissertation on Kaluza-Klein and the additional dimensions are still additional dimensions. KK is simple because there's only one extra dimension and so compactifying it just means it's a circle, and then (classically) the location around the circle is the phase of the electromagnetic potential; quantized it's photons. Being compact just means they're finite, it doesn't imply they're part of the 3-space. If they were they couldn't function to 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 with different topology, but you couldn't represent all the particles which was the whole point of string theory. Brent -- You received this message because you are subscribed to the Google Groups 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.
Re: Compact dimensions and orthogonality
On 10/25/2012 1:49 PM, Richard Ruquist wrote: 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 Dear Richard, That is what the 'x' in the string of symbols M_4 x X means. The relation is orthogonality such that we end up with 3 dimensions of space plus one of time plus 6 dimensions of the compact manifolds for a total of ten. Dimensions are by definition orthogonal to each other. -- 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 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.
