http://arxiv.org/PS_cache/hep-th/pdf/9603/9603161v2.pdf
Bizarre Physics and Ordinary Topology
I googled this article this morning as I had a few general ideas on this issue. The first is my question of what was really some original insight here and why would there be so many solutions to such spaces?
Surprisingly, several highly abstract ideas were actually discussed seriously in the article. Which were on my mind this morning including certain significant numbers and dimensions. For all the very complicated terms much of it comes down to simple counting and connectivity issues. If we aim to reach for the biquaterion of 8 space (here they toy with the idea of 16 and even 18 space) why bother with the F6th dimension?
What is it after all these topologists are looking for- if things are rather well understood concerning groups and all and the language is strict- what after all are they doing that has not been done before or is already a part of our general understanding of higher space? Of course I could be missing something. I had the feeling that what TGD hints at could be something original and abstract in the sense that ultimately what is symmetrical (that is have a sort of commutativity) and what is not meet somewhere. This would state the concept which after all does seem to fall out of the field of such traditions. Is there ultimately a neutral current that perhaps becomes a scale value that vanishes for all practical purposes to some remote point? What after all is this idea of a difference of compactification to a point but some sort of concept of "spacious singularity."
So, Poincare's conjecture is proven? (the only reference to this in the article was the hint as things maybe happening in natural five space with one of the dodecahedral groups involving 120 and not just the 24) the regions, the spacious singularities or even the curved ones- after all I wondered as if some sort of higher analogy to general relativistic ideas of gravity that with the complex numbers we decide the curvature of space and if this is what was proven for these compactified points then what is the big problem? Perhaps a lack of understanding as to what is really useful concepts of invariants in space. Certainly, in one of the 120 regions we expect if as mirrors that light will be contained in such a region and it needs not be more complicated. That is there is no center to be considered in such a region even if the ideas behind it are multiply layered in returned density (an idea of Riemann who showed this symmetry to be 96 fold.
Oddly, it was discussed that there are extra singularities- an idea of which I discussed in the concept of the wild cards or jokers- for last night I thought about adding the three to the 24 for the 27 multiplication table. What this would mean would perhaps show that say a system of rotation only over a set of cube transformation of the four fold crystal variety would have 10 and not 9 elements for we add the identity element as a joker. 1 + 7 + 9 + 10 = 27. Now this means we can say that in these isolated rotations systems the existence of the shadow jokers can result in multiplication tables that are not necessarily symmetric (or have inverses in that sense as a coordinate anyway is not clearly composed of binary elements of 1 or 0 and not * wildcards.
If this is in a sense true and extends throughout such overly rigid concepts of the topology of space then what after all does braiding mean- even in terms of interpreting it as gravity- if such a braid can be a loop that may reach a point of shrinking to a singularity to suggest the global space is equivalent to Poincare's sphere conjecture- if at such ideals it is not clear the braids ever loop together? If this is the case, and a more useful one in describing things as it has more abstract generality with specific counting- what do the ideas of string theory amount to reaching compactification singularities say in terms of gravity? What magic super-consciousness sorts our the warp and woof of patterns of the fabric made of strings?
Which brings me back to the other half of the picture, The first Quantum Relativity of Eddington in 1929. This article seems to me to suggest that these passing thoughts on it and for some of his methods may be worth more looking at seriously instead of free speculation. That these new topological theories are as bizarre is not as evident or obvious as in Eddington's or Dirac's quantum models. So, we can divide a region (here chose square or quasic) into 256 units and do what Eddington did- see the 120 or 136 of them as shadow or concrete regions to say that such and such is embedded in a sort of space (of which the 64 has the 4 fold coordinates for 256). Now since space is not as clearly defined in its natural dimensions the issue of the actual value of the fine structure constant -after all one of these cells, with a singularity or not- is a wildcard master joker. We should expect some constant variation on measure and the application in the detail of these dimensionless constants in nature short of the remote consideration of the universes existence. I guess, one person's dust is another person's shadow, and conversely.
But what did I expect when after all proof of any such sphere conjecture is after all a proof of sorts that we are discussing its equivalent Riemann plane be it complex or natural space.
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Lampion- Nature seems to obey a general rule short of complete chaos and that too is part of the picture- That all conceivable topologies somewhere apply as well as guarantees the success of arranging things into the several seemingly complete theories. Nature does not know which restrictions it has to limit its reality to.
The cells of a general (quasic) plane, symbolically square, each can take the several forms describing tori, cylinders, projective spaces, Mobius spaces and so on... I thought a little about the issues of yesterday and the use of such a plane to classify and categorize, visualize such things- but I still do not have enough energy to do more than suggest a way. In our era of theoretical expansion and a look at new ways to see old and fundamental ideas- we cannot say at this time what of course is not logically ordinary in topology nor what in physics is the correspondingly bizarre. It is doubtful that the new positions in this resurgence of classical geometry on steroids does well to address in certain new conventions of terms the young minds who in the joy and rhythm of life accept these as given even when they cannot know better- committing to something of organizing perceptions of reality and internalizing methods to deal with things at the risk of a generation if not limited to one comprehensive theory of everything soon obsolete then that the big picture of what science is becomes as fossilized at the culture defining and defined by it. But it has been clear that advances in topology take years to have some application and effect on our use of knowing- reality as such its own black box of touching the bottom but double blind in a sea take them or leave them uncertainties. Some ideas when solved are of such a general nature that the many paths to finding them- when there is perhaps a right one that stands out- solve so much all else of our efforts seem futile after the fact of duplicated efforts. But this is the way it is- today's hero and first with risks and awakenings, astronauts and cosmonauts into space, are tomorrow's bus drivers. Nature for sure does not skimp on its drama in its replete explorations once its self image is boring and bound- if indeed its creatures survive the turbulent wars and weathers.
But that in terms of numbers that are intelligible at all it still seems to me a drama which is still beyond the scope, save for amazing and magical hints, of our current but spectacular edifice of imagination. Yet, like trying to contain drinking water in our hands for long we still recreate the wheel of issues and conjectures lost awhile of concerns of the early last century.
In sweet Cujo before he became rabid, Steven King explained: "It is the virus that bites and not the dog." We earthlings who have become the writers of viruses. How sad against the face of the reality we do not realize when we are but in a dream.
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http://www.aanda.org/index.php?option=com_article&access=standard&Itemid=129&url=/articles/aa/full/2007/47/aa7656-07/aa7656-07.right.html
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So, in bioctonians how many times is the 120 multiplied? 480? 360? 360+24? all such numbers come up and multiples of 144 and so on... 5!/2 + 4! ... N x 27? But these were just floating around in my head last night between twists and turns of sleep and not written down. If we can make a geodesic sphere by dividing the 120 triangles into 4 why not a fundamental object of such symmetry? So much depends in one way or another on such regular objects, polyhedra and so on.
But we perhaps misapply the exotic math if we think such dodecahedra are the only finite models of the universe in the running.
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