Depth and Span Beyond Sub and Super Group Theory
The Next day in response to Ulla email clarification: I post here because the essential idea of subgroups not explicit as stated in the May 1st post, but is certainly implied. The ideas of a special position or part of space for a local phenomenon, or that singularity of points that would repeat (as in the article on the gluon formation in the string ideas presented in the lecture cited) in a pattern, that these are in a sense invariant singularities of global patterns...and can be found also in the patterns of a more general space and its dimensions - this too a principle that ultimately raises the question of the role of primes. The working our of ideas of (super-?)gravity of course is perhaps a still higher problem or it could be a result too of this default integration of all such locality phenomena.
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Ulla,
thanks for the clarity.
Guess we have to consider this at some level. My string friend and I did in 95 (he is not longer at the university however) that is the exotic group E8 which got my vote as he mentioned it as a possibility in his thesis I was correcting (things like spelling and so on). But I was deep into Coxeter long before his ideas have become more mainstream.
I think Lubos must read our blogs because comments seem to follow our postings way beyond the idea of synchronicity. Today is no exception- it is as if he addressed the from of my last post to dig hard for an alternative in his traditional claims for his style of physics. But from the higher view it certainly says that he acknowledges my and Pitkanen's concerns as worthy of investigation- and others involved too. But I still cannot see his thinking as merely an expansion from some surface- all these theory systems are not quite going into the depth, or the span of things. How can he be so blind as to promote the ideas of those whom do not know they are blind to the directions of things?
If I have a problem with the limitations of our foundational group theorems then that has some consequences that go beyond what is not then seen nor said.
There is a problem in finding the sub-groups and there is a principle that shows that one is prime p and another principle that p^2 will be a factor of the subgroup.
The problem in finding the subgroups 2^X shows that a group say X of the 'Monster" Group has an enormous number of them. In fact from E8, its snowflake symmetry of 198388 or so dimensions (or the 248 natural dimensions) is the maximum symmetry possible. We know that 240 eight space cubes surround one.
Obviously there is more to the symmetry of things than this initial but difficult exploration.
More symmetries in fact. And from one view we can consider them invariant- for what peculates out to our world to scientifically experience. That is in a world of pure space as we might envision it (nature may choose other fundamental spaces as well with apparently no restrictions philosophically) without mass or anything like it to which all else is ghostly fantasy- that is we are interested after all in what seems a concrete ground of our being- not such empty space, matter for itself, or vague promises in the clouds.
The exception seems possible in respect to organisms, and perhaps the brain-mind systems where it is thought.
Yet in living things, in the complexity of them, we see that this idea of groups can have wider paths of evolving and going into the depths or span of the model of the abstract space it so describes. Into the depth and span of such spaces there are other paths, ones that more or less determine in the flow and in the systems of things that seem invariant that they are as if solids or fluids (as in the simple link yesterday of which I suspect the 64% of the flow of sand in an hourglass is more like that involving phi, which of course goes into many directions of the mathematics.
So, we may say that we an factor in a sort of super-group idea (or subgroup idea for in a sense Pitkanen and I have turned the idea of applying numbers to space the other way) that p can go to other powers, like the Fibonacci series or Mersenne numbers and so on, p^2^n all should be investigated. But even here some paths while real may not be the only ones in the local expression of our genes for example.
A lot can happen when we finally realize we need to see things beyond the point, linear and vaguely continued point spaces assumed in an ad hoc time translation or motion translation spaces into at least the results of aleph 2 spaces of curves (Lubos sees this as a good idea in his article , a sort of default locality and after all, just as I said we may separate the group idea from what it is intimately connected with just like at some place we can so separate space and time to a more classical field- this happens in the turbulent world of such fluid and solid concepts- the old how to derive the classical again which is perhaps the resolution of special and general relativistic ideas within each other.)
Much that we do not suspect can be done in ordered paths (albeit they can be quasi-discretely different) actually may be so from some more comprehensive view of space and time and spacetime.
The PeSla
2Fsub(n) + Fsub(n-1) 1 11 111 11211 1123211 112353211 11235853211... makes for some interesting 2D patterns as an analog to cell differentiation.
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http://arxiv.org/PS_cache/arxiv/pdf/1103/1103.6140v2.pdf
From sciencechatforum com with interesting comments from Lincoln et al. "no respectable scientists think of singularities as physical things although we can play around on the surface of them- that is get help from the mathematicians who can cleverly solve some equations that are never the less wrong..." and so on...
This is a promising paper- wonder what they could mean by Ultra-relativistic?
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In comments to Pitkanen and his interesting replies- posted here as new post due to length of the one of May 1st.
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At 8:09 PM, Anonymous Matti Pitkanen said...
I am not enthusiastic about loop gravity. The reason is that it forgets all other interactions and is therefore doomed from the beginning. It does not even serve as a promising methodology since the canonical quantization of gravity serving as a starting point is simply mathematical nonsense: just a completely ad hoc attempt to generalize formally from finite-dimension to infinite dimension producing expressions which make no sense.
It is understandable that this kind of attempt to generalized from the case of hydrogen atom to the level of entire Universe was made at the time of Wheeler. Mathematicians had not worked with attempts to understand infinite-D geometry yet. But nowadays we should have learned that the geometry in infinite-D context is extremely intricate and the mere existence requirement fixes it to high degree.
For some reason this lesson does not seem to go through- probably the reason is what physicists call "pragmatic" attitude to mathematics meaning in practice beating head against the wall for a century instead of using it for its original purpose.
One might think that string theorists would have taken the lesson from the work of Freed about geometry of loop spaces seriously but this is not the case and they are still wasting their time with the landscape. If some-one happens to know a manner to stop super string theorist like Lubos and make him listen for a minute, tell the trick also to me;-)!.
At 12:49 PM, Blogger ThePeSla said...
This one you may find interesting:
Perhaps here too the ideas are clear enough that we should look beyond the "landscape".
from sciencechatforum com.
loops and things, well perhaps it is a good idea but not general enough in the detail of it all.
what would Lubos think of this? What do you think its worth as both a mathematician and physicists?
ThePeSla
At 12:52 PM, Blogger ThePeSla said...
http://arxiv.org/PS_cache/arxiv/pdf/1103/1103.6140v2.pdf
sorry, forgot to post the link to the paper... btw on my blog for comments on May 2 I tend to see our ideas approaching things from different scales macro and micro and yet we seem to share a lot of viewpoints and ways to answer some of these popular concerns and questions.
The PeSla
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I am always interested in how some of our theorist can boldly state that some idea does not apply beyond the general context of their expertise, especially when future generations may be watching.
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Came back to get phone number from fb for my pending trip South.
Here are some interesting developments- the latter thru the philosophchatforum :
http://www.imp.ac.at/contact/communications-department/press-releases/press-release/article/study-suggests-that-successful-blueprints-are-recycled-by-evolution/articleBack/3792/
http://www.sciencedaily.com/releases/2011/05/110502122138.htm
We are getting there, but it is too early to more than speculate with some of these articles conclusions.
I replied to earlier comment from Pitkanen in earlier post.
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