Wednesday, January 18, 2012
Natural and Deep Symmetry
Natural and Deep Symmetry L. Edgar Otto January 18, 2012
In the natural dimensions certain patterns persist regardless of the content of the numbers or sub-regions the Euclidean (plane) familiar n-space. I hoped that this approach, the natural dimensions on which we can fit the puzzles (Soma for example) into intelligible assemblies as a matter of local trial and error to which the artistic in us does not see that these may be in higher depths of mathematical connections globally, that this approach would give me the formulas for all the solutions by space theory of the 240 Soma sets where the "Jigsaw Sukodu" of several regions also across the plane as bilaterally symmetric, and in its representation in three space.
This came from a look again at the permutations of Sukodu (Extreme) in the form that has also two diagonals containing the nine numbers- and the symmetrical across the plane.
The classification from the inside or inversion- a deep Soma formula is not a matter of natural symmetry but of deep dimensional symmetry so far- I also suspect that 16 may have a solution (despite the exhaustive enumeration by computers) but this may be only a deep concept relating to deep symmetries- or a borderline or frontier intuition caused by unclear partial visions into the depths.
I also relate closer my recreations with the 30 color cube and deep permutation and dimensional theory such as that of Kea that goes beyond the natural or shallow symmetries albeit these the springboard for all of our intuitions.
I see that TGD posts today again on the generalization of Feymann diagrams as a proposal with promise (not from my view looking back from the actual implementation of this idea- I posted independently in previous blog posts- but it really shows the need for a generalization of the idea of matrices in general before we can be said to naturally use the group idea- such as the dihedral to operate on the matrix.
So such a generalization that we seem to be heading toward or dwelling in are all the same description:
1. The nature of symmetry in the quasic grid is or contains such a generalization if that is meant the symmetry of natural space and group theory involved.
2. The ideas of permutation and braiding of Kea in the intuition on the depths (as usual these debates go beyond the nature-nurture as that of instinct and intellect), as I show in the color cube theories, is or contains such a generalization. This is true for her use of the matrices as modeled by others as to what sort of main diagonals are involved.
3. In the use of number theory and ideas from modern physics (including the usual considerations of what is classical that falls from it if not that means natural) the aspirations of TGD seem to be leading to this sort of thing or converges to the intuitive idea of it, p-adics can also be such a generalization or leads to it.
4. This is not, as deep, a matter of metaphysics or philosophy only- for I can imagine in knot theory our ability to invoke matter from raw space- and that so far is in the realm of speculation only. There are generalizations beyond Feymann's reductions.
5. PeSla's and Kea's approaches emphasizes the informational aspects to ground the deep intuitions. This is not just a matter of debate for the objects we can be sure of as proposed (for example why do the neutrinos change flavors in the first place?) The Koide formula is an example as to which side of the depths and natural span we regard as solid science.
6. It is clear also that the planes, that is in general branes, and the polytopes generalized of Coxeter, are also the generalization again of Feymannian quantum ideas.
7. Ideas on partitions of space itself has to eventually merge the natural dimensional and the deep dimensional symmetry views.
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Associated Associahedra I thought I would check the spelling on a google search and found my posting first on the images and also in the text this most interesting pdf paper:
posted 3:30 PM CST at library.