Friday, January 13, 2012
Associated Associahedra L. Edgar Otto January 13, 2012 This is a paper on general applications of concepts which leads to things more properly matters of psychology and sociology- that is to speak in a hyper-language not based on our very deep fundamentals and questions of existence- but is not physic in its own way such a language?
First illustration added for color- small icons are 80x80 originally in this 1280 x 640 panel.
For awhile numbers started doing strange things so I had nothing more to post today as the calculations were confusing and mixed up. It is possible something is wrong with my small calculator (it occurs to me it is my roommates calculator and he dropped out of physics to become an artist). The exponential button does not work and
sometimes some programs run in the background. But I am sure I pressed the right buttons. Still, from the language for cognition theory and genetic predispositions the posts of yesterday certainly might apply to how we organize our brains for learning and become "hopeful monsters" who may not know they are victims of the patterns of dust within, or for that matter they are part monsters. Again, can knowing things help clear up (my roommates mood changes and diagnosis and effects of external chemicals?) or at least can we intervene as to what is lacking or needs to be done for the cognitive development of perception for our ever more autistic and addicted society? This sort of epistemology in the ideas of sukodu permutations of yesterday's post certainly applies to our grounding of physics which at times seems to get downright vaguely diagnosed as schizophrenic. A post to
Maybe that is not off topic, I mean remember the good old days when Omega minus made sense of the "particle zoo". Well, Lubos, your post has taken the
zoo to a whole new level. It just may be that nature has eternal forms things evolve to "inevitibly" from the nothingness. I mean, in the fine eyes of deep theoreticians
that is the correct way a giraffe is to be drawn when all our eyes clear up from some level of the fuzziness.
So, I notice that some things appear strange to me about factorials. That in the straightforward calculations of things like the group number of rigid rotations and inversions of orthogons, that two and five as ten can see them as (with mathematical induction or recursive concepts) as if a deeper program is running in the background.
The simple formulas in number theory may not be as simple after all. For example twice 384 times 5 = 3840. 2^4 x 4! times 10. But in general this role of 5, as I might expect from a hierarchy of repeating quasic patterns over integers, carries over to 2^n x n! in some ways. Now what happens if we solve the function like things for 5 to sort of inverse the idea of phi in the continuum- that is replace in phi the square root of 5 by such a function? This I need to look at again when my head is not confused at some frontier that may tell me (or other theoreticians like Pitkanen) what is wrong with my thinking or theory. His related to five too in the useful observation that of five things like axes when we allow a certain influence of concavity in the space +++-- divides the sequence or permutations of the axes into two sets +++ and -- which on this side of "an opaque mirror symbol ? as in 2^n x n? or better .V. for a symbol that does not connect +++++ to the density of the fivefold-ness that is 12345 and 13524 but 135 42 of which this to me has application in the stable construction of five sticks supporting each other in a crossing over for a pentagram.
This rather Omnitwistor level of ideas may also organize us (3+2)^n into false perceptions at the reversal of the Dark Mirror plane treating the whole as if a unity or a connection of isolated regions of ambiguity. Such a sukodu disconnect in mind and numbers as integrations evaluate and integrate for coherence's and seem to me one of the surreal properties of numbers where looking at the disconnects inside us or in the universe we have not distinguished the dark or reflective mirror planes. This is not to say some partial ideas are wrong, just rather not complete a theory.
An irreducible particle is a polytope (of iotas, point-rays string like) then in the abstract sense a lattice of such particles of so many types may be xtalline and intelligible in numbers including the count of holes. (see Conways link in my post yesterday linking to Kea on his new octahedra). Such lattices within a sufficient complexity convert convex and concave in some non-Euclidean sense of space regions.
If the Associhedra are one to a dimension, and these can be generalized (Grassman? I must look this up) then in a wider inter-dimensional and group world these have to be associated to some code context with the usual simple multiplication of groups- and yes as in the comments today the number 14 shows as in the hypercube as a rhombidodecahedral projection ... hmmmm of two types one more a phi diamond shadow.) In a sense these sort of asymmetric permutation directed polyhedra project through motion as well as rest to define what is irreducible as particles and the resulting nature of them in regard to some context of supersymmetries (superparticles as a coherent reality or not.)
One stray thought from all this is that we can also organize higher spaces as 3^n, that is there are also n-D analogs to the sukodu cubes that can remain distinct from other considerations of how such spaces are divided into permutations of isolated regions that may or may not correspond totally in the sequences in the flesh. I mean, we agreed that some of this world was half of nine dimensional or 4.5 D when trying to figure out the meaning (and we can justify dividing by group numbers and other powers like 27 across associated spaces) or as the numbers play tricks again until I find my unity of new conceptual challenges- 7/9 is trivially also 81/14. And of course 7 + 9 = 15.
Now in many ways of the counting of these various spaces of elements found in or not in such matrices, the value ratio comes out many places around 8-fold and this intelligibly meshes with our current speculations on the weights of dark matter etc.
Let us praise the leaders with a new fad of an idea- or let us not- if their theories are not even incomplete...
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