Wednesday, January 4, 2012
Quasic Permutation Space
Here I post a clearer graph- but it does not show the rows as in four colors and he interchanges possible as in the sketch... and of course the Catalin number of things such as with the various reading of powers or of parenthesis and so on... on this depends some of our more abstract or recondite systems concepts such as only the inversion of half of a set of four color etc...
Quasic Permutation Space (4 & 5 Colour) L. Edgar Otto Jan. 3/4, 2012
First I will post some very relaxed notes with many errors and really just suggestive formula like symbols (due to low light and distractions and a need to rally effort after the holidays) but I know that in between the lines there are powerful ideas, so I post it.- I am not sure how original.
Dreams can be views from outside them or inside them. Like reading a CD or having to go through a tape, these aspects of the element and the filament, the rest and the motion in my primitive terminology. In candle making my pouring machines for many coloured layers could happen all at once or the usual assembly line. But by avoiding the assembly line idea when production was behind the assembly line dimension only made things much faster of the space saving all at once quasar like focus then put into a filament of time.
So I give you the quasic space permutations as a generalization of the quasics. I note Lubos discusses this way to see permutations in reference to Bose, his post of yesterday, and I note in a comment on Kea's last post how she considers something like sub-permutations. I note also that I use four colours and the permutations of that is of course 4! So, in the subspace 5! requires 5 colors, a sort of sub-sub-set of permutations or a wider scope of any such supersymmetric like fields. To do this although it is not necessary, we can extend the elemental quasic plane(brane) in a filamental direction, but this does not really seem a time dimension although the foundations of many theories utilize this process- as well the extension of four colours by the duplication of things as in the complex plane (of this there are core ideas beyond that of duplication and viriality with qualitative analogs.) Note I use the octonion like 8 colours in the compliments when we have abstract duplications.
I assume the four colors can fit into the 24 permutations in 12 sets of the quasic crosses which in groups of four looks like Eddington's descriptions of vector types in his general quantum relativity theory of 1929, the Uranoid. In this sense and as a totality I give you the Hyperuranoid.
By the issues of viriality we begin to see why in large aggregates of entities we find directionality- and this time asymmetry begins with at least 4 (or 5n) space. As such we should not think of Galois as a limitation but the beginning of new generalization of algebra and space (this is what happens also when we reach the 9th dimension to the nature of higher dimensional spaces that we can go on to more abstract ideas on which to seek out physical evidence such as particles.
Let us also consider Bessel numbers for dealing with the algebra (of which I only caught a glimpse of over the holidays and need to explore it more. Certainly we have here examples of surreal like reaching zero values or in matters of evenness and oddness a result of 1 or -1 for such useful coefficients) In general the "faithfulness" of a Galois general group is not just to be limited, by permutations, linearity, or matrix theory to some finite slice of things necessarily. This area should be explored in such matters as morphism of representations. This applies too to the universe in general within our observation radii at least.
Of course there are a lot of parallel ideas in different views of a general theory for example, delta-n, the infinite honeycombs (flat polytopes) of Coxeter represent a cycle of five flat spaces that projectively cycle into the five states. I am not sure how this may relate to this more general quasic permutation space but it does also involve the powers and concerns of Galois and how to solve roots of equations by such algebra. I do not mean this as we have higher mirrors than say applying the virial Dihedral groups (there are 2^n such virialities to establish any creative space, qualitatively as active analogs). In particular we can map the 120 elements on the quasic plane (brane) as a sort of superposition with rules for the further elements of crosses for the quasic state- and thus in the sub-sub-symmetries we can again relate and map the coordinates for things like the electron configuration of atoms for the 120 elements- or the 240 in natural 8 space halved. Now perhaps we can go deeper than this abstraction still to describe nuclear configurations and so on depending on the factorials involved that do not cancel out as physical properties. In the idea of colouring the boundaries that are distinct in the natural or Euclidean plane the four colour concept is a useful one to the the extent that it applies (and to any surface or genus or its analogs) for its exceptions too in the application of what is intuited or proved by these concepts.
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I wish to correct a previous post- it is the veins and arteries that Pearson (around 1980) said was as if a cable system to which I said the general field (RF) that can grow all tissue over time replaces the nerves... Sorry for all these errors posted especially the use of color in the illustrations- I may correct that graphically someday... also the listing of the permutations of 4 very sloppy and not done with a formal method- then again we need to relate the 24 squares less ambigously to the 24 faces of the hypercube- I suspect a lot more is going on here than our very advanced ideas of Leech lattices, btw. Even if that is the most general description there would be analogs of this, at least conceptually.
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I thought also My Virtual Room recreations would be of entertainment interest for what was on my mind from time to time.