Thoughts on Hypercube Symmetries

Thoughts on Hypercube Symmetries (and the 24 faces or membranes to which the concept is a compromise between the p-branes and forebranes.

My living situation has not changed foreseeability for March. I thought I would look at some of my earlier ideas, as a matter of reference decided to post these.

Basically, I have labeled the 24 squares in the hypercube and with the closer look at the binary information of it all determine certain interesting properties and possible physical interpretations of these structures. The 8 cubes that bound the projected down or compactified hypercube are then labeled in a way that they can make a matching game each face actually a doubling with set orientation save that implied by the unique labeling. At first I used the 24 runes for an actual puzzle but then the alphabet, A and B for core symmetric modes then CDEF GHIJ KLMN OPQR STUV WXYZ for the 6 degrees of freedom. This amounts to an unfolding of the hypercube. Furthermore the labels of this cube have a coherent matching if we say move a ring of four of them along a line of the other four.

In general by the core description of the ordering of the quasic plane as z code or that as in cyclic code (as a link to Kea pointed out in the knot crossings) in this model results in this principle: A linear motion (of four cubes) in quasic space results in a cyclic motion in cyclic space and conversely, moreover, these have a certain supersymmetry of shadows and intrinsic symmetry breaking on the same scale level. In effect an interpretation as a particle is the moving or sense of motion that becomes a path but is the symmetries of various rotations of the hypercube. By this I suggest not SUSY in the usual sense but part of the picture of an intelligible topological variety (to which such an understanding and career effort surely is not wasted).

Clearly the situation of this model is not simply left and right symmetric (but of that and the next illustration of the line and circle relation I will post here soon) But of a more complicated or shadow variety. The question moreover of what is actual motion as in nature or as we see it- see my marquis video of yesterday where I as if the shadow or the light moves when turned on and off in 3's and 1.

Also, the circular circuit behaves much like that difference of the magnetic and electric effects, or of mass and energy interchanged. In this model we have the idea of the soliton of such a circle in motion around a line of them and with the consideration of recursive spaces and say friction we have the source of decoherence of which it simply cannot be a matter of the uncertainty principle.

As space as a dimensional concept is amorphous in my later conceptions- we definitely need to label coordinates not as simply a string of 0000's and 1111's but the coordinates can have various structural shapes including partition shapes and matrices in higher space representations.

In the representations moreover, as the complex or quaterion and so on ordering is intrinsic to the labeling- we note from view the ambiguity of one or double sided shadow forebranes we find a right angle rotation. This is true of the face of a cube with the map of the inverse within it or of the hypercube if we label the edges with four colors coherently.

As a minor point recall the 24 cell is composed of octahedra (whose volume equals 4 tetrahedra says Fuller) Here the multiplication by 4 = 96 which is 1/4 of 384. This a minor observation of possible global or general use in the raw counting.

I would expect, in say the matter of smoke rights which do focus rather coherently like some force, that these also oscillate say like hexagons alternately as in benzene in the gross conception of its changing inner bonds.

One important result of these sorts of labeling is that there are seven cubes on the inside and one on the outside. This is an important distinction as the surface of this model is negative filled with respect to a concept of its extension to infinity. But we also see in at least a fourth direction that these can be negative or wildcard (that is neutral to some level of heat like notions- what is the inside and outside- these suggest a quasi-independent concept yet symmetrical one of the dark matter ideas and so on) Furthermore, the question of distance in relation to broken (dual) structures as particles in this unity of chirality and parity issues is an intrinsic property of the structure even at a distance once set in motion and observed or not. + + + - or - - - + is the issue of this surface and what is declared inside or outside and a fourth direction in the coordinates of three space.

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I am trying to decide if my informal post here is profoundly deep or rather simple in its notions- and wondering if it can be seen that way as understood by others also.

Lubos post is interesting- I like the forth generation no ruled out comment. I wonder in the summary if "Higgs" determines the mass of some things then what does it mean that in a sense to do so depends on the Higgs mass? Another paradox to which things are not fundamentally discovered nor worked out.

Yesterday I watched some of Kiki's interviews, one on women in science, and a couple by Kaiku. In particular his concept of the "next big thing" where "we do not expect the increase in computation each year to continue indefinitely, silicon is a limit and silicon valley by 2050 or so could become a "rust belt". His suggestion is the next thing is quantum computation- coherence atoms and so on.

He said it is of interest in code braking (and the making of codes Kiki said but could we not have unbreakable encoding as a possibility?) Now we certainly can benefit from this level of breakthru. But it is only a suggestion of the "next big thing" as those here laying the foundation for the new physics are aware. The next big thing has possibilities we have only begun to imagine.

Kea's post today on Pythagorean Theorem is inspiring because it shows lines over some square that are familiar to me in my recent recreations with 8pt star symmetry or the "linear fractals". This alerts me to the idea of the angles described and possible relations between them. (btw these reversals of what is inside or outside of things I will dub for now "popcorn vectors".) But after all, what is relativity but a small variation on the Pythagorean theorem that took us a few thousand years- is it that incomprehensible in its simplicity? Kea, you are really sharp. If I were Kiki, for the sake of encouraging general science, I would have you for a radio interview.

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Art, metaphorical... but one can label a cube (in a few chiral different ways, with the usual 24 x 24 group multiplication table using i for identity, tau for the 4 three way corners, s for rotations around 3 axes and alpha for the diagonal planes. I began to list these but the chart takes too long here today- interestingly I used two such cubes as a sort of calculator to compute permutations of these group multiplications. It works on a dodecahedron too if we count the pentagrams in the pentagons as compudice.





I may come back to complete this illustration, but here is the general idea. Perhaps a formal presentation with all the standard 24 group symbols checked and the chiral form of this cube and its relation for the hypercube set. 48x48 = 9 x 256 ? I suppose as any number can be reduced to binary such a notation reduces some polynomials as sums in the more general binomial computations.