Mirror Tensegrity and the Discrete Helix

Mirror Tensegrity and the Discrete Helix

* There are many general reasons nature prefers the helix shape, a from that intelligibly relates to energy transfer. But it is not as foundational as physical constructable from topology itself.

* If physical constructable, and the theoretical model is replete and complete enough, form and process reflect physicality. (this with this philosophic grounding being asked a little deeper than even the idea of proofs we may understand that the interpretations of some physics terms and particles have a concrete reality.)

* Physicality tends to leap or sort its interplay and reflections, intersections..., of elements, its dialectic of the descried and continuous.

* In the hypercube (I divide poetically into Tygers and Siberian "half" Tygers, and later the eight colors in combinations applying to the "Lygers") in the xy plane we observe discrete "rayguns" (right angles) that in the mix of translation as rotation may 4 cycle as helices, but in the z direction as a series of planes.

* Planes are separated so as to represent the 8 of the 24 colors (from one grouping grounding) of edges that alternate in color or shadows as if empty. Perhaps from a higher view these make as planes a longitudinal hidden wave.

* Whatever the rotations through a plane tha the resultant figure is a point, edge, face, or cube projection and orientation of this abstract geometry, all the tygers are symmetrically invariant.

* Two helices in motion may combine to double or diminish, interferences, but the invariant structure guarantees that may separate to find their individual identity again at least maybe up to duality. Alternatively, these may exist in four space as in reality a doubled helix warp spin.

Based on the letter notation, and the 13 of them I used to derive these hypercubes in the illustration the matrix form (and fundamentally a Patrix form if we use the Dionysian and Apollonian archetypal models- but I hesitated to use the word even though particles in a sense can be seen as having gender.) That the description of this sort of labeling is equally well a matrix or wave equation formulation- as the greats have observed, but here in a more limited or simplified model. Of course these are limitations that ultimately make our world intelligibly balances between what would be a sea of complexity of explosive numbers or a flat boring simplicity.
Nature seems to have struck a balance in her trialities, Trinity really as a model of which we may say the rest of physics without this three in one we define as cult.

This exploration was an attempt to explore the eight colors of cubes in a hypercube and so match them and make a physical puzzle. I think it is promising among the many attempts for a better one or equivalent one. One new idea is that of the 28 positive and negative hypercubes analogous in four space to the Conway matrix in three space of cubes is that we exclude the EHJ* of them for the 24 as if in a tessellation of such hypercubes. We note in the lettered matrix the directions of things (or the spin of the helices) so as to center these 8 constructable or physically, ( After all the count of things in this 8x8 Conway matrix is replete with all our ideas of 5 and 12 if you want to find them. ) that what is carried over from the lower dimensions and how they deal with singularities as far as the directions of permutations in lower space carries over to the higher spaces. EHJ to EHJ* in particular. (are there topological objects one could call a Biassociahedron, even a Quadrassociahedron?) (Can such object make unit cells in abstract tessellations that in a sense clone the tygers?)

Well, perhaps the use of jaguars and other cats is a little too poetic for the more formal of tastes but even the notations may be changes, the P to Z of it I keep in four space just because I have learned the letter groups and colors in 3D already. But like these animals who compete in the wild and we mimic socially as in war for disguises and invisibility, other than clear colors or stripes we design our physics to be like ships at war- a lot of camouflage or a lot of razzle-dazzle.

Oddly, I did have a distant stray thought that actually asked about could these object describe pions really- as Pitkanen posted today. It must be part of the maths or from a simpler view from a past time. I passed it over, to look at my old map in the book of poems of pions and muons, but the thought or the questions is a whisper I did not feel my own somehow- and to read it today, that is very weird. Of course the world, if we admit it, is rather weird- only the magician does not let on that when his legitimate tricks work he is weirded out too. Perhaps, in some future physics or understanding of our sensations, whispers or voices of sound from each other can inhabit our shared synchronicities and synaesthesia too, geometrically.



By constructable here I also mean the making of this color matching hypercube toy in that four planes in translation and four in rotation of the 24 make a stable object say made of wood- and apparently the half of this will stand up also, and we can rather see thru it. There are perhaps half mirrors in this world.

The second illustration suggests to me that in higher space combinations the Fano symmetry slice projections can be broken in the observed physicality of particles.

A general stray thought: that at the absolute extremes we may not explain exactly what tanglement (entanglement) means over infinite or finite limits, only between them just over the fundamental background of things. Particles perhaps have a wide mirroring of gender in the primitive punch and slice quasic abstract motion functions, but how long can two be intertwined long after the light can send no signal between them? Or, at singularity are encounters but an instant that does not keep its meaning- save perhaps for but one with unrequited love? The vectors between two objects is the same description as from one to the other. Yet, in the greater scheme of things where the default human is ultimately an equality, we find that there is no question of possessing or becoming the other for like the double helix and doubled helices the entangled may bond yet keep their authentic identities.

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Here just some relaxed explorations for the art's sake.

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Ulla,

http://www.rose-hulman.edu/mathjournal/archives/2006/vol7-n1/paper13/v7n1-13pd.pdf

another interesting link. Yes, the role of enzymes as catalysts and so on, the applications to knot theory (perhaps they left out the essential way we also define knots as more of the moebious turns and twists) and well, Conway certainly gets around- Kea was wise to suggest certain things one might pursue from his directions- but he is not someone with a total theory of sorts, as fantastic as his 24 dimensional view is- we are still searching.

I agree with this paper as far as it goes- but it still does not go deep enough. As I think you see the role of carbon as a topological structure so too the deeper structures of the actual enzymes have this same sort of mechanism. What does it mean that given the four things in the equations (and I do not see the first two as "unknots" but they may unknot things) but to say that in string theory as partitions there are 5 things implied? Or simply 5 points determine four space?

I added an artistic illustration to my blog just now which tries to show that we need to sort out the idea of dimension in the general topology- but it is after all a statement on the shadows of crystals, some of which are imperfect in our normal representations of space in regards to say angles, they come close, close enough to make some atoms come together- but from a higher perspective I imagine this somehow reduces to a crystalline view of what makes the organism- of course we need to see the changes in live molecules. In any case it boils down a little, in these higher topological spaces, to what exactly is the space fillers. Lord Kelvin's is certainly one of them (of the five first discovered and what I suspect is the Ferdov solid when we combine some five dimensional view as in the art illustration- but it is an informal guess.

The recombination of genes certainly is a question to investigate and the discovery of jumping genes by that lady biologist was significant. The repeats of such things certainly have their own effects on many of the things we say are disease or vulnerability to it.

Conway in his use of null, plus and minus one, and potential infinity sign - I agree is a good start if we go beyond his surrealistic calculus. But I have already posted on this sort of thing.

But I get a strange idea from this link, Things evolve and in a sense we can say that life would not move as such without the enzyme mechanism, (by the way in 2000 I was invited to join the enzyme lab at Madison but for other reasons could not get student status among them an admissions freeze in general).

That life is a constructable system, somewhat in trial and error, and it seems in its development and evolving it is not aware of knot or any other topological theory globally, not to say its experiments are totally random. Or we perhaps do not see the overall picture as we are only so far along the way to such wisdom, thus so are our theories.

Keep up the magic insights and thanks for the links. I may post this for the theory's sake.

The PeSla

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