Monday, January 17, 2011
The Epsilon Honeycomb
The Epsilon Honeycomb
I found Lubos post today rather interesting with many points of agreement as far as the philosophy of science, the psychology of it, the question of professionalism, and key ideas of what was actually said or commented upon in the technical details- like: I mentioned terms like the distributive law and zero vectors (that may not necessarily reflect the vacuum in the shear metaphysics or physics of it.) But I am liberal enough to imagine most laymen can understand most of this for that is the origin really of the 1100 or so mathematics. But the measure of such insight let alone intelligence is only as good as what is out there to learn or to learn how to discover and discern its utility and truth. Can there not be deeper ideas to which our methods of recurring as the only ones in town have to remain a less elegant explanation? Certainly, Lubos is aware of some of these higher issues- understands them and has commented on such problems in the theory- but was it an original concern or that limitation he says on what one hears from others? Clearly, the grounding logic of it can be summed up like this: "It is a sorry time when the lay persons know more than their doctors." (Which I actually heard a doctor tell his nurse when a lady and her child with a shot reaction read in the lobby magi zine the latest recommendation of intervention.) And it also follows that (wow, news today said it is wrong to have two spaces after a sentence- but I had thought about that very thing typing yesterday as to what seemed to make more sense, especially on line.) "If we have such a hierarchy of intelligence there is always a bigger fish who can say to the others they are far from the deep understanding compared with them- only the peers beneath them cannot see as illogical in their intellectual stance." Indeed, where this gets off the deep end of speculation so as to claim it only from an emotional distance as great science with some truth in the intelligibilty of this seeming magic- or to be so cool emotionally that they feel not emprisoned by a no nonsense stance as if creativity can only be a child of arrogance- is when the debates lead to the absurd reality of physical conflict and perhaps for the nerds in the know to render unto the world cyber-war if that is taken abstractly to be what after all is becoming the reality of the world.
Still, in the the highly speculative concept I present today I wonder if anyone is there to understand it in the professions- after all it could be wrong or already out there somewhere. It does follow from my own grounding assumptions. As surely as someone believes in their worldview we have here an equalizer of sorts for the underlying symmetries in the greater scheme of things begins to explain why we can regard what to some who do not have a clue about the higher evolution of physics and its importance that their activities in the world are equally important.
The Epsilon Honeycomb Or, Platttopes or Platygrids (I have only seen three t's together in one book and that was a proper name). Vaguely, we call three space the great dodecahedra and so on, four space the grand and so on, so here I suggest the gross when we think about vague higher spaces and the role of symmetry especially in a superficial first magical way. Epsilon to follow beyond Coxeter's delta Honeycombs. Bare with me- in the end it is a rather simple picture of which I can put into a form that leads to more general notions than we have gleaned from the reference frames of geometry and algebra. The reason of this still amazingly another post was two things: Quasic connection and the idea that the grid with which we cover some region of space is equally abstract and important- and my short visit yesterday to the idea of the Monster group, especially as Conway can see into 24 dimensions and used the idea of a torus of such a shape as the 24 cell in that space.
[more later with illustrations] "To the corkscrew the knife is crooked." Kierkegaard
*a - we can imagine counting the cells in the grid that breaks the or a dimensions of a given space and that these can be regular divisions or mixed ones. We apply the principle of quasi-contiguity between quasic cells to describe still an other concept of vacuum between them, and an extension not into non-linearity of the linear relationships between these abstract cells and their motions for the styles of vectors are constrained by the general nature of the great grand quasic grid dimensions such that even the mixed vectors may on some level of associations keep the crystalline and integral count, moreover to imprint between them this idea which is like the mysterious ideas of quantum theory but on the vacuum only- and that these constitute a virtual imprint that may not be realized in the singularity of a non-simply connected region where that singularity is a being of matter and not a metaphysical connection to the other as vacuum- although these relations can exist.
*b - The grid can be composed of regular cells which do not seem so in lower dimensions. The 24 cell platttope is defined by octahedra (of euclidean volume of four or 2x2 tetrahedra only) without appeal to a simi-regular tessellation of three space to describe particle physics. It can of course be a cubic lattice.
*c - Just as we may imagine a sphere of maximum extent being a plane so to we can imagine a torus of such infinite extent as flat- even if only at each point. In this gross symmetry realm the recursive inelegance suggests some illusion effects such as the expansion of the universe or things appearing faster than light signal do indeed say something fundamental when compared over space and time to the epsilon honeycombs. It is not clear really how we should define such illusions nor just how far we should base concrete physis on them with our incomplete theories such as the relativity.
*L1 - [The multiverse turns out to have a crystalline vacuum structure also]
*L3 - [The volume of polytopes involves the recursive powers of pi but all these may reduce indempotently to just pi.]
*d - The 24 cell is self dual thus has the same symmetric singularity description as the tetrahedron as far as centers.
*L3 - [the existence of gross symmetries suggests levels and thresholds of evolving cosmology in reference to its composed particles and atoms which affect what we see when we try to classify the stars and galaxies.]
*e - Clearly, from the gross viewpoint of platttime and platttopology we can conceive a super steady state universe of indefinite expansion and creation centered on the field (of which we can indeed suggest or shore up things like Higgs fields but at the cost the idea is of less significance) For expansion as illusion containing a zero or added dimensional function (that is motion in all directions should go out equally to degrees of freedom and thus in a given dimension be at rest)
*f - Plattygrids and quasic grids may make joint motions described in matrices.
*g - The ambiguity of this general euclidean into non-euclidean as that between continuous and discrete spaces hold them as interchangeable including from the time view as with the flat to the hyperbolic in matters of what in actuality precedes things as cause at the vague and hidden epsilong honeycomb filled or empty cells.
*h - The subcells in the honeycomb as grids may themselves be quasic cells and thus in a sense part of or independent of the totality of a universe, even multiverse.
*i - Quasicontiguity as a rule of all spacetime is not necessarily conserved or applied.
*j - The holonic tenet of Wiber from the Buddhist should be considered in these gross contexts- that in any holon a part exists that may contain the whole of all other holons but this seems to have a certain state of description as complete as some level of complexity. This too important in matters of higher uncertainty and statistics that also averages out in the complexity of the ever more concrete space.
*k - The plattygrid spaces surrounded do not necessarily relate as say a dimension up or down to the subcells of the vacuum structure.
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Lampion 01-17-11n - For a more standard statement of concerns in the difficult but simple structures to describe- Given such structures with rules that begin at some level of grounding then tries to work around them where they are or are not unified in a wider understanding [it is reassuring to see others in the world dared to consider the differences and unity in what are discrete and continuous foundational issues], beginning with 1 our unity, a given, to say build an edifice of numbers and Pascal analog topologies- what rules generate the generator of unity- what adds up in the way other coefficients add up to make unity? Loops and fractal like echos or of the totality do not always address this mystery of number. Indeed, at the Omnium or sum total of things infinity, zero, and one not only have conceptual connections but we still have equations as series that in the general context of mathematics still make no sense despite the expert brains that dared to deduce and hone them. Some work only because they result in intelligible answers. Perhaps we are addressing in our time some of these very issues and methods to resolve in the highest generalizations possible and reasonable such symmetries behind the roots of unity.
I find it interesting for example in the idea of a quasic grid in which we find the multiples of five to be the grid and each cell (whatever the design logic of the hidden grid in say the paintbrush program) thus easy to find which pixels are on the grid and which in the contained 2n^2 space- that when n is 2 and counting the grid of 16 pixels plus 4x16 pixels we get a gif avatar of 80 x 80, with the completed grid we have 81. Inside the cells we can further encode numbers say with colors and shapes and so on- and in a sense we can combine them or reduce them without the 5's grid. What this platttope idea considers is the hidden motions and symmetries between the cells of the 5's themselves and possible influence on the quasic 4 space of the cells. Abstractly, we extend linearity and orthogonally a little further in depths than our ideas of when these become non-linear in less complex but common sense reduced small dimensions and numbers.
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From an alternative view, in this level of supposed epsilon honeycombs, one can ask if these are real and a part of the general expressed reality. As with all assumptions involving our sense of the concrete and of balance- the symmetry issues in thermodynamics coming to the forefront of frontier issues for example- we can imagine such honeycombs as not having a plattygrid to outline themselves. Their plattygrid in a sense is bootstrapped to the distinct lattice of the grids they contain. But whatever the case in a more general view of grounding topology these possibilities may make our organic chemistry more manageable and intelligible. For from first principles alone we can imagine such local changes in abstract motions thru the dimensions, overt and hidden, to show in an evolving system that slow mutations may accrue or sometimes be catastrophic as in recent observations on the more or less immediate challenge to the integrity of some individuals DNA configuration. The idea of sheets of topological things, tied or not to the reality of more general physis laws that make intelligible the organic and inorganic interface as it seems arbitrary connected is an old idea (for me 1964, leonic fields) but to try to relate these to ideas of opacity (dark matter notions of which the ratio to concrete matter seems a matter of counting the subcells as if these were concrete structures- thus a vague consideration of mass also) is of a more recent dawning to our sense of the complexity of nature's laws. Such today is referenced by another blogger I follow in a more formal article linked that asks what turns on the mechanism of the quasars- for now not enough to consider it a matter of some sort of critical mass of such objects interacting. But the same mechanism to describe the breakdown of DNA also ground its ability to self correct itself from existential errors at least. Some of our gross speculations then incomplete a description of the bigger picture.
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