Saturday, August 28, 2010
Decapolis (Compactified Broken 10- Symmetry)
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Decapolis (Compactified Broken 10-Symmetry)
A further idea came to me casually at a moments reflection on the five-fold symmetries of the pentagonal dipyramids in relation to the 18-faced deltahedron.
A Decapolis or Pentapolis (the pentagonal dipyramid itself)is imagined to be composed diffusely of five tetrahedra but not as a strict and symmetrical polytope, nor if inside a regular polytope or polyhedron these as convex have intelligibly balanced numbers such as the number of faces or edges that intersect at a point.
The tenfold metric is everywhere in the pentagram structures which of course involve the golden ratios (said in Rowlands the reason for string like symmetry breaking). But the problem in general is the treatment of such edges coming to a point to so define classes of structures outside the generality of local points and methods of developing linear algebra from such a point over the polyhedron to evaluate vectors, or at the generality only such as the global formulas of Fullers geodesics. One answer appears to me is that in these offered notions of quasi-convex solids, and that decoherence as the vacuum may have such structure but as quasi-coherence, is that in the classical sense (and things like quantum collapsing seem to be that which somehow linearly is approached and the linearity of it considered the concrete real)we can have degrees of compactification (based on the dimensionality or compression or density - say of mass to the surface of things holographically). But which of the in-sphere ratio differences and in which dimension is the surface and mass compression in general?
We can imagine two dipyramids together such that there are only 18 faces- but there are internal and external ones with regard to the overall spherical top structure. In which case we view as if these loosely on a sphere- ten triangular faces by which we may assume on the other side of such a mirror we are observing an icosahedron of twenty faces.
This quasi-density linearized compactification structure is realized in the spirals and twists of chains of organic molecules including DNA. But what sets the direction and chirality of these helices when they should be equally probable? This 20 and 18 faced difference for coherence structure suggests adaptation in freedom freedom to interpret or express these mechanisms of ambiguity. In a sense from the psychological view of such and consciousness theory we as we set the memory in the structured vacuum so set them in the decoherence or entropy structural vacuum. We establish a path of belief and enquiry and elaborate theory which has the ability to choose steps for remote improbable options yet can accrue what persists as false memories also. From what respect is the inheritance to be defined as imperfect? In this topological view of things, structures, linear and local or neither, is the truth of a model rather than the thing (like physics) the models try to describe- thus the paths and history of conscious speculation and contemplation of scientists while restrained decoheres or vaguely coheres as groups of theories (as if a n-polis)with evolving mnemonics and traditions- and yes, in less unification of what in theory constitutes intelligibility, Darwinian struggle between self-centered agents.
Now, like in the dropping of feathers and Cannon balls in a vacuum (of which the act in a sense can invoke the concept of gaining "heat") on the meso level as the organic one of body and mind we find the same description of the idea of subatomic and cosmic effects such as the Casmir as a "dark force" or some equivalent idea of particles in a sea of real or virtual mediators. (Rowlands who makes the analogy with the Vanderals Force- I suspect more than its strict explanation is involved here
as effects if dialectical charges at certain ranges.) We find therefore that the coherent topological structures that existentially allow the compaction of and wider freedom of choices in the general sea of uncertainty and possibility, between our ideas of freedom and necessity, that these general notions are matters that explain and exceed some level of attachment strictly to scales of forces. Otherwise we would not find intelligible mathematics and models of lesser general systems work so as to be part of the picture and have real physical and chemical effects analogous to biological pathways of persistent symmetries in the quasi-finite universe.
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* * * NEXT DAY:
A further thought on the implications of this is that I am talking about the state of bilateral symmetry structure and breaking including the historical path from such rearranged connections as if the initial polytope was spherical symmetry- Thus as with the chirality of nature in general we have bias to one handedness and yet have a center of netruality in organic and universal development. The rearrangements of course are arithmetically intelligible. This is the grounding of the doubling and halving of things itself a foundational principle.
A metaphor would be that between the symmetry of a reed or a lilly pad where each one is a goal of some evolution we observe that while we have bilateral symmetry the heart is not exactly the center of the design. But the restraints, globally and locally, of this quasi-deterministic symmetry alow for the potential shifts and variations at those very cusps where the chirality may be neutral such that the effects of such symmetry as a sort of quasi-morphogenesis (across scales thus non-degenerately in organic systems including mental) does not necessarily change). The "leonic" field of the expression of energy say in biochemical pathways and less than default to the center expendure of energy is a rather quasication of the idea of behind the materialization morphogenic fields- as if fractal and looping effects may be observed as field subsets of quasic dimensionality.
Where the ten-fold metric applies in this loose sense of quasi-determinism of the bilateral topological symmetric potential effects (including roughly determined do-first of the so called non-linearity of say protien structure) the mistake of finding the golden section as some value divided by some value plus, so as to approach the golden number- is more a quasi-mistake to distinguish or not if the numerical coincidence acctually applies intelligible physical design effects. Then again the depth of understanding things like ball lightning or specter of the Brocken and the like- as apparently all effects not clearly science or supernatural as we do not have a strong enough foundation of our intellible math and logic, beyond being questionable by be only quasi-observable for experiment and only organically resonating as experience- and like phereomones as odorless the non-isolated effects may observe and react with the developing world behind the scenes.