Thursday, December 27, 2012
Lampions Footnotes: Late December 2012
Lampions Footnotes: Late December 2012
L. Edgar Otto
Dimension and Concrete Symbols 2012-12-25
23:36:25 - A general concept of what by virtue of being in a lesser adjacent natural dimension gives it in a sense concreteness, as if a materiality which in the freedom of a general theory of space grounds our idea of touch in what is an abstraction. This idea works grossly in some science fiction scenarios including the use of the concept on actual material things implying a certain space of wider immateriality if these essentially quasifinite "flangelations" that is conceptual and real geometrical and structural focusing in worlds of nonnecessary contiguity.
It follows that a great deal of mental development is the learning innate in children of this freedom to explore symbols as if concrete objects of which to form a relevance of what amounts to tangible but abstract structures that correspond to various levels of evidence when grounded by and experiencing the familiar and intelligible levels of the world.
In the abstract, between interactive dimensions and the counting with a tendency to move things in one of absolute directions for wider symmetry and what may be thought of then as articulation of these abstract geometrical objects- that is what we can combine, such as cubes formed into shapes in familiar space become the same stereonometry and tactical conductibility as if such objects are actually material objects so constructed. Learning is on the same level of reference in this mental space as to what is imagined as a simulated system and how it applies to those encountered in the real world- moreover, these levels of such functions in an actual organism may loop in reference to these laws, and may be open or closed in the hierarchy or analogies of real or imagined encoding parallels of systems- these to some degree constrained where totalities are constrained if they have a matching totality of the excluded mirror or field possibilities of objects within an organism as if these at any point partake of restrained intelligible unity.
If geometry, abstract but as if defined by touch and sight, do not have such principles at the foundation the explanation of imaginary and real structures will not be philosophically resolved as to which dualism substance is said to be the actual and the concrete- and the widest reach of the real of system possibilities to which we may on the more general level imagine a weight of what is intelligible.
Let me add that in the articulation of these abstract objects that there corresponds in the material world limitations of the order of conductibility which in our time the levels of understanding assume the concrete from statistical methods. The extreme of this as a concept is the denial of any dimensions whatsoever beyond the three, or the permission assumed needed for a time dimension added that vanishes in the idea of the abstract motion thru time.
It is possible that where still higher systems of contiguity will fit into a matrix of color matching these have to be done to n-dimensions as triangular matrices only of which the main diagonal of colors to the desired number if we imagined it mirrored would contain double or multiple diagonal elements, alternatively these can be dihedron half elements.
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I notice that in the path fractal-like multiple possibility of filling a limited natural plane by linear dimensions, these in the hypercube imagined as motion thru space elements, or thru the 32 edges, that of the 256 combinations of axes we subtract an abstract row of 8 colors (the 3-space faces of a hypercube as opposite pairs) for what is considered the 248 dimensions in those theories- of which we should check again the number used for constructable hypercube unfoldings.
Let us recall that there are 240 Soma cube solutions (which of course may be considered of the important number 480 in some particle physics theories. That of the pentominoes of five cubes we can add one abstractly to the whole as if in a distant four space. Note also the 230 (that is 32 kinds and the translations) crystal groups in three space. These are found without recourse to the idea of more abstraction than the constructable arithmetical axioms.
256 - 16 = 240; 256 - 26 = 30; and so on that we need to formally relate into arithmetical concrete systems upon the materialization available from abstraction. I do not know how in the literature these core numbers were derived other than it seems to take a lot of people working a long time in what is considered a very large field of number combinations by principles but far from the tangible computation and concrete but lesser number of pattern visualization.
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As far as conductibility goes, connected or divisible by flange stereonometry asymmetry in mirroring does not necessarily define primacy as indivisible in the factor relation to unity. Geometrically a number times one is not the same as one times the number- a sort of quasi-prime concept.
This is reflected globally in the convergence differences in mirrored log or exp functions and such asymmetry may be treated as powers of the |x> quantum convention symbol as the power of itself, including this reversed (4 possibilities).
The division of subcells continues this quasi-primacy so sometimes in a wider system where there is a concrete unity it may act as prime fundamentally.
Perhaps a cyclic prime like 89 can be translated into other base representations via this mirroring asymmetry.
We note also that a linear motion thru the ensemble of the 24 hypercube square subcells at each edge crossing has two sign choices, alternatively. Quasi-cycles.
We also note in the 4 x 4 matrix doubled as subcell edges the relation between given points, divided into two sets that compliment the mirrored information the shift from one such point to another may have a first or second generation skip in the quasic brane, qb for continuous sets, 8 cycles and 8 cycles as if two of many parallel paths of cubes, of the 24 implied cylindrical squares by the edges in cycle there are 8 that are independent or discontinuous for the total of 32 edges.
Pi is for principia. It is obvious in the coloring and number of edges that meet in a point in say alpha 4 (5-cell simplex polytope) or the faces so colored or the volume integral of the polyhedra that the group numbers can be intelligible arithmetic with operations of absolute values where addition and multiplication my be indistinguishable or correspond as in the magic numbers of electron configuration in atoms. The primacy as concrete 2 shows up here in the nature of division and unity of systems- 96 is of course the 24 octahedra in the 24 cell polytope of the group 1152 that intelligibly are defined by rigid and inverse rotations unto the dimension in question.
Higher generations defined structurally and quasicly involve wider ideas of dimensions and symmetry of which the platonic figures and their four space analogs are especially significant for conductibility in the lower dimensions.
If in a set of points, orthogonal for a start, in the virial shift fault pairing by the dihedron at singularity or zero, or the 6 10 14 18 and the implied 50 we choose a pair of them of unity linear motion or zero change of binary coordinates we can open or divide the orthogon (including greater than 5 space) as if it is not a matter of a looping circuit but an open circuit at both ends where the choice of sign allows extended mirroring if the sign path respects differences by halving the path division as in edges at these points (a memory action at a distance entanglement for example.) Such global memory effects applies to unfoldings via numbers greater than 2 also in the flange or rim natural stereonometry of condensing or expanding dimensional structures shifted interdimensionally.
In a consistent integral system that involves exponentiation the value of one half as constructable contains other magic values if there is general dimensional entanglement of said memory or the unity of a space is alternatively to be seen as parts that are discontinuous, manifold spaces add to their complexity by these unity or quasi-prime quasi-logical states of an evolving classical system as if he hidden forces and wider laws of symmetry define materiality as constructable.
Structurally, that implied in the 24 or 32 duality difference of the faces and edges of the hypercuble may interchange the idea of 8 independent elements or in the circuits describable as if distinct squares a series of 8 mirrored are a continuous prime, both meeting intelligibly at contiguity where the functions are looping.
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Quasic Plane Ordering
In this iI list of 16 edge elements I put 16 elements of the quasic plane in the logical order I called the quasic order (sometimes the Zz code but I am not sure the Z code term applies here the same way. The imagined path or motion function between these points in a two space or brane representation of four dimensions will physically appear as discrete points where in the four into three space representation we can imagine these are continuous motions. We then see that at each point in either representation there are four choices of the at each point for 64 in regard to the four axes. This is 48 should we allow no reversals at an edge, and if we mirror and expand the path (not including the cases of motion thru other subcells, here thru a cube face at each point - that also considered a linear motion without a right angle shift which would describe the 6n usual degrees of freedom of such ensembles) we can apply this to the doubling or halving of the covering planes of the 32 elements as if the possibility of the natural doubling of subcells elements to extend the orthogon another 2^5 natural dimension.
In loops these are transitive in function over any of the sixteen points, the ordering being chosen from one of them privilege as a standard- the topological methods as in a Karnaugh graph is not just a matter of the illusion of elements on the plane that is presumed transitive as discreteness into a wider range of discrete adjacency as the foundations of such abstract quantum like jump motions. The tenuous continuity between these elements can be readily seen where they on the simplest or reduced (flanged)level applies to codon genetics. Note the symmetry that in a table cloth fractal like manner divides the symmetry of the totality into quadrants even in the 4 x 4 representation for the underlying logic and validity of such point-class codon expression possibilities. Here we also see in a asymmetrical direction existentially at least the non-necessary but not strictly non-linear unto a given basis of a natural dimension the area of choices at an element point that may or may not depend on its preceding history nor what possibilities in a consistent universal aspects of the system may follow in a tachyonic like or teleological directed like abstract and absolute motion system. The general fixity of our concepts of a physics field, either as the case of randomness for itself or as overly mechanistic misses the sublty of these interdimensional and inter brane or group sub-possibilities (of which we vaguely interpret in terms of say the second physics, quantum theories with the problems of how we see such physics of vague clouds materialize as the classical concrete.
The general quasic plane is not restricted to any level of the n dimensions but we can make global confusions or decisions as to what we consider concrete or as illusions of our perceptions (of which we have the adaptability in our life and thought paths to discern what is concrete and what is hidden in our evolving world.) These brane quasic generations may be multiple around a full or empty singularity vacuum point as well the idea of manifolds of multiple branes as if vectors of natural dimensions. These persists in their discrete properties also.
If in the quantum |x> notation we represent asymmetry in discrete or continuous systems, the powers not just inverses of functions generated, these too may be considers relatively continuous or discrete as logical possibilities of the quasi-complimentary mirror powers or that powered as the grounding dimensions.
At a given point or quasic region we can also imagine that entry into the next point may affect in the multiple choices sign reversals in intelligibly all of the direction possibilities in question for a sort of complete or partial "quasic inversion".
Two such general quasic fields, in ideal completeness or unto some part of the totality of each, may combine or may influence the conformal structure on many levels as if a unity or division of the properties of each other.
When we do consider different subcell motions as quasifinite from some set of elements in the quasic brane we may note or have a rough measure of the weights or energy involved as if between rays or stings as edges between them and the effect when seen directly or not may materialize intermittently as does the core positive existence over the zero or negative in the omnium as logically unified and fixed yet expanding and self looping quasifinite universe.
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