Sunday, March 3, 2013

Toward General Abstract Dimensional Notation

Toward General Abstract Dimensional Notation

Back to the Photos of Equations on the White (Drawing, Caulk, or Robin's Egg Blue)  Board...

L. Edgar Otto

Saturday, 02 March, 2013

*3:38:31 PM  the content or dimensional number of an Euclidean construct, points, edges, faces ... is considered locally independent of the embedding condensed or natural or expanded global symmetry representation for counting purposes including abstract real or virtual singularities.

* such numbers squared intelligibly relate to the natural higher basis of subsystems in the dimensions in question.

* the general concept makes of stereonomic geometrical structure a universal code for they can be added as in the ground for a Turing universal calculating machine for information as numbers.

* we are now free to emphasize a basis as perceptual including consideration of it as the case or a privileged theory of everything; for example if we have 40 abstract objects we may match them to 5D close packing systems.

* but without a more general and relaxed theory a space say composed of 240 objects squared, assuming there is a way to handle the exceptions we encounter in lower subgroup interactive dimensional structures, the grounding does not necessarily make a unique totality of all possible ones in the general omnium reality as a theory of everything.  It is thus not a strict omega idea of a Turing machine nor can it be expected necessarily (but with exceptions) to translate higher encoding as if the universal Touring machine at least in the empty and possibly not connected coherence of this maximum symmetry locally and in observable isolation toward anything hidden, absolutely perhaps if the structures are ultimately closed and limited or at some state become fixed so indefinitely.

* interestingly, the quasic matching of these shadow condensings are neither necessary nor socially interacting to which a wider freedom of theory may ultimately ground any fixed or vague system of material or subjective modeling- that there is an exception to anything unique as a generalization of the question of fractional transfinite infinities in regard to a fixed or moving quasi-included null singularity complexity continuum.

* a set of singularity integer in the structure and count may be seen as the basis as grounding other approaches to the privileging of concepts for a theory or the general use of an intelligible informational structure as the generating representational dimension in its logic of design.  Or in the subsets we may generate a system whole that is defined by the isolated parts and their interactive properties quite independently of issues of some theory of space embedding as if necessity that such for all observational and practical purposes may be said not inferred or exist save perhaps in what amounts to higher systems that drive or is driven by higher consciousness or intuitions.

* if in cross eyed viewing, the universes unfocused into individual, say hyperbolic discs as a sea of these in an unspecified empty space, we can imagine for a doubled or singular universe that these superimposed views is the source outside or inside of a total theory of our intuitions of parallel universes of at least adjacent ones abstractly unto the complexity of a grounding symmetry such as duality.

* or the building up from the small as a possibility for a grounding design structure may itself describe a ground for a more general theory as the space it so describes as well as its description as concrete distinct from that what of a general space is so built up can generate and focus the structures built down from it.

* we now should specify the structural rearrangements between these interactive groups and dimensions within this general theory, with dynamic operations that may apply to the visualization of such quasifinite systems as computation.

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*03 March, 2013  1:46:02

* Symbol: double the number of integral potential singularities and sum to a positive number. -= vertical

* symbol: halve the number of potential singularities and sum to a positive  concrete number. =-

* symbol: consider the resulting concrete numbers in some dimensional system also transitive over any point of identity as to which is derived yet distinct from the set of such singularities.= =

* symbol: exclude all but the specific point singularity. - -

* compute levels of generational n(n+1)/2 count over a particle totality as in thirds, (9-3)/2 = 6 which for example is 3 concrete of 9 flavor independent valid concrete containment's. Analogs exist over flat brane or abstract a natural dimensional basis.

* assume such independence if ideally linear may integrate or separate, decay, these independent sub-dimensional sub-group entities or that these may from a continuous totality over an interval add or subtract total energy.

* Independent quasi-virtual point singularities may have their own mirrors and negation and generational levels within a higher or lower generational symmetric system that may move independently from the quasi-isolated systems or between them in a quantum or quasic informational manner.

* assume that an intelligible system of point singularities represent the possibility of a different generational dimensional basis or this only a random potential case.

* assume that over such mutations of systems between the necessity and chance a system may concretely evolve theologically to a different yet time independent state.  Consider this as a nonnecessary case for space of dimensions or other properties in higher generality.

* assume that what so potentially distinct as to its concrete or virtual expression may be interchanged in higher generality contain all the sub-properties of quasi system algebra and geometric count as if quasi-conserved phenomena.

* the every other partition number divisible by five is akin to the strict idea of interpretation of even and odd integers where the computation negative or positive is concrete.

* number patterns as well as the potential properties of nonnecessary point singularities persist intelligibly as we extend the hierarchy of numbers to states of higher complexity and may persist quasi- intelligibly and coherently.

* in particular we may erect systems geometrically as if a the interface of Euclidean local-general branes and sub-branes.

* at a nonnecessary Omega of computation, purpose, or infinity as if an end the generalization returns on all potential dimensionless scales to Being as paradox and quasi-contradiction as absolutely yet creative potentiality divergence from the stance of perpetual ending, creation and change or all purposes subsumed to the reality of a general yet philosophic continuum of a theory of everything, being and non being or all models that are inclusive of realty where they can also be mathematical models as if in between.

* one sufficiently extended interval of ephemeral existence may establish potential intervals of everlasting or eternal extension of said unified totalities as if the everything.

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12:00:05 PM

* Two further illustrations may help to visualize the combinatorial concepts of these abstract point singularity spaces.

The first relates to a certain threshold of intelligibility between independent singularities of a higher group dimensional space such that we may describe a social model as if between persons and their interactions.

The second involves weighted dice of various colors in the biocolor code in a triaconway matrix which point out the role of diagonals.  But this is also a matter of applied probabilities along with the space pattern symbol substitution that seem to confuse the reading of color words spelled in a different color. God's dice would be of a wider subjective nature if He did play dice with the cosmos, even if in some standard stance He can load the dice or not.

But both illustrations suggest a certain independence on several, especially the next, dimensional level of the count of singularities to which such variations on phenomena will be expected or if in a data system assumed but outlier exceptions.  In a sense these dice or systems have to reach a threshold of complexity in the organized count wherein say in the passing of that waged between three players the advantage moves in a looping direction cycle of tighter and higher pip counts.  Without this looping we have no definite direction of the wagers and wins- we in effect define temperature as if by the zeroth law of thermodynamics.

We may take the raw number of pips imagined in all the counting possibilities, such as 30 x 6 faces or also for space color cubes x 21, or x 28 for four space... the pips over three axes intelligibly sum to 21, that is 7plus7plus7.  By the labeling with such pip numbers we can describe the inversions of the cubes with just a positive notation across the triaconway matrix.  These sometimes add with an excess or remainder of twice 28.

In spending some time with the actual thought to manufacture these new takes on old mathematical recreations I have other game ideas to investigate the last illustration here, for example to take 8 of the 24 hypercube faces as a point and add 16 of its points thence to find the symmetries of connected successive play connecting them by two players.

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