Monday, November 5, 2012

Unitary Topology (Toponomy)

Unitary Topology (Toponomy)

L. Edgar Otto  03 November, 2012

Having the feeling I have reached a plateau essentially stating the formal principles of this enquiry into physics I return here in the informal spirit of play not knowing if what follows is of any unique value, again if it exists somewhere in the literature, or is just another wrinkle on general systems of which the established idioms work just as well as we add to the source of the mathematics.  Take this at this time then as a mathematical recreation.

In that it concerns topology as what remains after wide transformations the gist of such theories as these alternative principles suggests wider transformations and generalization so to define topology in a foundational way where we strive to grasp things perhaps beyond such foundations.  A new topology so to speak, and one that acknowledges physicality.

Geometry as a combination of touch and sight should look further into this distinction of our senses, and how the mind's eye sees as if to hold representations and models in our subjective hands.  That we can have a hidden program changed by those who share the dialog or that we can have individuals with new methods and innovations is in a sense then only a simulation to which we focus our dialect of dialog to which the core foundational ideas tend toward invariance.

Today, we touch the screen for some interaction with the internet and computers... the product of the hidden programs can be essentially a vision or sight.  But these groundings are equivalent as much as the choice of description not relevant to the core of systems not as if more invariant in the evolution to what we intuit as the truth of things.

The illustration includes two cursive signs based on the Gregg shorthand which is as much an alphabet as that the carrier of meaning to the language it refers and these symbolically or descriptively meet in the product as unity.
The first means abacus, for the digital, the abacus effect simply that in our reliance on touch of concrete devices such as the abacus in its age the minds eye atrophies in its ability to mentally calculate.  We in effect do not see our intuition of the continuous.  The dialectics of the continuous and the discrete plays against in symmetry the dialectics of the touch and vision of that unified as accented preferences or privileging, artful tastes, perhaps intrinsic chemistry and learning.

We can envision in three space the Klein's bottle of which only abstractly is it a one sided surface for in our focused reality it must have intersections, and it can as if a bottle hold water of which this trivial principle may have deeper meaning in the context of how nature herself expresses or sees dimensions.  In a unitary topology we ask of such a space can it represent say a fundamental particle.  If this particle breaks down into two others, photons for example, the intelligible vision is that a Klein's bottle breaks down into two Moebius strips. 

This develops things from the viewpoint of continuity and continuous transformations acting on some discrete entity assumed point-like or sub-divided but is the issue of the intersections as geometrical objects thus we have the unification as well as the field breaking of all the unlimited directionality of limited or slices of all geometries over the Euclidean and non-Euclidean universal set.  But in a more general toponomy we have to discover methods that can finally deal with the singularities and complexes as one just as we have to find the deep unities in the divisions of mathematics and the parallels of the divisions, in a sense we can see algebra as the abacus effect or as the grounding or the hint of a few visual clues that the mind in its greater clarity and inborn touching of geometric relations sees with a higher comprehension.

The pseudosphere if it is to be stretched or folded into all directions yet maintaining its representation as a slice of which we feel we only see part of a presumed wider picture of such a space can be transformed into a Klein's bottle but in a continuous way.  The logic of it is a quantum logic as it is the choices of what happens within the paradoxes of that logic to the more flatland surface space as itself we touch or see as but a part of more general space.

In the familiar world, moreover, the embellishment of the mathematical processes comes from a ground that seems a given or a weak but concrete level of activity, being, source amplification so to add on this skeleton more general content.  It is at the opposite poles of a psudeosphere that upon the surface the gyres spin that enables the violation of conservation of chirality or say the intermittent truth that violates the idea of time reversal to describe antimatter- chirality and charge are intimately related in this matter and can be views to some extent as the same thing.  While the continuous view is the realm of the measureless we know that what is continuous or not itself is a quasifinite nonnecessary conserved entity in the expression or concepts of physical laws.

The poles can abstractly be put end to end for not a bad description by topology alone (without the algebraic or even the quantum formalism) to describe some particle interactions.  Such pseudosphere objects, the question of complex space aside (although we can hold the relation between such spaces as a dynamic division of octonions by the quaternions on some level) can be developed as continuous topological transformations with wider but current methods to which we may ask, that is if a wormhole for example is more than the possibilities of Riemann manifolds in higher space, if it is not simply a restricted cylinder in concept or even a torus, if we keep in mind the recursion at and between the intersection and the plane to sphere idea of space itself where choices are made at the remote extremes in regard to such things as handedness.

Also the main diagonal of quasic (and brane or even quantum spaces) itself can information be broken down such that it contains loops and strings of unitary topological structure.  This the teleoscoping principle a dimension down and not always realizable without the context of the higher dimension or at least clearly unambiguous as to the themes that do not reduce down into less than transcendental cycles. 

A biological instance of this vision is the realization that genomes may indeed be considered the incorporation of viruses as the explanation of higher states of organisms but these can be understood in the structures and context in a more precise way than our experimental approach alone seems to do so in our day.

The quantum logic of it is also limited in application if we so choose or can be wider in scope or grounding in that we can apply the more general principles to a space, even one virtually finite but unbounded or literally a plane of open extent, such that we can merge programs as if merging the games that seem to encompass a totality of discourse, in this case there should be wider applications in what we now imagine the three dimensional printing and three dimensional viewing into higher space and actual constructions- but these need the quasic logic to program more than as if the hope for efficient results from the sensitivity reception and divisions intelligibly in our models.

Love is timeless and yet it spans our memory rooted deep in growth...

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Gravity and its analogs as if continuous things such as space, mass, charge is what we find left over in directionality after the general interaction of the truth of all geometries Euclidean or not.

This amounts to a dawning but radical change in our world view that we do not have just a single origin at a singularity center nor the idea of endless or successive expansion any more than a fixed and stable geometry of space or time.

But while there is activity on the ground in symmetry and mirror detection, a diode, on the shifting topolonomy we have intrinsic amplification and accelerations of accelerations by virtual of stereonomic structure and quasifinite laws of symmetry in finite space and time, matter and charge-chirality.  At geometric unity, as perhaps hinted in a model of a foundational change in world view to suggest like Hawking finite in real space but infinite in complex time this universe, we understand dimensions as the n-sphere rim to which distinct objects may fall into potential wells, black or worm holes and other creative objects.  Yet where these meet at the extremes over a continuum the directionality of spin may switch  or braid and we contain all the ideas of the landscape of compactification forms wider than simply the next Riemann manifolds or the universal topology that unites only the zero and positive forms of general geometry.

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