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...

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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