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Commentary :: Education
physical description
22 Apr 2013
The propaganda-education system teaches the public to obey authority, but whatever authority in which a person might believe, the new ideas, based on many-dimension being partitioned by a finite set of discrete hyperbolic shapes (and expressed in this paper), describe the stable structures of the very prevalent many-(but-few)-body systems, and this is something which modern physics, based on (indefinable) randomness cannot do.
It is only the stable “geometrically-separable” shapes defined in a linear, metric-invariant context…,
[where the metric-space must also be a metric-space of non-positive constant curvature…, where the metric-function only has constant coefficients, and the metric-function, ie symmetric 2-form, is a symmetric matrix]
…., in which
1. stable (math, or physical) patterns exist,
2. measuring is reliable, and
3. there is quantitative consistency,
and where linear metric-invariance implies a need for a separable shape (or a geometrically-separable-shape) ie continuously locally diagonal coordinate transformation relations or locally orthogonal local coordinate relationships.
The stable shapes of the set of discrete hyperbolic shapes can be used to determine subspaces of dimensional levels (where this can be done by partitioning an 11-dimensional hyperbolic metric-space with a finite set of discrete hyperbolic shapes) within which:
1. measuring is reliable,
2. stable systems exist,
3. these stable systems can change between different types of stable shapes, or
4. the containing metric-space identifies stable orbits for condensed material,
where condensed material is material components which are too small to be interactive (material) shapes within the containing metric-space, but they are components of a particular dimension which resonate with some aspect of the finite spectra (of the proper dimension), which is defined for the over-all 11-dimensional hyperbolic metric-space which is the containing space,
That is, some stable material can exist as condensed material in stable planetary orbits.

In a containment context, where measuring is reliable, local linear models of measuring, ie (partial) differential equations, make sense, and stable solution functions are related to resonance of either low-dimension system-shape models, or to the orbits of the containing metric-space’s (orbiting) condensed material (which can often be charge neutral), but the resonant metric-space, and its orbits are actually contained in a higher-dimensional subspace.
That (partial) differential equations make sense in a context within which measuring is reliable can be interpreted to mean that because feedback for non-linear systems…, based on the critical points of non-linear (partial) differential equations (and an associated limit-cycle convergence [or divergence] structure)…, works--- then this seems to indicate that the context within which we exist is, in fact, a (narrowly defined, or highly constrained) context within which measuring is reliable.

Though this math context is built from the simplest of math patterns,
1. They are stable patterns (shapes)
2. So that measuring is reliable, and that
3. The stable solutions…. to either orbiting dynamics or to stable system component shape, ie the patterns fundamental to existence (or which determine the properties of existence)….. are related to lists of spectral-geometric stable properties (or quantitative sets), which are both microscopic and macroscopic properties, which are defined by resonances with the finite spectra of the over-all high-dimension containing space.
But
4. The over-all high-dimension context…., in regard to:
a. metric-space-shape size for the dimensional levels and
b. subspace structure, and/or
c. the (dimensional-size) tree-structures of set-containment,
(in regard to metric-space shapes which partition the 11-dimensional hyperbolic metric-space),
….. can be very complicated, and
5. The relation of a component (or shape) to the containing metric-space…,
… (where the metric-space is also a shape of some size)
[eg a metric-space containing subspaces of particular dimensions (ie contained components within [bounded] metric-spaces)]
…, in regard to:
a. infinite extent discrete hyperbolic shapes, eg the infinite-extent neutrino of the electron-cloud, contained within a bounded metric-space, as well as,
b. the property of action-at-a-distance, as well as
c1. the determination as to whether an infinite extent shape of low dimension is either bounded by a higher-dimension containing metric-space, or
c2. if it extends out to an infinite subspace,
d. and thus such a shape (defining an infinite-extent subspace) is also relatable to other infinite-extent stable shapes (other 11-dimensional hyperbolic metric-spaces, within which finite spectral sets define other existences)
…, can be difficult to actually determine.



Though charge is likely not a 1-dimensional construct, but rather a set of charged 1-flows which fit into (at least) a 2-dimensional discrete hyperbolic shape, so as to allow spin-rotations of opposite pairs of time-states.
On-the-other-hand mass (or inertia) can be 1-dimensional, a circle, since a circle’s center is a distinguished point, in regard to position in space, for translations or rotations, but any point on the circle could be a distinguished point for rotations, or a pair of opposite points, a diameter, or two pairs of opposite points so that each diameter is orthogonal to the other diameter, and furthermore, the orthogonal pair identify the circle’s center. Thus, such an orthogonal pair represent both rotation frames (rotating stars) and translation frames (fixed stars).
So that, the circle and its center can be mapped into one another, so as to represent the map between translational and rotational frames of the circle on the plane.

A new context

Though the new descriptive context agrees with particle-physics that the description is unitary, due to metric-space containing opposite metric-space states, these opposite states are related to spin properties of material components, and that the containment space is an 11-dimensional hyperbolic metric-space, but that such an 11-dimensional hyperbolic metric-space can be related to other such 11-dimensional hyperbolic metric-spaces, and that the stable properties of “material,” which are contained in each such a space, must be in resonance (and in the correct dimension) with the finite spectral set defined by the metric-space subspace-partition of each of the over-all containing 11-dimensional hyperbolic metric-spaces.

In the new descriptive structure there is a new context for angular momentum.
That is, angular momentum is defined on the various toral components of the stable shapes, which are allowed by the containment set (where the high-dimension containment set defines a finite set of stable spectra-geometric measures, to which the existing stable shapes must be in resonance), and on possible links, defined by angular momentum, in turn, defined on the various toral-components of the system’s shape.

Links
There are unbounded stable discrete hyperbolic shapes, which exist on all dimensional levels, and these unbounded shapes are associated to stable material components, ie stable discrete hyperbolic shapes defined by their being part of the partition of the various subspaces of the containing space
[which is partitioned by (into) a finite set of stable discrete hyperbolic shapes of all the dimensional levels of the over-all containment set].
On-the-other-hand the 2-, 3-, and 4-dimensions are relevant to the descriptions of “material“ components contained in hyperbolic 3-space, where these stable shapes are also related to both bounded and unbounded, or semi-unbounded, discrete hyperbolic shapes, where an example of a semi-unbounded shape would be the neutrino-electron structure of an atom’s (2-dimensional) charged components (which is also called an electron-cloud of an atom, eg for an atom the nuclei are bounded shapes while the electron-clouds are semi-unbounded), so that all “material” systems are linked to an infinite-boundary of the over-all high-dimension containing space. Thus, one can think of angular momentum as a controlled (or controllable) link which can exist between the many different 11-dimensional hyperbolic containing metric-spaces, due to the existence of such unbounded and associated bounded (angular momentum) links (between 11-dimensional hyperbolic metric-spaces).

Thus, one can consider a “possible consciousness” for people (or their realm of creative intent) would be related to their ability to examine (perceive) the different creative structures of these different universes, where the individual 11-dimensional containment sets, for the different universes (or perhaps different galaxies), might be perceived as intricate bubbles of different types of perceptions, into which our awareness can enter, and within which we can control our journey, since we are in touch with the infinite reaches of these various types of separate existences. (see below for a high-dimensional model of life-forms, eg models which allow all life-forms to possess a mind)
Is this the true context within which the human life-force is to develop knowledge, and to intend a creative
expansion of such a context?

To re-iterate
Though charge is likely not a 1-dimensional construct, but rather a set of charged 1-flows which fit into a 2-dimensional discrete hyperbolic shape, so as to allow spin-rotations of opposite pairs of time-states.
On-the-other-hand mass (or inertia) can be 1-dimensional, a circle, since a circle’s center is a distinguished point, in regard to position in space, for translations or rotations, but any point on the circle could be a distinguished point for rotations, or a pair of opposite points, a diameter, or two pairs of opposite points so that each diameter is orthogonal to the other diameter, and furthermore, the orthogonal pair identify the circle’s center. Thus, such an orthogonal pair represent both rotation frames (rotating stars) and translation frames (fixed stars).
So that, the circle and its center can be mapped into one another so as to represent the map between translational and rotational frames of the circle on the plane.

That is, the different 11-dimensional “bubbles of hyperbolic metric-spaces,” ….
…., between which human life might be able to enter (or exist) so as to travel between [or link between] these different 11-dimensional bubbles of different perception-types, so as to do this with an intended purpose, that is, if one’s higher-dimensional structure is understood and/or perceived,
…., seem to depend on sets of 2-planes which can carry the essential “inertial orbital-structure” for the various bounded regions of an 11-space, wherein (on these 2-planes) the pairs of opposite states on inertia (matter and anti-matter) which can be defined
[for each of these particular regions sliced by 2-planes which determine the organization of inertial properties of the region (or for these particular bounded regions)].
These sets of 2-dimensional regions are bounded since inertia is defined in relation to only the bounded shapes of discrete Euclidean shapes, where Euclidean space is the space of position and spatial displacement, ie Euclidean space is the space in which inertial properties are contained.
That is, these sets of 2-dimensional regions could be used to map the different 11-dimensional “bubbles of hyperbolic metric-spaces.”

Life
There are natural stable shapes, those of odd-dimension (3,5,7,9) and with an odd-genus (where genus is the number of holes in the shape, eg the torus has one-hole, or a genus of one, ie the genus is the number of toral components of a discrete hyperbolic shape) which when fully occupied by its orbital charged flows are charge imbalanced and thus would begin to oscillate, and thus generate their own energy. This would be a simple model of life.
Thus such a shape which possesses a higher-dimension could cause the lower dimensional components to, in turn, possess an order which can be controlled by a higher-dimensional shape, through angular momentum states (properties).
Down in 3-dimensions this control by a higher-dimensional structure could be the complicated microscopic-and-macroscopic structure of life, which appears to be run by complicated molecular transformations, eg relations between the structure of the living-system and enzymes, proteins, and DNA.

This is simply about considering the results in regard to assuming that stable shapes determine the underlying order and stability which is observed, and the fact that these stable shapes (mathematically) have a dimensional structure associated to themselves.

However, according to the currently accepted laws of physics both the stable properties of quantum systems, eg nuclei atoms molecules etc, and the stable control which is possessed by life, are unexplained (or unexplainable within the currently accepted descriptive constructs).
The patterns of stable physical systems are unexplainable within the current dogmas about the material world, since the current dogma is based on the dimensionally-confining idea of materialism, and within such a confinement, descriptions seem to be based on indefinable randomness and non-linear systems (or non-linear patterns which are quantitatively inconsistent) defined on a (quantitative or coordinate) set which is assumed to be a continuum.
Such indefinably random and non-linear patterns are fleeting and unstable, though their decay times can, sometimes be of relatively long duration.

Suppose human life is associated to a 9-dimensional shape of an odd-genus, then such a shape is an unbounded shape (noted by D Coxeter), and thus it could well be relatable to many such 11-dimensional hyperbolic metric-spaces (bubbles within which perception and action might take place) (ie why should an unbounded 9-dimensional stable shape, generating its own energy, be confined to any particular unbounded 11-dimensional containing space?) wherein (each different bubble of perception) the living system’s lower dimensional (material) structure may be quite different (in the new containment structure), and thus the living system’s perceptions and interactions could also be quite different within the other (different) 11-dimensional containing spaces.

There can be many of these 11-dimensional hyperbolic metric-space containing spaces in regard to a stable reliably measurable set of experiences.
These 11-dimensional sets could
either
be in the same space, so as to be organized around different sets of finite spectral-geometric sets,
or
they could be related to a set of fiber-group conjugations, which could be defined between these different 11-dimensional (hyperbolic metric-space) sets (or spaces).
This second construct would be similar to a model of conjugations between (say) galaxies so that the galaxies drift apart due to the structure of the group-conjugation.
This would be an account of (a new interpretative context for) the, so called, expanding universe. This structure, which focuses on galaxies actually being 11-dimensional spaces, would be organized around a primary 2-plane for the galaxy’s inertial properties (but this primary structure would only be) in regard to our planet’s (or our galaxy’s) inertial structure.



Elementary considerations


Consider the observed patterns of the physical world which have been associated to sufficiently precise descriptions so that other systems can be built by using reliable measuring processes associated to a system’s properties, and the system placed within a describable context, so as to be related to practical useful creations.
Or
Such precise descriptions fitting into some type of descriptive context, thus forming an informative descriptive context.

Classical physics

Thermal descriptions associated to closed systems composed of a particular number of components and associated to thermal properties, eg temperature, pressure, volume, component-number, energy, entropy, etc, of a closed system, where differential-forms can be used to define thermal equations.

Newtonian
Material components of mass or charge contained in space and/or time with positions in space or measurable properties of the system-component which can be associated to measurable displacements in space, in turn, related to a causal material-geometric relationship (or changes of state) or pattern sufficiently precisely related to spatial displacements (or changes in state) of position in space and time. This is the ma part of Newton’s F=ma definition of either force or mass.
And then there is the relation of material geometry and material motions surrounding a material component and its relation to force, ie the F part of F=ma equation.
These ideas are developed in both the forces (or force-fields) of gravity and electromagnetism.
In inertial systems there are the conserved systems of a spherically symmetric force-fields constrained to a plane associated to planetary orbits for a two-body system transformed into a center-of-mass coordinates so as to identify elliptic orbits, but for the 3-body system, the equations are non-linear and there are no stable solutions, and “why is a spherically symmetric force-field constrained to a plane?” yet the solar-system has, apparently, been stable for billions of years, why?

Faraday’s model
For charged systems it is electromagnetic waves (hyperbolic wave-equation) and currents defined in linear circuits, as well as motors, where solutions to solvable equations allow for a great deal of control over system properties, and thus being able to use these properties.
There are also the relatively still charged systems which have spherically symmetric force-fields, as well as some simple, usually cylindrical geometric, geometries associated to currents, wherein the force-fields define useable relatively stable properties.
Often these systems of waves and circuits deal with oscillatory signals (or couple-able properties).
These descriptions of force-fields depend on local linear relations which exist between local geometric measures, ie alternating-forms (or differential-forms), and (of) a charged system’s (or charged component and current) geometric properties.

But, accelerated charges imply the emission of electromagnetic radiation and the charged system’s loss of energy, ie such a system would be unstable. This would mean that bounded interacting charges would define an unstable system unless the system was actually an internally closed metric-space which confines the charged components.

Thus consider atoms:
These are considered to be quantum systems, where a quantum system is characterized as small components composing a stable system where the small components (or particles) are related to random spectral-particle-position events in space and time (or in space-time). Thus a quantum system becomes a function space represented in a spectral construct (or system wave-function) associated to sets of linear differential operators, eg wave-operators (or energy-operators) and the point is to find the operators associated to the quantum system’s spectra, or to diagonalize the function space, ie give the function space a spectral representation by applying sets of operators which commute. The spectral functions of the function space are supposed to represent the probabilities of random spectral-particle-events.
But
One cannot find such diagonal operator-function-space constructs for general quantum systems, ie there are no valid measurable descriptions of general quantum systems, eg nuclei, general atoms, molecules, crystals etc.

It is assumed that quantum systems reduce to particle-components governed by (probability-energy) waves in a context of stable spectral (wave) properties of quantum systems.
Quantum interactions are descriptions based on particle-collisions, which are high-dimensional, non-linear, and unitary-invariant.



Particle-collision experiments in particle-accelerators find many unstable particles and a few stable particles eg electron, proton, etc, where it is assumed that these particles are associated to the quantum system’s reduced particle-components, which are assumed to compose a quantum system.
Is it valid to assume that unstable particles are a part of a stable systems component structure? [No! This implies higher-dimensional macroscopic metric-space structure]
Then model the wave-function with internal particle-state properties associated to a non-linear (wave) equation representing the particle-collision interactions, where the interactions perturb (or alter) the particle-states of the wave-function, where the resulting perturbation series is summed to identify the stable systems new properties dependent on the new interaction structure brought about by particle-collisions and changes in the internal states of the (assumed) quantum system’s composing particles. This adjusts a wave-function, where the wave-function is now divided into particle-states if the original wave-function is close, but virtually no original wave-functions are close to the system’s spectral properties which have been observed.
It is claimed to perfectly adjust one of the energy levels of a H-atom’s energy structure. Such a claim, where the answer is based on subtracting infinity, is a dubious claim, especially since there are so few contexts within which the particle-theory is relevant.
The containment space of quantum physics (there are various ideas about this(?)) is a non-commutative function-space, along with a non-linear, but unitary-invariant, and higher-dimensional equation (or operators) of quantum interactions, ie particle-physics ensures that there will be non-commutativity, and thus the spectral identifications of any quantum system is impossible.
In fact, the math structure of particle-physics only identifies the properties of unitary invariance and the possibility that higher-macroscopic-dimensions exist, since unstable particles can be best interpreted to mean that higher-dimensions exist, and these higher-dimensions would have a macroscopic structure.

This work is in the public domain