Geometrization and the mathematical context for the solution of physical stability:
author: m concoyle
 e-mail: martinconcoyle@hotmail.com
Abstract (see Scribd.com for books listed in refrences about this subject)
There are (moded-out) "cubical" simplexes in a many-dimensional context, whose structure is determined by hyperbolic metric-spaces, which can, themselves, be modeled as moded-out "cubical" simplexes. Transition between the different dimensions determine physical constants, and the value of these physical constants can imply that:
1. the different dimensional levels can be hidden from one another, ie the size of the interacting materials change from dimensional level to dimensional level and the geometry of the interaction can also change, ie material interactions are not usually spherically symmetric.
2. The over-all high-dimension containing space can be defined as having a finite spectral set.
3. The descriptions of both mathematical and the physical systems are (or can be) stable, because the "cubical" simplexes can define discrete hyperbolic shapes.
Metric-spaces have properties and subsequently an associated metric-space state, and this determines the dimensional distinction between Fermions and Bosons, as well as determining the unitary (invariant) mixing of (metric-space) states in subsets of complex-coordinates.
Unitary invariance implies continuity, or the conservation laws, eg the conservation of energy and material, etc.
Each dimensional level is a discrete hyperbolic shape, and this implies such a set can define a finite spectral set for the entire space.
|
Abstracts
Introductions... .4
References and books... ... 10
Speech 1.... 11
& re-iterations
Speech 2.... 24
Speech 3.... 28
Dimensions* (technical stuff) etc ... .34
Empty of content (Apparently, no stable patterns exist)... ... 44
Diagrams... .59
Abstract 22
Abstract for Arxiv
This relatively new (since 2002) and relatively simple context of math containment provides the setting for a solution to the problem of finding the math structure for the observed stable material systems which are so fundamental and so prevalent. It also provides a basis for a quantitative structure which is defined on a finite set. However, these stable physical systems go without any valid math structure (for these systems) in a currently accepted math context of indefinable randomness (eg improperly defined elementary event spaces), non-linearity, (global) non-commutativity, or only locally commutative, (eg quantitative inconsistency, eg chaos) all defined by a contrived descriptive structure of convergence and divergence onto a continuum. Where these math structure are together used to explain (or identify) the (stable) properties of physical systems. But such a math context really only applies to physical systems in a chaotic transitioning process (eg reactions in weapons) and for feedback systems (eg guided missiles) whose range of applicability is difficult to define and it is a context which applies to quantitative complexity (eg secret codes). But it is also used by the media to create an illusion of expert "mastery" and "expert complexity."
Though many difficult problems now have solutions: nuclei, general atoms, molecules, a new way in which to analyze crystals, and the stable solar system, due to these new ideas, this means that these relatively new ideas should be dominating the attention of the professional mathematicians and physicists, but they are not. Note: Apparently, waves which possess physical properties can be successfully related to solutions by function-space techniques.
Apparently there are stronger social forces involved in an inability of a public, or of an expert-class, "to discern truth."
The US propaganda system is the sole authoritative voice for all of society and it is the propaganda system which directs the attention of the researchers. These researchers are dependent on a funding process. However, these same researchers claim to be the personifications of the highest cultural attainments in the society, nonetheless they have social positions of being both wage-slaves and society's, so called, top intellects in regard to a religious personality-cult, expressed through the media, so public-worship consolidates their belief in their far too authoritative mathematics and physics dogmas, which has failed to solve the problem of the cause of physical stability for nearly 100 years (ie it is a failed dogma), ie the media turns "top intellectualism" and the dogmas upon which such a "measure" of intellect rests (the "intellectual winners" of the competition whose rules, in the education system, are defined by an, essentially, absolute authority) into a religion, this deep religious belief in what the media labels as science [Copernicus would have a more difficult time persuading others to consider an alternative way in which to organize and fashion language within such a current religion (2013) of expert authority, than the difficulties he had in regard to the authoritative religion of his time].
The professionals are following their "deep beliefs" as dictated to them by the propaganda system. Apparently these professionals can rigorously prove properties which are contained in a world of illusion, eg where a description based on randomness also possesses well defined geometric properties, eg particle-collisions.
It should be noted that the best interpretation of the Godel's incompleteness theorem is that precise languages can be very changeable when reduced to the elementary levels of assumption, context, containment, organization etc. Yet the failure to describe the stable underpinnings of physical existence has not been seen as a crisis of the knowledge which is being derived from the currently accepted authoritative dogmas of math and physical description.
There is other social organizational properties which manage society, and with which one must deal with, there is a vast social organization in regard to management which manage the math and physics (or science) communities, eg managing personality types similar to the management of personality types in politics and the justice system.
In the new context of containment one uses the most prevalent of the stable geometric patterns identified in the Thurston-Perelman geometrization, namely, the discrete hyperbolic shapes and the properties that these shapes possess as identified by Coxeter.
Furthermore the ability to "surround" a "hole" by a closed shape, so that a continuous deformation is limited, ie the "holes" introduce stable properties into the context of the continuity of shape.
The discrete hyperbolic shapes [with component interactions mediated by discrete Euclidean shapes (tori)] are also very rigid shapes with very stable spectral properties.
That the solar system is stable is evidence, which can be interpreted, to prove this new context for mathematical descriptions of the physical world is true, especially, since the professionals have no valid model of stability for these stable systems.
Abstract II
A new context in which to apply geometry to: math, quantum physics, and the solar system, etc
Quantum physics assumes the global and descends to the local (ie random particle-spectral measures).
Is geometry a better vehicle to define the stability of quantum systems rather than function spaces?
Is the stable construct to be the very stable discrete hyperbolic shapes, in a many-
dimensional context?
A geometrically stable and spectrally finite math construct, where, in adjacent dimensional levels, the bounding discrete hyperbolic and Euclidean shapes are defined, and then mixed as "metric-space states" in a Hermitian (or unitary) context, can provide a structure for stable properties.
Assume that math be consistent with (local) geometric-measures of stable shapes, which define finite spectral sets, contained in higher-dimensions.
The stable shapes in the different dimensional levels are con-formally similar, and resonate with a finite geometric-spectral set contained in a high-dimension space.
A new interaction type consists of a combination of hyperbolic and Euclidean components, but when in an "energy-size range" the system can resonate with the spectra of the containing space, and thus it can change to a new stable, discrete shape.
Abstract III
There are (moded-out) "cubical" simplexes in a many-dimensional context, whose structure is determined by hyperbolic metric-spaces, which can, themselves, be modeled as moded-out "cubical" simplexes. Transition between the different dimensions determine physical constants, and the value of these physical constants can imply that:
1. the different dimensional levels can be hidden from one another, ie the size of the interacting materials change from dimensional level to dimensional level and the geometry of the interaction can also change, ie material interactions are not usually spherically symmetric.
2. The over-all high-dimension containing space can be defined as having a finite spectral set.
3. The descriptions of both mathematical and the physical systems are (or can be) stable, because the "cubical" simplexes can define discrete hyperbolic shapes.
Metric-spaces have properties and subsequently an associated metric-space state, and this determines the dimensional distinction between Fermions and Bosons, as well as determining the unitary (invariant) mixing of (metric-space) states in subsets of complex-coordinates.
Unitary invariance implies continuity, or the conservation laws, eg the conservation of energy and material, etc.
Each dimensional level is a discrete hyperbolic shape, and this implies such a set can define a finite spectral set for the entire space.
A new interaction type consists of a combination of hyperbolic and Euclidean components which are one dimension less that the dimension of their containing metric-space. A 2-form construct emerges from this geometric context which is the same dimension as the adjacent (higher) dimension Euclidean base space of its fiber group which determines discrete spatial displacements. This interaction construct is either chaotic or it could begin to resonate during the interaction and, subsequently, to become a new stable spectral-orbital (discrete hyperbolic shape) structure, by means of its resonance with the spectra of the many-dimension containing space.
Introductions:
Math flyer (1), San Diego joint math meeting (2013)
(come to talk 1-12-13, rm 6E ?(main bldg) 3:30 pm, #1086-VR-413, Assorted Topics II)
A new context in which to apply Geometry to: Math, Quantum Physics, and the Solar System, etc. By M Concoyle
I. This new "math construct" addresses unsolved problems, as well as unrealized models of quantitative containment (within a finite quantitative construct). This is done by using the simplest of math structures, and elementary ideas about quantity and shape.
II. The unsolved physical problems are about finding the context within which one can describe very stable fundamental physical systems: relatively stable nuclei, general atoms (atomic number greater than five), molecules and their shapes, crystals (BCS predicted a critical temperature which has been exceeded), and envelopes of orbital stability for orbital planetary systems, [and dark matter, dark energy] etc.
These problems cannot be solved in the math structures (dogmas) based on a non-linear, and an indefinably random context. Nonetheless, this is the context which is used by today's math and physics professions. Such a context leads to the statement, that "the stable properties of fundamental (physical) systems are 'too complicated' to describe," and the focus of the description is on describing fleeting, unstable patterns, in a quantitatively inconsistent manner, and this is done within sets which are "too big," eg the continuum, so as to possess the capacity to be logically inconsistent (eg geometry defined in a random context, allowed by defining various convergences), ie they focus on non-descriptions and irrelevant issues, which they try to describe in too great detail.
III. The new math context is ultimately about, "How to guarantee: stability, quantitative consistency, and to define finitely generated quantitative sets," and about "How to guarantee the stability of a uniform unit of measurement, within descriptions of fundamental systems, which possess stable measurable properties."
IV. The new math context is about basing physical description, as well as stable quantitative structure, on stable geometry. Namely, the geometry based on the discrete hyperbolic shapes, in conjunction with discrete Euclidean shapes, as well as with other metric-space "discrete shapes" associated to non-positive constant curvature spaces, with metric-functions with constant coefficients, eg the R(s,t) metric-spaces and C(s,t) Hermitian-spaces (of finite dimension), (C(s,t) is a result of (4) below), where, s, is the dimension of the spatial subspace, and, t, is the dimension of the temporal subspace, and s+t=n is the dimension of the metric-space. [and where R = real, C = complex numbers]
These are the circle-spaces ie spaces related to "cubical" simplexes or rectangular simplexes (where cubical simplexes are related to circle-spaces by equivalence topologies, ie a moding-out processes).
V. Just as Copernicus and Kepler provided the correct quantitative-geometric context for the properties of the solar system, which could be fitted by Galileo's law and Newton's global solutions to (Newton's) differential equation models of the 2-body, "center-of-mass coordinate" model of the solar system... .,
which is a more useful context, in regard to feedback systems in gravitating systems, than is the "practically useless," 1-body, spherically-symmetric model of gravity, given by an
unrealistic (1-body) non-linear, general relativity theory,
(over) (1)
... ., this new math context provides the answers (the types of shapes for a solution function) for stable material systems (as well as metric-spaces) modeled in a stable, geometric context, where the assumptions provide the context for the existence of solutions to stable systems, and by modeling metric-spaces as stable shapes, this allows for a finite spectral set to be defined.
But the new context also organizes math patterns, and provides new types of quantitative processes through which fundamental stability can be placed into a general descriptive context, in relation to wide ranging applications, which can lead to sufficiently precise "stable spectral-orbital" descriptions (constructs), which are geometric and thus the information provided can be used in a practically creative manner.
VI. The stable spectral properties of general atoms and nuclei (as well as the other stable material systems) are related to finite (integer) values, ie number of charged components (atomic number), and a number of (uniform) nuclear components (atomic weight), respectively, but they do not have valid descriptions based on physical law, and it has (also) not been understood "how envelopes of orbital-stability form in a macroscopic solar system," but all of these systems can now be modeled, based on stable geometry, ie similar stable geometric constructs hold for both stable microscopic spectral systems, and macroscopic orbital-envelopes of stability.
VII. There are 6 fundamental aspects to the description:
1. The metric-spaces and their associated isometry groups fit into a principle fiber bundle (one ends-up using this construct more later, and it is just as easy to introduce it first).
2. The fundamental shapes of existence: both metric-spaces, and material systems, are to be modeled in the context of discrete hyperbolic shapes and discrete Euclidean shapes (tori), or in non-positive constant curvature spaces for metric-functions with constant coefficients. This is related to the classical Lie groups of both SO(s,t), and spin groups, and SU(s,t) [see 4. below]
3. The containing space is many-dimensional (11-dimensional hyperbolic metric-space) so each dimensional level, as well as each subspace of the same dimension, is to be identified with, either a macroscopic or a microscopic, stable discrete hyperbolic shape.
4. There are (physical) properties associated to metric-spaces of various dimensions, and they are associated to various metric-spaces of the type R(s,t). This leads to metric-space states which come in opposite-pairs. These pairs of opposite metric-space states can be fit into both the real and i(real) [or pure imaginary] subsets of complex-coordinates. Thus the description is (can be) related to SU (unitary) fiber groups. Such descriptions, of opposite metric-space states, also relate to spin-groups, and Dirac operators.
These properties of metric-spaces can be related to both math and physical patterns since the properties deal fundamentally with "position in space" (Euclidean space), and "a stable existing pattern" (continuity of stable patterns in time, an implied assumption in mathematics), eg energy, mass, and charge conservation assumptions.
5. The derivative as a discrete operator which can be related to: (1) material interactions as discrete operations, (2) dimensional levels involved in dynamics (also physical constants can be modeled as discrete operators defined between dimensional levels) (3) Weyl-transformations are discrete angular transformations, and deal with the shapes of discrete hyperbolic geometries of a physical system's related orbital-spectral properties.
6. A new way in which to model both life and mind.
(over) (2)
Introduction 2
Describe the properties of the stable spectral-orbital systems, How does one describe the very stable, many-body, spectral-orbital physical systems which exist at all size scales from nuclei to solar systems, as well as life and mind?
The subject of stability is mostly about using very confining, but very simple set of geometric shapes, and some simple calculus, as well as a few other (local) geometric properties defined in a context of a principle fiber bundle with a many-dimensional base-space, where the base-space is (dimensionally) partitioned into sub-metric-spaces which are identified by discrete shapes, which are open-closed (when observed within the metric-space which possesses the discrete shape), but these metric-spaces (with shapes) form a boundary when viewed from an adjacent higher-dimensional metric-space which contains the discrete shape.
The math properties for stable solvable physical systems, The simple math properties which allow partial differential equations (or differential equations)... , which are used to model physical systems (either geometric-inertial or spectral)... , to be solved can be listed.
That is, solvability is related to the set of properties: linear, metric-invariant, separable (locally linear and commutative (diagonal matrices at each point in the global coordinate system)), where the metric-functions can only have constant coefficients, (for the various R(s,t)-metric-spaces {where s-space, and t-time; dimensions}, and associated metric-function signatures, where these different metric-spaces are, in turn, related to new types of materials).
[These new material-types are characterized by their properties of being odd-dimensional spatial subspaces, with an odd genus-number, (analogous to discrete hyperbolic shapes) so as to be charge-unbalanced, and thus, naturally oscillating and energy-generating material systems, which model life. Life is defined as new material-types, which are contained in either: R(4,0), R(6,0), R(8,0), or R(10,0) Euclidean spaces.]
The properties of stability are properties which are possessed by the circle-spaces. One can note that, circle-spaces can be modeled as metric-spaces of non-positive constant curvature, whose discrete shapes (or discrete isometry subgroups) are determined from lattices (with an associated fundamental domain, which is related to right-rectangular (or "cubical") simplexes, by a moding-out process (or a process of defining an equivalence topology on the cubical shapes of the fundamental domains).
[Note: The quasi-spectral-geometric properties used to describe particle-physics, ie the non-linear-random-geometric model of particle-physics... ., which deals primarily with probabilities of particle-collisions {which, in turn, only model (nuclear) reactions}, and which is a completely irrelevant and practically useless descriptive construct... ., are excluded from consideration, since these descriptive constructs only provide... , in a chaotic or random fashion... , brief and fleeting descriptions of unstable patterns. It is a model which is only applied by means of its relation to reaction-rates.]
Holes-in-space, spectra, force, and the circle-spaces, are all defined within a many-dimensional space
The simple math structures of circle-spaces, as the basis for the stable (geometric) properties of existence, causes both spectral properties and force-fields, to have an analogous (or parallel) math structure... ,
[in relation to holes in space caused by either the shape of a metric-space or by rigid material shapes, eg (usually) 1-dimensional currents defined by rigid material defining a closed curve]
... , than is usually believed to be true (ie the material-shapes are equivalent to spatial [or metric-space] shapes).
The very stable "discrete hyperbolic shapes" are used as models for both material components and metric-spaces,
so as to construct a very rigid geometric structure, in a many-dimensional context, so that Newton's laws still define inertial dynamics. Discrete hyperbolic shapes are stable, with stable spectral properties, and they provide a constrained and stable and very rigid set of boundary conditions for both material containment (confinement) and material interactions, so that differential equations, at first, appear to have a very restrictive containment structure, but this is needed to model stable systems, and it can also be used to model living systems in new ways.
Most material components, as well as metric-spaces, which are contained in this new many-dimensional context, have the shapes of circles-spaces, in particular the "discrete hyperbolic shapes" define a very rigid set of both constraining contexts and boundaries for measurable descriptions. In this new context, descriptions which are related to (partial) differential equations, require that material interactions be mediated by discrete Euclidean shapes, which in turn, are related to the differential equations associated to metric-invariant differential-forms of the force-fields, ie the descriptive structure is based on the geometry of circle-spaces (and holes in the shape of space). Force-fields are applied to material shapes by Newton's law of inertia, which is defined in absolute Euclidean space (which also allows for action-at-a-distance), in this context of very rigid, and confining, geometry (but Newton's universal law of gravitation is modified).
Stable spectral shapes, and material's orbital properties, and the properties of (condensed) "free" material components in space, There are "free" material systems, and orbital material systems, where "free" material components can condense into limited orbital structures, or condensed material can be guided by highly confining orbital constructs, because these (condensed material) components do not have the "correct" size to be stable material components, in their (particular containing) dimensional level, as well as particular subspace, so that the resonances... , which allows the existence of material components... , are either from another subspace (of the same dimension), or are determined to be from resonances which are defined on the facial structure of the stable simplex structure of the condensed material, in order to have a stable spectral structure for the condensed system. If a higher-dimensional material component is not "big enough" to be a material component, in its particular subspace (of some particular dimension), but nonetheless this higher-dimensional material component does (can) interact. However, the property of "the faces of the material component," which is interacting on a higher-dimensional context, are contained in a closed metric-space. This causes the dynamics of the interaction (in a higher-dimensional level) to be defined on the entire material-containing metric-space. The entire, rigid, metric-space being pushed by the interaction is not noticeable within the rigid geometry defined within the metric-space, ie a perfectly rigid-rod can transmit a "push" instantaneously across the space it occupies.
An example of a true manifestation of inertial affects defined in general relativity, "Free" material components can also be related to orbital structures, where most often condensed material constrained by the orbital structures of discrete hyperbolic shapes, wherein geodesics can (now) affect inertial properties of these "free" material components, and can be described in an explicit manner in a stable (linear) context, ie general relativity is being defined beyond the 1-body problem with spherical symmetry, so that the description is stable, since the geometry in the new descriptive structure is linear, metric-invariant, and separable, so as to define a stable orbit.
[Note: An orbit defined on a discrete hyperbolic shape is pushed... , to the limited and rigid structure associated with the shape's geodesics... , by the coordinate structure of hyperbolas, which exists away from the geodesic paths (where geodesics will be contained on the faces of the simplex of the discrete hyperbolic shape's fundamental domain)].
The interaction "discrete Euclidean shape," or the interaction torus, Euclidean space-forms (a synonym for a "discrete Euclidean shape") mediate material interactions within the rigid constraints of the "discrete hyperbolic shapes," which model both metric-space existence and material existence. During a material interaction a differential-form is defined upon the geometry of an interaction torus, ie a differential 2-form model of a force-field is defined on the interaction torus. Yet, a "discrete Euclidean shape" of an interaction can also transform, so as to become a toral component of a newly formed discrete hyperbolic shape, where this can happen if both (1) resonances exist for the interaction, and (2) the energy and size of the interaction is within the "correct" energy and size ranges. The geometry of the 2-form is related to the geometry of the fiber SO(n) group in order to determine the direction of the force-field's push [in the base-space containing the interaction torus]. Then the spatial positions of the interacting material's vertices are locally transformed, in a (local) context of opposite metric-space states.
A finite spectral-orbital set, defined upon a many-dimensional containing space, A finite spectral set can be defined on an 11-dimensional hyperbolic metric-space, which is an over-all high-dimension containing space for (of) a model of existence (where the existence is defined by the finite spectral set). This is possible because in each dimensional level (and for each subspace of the same dimension) there is a maximally-sized discrete hyperbolic shape in regard to the finite set of discrete hyperbolic shapes which are used to model the subspace metric-spaces (subspaces of the 11-dimensional space), so that the spectra defined for all the dimensional-levels and subspaces of each of those different dimensional-levels is finite, and thus, it can determine a finite spectral set, upon which all material properties... , which are allowed to exist in this 11-dimensional hyperbolic metric-space... , depend.
Defining angles between toral components, Weyl-transformations of angles between a discrete hyperbolic shape's toral components, (or a set of folds allowed on the base-space lattice structure), so that there are a finite set of angular relationships which can be defined between the toral components of a discrete hyperbolic shape. These folds between toral components allow envelopes of orbital stability to be defined, based on the orbital (or metric-space shape) structure which a discrete hyperbolic shape can have after its toral components are transformed by certain angular values.
The operation of multiplying by a constant factor, Constant multiplicative factors can be defined... , so as to affect the properties of: shapes, sizes, orbits, and the stability of "discrete hyperbolic shapes" :
... , between dimensional levels,
... , between subspaces of the same dimension, and
... , between toral components of a discrete hyperbolic shape.
Physical properties (and math properties) attributed to metric-spaces, There are physical properties associated to metric-spaces. Two examples of physical properties are: (1) position in space of a system's vertex, in regard to the distant stars, (2) the stability of a system's (or a mathematical) pattern.
This results in the definition of "metric-space states" of opposite physical properties, eg (+t) and (-t). These opposite metric-space states are a part of the dynamic processes of material interactions, eg fixed stars, rotating stars (Euclidean); forward time, backward time (hyperbolic space) etc.
In turn, this implies unitary containment, in regard to the containment (of opposite metric-space states), within both real and pure imaginary subsets of finite-dimension Hermitian containing set of coordinates, as well as allowing the definition of the spin-rotation of metric-space states, so that this spin-rotation of metric-space states is defined on opposite metric-spaces states so that these opposite states are a part of the dynamic process. The (time interval of the) period of the spin-rotation of opposite metric-space states is a property used in the dynamic (or inertial) material interaction process.
In this description there is no need of a continuum, instead rigid geometric stability is used rather than using (indefinable) randomness and non-linearity as a basis for (physical, or mathematical) description.
Indefinable randomness and non-linearity seem to possess the properties which are needed to briefly describe patterns which are unstable and fleeting in duration, which, at best, are relatable to feedback constructs, ie it is a description which depends on the validity of the fleeting pattern of a system modeled as a partial differential equation, which has limited descriptive value, and which is used in a relatively unimportant contexts, ie it is a flawed viewpoint which cannot be used describe the observed stable spectral-orbital properties of physical systems at all size scales. (2) (over)
References and Books
San Diego Joint Math Meeting (2013)
A new context in which to apply geometry to: math, quantum physics, and the solar system, etc.
# 1086-VR-413,
Saturday, 1-12-13, 3:30 Rm 6E (main building), Assorted Topics II,
Martin Concoyle PhD.
Order books: scribd.com, (3-7) or Trafford.com (1 and 2) (see below)
Just as Copernicus, Kepler and Galileo provided a quantitative-geometric context for the properties of the solar system, which were then precisely identified by the solutions to (the) solvable differential equations of Newton; Martin Concoyle now provides the stable geometric structures which fit... , both macroscopically and microscopically... , into a
many-dimension containment set (hyperbolic 11-dimensional), so that these shapes are the solutions, ie the geometries of the stable spectral-orbital properties, of all the fundamental stable systems which have stable spectra and orbits: nuclei, molecules, solar-systems, etc, and it is the basis for a quantitative system (the spectral set of a measurable existence) which is finite,
and
These ideas are discussed in the following books: (available at math conference, 2013)
1. A New Copernican Revolution (p286), B Bash & P Coatimundi, Trafford Publishing, 2004.
2. The Authority of Material vs. The Spirit (p483), D D Hunter, Trafford Publishing, 2006.
3. Introduction to the Stability of Math Constructs;
and a Subsequent General, and Accurate, and Practically Useful Description of Stable Material Systems (p262), 2012, Scirbd, Martin Concoyle, and G P Coatimundi.
Scribd.com/doc/117624815/ ($5.00)
4. A Book of Essays I: Material Interactions and Weyl-Transformations; (p234), 2012, Scribd, Martin Concoyle. Scribd.com/doc/117625529/ ($5.00)
5. A Book of Essays II; Science History, and the Shapes which Are Stable, and the Subspaces, and Finite Spectra, of a High-Dimension Containment Space (p240), 2012, Scribd, Martin Concoyle. Scribd.com/doc/117625961/ ($5.00)
6. A Book of Essays III: Elementary Topics; (p303), 2012, Scribd, Martin Concoyle.
Scribd.com/doc/117855379/ ($5.00)
7. Physical description based on the properties of stability, geometry, and quantitative consistency:
Presented to the Joint math meeting San Diego (2013), (p211), 2013, Scribd, M Concoyle
Scribd.com/doc/118989388/ ($8.00)
3-7 are sold at Scribd.com.
SD-2013
(talk) Use geometrization (in particular, that the most stable geometric shapes are the discrete hyperbolic shapes)
to turn physical description into a geometric exercise as opposed to an exercise about indefinable randomness and (the quantitatively inconsistent) non-linearity
Should physical description be about:
1. Unstable patterns and fleeting contexts (hopefully) relatable to feedback systems, eg guidance systems, and
2. To chaotic contexts of systems briefly transitioning between relatively stable states, eg nuclear reactions,
3. That is, descriptions of marginal, unstable contexts related to the fine-tuned interests of big business, such as improving a complicated instrument's capacities (eg guiding a missile), defined within a fixed descriptive context, so as to help big business. Note: Computing is about speeding up a computers rate of switching, but a computer is limited to operating on numbers or on symbols strictly related to a process (which might be a symbolic goal). That is, new contexts can establish new ways in which creativity or new ways in which to achieve a goal (or a process). Furthermore, the increase of switching rate for a computer is approaching the obstacle of the limitation of relevant knowledge, ie traditional knowledge has great limitations, it now is being related to many failings, eg the calculations of business risks has failed because the math is failing.
Is math and science about serving commercial interests, and developing complicated instruments (for business interests) but there are limits to an instrument's performance, and/or (in regard to mathematics) does a fixed context and a (fixed) set of authoritative traditions, which are associated to business interests, also have a limit to its performance (or such a context's capabilities, such as in regard to its descriptive range)?
or
Is the range of a measurable description to be determined by a very large set of equal independent free-inquirers, all of whom are to be regarded as equal creators (not simply creators in regard to narrowly defined business interests, ie why should "big oil" or "big banks" be determining the structure of knowledge and hence the structure of creativity within society)? This allows the society... , ie big business who in turn has controlled big government so that now big government serves the needs of big business... , to identify a small set of pompous intellectual aristocrats (university academics), who are given great authority in society, but who possess a very limited and narrow range of thought, or who have limited intellectual range concerning the possibilities of precise descriptive knowledge, and its possible relation to new creative contexts.) one can only establish oneself as being correct in a fixed context, but fixed contexts are not conducive to the new "development" of precisely described knowledge, nor conducive to the developing new contexts for creativity. (big business is most profitable when the context within which it makes the most money stays fixed). Equality supports development, inequality is defined within a fixed context.
(talk)
What are stable math patterns? [They are simple math patterns]
Nuclei, atoms with more than 5-charged-components, molecules, crystals, the solar system (etc), are all stable physical systems (which implies that they are formed under controlled linear conditions) but none of these (general) systems have valid descriptions (beginning with the laws of physics and then deriving the spectral [or orbital] properties of these systems).
Is one to try to improve the descriptions of these systems by means of more complications?
or
Should one consider new contexts, and new interpretations upon which to base description?
Gödel's incompleteness theorem can be interpreted to mean
"math and science are trying to do the same thing"
{Hilbert wanted to place physics on an axiomatic basis, but when it was shown that math cannot be completely developed by it having an axiomatic basis, and that both disciplines are about developing measurable descriptions of observed patterns, then this leads to this interpretation}
In this context, truth is finding "simple" patterns and processes which are:
1. Widely applicable to general systems (observed properties or observed patterns)
2. Can describe observed patterns accurately and to sufficient precision, can describe definitive, stable patterns, and
3. Strongly relates to practical creativity (measuring, fitting, selecting material or subsystem structure, building, or putting together, and controlling "physical" systems).
Geometry can be both stable and controllable, especially the geometric systems which are contained within a linear, metric-invariant, and separable (or solvable or commutative everywhere) context for their descriptions, (descriptions of physical systems (or shapes))
Geometry is more related to practical use than either randomness or non-linearity (etc).
Note: Random description of systems with only a few components have no practical value (other than perhaps to be used to identify a betting game).
The new idea:
Use the stable circle-spaces, in particular, the discrete hyperbolic shapes, to identify the stable spectral-orbital properties of observed physical systems, or to identify a finite spectral set to be used as a basis for a description's quantitative structure. Note: "Discrete Euclidean shapes" are also needed in regard to describing material interactions.
The new context:
Partition an 11-dimensional hyperbolic metric-space by means of a set of different dimension discrete hyperbolic shapes so that each subspace of each dimensional level is assigned both a discrete hyperbolic shape (of that dimension) and a multiplicative constant (equivalent to physical constants, eg c h etc). One can think of these discrete hyperbolic shapes as being "uniform" shapes, where each face of the shape's fundamental domain has the same geometric measure, ie the same spectral value. Thus the multiplicative constants are the mechanism through which the spectral sizes change between either dimensional levels or between subspaces of the same dimension.
Properties of discrete hyperbolic shapes [Coxeter]
1. The 10-dimensional discrete hyperbolic shapes are the highest dimensional discrete hyperbolic shapes which exist. Thus, the containment set contains all of the discrete hyperbolic shapes.
2. The highest dimension discrete hyperbolic shape, which is bounded, has dimension-five. Thus the 5-dimensional spectra, defined by the 5-dimensional discrete hyperbolic shapes, are the last hyperbolic metric-spaces which are related to spectra with finite values. Note: the 5-dimensional discrete hyperbolic shapes are contained within 6-dimensional discrete hyperbolic shapes, which are unbounded shapes. (Question: Are some of the faces... . of the fundamental domain of an unbounded 6-dimensional discrete hyperbolic shape [actually]... .. bounded 5-dimensional discrete hyperbolic shapes?)
The spectra of an "n-dimensional discrete hyperbolic shape" are determined by the geometric measures of the (n-1)-dimensional faces of the "n-dimensional discrete hyperbolic shape's" fundamental domain.
For example, the spectra for "3-dimensional discrete hyperbolic shapes" would be the 2-dimensional spectral set, but the existence "3-dimensional discrete hyperbolic shapes" in a "4-dimensional hyperbolic metric-space" are determined by the 3-dimensional spectra of the 3-faces of the set of "4-dimensional discrete hyperbolic shapes." Thus, in order to fit into the "4-dimensional hyperbolic metric-space" a "3-dimensional discrete hyperbolic shape" must be in resonance with a set of 3-faces which are smaller than the metric-space within which it is contained, ie it must be in resonance with the spectra defined within a different 4-dimensional subspace (which is itself also modeled as a "4-dimensional discrete hyperbolic shape," but of a "smaller size" than the "4-dimensional discrete hyperbolic shape" within which the (given) "3-dimensional discrete hyperbolic shape" is contained).
The 1-dimensional spectra are "additive" since each higher-dimensional discrete hyperbolic shape also contains a subset of 1-faces, which would also be a part of the set of 1-dimensional spectra. Thus, the set of 1-dimensional spectra is greater than the combinations, 11C1=11, and in the dimensional level and subspace partition by discrete hyperbolic shapes, wherein, if one assumes a uniform shape for each element of the partition, then one ends-up with about 1000 different-sized 1-dimensional spectra for the entire containing space.
That is, it is simplest to model this idea in relation to requiring that each discrete hyperbolic shape be a uniform shape, ie each face has the same spectral value, and then the different sizes are determined by the multiplicative constants defined between both "the different subspaces of the same dimension" and "the different dimensional levels." This simple idea of course can be adjusted.
Results:
The new context identifies a finite spectral set.
There are (can be) other "components=material" of various sizes (but contained in some one of the hyperbolic metric-space) but which must resonate with some value (with the correct dimension) of the given finite spectral-set defined by the new (descriptive or containment) context
[ranging over all the various subspaces of the given dimension of the given spectral component, which is to be in resonance with the identified finite spectral set {of the 11-dimensional hyperbolic metric-space}]
Physical description of stable systems is about the set of discrete hyperbolic shapes identified by this finite spectral set in the 11-dimensional hyperbolic metric-space.
Now it is better to model functions... , used to describe stable physical systems and which define a function space... ., to be discrete hyperbolic shapes. By doing this the idea of "global commutative math structures" defined on such a function space will be more directly related to the properties of physical systems.
Sorting-out our containing 3-space
The spectral values of charges, nuclei, atoms, molecules are "small sized" and some of these shapes are, apparently, close to the "same size," and are either of dimension-2 or dimension-3, while our 3-dimensional containing (spatial) metric-space, ie our 3-dimensional discrete hyperbolic shape, is the size of the solar system, but nonetheless many "small" either 3-dimensional components or 3-dimensionally contained components resonate with the spectra of different 3-subspaces, and/or different 2-subspaces.
In such a large shape, an observer's local probing of the metric-space's shape would not detect such a large hole structure. Furthermore, the observer would "see" that which is "far away," in relation to the lattice of the fundamental domain upon which the "metric-space's shape" is identified, where the lattice is defined on an unbounded hyperbolic metric-space.
It is the hole-structure of the very stable discrete hyperbolic shapes which allows very stable spectral and stable orbital properties to be defined, and it is the stable properties of the solar system, where the orbits are filled with condensed material which takes on a spherical shape because the new structure for interaction has spherical symmetry for (free) condensed material in Euclidean 3-space, and the existence of the stable spectral-orbital properties provides evidence to show that this descriptive structure is the correct model for the containment space of stable "material" systems. These shapes solve both the stability question for the solar system, if the authorities have a better solution please present it to the world, and with the "discrete angular transformations" related to the Weyl-transformations, so that a discrete hyperbolic shape can take-on the shape of concentric orbits, thus it is a descriptive structure which also "solves" the quantum-radial equation, where charged components fit into the exact shapes of the spectral flows of the discrete hyperbolic shapes of the nuclear and atomic system's.
The real point is; that the current descriptive context fails to describe the stable properties of these many fundamental systems, and because it has failed to provide these descriptions, the new model carries more authority than does the currently accepted fixed structure for math and science.
That is, this method of both choosing and organizing a containment set is providing a measurable description for the stable spectra and orbital properties of the observed stable physical systems for the fundamental systems of existence for the physical systems of the sizes ranging from atoms to the solar system. That is, this new descriptive language is already a descriptive structure which is verified by the observed properties of stability for these systems. This is stronger evidence for the verification of this new model than that verifying evidence actually exists for the current authoritative dogmas of physics, as well as math.
The new context also allows for second order parabolic equations related to angular momentum, but the new context has more geometry within circle spaces, in regard to the set of possible angular momentum properties of the new descriptions of physical systems, where this angular momentum can link between different dimensional levels.
Note: If infinite-extent discrete hyperbolic shapes (6-dimensional and higher dimensions) have bounded faces in their fundamental domains, then the size of these bounded faces is determined by the sizes of equivalent lower-dimension discrete hyperbolic shapes which are a part of the partition. The existence of bounded faces on a 2-dimensional infinite-extent discrete hyperbolic shape would be a way of modeling electrons and neutrinos which compose an electron-cloud in an atom or a molecule.
Take Notice!
This solves the most fundamental problem in physical description, the stability of the most fundamental physical systems. This problems has been ignored since it was believed that it was too difficult that these fundamental systems are too complicated to describe, but now it is solved and its solution results in a quantitative construct based (generated) from a finite set (or stable spectral values).
In the new context the descriptive structure is "bounded" by the very stable discrete hyperbolic shapes which model both the "material component" containing hyperbolic metric-space as well as the "material components" whose dimension is one-less that the dimension of their containing metric-space. This means that the very simple but stable geometry has a dominating influence on physical descriptions (not differential equations). However, material interactions are defined between the material components... , though discrete [newly determined in a discrete manner every about 10^-18 sec]... , and these interactions are mediated in a continuous manner, in regard to space, by the discrete Euclidean shapes [or Euclidean tori] (which allow spatial continuity for the dynamic processes) so that the interactions between components are generally non-linear and they are defined in a metric-space so in 3-space there are the usual 2nd order elliptic, parabolic, and hyperbolic partial differential equations which are part of the continuous descriptions of locally measurable properties, though now there is a new geometric context for angular momentum.
Note: The solutions to the linear, metric-invariant, and separable partial differential equations related to the discrete hyperbolic shapes has been discussed by L Eisenhart in a chapter in his "about 1930's" book Riemannian Geometry.
However, for interactions between micro-components contained within, say, a thermal reservoir, it should be first noted that these micro-components are always colliding and thus the components are constantly changing from neutrally charged to being ionized, so the interactions identify a Brownian motion for each component. E Nelson (Princeton, 1967) has shown this Brownian motion for micro-components is equivalent to quantum randomness. Furthermore, the vertices of the fundamental-domain of the discrete hyperbolic shapes identify a distinguished point for each shape, about which micro-material interactions are centered. Thus, this accounts for the random motions about an apparent point-like structure for micro-material.
Outline of ideas
Describe the properties of the stable spectral-orbital systems, How does one describe the very stable, many-body, spectral-orbital physical systems which exist at all size scales from nuclei to solar systems, as well as life and mind?
The subject of stability is mostly about using very confining, but very simple set of geometric shapes, and some simple calculus, as well as a few other (local) geometric properties defined in a context of a principle fiber bundle with a many-dimensional base-space, where the base-space is (dimensionally) partitioned into sub-metric-spaces which are identified by discrete shapes, which are open-closed (when observed within the metric-space which possesses the discrete shape), but these metric-spaces (with shapes) form a boundary when viewed from an adjacent higher-dimensional metric-space which contains the discrete shape.
The math properties for stable solvable physical systems, The simple math properties which allow partial differential equations (or differential equations)... , which are used to model physical systems (either geometric-inertial or spectral)... , to be solved can be listed.
That is, solvability is related to the set of properties: linear, metric-invariant, separable (locally linear and commutative (diagonal matrices at each point in the global coordinate system)), where the metric-functions can only have constant coefficients, (for the various R(s,t)-metric-spaces {where s-space, and t-time; dimensions}, and associated metric-function signatures, where these different metric-spaces are, in turn, related to new types of materials).
[These new material-types are characterized by their properties of being odd-dimensional spatial subspaces, with an odd genus-number, (analogous to discrete hyperbolic shapes) so as to be charge-unbalanced, and thus, naturally oscillating and energy-generating material systems, which model life. Life is defined as new material-types, which are contained in either: R(4,0), R(6,0), R(8,0), or R(10,0) Euclidean spaces.]
The properties of stability are properties which are possessed by the circle-spaces. One can note that, circle-spaces can be modeled as metric-spaces of non-positive constant curvature, whose discrete shapes (or discrete isometry subgroups) are determined from lattices (with an associated fundamental domain, which is related to right-rectangular (or "cubical") simplexes, by a moding-out process (or a process of defining an equivalence topology on the cubical shapes of the fundamental domains).
[Note: The quasi-spectral-geometric properties used to describe particle-physics, ie the non-linear-random-geometric model of particle-physics... ., which deals primarily with probabilities of particle-collisions {which, in turn, only model (nuclear) reactions}, and which is a completely irrelevant and practically useless descriptive construct... ., are excluded from consideration, since these descriptive constructs only provide... , in a chaotic or random fashion... , brief and fleeting descriptions of unstable patterns. It is a model which is only applied by means of its relation to reaction-rates.]
Holes-in-space, spectra, force, and the circle-spaces, are all defined within a many-dimensional space
The simple math structures of circle-spaces, as the basis for the stable (geometric) properties of existence, causes both spectral properties and force-fields, to have an analogous (or parallel) math structure... ,
[in relation to holes in space caused by either the shape of a metric-space or by rigid material shapes, eg (usually) 1-dimensional currents defined by rigid material defining a closed curve]
... , than is usually believed to be true (ie the material-shapes are equivalent to spatial [or metric-space] shapes).
The very stable "discrete hyperbolic shapes" are used as models for both material components and metric-spaces,
so as to construct a very rigid geometric structure, in a many-dimensional context, so that Newton's laws still define inertial dynamics. Discrete hyperbolic shapes are stable, with stable spectral properties, and they provide a constrained and stable and very rigid set of boundary conditions for both material containment (confinement) and material interactions, so that differential equations, at first, appear to have a very restrictive containment structure, but this is needed to model stable systems, and it can also be used to model living systems in new ways.
Most material components, as well as metric-spaces, which are contained in this new many-dimensional context, have the shapes of circles-spaces, in particular the "discrete hyperbolic shapes" define a very rigid set of both constraining contexts and boundaries for measurable descriptions. In this new context, descriptions which are related to (partial) differential equations, require that material interactions be mediated by discrete Euclidean shapes, which in turn, are related to the differential equations associated to metric-invariant differential-forms of the force-fields, ie the descriptive structure is based on the geometry of circle-spaces (and holes in the shape of space). Force-fields are applied to material shapes by Newton's law of inertia, which is defined in absolute Euclidean space (which also allows for action-at-a-distance), in this context of very rigid, and confining, geometry (but Newton's universal law of gravitation is modified).
Stable spectral shapes, and material's orbital properties, and the properties of (condensed) "free" material components in space, There are "free" material systems, and orbital material systems, where "free" material components can condense into limited orbital structures, or condensed material can be guided by highly confining orbital constructs, because these (condensed material) components do not have the "correct" size to be stable material components, in their (particular containing) dimensional level, as well as particular subspace, so that the resonances... , which allows the existence of material components... , are either from another subspace (of the same dimension), or are determined to be from resonances which are defined on the facial structure of the stable simplex structure of the condensed material, in order to have a stable spectral structure for the condensed system. If a higher-dimensional material component is not "big enough" to be a material component, in its particular subspace (of some particular dimension), but nonetheless this higher-dimensional material component does (can) interact. However, the property of "the faces of the material component," which is interacting on a higher-dimensional context, are contained in a closed metric-space. This causes the dynamics of the interaction (in a higher-dimensional level) to be defined on the entire material-containing metric-space. The entire, rigid, metric-space being pushed by the interaction is not noticeable within the rigid geometry defined within the metric-space, ie a perfectly rigid-rod can transmit a "push" instantaneously across the space it occupies.
An example of a true manifestation of inertial affects defined in general relativity, "Free" material components can also be related to orbital structures, where most often condensed material constrained by the orbital structures of discrete hyperbolic shapes, wherein geodesics can (now) affect inertial properties of these "free" material components, and can be described in an explicit manner in a stable (linear) context, ie general relativity is being defined beyond the 1-body problem with spherical symmetry, so that the description is stable, since the geometry in the new descriptive structure is linear, metric-invariant, and separable, so as to define a stable orbit.
[Note: An orbit defined on a discrete hyperbolic shape is pushed... , to the limited and rigid structure associated with the shape's geodesics... , by the coordinate structure of hyperbolas, which exists away from the geodesic paths (where geodesics will be contained on the faces of the simplex of the discrete hyperbolic shape's fundamental domain)].
The interaction "discrete Euclidean shape," or the interaction torus, Euclidean space-forms (a synonym for a "discrete Euclidean shape") mediate material interactions within the rigid constraints of the "discrete hyperbolic shapes," which model both metric-space existence and material existence. During a material interaction a differential-form is defined upon the geometry of an interaction torus, ie a differential 2-form model of a force-field is defined on the interaction torus. Yet, a "discrete Euclidean shape" of an interaction can also transform, so as to become a toral component of a newly formed discrete hyperbolic shape, where this can happen if both (1) resonances exist for the interaction, and (2) the energy and size of the interaction is within the "correct" energy and size ranges. The geometry of the 2-form is related to the geometry of the fiber SO(n) group in order to determine the direction of the force-field's push [in the base-space containing the interaction torus]. Then the spatial positions of the interacting material's vertices are locally transformed, in a (local) context of opposite metric-space states.
A finite spectral-orbital set, defined upon a many-dimensional containing space, A finite spectral set can be defined on an 11-dimensional hyperbolic metric-space, which is an over-all high-dimension containing space for (of) a model of existence (where the existence is defined by the finite spectral set). This is possible because in each dimensional level (and for each subspace of the same dimension) there is a maximally-sized discrete hyperbolic shape in regard to the finite set of discrete hyperbolic shapes which are used to model the subspace metric-spaces (subspaces of the 11-dimensional space), so that the spectra defined for all the dimensional-levels and subspaces of each of those different dimensional-levels is finite, and thus, it can determine a finite spectral set, upon which all material properties... , which are allowed to exist in this 11-dimensional hyperbolic metric-space... , depend.
Defining angles between toral components, Weyl-transformations of angles between a discrete hyperbolic shape's toral components, (or a set of folds allowed on the base-space lattice structure), so that there are a finite set of angular relationships which can be defined between the toral components of a discrete hyperbolic shape. These folds between toral components allow envelopes of orbital stability to be defined, based on the orbital (or metric-space shape) structure which a discrete hyperbolic shape can have after its toral components are transformed by certain angular values.
The operation of multiplying by a constant factor, Constant multiplicative factors can be defined... , so as to affect the properties of: shapes, sizes, orbits, and the stability of "discrete hyperbolic shapes" :
... , between dimensional levels,
... , between subspaces of the same dimension, and
... , between toral components of a discrete hyperbolic shape.
Physical properties (and math properties) attributed to metric-spaces, There are physical properties associated to metric-spaces. Two examples of physical properties are: (1) position in space of a system's vertex, in regard to the distant stars, (2) the stability of a system's (or a mathematical) pattern.
This results in the definition of "metric-space states" of opposite physical properties, eg (+t) and (-t). These opposite metric-space states are a part of the dynamic processes of material interactions, eg fixed stars, rotating stars (Euclidean); forward time, backward time (hyperbolic space) etc.
In turn, this implies unitary containment, in regard to the containment (of opposite metric-space states), within both real and pure imaginary subsets of finite-dimension Hermitian containing set of coordinates, as well as allowing the definition of the spin-rotation of metric-space states, so that this spin-rotation of metric-space states is defined on opposite metric-spaces states so that these opposite states are a part of the dynamic process. The (time interval of the) period of the spin-rotation of opposite metric-space states is a property used in the dynamic (or inertial) material interaction process.
In this description there is no need of a continuum, instead rigid geometric stability is used rather than using (indefinable) randomness and non-linearity as a basis for (physical, or mathematical) description.
Indefinable randomness and non-linearity seem to possess the properties which are needed to briefly describe patterns which are unstable and fleeting in duration, which, at best, are relatable to feedback constructs, ie it is a description which depends on the validity of the fleeting pattern of a system modeled as a partial differential equation, which has limited descriptive value, and which is used in a relatively unimportant contexts, ie it is a flawed viewpoint which cannot be used describe the observed stable spectral-orbital properties of physical systems at all size scales. (2) (over)
References and Books
Book list
San Diego Joint Math Meeting (2013)
A new context in which to apply geometry to: math, quantum physics, and the solar system, etc.
# 1086-VR-413,
Saturday, 1-12-13, 3:30 Rm 6E (main building), Assorted Topics II,
Martin Concoyle PhD.
Order books: scribd.com, (3-7) or Trafford.com (1 and 2) (see below)
Just as Copernicus, Kepler and Galileo provided a quantitative-geometric context for the properties of the solar system, which were then precisely identified by the solutions to (the) solvable differential equations of Newton; Martin Concoyle now provides the stable geometric structures which fit... , both macroscopically and microscopically... , into a
many-dimension containment set (hyperbolic 11-dimensional), so that these shapes are the solutions, ie the geometries of the stable spectral-orbital properties, of all the fundamental stable systems which have stable spectra and orbits: nuclei, molecules, solar-systems, etc, and it is the basis for a quantitative system (the spectral set of a measurable existence) which is finite,
and
These ideas are discussed in the following books: (available at math conference, 2013)
1. A New Copernican Revolution (p286), B Bash & P Coatimundi, Trafford, 2004.
2. The Authority of Material vs. The Spirit (p483), D D Hunter, Trafford, 2006.
3. Introduction to the Stability of Math Constructs;
and a Subsequent General, and Accurate, and Practically Useful Description of Stable Material Systems (p262), 2012, Scirbd, Martin Concoyle, and G P Coatimundi.
Scribd.com/doc/117624815/ ($5.00)
4. A Book of Essays I: Material Interactions and Weyl-Transformations; (p234), 2012, Scribd, Martin Concoyle. Scribd.com/doc/117625529/ ($5.00)
5. A Book of Essays II; Science History, and the Shapes which Are Stable, and the Subspaces, and Finite Spectra, of a High-Dimension Containment Space (p240), 2012, Scribd, Martin Concoyle. Scribd.com/doc/117625961/ ($5.00)
6. A Book of Essays III: Elementary Topics; (p303), 2012, Scribd, Martin Concoyle.
Scribd.com/doc/117855379/ ($5.00)
7. Physical description based on the properties of stability, geometry, and quantitative consistency:
Presented to the Joint math meeting San Diego (2013), (p211), 2013, Scribd, M Concoyle
Scribd.com/doc/118989388/ ($8.00)
3-7 are sold at Scribd.com.
Concerning the media and professional math and scientists:
Succinctly-put the media makes bigger-suckers out of the "successful" professional intellects, than it makes suckers out-of the public, since it traps the professional intellectuals into a fixed context upon which the social value of these professionals depends, and it is a dogmatic context within which all valid authoritative ideas are "to be" expressed, eg peer review.
However, Gödel's incompleteness theorem implies that the professionals should also seek to consider new contexts within which to express math and physics ideas, ie professional publication should not be peer reviewed but rather the assumptions upon which ideas are expressed should be made clear and then the expression of ideas should be placed into categories
Where one category needs to be marked the context which most supports (big monopolistic) businesses.
These new ideas are expressed in a new context, in a similar way as Copernicus expressed a new context which was different from the authoritative context of Ptolemy.
It is the professionals who need to enter the new context so as to discuss the new ideas, new ideas which solve the very difficult problem of the stability of fundamental physical systems and the solution in the new context is very simple (the hallmark of a superior context (or a new paradigm)) the new ideas do not need to accept their context, even though it is their context which allows them to play the roles of wage-slave professionals who serve monopolistic business interests, the new way of expressing ideas only needs to provide an interpretation of the observed data.
Addenda:
It is strange that when confronted with such a simple solution the current authorities find the pattern interesting, but do not comprehend the significance of the true authority (its truth and great capacity for wide ranging usefulness) of this new context.
They are so caught-up in their own dogmatic authority, that they do not realize that they have been dethroned, and that their authority has already been lost. This is because they are so self-important, but it is the social structure which has created their sense of being so superior, and so fixed and traditional in their sense of possessing authority.
The overly authoritative fixed structures of containment and interpretation are used to define the "aristocracy of intellect," those chosen few, who are so keen to be intellectual aristocrats, but who, in fact, so weakly... ., (in relation to mental awareness about the society and about either what knowledge is, or what knowledge does (is supposed to do) within society, and how big business corrals and uses knowledge for its selfish interests)... . serve the interests of big business, with their business monopolies, which allow them to be such very domineering social forces, where these dominant monopolies are allowed to exist in a society, because the laws of our society are set-up and enforced, so that it is a society which values property more than both life and creativity.
Pompous, self-important math and physics professionals "believe the hype" and they believe that they are the "culturally superior people" of the society, but who are, in reality, people with personality flaws; they are manipulative, narrowly obsessive, authoritarian, and selfish people who are themselves easily manipulated by social forces (eg mainly by-means-of the media) which is why they were chosen to have these social positions, where these superior people dutifully are servile to their own image of being uppity where they promote within society the social traits of domination and fixed-ness of knowledge and its uses, due to their servile social positions, which are, in fact, anti-knowledge and anti-creativity social positions, so as to assure the rich owners of society that the façade of knowledge is all about complicating descriptions to filter the public out of social positions which would allow them greater capacity to create, and thus causing a competitive structure for products within the so called free-market.
These professional authorities are presented to the public by the media as those people who have attained the highest cultural achievements within society, but they do this by serving the few owners of society. Because they depend on their pay-master, this makes them lesser people rather than greater people. They retreat behind the big bully (the owners of society, and these bullies allies in both the government and in the justice system) who create the social images of these, so called, experts, and this is done so as to serve the interests of the owners of society.
SD-2013 II
The problem is the propaganda system, which is the society's sole authoritative, reliably-truthful vehicle of social expression (but which only promotes monopolistic interests) where it continuously spews-out mis-information which, when placed in the "context" of honest reporting, the public always interprets to be an absolute truth.
Thus when monopolistic, unregulated, but almost completely controlled "market-place" fails in a complete collapse, due to criminal fraud aided by the justice system and the congress the propaganda system continues to "sing the praises" of (and need for) the "magical" unregulated "market-place", where it should be clear that "unregulated", now especially, means license to steal along with a complicit justice system and political system, since these institutions have been manipulated by the propaganda system so as to simply to have become a part of the propaganda system, themselves.
The authorities (or technical experts) which serve this system by adjusting the complicated instruments for the monopolistic ruling interests (the interests of the owners of society) are also controlled by the absolute-truth espoused (in the context of "honest" reporting) by the media related to "technical-development" (but really only small adjustments to fixed traditional technologies, since the context of math and science is not allowed to seek new creative contexts within the context of stable math patterns, ie the monopolies depend on society continuing to use products and resources in a fixed way which allows the monopolies to continue to make money based on their products), where for the intellectual class, the academics, the authoritative experts, are provided with a set of "prized" problems whose context is:
Indefinable randomness
Non-linearity
Non-commutativeness, or
At best locally commutative in a context of a general metric but non-linear in regard to the containing coordinates of geodesic coordinates or set of functions
So that the propaganda system, validated by certain narrowly interested experts insists in "big bangs" particle-physics, string-theory geometry which are needed to understand the singular points of a black hole's gravitational field, and it is claimed by some possibly charges related to black holes and in regard to singularities within nuclei, so as to realize a "grand-dream" (truly a pipe-dream) of the control of worm-holes in space, or control over a "many-world" context of existence, though the math structures through which these ideas are to be described, based on probability and non-linearity, does not allow any control,...
since there are not any stable patterns in their descriptive context
Nonetheless these math structures do apply to the business interests:
Is math staying too traditional, fixed, formal, complicated, irrelevant?
Is math only about serving business interests in regard to:
1. Unstable patterns to be used in fleeting contexts (feedback systems),
2. Chaotic transitory systems, eg nuclear reactions, transiting between two stable states,
3. Manufacturing complications, eg formulating security codes, etc,
4. Pulling the wool over the eyes of the public, so as to provide irrelevant and inadequate descriptive structures for physical systems?
... , of such constructs even if they are mathematically modeled (as it is so claimed that quantum systems are correctly mathematically modeled) due to the properties of the math constructs and due to the over-whelming complexity of such models these models (of controlling a "worm-hole") cannot possibly be controlled, as the propaganda system is suggesting that they can be controlled. Consider, if the current descriptive context cannot describe the stable, definitive fundamental systems, systems so stable that it implies that these systems form in a linear controlled context, then how can their exotic models of physical systems (changing between worlds, in a many-world model) ever be realized, if they are models which are not consistent with the actual structure of the (external) world? or of these ideas
That is, these prized problems are delusional-ly based, yet the propaganda system promotes them as do the experts themselves so they become the basis for identifying an elite in-crowd of "knowledgeable" experts.
This, in-crowd, of so called superior intellectual elites, obsessed with complicated math patterns (one must note the autistic connection, the manipulation of personality types by institutional managers, used for the purpose of deceiving the public) who are led to believe, by the media itself, that they are zeroing-in on the wonderful goal of their great intellectual prowess and intellectual creativity.
Yet it is clearly a failed intellectual exercise since there are basic stable definitive physical systems which exist at all size scales but which go without valid description (based on physical law).
Nonetheless (however) when these stable systems are actually solved the intellectual community and society has a great mental inertia (almost entirely caused by the propaganda system, it unwillingness to publish the new solutions, since they define a completely new math and physics context) to realize just what they have heard, but nonetheless assured that it is they the intellectual elites who will be the ones to forge new roads into new technical landscapes and thus the elites will not (will refuse to) listen to the new ideas which must originate from an inferior mentality and thus must be wrong and surely wrong within the dogmatic authority which defines their truth for them. The elites only find these new ideas somewhat interesting but from an intellect inferior to their own since they have memorized their contexts and their always correct interpretations and their always intelligent evaluations of the state of knowledge, they are not tricked by prized problems, no not them.
That is, the propaganda system is a communication system (vehicle) which expresses a dogmatic authority (an absolute truth) which is followed by the experts which in fact determines the faith of the high-valued institutions which serve the ruling class and the experts have an absolute faith in the authoritative truth of that dogma. The propaganda system defines the true religion of society and it is a religion of personality-cult (not unlike Roman emperors or Egyptian pharaohs) and a deep belief in inequality and a manufactured property of a society dominated by selfish monopolistic interests, ie it is a society opposed to life and opposed to adapting to change
Wake-up you popes of the religion of science and math, eg general relativity, particle-physics, string-theory, indefinable randomness, non-linearity non-commutativity or only locally commutative.
Gödel's incompleteness theorem has a simple interpretation:
Because precise language has sever limitations the axiomatic basis, the containment set, the organization of this containment set, the context of the description, and the interpretations of the observed properties (of the observed measurements must be fully considered and when an alternative, well defined example of new ways in which to present axioms and contexts is provided, especially if it solves the most difficult problems in math and physics then the math physics community of experts should listen and take it seriously.
Please pay-attention (ironically) it is, me, your superior, talking to you, and it truly is, the irony is, that, in fact, we are all equal, but you have tried to achieve in the eyes of the paymaster and you have lost your way and you have made yourselves lesser (not superior), so now by artificial measures I am smart and you old experts are now stupid and disposable which is the context which your over-reaching superiority has caused the public to be, ie the public is disposable since we have you the great experts
The crux of the problem with knowledge and education in society is its capture by corporate and private interests capture by the owners of society even though it is most often "public" education institutions, nonetheless the professors are trying to adjust the complicated instruments for the corporate and private interests and they are not concerned with descriptive knowledge in its most general and most powerful sense where new creative context get developed by new contexts for descriptive knowledge which result when assumptions, contexts, containment, organization of pattern use are considered at their most elementary levels, as Faraday developed the language of electromagnetic description while he also developed a new context in relation to the instruments related to electromagnetic properties. Though such a dramatic chain of developing events is not a necessary attribute for developing a new descriptive context at its most elementary level it means that new languages can be related to new creative contexts.
Since the professors of public universities have been captured by corporate and private interests through the mechanism of funding research and identifying prize problems in math so as to keep math traditional and under the control of peer review the talks at conferences, such as at the joint math meeting in San Diego 2013, are
either
about developing even more complicated theories and more complicated formal professional math language where these formal math languages have very limited if any relation to practical development they may only be marginally related to corporate interests, essentially related to bomb technology,
or
About applying technical complicated math so as to be able to adjust rather complicated instruments of interests to corporate and private interests, eg feedback systems, imaging systems, recognition systems and improperly defined statistical constructs which often appear to be valid, since the propaganda system is capable of making all of society to continue to use language and product in very certain narrowly defined ways so as to place an artificial stability on the statistics where such stability of the statistical context does not really exist.
Propaganda, in regard to science and math is provided in the context of great breakthroughs and, supposedly, new things but which has little bearing on the uselessness of the descriptive language except in regard to weapons technology
Science and math are often about making adjustments to systems which will reduce labor if things remain in their fixed social context in regard to the corporation's products
That is developing new knowledge in regard to new contexts and new ways in which to organize descriptive language, in regard to solving fundamental mysteries, is effectively stopped by peer review prize problems traditional authority and mostly by the process of funding which is controlled by the corporations and private businesses.
Nonetheless, there are many unsolved fundamental problems in physics which are ignored due to dogmatic authority of math and funding traditions within public educational institutions an authority which is essentially related to military development and banking investment interests
The sad thing is that now (2013) these fundamental problems have been solved but the structure of both propaganda and the "knowledge institutions" keeps-out ideas which are different from the inter-related interests of business and traditional academic authority.
Academic science was invented by the mercantile class in the 1600's (after Newton) to support their investment and productively-creative interests, in the 1500's science development based on measuring was centered around schools and about literate people, so that investment in science was centered around the schools (or universities).
However, public schools should take notice of Godel's incompleteness theorem and the logical positivists who proclaimed to limitations of precise language (or the limitations of measurable descriptions) and to consider the example of Faraday wherein he both invented a new math language to describe electric and magnetic properties but he also created the instrumental context through which these properties could be used and controlled
That is, descriptive knowledge best leads to new contexts for creativity at the elementary level of language assumption context interpretation etc not at the complicated formal level, eg no one can use the principles of particle-physics to describe the stable spectral properties of general nuclei.
That is, one wants new contexts for creativity to come from precise descriptive languages one does not simply want adjustments to complicated instruments since instruments also have limitations as to their capabilities or if there is not a better instrument to do the same thing, though digital electronic seems to be able to deal with arithmetic and math patterns well but this has led to an attempt to deal with non-linear systems but non-linear systems can only be related to feedback systems and only for limited ranges of time or distance in regard to arithmetically determined solutions.
There are many mysteries in regard to fundamental physical systems: why do there exist stable physical systems with definitive measurable properties, eg nuclei, general atoms, molecules and their shapes, crystals, life stable solar systems, there are many galaxies with planar spiral structures, etc.
These fundamental physical systems go without valid descriptions based on what is considered to be "physical law" instead one hears about all the hyped-up ideas through the propaganda system and the professional mathematicians and physicists about "big bangs," Black holes, worm-holes, Higg's particles, transforming neutrinos, all related to general relativity, particle-physics grand unification and string-theory etc, are all expressions which are wild speculations if they cannot describe the stable properties of fundamental systems whose stability implies that they come into being in a controlled context, while believing the wild speculations is mostly driven by (or caused by) the propaganda system and a traditional context of math and physics authority and a personality cult which forms around these academics who mostly interfere with the development of new contexts for knowledge and creativity but the monopolistic business interests do not want new contexts for creativity. Where it might be noted that general relativity was shown to be untrue in regard to the non-local properties of material interactions in Euclidean space since non-localness was demonstrated by A Aspect's experiments.
The correct answer as to why there are stable fundamental systems require s that the context of containment be changed in a drastic manner from 3-space and time (quantum, Newton) or space-time (electromagnetism, particle-physics (?)) and materialism where the measurable descriptions are either
Classical often leading to non-linearity
or
Quantum indefinable randomness, spectra supposedly derived from 1/r potentials, function spaces usually non-commutative and Lie groups all used in the context of a continuum and a loose idea about convergence to this continuum, eg renormalization (something Dirac rejected) but apparently personality cult and propaganda was able to establish as an authoritative technique.
Instead consider a new context:
An 11-dimensional hyperbolic metric-space is partitioned... into its different dimensional levels and the different subspaces of the same dimensions... by discrete hyperbolic shapes which exist up to hyperbolic dimension-10. This can be used to define a finite spectra on the over-all 11-dimensional hyperbolic metric-space.
The set of all resonating discrete hyperbolic shapes which are contained within this high-dimension containing space form the bounding stable structures of the more usual physical description of material defined as one-lower dimensional shapes in each dimensional level, where the usual metric-invariant, second-order elliptic, parabolic, hyperbolic, differential equations... associated to material interactions or material properties... are defined, but the stable elliptic structures are defined on the discrete hyperbolic shapes. The elliptic case is mostly about describing condensed material contained within a (higher-dimension) discrete hyperbolic shape, or the orbital path of a material component is (becomes) resonant with the discrete hyperbolic shape upon which the component is contained (or can become "so contained," due to resonance).
The stable physical systems are the discrete hyperbolic shapes of the various dimensional levels which are in resonance with the finite spectra of the over-all 11-dimensional hyperbolic metric-space which has been so partitioned.
Each n-dimensional level "sees" the bounding geometry of the (n-1)-dimensional material "surfaces" but the open-closed topology of these shapes allows light to be observed from outside the metric-space shape's fundamental domain out to the unbounded lattice, this is especially true for metric-spaces whose fundamental domains are large eg as large as the solar system, where it should be noted that lower-dimensional shapes than (n-1)-dimension tend to condense onto the (n-1)-material's shape.
That is, the shapes imply the discontinuity of a metric-space experience between dimensional levels.
Interactions between micro-components imply Brownian motions which implies (due to E Nelson 1967) quantum randomness. Furthermore the distinguished points on discrete hyperbolic shapes implies that the interactions appear point-like, but, nonetheless, mediated by discrete shapes.
It might also be noted that this descriptive context provides a definitive spectral relation between different 11-dimensional containment sets, ie there are many different worlds where each world is well defined by a definitive spectral set, and the best instrument to realize transitions between these world might very well be a (human) life-form.
Speech 2
The observed stable, precise, patterns of physical systems are associated to finite properties, eg bounded-ness and/or the finite number of a physical system's components, eg atomic-number, and these stable physical system properties are fundamental and observed features of a reliably measurable context associated to the observers of physical patterns. This implies both the existence of stable patterns which allow reliable measuring, (or which are associated to the context of measuring (for an observer)), and the existence of stable-controllable patterns associated to a set of fundamental physical systems which possess stable features of "what may, or may-not be" "material" systems, eg nuclei, general-atoms, molecules and their shapes, crystals, solar systems, dark-matter (ie orbital properties of solar-system's in galaxies) etc, the physical patterns upon which the relatively stable aspects of our life experiences depend, and upon which our mental constructs also depend.
Thus, science and math are about identifying stable, quantitatively-consistent, math patterns which are generally applicable to these stable, measurable, and apparently controllable, physical properties so as to result in descriptions of these patterns which are accurate (to sufficient precision), and general so as to be able to describe the observed stable physical patterns of existence, so as to provide a context for practical usefulness, ie measurable and controllable, so that one can: measure, fit together (or couple), and interact with these various patterns (using the natural structures of these patterns, eg life-forms and its coordinated chemical properties (but, apparently, coordinated by an unknown structure), ie not feedback mechanisms nor carefully prepared structures so as to cause reactions), so that this descriptive knowledge can be related to "practical" creativity (as opposed to literary creativity, essentially associated to a world of illusion, ie a world without stable features).
What are (math) patterns?
Patterns are:
1. consistent relationships, or
2. operators acting on quantitative sets so as to have fixed "consistent properties" related to the application of an operator on a quantitative set, and these consistent patterns are related to the "meaning" of the quantitative-set's elements (where quantities represent properties of: type and [measurable] size), or
3. stable shapes, etc.
Can the current descriptive language of mathematics and physics describe stable patterns? [Apparently not.]
There are essentially the three ways in which to try to describe stable math-physical patterns... ,
I. stable geometry, which strongly limits both a descriptive context and the patterns it is trying to describe (the new context for physical description, the circle-spaces, or the very stable discrete hyperbolic shapes),
II. differential equations in a geometric context (unfortunately, this method most often leads to non-linear patterns),
III. differential equations in an operator context (this methods seems to only work for harmonic properties which possess actual physical attributes) )
... , so as to try to use quantitative descriptions so as to try to identify stable patterns which provide valid information, as well as control, over relatively stable (physical) system properties.
A new interaction-construct can be constructed which is general, but its stable properties are determined from a context defined by a many-dimensional set of discrete metric-space shapes, which, in turn, define existence.
The professional mathematicians and scientists in regard to descriptions of fundamental stable physical systems express symbolic nonsense, ie they provide a set of nonsense symbols which result in descriptions which are neither general, nor accurate (to sufficient precision), nor do they provide a practical context for useful creativity.
Physical systems which are very stable and definitive, but which are many-(but relatively few)-body systems, nonetheless, because these systems are so stable and definitive, it is clear that they are forming within a very controlled context,
so that the descriptions (of the professionals) which are based on:
1. (vague) randomness (which is an uncontrollable description for a system which is composed of only a few components),
2. non-linearity (quantitatively inconsistent, and chaotic), and
3. non-commutative (not invertible, or equivalently, not solvable, eg non-linear or spectrally-un-resolvable),
context, which is
4. contained in a continuum (a containing set which is far "too big" allowing logically inconsistent descriptive constructs to be put-together as if they belong to the same containment set), and
5. it is a description (when based on randomness) which begins from a global viewpoint (a function space) but the methods of the description focus on local spectral-particle events in space, ie it is a description which gives-up information leaving one in an inaccurate and non-useful context in regard to information.
It is a description which "in general" is not accurate, yet it also is a description which is "intent on" losing information about the stable definitive properties of the [assumed to be random] system.
That is the descriptive structure of the "dogmatically pure" set of experts of math and science is simply a bunch of nonsense.
Yet one must list the places and contexts within which it is a valid descriptive context:
1. It is a description which is relatable to a system whose initial conditions, and initial properties are carefully put-together so as to be a system which is easily broke-apart, so as to form a transitioning system which is chaotic, so that the rates of reactions (in this context, based on component-collision probabilities) are determined by cross-sections of the broken-apart components, where these cross-sections determine the rates of certain aspects of the (a) reaction,
and
2. They are descriptive contexts which relate a limited set of metrically measurable (observable) properties to a feedback structure, which is mostly associated to the critical-points and limit-cycles of a non-linear (usually classical) partial differential equation, where the range of relevance of the differential equation is difficult to determine or to control. Furthermore, the initial or boundary conditions of this type of a system relate to the properties of the descriptive context (or properties associated to the solution) of the system's differential equation in a chaotic manner.
That is, difficult math methods... , which are related to fleeting, unstable math patterns... , are descriptive constructs which have no content (and possess no useful information), they are patterns which apply only to unstable contexts, where control emanates from a higher abstract, and manipulative, context imposed on properties which are only definable in a metric-space, and which requires a lot of preparation (in regard to sensing and reacting in the desired way to the detected properties), a context which is at-odds with the system's natural properties, ie rather than controlling a system by simple adjustments to affect the system's properties in regard to affecting the properties of several system-components being coupled together.
So we have the tradition of "western hypocrisy," where failure is rewarded if those who perpetuate it, are in the high social classes.
What is wanted, by the owners of society, is that the social structures through which the powerful derive their power are kept in place.
That is, it is a social structure which is opposed to new, creative changes and thus it is also opposed to equality and the creativity associated to equality. However, the traditional social structure which upholds dominant interests so violently, and it expresses its interest in "lyrical creativity" in regard to the science and math experts... ., where these authoritative experts define the "literary" creative development of science and math, which is authoritative, but unrelated to practical creative-development, and the owners of society support the "creativity" of the elite artists, those who also compete in a "narrow context of authoritative cultural value," as well as those journalists and intellects whose ideas are judged (by the owners of society) to possess "cultural value," so that the ideas expressed are consistent with the ideas of (or can be used by) the owners of society, so as to be distributed by the material-instruments of the media, which are owned and controlled by the owners of society... , then even the failures of the experts can become part of the social structure which allows the powerful to remain powerful.
The top-intellects and top-artists are defined as a social class, along with artists and journalists, so that the intellectuals can dogmatically dominate those many-others who question the authority of assumptions, or who have different ideas.
The main tool used to maintain the power of the owners of society is the single voice of authority which the media has become (most clearly controlled by ownership, or by a set of funding processes).
That is, it is violence and domination (intellectual domination) which is fundamental to social power, not knowledge.
Knowledge is relevant, within today's social structure, only in regard to the creativity which is a part of the organization of society (ie business productivity) which, in turn, maintains the power of the few. However, the organization of society, and the use of resources and the ownership of technology within society, essentially, remains fixed and traditional.
For example, the many-purpose phone, eg an i-phone, is about developing 19th century ideas of electromagnetism, and the micro-chip circuit boards in these devices depend on 19th century optics.
Whereas identifying stability "as a needed property" in both math and physics, in regard to the useful descriptions of controlled (or controllable) physical systems, is a focus (in regard to the valid descriptions of math patterns) which the math professionals, apparently, have not considered.
Furthermore, very simple math patterns can be used to create new math patterns, which can be used to describe the stable material properties, so that these descriptions are based on a finite quantitative set, within which the descriptive containment of physical properties depends, ie the containment set is not a continuum and the derivative and its integral-inverse function-operators become discrete operators (the continuum can, instead, be the set of rational numbers).
In fact, the math patterns of stability are very simple, and relating these simple structures (which are best characterized by the stable discrete shapes, or circle-spaces) to many-dimensions, can be done by a simple process of partitioning the dimensional-levels of a hyperbolic 11-dimensional containment metric-space (base-space) by means of stable shapes, ie partitioning the dimensional levels by means of the discrete hyperbolic shapes (or circle-spaces), so as to form a finite spectral-orbital set, where the sequences of spectral-size are defined (either increasing or decreasing) as the dimensional level increases, so that these size-sequences of spectra are fundamental, in regard to how the description is organized, so that a finite spectral set is the basis for physical descriptions of the observed spectral-orbital-material order which the stable (material and containing metric-space) structures of existence possess.
Speech 3
Stability
In order to describe stable, "measurably consistent," and precise patterns of material systems one needs stable, "quantitatively consistent" math patterns.
In math such patterns are (quite often related to) linear, metric-invariant, separable partial differential equations, ie non-linearity does not work. Stable and quantitatively consistent math patterns also deal with the geometric models used for measurable quantities of the line (or line segment) and the circle, where these two geometric (or quantitative) structures can be easily organized so as to be quantitatively consistent with one another, eg the real-line and the complex-number-plane.
Circle-spaces
The circle-spaces fit both categories which identify reliable and stable quantitative descriptive (or measurable) constructs. The circle-spaces are the tori (the dough-nut shape) and those shapes with toral components, these include the discrete Euclidean shapes (single torus) and the discrete hyperbolic shapes (composed of toral components). The patterns of the circle-spaces are stable and quantitatively consistent. The circle-spaces are characterized by the properties of being related to non-positive constant curvature metric-spaces where the metric-functions have constant coefficients. The geometric properties of circle-spaces fit into the geometric structure of analytic complex-functions (where an analytic function is supposed to be consistent with the algebraic structure of quantitative sets, but the series must be put into the context of finitely defined polynomials to ensure quantitative consistency)
Lie groups
These are also the discrete isometry subgroups of the classical Lie groups (associated to metric-invariance). These spaces (shapes) include the discrete Euclidean shapes of R(n,0), the discrete hyperbolic shapes of hyperbolic n-space, which in turn, is associated to the general (n+1)-space-time spaces of R(n,1), as well as more general R(s,t) spaces and their associated discrete shapes related to circle-spaces.
Properties associated to metric-spaces
These metric-spaces, which may be modeled as discrete shapes, have associated to themselves both math and physical properties, so their discrete shapes can identify both metric-spaces and stable material components within the metric-spaces.
That is:
1. The property of position in space (in relation to the distant stars), these are related to the Euclidean spaces, which includes the property of action-at-a-distance, when the shapes have distinguished points and the context is the very rigid properties of hyperbolic spaces filled with sets of very rigid discrete hyperbolic shapes.
2. A stable well-defined pattern or shape, ie properties which are continuous in time, or conserved properties (or conserved patterns, or shapes), this property is related to the hyperbolic spaces [and the R(s,t)-spaces]. Time states are defined by the properties of the opposite flow of time advanced and retarded potentials, as well as the opposite pair of wave-equation solution functions.
Opposite time states and wave-propagation
How are these properties related to the propagation of wave-functions in either odd-spatial dimensions of a metric-space (distinct directions of time associated to wave-propagation [surface]), or even-spatial dimensions (always a mixture of time states, waves fill space after propagation "surface" distinguishes a wave property of a solution wave-function)?
Spin and unitary fiber groups
The assignment of properties to metric-spaces leads to the existence of pairs of opposite metric-space states and this, in turn, leads to the two: real and pure-imaginary subsets, of the complex coordinates, and the unitary fiber groups, as well as the spin-groups, where the spin-groups spin-rotate between the pairs of opposite metric-space states, where pairs of opposite time-states (associated to hyperbolic-space) are a part of the local dynamic process, and they are a part of the stable spectral-flow structure, which exists on the discrete hyperbolic shapes, and is related to the sub-face structure of a discrete hyperbolic shape's fundamental ["cubical"] domain.
Note: For new (3-dimensional) material associated to (or contained in) R(4,2), there are two time-dimensions so that each direction of time can be associated to a different domain space for the spatial positions of distinguished points (of the discrete hyperbolic shape models of material components) being transformed by SO(4)=SO(3) x SO(3) in (x,y,z,w)-space.
Size (Cardinality) of quantitative sets
[problems in description which are introduced by using sets which are too big]
There is another problem in regard to the size (cardinality) of a containing set, which is used in descriptions. The continuum is "too big of a set" allowing the inconsistent properties of both stable geometry (of particle-collisions) to be defined by means of convergence to the domain (or containing) space so that this explicit geometry (of particle-collisions) is defined in a context of assumed fundamental randomness, in regard to quantum physics, and (non-linear) particle-physic's random math structures do not allow microscopic material geometries (such as the geometry of a particle-collision). The continuum is "too big of a set" since it allows inconsistent constructs to be defined through convergence into the same containing (or domain) space, which is a continuum (containing both particle-collisions and fundamental random math structures).
To create a finite quantitative set
Thus, one needs to base quantitative descriptions, especially of physical systems, on a quantitative set built upon a finite spectral set. That is, one needs a stable, quantitatively consistent, and finite based quantitative set upon which to base a measurable description of physical systems.
Properties of discrete hyperbolic shapes
By following (or using) the patterns associated to the stable discrete hyperbolic shapes:
1. the last type of discrete hyperbolic shapes which is compact is 5-dimensional,
2. the dimension of the last type of discrete hyperbolic shapes to exist is 10-dimensional (hyperbolic-dimension) and it is an unbounded shape.
Partitioning a many-dimensional containing-space with shapes, so that the partition depends on dimension and the set of separate subspaces (of the same dimension, as well as of different dimension) which are defined on a many-dimensional space.
The number of n-dimensional subspaces "for n less that 11" is given by the "combinations" 11Cn, eg 11C2=55.
The properties of the dimensional partition
The idea is to partition the different dimensional levels... , and the various subspaces of each dimensional level, of the 11-dimensional hyperbolic metric-space... , by a (finite) set of (bounded when possible) discrete hyperbolic shapes, ie circle-spaces. Thus an 11-dimensional hyperbolic containing metric-space which is so partitioned is only continuous within each dimension, and subspace shape, of n-dimensions, and the continuity defined in such a n-dimension subspace is mostly defined (identified) in regard to the set of (n-1)-dimension boundaries of the (n-1)-dimension material component shapes contained in the containing n-metric-space, which, in turn, is contained in an 11-dimensional space. Inside a discrete hyperbolic shape, one does not see holes in the shape, but instead sees an open-closed topological space, ie one sees the space within which the lattice [("cubical" partition) of the discrete hyperbolic shape] is defined.
The nature of the spectral sequence based on the partition
That is, one is defining (on most of the "many sets of subspaces," defined within the 11-dimensional space) an increasing spectral sequence (as the dimension increases), and where the spectra are defined on the bounded, discrete hyperbolic shapes, which are a part of the (finite) partition, though on some subset of "the set of subspaces" there may be
some decreasing spectral sequence defined (as the dimension increases).
This can be used to define a finite spectral set upon which the stable shapes and components must be resonant in order to be contained within such a containing set (or metric-space) structure.
The sets of subspaces within which an increasing spectral set is defined (as the dimension increases) (can) have material-components contained within themselves (within the discrete hyperbolic shapes which model hyperbolic metric-spaces) so the contained material components (within the partitioning shapes) will have stable geometric-spectral properties which resonate with the finite spectral set of the partitioned 11-dimensional over-all containment space. Furthermore, condensed matter... ., ie material components whose size is too small, in regard to both the dimension and the subspace (of that same dimension) within which the material component is contained... ., will still be contained within a discrete hyperbolic shape, within which the condensed material can be in an orbit (orbital structure defined by the discrete hyperbolic shapes, within which the condensed material is contained). That is, the stable solar system can be interpreted to be evidence which proves that these ideas are correct.
Thus, the idea that "geometry dominates (or is more important than) the traditional authority of the partial differential equation of a physical system, defined in a context of materialism, non-linearity, and (undefined) randomness."
The decreasing spectral sequence, as dimension increases (the current, fixed, overly authoritative viewpoint)
On-the-other-hand a decreasing spectral sequence (as dimension increases) will not have any stable properties "to speak of," except for the material components themselves, and in such a decreasing spectral sequence (as the dimension increases), the high-dimension containing metric-space should be continuous for all the material components, but since this is not observed (that is, we do not experience the fact that we are in an 11-dimensional space, when we confine our observations to a low-dimension subspace of this 11-dimensional containing space) so these small spectra are curled-up, eg string-theory, so that the idea of materialism is maintained... ,
where the existence of material, ie materialism, is related to the fact that both the 1-dimensional discrete hyperbolic shapes and 2-dimensional discrete hyperbolic shapes are close to the same size, while the size of 3-material-components, in our metric-space, are the size of the solar system, thus, in our containing metric-space, the atoms and molecules (which are 3-dimensional discrete hyperbolic shapes) are condensed material, which have relatively smaller energy ranges of stability, than do nuclei,
... , and with a decreasing spectral sequence (as dimension increases) (in a metric-space whose subspace structure of a higher-dimension containing space is not detectable), one is left with descriptive structures which are unstable, indefinably random, and quantitatively inconsistent, where logic becomes irrelevant, as is now the "current way" in which quantitative language is now being organized to describe the observed material properties. Furthermore, this organization of precise language is held onto with stifling authority, and this is because the probabilities of particle-collisions are used in the randomly-directed transitioning system (of a nuclear reaction), so as to identify properties of rate and energy release of such a reaction (where a reaction is randomly transitioning system, wherein material interactions are modeled as collisions).
That is, the current descriptive context assumes that the spectral sequence of the containing structures decreases as the dimension increases, so all of the "many-component systems" (but still containing relatively few components), become "too complicated to describe," if one is trying to describe their stable patterns based on material interactions, which, in turn, are based on random, non-linear, (but nonetheless geometric) particle-collisions.
Other new attributes of description
In the new description there are new sets of operators, or properties, but the geometry of the description becomes the dominant attribute of the description, often this is because the new geometry describes (identifies) the new context, in a most dramatic way.
1. There exist conformal factors defined between dimensional levels (ie physical constants), as well as between different subspaces of the same dimension,
2. (perhaps) conformal factors can be defined between toral components of a discrete hyperbolic shape (though this might simply be relatable to the existence of particular varied discrete hyperbolic shapes which can exist based on the reflection group structure of the lattices at vertices which can also be related to the various possible sizes of the faces of the fundamental doamin)
3. Discrete Weyl-transformations of angles can be defined between toral components of discrete hyperbolic shapes (these Weyl-transformations define "allowable folds on the lattice" of a discrete hyperbolic shape).
The derivative becomes a discrete operator in regard to:
1. Time intervals defined by the periods of the spin-rotations of opposite metric-space states
2. Dimensional levels
3. (possibly) Between toral components of a discrete hyperbolic shape
This new descriptive structure defines material interactions using many aspects of Newton's law of inertia. Thus, there are also the "usual types" of 2nd order material interaction math (or equation) patterns:
1. elliptic (or orbital)
2. parabolic (or free, or angular momentum)
3. hyperbolic (waves with physical properties, or collisions of material components)
But these types of interactions depend on the spectral values, and they apply in a more restricted geometric context, but now it is within a more diverse many-dimensional construct where quantitative descriptions are to be guided by the geometry (both shape and size) of any of the dimensional levels.
Note:
It should be noted that with both materialism and the belief that the spectra of higher-dimensions need to identify a decreasing spectral sequence as the dimension increases, means that conventional science tries to sort-out the spectral properties, of quantum systems composed of "five, or more," charged components, by attaching a 1/r potential (also associated with spherical symmetry), for each charged component, where the assumed spherical symmetry, of each 1/r term, is "deduced" from the assured-ness that the random-particle model of material interactions is to be spherically symmetric in each dimension (if the dimensions are not curled into small shapes), because of fundamental randomness, so if particles are being emitted from a "force-field source," then the field-particles will emanate in any random direction, and then this will define a spherically symmetric force-field.
But such a model... ,
(or such an assumption that a "physical description of material interaction is to be based on fundamental, indefinable-randomness, associated to random particle-collisions," so that particles are emitted in random directions from a "force-field source" so as to cause a spherically-symmetric force-field, in all dimensions)
... , is far from the truth.
In fact, material interactions are mediated by a toral shape, associated to action-at-a-distance toral shape defined for each (small) time interval (~10^-18 sec), where this time interval is defined by the period of the spin-rotation of metric-space states, so that the tangent structure of each interaction-torus (defined for each time interval) is related to a 2-form force-field, which, in turn, is related to the geometry of the fiber group (of the containing space of the interaction torus), and this geometry (of material interaction) only results in a spherically-symmetric force-field for SO(3), ie the interaction torus which is contained in R(3,0).
Quantum randomness of point-particles
The new model of material interactions, defined for small components whose properties of "being neutral" or "being charged" changes rapidly, results in these small material-components defining Brownian motions, where these Brownian motions, in turn, determine an appearance of quantum randomness. Furthermore, the vertices of the fundamental domains of the circle-space shapes, define a distinguished point on the circle-space shapes, about which material interactions are defined. This, in turn, creates the illusion that material-interactions are interactions between point-particles.
The commercial world is related to a fixed stationary way of behaving or acting, a commercial structure is a very narrow context, based on a limited range of creativity and a fixed way in which to use material resources. The power of business monopolies depend on society not changing how it uses the material resources a business monopoly supplies to a society. The law is supporting this type of narrowness, essentially based on property rights and minority rule (creditor vs. debtor, smart vs. stupid, etc), and it supports such selfish actions with great violence. In fact, the economy is tied to a fixed narrow way in which to live and create, and this model of monopolistic economies is being used as a means to conquer ever larger populations, but it is being put into-place by means of extreme violence and coercion (often an economic coercion).
Does one want a society to be based on a fixed way to use material, and a fixed way in which one is to serve the material based, and fixed structure of society, and a fixed overly authoritative organization of descriptive knowledge, so that this type of power, and associated narrowly defined knowledge, depends on expansion in the form of an ever greater exploitation of particular types of material (usage)?
Dimensions, shape (holes, stability), size, measurable description, and spectra
The dimensions of the set of 2-forms defined on an n-metric-space is also the dimension of SO(n), where dim(SO(n))=dim(spin group of SO(n)).
In the new descriptive construct the geometry of the 2-forms in an n-space is related to the local (tangent) geometry of an (n-1)-dimension "discrete Euclidean shape," ie an (n-1)-torus, which in turn are related to the geometry of the SO(n) fiber group of the n-base-space, in regard to the local coordinate changes of the positions of the interacting materials (determined by both the 2-form force-fields and the local coordinate transformations) where these local coordinate changes are associated to each discrete time interval, in turn, defined by the spin-rotation of metric-space states (~10^-18 sec).
Thus dimensional relations can be found between the various possible spaces related to a material interaction and the associated spectral properties (ie properties of spectral-size) of the different containment levels.
The list of the dimensions of the 2-form spaces of the different dimensions up to Euclidean 6-space... , since the spectral sizes of discrete hyperbolic shapes of dimension 6 and up to dimension-10 are infinite extent, so that shape loses its intuitive sense of bounded-ness, thus the geometry of the interaction-shapes are difficult to identify... , are as follows:
2C2=1, 3C2=3, 4C2=6, 5C2=10, 6C2=15
From this list... ., and along with some information about the geometric structure of the SO(n) fiber group, such as SO(4) = SO(3) x SO(3)... ., one can make some determinations (or guesses) about the nature of force-field interaction geometry. The relation of the fiber group geometry to the 2-form geometry to the geometry of the containing n-dimensional metric-space, or possibly the geometry of an (n-1)-dimensional metric-space associated to the: subspace, material, and dimensional structure of our containment set.
That the 2-form on n-space has the same dimension as SO(n) means that there needs to be a geometric-vector relation to force-fields acting on (n-1)-shapes contained in n-space. The "charges" on (n-1)-shapes are the (n-2)-flows (or (n-2)-faces of an (n-1)-shape) so the geometry of SO(n) is related to the geometry of (n-2)-flows on (n-1)-shapes in turn, contained in n-space.
1. For 3-shapes contained in 4-space it is useful to identify the normal to the 3-shape with time instead of the 4th spatial-dimension, so the geometry of the 2-forms is related to 3-space, while
2. for the 4-shape contained in 5-space so the geometry of the 3-flows (or the 2-forms) is related to 5-space, but
3. for 5-shapes contained in 6-space the 4-flow (or 2-form) geometry is again dimensionally more convenient to treat is being related to the toral 5-shapes again letting the normal-direction of the 5-shape to be associated to a time-direction, etc.
In regard to odd-dimensional spatial subspaces, which are the material-component containment spaces, the dimensional properties of the 2-forms are related directly to the local tangent geometric properties of the containment space.
In regard to even-dimensional spatial subspaces, which are the material-component containment spaces, the dimensional properties of the 2-forms are related (directly) to the local tangent geometric properties of the interaction toral shape which is 1-dimension less than the dimension of the containment space, with the normal direction to the toral shapes being associated to a time-dimension (instead of the extra dimension of the containment space).
The most important geometric relation in regard to our "3-space experience" is that the geometries of the 3-space and the 4-space can have a fairly complicated relation with one another, especially since (or if) the spectral-size of 4-space seems to be the size of the solar system, thus the geometry of the 3-tori do not manifest, in regard to our human size-scale on earth, in 4-space, but rather are related to the 3-space in our experience (due to their spectral and subsequent resonance relation with another 4-dimensional subspace, a subspace which possesses "smaller spectral values" than does the 4-space within which we are contained, where our planetary-orbits are defined by the large 4-spectra of our 4-subspace containment). That is, our 4-space material geometries are in fact 2-surfaces contained in a 3-space, due to issues of spectral size in our subspace for 3-shapes, thus the 2-forms defined on a 3-torus (contained in 4-space) which define the interactions of 2-surfaces, which model material components in 3-space, must be related to 3-space. This is possible since SO(4) = SO(3) x SO(3) so for 4-space, (x,y,z,w) can be separated into a pair of 3-spaces (x,y,z) and (x,y,w) subspaces of the 4-space, and thus relatable to 3-space and to a 2-plane in 3-space.
Thus, there is a geometric relation of the condensed material of our 4-subspace to the spectra of our 3-space containment, allowing a 6-dimensional electromagnetic-field, etc.
Whereas for a 2-form defined on a 4-torus contained in 5-space, the 5-space relates to either a 4-field (or a 4-vector) and a 2-form of 4-space structure, or a pair of 5-fields (or a pair of 5-vectors).
Whereas a 5-torus defined in a 6-space can be related to three 5-vectors, or a 5-vector and a 2-form of 5-space, etc. or a pair 2-forms defined on 4-space and a 3-vector defined on 3-space (or a 2-form defined on 3-space), or a 2-vector-field defined on 2-space, the intersection space of a pair of 4-subspaces defined on 6-space.
The geometry of the 2-tori in 3-space, ie the vector-fields defined on the 2-torus which is contained in 3-space is, thus, associated to SO(3) (which has the geometry of a 3-sphere), is the geometry which causes inertial interactions to be spherically symmetric in 3-space, while the geometry of 4-space and SO(4), along with the spectral sizes of 3-dimensional discrete hyperbolic shapes in 4-space seems to also allow for some aspects of spherical symmetry for the inertial properties of material interactions being related to 3-tori, which are contained in 4-space.
The partition
Partitioning the dimensional levels by defining a discrete hyperbolic shape for each subspace of each dimensional level.
On the other hand, the new viewpoint requires that a catalog of spectral values be found for the different dimensional levels, which are related to (or modeled by) bounded "discrete hyperbolic shapes" of which the 5-dimension "discrete hyperbolic shape" is the last such "discrete hyperbolic shape" which can be a bounded shape.
This spectral-catalog would be similar to the periodic table of the elements.
Thus there is:
The spectra related to subspaces as follows:
[11C1 + 11C2 + 11C3 + 11C4 + 11C5] = [11 + 55 + 165 + 330 + 462] (respectively) = 1023,
... , where 1023 is the number of subspaces of the various dimensions in regard to the 11-dimensional containment set, where each subspace of each dimensional level can be associated to "discrete hyperbolic shapes," whose shapes might be bounded, so as to define a specific (well-defined) spectral set for each subspace.
This number, 1023, may also be interpreted to be the number of 1-spectra which compose the finite spectral set upon which all material systems (or bounded discrete hyperbolic shapes) depend for their existence by means of resonance with this finite spectral set.
This spectral set will define sequences of spectral size where the sequence is defined as the dimension increases, so that these spectral sequences may be increasing (allowing for stable material structures) or decreasing which would imply that order to material systems would be much more limited, where an increasing spectral sequence allows the lower dimension shapes to be contained in the upper-dimensional shapes.
The time subspaces in higher-dimensions
Consider the metric-spaces whose metric-functions have constant coefficients, R(s,t), such as R(3,0) [Euclidean 3-space] and R(3,1) [space-time], where s is the dimension of the spatial subspace, and t is the dimension of the time subspace of R(s,t).
In such spaces the time-dimension changes when a new material is added to the structure of existence.
For example, one can hypothesize that for R(2,0) there is only the material property of inertia, which exists as a 1-dimensional discrete shape, when charge is added into the descriptive context, it is a 2-dimensional discrete hyperbolic shape, and then it is contained in R(3,1). Thus, one might hypothesize that there is a new type of material to be contained in R(4,2), namely, the odd-dimension 3-shapes which possess an odd-number of holes in their shapes, ie an odd-genus, but nonetheless, the inertial properties of the material interactions, ie changes in spatial position, of the material contained in R(4,2) would be in R(4,0) space, so "in general" inertial changes of interacting materials' positions in an R(s,t) space would be identified in R(s,0) Euclidean space.
Sizes of discrete hyperbolic shapes
The spectral size sequence, defined as the dimensional levels increase, can be increasing, decreasing or neither increasing nor decreasing, but the sequence of increasing spectral sizes allows the associated material systems to be ordered and stable, while decreasing spectral sequences do not allow for the order of material systems, or decreasing spectral-orbital sequences only allow for a limited (stable) spectral-orbital order to exist.
There is also the issue of infinite-extent "discrete hyperbolic shapes," where the last existence of bounded discrete hyperbolic shapes existing in a 5-dimensional discrete hyperbolic shapes contained in a
6-dimensional hyperbolic metric-space, where the idea that lower-dimensional shapes are contained in a larger higher-dimensional metric-space which (also) posses shapes would only exist (or be possible) for an increasing spectral sequence.
However, there are discrete hyperbolic shapes which have the property of being "infinite-extent" (or unbounded shapes) within (or for) all hyperbolic metric-spaces.
The neutrino is best modeled as an (semi) infinite-extent discrete hyperbolic shapes, due to its , apparent, zero-mass, where its property of being semi-infinite-extent allows a neutrino to be both infinite-extent and to possess a spatial position (associated to the atom which the neutrino is a neutrally charged component), but such an infinite-extent model of a discrete hyperbolic shape (at low dimensions) allows the "infinite-extent property" to, subsequently, be contained in a higher-dimensional metric-space shape, which is bounded, and this allows the low-dimension material systems, wherein these low-dimension systems possess components like neutrinos, whose unbounded geometric property comes to be contained in a bounded metric-space shape.
The infinite-extent properties of neutrinos can be contained in a bounded metric-space. Thus, the systems which contain neutrinos can still be contained in a bounded spectral (or metric-space) set, thus metric-spaces of higher-dimensions can carry within themselves the finite spectral-set which defines a "world of experience."
In turn, this would allow other higher-dimensional infinite-extent discrete hyperbolic shapes to determine (by containment) an "arbitrary" bounded, (relatively) low-dimension spectral set, so that this spectral set can include atomic-type systems, whose components are neutrinos.
However, such arbitrary bounded spectral sets require a higher dimensional experience, ie higher-dimensional containment.
Blurbs
I
If a fiber group's (primarily isometry, or unitary) local matrices are always diagonal (or commutative) on the global coordinates of a shape's locally-identified vector-field then the geometry is stable, quantitatively consistent, and simple enough to be considered to be a good candidate to be an element in a set of shapes which is to be used to model existence in a many-dimensional, macroscopically-geometric context so that stable spectral-orbital properties of physical systems [which exist at all size scales, eg nuclei to solar systems] can: generally, accurately (with sufficient precision), and practically usefully; be described (where a stable geometric description is a practically useful description).
Basically these simple commutative shapes are the stable circle-spaces, defined within metric-spaces of non-positive constant curvature, where (but) they are also primarily the
"discrete hyperbolic shapes," though metric-spaces which are different from R(n-1,1) [which is either a general space-time or an (n-1)-hyperbolic metric-space] can be considered, such as R(s,t), wherein new higher-dimensional material can be (newly) defined, and a higher-dimensional model of a life-form can be defined.
Furthermore, the metric-spaces possess intrinsic properties, which exist as opposite pairs of metric-space states. This leads to complex coordinates and unitary fiber groups, as well as fiber spin-groups and the spin-rotations of opposite metric-space states.
The different dimensional levels are to be modeled as discrete hyperbolic shapes, where up to and including hyperbolic dimension-5, these shapes may be assumed to be bounded, and assume there is a shape which is maximal for each dimensional level and for each subspace of that same dimensional value. This is the basis for defining a finite spectral set, associated to the over-all high-dimension containing space, ie an 11-dimensional hyperbolic metric-space, since the last existing infinite-extent discrete hyperbolic shape has hyperbolic dimension-10.
Thus, the different dimensional levels of the higher-dimensional (over-all) containment space are partitioned by open-closed shapes, which are associated to "rectangular-like" fundamental domains in hyperbolic space.
The "rectangular" simplex fundamental domains for the metric-space within which we and our solar system are (both) contained are 4-dimensions, upon which our metric-space is a 3-flow, and this fundamental domain would be the size of the solar-system, these block-like fundamental domains (or equivalently circle-space metric-spaces) would appear open, and thus the incoming light (from outside the solar system), where light is modeled as an infinite-extent discrete hyperbolic shape, would pass through the blocks from far away, while on-the-other-hand the apparently infinite extent neutrino discrete hyperbolic shapes which define the 2-faces of the "discrete hyperbolic 3-shapes," which model electron clouds, would (could) have its infinite extent defined by being bounded by the bounded discrete hyperbolic 4-shape metric-space which is also a model of the discrete hyperbolic 4-shape of the solar system. Thus, one has that when one looks away from the rectangular 4-simplex of the solar system (or looking out to the universe) one would see light coming in from the distant places, while looking within the rectangular 4-simplex one would see the closed boundaries of bounded discrete hyperbolic 2-shapes
(and/or possibly bounded discrete hyperbolic 3-shapes) modeling the material components contained in the 3-flow model of our containing metric-space
In this context, the way to use higher-dimensions is to model the different dimensional-levels as the stable circle-spaces, and the way in which to get a (math) pattern which is associated to the existence of stable spectral-orbits is to multiply the different dimensional levels by constants, ie the nature of physical constants, so that the spectra... , of the adjacent next higher dimensional level... ., increases in value, where this allows the lower-dimensional shapes to be contained within a stable shape, where, in turn, this shape can define a relatively stable orbital geometry, for the material which is contained within the shape (ie the metric-space is a shape).
The idea of materialism as well as of quantum physics and particle-physics (both consistent with the idea of materialism) assumes that the higher dimensions are either continuous, in an open context, and that material reduces to point-particles and the spectra (associated to the physical systems which these point-particles occupy) decrease in value (spectral size) as the dimensions of containment increase, where in both cases (continuous and discrete particle context) the force-fields are assumed to be spherically symmetric (though perhaps not always inverse square), but this spectral structure implies that no stable spectral-orbits exist (that is, where does one now (2013) find valid descriptions of the general and spectrally relatively stable: nuclei, atoms, molecules, crystals, and solar-systems?).
The derivative operator can be re-defined as a discrete operator, defined between: (1) dimensional levels (2) time intervals, and (3) toral components, wherein Weyl-transformations can be used to identify stable orbital shapes associated to a set of angularly-deformed "discrete hyperbolic shapes," which in turn, define envelopes of orbital stability for the condensed material components, which these metric-space shapes might contain.
II
Topic list
The stable properties of general sets are related to precisely identifiable properties of physical systems where these precisely identifiable properties of physical systems exist at all size scales; from nuclei to solar systems, and these fundamental systems have no valid descriptions, eg Hartree-Fock etc.
List of fundamental topics concerning these new math-science ideas:
From
1. precise language (build new languages at an elementary level of assumption, and context, and interpretation, in order to broaden the capacity to create; Godel's incompleteness theorem can be interpreted to mean add more assumptions or it can be interpreted to mean review and alter one's precise language at the level of assumptions),
Does language fit into a "fixed scene" (which is implicitly assumed to be moving toward some absolute truth) which is similar to the idea that an authoritative math language is always relatable to ever more complicated instruments, but in an industrial society all the instruments are built so as to be based on the same principles (electromagnetism or other classical theories which allow stable patterns which are controllable), so that when the instruments are adjusted in their "complicated context," they either improve or they reach their limits of performance, likewise physical theory and math patterns are carefully adjusted within the realm of fixed principles, but the math and the physics do not work, and the careful adjustments either do not work or they have already reached their limits of performance (and thus, they have lost their relevance), to
2. quantitative structure
(continuum, quantitative consistency, comparisons [length, time, material {particle-number or density}]
or spectral values
[momentum, energy {single-valued in regard to holes in the shape of the domain}, as well as an assumption of fundamental randomness [which apparently, for physics, cannot be defined as a valid elementary set of random events]]), to
3. failing descriptions (for valid descriptions of the stable spectral-orbital physical systems which exist at all size scales, rather the descriptions are of fleeting and unstable patterns), to
4. the stability of mathematical patterns (how can their stability be established), to
5. the proper role of geometry (stability of patterns, a measuring context, a useable context), to
6. interpreting observed patterns (Are the incessant examination of the properties of elementary-particles best interpreted to mean that existence is higher-dimensional and unitary? Furthermore, the existence of high-energy cosmic-rays, as well as an apparent property of dark-matter, are best interpreted to mean the existence of a large-scale spectral structure which exists in higher-dimensions), to
7. fundamental structure of math, functions vs. numbers, (algebraic equations and partial differential equations, is math really about finding the stable geometric confines related to the existence of stable describable math patterns or stable measurable properties).
For example, How to determine the structure of the derivative?: {From a derivative interpreted as
1. an operator on a function space, to
2. a model of locally measured properties within a sufficiently determined containing space, to
3. a discrete operator in a finite math structure determined by (discrete) stable geometry in a newly organized, many-dimensional, containing space with new interpretations, which can lead to many more possibilities (the functions in the function space are [now] the discrete shapes).}
Math is about quantity and shape,
... , but when shape is considered primarily in terms of measurable quantities and functions (or functions and their coordinate domain spaces), it (the shape which is being described) is most often non-linear and unsolvable, except locally (the fiber diffeomorphism group is locally invertible), but non-linear quantitative properties are chaotic, so the local pieces of shapes cannot be put together in a quantitatively consistent manner, and
... , thus it (shape) fits into an indefinable random structure, in turn, to be fit into function spaces which, in turn, depend on indefinable sets of spectral functions (whose associated operator structures, or measurable properties, usually do not commute).
However, Thurston's geometrization finds that the variety of stable geometric systems depends most strongly on the discrete hyperbolic shapes, while Coxeter found that the last bounded discrete hyperbolic shapes are 5-dimensional, and the last set of infinite-extent discrete hyperbolic shapes are 10-dimensional.
Consider:
1. The stable properties of general sets of precisely identifiable physical systems which exist at all size scales; from nuclei to solar-systems, and these fundamental systems have no valid descriptions, eg Hartree-Fock, general relativity, etc.
2. Basing measurable descriptions of systems which possess stable properties on a quantitative set which is determined by a finite spectral set, put into a context of stable (linear, solvable) geometries, contained in a higher-dimensional set which is also organized around stable shapes, ie organized around stable circle-spaces. Namely, a finite number of discrete hyperbolic shapes contained in an 11-dimensional hyperbolic metric-space.
Where as consider the following patterns of spectral values associated to a containment space, as the dimension increases there is either:
(a) an increasing finite sequence of spectral values with an upper bound, or
(b) a decreasing finite sequence of spectral values with a lower bound.
That is, (a) is the new proposal, while (b) is essentially what is assumed today (2012) when guided by the principle of materialism and the principle that material reduces to a set of fundamentally random elementary-particles, where (b) is helpful in regard to building nuclear weapons.
The consideration of (a) is about circle-spaces, which in turn, are associated to complex-numbers and subsequently complex-coordinates, and, in turn, the relation of circle-spaces to: quantitative consistency, stability of measured patterns, and the relation of the shape of a circle-space to both spectral values and the geometric properties of spectral constructs (multiplicative constants, and Weyl-transformations [or allowable folds] on the lattice of a discrete shape, as well as action-at-a-distance {or non-local} structures of material interactions) and the subsequent rigidity of measurable structure (eg analytic [complex] function structure), and its relation to the stability of pattern, and the existence of either analytic continuation, or the controllability of linear solvable systems.
Though the apparent randomness of point-particles, may appear to dominate observed material phenomenon, it is really the confinement to a set structure which allows for stable patterns to: exist, be measured, and used, ie controlled (and/or formed). This is about how material components relate to either a stable math structure of their own, or a stable math context needed for reliable measurements (existing in stable orbits or existing as free components in a metric-space, which in turn is about the math structure's, eg spectral values of the different dimensional levels, as well as the energies of an interacting context, which determine condensation vs. resonances with the existing constructs of the stable circle-spaces, where resonances allow for a system's stable math structure to form within itself).
3. Life: The odd-dimensional discrete hyperbolic shapes which also possess an odd-genus, when their faces (or spectral-flows) are occupied then they are charge unbalanced, and would naturally oscillate and generate energy, ie a simple model of life.
4. Mind (related to the spectra which can be contained within a maximal torus of the fiber group)
5. Intent (directing the flow of energy within a cognizant system)
6. Creativity (creating and expanding the possibilities of existence, itself, in a direct manner, or how the instrument of life can be used)
Etc.
The truth of a precisely identified pattern should be determined by the relation that the pattern has to practical usefulness, generality of application, so as to provide a wide range of accurate descriptions, made to a sufficient level of precision, based on simple easily applicable laws, or based on the "correct" context which can be seen to limit possibilities, so the information is accurate and the context is practically useful. That is, math truth, not necessarily a context about so many independent variables defining containment so that the description needs the same number of independent equations. That is understanding the context of existence in the context of its stable shapes which organize the different dimensional levels of existence.
There are all types of social issues concerning the expression, and consideration of new ideas, where these issues get mixed up in the way in which tradition and authority dominate the published expressions of a society, but more strikingly the structures of investment and the condition of wage-slavery which afflicts the development to of knowledge, and the subsequent set of lies about personal value and worth as well as competition, where both worth and the competitive game are narrowly defined by the investors, and these forces constitute the social context, and it is a context which opposes new ideas and new expressions, the investors require that knowledge serve the creative interests of the investors, thus such a system grinds itself to a halt, because of the highly enforced narrow viewpoints. It should be noted that, these social structures, which are based on inequality, are created and maintained by means of extreme violence, this emanates from the justice system, and from a militarized management system.
One needs the math properties of stability:
1. Linear (partial differential equations)
2. Metric-invariant, with non-positive constant curvature, where the metric-function has constant coefficients,
3. The shape must be parallelizable and orthogonal at each point of the global shape of the containing coordinate system, ie the partial differential equation is separable so that the locally linear matrix structure associated to derivatives and differential equations is always commutative, or diagonal.
These properties of stability are about the properties which the discrete Euclidean shapes and the discrete hyperbolic shapes, possess, as well as being possessed by the (discrete) shapes in R(s,t), where space-time is R(3,1).
Other properties:
I. principle fiber bundle with metric-space base spaces and isometry and unitary fiber groups
II. the metric-spaces possess properties, eg properties of position and the property of a stable pattern. This leads beyond the isometry Lie groups to both spin-groups and unitary groups
III. Both the metric-spaces and the material components are discrete hyperbolic shapes, essentially modeling adjacent dimensional metric-spaces, ie a higher-dimensional context is not based on continuity of the lower dimensions until one reaches the discrete shape which defines a particular dimensional level, a 3-shape does not see a 7-shape as part of its containment context.
IV. The containing space is an 11-dimension hyperbolic metric-space, a hyperbolic metric-space is chosen since the discrete hyperbolic shapes are so stable in both their shapes and their spectral properties. There are constant factors defined between dimensional levels and between toral components of discrete hyperbolic shapes
V. The derivative can be defined as a discrete operator between
(a) dimensional levels, between
(b) time intervals, and between
(c ) toral components of discrete hyperbolic shapes by way of the Weyl-transformations.
VI. Life, mind, etc
As well as:
Holes in metric-spaces; material either resonates with a shape so as to occupy a hole, or spectral-flow, defined within a discrete hyperbolic shape, or it condenses and orbits around the holes (spectral flows) defined by a discrete hyperbolic shape which is much larger than the size of the condensed material.
Increasing or decreasing spectral-size sequences
[The properties of a physical/mathematical construct of an increasing spectral sequence, as the dimension increases, can be organized, based on: shapes, sizes, and formation processes (or formation structures) so as to cause an observer within a particular dimensional level to not perceive the higher dimensions. Furthermore, in an n-metric-space the observer mostly sees only the (n-1)-material components. In a decreasing spectral sequence, as the dimension increases, which is the assumption of both particle-physics and string-theory, it is assumed that there exists the property of continuity between all dimensional levels, and all subspaces, so the spectral sequence must decrease, as the dimension increases, so the observer cannot see the affects of the higher dimensions, thus the higher-dimensions are curled into small shapes which possess small spectral values, but such an assumption of continuity between dimensional levels is not needed, and it is certainly not necessary.]
Material condensation (often due to the material sizes which are defined in a particular subspace of a particular dimensional level, where the condensed material is smaller than the material-component sizes, ie discrete hyperbolic shapes, of the particular dimension and subspace [of that same dimension])
Only valid model expressing the principle of inertia, as identified in general relativity, is "orbits of condensed material on the discrete hyperbolic shapes of the condensed material's containing metric-space."
A main issue is: "finding one of the finite spectral sets, which identify the stable context of an 11-dimension hyperbolic metric-space."
Empty of content (Apparently, No stable patterns exist)
The content, or focus, or motivation of today's science and math languages used in professional (peer reviewed) journals are the elaborate and complicated techniques that are either unrelated to the observed patterns, ie the observed stable patterns of material systems, or these techniques are unrelated to reliable descriptions of stable, well-defined, measurable patterns,
(where well-defined patterns are: shapes, reliable quantitative relationships, observed stable and precise properties, laws which are truly applicable to a wide range of different contexts so as to provide relatively accurate solution functions (or spectral sets), and the math-physical conditions which allow for reliable measurements). The dogmatically authoritative literature of the science and math communities has become devoid of content. It has become elaborate complicated descriptions of a world of illusions. Its main social function is to define an authority which identifies inequality, yet its descriptive context is primarily formulated to develop weapons and to allow ever more control over communication (channels).
Today's professional math-scientists are not describing stable patterns, since the context of the authoritative descriptive precise language, and its associated techniques, are unrelated to describing stable identifiable patterns, rather the intellectual content of their descriptive focus is only about describing complicated elaborate calculating techniques which are unrelated to the observable order of the world.
The context of the professional dogmatists is defined by:
1. indefinable randomness (the elementary random events are not stable and they are not well-defined),
2. non-linearity (quantitatively inconsistent), and
3. contained within a set of measurable properties (or measurable coordinates) which have the properties of a continuum (a very large set, high cardinality), and either
3a. geometries or
3b. functions spaces
both of which whose properties are non-commutative, where
3b1. the functions-space spectral techniques associated to random descriptions are focused on local spectral properties, as opposed to
3b2. solution functions which provide global system information, and
4. the description has the property of being about random descriptions of the relatively few components which compose a stable system, the logic of this construct is inconsistent.
Furthermore, it is a description which is logically inconsistent where convergences... of geometric properties which are based on random descriptive structures... where such geometry and randomness are both defined upon (into) the domain space's continuum structure.
Furthermore, there is an improper focus on "as to what constitutes" a valid frame of descriptive reference for a physical system:
I. A valid "frame" for the containment of a physical system's properties is not about coordinate frames associated to motions as in general relativity, this unduly narrows the context within which a physical system obtains its ordered-form, but rather
II. Physical systems are determined by, and contained within, the shapes (both macroscopic and microscopic shapes, which are defined for all dimensional levels) of metric-spaces, where these discrete (isometric) shapes are models of metric-spaces, and where these metric-space shapes are needed in relation to a finite spectral-orbital set observed for the observed material systems at all size scales, where a finite spectral-orbital set is to be defined on "an over-all" high-dimension containment set (an 11-dimensional hyperbolic metric-space), in which, the partition of the dimensional levels by shapes, defines, either "increasing or decreasing sequences of spectral-sizes as the dimension increases" within the high-dimension containment set... ,
... , so that, within the partition of the dimensional levels by spaces with stable shapes, there is an associated, and prevalent, stable set of holes on these dimension-partitioning shapes.
Note: The genus of such a shape is the number of holes defined on the "discrete isometric shape," upon which the "holes in space" are prevalent, but these holes are not seen by the observer who is contained within a (particular) dimensional level.
Furthermore, there is an inability (of a learner) [in a society dominated by monopolistic businesses] to question the traditions and authoritative structure of "what has come to be thought of as a discipline," but dogmatic authority, ie religion, is a fallacious mental context "in which to develop both knowledge and a descriptive language," where the descriptive language should not be fixed, but rather a change should (always) be considered in regard to a precise descriptive language. That is changes in a precise descriptive language "should be the main focus" in regard to the intellectual context (or condition) of causing changes in descriptive knowledge for the better.
The both overly-authoritative and fixed intellectual state (of our US society) is a result of the experts "need to be subservient to the process of 'peer review,'" which protects, or ensures that, the knowledge fits into the interests of the monopolistic businesses which dominate the society.
That is, one needs to question:
1. the continuum,
2. indefinable randomness,
3. non-linearity,
4. materialism,
5. what are the fundamentals of a differential equation, and
6. the context (of knowledge associated to business interests) of newly forming systems
... ., after a stable system has become unstable and has broken apart so as to transition to a new stable state by a series of many-component collisions (where business concerns are interested in the probabilities of collisions and its relation to rates of reactions).
These dogmas need to be questioned if one wishes knowledge to develop and change.
Yet one must list the places and contexts within which it is a valid descriptive context:
(see below for more details)
1. It is a description which is relatable to a system whose initial conditions, and initial properties are carefully put-together so as to be a system which is easily broke-apart, so as to form a transitioning system which is chaotic, so that the rates of reactions (in this context, based on component-collision probabilities) are determined by cross-sections of the broken-apart components, where these cross-sections determine the rates of certain aspects of the (a) reaction,
and
2. They are descriptive contexts which relate a limited set of metrically measurable (observable) properties to a feedback structure, which is mostly associated to the critical-points and limit-cycles of a non-linear (usually classical) partial differential equation, where the range of relevance of the differential equation is difficult to determine or to control. Furthermore, the initial or boundary conditions of this type of a system relate to the properties of the descriptive context (or properties associated to the solution) of the system's differential equation in a chaotic manner.
These contexts identify structure related to (1) nuclear weapons and (2) guiding missiles and drones.
Furthermore, there are the overly general contexts, wherein the experts consider holes in shapes, but they view holes in shapes as arbitrary structures, which most often, the experts, relate to complicated shapes and distortions of very general, but unstable, geometries, and these overly general contexts also need o be questioned, though seeking generality can have great value, it should not be a dogmatic command, since it is the limitations which allow useful information about patterns to be found.
Though there is a great imagination, by the experts, for great generality, but nonetheless there is an unimaginative viewpoint about "how holes in shapes" can be (might be) related to physical descriptions.
The nature of shapes, and shapes with holes in themselves, identifying valid descriptive frames (or frames of containment) through which the spectral-orbital properties which characterize physical systems can be modeled.
Holes in space affect (or interfere) with single-valued-ness of values determined from integral operators, yet the relation that holes have with stable spectral values is seldom considered. Namely, the discrete hyperbolic shapes, placed into a new construct, which is to be used for a new precise descriptive language.
One might note that:
The observed stable, precise, patterns of physical systems are associated to finite properties, eg bounded-ness and/or the finite number of a physical system's components, eg atomic-number, and these stable physical system properties are fundamental and observed features of a reliably measurable context associated to the observers of physical patterns. This implies both the existence of stable patterns which allow reliable measuring, (or which are associated to the context of measuring (for an observer)), and the existence of stable-controllable patterns associated to a set of fundamental physical systems which possess stable features of "what may, or may-not be" "material" systems, eg nuclei, general-atoms, molecules and their shapes, crystals, solar systems, dark-matter (ie orbital properties of solar-system's in galaxies) etc, the physical patterns upon which the relatively stable aspects of our life experiences depend, and upon which our mental constructs also depend.
Thus, science and math are about identifying stable, quantitatively-consistent, math patterns which are generally applicable to these stable, measurable, and apparently controllable, physical properties so as to result in descriptions of these patterns which are accurate (to sufficient precision), and general so as to be able to describe the observed stable physical patterns of existence, so as to provide a context for practical usefulness, ie measurable and controllable, so that one can: measure, fit together (or couple), and interact with these various patterns (using the natural structures of these patterns, eg life-forms and its coordinated chemical properties (but, apparently, coordinated by an unknown structure), ie not feedback mechanisms nor carefully prepared structures so as to cause reactions), so that this descriptive knowledge can be related to "practical" creativity (as opposed to literary creativity, essentially associated to a world of illusion, ie a world without stable features).
The violent nature of today's society
The entry into science and math of a set of overly authoritative dogmas (essentially, defined by the authority of the peer-review process), which are overly protected (dogmas), where the protection is accomplished by means of extreme mental, social violence, and the extremely violent-intellectual demands of the dogma, which are required for a person to be admitted into the realm of being a "valid authoritative person within society." It is authoritative dogmas which also define the image of "true science and math" and this adherence to narrow dogma turns the wage-slave scientists and mathematician into a protector of a fixed viewpoint of high-valued knowledge. However, this overly demanding authority comes to be knowledge which serves only the narrow, monopolistic, dominating, business interests (the interests of the owners of society) within society.
The social-instrumental structure with defines both high-value and an "authoritative truth" for all of society is the media, and the ideas which are authoritative are the ideas which are to be expressed on the media, all of the media (including the alternative media).
Most of what the professional (peer-reviewed) science and math communities do, is marginal at best, and it is essentially irrelevant, where its focus is on creating (in a literary sense) [not in a practical sense of creativity] elaborate methods which are associated to unstable contexts which possess only fleeting patterns (measurably distinguishable, but in an unstable context) which are only useful within a larger global context (than the structure of observed stable measurable patterns) of measuring abstracted components of an (unstable) arbitrary context (a context within which stable measurable patterns [associated to the partitioning-components of the measurable attributes] do not exist).
That is, distinguishing features in an arbitrary and abstract context is not evidence that there exist stable patterns within such a context.
An idea appears to be about a context, but one also needs to identify properties, and one needs to possess an ability to measure these properties in a reliable context, and furthermore, these properties also need to be associated to (valid) measurements which are described within a context, wherein, the properties and the contexts are (should be) related to the capacities of human capabilities to create in a practical manner, to measure and to control the patterns. This is about the relation that a measurable descriptive knowledge has to creativity.
The unstable contexts, which nonetheless possess short-lived, identifiable (or measurable) [but unstable] patterns can be used... ..
... . either
in a context of feedback-systems where the "relevance of the measurable context" is difficult to define (determine)
or
in the random context of a transitioning system, [from a broken-apart system, so as to transition to its final (relatively) stable state], where this transition takes place under a context of component-collisions, and where the probability of these collisions is related to the rate of the reaction, ie the context of nuclear reactions... ,
... , this is one of the main business interests associated to our society's fixed way of organizing society, so that this fixed structure is upheld and maintained by extreme violence, in which the violence and coercion is needed to in order for the society to remain fixed, so that the monopolistic business structure can continue to exist.
In the context of feedback of locally measurable (and non-linear) properties the observed properties (observed in the context of a metric-space) seem to be "relatively stable," but in fact, are fleeting and unstable patterns, which are built upon abstract interpretations of contexts, [in turn, built upon an underlying set of fundamental stable material properties].
The social context of the descriptive structure is built upon an overly fixed social-structure, and the symbolic structure, which the owners of society impose on material constructs which define the products of businesses within society. If knowledge is structured primarily to be used to build weapons and to control knowledge and information then this is what people will be best suited to create.
However, the context of un-identifiable spectra, or the context of unstable events placed in a context of physical attributes which are measurable in a metric-space, is a descriptive context which possesses virtually no relation to:
1. the stable patterns [of "stable spectral-orbital material systems" which exist at all size-scales], nor to
2. valid models of chemistry,
3. models of life, or
4. mind, and even at
5. the higher abstract level of human experience, often labeled "religion," where one can perceive the "world as it really is," or as it could possibly "appear to be" in regard to the "true nature" of a living observer (What is the complete context of life?).
The dogmas of science and math are expressed in the social context of "intellectual exclusion," and it is formalized (or defined) by peer-review, where these authoritative dogmas are used to protect business interests.
This is possible because of the fact that the dogmas and the "elite structure of science and math" exclude the development of knowledge, in regard to creativity, which is not under the control of the monopolistic business interests (which the justice system so violently upholds), where business can control science by, controlling (1) an authoritative media (2) the laboratories, and (3) educational institutions, which are owned and/or controlled by the business interests, and thus these institutions serve these (same) business interests.
It is these institutions, and the associated authoritative dogma so presented by the media, which is used by the media to express both the identity (and absolute authority) of science and the business interests of those few people who dominate the society and its organization.
What are (math) patterns?
Patterns are:
1. consistent relationships, or
2. operators acting on quantitative sets so as to have fixed "consistent properties" related to the application of an operator on a quantitative set, and these consistent patterns are related to the "meaning" of the quantitative-set's elements (where quantities represent properties of: type and [measurable] size), or
3. stable shapes, etc.
Can the current descriptive language of mathematics and physics describe stable patterns?
Consider:
I. A new context which is identified by the special shapes (circle-spaces) which relate the local quantitative operators more directly to a more stable (and fixed) set of separable solution-functions (which might exist for a system's set of partial differential equations), where the process has a more significant, and more restrictive, geometric dependence (than does the notion of materialism), each dimensional level is given a more restrictive context, but in this new construct there is a many-dimensional context which is highly relevant to the set of observed properties, and how math constructs can be related to these observed stable, definitive patterns of existence.
II. Partial differential equation (a process for finding formulas for measurable properties of a system by relating local measures of the system's measurable properties, to the local measures of the containing space's coordinates), ie sets of locally linear operators which relate function values to domain values, seems to be a construct which is "less important in the new math construct" than are the importance of shapes.
III. But, in the current "descriptive authority," derivatives are being used to identify "local" spectral values "associated to random local particle-spectral events," so that operator-types are believed to be related to various spectral-types. Thus, the descriptive context is about finding (complete) sets of commuting Hermitian operators, which identify (in a unitary-invariant (or energy-invariant) context) a system's set of identifying local particle-spectral set which, supposedly, can be used to identify the system's set of spectral-measurable properties.
That is, the containment set is defined in a context of measurable, local, random spectral-events, so functions represent the randomness of the system's components, and the spectral sets represent the containment set of the system's identifying measurable properties.
After, nearly 100-years this idea has not been successful at a level of generality which is needed to make such an idea valid.
That is,
There are essentially the three ways in which to try to describe stable math-physical patterns... ,
I. stable geometry, which strongly limits both a descriptive context and the patterns it is trying to describe (the new context for physical description, the circle-spaces, or the very stable discrete hyperbolic shapes),
II. differential equations in a geometric context (unfortunately, this method most often leads to non-linear patterns),
III. differential equations in an operator context (this methods seems to only work for harmonic properties which possess actual physical attributes) )
... , so as to try to use quantitative descriptions so as to try to identify stable patterns which provide valid information, as well as control, over relatively stable (physical) system properties.
If a measurable descriptive language is without the properties of stability (ie stable properties of the description do not exist) and the descriptions are also without the property of quantitative consistency, but the descriptions are still associated to relatively distinguishable patterns, which, unfortunately, are unstable and fleeting patterns, then one's math methods end-up being only complicated exercises, which possess no content (or, at best, unstable patterns may allow for control by feedback in a fleeting pattern whose range of stability is even more difficult to identify than is the unstable pattern).
If a descriptive structure is associated to many elaborate techniques for "framing and describing" observed physical phenomenon, but if actual, generally accurate descriptions are not forthcoming from such techniques, and the context has virtually no practical purposes, then such a descriptive structure is without content, and is only the basis for elaborate, but irrelevant, techniques, which are devoid of any content, and such techniques are without the capacity to identify (in an accurate manner) stable patterns.
That is, the descriptive patterns of the current (overly authoritative) beliefs (dogmas) of math and science are (have become) irrelevant, in regard to using these (such) patterns to describe the observed, "relatively stable" and definitive, and (often) discrete, patterns of material systems. Furthermore, they are "descriptive" patterns which have no relation to practical creative developments. That is differential equations based on geometry work for some classical systems, and the operator viewpoint acting on function spaces only works for waves (harmonic functions) whose attributes have physical properties, but not for general, stable, precise quantum systems (whose defining property has been assumed to be the randomness of their spectra-carrying particle-components), so it seems that only the context of a very limiting geometric context which also defines a new context for the derivative as a discrete operator on discrete geometries is available for a valid way in which to represent and quantify descriptions of stable observed patterns.
The question is open: What other ideas are there?
When (If) math procedures are: non-commutative (in regard to both geometry and when used in the context of function spaces), non-linear, and indefinably random... .
(where indefinably random events are events which are neither stable nor calculable),
... .. then the math patterns, which these procedures are trying to describe, are fleeting, unstable patterns, which are neither "generally accurate," nor do such unreliable-patterns have any practical use.
That is, difficult math methods... , which are related to fleeting, unstable math patterns... , are descriptive constructs which have no content (and possess no useful information), in regard to the stable observed patterns which do exist.
That is, we are equal creators, and this needs to be expressed in a context of equal free-inquiry where a precise description needs to be related to some type (preferably new types) of practical creativity, creativity intrinsic to the intent of life, not creativity which identifies and maintains inequality and its associated violence.
Knowledge is not fixed, and knowledge does not need to only be related to some intricate instrument's further development, or to some intricate authoritative viewpoint about "how knowledge should be developed." That is, knowledge is based on elementary properties of language and the patterns realized which are related to these beginning elementary language structures are sets of assumptions, and contexts of a set of descriptive patterns. Furthermore, a particular set of assumptions, contexts, and interpretations is not moving toward an absolute knowledge, where this is because descriptive knowledge is limited as to the patterns which it (the language based on assumptions) can describe, and the limits of the patterns and/or the practical usefulness of a set of patterns (of a precise descriptive language) can be reached, so that further development leads to irrelevance and illusion. This is analogous to the idea that there are limits to the capabilities of instruments (precise descriptive languages built upon sets of assumptions), and other contexts might very-well be related to a better way to do the same (functioning aspects to which the patterns of language are related) capacities of the fixed set of (complicated) instruments.
The set of assumptions about which the current overly narrowly defined authority depends are both "far too general" and also "far too restrictive" based on an (almost) arbitrary narrowness emanating from (social) authority. There is the very narrow idea of materialism (which assumes that no-holes exist in the material-containing coordinate-space modeled as a continuum), continuity of dimension (or the holes of spaces which define higher-dimensions, and the spectral-lengths which fit-into these higher-dimensional constructs, get smaller), and randomly based spherically symmetric force-field geometry (often an inverse square field), which emanate from material-particle components, where a quantitative structure (a measurable pattern) is imposed on a blank-canvass (but consistent with materialism) either by means of a (geometric) solution to a differential equation, or by a set of operators acting on a function-space (which model the randomness of harmonic local point-particle-events), both of these structure-imposing constructs are defined upon what is believed to be a blank structure, wherein a prevalent spherically-symmetric inverse-square force-field is always assumed to be that which imposes a spectral-orbital structure, but wherein holes, twists, and cuts-points (in all generality) are believed to be relevant (valid), apparently for shapes imposed by material properties, or properties of high-dimension space whose spatial regions are assumed to diminish in size, while [and analogously] the high-energy spectra (observed in particle-colliders), whose origin is assumed to be in higher-dimensions, the values of the spectra must descend in size (implying increased energy). The idea is that if one finds either the force-field or the energy structure which applies to the operator structure (associated to a material system) then one can identify, by calculation on a blank canvass, the observed order of the material system.
The construct of "a blank canvass which hosts the "material" of random points of spherically symmetric force-fields, modeled as non-linear random relationships," has no relation to any (general) precise stable pattern which is re-construct-able from the laws of this context. This description has no relation to a stable pattern.
It is a descriptive context which is neither general, nor accurate (so as to have sufficient precision), nor practically useful. It is relatable to a state of free-material components transitioning between stable states, ie the reaction rates (or collision probabilities) of transitioning systems, where the original system has broke-apart.
Instead (alternatively), holes are prevalent at all dimensional levels (and in all subspaces), the dimensional structures are partitioned by an increasing set of spectral-orbital values as the dimension increases (at least on most [or some] subspaces), so that the spatial structure of the high-dimensional containment set is not "continuous between dimensional levels," ie furthermore continuity in n-space is defined by the continuity of (n-1)-faces of the lower-dimension metric-spaces, (or equivalently "the material-components," which the n-space contains, or a system's spectral-functions (or the functions in the function spaces), are tied to the geometric structure of the coordinates,
so that: orbits, angular momentum, the state of being free-material-components, and component-collisions, as well as the properties of physical waves are all "closely tied" to a limited set of stable shapes and the usual second-order differential equations, whose context is now (in the new context) limited to the prevalent shapes (of existence), on which both spectra and orbits are analogous constructs. These fundamental spectral-orbital properties are related to a hole structure of the shapes, but the shapes are placed in a many-dimensional context, which allows material-components to be contained on (or to exist on) "linear shapes," which, nonetheless, guide the material to an orbital structure based on the material trying to adhere to the geodesics of the (linear) shape (defining envelopes of orbital stability).
The spectral-orbital properties which determine the organization of material structures are defined by the geometric-measures of the faces of the (difficult to perceive) fundamental domains which determine the shapes of the metric-spaces and the material components which determine existence (though there can also exist condensed material).
The new interaction construct is general, but its stable properties are determined from a context of the metric-space shapes of existence.
Re-iterating
A new interaction-construct can be constructed which is general, but its stable properties are determined from a context defined by a many-dimensional set of discrete metric-space shapes, which, in turn, define existence.
The professional mathematicians and scientists in regard to descriptions of fundamental stable physical systems express symbolic nonsense, ie they provide a set of nonsense symbols which result in descriptions which are neither general, nor accurate (to sufficient precision), nor do they provide a practical context for useful creativity.
Physical systems which are very stable and definitive, but which are many-(but relatively few)-body systems, nonetheless, because these systems are so stable and definitive, it is clear that they are forming within a very controlled context,
so that the descriptions (of the professionals) which are based on:
1. (vague) randomness (which is an uncontrollable description for a system which is composed of only a few components),
2. non-linearity (quantitatively inconsistent, and chaotic), and
3. non-commutative (not invertible, or equivalently, not solvable, eg non-linear or spectrally-un-resolvable),
context, which is
4. contained in a continuum (a containing set which is far "too big" allowing logically inconsistent descriptive constructs to be put-together as if they belong to the same containment set), and
5. it is a description (when based on randomness) which begins from a global viewpoint (a function space) but the methods of the description focus on local spectral-particle events in space, ie it is a description which gives-up information leaving one in an inaccurate and non-useful context in regard to information.
It is a description which "in general" is not accurate, yet it also is a description which is "intent on" losing information about the stable definitive properties of the [assumed to be random] system.
That is the descriptive structure of the "dogmatically pure" set of experts of math and science is simply a bunch of nonsense.
Yet one must list the places and contexts within which it is a valid descriptive context:
1. It is a description which is relatable to a system whose initial conditions, and initial properties are carefully put-together so as to be a system which is easily broke-apart, so as to form a transitioning system which is chaotic, so that the rates of reactions (in this context, based on component-collision probabilities) are determined by cross-sections of the broken-apart components, where these cross-sections determine the rates of certain aspects of the (a) reaction,
and
2. They are descriptive contexts which relate a limited set of metrically measurable (observable) properties to a feedback structure, which is mostly associated to the critical-points and limit-cycles of a non-linear (usually classical) partial differential equation, where the range of relevance of the differential equation is difficult to determine or to control. Furthermore, the initial or boundary conditions of this type of a system relate to the properties of the descriptive context (or properties associated to the solution) of the system's differential equation in a chaotic manner.
These contexts identify structure related to (1) nuclear weapons and (2) guiding missiles and drones.
That is, difficult math methods... , which are related to fleeting, unstable math patterns... , are descriptive constructs which have no content (and possess no useful information), they are patterns which apply only to unstable contexts, where control emanates from a higher abstract and manipulative context imposed on properties which are only definable in a metric-space, and which requires a lot of preparation (in regard to sensing and reacting in the desired way to the detected properties), a context which is at-odds with the system's natural properties, rather than controlling a system by simple adjustments to affect the system's properties in regard to affecting the properties of several system-components being coupled together.
These professionals are deemed, by the media, to be the intellectual top-experts of the society.
Yet their failed descriptive context is claimed to be the best descriptive range that they can offer. Namely, a descriptive structure which essentially destroys the context of creative development, by the experts providing a failed descriptive structure.
Nonetheless, these experts proclaim that only "the dogmatically pure" can join in on the discussion.
That is, the professionals are getting high-marks (big salaries) [by the owners of society, ie those few who assign value within society] for playing a role of top-intellect in society. Yet their true goal, which they seem to not be aware of, (which is to develop knowledge, which, in turn, is useful and applicable over a wide range, in regard to developing practically useful physical systems).
All that these, so called, top experts do is to develop contexts which are hopelessly narrow in their application, but which demonstrate elaborate and complicated methods, but they are methods which do not describe stable patterns, they do not (one cannot use the laws of quantum or particle physics to) generally and accurately describe the observed stable patterns of existence (of general but fundamental quantum systems), and these descriptive structures have virtually no relation to practical creative development. That is, the experts can provide patterns which have literary interest to other experts, but these, essentially, unstable patterns... , (which are contained in an illusionary world) upon which the experts dwell... , have no physical interest (or they have no relation to the stable patterns of the physical world).
Like most aspects of the current society, those on the top tiers of society are held in high social esteem for being total and complete failures (the media and the corruption of institutions allows this).
This is the result of the justice system of the US society, where according to the Declaration of Independence US law is supposed to be based on equality... ,
(the point of "freedom based on equality" is about each person having the right to develop knowledge as they want (by the process of equal free-inquiry), so as to be able to create what they envision, and then give as a gift, which the individual can give to society in a selfless manner, where the society cannot judge their value, and the society is committed to giving everyone the material needs to live, prosper, and, subsequently, to create in a selfless manner [note: only in this context can a truly free-market exist, but the profits of the most successful products should be well below 1%]),
... ., but the elites, who opportunistically began administrating "the independent US nation," instead of instituting equality within the law, so that selfishness was to get punished, acted in a selfish manner, so as to base law on property rights and minority rule, [which is the essential law of the emperor of the Holy-Roman-Empire]. That is, the US governance began as a total failure, so as to be run by opportunistic elitists, who instead of instituting equality and "free-inquiry based on equality" so that knowledge and creativity were to be developed by the culture, instead the elitists in charge used to law to steal, coerce, and destroy, those in the lower social classes, in the name of their own selfish advantage, the selfish advantage of the few, ie power and production were based on social domination of the many by the few.
So we have the tradition of "western hypocrisy," where failure is rewarded if those who perpetuate it, are in the high social classes.
What is wanted, by the owners of society, is that the social structures through which the powerful derive their power are kept in place, ie it is a social structure which is opposed to new, creative changes and thus is is also opposed to equality and the creativity associated to equality. However, the traditional social structure which upholds dominant interests so violently, and it expresses its interest in lyrical creativity of the science and math experts... ., where these authoritative experts define the "literary" creative development of science and math, which is authoritative, but unrelated to practical creative development, and the owners of society support the "creativity" of the elite artists, those who also competed in a "narrow context of authoritative cultural value," and those journalists and intellects whose ideas are judged to possess cultural value, so that the ideas expressed are consistent with the ideas of (or can be used by) the owners of society, so as to be distributed by the material-instruments of the media which are owned and controlled by the owners of society... , then even the failures of the experts can become part of the social structure which allows the powerful to remain powerful. The top-intellects and top-artists are defined as a social class, along with artists and journalists, so that the intellectuals can dogmatically dominate those many-others who question the authority of assumptions, or who have different ideas. The main tool used to maintain the power of the owners of society is the single voice of authority which the media has become (most clearly controlled by ownership, or by a set of funding processes). That is, it is violence and domination (intellectual domination) which is fundamental to social power, not knowledge.
Knowledge is relevant, within today's social structure, only in regard to the creativity which is a part of the organization of society (ie business productivity) which, in turn, maintains the power of the few. However, the organization of society, and the use of resources and the ownership of technology within society, essentially, remains fixed and traditional.
For example, the many-purpose phone, eg an i-phone, is about developing 19th century ideas of electromagnetism, and the micro-chip circuit boards in these devices depend on 19th century optics.
Whereas identifying stability "as a needed property" in both math and physics, in regard to the useful descriptions of controlled (or controllable) physical systems, is a focus (in regard to the valid descriptions of math patterns) which the math professionals, apparently, have not considered.
Furthermore, very simple math patterns can be used to create new math patterns, which can be used to describe the stable material properties, so that these descriptions are based on a finite quantitative set, within which descriptive containment of physical properties depends, ie the containment set is not a continuum and the derivative and its integral-inverse become discrete operators (the continuum can, instead, be the set of rational numbers).
In fact, the math patterns of stability are very simple, and relating these simple structures (which are best characterized by the stable discrete shapes, or circle-spaces) to many-dimensions, can be done by a simple process of partitioning the dimensional levels of a hyperbolic 11-dimensional containment metric-space (base-space) by means of stable shapes, ie discrete hyperbolic shapes (or circle-spaces), so as to form a finite spectral-orbital set, where the sequences of spectral-size is defined (either increasing or decreasing) as the dimensional level increases, so that these size-sequences of spectra are fundamental in regard to how the description is organized, so that a finite spectral set is the basis for physical descriptions of the observed order which the stable (material and containing metric-space) structures of existence possess.
Furthermore, these simple ideas seem to be much better ideas than are the ideas which the experts possess, [ie than are the ideas that the professional "dogmatically pure" intellectual-army of experts (who work for the owners of society) possess], where the "top-intellects" of society (as proclaimed by the media, where the media is the single authoritative voice of the society) allow the ownership (the management) to bend the minds of these so called experts, ie the pay-masters bend the minds of the salaried-help, but those who possess the best resume's get the best jobs (as everyone competes to help develop the high-value of society, but the high-value of society are those ideas which are proclaimed [or expressed] by the media) the minds of the experts who serve the high-value (defined by the media) have their minds bent in any way which the management wants to bend their minds.
That is, demonstrating high-value in regard to an external model of high-value compromises the internal value (and thus the real creative value) of a person, and it destroys (or greatly limits) knowledge and creativity.
That is, the commercial world is related to a fixed stationary way of behaving or acting, a commercial structure is a very narrow context, based on a limited range of creativity and a fixed way in which to use material resources. The power of business monopolies depend on society not changing how it uses the material resources a business monopoly supplies to a society. The law is supporting this type of narrowness, essentially based on property rights and minority rule (creditor vs. debtor, smart vs. stupid, etc), and it supports such selfish actions with great violence. In fact, the economy is tied to a fixed narrow way in which to live and create, and this model of monopolistic economies is being used as a means to conquer ever larger populations, but it is being put into-place by means of extreme violence and coercion (often an economic coercion).
Does one want a society to be based on a fixed way to use material, and a fixed way in which one is to serve the material based, and fixed structure of society, and a fixed overly authoritative organization of descriptive knowledge, so that this type of power, and associated narrowly defined knowledge, depends on expansion in the form of an ever greater exploitation of particular types of material (usage)?
|
contribute to this article
contribute to this article
add comment to discussion
view discussion from this article
|
While interesting, your papers do not in any way constitute the kind of media that this site is intended for.