Connect the “spiritual” with the material worlds
One can connect the "spiritual" with the material worlds if one allows the math context of physical description to change (where the "spiritual" and the material worlds represent different dimensional levels of the new (and correct) model of existence [see below]),
A new context which can be used to describe all the observed physical properties, ie it describes classical physics, and the origins of (what appears to be a fundamental) randomness, and it describes non-linear patterns, and it describes the higher dimensional structure of particle-physics (but the new description is either a macroscopic or a microscopic context, but apparently it is mostly a macroscopic context).
The "spiritual" is about "perceiving the world as it really is," or "mathematically modeling the (real) world which can be perceived in higher dimensions," along with the information which is associated to some surprising new models of living systems, which include surprising information about the size scale of life within these new models.
Life is such a highly controlled "material" system that it must exist within some very stable (geometric) context through which this control is possible, in a similar manner the stable, definitive material properties, such as the spectra of general nuclei, must emerge within a controllable context (all nuclei with the same number and same type of components have the same spectral structures, so the context of their formation must be causal).
The change in math structure is:
A containment set both
(1) ruled by the (unnecessarily narrow) idea of materialism (an idea to which particle-physics is structurally opposed, ie it has a higher dimensional structure than is allowed by the idea of materialism), and
(2) determined by a focus on functions as the primary model for measuring, or the function is the primary means upon which a model for measuring is to be dependent,
eg entropy depends on an abstract "function space" model for the density of energy-states, but has no clear stable structure by which this idea can be carried in a physical context.
For example, functions (in the current structures used for the math descriptions of the physical world) are
(1) often associated to spectra and randomness, and depend on being related to both "function spaces" and to sets of operators (where together the system's associated set of operators define [what are supposed to be solvable] the system's set of differential equations, ie a complete set of commuting Hermitian operators) and this relation between function spaces and a system's set of operators has the math structure of algebra and analysis, and
(2) to a lesser extent (in the current context of physical description) functions can be geometric (but in the current context this mostly deals with non-linear geometry and manifolds, where "function spaces" are again used in a context of averaging over quantitatively inconsistent, and thus chaotic, solution functions, and
(3) in regard to non-linear geometric functions, the properties of functions related to an unsolvable non-linear differential equation (which is used to model the non-linear geometry) is (crudely) related to critical points of the system's differential equation, which in turn are related to "limit cycles" which define boundaries for regions in the domain space of the solution functions in regard to which the various solution functions converge or diverge [move toward or move away from, respectively]).
The context of function spaces is, essentially, a math context of indefinable randomness, or data-fitting, where the data-fitting has a probabilistic model. [quite similar to the epicycle, data-fitting, structures of Ptolemy's model of the solar system]
Where the new math structure is changed
A new focus on stable, quantitatively consistent and logically consistent sets of geometric math patterns, which (in the context of functions) implies a context of linear, "parallelizable and orthogonal" (or geometrically separable, eg a differential equation is separable), metric-invariant, geometries (or functions)... ,
ie a context of mathematical diagonalization (of the matrices which compose the physical system's descriptive structure),
... , where these geometric spaces (or shapes) are of non-positive constant curvature, for metric-spaces whose metric-function's have constant coefficients.
Note: These geometries are, essentially, the discrete isometry and unitary subgroups of the classical Lie groups, as well as having these simple geometries be associated to symplectic spaces, eg x^p. So that, these geometries are the basis for stable physical properties, and the other random and non-linear math (or unstable and fleeting) structures fit into (or between) this stable containment structure.
These stable geometries are placed into a many-dimensional context, where the metric-spaces (at each dimensional level) are, themselves, these same discrete shapes.
These discrete shapes are related to "cubical" simplexes, which in turn, are related to geometrically separable circle-spaces, eg tori (Euclidean) and two or more tori attached to one another (hyperbolic, ie the equivalent of space-time).
In this context, material is equivalent to a (closed, and often bounded) metric-space, which have discrete shapes associated to themselves.
Our traditional model of material is that of objects of a certain size, which exist in 3-spatial dimensions.
However, in this new math model, the model of material interaction is very geometric, and this causes the "material" contained in the different (spatial) dimension metric-spaces to be geometrically independent of one another, ie it is difficult to perceive higher dimensions, especially, if we have limited our notion about what dimension and size we, ourselves, possess. That is, the observer can have a very different (real) "physical" structure which is not consistent with the idea of materialism (eg infinite extent).
The emphasis of physical description on stable geometry allows a high-dimensional containment space in which the dimensional levels are, essentially, geometrically independent of one another.
This new math context is about stability, quantitative consistency, logical consistency, and it is about the predominance of "simple" diagonal geometric shapes (ie diagonal, in relation to the matrices which are used to describe these stable geometric shapes). Geometric descriptions have shown themselves to be very relatable to practical creativity.
The current math structures are based on indefinable randomness and non-linearity, which are neither logically consistent nor quantitatively consistent, and they seem to have only a very limited relation to practical creative development.
The new model for measuring, when compared to the current (old) model of measuring, modeled as functions, is that of a function which is linear, diagonal (matrices) in its geometric-algebraic math structures, metric-invariant, and a geometric function.
In the new context, the spectral structure of material (as well as its energy-density structure) is a relation between (individual) discrete shapes, where these discrete shapes have well defined, stable spectral properties, [which are possessed by the many different dimensional (metric-space) subspaces of an over-all high-dimension containing metric-space, ie an 11-dimensional hyperbolic space (see D Coxeter about hyperbolic geometry)] and the existence of a resonance that these discrete shapes (must) have with the spectra of all the (discretely shaped) subspaces of the a high-dimensional containing space, where this large spectral set is related to all of the subspaces (sub-metric-spaces) which the high-dimensional containing space, actually, contains.
The model of material interaction is geometric (the functions which represent measurable properties emerge from a pattern which is primarily geometric), and depends on action-at-a-distance discrete shape which exists in Euclidean spaces, where gravity is, essentially, 2-dimensional (but contained in 3-dimensions), and electromagnetism is 3-dimensional (but contained in 4-dimensions).
The interactions cause changes in measurable properties, ie changes in (geometric) functions, and this interaction is based on a Euclidean torus which relates the material geometry, ie stable discrete hyperbolic shapes, to the geometry of the (Euclidean) fiber group by means of 2-forms (2-differential-forms) defined on the Euclidean shape (of an action-at-a-distance interaction torus). The (action-at-a-distance) torus changes with short time intervals whose time periods are defined by each (full) spin-rotation of metric-space states, where the metric-space states are modeled in (or contained in) complex coordinates.
The dimension of the "2-form space" (defined on the Euclidean shape of interaction) equals the dimension of the Euclidean fiber group. The local vector properties of 2-forms can be associated to the local vector properties of the base space, since they are defined on the base space, but it is a base space which is one-dimension higher than the dimension of the space which contains the material which is interacting.
Thus, the dimension of the "2-form space" exceeds the dimension of the material containing metric-space [[the base-space is one-dimension higher than the dimension of the space which contains the interacting material]] (the domain space for the material geometry, which the base-space contains) by at least [[more than **]] one, thus the direction of an interaction can be within a subspace of the "2-form space," (or equivalently within the fiber group) where only a limited number of directions [of the interaction] would be consistent with the geometry of the space which contains the interacting material. Thus, it is possible that some of the energy (or direction for a new rotation) of the interaction can exist in the "2-form space" (or fiber group space) so as to not immediately affect the material interaction... , an interesting possibility. (This is even true in 3-space, where the material is contained in 2-space**)
This could be the basis for "the envelope of stability" where the "new direction of rotation" would be in the (higher dimension) Euclidean interaction space so as to define a new circle in the interaction so as to define a (Euclidean) torus about an orbital path defined directly by the interaction, but the orbital path would exist within the interacting-material containing metric-space (not the Euclidean interaction space, ie the space where the [action-at-a-distance] toral interaction shape would exist).
One might hypothesize about "where this extra interaction energy might come-from?" Perhaps it is the from the set of interactions with the other individual many-bodies in the solar system which are different from the central mass (ie not interacting with their circular envelopes of stability), which contribute to the tangent direction (tangent from the space of the central mass and the one interacting planet of the 2-body system), and subsequently (contribute) to an "envelope of stability" for the 2-body (planet-sun) center-of-mass interaction.
This model of material interactions can be used (at the microscopic level) to derive quantum randomness (which exists at the "microscopic size scale" between the bounds of stable geometry), and it also allows non-linear interactions to be prevalent. The interaction structure is essentially similar to a connection-type derivative, ie a derivative defined in a non-linear context.
"Material" interactions, which can be modeled, essentially, as classical collisions, can be related to (suddenly) newly emerging stable systems through (or by means of) a resonance (between the interacting system and the spectral structure of the over-all high-dimension containing space), which can result in a stable new system (if the interaction has an allowable range of energy, so as to allow the resonance to become stable).
However, after a material system exists within a stable structure, such as a stable planetary orbit, the math becomes consistent with the math of geometrically separable "circle spaces," ie discrete hyperbolic shapes, which define an "envelope of stability" for the system (apparently, this envelope is defined within the range of energy, which allows the resonance of the system to become stable when it emerges from an collision interaction), eg elliptic obits can exist within an envelope of stability.
This envelope of stability allows what would be a many-body problem to be reduced to a 2-body problem, where within the envelope the other circular envelopes average to zero, the circles pull on each other in a symmetric way so as to have no affect on one another. Thus, leaving only the material in the envelope and its relation to the material near the center, ie a 2-body problem.
The context of interaction is Euclidean, which is to (can) be associated to a stable 2-body problem (such as the interaction between a planet [in a stable orbit] and the sun) in relation to the "mass averages" (or a center-of-mass coordinates, which redefines a 2-body problem as a 1-body problem, with the 1-body orbiting about the center of mass) a math context within which the Euclidean 2-body orbital problem is solvable, where the subsequent elliptic orbits must stay within the envelope of stability.
This could also be true for atoms as well, since A Somerfeld's elliptic approximations to Bohr's orbits of the H-atom are as valid and precise an approximation to spectral structure the H-atom's spectral properties as are any other techniques based on function spaces and indefinable randomness, which are used with some "difficult to (mathematically) justify" "data-fitting" spectral approximations, within the calculations on function spaces.
The new descriptive context is geometric, within which functions can be used to describe measurable properties, which fit within a bounding structure of the new (underlying) stable geometric structure for existence.
Though the linear, metric-invariant, locally diagonal properties of the geometric aspect of current physical containment and description structure, is only a small part of the current description, but it is the part from which, virtually, all technical development comes.
That is, today's math structures are based on indefinable randomness, and non-linearity, but nonetheless it is the "linear, metric-invariant, locally diagonal geometry" from which our society's technical development depends (eg electromagnetism related to: computers, TV's, etc, ie the development of 19th century science).
This is an inductive proof that the new linear, diagonal geometric context should be taken seriously.
Furthermore, there is the fact that the idea of materialism, and randomness, and non-linearity cannot describe spectral properties of general quantum systems, and are not even close to describing the properties of life. Consider the quite complicated chemical processes which perform in such controlled and relatively stable manner within living systems, where taken together... ,
(ie not capable of describing general quantum systems, nor providing a context through which life seems to control very complicated chemical systems)
... , are also reasons to consider new ideas, so as to sweep the unthinking (narrowly defined, technical) authorities down to their proper level of "intellectual equality,"
(as demanded by both Godel's incompleteness theorem [which implies a need to always adjust the elementary language of axioms and definitions and contexts] and the Thurston-Perelman geometrization [which states essentially that the discrete hyperbolic and discrete Euclidean shapes are the fundamental non-linear geometries of mathematics]).
The "false model of an 'expert of complicated technical language'" is an integral part of the propaganda structure, where the main message of propaganda is inequality, and thus the subsequent superiority of the few, and their right to "lord it over" the inferiority of the masses.
Thus the "oligarchic few" have the right to enslave the masses (by wage-slavery) because of the superiority of the "oligarchic few."
This is the idea (of masters and their wage-slaves) which the American revolution opposed, where the American Revolution, which emerged from egalitarian Philadelphia, Pennsylvania, said law must be based on equality and the rights and welfare of the governed, and that the "spirit of the law" needs to be enforced (ie law is not about the oligarchs discussing with the court how the "letter of the law" should be framed to support the needs of the oligarchs). Furthermore, the law does not need an army of "justice system" officers to impose the letters of the law which the oligarchs want imposed on the public. Pennsylvania had no police at the time of the American Revolution.
This notion of equality means each person has a right to equal free-inquiry (one does not have to technically qualify for a vocation within the hierarchy of value defined by the oligarchs, eg earning PhD's) so that (relatively) elementary descriptive language can be developed (as [correct interpretation of] Godel's incompleteness theorem implies, and as evidenced by the geometric discussion about math in this paper) so as to be related to practical creativity, and leading to an American society where everyone is an equal creator.
Scientific truth must not only be consistent with data (but it is also an important point as to "what data is relevant?" ie trying to describe too much detail leads to confusion), but the scientific description must also be practically useful, in regard to creativity.
Note: "Indefinable randomness" is based on elementary-event spaces whose elementary events are:
(1) not stable,
(2) they are indefinite (the spectral of general quantum systems are not calculable),
(3) they are not conclusively defined (the elementary event space is an infinite set), and
(4) further elementary events keep getting added to the elementary event space, eg the dark-matter particle, ie counting events is not logically consistent in such a (set) context. Thus, the probabilities for such spaces cannot be valid, ie it is a description of nothing except the randomness that is observed between the stable geometric shapes of metric-spaces.
Note: The physical property of entropy being modeled as an abstract mental (or math) structure is similar to the descriptive structure of particle-physics, where
String-theory is all about trying to provide a geometric structure for the higher-dimensional assumption which is associated to elementary-particles, but in the geometric model of string-theory the idea of materialism is preserved, and similarly
In regard to action-at-a-distance, but now action-at-a-distance is a concept which has evidence to support its assumption (or claim), eg A Aspect's experiment concerning non-locality, but also, non-linear (classical) models of satellite orbits assume action-at-a-distance, and these action-at-a-distance models are actually being used to control satellite orbits
[this could be interpreted to mean that the properties of material inertia are contained in Euclidean space, an idea which E Noether proved long-ago (in regard to spatial displacement symmetries)].
In regard to physically measured properties,
there are the:
(1) geometric properties of classical physics (where this new math model is mainly consistent with the most stable of these physical models, ie essentially the linear and solvable models of classical physics, ie the models upon which (almost) all the technical development of our civilization depend.
(Note: Observed quantum properties can sometimes be coupled to classical systems, eg the transistor, spin imaging, tunneling etc, and thus used, but these uses do not depend on the calculations of quantum descriptions, eg However, the spin properties at crystal lattice sites have not been coupled to classical properties [such as electrical currents] and this is a failing of the quantum model of the crystal. This is related to the overly hyped idea of quantum computing, remember that fusion still has not been related to a cheap, clean energy source, something promised by the nuclear physics community in the 1950's).
The only models of quantum physics which seem to have relevance are the H-atom and the quantum system modeled as a box (not a convincing list, especially when the spectra of quantum systems are so stable, discrete, and definitive [ie these systems seem to exist in a geometric (linear, diagonal) context of controllability]). It should be noted that both of these systems (H-atom and box) are geometric, yet quantum randomness is not consistent with geometry. Nonetheless, the model of "quantum interaction" is the highly geometric model of particle-collisions with a non-linear connection.
(2) the state properties of thermal systems, where (closed) thermal systems (in thermal equilibrium) are modeled by scalar functions (p, V, T, N, Energy, Entropy) where energy and entropy are placed into linear 1-forms. The functions upon which the exterior derivative acts are built around the scalar functions of entropy and energy, and the rules of "conservation of energy" (ie energy is a continuous function) and "the increase in entropy" (ie heat flows from hot to cold), where now, in the new math structure, there is a geometric model for the "density of energy states," as well as conservation of number of a thermal system's components (ie atoms). The property of a thermal system being closed seems to force the conserved values of energy and component-number, to remain consistent with the metric-function associated to the measurable thermal property of volume, so that the context of differential-forms is really about the measured thermal values being consistent with a metric-invariant metric-space (associated to volume).
Of course this thermal model has a relation to the statistical properties of inert-particles colliding in a geometric context.
(3) the spectral properties of the unexplained stable properties of general quantum systems. The claim is that within the function space there exist oscillations about some geometric structure for the quantum system. In a general atom (or H-atom) this oscillation is about a 1/r singular geometry. Thus, one can ask, "How is discreteness selected, in regard to a 1/r term, which has no distinguishing discrete physical attributes?" The solution to the radial equation (the differential equation which contains the 1/r term) diverges, but arbitrary truncation of the series can be selected so as to fit the data. Why? No answer (other than, "it works"). However, discreteness based on arbitrary spectral approximations cannot be realized on the 3-body problem.
Today, so called, physical models of observed physical properties are most often about manipulating abstract math models, and using overly simplified models (which in turn, are made very complicated) rather than they are about assessing and re-interpreting the observed properties of the physical system.
(3b) the spectral properties of classical-waves fit into "math context" of continuity and geometry, but the geometry of electric circuits are 1-dimensional, and often quantum discreteness is an assumed property of a system of electromagnetic-wave's spectral values, furthermore spectral approximations have physical (or system, or geometric) causes [but the cause for a quantum system's discrete spectral properties is still a very big mystery].
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