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Commentary :: Education
Social failure is also about the failure of “high culture”
31 May 2012
Capitalism has failed, the justice system has failed (and the justice system is used to destroy free-speech for the public, and this is done in order to protect the propaganda system), and despite the public’s belief in the propaganda about science both “fundamental science and math have also failed.”
The point is that many interesting ideas need to be considered, which could be related to many new ways to create, not simply the ideas and creative actions which monopolistic economic interests want funded, or not simply the ideas which the traditional authorities are considering in math and science (which are heavily influenced by the big economic interests).
That is, the dogmatic nature of modern (2012) science and math are funded to support (narrowness).
Capitalism has failed, the justice system has failed (and the justice system is used to destroy free-speech for the public, and this is done in order to protect the propaganda system), and despite the public’s belief in the propaganda “they are provided” about science and math, (but) in fact, the idea should be presented to the public that “fundamental science and math have also failed.” The observed stable spectral-orbital properties of fundamental general physical systems, from nuclei to the stable solar system cannot be adequately described (see below), and the limited descriptions are not practically useful.
The Propaganda system (by allying itself with the oil-banking-military complex within the US) has become extremely successful, and it has become highly protected, so that the propaganda system has been able to maintain the dogmatic absolutist institutions of western culture long after these institutions have failed.
Everything which is allowed on the media (on the propaganda system) is carefully decided, so that the main idea expressed by the media of the capitalist-oligarchic US society is that people are not equal. This requires that “the authorities” tell the public “what is true,” (because the public is not capable of determining the truth for themselves because the public is inferior). The result is that, science and math have become as dogmatic as religion was in the 1500’s, because “like the politician” science is also funded to do particular types of jobs (to create and develop certain types of well funded projects) and it is all upheld by an appeal to each person’s belief in inequality, a belief which was taught to them by the propaganda system. The result is that the propaganda system tells the institutions of science “what is true,” based on business interests. This is equivalent to the Pope telling Copernicus “what is true” in the 1500’s.

To reiterate, Capitalism has failed, the justice system has failed (and the justice system is used to destroy free-speech for the public in order to protect the propaganda system), and despite the public’s belief in the propaganda “they are provided” about science and math, (but) in fact, the idea should be presented to the public that “fundamental science and math have also failed.”
The observed, stable, discrete, definitive spectral orbital properties of physical systems from nuclei to solar systems cannot be described using both the laws of physics, and the math descriptive structures of spectra which are now (2012) being applied to stable material systems by the professional math science community,

including trying to describe the stable material geometric systems by means of using non-linear math patterns (in the spectral context of the heat equation and Ricci flows of metric-functions).

The main idea of all these papers is that math needs to be based on its own stable (math) patterns which are quantitatively consistent, so as to have a truly valid basis, within which the “intent of math” (used by humans) can be realized. Namely, to describe measurable math patterns so that the math descriptions are accurate for a wide range of general physical systems (to a sufficient level of precision), and measurements within the descriptions of patterns can be related to practical usefulness.

Math patterns are not measurable in a reliable (or practically useful) context if they are based on either
1. improperly defined (or indefinable) randomness, or
2. based on quantitatively inconsistent non-linear relationships, or
3. if the set structure upon which its logic is based is invalid,
either
the sets upon which math patterns are defined are “too big” so that distinctions between “what should be different types” are blurred, (by a set structure which is “too big”),
or
an unstable or invalid relation is being used to map between an identifiable property and its (assumed) quantitative structure [(an invalid relation is being used) so as to try to identify (the assumed) mathematical property’s mathematical patterns].

The problems which math has are about (or stem from) “how the math community has never understood the idea of a differential equation,” which was originated by Newton.
[But professional math communities cannot say that they do not understand something that “has to do” with math.]
Instead of admitting this problem…, which is the truth, and should be the basis for the educational process of free inquiry…, mathematicians have uncovered many patterns concerning a differential equation’s relation to either local measurement and geometry or to a function space (which is the domain spaces upon which the “calculus operators” are defined), but these patterns are described in a way which is too authoritative, yet they are (math) structures which have not adequately solved the problems upon which they are being applied, [or upon which they “do focus” (or should be focusing)], eg namely, trying to describe, with a precise math pattern, the observed stable spectral-orbital properties of all general material systems from nuclei to the stable solar system.

This is why the process of education, in regard to science, should not be about the dogmatic traditions of the math authorities (this is the same as requiring that Copernicus begin by assuming Ptolemy’s structures and then prove his new ideas), but rather should focus on both the simplest of models and the basic contexts and definitions so as to get at the basic ideas (or patterns) about which a descriptive structure is dealing.

One finds intellectuals (at western cultures absolute institution of absolute dogmatic knowledge), such as Chomsky, who cheer-lead for the absolute institutions, because their “reputations” have been built around these institutions (and from which they are given a voice on the media).
Chomsky claims that the professional researchers at MIT do “question authority” and consider “all possible assumptions,” and it is from their knowledge (the knowledge at MIT) that modern technologies are developed and then handed over to private industry.
But this is totally misleading, since “what is researched at MIT is exactly what industry wants MIT to research.”
MIT is an absolute institution which serves the interests of the owners of society.
Such a belief in a narrow absolute institution (“of learning”) misses the obvious pattern of over whelming domination which the owners of society wield over their society of wage-slaves.
Apparently Chomsky believes that….,
in a culture based on narrow authoritative absolute and monopolistic institutions wherein the owners of society have become dominant, deceptive thieves who base (build) and maintain their absolute institutions on extreme violence, wherein the public has been reduced to wage-slavery,
…, some institutions (such as the math-science based MIT) still have a shred of integrity.

MIT is based on dogmatic competitions of “intellect,” memorized, complicated dogmas…,
(similar to an old technology which has become quite complicated, eg a computer [existing since the 1920’s]),
…, which serve the interests of the owners of society. These absolute institutions are populated by many of the same dominant psychopathic personality types as compose all the unbalanced narrow absolute institutions of western society.
As Vannover Bush stated in the 1940’s “research to the level of proof of concept, and then let private enterprise develop the technology” . This is the idea which Chomsky is echoing, but it is clearly an illusion.

What has been proved in the “top” US universities are a set of concepts unrelated to the actual world of practical creativity, except that a certain subset of those ideas can be related to the world of military and military weapons. For example, probabilities of particle-collisions can be related to rates of (nuclear) reactions, but they cannot be related to in any convincing way to the observed stable spectral-orbital properties of a wide range of physical systems.

Institutions such as science and math, whose value can only be maintained if they accept “equality of ideas,” have made themselves ever more irrelevant due to their over-bearing claim to be in possession of absolute authority, an authority which they do not possess but which (nonetheless) is upheld in a context of militarism and police-state-ism. Function space techniques can be used to solve many differential equations, but they have not been successful at solving the spectra of a general quantum system in a wide ranging manner so as to provide a precise enough description to be adequately consistent with the observed properties of the quantum system.

Basically the level of the knowledge which is possessed by the absolute institutions of western knowledge is pathetic.

Consider:
1. Particle-physics provides no valid model for a general nucleus,
2. Quantum physics provides no valid model of a general atom,
Thus quantum physics (for either nuclei or general atoms) is not capable of providing an accurate description of the spectral properties of general quantum systems, ie the random function space structures which are used to try to describe the observed spectral properties of general quantum systems cannot identify the general quantum system’s spectral properties (for either nuclei or general atoms).
This failing is the basis for attributing to quantum description the property of being an “indefinably random” description.
3. Chemistry has no valid models for molecules and chemical shapes, nor of controlling chemical compositions. Chemistry has no idea about “how the chemistry of life” is orchestrated “to maintain a living system,” let alone “how this life is related to DNA.”
For example, spider genes are implanted in goats so that the protein of spider webs can be recovered from the goat milk, because chemists still cannot make this protein. That is, science (chemistry) is now only tinkering around the edges of observed patterns, but with no idea of their own about how these patterns can emerge into a stable context. Similarly the nuclear and thermonuclear bombs are based on the 19th century chemical model of rates of reactions being related to probabilities of particle-collisions (and this is also the basis for particle-physics).
4. Material science has no valid model of a general crystal, eg the superconductivity of materials has no valid model, ie the critical temperature predicted by BCS (superconductivity theory) was exceeded by high-temperature superconductivity, and the BCS model has never been “repaired,”
5. The physics of the solar system, in particular general relativity, has no valid model of the stable solar system [general relativity only deals with physical models which have only one-body].
Etc
Etc.
The only aspect of modern physics which has any relation to technical development which is different than figuring out how to couple a classical system to a quantum property is the laser. (That is, tunneling, micro-chips, spin resonance imaging, etc are all quantum properties which are coupled to classical systems, eg metals attached to crystals, so they are used in the context of classical physics).

The western society is collapsing since its knowledge has failed, and there is no new technical development, (all technical development of western culture is now the result of 19th century classical physics, or it is about nuclear weapons) This has been mostly brought on by the extreme domination of all aspects of the western culture by the monopolistic businesses and their associated propaganda systems which are controlled by the owners of society.

Society’s failures

The US society as a capitalist oligarchy (a propaganda state) which has failed as a society. This is easy to prove by considering the extreme amount of poverty and injustice which pervades the US society. One-half the population is either at extreme poverty or is being pushed into ever greater poverty, and 95% of the population is being attacked by the US justice system, as opposed to being protected by it.
After 9-11-01 the policy of the US was explicitly identified as a torture-state, and this heralds a society which is beginning to become engaged in the enslavement and extermination (by the oligarchs) of the public (over which the ruling few dominate in an extreme manner, and) those exterminated are those whom have no value to the oligarchs.
The economic collapse of 9-16-08 has begun a process of the complete destruction of the US society, as the people responsible for the collapse (the oligarchs) have shown their complete incompetence and criminality by destroying and looting the economic system, and then to have their “political puppets” re-capitalize the biggest failed monopolies (and then to become engaged in policies of torture, enslavement, and extermination aimed at the public) [oil should have been abandoned when J Carter said it should have been abandoned in the 1970’s.]
The economic collapse of 9-08 was a greater act of criminal terrorism than was the act of 9-01, but it was the ruling class who orchestrated the economic collapse of 9-08, thus the justice system and militarized state aided them in this act of economic collapse of 9-08.
Unfortunately, because they (the oligarchs) control:
the justice system,
the governing bodies,
the propaganda system, and
the education system, and
thus these oligarchs cannot be identified by the society as being both totally incompetent and extremely criminal [the true terrorists of the western culture].
(The British justice system identified R Murdoch as an incompetent and totally corrupt, which can only mean that R Murdoch is only a small player, an incompetent handler of the political puppets, but in the US Murdoch might (still) be the “puppet master,” he seems to control Obama, and corruption seems to run much deeper in the US political system than in the British system).

Knowledge of math and science

Thus one wants to consider math knowledge in a very critical context.
One wants to find the basic patterns which work, and present their simplest concrete structures (for educational purposes).
The authorities have no basis to claim they possess knowledge about general spectral systems which has either any useful value, or any accurate descriptive value, so as to provide a believable level of general applicability, in regard to providing an “acceptable level of precision” for a wide array of general physical systems.
Yet, spectral-systems are stable, discrete, and precise in their observable properties.

Are differential equations about the idea of local measures of measurable properties (ie properties of the solution functions), which are defined over (in the variables of) the function’s domain space and thus principally related to geometry on the domain space of the functions?
Are the rates of change defined on curved coordinates (or defined on flows) so as to identify vector fields on domain spaces of the individual functions (ie on the coordinates of the metric-space), where vector fields (also) have shapes?
or
Are differential equations (really) operators defined on functions spaces, where functions are usually defined as sums of many harmonic functions?

Can harmonic functions be summed-up so as to define a vector field (or a coordinate function when the vector fields are solved as a system of first order differential equations) where the harmonic functions identify a signal which expresses a general curved coordinate in a metric-space?

Are differential equations (sets of) operators defined as local coordinate transformations associated to a particular types of (say, metric-invariant) coordinates, which are defined on the base space of a fiber bundle?

But differential equations are essentially only solvable if they are:
linear,
metric-invariant, and
geometrically separable ie parallelizable and orthogonal,
ie defined on natural coordinates associated to the system’s allowable local coordinate transformations (or local coordinate changes). This seems to be true whether one is solving in a context of geometry or in the context of a differential operator acting on a function space.

But this means that summing over harmonic functions, in order to obtain an approximate solution function (or coordinate function) in the context of a non-linear differential equation is not a reliable method for finding a solution for math structures which are neither linear nor diagonal transformations of either metric-space coordinates or (diagonal) eigenfunction expansions of a spectral system.

Such non-linear math structures are quantitatively inconsistent, and the spectral set of general spectral systems cannot be obtained by this method, nor can the stable orbits of general planetary systems be obtained by this method. That is, it is not clear that using unstable harmonically summed solutions in regard to some “renormalizing method” of data fitting, or in regard to some irrelevant spectral expansion, ie the spectra used are unrelated to the spectra of the system being described, can have any validity.

Careful arguments within a fixed axiomatic structure might be best abandoned, so as to begin a new language based on a new set of assumptions.

Furthermore, differential equations only remain linear in the context of allowable, metric-invariant, local coordinate transformations so that the local coordinate transformations can consistently be kept in a diagonal form, and this requires that they are defined on (linear) shapes which have a non-positive constant curvature, ie with metric-functions which only have constant coefficients.

Many general math conditions are considered, but very little (or relatively little) useful information emerges from these general contexts.

The viewpoints which are consistently considered are:

(1) The viewpoint of geometry.
Solvable forms of a differential equation defined in regard to local measurable properties of both position and motion set equal to an equivalent geometric model of the same property, eg F=ma, is accurate to a sufficient level of precision over a wide range of general systems, and it is very useful in a sense of practical development of measured properties which can be used to build and control systems in a context of geometry of the solution function’s domain space. But in its classical form it is not applicable to quantum systems.

There is also the physical equation of energy, E = KE + PE, which (for gravity and static electric charges in 3-space) is about the relationship; that the (PE) potential energy (1/r) is proportional to the kinetic energy (KE). or In a more general geometric context, sectional curvature is related to kinetic energy.

Is a differential equation primarily to be about local measurement of a function (or a measurable property) being related to an equivalent number-type which is found by means of a geometric (or numerical, eg variation) relation?
It is a mystery about the math structure of existence which assigns a geometric relation to a local measures of motion changes.
How can a math pattern relate these two things (local measures and geometry defined by distant material) which appear to have no obvious pattern connecting them.
Why not consider action-at-a-distance and discrete Euclidean shapes. This is a new context which is being added to what is essentially still a classical math construct.

It is this geometric viewpoint which has led to all of our culture’s technical development, in mechanics, electromagnetism, and thermal physics.

Yet math has explored many patterns which relate local measuring to functions, both to function spaces and to geometric function properties.

How is geometry related to local patterns of local measuring?

Geometry (in the communities of professional mathematicians) is usually about putting together local coordinate functions (within small neighborhoods into which the shape has been partitioned) which are solutions to non-linear differential equations, related to either curvilinear coordinates (defined on the shape) or to general metric-functions defined on the shape (where by means of determining the shape’s metric-function local geodesics can be found on the shape). However, these non-linear patterns cannot be put together in a quantitatively consistent pattern, ie a uniform unit of measuring cannot be consistently associated to the non-linear patterns which are being described on the shape (or space, or manifold).

This general context (of non-linear manifolds) is assumed to depend on abstract concepts such as holes in a space (or holes in a shape) ie non-zero cyclic integrals of functions defined on these shapes can only exist about holes in the space, and apparently these holes can be found by the continuous deformations of simple closed geometric shapes, or rather by the inability to continuously deform simple closed geometric shapes because the shapes get “hung-up” by the holes in the space.
The general context depends holes in a space as well as, strange folds, turns, and twists about holes, and changes in a region’s orientation, all defined in a non-linear unstable context of a fleeting existing geometric pattern.

But do holes have a stable structure? (One would expect that holes are not stable.)
If they are stable, What is the structure of their stable properties (within what context can one be assured that they remain stable)?
Answer: The basic math structure for stable shapes which contain holes so that the holes remain stable, and which carry stable spectral properties, are the discrete hyperbolic shapes, while discrete Euclidean shapes can have properties of stability when they are associated to discrete hyperbolic shapes (eg by resonance).

These discrete hyperbolic and Euclidean shapes are much simpler to describe than are the abstract “holes in space.”

What does the simplification of math and physics imply for society? That is, great math generality reduced to simple linear, diagonal, metric-invariant (concrete) shapes of discrete hyperbolic shapes. These shapes can be related to both large stable orbital properties as well as to stable spectral properties, and the properties of sectional curvature of these shapes, 1/r, exists only for certain discrete values of r.
It means that knowledge including math knowledge’s relation to creativity can be simple stable and geometric (but now in a higher-dimensional context) and this context can give to the public very sophisticated creative skills, ie it equalizes society.

But a new implication in regard to the new math-physics descriptive context is that human creativity is not confined to the material world. This is because the patterns of discrete shapes extend up to higher dimensions but the structure of their interactions makes detection of higher dimensions very difficult (higher dimensions are hidden from any particular dimensional level), or at least it requires a new context for exploration.

The great generality of “holes in space” is not needed, since the most important examples of holes in space are the holes in the closed shapes which are discrete isometry subgroups (mostly discrete hyperbolic and discrete Euclidean subgroups) which are the cornerstones of the math properties of stable math patterns (both geometric and spectral).

(2) Is a differential equation primarily about discrete values associated to the oscillations of (or about) the system which averages itself so as to be values (averaged, or defined) about a measurable property, eg energy, momentum, etc?
Unfortunately, no relation between a system’s eigenvalues and local (or operator) properties associated to the system’s…:
geometry or
motions or
quantum states
(as these properties are assumed to exist in modern physics in regard to quantum systems)
…, have been found [which apply to general systems, and subsequently, identify each of the general system’s properties to sufficient precision] except for two-body systems which interact in a spherically symmetric context, ie the H-atom, but the radial equation of the H-atom diverges and is artificially truncated (cut-off) so as to fit data.
Ideas about function spaces and their relation to quantum systems deal with modeling the quantum system by means of global functions (eigenfunctions) related to particular discrete eigenvalues, where this discreteness is related to the randomness of particle events in space, but discrete material systems and global averages of random oscillating behaviors (defined about a system’s energy) cannot be reconciled; sets of operators cannot be found to relate the observed discrete values to either system averages or to global distributions of particle eigenfunctions, which are consistent with the observed system’s discrete properties.

The physical equation of energy, E = KE + PE, can be used as a differential operator to allow an eigenvalue structure to be defined on a function space. But it is related to only a few solvable, mostly artificially defined, quantum systems where these few artificial systems possess sufficient precision to correspond to observed data.
But this energy description of “energy eigenvalues defined on a function space” is given a probability interpretation, but for any many-particle (quantum) system (1) solutions cannot be found (or operators cannot be defined) and (2) it is probability information and this probability information cannot be used to control a system, yet these systems interact in a highly controlled context, since their spectral properties are stable, discrete, and definitive (precise).

When one looks in a demanding and critical manner at “how spectral math methods are used in the descriptions of physical systems?” one sees that they may work for circuits, but they are, essentially, unworkable (or irrelevant, or of no value) in the context of the descriptions of general physical systems wherein either the laws of quantum description, or the laws of non-linear geometry are concerned, ie spectral methods do not work for functions whose domain spaces are unbounded and completely contained within metric-spaces, wherein only metric-invariant contexts are even remotely close to being useful contexts for math description.
In a circuit, the frequency (spectra) of a voltage (energy) signal can be controlled, or identified by the loop geometry (eg phase shifts in the wave-forms of the voltage signal), but in a metric-space the ability to identify the source of a “spectral energy structure” seems to not be possible by means of either (the currently assumed) geometric properties of a quantum system or by cut-offs to the system’s spectra, or upper and lower bounds to the system’s spectra.
Thus there are two mysteries, “How do geometric relationships manifest in a metric-space?” and “How do spectral properties manifest in a metric-space?” But, the answers to these two questions seem to be unrelated to non-linear math patterns.
However, both questions can be answered in the context of discrete hyperbolic and discrete Euclidean shapes.

Operators cannot capture the spectral properties of general quantum systems, since operators (differential, or their dual) deal with either (the “currently” assumed) geometries of quantum systems, or with spectral cut-offs.

Apparently this is because the spectral properties (of quantum systems, or of spectral systems) come from outside of the space within which the quantum systems exist, and this also has little to do with the intrinsic (local) geometry (or particular states, or energy ranges within which a spectral system can be defined (or contained)) of a general quantum system, though it might seem that an energy term with a 1/r factor could contain spectral information, but it seems that it would only be accessible if the assumptions about the geometry of quantum systems changes from spherical symmetry to the shapes of discrete hyperbolic shapes.
Indeed…, that
“the spectral properties of quantum systems come from a structure which is outside of the metric-space within which the material systems (which are being measured) are being contained,”
…, is the main idea of particle physics, as well as all the other “physical” theories derived from particle-physics, eg string theory.
But particle-physics is simply the statement that “there is a hidden geometry, but the geometry (when associated to particle-collisions) is only saying that there is a set of ‘spectral bounds’ or ‘spectral cut-offs’ (where the cut-offs are determined by a method of data fitting), which determine the spectral properties of a quantum system.”
String theory is trying to say that geometry is significant in quantum description, but the circular argument concerning the idea of materialism associated to the process of measuring “which necessitates that measurements be related to material attributes,” requires that “the geometric properties only be related to a statistical non-linear (supposedly) measurable descriptive structure,” which particle-physics defines.
But this descriptive context is useless, “data cannot be fit” and the “information (of randomness) cannot be used.”
Furthermore, “more and more” elementary-particles are being added to the elementary-particle structure of particle-physics, eg the dark matter particle, the dark energy particle, the Higgs particle (where the Higgs particle was sort-of predicted) etc, thus, the probability structure is not well defined, ie the elementary-event space of elementary-particles seems to be unknown.
This undefined probability structure has the property of being an “epicycle structure” with which the authorities are trying to fit data by means of complicating the descriptive structures to the point where “their authority” cannot be questioned (by the public).

While, classically, geometry can be related to locally measurable properties so that the resulting description is accurate and useful in a practical sense, (but “how does this geometry manifest so that the differential equation is valid?”). On the other hand, in general, energy cannot be related to a set of spectra for “charged and inertial” material systems contained in a metric-space. Though the cornerstone of modern (2012) physical law, is that, energy can be (so) related to a set of spectra for “charged and inertial” material systems contained in a metric-space.


Rather the spectral properties of a quantum system are (can be) related to the spectral properties of an over-all high-dimension containing space, where a high-dimensional over-all containing space can have very significant geometric-spectral properties associated to itself. This can be made mathematically possible by considering a new math context, in a new containing space, with new types of models of material interactions. That is, the high-dimensional structures are macroscopic, yet they remain hidden. However, reconsidering one’s own living context may allow one to have a direct experience with the higher-dimensions, so as to allow a new context for measuring, when the patterns one is trying to see (expecting to experience) are properly (accurately) described.


However energy can be related to a set of spectra if the energetic signal exists in a geometric context of [an energy signal which has] (geometric) energy oscillations in time, eg voltage signals in electric circuits. But this is in the geometric context of the classical physics of electromagnetism, which, in turn, is contained within the geometric context of electric circuits. In a circuit, geometric measures, eg length of a circuit’s loop, can be related to the angular phase of a wave’s period, as in the cyclic period of a sine-wave, ie geometric properties of the circuit can be related to the intrinsic phase properties of a voltage signal’s wave-function.
However, the loop structure of an electric circuit can also define a hole-structure in a space, eg a space of loops.

Homotopy and co-homology are fairly general math constructs concerning group structures and function space structures attached to the holes of geometric shapes, (holes are assumed to be topological invariants, and thus related to the continuous deformations of homotopies, where holes (it is believed) can be detected by how holes (can) interfere with continuous deformations, in various shape-dimensional contexts) but the significant patterns of homotopy and co-homology are most clearly described in the context of discrete isometry subgroups (or discrete hyperbolic shapes and discrete Euclidean shapes).
That is, using abstract general constructs to explore a shape’s “set of (it is hoped to be, distinguishing) geometric-function-group properties,” is mostly unimportant. Rather, geometric shapes which possess holes are best described (and considered) in the simpler context, wherein “math stability” exists, namely, in the context of discrete isometry subgroups (or discrete linear shapes in a metric-invariant context on spaces of non-positive constant curvature).

The main idea of Thurston (geometrization) is that shapes of 3-space are of (or reduce to) certain simple types, and these simple types are mostly discrete hyperbolic shapes.
This idea has been proved by moving from the general setting to a simpler setting (of discrete isometry shapes) by considering the properties of Ricci flows of a shape’s metric-function. This is a differential equation which is the second derivative of the metric-function (reduced to the Ricci curvature tensor) set equal to a constant multiplied by the time derivative of the metric-function, ie the heat equation, where the general (non-linear) metric-function is being deformed in time.
But how can descriptions which depend on adjusting harmonic functions in a context of singularities (and critical points) of non-linear functions be believed?
Why should a metric-function of a fixed geometric shape naturally deform within the context of a set of harmonic functions with which one is trying to identify solutions to the heat equation?
Is the oscillation structure of harmonic functions needed to maintain a relation between a non-linear unstable shape and a uniform (stable) set of measurable values (ie a reliable set of coordinates for the shape) and thus the oscillations are more of an abstract idea not associated to the shape, or does the shape oscillate? If the shape is oscillating about some non-linear shape, then how is this oscillation possible? Where is there are spectral source for the non-linear shape to oscillate?
Is not a shape supposed to be stable, so as to not deform due to the shape’s own properties of curvature?
Can curvature be related to energy? Yes, sectional curvature can be related to kinetic energy. But, within the (fixed, ridged) shape “what would move?” Can sectional curvature be related to kinetic energy within the patterns of mathematics, or is this a physical assumption?
Furthermore, “How can an assumed continuity of geometry be related to discrete material models?” ie “How is a smooth geometry related to harmonic functions, where harmonic functions have a relation to discrete spectra?” But where do the discrete spectra come from?

The stable linear shapes of the “discrete isometry shapes” can be found by relating (equating) differential-forms (functions intrinsically related to geometric measures, which in turn, relate functions to integrals) to the stable spectral flows, defined on the discrete shapes, ie the equations of electromagnetism. The (spectral) flows are defined on the stable facial structures of the discrete shape’s relation to its “cubical simplex structure,” ie the equation is related to the properties of its fundamental domain, where a fundamental domain is one piece “of the lattice into which ‘the shape’s’ discrete subgroup, partitions the coordinate base-space” (where the base-space is the metric-invariant metric-space upon which the fiber group acts (in terms of local coordinate, and their allowable [eg metric-invariant] transformations)).

How are “energy-shape” (eg sectional curvature) and “spatial-shape” related? Answer: It is the same shape. (Is it?)

Why should the shape of space be the cause for space to deform itself? That is, “local curvature” should not deform the space’s shape.

The formulation of (1) is virtually always represented (by professional mathematicians) in a context of non-linear geometric properties, and in physical problems there is an absolute idea about material geometry, eg material interactions are always spherically symmetric (and the belief that material existence would always “define a set of continuous geometric relations” on the “domain” space of a function, which defines a geometric property, [for whatever fixed dimension that material defines]), where the dimension within which material is contained, is always given special consideration, ie 3-Euclidean space or 4-dimensional space-time, and geometry is most often related to an abstract manifold, whose description is non-linear.
Shape is almost always considered in its most general contexts, namely that shape is mostly distinguished by the set of holes which exist in a space, and about these holes there are many “folding” geometric structures, which can fold back on themselves and which twist and identify discontinuities and other types of critical points also exist.
This generality is unnecessary and mis-leading.

Newton considered (in regard to differential equations) how models of local linear measures, ie slopes of tangent lines to a (solution) function’s graph (where the function indicated an object’s position in space), can be related to a (local) slope formula for functions, which in turn, relates functions to other functions in regard to well defined patterns, whereas these patterns imply inverse relations.
Thus, Newton was able to formulate and solve (using inverse operators) a physical system’s differential equation, essentially following the ideas of Galileo, F=ma, and comparing his solutions to the “correct” answers provided (to Newton) by Copernicus and Kepler.

It should also be noted that Sommerfeld’s elliptic corrections to Bohr’s H-atom (of circular orbits) are as precise (in regard to fitting observed data) as are the other more modern models of quantum systems of the H-atom.
But the elementary-particles of particle-physics fit into the particle-collision model of nuclear weapons, and thus quantum description was forced into the structure of particle-physics.

Much emphasis is put on critical points of general (often non-linear) differential equations. In particular, where the derivatives (of a differential equation) are zero (or are undefined), where “about these critical points,” limit-cycles can (often) be identified.
But instead of questioning as to…, “Why these general (non-linear) differential equations have any stable (limit cycle) properties at all?” (where the property of stability might require drastic limitations concerning the descriptions based on solutions to (non-linear) differential equations)…, these structures are placed in spaces and contexts of even greater math generality (where it is assumed that chaotic patterns can be fit together), where their stability is even more questionable.


Eg Bizarre function properties, which relate spectra to (geometric) infinities, in the dual pairs of function-spaces and its dual-function-space, such as the Dirac delta functions and Green operators

( “kernels” of [linear] differential transformations of functions [not if “only one point is assigned to the identity (or zero point)” by the transformation.] Rather if many points are assigned to the identity (or zero point) by the transformation, then both (1) invariant properties of the differential equation as well as (2) boundary conditions are needed for solutions to exist (to be found)).

In the context of differential equations, Dirac delta functions are (most) often associated to singularities of a geometric system (also to the singular point of point-particle collisions), either of a spherically symmetric charge distribution (when a “solution function” is found), or the (untenable) elementary point-particle collisions (of particle-physics), where in both cases this is really about insisting that, there exists a very stable system structure, so that geometric infinities can be ignored, or the geometric infinities are placed in a new context, which is related to spectral properties, but without really knowing (in regard to being able to discount infinities) what aspect of the system is being related to spectral properties, which would imply that certain aspects of the (now assumed) spectral-system are stable, eg (hopefully) the spectra, yet the set of spectra which are assumed to be present are really not known. Why would particular aspects of a (spectral) system be stable? or Why would such an approximation (of infinity) work?


The problem with quantum physics, is that the spectral properties of quantum systems are not related to the geometry of the system, nor are they related to placing constraints on the domain space of either the geometric (domain of the solution function), or constraints on the eigenvalues of the eigenfunctions of the function space (the domain space for the set of operators which are supposed to identify a quantum system’s spectra), and, furthermore, the mass spectra of elementary-particle collisions, being imposed to adjust the quantum eigenvalues does not provide enough (spectral) structure for the particle-spectra to be of any value.

Rather the spectral properties of a quantum system are (can be) related to (1) a discrete hyperbolic shape for a quantum system, and (2) the spectral properties of an over-all high-dimension containing space, where a high-dimensional over-all containing space can have very significant geometric-spectral properties associated to itself.

This is a simple math context which has never been explored by the math experts, who have been trapped by a language. They are ultimately hemmed-in by the idea of materialism, and by their unwillingness to begin their educational efforts with the admission that they do not understand the context of differential equations, eg that non-linear geometries are unstable and that neither geometry nor ad hoc estimates and/or restrictions on the containing quantitative structures (of a differential equation’s solution function) can lead to finding a general system’s spectral properties.

That math and science is to be based on equal free inquiry.

Math science experts fit into the designs of a corrupt business class, which dominates society.
The math science experts keep science narrow and complicated.
The proof of this is, that the only science person of the 20th century who was interested in ideas was Einstein, and subsequently the only ideas entertained by science today are those ideas considered by Einstein, and this is too narrow.
Professional scientists are more concerned about their own authority than they are concerned about ideas. This is because the math science experts serve the owners of society, who want narrow ideas dealt with by experts who “correctly” deal with the details which are of interest to the owners of society.
But science and math only develop if ideas are considered.
Math professionals act as if they are honing-in on some “set of absolute math truths,” but they are really diverging (converging ?) into delusional worlds, and this decent into illusion is caused by the narrowing influences (on precise description) caused by adhering to authoritative dogmas, which are believed by a group of people who think that they can never be wrong (but apparently their truth is a truth which belongs to someone else, rather they use the idea of ‘truth” provided to them by others so that they can compete for important social positions, within an authoritarian educational and industrial system.

Equality and clarity are the correct disciplines of technical development, not memorization of abstract baloney.

By means of clearly questioning:
assumptions and
interpretations and
contexts and
questioning how infinities are defined, or whether infinities can be used, (ideas can be developed).
These are all questions of central importance, in regard to developing new ideas, and such an elementary context is the true structure of language within which ideas are developed.

Assumptions always need to be questioned.

(2) the viewpoint of harmonic functions, or bounded, integrable functions, with “natural” cut-offs (most often arbitrary cut-offs) in their domain spaces, where these harmonic functions oscillate about either an average (system) structure, or which oscillate about a set of approximate cut-offs within which is to be defined the pattern (one is trying to describe) which is assumed to exist (or cut-offs that the (assumed) pattern requires).
These patterns of oscillation require an associated infinite set of eigenvalues which are supposed to be consistent with the cut-off approximations, or so that infinities can be defined (in a context of oscillating functions) without disturbing an underlying stable structure.

But the natural domain of the eigenvalues is really a high-dimensional containing space which is associated to very simple discrete geometric shapes, and to conformal factors which exist between dimensional levels.
It should be noted that the dimensional structure of interactions (as well as the definition of material) makes higher dimensions invisible to any particular lower dimensional level, a dimensional level wherein material shapes are being observed and measured, and/or precisely described.

It is not the failure of classical physics which defines quantum physics, rather it is the high-dimensional spectral context within which the geometry of interaction (and the realization of a stable shape from an interaction) needs to be described, which determines how classical physics should be re-adjusted.
Though the interaction implies a general non-linear context, nonetheless the descriptive context is stable, linear, metric-invariant, geometrically separable, ie parallelizable and orthogonal, and based on the shapes which have non-positive constant curvature, ie tori and tori attached to other tori.

But more importantly, these many papers are about considering new contexts for mathematics.

Authority of math is based on the established patterns of authorities, and a belief by authorities, that exercising with word relations in a context of established (traditional) word agreement, is enough to establish a math truth.
It is claimed that this is all math can do.
But this is clearly wrong, since math is about describing measurable quantitative patterns, or relationships, and measuring is about building something new, based upon using the patterns which are observed in the world.
Truth is about a precise description’s relation to practical creativity.
Being able to measure should mean that one is able to build.
If what is being described is indefinable randomness, then measured values have no relation to building within a descriptive context. Yet, the physical systems, themselves, do build very stable structures in a very regular manner.
Thus the descriptive context of indefinable randomness should be discarded, and new contexts considered.
But this steps on the toes of the authorities.

Similarly the authorities of business are involved in lying and stealing, but their authoritative positions, essentially based within the justice system and protected by the justice system, has led people to believe that these corrupt business people are indispensable.
But this is far from being true.
The math authorities, and the business people are both errant and corrupt, and they should (both) have the carpet pulled from underneath their feet.

But in society the real error, is to base law on property rights (which has resulted in an interpretation of law which allows social domination by the few, who are now hopelessly corrupt), rather than basing law on equality (where equality is related to free inquiry and equal creativity).
Property rights was about material development at the level of survival, but that technology (or technique) has been developed.

The main issue today is creativity, and math is at the core of any type of controllable method of creativity.
But it appears that the best math is “very simple math” but it is defined in a new context, a math context which is not a part of the authoritative math traditions. Thus these new ideas are ignored.

Very simple math means that the context of creativity is very much about equality.

If one reads the math experts, or the public relations people who praise the math experts, one sees that the professional mathematician is all about the exclusion of the public from the expert class.
One has to prove oneself within a narrowly defined dogma wherein there is a right and a wrong, ie tests can be devised, to get into the professional class.
But the abstraction which these professionals describe have very little to do with practical creativity, whereas a measurable description should be about being related to building things in a practical manner. Abstractions which are used mainly to define an exclusive group are about the corruption of the intellect.



Should one consider:

1. Holes in space
or
the number of toral components of a linear shape?

2. Order of operations, where the commutative property is not satisfied for non-linear shapes (and thus non-linearity cannot be placed in a quantitatively consistent structure), and inverse operators, which can only exist in very small regions if the quantitative structures of the description of several dimensions, essentially, do not commute,
Or
Should one consider linear, geometrically separable shapes, where differential operators on functions are (almost entirely) globally diagonal, ie they (nearly) always commute?

3. For non-linear, non-commuting systems, which are either contained in coordinates or placed in a (harmonic) function space,
Should one consider:
Going to a limited, non-linear, fixed spectral structure which increases the dimensional structure of the spectra, ie the random collisions of elementary particles used to perturb the spectra of a wave-function, where the original spectral wave-function (which one wants to perturb) cannot be made to even come close to approximating the system’s spectral values, but in this case the higher dimensions which contain a fixed mass spectra, are irrelevant as perturbing agents, but nonetheless, this model conforms to the idea of materialism, and it mostly relates probabilities of particle-collisions to rates of (nuclear) reactions,
Or
Are oscillating functions, based on an indefinable spectral structure, being used to try to recover the system’s descriptive measurable structure, which has (requires) a stable uniform unit of measuring (which the indefinable spectra as well as the property of non-linearity destroy), so as to model an approximation to a flow of a vector field (or sets of differential operators) which is supposedly defined by a geometric shape (but “is the geometric shape stable or unstable?” ).

Answer: Neither case seems to be usable, thus the non-linear, non-commuting context seems to mostly be irrelevant.

4. Non-linear metric-structures, where one can be assured that chaotic vector fields, identifying the local “linear” structure of a geometric shape, cannot be placed in a continuous (or smooth) measurable context which determines a quantitatively consistent measurable pattern, since there are properties of both space and set-containment which cannot be formulated in a non-linear (quantitatively consistent) context.
Or
Place the descriptive context in metric-invariant metric-spaces with metric-functions which have constant coefficients in metric-space which have non-positive constant curvature (where a spherical shape is only valid if it remains unperturbed, and thus the sphere is only about identifying the bounding regions where stable structures of math description can be defined). Note: The sphere is about defining regions of opposite metric-space states, in regard to material interactions, eg related to the advanced and retarded wave solutions (or advanced and retarded potential functions) in regard to electromagnetism.

5. Are limit cycles a result of defining measurements within a geometric context wherein vector fields are chaotic, thus requiring a relation to an assumed geometry, ie to some bounding, stable geometry (a necessary region which has some stability [continuity] needed for measuring, ie is the system truly in a measurable context, ie the material is stable but the interacting system is transitioning in a non-linear context, so its measurable properties are unstable and quantitatively inconsistent. That is, there is a valid context for measuring (the material is conserved, or identifies a continuous geometric [or spectral] structure) but it is non-linear, so there can be (can exist) stable shapes in the descriptive context (associated to the stable geometric [circle] structures of the fiber Lie group).

6. For a bounded system should one consider a harmonic function space if neither geometry nor spectral cut-offs [or spectral estimates] can be used to determine the system’s observed stable discrete spectra,
Or
Should the system be placed in many dimensions, with the dimensional levels modeled as stable shapes, and lower dimension stable shapes are contained in each (independent) dimensional level, thus forming a new source for a system (at a particular dimensional level) to have (possess) particular spectral properties, ie the properties which already exist within the higher dimensional containment set, composed of different dimensional levels, which in turn, are modeled to have stable (spectral) shapes.




Spectra can be used in a discrete spectral context where the spectra of a stable (spectral) system can be enumerated, but how can the eigenfunctions be interpreted?
Are they related to random distributions of the spectral event to which they are associated?
or
Are they oscillations about a relatively stable geometric continuum?
That is, spectra can also be used in a geometric context, but what set of spectra can be related to any particular geometry?
and
By what principle are spectra to be related to any particular geometry?
One obvious relation would be spectral properties associated to some of the geometric measures of any particular shape.
Is the geometric relation to spectra the only valid inter-relationship which exists between spectra and a system’s description?
Must physical system description, even spectral systems, always be about geometry?



The book The Poincare Conjecture by D O’Shea, 2007, is an example of the type of propaganda which is used to maintain a math and physics model of the world which has become useless and inaccurate. The main idea of the book is that math authorities need to only consider the ideas which come from the authoritative past, and live within today’s authorities who have proven themselves by winning math contests.
But the context of the “proof” of the Poincare conjecture, namely Thurston’s geometrization, and Perelman’s proof “based on solutions to Ricci flows and renormalization,” has forced the hype about the authority of math and science to become understandable in regard to “how math complication is all about deceiving the public into uncritically believing in absolute institutional authority of math and science,” even though it is clear that these overly general, and overly authoritative ideas do not “hold water.”
This is because Thurston’s geometrization is about reducing geometry to its simplest “simple shapes” so that the math descriptions can be put into an understandable context, ie the context of cubical simplexes of the discrete Euclidean shapes and the discrete hyperbolic shapes.

Essentially, the set of allowable metric-invariant local coordinate transformations are diagonal for each cube, and defined by “angular properties between the cubes” at the vertices where they intersect, where the “angular properties between cubes” are related to either a continuous set of angles within one of the Weyl chambers (in the maximal tori of the fiber group), or they are transitioned at a particular angle so as to be caused by a “fiber group conjugation” which transitions to another Weyl chamber (in another maximal tori) in a discrete manner.
Will these be the reflection angles defined by Coxeter?
That is, “How can angles between cubes be defined?” Between adjacent edges (of the different intersecting cubes)? or Between the cubes’ diagonals?

By the way, much of the economic collapse is related to inaccurate math descriptions of risk, but they are descriptions based on what is considered to be authoritative math properties, or random properties which cannot be consistently related to numbers.

The point is that many interesting ideas need to be considered, which could be related to many new ways to create, not simply the ideas and creative actions which monopolistic economic interests want funded.
But the dogmatic nature of modern (2012) science and math are funded to support (narrowness):
only one context,
only one way in which to organize a descriptive language,
only one way in which to interpret observed patterns,
and
that is, essentially, the one way expressed by the dogmas of religion and/or the dogmas of science, both of which are funded to serve the monopolistic economic interests, which are the (singular) interests which the justice system exclusively serves, and which the corrupted governing body have been bought so as to uphold, by means of a propaganda system, ie the control of language within society.

Math is about the subjects of:
Quantity
Measuring
Algebra
Operators
Order of operation
Inverse operators
Shape (dimension)
Holes in space
Folding of shape
Periodicities
Twists of shape
Length
Invariant group properties
Set containment
Variables (arbitrary element of a set)
Functions (quantitative relations between sets, coordinates, shapes, random sets of discrete events, etc)
Domain sets
Set of function values, (a function’s value is a “measured value” defined on a set, ie a domain space)
Derivatives and integrals
Define operators on function spaces,
or
Define differential equations and their solution functions


Solution functions of differential equations (or differential operators) can be about:
Shapes,
Spectra, (but the spectra need to be relevant to the properties of the system which is being described), or
Randomness.

Note: The introduction of spectra into a mathematical description of a system (or a set), except for systems where a spectra is controllable, eg an electric circuit, it is not clear that the assumed spectra have any relation to a physical system, where often the spectral properties of the physical system are: stable, discrete, and definitive.

In regard to functions defined on spaces, or defined on shapes, there is a small set of basic types of function spaces:
Continuous functions
Smooth functions
Polynomials
Exponential functions (and logarithmic functions)
Periodic functions
Functions which converge to zero so that definite integration (on the function) is finite (or converges), eg L^2-functions.

Domain spaces can be:
Spherical
Unbounded isometric spaces (Euclidean and hyperbolic metric-spaces)
Discrete isometric spaces, both bounded and unbounded, (but not spherical, ie spaces of constant non-positive curvature)
Diffeomorphism manifolds.


Physics is about:

Containing spaces of material (positions and motions, where calculus operators inter-relate positions and motions of a material object) where materialism implies a particular dimensional relation for the domain space of a function,

Measuring distinguishable types of properties,
either
local measures of a physical property represented by a (solution) function,
or
an oscillating (random event) property of a particle which possesses a particular discrete spectral value of a system being described, where the system is being described with a function space and a set of eigenvalues of the stable discrete definitive spectral-orbital system,

Geometry (today, a general manifold geometry of an unstable non-linear shape, ie general relativity)

Discreteness (atomic hypothesis, as well as the observed stable discrete properties of a quantum system’s energy structure), and

Randomness (it is assumed that quantum systems are fundamentally random in regard to both (1) finding particles, which have particular spectral properties, as random events in space and time, and (2) material interacts are modeled by means of random elementary particle-collisions)

Force and energy are related by calculus, by integrating force acting on a test particle along a path in the test particle’s containing space,
Force is easier to think about for motions of a material object
Energy is easier to consider for thermal systems or in regard to continuous (or conserved) systems.

The main problem of physics today, but which is ignored, is about “how to relate a discrete system’s observed properties to the assumed set of descriptive structures?” That is, the observed stable spectra-orbital properties cannot be derived from the descriptive laws for general systems, and this is true for all size scales. There is only one idea which is applied, wherein 1/r is used in an energy operator (potential energy operator) along with some estimated spectral cut-offs, are used to obtain all the possible spectra, but the cut-offs seem to “not do the job.”
However, in some cases 1/r can be related to the value of the kinetic energy, but this would give a continuum of spectral energy values, and explicit relations of a spectral continuum to radial spectral values seems to evade these types of descriptive methods.
The angular momentum values for a spherically symmetric interaction give some crude estimates of a quantum system’s spectra, but the many-particle quantum system usually does not have spherical symmetry.

The main idea in physics today (2012) is about how to determine stable properties from an assumed random context. This is logically backwards.
Because, hidden in the idea of quantity is the idea of stability, a hidden axiom.

Randomness is mathematically valid only when the random set of events is finite and each event is stable. Randomness is not used in this context in modern mathematics, and this can be the reason that math has become so ineffective at solving for fundamental general physical systems.

Thus, the logically consistent structure of physical-measurable description is to begin with stability and derive the properties of randomness from an assumed stable structure.
This has already been done, but it is ignored.

Academics are self-absorbed people…,
characterized by:
Autism
Arrogance
Obedience
Aggression,
Competitive, and
Mostly they are from the upper professional class,
…, who believe that testing and contests are valid measures of personal worth, ie they are easily duped.

Of course they are also intimidated and motivated by the social condition of wage-slavery.

Academics are self-centered and arrogant, and subsequently they are protected by industry due to their successes within the contests devised for academic wage-slaves (to serve business interests).
Academics do not believe in equal and free inquiry, even though math and science demand equal and free inquiry, as illustrated by the birth of European science in regard to Copernicus proposing a new language different from the language of the authorities of his age.

Today’s successful academics do not care about knowledge, ie considering the limitations and possibilities of a precise language, which means that (descriptive) knowledge is about the elementary aspects of language, assumptions, contexts, interpretations etc. Today’s successful academics are all about authority and its associated complications and abstractions, but which have led the academics into a world of delusions.

Wage-slavery is how the justice system serves the banking industry.

The academic structure of the US was adjusted and developed after WWII, when the US society was being militarized and police-state-ismed, and Manhattan project physicists (those who developed nucl

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