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State of man

Is mankind about violence or about creativity?
Of course mankind is about creativity
If
oligarchic rule is based on: violence, monopoly, and propaganda; then the key to opposing this failed social structure is propaganda... ,
since "the rules are bought" from the "propagandistic political structure" (the propaganda of selling laws, which are put-up for sale by the government [by the politicians, who become a part of the propaganda system]) so as to exclude competing cooperatives, or to exclude competing alternative energies etc, while the destructive monopolies are protected by the US justice system,
... , thus the focus of those who support equality... ,
(vs. those who support inequality, as expressed by the propaganda system) is to be about breaking apart propaganda ie this is done by free speech,
... , is (should be) about presenting new ideas which are superior to the existing dogmas, and necessarily this depends on talking about ideas at the level of assumption, interpretation, contexts, and containment... , [authoritarian science is not valid science, it is mostly about "nuclear weapons engineering," though "global warming correlated to CO2 concentrations" is obvious; according to the propaganda system those who hint at challenging "authority based science" are also grouped together with the "deniers of global warming." But this view, defined by unresolved opposites (the structure of communication within the propaganda system), is really about the deep-cut into the psyche which propaganda makes. The CO2 concentrations being correlated to atmospheric warming are as "strong correlations" as are the correlations between vitamin C and scurvy.]
... ., but it also means that these (new) ideas will be excluded from all "funded media," alternative media are afraid of new ideas, since the new ideas are not authoritative, where the public demands (thanks to the propaganda system) that they (the public) be protected from ideas which are not authoritative. That is, they (the public) demand that someone like Copernicus not be allowed to express their ideas (in any meaningful way), this belief is apparently because they (the public) believe the propaganda, that our culture already possess absolute knowledge concerning science and math.
Then
"What other forms of social organization should be considered?"

and in regard to this,

"What is the best representation of man's natural interests?" :
Either
"domination and violence"
Or
"creativity and equality" ?

The US Revolutionary War was about opposing "rule by domination," and instead "base rule on equality" (it followed the Pennsylvania colony, which was based on equality), but the US society (the other colonies), at that time, already existed as societies of "rule by ownership," it was a copy of European society, along with all of its hypocrisies, and they followed the idea of "rule by violence,"
thus the rich could railroad a "law based on property rights and violent domination," ie the US Constitution,
yet this was not "made law" until the Bill of Rights was "agreed to," but the rulers have never enforced the Bill of Rights, and
thus the Constitution has never been a valid form of law.

The only way in which to rid the country of all of its (overwhelming destructive) corruption is to have a "new Continental Congress" and place law within a structure of equality, wherein true "selfless giving" can be expressed, and the true relation of descriptive knowledge to practical creativity can also be expressed. To form an equal society where everyone is an equal creator, so that a "truly free market" can exist.
In an equal society the focus on inter-personal judgment is to be judgements about: selfish-ness vs. self-less-ness (one cannot judge another person's creative contributions), but acting for selfish advantage is easy to detect over time.
Today, a person's value is judged based on their contribution to the destructive monopolies of the oligarchs, and this judgment is enforced by means of extreme violence, ie one cannot steal a loaf of the oligarch's bread.

The state of mankind

Is man about:
(0) material needs for survival (but this is minor, hunter gatherers had more free-time than does modern man),
(1) knowledge and creativity, where creativity is an inward virtue (an expression of personal power) and it (creativity) is thus done selflessly, whereas the material needs for survival are readily available from the earth.
(2) selfish, violent (animalistic), interested in controlling material-properties for one's own selfish exploitation (in a way consistent with a narrow set of needs defined by the few for the people within society, narrowly defined by some selfish controlling person). That is, this is about "conservatism," where people are led to insist on the current stable structures, and in so doing they support the social structures upon which the ruling few base their social power, so that this structure of selfish exploitation, within a context of knowledge and narrowly defined social needs, is identified (or confined) and upheld by even greater violence, in a society where man can be reduced to narrowly defined robotic (but animalistic) absolutes.
(3) sexuality, and selfish sensuality, for the building of a larger narrowly defined community with an ever greater population (empire built around an absolute "truth"),
or
for the purpose of maintaining DNA (another absolute truth, but in the context of materialism which is ruled by indefinable randomness) in an environment of competition over... what?... absolutes, survival, absolute hierarchy... ?
(4) sexuality for procreation.

If (1) is true, then society is about providing material needs for survival and providing a culture which is about knowledge and creativity, similar to the early colony of Pennsylvania.
Law is to be based on equality and on "not overly exploiting resources."
If (2) is true, then law is to be based on property rights and minority rule, a minority whom define knowledge and its uses. In such a society narrow hypocritical virtues (morality defined in absolute terms) are imposed on the people, and survival is based on fitting into the "law of this jungle" of a narrowly defined society which supports the selfish interests of a few, which are upheld by extreme violence. (3) is a part of (2) when business is placed within a context of (material based) science and propagandistic virtues, [though DNA may be important it possesses no absolute position within the knowledge about life, in regard to such knowledge which we actually possess].

(2) is the model of the "Holy Roman Empire" (or equivalently, of US Puritanism), where extreme violence is used to uphold absolute-values and to exploit the resources of "personal property" for selfish purposes attached to (or consistent with) the social hierarchy, (related to possessing knowledge within a limited, narrow, social framework, which uses material resources in particular narrow ways within a stable social hierarchy).

(1) is about following the "spirit," where virtues have value within an individual person, but have no value as absolutes, used to measure social worth, and impose an arbitrary hierarchy, upheld by extreme violence.

What is knowledge? It is directly related to the context of creating, and is
either
perceiving existence as it really is (and creating directly),
or
it is about using (precise) words and measuring to identify truthful patterns (of quantity and shape, consistent with observations) where these consistent patterns can be used for practical creativity, measuring and building etc.

Are words to be used in an absolute manner, so as to realize and absolute truth from which all possible creativity emerges?
Or
Are words to be used primarily at the level of: assumptions, interpretations of observed patterns, so as to be placed in many varied contexts, and to have many different ways to envision containment, using many different identifiable patterns (of quantity and shape), and organizing ideas and concepts in many different ways, such as the following organizational method:
1. Set containment
2. Identify properties and their measuring values
3. Determine models of measuring
4. Identify measured properties
5. so as to have a precise description which is (practically) usable in regard to practical creativity (though creativity does not need to be based on, nor depend on, the material world).

Narrow, overly authoritative "truths," lead to descriptive patterns which become overly complicated and which have no practical value because they eventually become "truths of an illusionary world" of words and "icons of value," which are unrelated to practical creative development.

Equal and free-inquiry is about discussing ideas so as to "discern a truth" as a precise description which is geometric, so it can be used for a practical type of creativity.
There are many types of practical creativity, and it can transcends the material world by using a geometric map of higher dimensions. Many different descriptive structures can be invented.
A descriptive truth is not absolute, it fits into a context.

What exists within our absolutist, extremely selfish, and extremely violent society today (2012)?

A limited set of resources is being dangerously exploited for extremely selfish purposes.
The exploitation of these resources is being protected with extreme violence, ie state-aided corporatism.
Exploitation through propaganda and extreme violence, done by a few oligarchs (council of emperors), has resulted in the impoverishment of over 65% of the worlds populations, throwing many of them into extremely violent wars (control by psychopaths) as well as living under tyrannies (further, control by psychopaths).
Only about 7% of the world population fair-well materially and socially (or about 12% of the US population fair-well), under this social organization, and these 7% live extremely destructively, they are absolutists, and live violent and wasteful lives, though they view themselves as being peaceful and concerned, while they see themselves as possessing a set of superior intellectual truths (the truths of the Empire righteously being imposed on the ignorant masses of people).
They assume that their knowledge has "superior value," but their knowledge has become untrue.
Yet, they insistent on an absolute-form, in regard to their failed knowledge, which is imposed by a propaganda system on all the population.

What knowledge does this system rest upon?

Propaganda is based on absolutes defined in narrow contexts
Law is based on the selfish interests of minority rule, expressed in an absolute fashion as property rights, which are upheld by extreme violence.
Social hierarchies ruled by a few; control and manipulate society and its absolutely defined institutions [oil, military, finance, propaganda, big-pharma etc]
This is the model of the "Holy-Roman-Empire" of Constantine (or equivalently, US Puritanism),
The power of this social hierarchy is also upheld by the:
19th century physics of: electromagnetism, thermal and statistical physics, and mechanics.

What has: quantum physics, radioactivity, particle-physics, general relativity, string-theory etc, brought to the technical development of society?

Some quantum properties can be coupled to classical systems (usually electric circuits) and this has allowed clever "material use," and miniaturization of electric circuits, which has aided computing and its circuitry, but the technical systems are still computers, TV's and thermal systems etc eg 19th century science.
Technologists have been able to manipulate material properties, but this is almost entirely the result of clever lab work and classical physics, though applied to a very poorly understood crystal lattice structure.
Nuclear weapons,
A form of nuclear power which is dirty and "socially unsafe," (used primarily to maintain nuclear weapons) and
Lasers.

And that is about it, nuclear weapons and lasers,
... , otherwise technical development is still the development of 19th century physics.

That is, quantum physics, particle-physics, general relativity, string-theory etc are all scientific failures, since at best they fit very limited and/or "cherry-picked" data (specially selected data), they cannot describe the observed properties of general quantum systems or gravitational systems with more than 1-body, and they have no relation to practical creative development. The nuclear bomb is modeled after a 19th century chemical model of "the rate of reaction being related to the probabilities of particle-collisions."
As scientific theories they should be judged to be "utter and complete failures," yet they are used in propaganda as icons of "superior intellectual value."
Their failure is a result of the math which is used to model these theories.
The basic patterns of math upon which modern (2012) science and math descriptions are based is indefinable randomness and non-linearity (which is also indefinably random), where one can conclude that stable highly ordered systems cannot have their stable properties described by using the patterns of randomness.

However, quantum systems are very stable, definitive, discrete systems, and this implies highly controlled physical systems which need to be modeled with very stable math structures, eg linear, metric-invariant, and solvable (geometrically separable), ie the useful math structure of classical physics.

The math of the authorities is based on:
Set theory
Geometry
Algebra
Analysis
Topology.

Set theory uses sets which are "too big" leading to lose of clarity.
The geometries which are (almost) always considered by mathematicians is non-linear geometries of manifolds, algebraic geometry (the geometry of polynomials, which oscillate, so it is similar to the geometry of circles), or the more general subject of topology, which focuses on "holes in spaces" and continuous deformations. This has "too much generality" associated to its structures, and it has led to confusion (they seem to have no global context within which order is stable) and nothing of practical value has emerged from these descriptive patterns, eg string-theory is mostly about piecing together meaningless, invalid, abstract patterns of math.
The vast majority of math is based on function spaces and their associated operator spaces, ie analysis. Used to solve spectral systems... ,

[which it can do in the classical context, of modeling systems with geometrically motivated differential equations where physical properties are continuous and conserved, the waves have physical properties associated to themselves, and there are causes within the system for spectral approximations and cut-offs, as well as when classical electromagnetic waves are placed into a quantum context then a discrete spectra is assumed.]

... , but not for quantum physics, particle-physics, or general relativity.

The function space techniques are based on the idea of indefinable randomness, and when used in quantum physics, or particle-physics, or to identify financial risk, or for non-linear geometry they do not provide either valid information, or an understandable model, eg particle-physics is a permutation of a wave-structure which fails to identify the spectra of general several-component quantum systems, and such a permutation, in turn, requires a readjustment of the nature of space and its relation to energy. This is deeply absurd.

That is, non-linearity, and indefinable randomness contained in set structures which are "too big" are failures as identifying a basis within which to form math patterns, and their descriptions have (mostly) turned out to be useless, and that is why technical development is still about developing 19th century ideas about science. Propaganda has turned "science authorities" into over-bearing dogmatists so as to be in charge of the religion of materialism. These science authorities function mostly as "icons of high intellectual value" within a propaganda system, since their science and math is virtually useless.

Capitalism has failed because it is narrow and monopolistic. Basing law of property rights has allowed monopolistic capitalism to turn government into a propaganda system, which serves the interests of the oligarchs (the few owners of society), so government has failed and the corruption of the justice system is the main cause of all the corruption and failures of society, because by the justice system upholding "might makes right" instead of equality, an authoritarian state has emerged defined by narrow markets and the absolute dogmas of religion and materialism.
[Where, according to the Declaration of Independence, equality is the basis for US law].
Law has degenerated into a discussion, by the oligarchs (with the propaganda system) about the "letter of the law" being placed into a context which supports the narrow interests of the oligarchs.
Nonetheless (or of course) the propaganda system still "rules the day"... ,
(and of course this is because it is the only voice allowed, which is the result of the public demanding that only "authoritative truths" be allowed in the media)
... , despite a clear sign that the hierarchical social institutions have failed:
energy,
science and math,
justice,
capitalism,
monopolistic businesses,
but the violence centered governing and propaganda systems have not failed,
... , except that the propaganda system is the reason that all the other social institutions have failed.

Nonetheless, it is the interests of the monopolistic businesses about which the propaganda system expresses great amounts of progress are still being made, by this narrow monopolistic system which propaganda serves.

The media insists on maintaining an illusion of careful-correctness (whereas it misrepresents and deceives) and excluding all voices, but the one-voice "which is allowed,"
... , it maintains the illusion that all the failed institutions, about which the propaganda system has been built to serve, are "not failed"
... but rather they represent institutions of grand and "superior value."

By destabilizing almost the entire world, most choices of societies are between tyrannies and extreme violence (or at least that is the image).
That is, though it has failed, the propaganda system (or [military] communication systems) is so highly controlled that the image of high-value is all that is needed... ,
as the west drags the world into its special style of barbarism,
... , where different sides represent different illusions of absolute truths, defined by a social hierarchy upheld by extreme violence and the propaganda system, ie military communication systems.

The only way to be-fuddle a communication system (a propaganda system) built on sets of "dialects of Hegelian opposites" is to be outside such a set, but this is really what Gödel's incompleteness theorem implies is the "actual place wherein language is (to be) changed at the elementary level of assumption" and where knowledge is best developed.

Western culture, emanating from the (totalitarian) Roman Empire, has become (or has remained) the dominant enforcer of extreme violence within the world, (a world made smaller with communication technology), and the Western-Empire is the "icon of superior intellectual value,"...
... , but that intellectual value has become empty.

This seems to not matter, since western culture is a social hierarchy of selfishness which is ruled by a dominant few (the owners of society) an empty Empire, floating on its propaganda system, and very-fine (or very deceptive) communication systems.

The hopes of humanity, as a species of knowledge and creativity, lie outside the western culture, the same extremely violent culture to which the American Revolutionary war was opposed.


Why has limited development due to science and the failure of rigorous (MIT) academic math to be able to calculate financial risk (in a context of indefinable randomness) been accepted?

This is a result of monopolistic domination, developed through:
controlling material,
hierarchical social organization,
authority based education systems (which identify an academic game, whose winners are picked to serve the interests of the oligarchs with high salaries), and
control of laboratories through research investment (of either business or the government, but both investment sources choose to serve oligarchic interests).
The result has been larger, faster computers which have been allowed by microchips, large amounts of effort has been put into computer programming, including developing "expert computers" ... ,
(which can beat Jeopardy champions, apparently correlating word meaning [the goal] with memorized information strings, meaning has a statistical relation to word strings, thus the word strings must be directly related to the narrow word usage (or word structure) of the game),
... , an ability to manipulate (by fast switching) electric signals in very small time intervals.

This is an excellent example of incremental technical development which fits into the narrow interests of big businesses.
This is fairly impressive, but it is a limited range of knowledge kept within a narrow context, and kept exclusive and overly hyped (it is claimed to be more complicated than it actually is, and in this grand context it is made very competitive, thus hiding the knowledge, because (through competition [which is centered on a few people working on particular projects] the knowledge can be controlled by a relatively few number of experts).
It is common information about circuits which, nonetheless, is being protected (as trade secrets), ie dominate resources and knowledge and creativity, though computer circuits are (can be) intricate, nonetheless circuit properties have been studied for over 150 years.
That is, it is (really) not all that impressive.

Science is hyped in a similar manner, so as to hide knowledge, and to protect a business's creative capacity from competition (brought about by new scientific ideas), though (on the other hand) competition is a very good way to hide knowledge if the competition is highly controlled and with few contestants focusing on a single narrow context.
Thus science is about incomprehensible, and practically useless, particle-physics, general relativity, strings, etc all with descriptive language structures which are too complicated to be practically useful.

The main message of today's science is that "science is too complicated for the public to understand," that is, "people are not equal," and this is an important method (or technique) for propaganda which is protecting the interests of an oligarchy.

This is the correct (narrowly focused) realm (of mental states) in which to effect monopolistic control of society, where science is (now, 2012) narrowly controlled, and it is focused on militarism:
weapons,
communications,
logistics,
psychology, and
during the militarization process in the 1950's (J McCarthy's age of terror crushed all free expression) politics was made into an arm of a militaristic propaganda industry.
(where the effective dialog was,
"Yes, we must take money away from the New Deal in order to build the armaments industry, so that the 'oligarchy based on capital' would not be over-come by an 'oligarchy whose propaganda was based on the-worker.'")

It is important to note that the armaments industry promised clean, cheap fusion energy by the end of the 1950's, but such failures are ignored by the propaganda system which was designed by the military (intelligencia) and its allies, and built around oil and monopolistic finance.
Furthermore, the propaganda system provides a non-stop re-iteration about how much technology was developed through NASA, or the space-program, but in fact, it has been "all about" developing 19th century science, where this development has focused on the military objectives of weapons and communication systems.


As usual western oligarchs fought with other western oligarchs, but Marxism (Mao) invaded China (at the end of WWII), and Marxism is about the single pair of opposites of material and religion, the foundation of thee Holy-Roman-Empire, subsequently western style oligarchies have been developed (in China), so as to provide a new set of rivals for a western style conflict. Propaganda systems need to be compatible in order to develop conflict.

That is, narrowness, absolutes (moral and material), and domination by extreme violence has been the model of religious based empire since the Holy-Roman-Empire of Constantine, where now science has been made into a religion of authoritative dogmas which is fashioned about a religion of military weaponry.
This has led to the collapse of science and math, while monopolistic state-sponsored capitalism has been expanded by coercion, but its narrow context has resulted in its own demise (collapse).

The real point of Copernicus was that there is a limit to authority in regard to development, where today quantum physics, particle-physics, general relativity, and their other derived-theories have many unjustifiable similarities to the data-fitting epicycles of the Ptolemaic system, and they similarly limit practical development, yet the propaganda system has formulated quantum physics, particle-physics, general relativity, and their other derived-theories as representing the science which Copernicus developed, but the truth is that Copernicus demonstrated that any dogmatic authority is very limited in regard to its descriptive value.

The professional scientist is: obedient, competitive, narrow, obsessive (autistic), and arrogant, who seek dominant social positions ie their personalities are consistent with the immature psychopaths who are the owners of society as well as the psychopaths who are the enforcers of narrow absolutes (science will remain orderly [progressing in the direction of authority] and continue to serve the interests of the oligarchs).

The self contradiction of capitalism is that it claims to be about an equal, free market, built around the value of property (material resources) but controlling property has nothing to do with being equal and free, rather it is about violent domination of society and the subsequent social hierarchy needed to maintain this domination. And that capitalism is based on competition, but again competition means being contained within a narrow fixed context and thus it is about both inequality and controlled markets.
Western culture is about violent domination based on propaganda, where violence and technical superiority merged with propaganda under Constantine and the Holy-Roman-Empire.
Note: (perhaps) Equivalent to technical expertise is the capacity to control social organization.

It may-very-well-be that the model of Constantine was the model which Mohammed copied, as Islam has the same social organization as the west, ie that of an oligarchy.

It was the American Revolution, modeled after the egalitarian Quaker colony, which consciously sought to break-away from this western culture of oligarchy, to have an equal population, where one is free to express ideas, and one is equal in their freedom to be (practically) creative.
Unfortunately, most of the other colonies were based on European style violence and social hierarchies built around property rights.

Though psychology might have some affect on propaganda, which may or may not be of some significance, it is controlling the communication channels, ie the equipment of communication, so as to only allow one-voice (one expression of ideas) excluding ideas deemed to be un-authoritative, which is central to the effectiveness of propaganda.
For example, J McCarthy's attack on expressing ideas, even though the real issue was choosing between "one oligarchy" or "another western oligarchy," but each with different propaganda strategies, ie these are not debates about ideas rather it is about protecting propaganda strategies... , no... , rather it is about the oligarchs of the two sides getting rich (equipping and supporting both sides) while a conflict is given organization in the two societies,
ie the "new deal" money (or the energy of the society) does not go to the people rather it goes to the oligarchs (or to their supporting institutions).

Peer review in the professional science and math journals which keeps the dogmatically authoritative channel of military-centered science and math clear of any new ideas, all new ideas about science and math will be within the realm of existing military technologies.


US institutions are, largely, under the control of psychopaths. This is possible because the US has been militarized since the early 1940's. Thus, there are military files which identify those who are good at violent coercive methods, and this information has been used to select managers of institutions.


Defining languages at the level of "assumption," allows one to authoritatively argue, so as to challenge the dogmas of the authorities at "the fundamental levels" of their own descriptions.

For example:

The problem with function space techniques as a basis for describing locally determined measurable properties, ie either values of functions or spectral values associated to a function space's basis set of spectral functions (both of which are) defined on domain metric-spaces, is:
(1) their focus is on global functions, which collapse when local discrete measures are "taken," so Is it a local or a global model?
(2) the focus is also on the phase properties of a wave, which are supposed to be related to the globally measurable properties of the physical system, eg energy of the system, thus
(2a) it should be noted that different geometric properties in different spatial directions can affect the local properties of waves, and their relation to wave-phases, in different ways (especially for mechanical and electromagnetic waves), yet the phase is the means through which the global system properties, eg energy, must depend (or must be identified), but this energy would be an average property, yet the individual particle-spectral events associated to the system are particular eigenvalues, which can be a part of the average energy value of the system. How can a wave-phase be associated to two different values for the system's energy (an average energy, and a particular energy level)? or How can a spectral (quantum) system have an infinite number of spectral values associated to it simultaneously?
(2b) if wave-phase properties are independent and random (and perhaps unrelated to local geometry) then they are properties which cannot be linked to a system's global properties, and thus the question, "Where, then, is the basis for a (quantum) system's ordered spectral structure to be found?"
(3) thinking inductively; the only descriptions of physical systems which are based on randomness... , and are composed of relatively few components, and which have a clear relation to a set of observed stable, discrete properties of spectral systems... , are those systems which have definitive geometric constraints associated to their operator structure, (eg 1-body boxes, and the 2-body H-atom) ie it is the geometric boundary conditions which force the system to have certain types of stable, discrete spectral properties.

Despite what certain authoritative figures "might have believed," and so "stated those beliefs," about the observed properties of (quantum) system being dependent on "the phases of waves," such as H Weyl or S Weinberg, or S Hawking, this simply means that they believe that sets of operators can be found which can be used to manipulate wave-phase so as to fit data, but it is a model which has not worked after over 100 years of effort.... ..
[based on the laws of quantum physics, where are the sufficiently precise descriptions of the electron orbits of (say) Pb-atoms,... . based on the laws of particle-physics, where are the descriptions of the stable orbits of the components which compose (say) the Pb-nucleus?]
(the physics-math professionals have reduced global (function) structures to local structures (ie observed particle-spectra data) by means of the basis structure of function spaces (wherein material geometry cannot exist), and then the physics-math professionals have defined material interactions as random, non-linear, point-particle collisions (an extreme form of a definitive geometry which, nonetheless, is non-linear, and thus [still] indefinably random) which in turn adjusts the (phases of) global functions by means of "sets of particle-collision possibilities (identified in the non-linear context of differentiation)" defined at a point (the point of the particle-collision), ie the local phase changes [or local adjustments to the wave-phase], in turn, are to be used to determine the properties of a global function),
[perhaps there needs to be considered a mechanism through which some action-at-a-distance "changes in phase" might exist, but this would imply the existence of stable geometry],
... ... , and it is a model which has no relation to technical development; despite the observed spectral properties of stable, discrete, definitiveness, which these ("so called, randomly based") quantum systems are observed to possess (that is, a stable descriptive context has not been devised so as to describe, and subsequently use these stable properties) ie but they are definitive systems whose descriptive context is assumed to exist in a context of indefinable randomness (and thus the properties of these few highly controlled components of the spectral system are forever inaccessible to practical creative use).

It might be noted, in the context of the US propaganda system, this is a defeatist attitude, in regard to the point of science description (the practical use of information about physical systems), and in regard to the stable discrete properties observed for the spectra of general and fundamental systems as diverse as:
general nuclei,
general atoms,
general molecules,
general crystals,
Then there are the:
linear, solvable, macroscopic classical systems (the part of the description which seems to be correct), and
the stable properties of the planetary motions in the solar system.
and
(Perhaps) Other math structures, which are different from "a continuum defined by the idea of materialism" (ie new models of material which fit into higher-dimensional containment structures)... ,
need to be considered:
(1) in regard to the "ordered" structures of material motions within galaxies, and
(2) the relative (expansive) motions of galaxies,
... , such as stars having a higher-dimensional relation to the materials,
eg each of the stars having a higher-dimensional relation to the material interactions within their associated solar systems.

It is only in the context of absolute authority, which such a defeatist image is to be expressed by the authorities of science and math dogmas.
These authorities provide a "defeatist state of knowledge" which the competitive, authoritatively-dogmatic education and intellectual aristocracy system will not allow anyone to challenge.
The experts are used by the propaganda system to defeat the "will of the public" who want to know and to use... ,
the patterns of stability which are observed,
... , in new creative contexts.

The context of geometry (contained within a metric-space)

It should also be noted that in a "descriptive context" in which the "phase of a wave" is the main structure through which information about physical systems is carried, as an "information structure" which is a part of the description of existence, then for the operators acting on wave-functions (which are expanded in terms of "spectral" basis function-elements) why would the pattern, ddf=kf, exist everywhere on an unbounded domain metric-space? ... ,
(that is, the exception to, ddf=0, is "not" clearly defined in the context of a domain space (of the general wave-function) which is a metric-space, and apparently the exception is based on some math formality, perhaps a formality as simple as demanding a wave's phase to have a relation within the heat-equation, ddf = df/dt, ie an operator which (it is claimed) has a non-zero relation to the wave's phase at (nearly) all domain points (with exceptions for critical points) [even though the domain space is a metric-space]),
... , but in a geometric context, eg within a metric-space, there would have to exist the relation, ddf=0, unless there are "holes in space (which is too general of a concept)," or more specifically, there would need to exist discrete shapes (within [or upon] which are defined holes) about which a spectral property of a material system can be defined.
This is a fundamental question, which no clever "authoritative quip" can resolve, especially in the case where the wave has no actual physical properties, but rather resolve unto local particle-spectral random events (where the randomness is indefinable), ie it blurs the distinction between properties of derivatives (which are applicable to function-values) and properties of (spectral) functions, ie the distinction between measuring local-values of functions and local properties of a global function.
That is, a system's spectral properties are "global" in regard to closed-open (most often) bounded metric-spaces, which also define the material system, ie spectral systems are (most often) not-defined on unbounded global structures.
Since the idea of indefinable randomness as a basis for description of physical properties has shown itself to be "practically un-useful," then the new structure based on geometry seems to make better sense, wherein the spectra are defined on discrete (stable) shapes, eg discrete hyperbolic shapes.
Spectra are defined on discrete hyperbolic shapes whose material interactions (where these interactions are associated to spatial displacements) are defined in regard to discrete Euclidean shapes, so that the discrete hyperbolic shapes are approximated by discrete Euclidean shapes, which define averages between "the amounts of interacting materials," ie defined in the center-of-mass coordinates (or the average masses) of a pair of interacting material structures.



What one wants in science and math are descriptions based on stable (math) patterns which provide information which is practically useful. If the description is not stable then the information provided is not reliable.

Adding and counting is about a number system's ability to make comparisons, while the arithmetic operation of multiplication is about adjusting different number systems to conform to one another. That is, math is most about number systems and changing number systems.

The interest in stability is (mostly) about how to relate multiplication to geometry, ie the geometric measures. This is often done by means of differential equations, and quantitative consistency (which allows for stable relations between different measuring sets) is about linearity and geometric consistency [geometric measures do not remain consistent outside a context of geometric reparability (analyzable and orthogonal)]. Though geometric measures can be related (by alternating forms) to parallelograms, the shape of a parallelogram does not allow "multiplicative independence (along the independent coordinate directions)," whereas a diagonal multiplicative relation between coordinate changes does allow "multiplicative independence" and in this case a function's values can be related to its domain values [ie to each functional factor (of the solution function) there is "one" coordinate value] in a quantitatively consistent manner (with the local domain coordinates) if multiplicative independence exists.
Though parallelograms are related to valid stable geometric measures, but it is the rectangular measurable patterns which are the types of patterns which, if they exist, can be used to solve linear, metric-invariant differential equations (so as to have each functional factor associated to "one" coordinate value).
The properties of local coordinate directions which stay parallel and orthogonal as one moves about a geometric pattern of coordinates, where the coordinates both conform to a system's geometric shape, and contain the system, ie a system containing (global) coordinate system, allows one to solve a linear differential equation which exists in a metric-invariant context, where the (measurable) information is measurably reliable, and useable (since it is a geometric description), and the solution is controllable.

This discussion is about the math patterns which are practically useful in regard to "using information about measurable properties in practical ways" where measurable properties are functions defined on sets of independent coordinates (which contain a system, upon which are defined the functions which identify the system's measurable properties).
How are functions related to measurable properties so that these properties are reliable and useful?
By differential equations defined in a context of: linear, metric-invariant, geometrically separable (so there remains multiplicative independence in each coordinates) differential equations, where such differential equations relate different representations of the same number-type (or the same property), ie differential-forms, which identify geometric properties, are related to local spatial displacements.
(or variation techniques can be applied to a system's energy representation).

Spectral properties can be described if these properties remain consistent with these geometrically measurable properties of a (the) physical system. The wave must remain related to a system's geometric properties, ie phases of waves cannot be used to describe a spectral system's properties, a system's different properties depend on the system's relation to geometry.

Functions are about measurable properties (eg differential-forms based on local coordinate measures) and are identified in a geometric context of coordinate measures and (these functions, or the system's measurable properties) need to be defined within a very limited geometric context in order to be diagonal...


In regard to measuring what is a differential equation?
This is still not understood in regard to useful physical descriptions.

Stability of math patterns

There is a stable set of shapes; the discrete-hyperbolic-shapes (DHS), and the discrete-Euclidean-shapes (DES), which define both the set of stable material and metric-space systems (the DHS), and a geometric framework through which "material" interactions take shape (on the DES). These discrete shapes are (or can be) linear, metric-invariant, of non-positive constant curvature whose metric-functions have constant coefficients and they are geometrically separable (ie analyzable and orthogonal). The discrete hyperbolic shapes are rigidly stable while the discrete Euclidean shapes can take on continuous size changes so as to be able to fit continuously into dynamic processes.
These shapes are defined over a range of different dimensional values, from space-time dimension, two; up to space-time dimension-12, [or from hyperbolic 1-space; to hyperbolic 11-space].


D Coxeter classified the stable discrete hyperbolic shapes in the (these) different dimensions based on spectral measures (of these stable rigid shapes) as well as the set of rotation (or reflection) angles about certain lattice points, which define angles between adjacent faces of the fundamental domains of the "cubical" discrete hyperbolic shapes, where the spectral measures of a (discrete hyperbolic shape's) fundamental domain's faces determine the stable spectral properties associated to any particular discrete hyperbolic shape. The "cubical" (or rectangular) nature of the fundamental domain (of these discrete hyperbolic shapes), and its subsequent geometrically separable structure, require that the reflection angles defined at lattice points of the shape's lattice be discretely related to a "90-degree fit" into the fundamental domain so as to define a geometrically separable shape.


The math patterns about which mathematicians focus their attention


There are many other math properties about which discrete hyperbolic shapes or their 2-dimensional and 3-dimensional sets of such shapes have to complex numbers, and to analytic math properties and to other math properties:
Analytic (for real functions the property of being smooth and with a converging power series for each point of the domain space)
Holomorphic (for complex functions, if the function is differentiable in a region then it has the properties of a real analytic function [or a pair of real analytic functions])
Real functions, real domains,
Complex functions, complex-number domains,
Meromorphic (analytic complex function which has a limit defined for its value at the infinity point of the Riemann sphere)
(Abelian) Differential-forms, and
Meromorphic-fields (or division-rings), ie stable quantitative number systems with some different properties for multiplication,
Complex analytic functions with zeros and poles depending on how one partitions the shapes in relation to domain regions of the function.

It is not clear how these math patterns are related to useful measurable descriptions. The math authorities do not make it clear by means of "what simple math properties" they are trying to make these math patterns related to useful descriptions.
For example, the property of being analytic may be related to the idea of quantitative consistency, where analytic means a smooth function upon which can be defined a power series (or a polynomial, ie a finite number value) which converges on non-empty regions about each point of the function's domain space, whereas a polynomial has the structure of a number in a number system. But it is not a number approximation, rather it is about using the polynomial as an approximation to the given function's values on the limited region of convergence (it is about changing the form of a function). The type of information which a polynomial representation of a function would readily provide is "order of magnitude estimates" of the function's value at certain points in the domain space. For example, the polynomial can be used to identify first-order and second-order corrections to a function's value within some domain region.
It is guiding principles, such as the idea of relating the structure of numbers to approximating number values and in turn applied to the structures of polynomial representations of functions (as polynomials), which are needed in order to discuss math ideas in meaningful ways.
Otherwise the math authorities talk about math patterns directed at... "what purpose?"
It seems that much of their purpose is related to their not understanding some of their main mathematical constructs, such as the derivative (which approximates a local linear measurement of a function, where the function, in turn, represents a measured property of a system), which leads them to explore the patterns which emerge from actually doing derivatives, while the idea of "solving equations" rather than the idea of describing "the patterns of existence in useful ways" seems to be their main motivating idea.
Why create math structures simply in regard to the math focus of particular math patterns, eg the patterns of algebra "focus on solving (algebraic) equations," when solving for functions in differential equations, ie determining the measurable set of properties of a physical system which the function represents, requires a very limited context in order to be able to understand (or use) those properties in some further creative process.
Yet mathematicians do not want to be limited by these substantial constraints on math patterns.

It seems as though mathematicians will look at any abstract patterns which was first observed and "written about" by some math-authority, similar to how Picasso was considered interesting because he had demonstrated his capability to draw at a level which caused him to be considered an authority (or master of the arts), such identifications of value are arbitrary, whereas there are many abstract patterns in math which non-authorities might have considered, but then such abstract patterns have no interest for the mathematician who wants to be a professional.

Functions are "maps" between sets, most often quantitative sets.
The local measurable properties of functions need to be studied with derivatives (along with their inverse integral operators), and defined in differential equations, which (in regard to physical systems) relate local measurements to equivalent values (but different representations) which are placed in a context of cause and effect, eg changes in motion caused by geometric properties of an object's surrounding material, dynamics of an object is caused by the (geometric) properties of (second-order) differential-forms (whose properties are defined at the same point (location) as the object).
For descriptive purposes one wants to find measurable properties of a system contained in a structure of measurable quantities in a context in which what is measured (the measurable properties) are:
1.reliable (consistent and stable),
2. the measured values are accurate (actual, and apply in a general context, and precise to a level where the system operates) and
3. useful for putting together new systems, and
4. controllable.
This defines a limited descriptive context. Apparently mathematicians find these limitations too confining, but it should be noted that descriptions which are outside this realm have a limited relation to being a part of the measurable world of practically useful descriptions.

There are many other relations between discrete hyperbolic shapes and more general shapes, where the stable structures are mapped (or transformed) into more general, but unstable, geometric patterns. Mathematicians like to dwell on these patterns with greater math generality but with less relation to useful math descriptions.

Mathematicians tend to act, so as to identify sets with a lot of structure, where that structure can be either algebraic (including analysis) or geometric, and then start mapping between these identified sets. But little care is taken in regard to how stable and reliable the identified patterns are, in regard to (reliable) measuring, ie in regard to quantitative consistency, and in regard to whether (if) the pattern defined;
"is substantial, and stable, and properly defined in regard to its quantitative validity," eg
(1) non-linear relations are not quantitatively consistent...
(the issue is "why do limit cycles form around the critical points of a non-linear differential equation?" the answer is that conserved (continuous) objects are being measured in a metric-space where events associated to an object can be measured but the non-linear relation is not quantitatively consistent, so the differential equation has relevance but the measured details of the components of the non-linear system do not have relevance, because they do not [properly] fit into stable (reliable) quantitative structures), and
(2) one needs to count stable (random) events if one's random descriptions are being properly placed into a quantitative context.
It would be better, if in regard to these many maps between mathematically structured sets, there were a vision of causality, where there are two different types of measurable properties, eg the object's moving properties and its relation to how differential forms relate to the material geometry surrounding the (moving) object, but of the same type of number, but these equivalent measurable values (numbers) have different representations, but which can be set equal to one another (and these types of causal patterns, used as a basis for descriptions, needs to be identified).

Such a discussion could be about number properties and/or about the limits of stability of a quantitative structure, but (arbitrary maps seeking general relationships but relationships which might not be reliable in regard to measuring, so that) this is a bit of a reach, as to whether if this is a valid motivation for a study (of math patterns), which may or may not have validity.

Apparently quasi-conformal maps could be about trying to describe changes in a very rigid and isolated discrete hyperbolic shapes, or perhaps, about changes in discrete (isolated) velocity-space properties.
However, the small nature of the discrete hyperbolic shapes which are used to model physical systems, such as atoms and nuclei, means that (expanding) their lattices to represent a discrete velocity-space structure would suggest that such discrete jumps could appear to be continuous to a very small numerical value, ie epsilon could be chosen very small and delta could still be found at that same approximate size, ie they would appear to be continuous changes if that lattice structure remains relevant to a "material component's" motions.

Meromorphic functions define a field, and are about maps between shapes, so that shapes become numbers, but it is not clear such meromorphic fields of numbers are continuous or that they remain consistent with the context of the dynamics of the material one is trying to describe, that is, "Should the dynamics of the material be defined on a particular type of lattice?".

Velocity space is also energy space, ie potential energy and kinetic energy properties, in the simple context of discrete shapes, kinetic energy is related to 1/r (the sectional curvature of a 2-dimensional discrete Euclidean shape), in regard to discrete Euclidean shapes used in the descriptions of (material) interactions (within a continuous descriptive context associated to spatial displacements).
Such patterns of velocity changes defined on hyperbolic shapes (or hyperbolic spaces) would be about dynamics in space-time, ie dynamics in the context of special relativity.
It could also be about using variation techniques on an action (or energy) space (but are they the correct space for the material?)
Again the authorities seldom relate the subject of their math patterns to a useful and simple contexts.

The apparent motto of a mathematician is "why consider a simple pattern when one can consider a complicated pattern which cannot be understood or used."

Numbers are about adding and subtracting, while multiplication is about relating two different number scales, as well as being about relating two different types of numbers, (where one wants such math processes to be done in a quantitatively consistent manner).
These are simple ideas which are predominant in all math patterns, and should be referenced often, simply to provide a context of simple ideas about numbers and measuring in the various complicated patterns which are being considered.
Numbers can be useful in the context of measuring, and measuring is quite often about practical creativity.