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Revolution in math

If ideas are revolutionary then one will not get a good audience within a monopolistic business oligarchy, such as the US.
Thus, one must try to express the reason for the corruption which causes a public or a society, ie those few who own the society (the oligarchs), to be antagonistic to new ideas.
The main reason the society is antagonistic to new ideas is because it is an unequal society.
The main reason the society is antagonistic to new ideas is because it is an unequal society, where authoritative dogmas and traditions define both a stable context for monopolies, and "what a valid idea 'is.'" Furthermore, the "valid" ideas, of course, are also the ideas which the owners of society have "an interest in supporting," since they are the ideas upon which the businesses of the owners of society depend.
The owners are the individuals and corporations which deal with: oil, banking, the military, electronics, and (health) insurance (define our society's oligarchy). A society which is held together both by practical behavior, which is remarkably stable and fixed, eg houses are built in the same way and this process is controlled by a monopolistic business structure (so houses stay, essentially, the same), and by extreme violence, which is used to define and maintain a narrow society, which resists other types of practical behaviors, ie behaviors of people must be controlled by investors.

There is a misrepresentation by the media (the propaganda system) concerning the image of experts. Namely, that experts always get everything correct.
The expert who gets everything correct is an expert who serves the owners of society, since in (a valid) educational structure one should always be seeking revolutionary ideas, which serve the creative interests of everyone, with a very-wide range in regard to all of people's creative interests, not only the creative interests of the few owners of society.
True experts are interested in many ideas, so as to be able to describe existence in a practically useful manner, and in this pursuit there are many ideas to be explored, where "many of these ideas will be wrong" (yet an underlying idea-basis may still be correct).
Nonetheless, the structure of education, is controlled by the owners of society, where in the education system (The US educational system focuses on an authoritative truth, upon which educational competitions can be defined, competitions which serve narrow business interests, ie finding well trained people who focus on the ideas of interest to business interests) only narrow and authoritative ideas are expressed, so these dogmas... , and subsequent expert-authorities identified by the education system as the winners of the educational contest... , serve the interests of the owners of society.
For example, the fact that physics is now based on material interactions being modeled as random particle-collisions, this means that physics serves the interests of the military businesses which design nuclear and other military equipment, because the properties of random particle-collisions are related to rates of (nuclear) reactions (but the properties of random particle-collisions have virtually nothing to do with developing other new technical systems).
The ideas concerning electromagnetism, which were developed in the 19th century, are being developed by the electronic industry in a very slow manner based on monopolistic interests.
S Jobs was a slight exception to monopolistic business practices, in that he developed several different types of electronics instruments, monopolies are usually about domination centered around a single product.

It must be noted that the relation between "how semi-conductors function," and their role in electric circuits is not determined by calculations done in the context of quantum physics, but rather it is a result of (determined by) the thermal manipulation of the chemical make-up of metals within a semi-conductor crystal, and the resulting semi-conductor properties, associated to charge-migration and the crystal's energy levels (determined by experiments, and not by quantum calculations), can be coupled to the circuits and manipulated because the (voltage) properties of electric circuits are so easily controlled, so as to be able to use the intrinsic voltage properties, which the semi-conductor crystals possess, within the electric circuit's controlled voltage structures.
On the other hand it was the micro-processor which allowed a more innovative technologist, S Jobs, and less-innovative micro-processor programmers, B Gates, to enter the market and compete with monopolies, namely IBM, a business which thought it had cornered the main-frame computer market, and subsequently, how computers would be used by industry.
But monopolies basically do not want this type of competition to enter their highly controlled, and usually very traditional markets.
The propaganda system is willing to consider innovations on communication systems as long as they (the owners) still possess a "material control over delivery systems" so as to maintain the "one authoritative voice" of the propaganda system.

Why is capitalism failing, well its not really capitalism, it is a society which has the same structure as the Holy-Roman-Empire with the owners of monopolistic-businesses the actual emperors.
It is clear that the difference between Chinese communism (a western oligarchic social structure) and US monopolistic-capitalism is only about who is in the top social-positions, with corresponding slight differences in the propaganda systems.

In fact, this is most likely the reason that the narrowly competitive monopolistic capitalistic economic system is failing, because the, so called, capitalistic system wants to narrow the range of knowledge in regard to knowledge's relation to new-creativity, so that knowledge and the high-value of the culture serve both a set of propaganda strategies, and serve the narrow creative interests of dominant monopolistic businesses. Math and "high-level" science are more adept at arbitrarily quantizing models so as to fit an improperly defined random structure of data than they are capable of identifying a descriptive and interpretive context of the world's observed patterns which would be useful at the level of practical creative development, let alone the idea that their descriptions (calculations) should be widely applicable to general systems with a fairly decent ability to approximate the stable (measured) properties of general physical systems, something which is not being done by the so called "top-notch" intellects selected to be an aristocracy-of-intellect for the society, ie either the psychological methods of classifying people's abilities are failing or they are designed to select obedience rather than capability to discern truth (the psychological methods [or processes, or techniques] are actually designed to select adherence to authority and facility with culture, or language).

That is, authoritative experts who serve the big business are obedient, competitive parrots (birds), whose voices serve the narrow authoritative structure upon which the competitive structure of the education system is based.
The winners of the educational system competitions get to impress and serve the owners of society (with their domineering correctness) in very narrow contexts for how knowledge is used within society. For this effort they are given what are called "high salaries," ie the well-trained experts function as wage-slaves.
The authoritative experts are mostly about deluding the public concerning knowledge, the experts stay true to their narrow range of authority, and in dong this, they support "the basic tenet of western culture since Rome," that people are not equal. Subsequently, one sees the adeptness of these math-science experts for quantizing arbitrary patterns, but little capacity to describe (calculate) the stable properties of general fundamental quantum and other stable, spectral-orbital systems.

However, the American Revolution was an (a weak) attempt to oppose this aspect of western culture...
[a culture which opposes both equality and creativity and a highly controlled vision for the development and use of knowledge]
... but the American revolution's, so called, leaders were either the very rich, or those who served the very rich.
There was T Jefferson, who championed equality, but he could never put his ideas into a consistent intellectual structure, apparently because of his own wealth, and his actions were never effective at developing the idea of equality, eg he purchased Louisiana from the French, but Louisiana was really Indian land. A Jackson fought the big bank, but he was a violent adjunct to the US's expanding empire, ie stealing the land from native peoples by exterminating the native peoples.
The European context was too familiar to the Europeans to actually be able to support the idea of equality.
Yet, many of the Native cultures were very much egalitarian societies. But instead of the Europeans being perceptive and honoring their cultural accomplishments, instead the Europeans slaughtered and exterminated the native peoples, so as to steal their land so as to individually get rich within the cultural context of European social-values.

But, in fact, the idea of equality is central to the development of knowledge.
The correct interpretation of Godel's incompleteness theorem is that the language of math, if it is not currently (eg 2012) related to useful developments, then that language should be in (continual) revolutions; where the assumptions, and contexts, and interpretations, and organization of the language of the authorities are always to be challenged.
"Peer-review science" is presented as protecting truth, ie keep the ignorant public from expressing ideas, so as to only give the "proven experts" a voice, but it is really about protecting monopolistic businesses, and how these businesses control the knowledge of the culture, wherein the authorities can be obedient to a narrow view of knowledge and its limited relation to creativity.
"The lie is," that only the investor-class are the type of high-level people who are capable of using the knowledge of the (a) culture in a useful way within society. This is proven in a circular argument, since only the rich are allowed to determine what is created within society.
In a similar way, all economic analysis of the "economics of energy" claim to show that "oil and coal" are always (if done in 2012) the cheapest energy. But, this is because almost all energy systems in the society are built to use oil and coal. Thus, changing to "other energy sources" would be expensive, ie investing in new equipment, ie a circle in which the public is trapped by the owners of society (as is the usual case, since the public internalizes the values of the oligarchy since that is what exists on the solitary voice of the propaganda system and communication system which represents an absolute authority).
This is based on convincing the public to accept money, controlled by the investment class, as a valid measure of social-value, and that living as a wage-slave, and not living, independently, on farms, where one can be self-sufficient.

Indeed, within the US, immigrants were used to develop and solidify the idea of wage-slavery.

Math can be used to describe the structures of material systems in very precise ways, so that this information might be useful in regard to control and use of a system's properties within a new system.

So "about what" is math concerned?

Math is a (precise) discussion about:
1. Sets, and set structure associated to ideas about containment, nearness, randomness, etc
2. Quantities, built from a uniform unit, along with the math operations of addition, and multiplication, where multiplication is used to change scale (and to define fractions, ie to define size, and thus to define nearness, but to do this on coordinate containing spaces one needs geometric measures, eg metric-functions),
3. Shapes, [lines, circles, curves, and twists, etc, placed in a many-dimensional context]
4. Randomness, (a fixed, stable, finite, well defined, and calculable, set of elementary-events), and
5. (Stability) {shapes and quantities as well as sets [such as valid elementary-event spaces] which are stable, and form the basis upon which measuring [or counting] and patterns are defined and described}.

But the property of stability, given by these above fundamental constructs, is never considered, or it is always assumed, but this assumption is quite often not valid.
This has come to be math's most fatal flaw.
Shape is most generally related to unstable non-linear shapes, since most fleeting shapes which are observed, are non-linear, but because of this non-linearity they are unstable.
Quantitative properties float as measurable properties or distinguishable events.

That is, (it is assumed that the following constructs are always valid)
1. countable events,
2. properties in a context of both non-linear, but unstable, patterns, and
3. indefinably random descriptive constructs, wherein the elementary event space cannot be identified,
[ie it is not completely identified or it cannot be calculated, yet it might be observed, eg this is often the case of quantum physics.]

One can describe math patterns with the following fundamental (defining) math constructs, and these constructs are used in the following fundamental ways:
1. Sets, the set structure of functions, containment sets, eg coordinate spaces, metric-spaces, Hermitian spaces, and elementary event spaces for random processes, eg rolling-dice etc.
2. Quantitative properties; eg define equations, equating the same concept which has two (or more) different mathematical representations (or a claim that such representations are equivalent, ie physical law), find solution sets to equations, define functions, eg which might represent a measurable property defined on a system containing coordinate (or domain) set, thus, the (measurable) property can also be measured (locally) in the quantitative structures of the system-containing coordinates, etc
3. Shapes; geometric measures, functions can represent measurable (physical) properties, local measuring, and stable discrete shapes, eg the discrete hyperbolic shapes and geometrically similar discrete Euclidean shapes. Shapes based on circles and lines, or shapes based on various sets of general curves.
4. Probabilities; based on elementary sets of events about which random occurrences depend on the probabilities of the events, whose random structure can be finitely contained (if it is a valid quantitative description) but not controlled.

All four of these fundamental math categories have very great limitations in regard to identifying a stable pattern which actually exists, ie the patterns is stable, measurable, and controllable.

5. Stability, And the always forgotten idea of "Stability," and the stable uniformity of a measuring unit.

The highly precise and stable, discrete, measurable properties of many fundamental quantum systems... ,
eg nuclei, atoms with more that five components, etc,
... , imply that these systems exist in a math context which is stable, measurable, and controllable [as opposed to these fundamental quantum systems existing in a math structure which is fundamentally "indefinably random and non-linear"].

Equations: the same quantitative type (or the same measurable property) given different mathematical representations (or are claimed to be the same types of property, ie physical law) allows equations to be defined.
This often depends on defining (identifying) a stable [material] component which is to be measured, eg position and motion, and these properties of a component, in turn, being related to the component's surrounding material geometry, ie the surrounding shape of material about the component, where a material component is defined by a constant independent-value of the component, where the constant-value (given for the material of a component), eg mass or charge, is a different type of number from the set of coordinate (geometric) measures.

Descriptive contexts which are related to a wide array of ideas

1. Set structure (containment, coordinates, elementary events, higher dimensions applied to function values (eg internal particle-states of elementary particles), etc)
2. Applying operators, eg + x , to quantitative sets, so as to form functions, but these operators are also central to defining quantitative sets, themselves, etc,
3. The set structure of functions, eg single-valued, function values and domain sets,
4. The set structure of nearness, images and inverse-images of functions, ie topology, and the properties of convergence and divergence, etc,
5. Applying operators, eg d/dx, to function spaces, or in order to define a local model for a measuring process between a property, ie a function's value, and the variables of the function's domain space.

The main constructs upon which the professionals tend to dwell:

For math there are, the general and abstract contexts of both:
I. indefinable randomness
ie (function spaces) related to the general set of absolute spectral states [or components] to which a material system reduces, and (in general) upon which no valid set of commuting (Hermitian) operators can be identified,
and
II. non-linearity
ie (general shapes related to local geometric measures through local linear models of measuring within a general (or natural) system-containment set of curved coordinates, wherein the local matrix operators (relating the coordinates to a measuring processes) do not commute).

This context (of indefinable randomness and non-linearity) is almost always associated to solving systems of equations concerning either metric-functions or spectral sets,
where function spaces, which model fundamentally random physical systems (as well as other random systems), are related to an algebra of operators, in turn, associated to a set of measured values (or operators) which contain,
either
the (full set) measurable properties of a system which is modeled as a function space,
or
a general shape,
[where the general shape may also be a shape defined in a context of algebraic geometry, ie solutions to systems of polynomial equations].

In this general context, there are no patterns of measuring processes which are assigned to... ,
either
coordinates
or
function spaces
... , which are (in general) commutative, ie they (in general) are non-commutative math relations involving many-dimensional coordinate sets (as domain spaces).

Note: Commutative means
either
the local matrices associated to "local coordinate related measures" are diagonal
or
the set of operators (or set of measurable properties) acting on the function space are diagonal

With regard to coordinates, the idea of commutative (or diagonal) matrices is related to:
either
linear patterns (the diagonal elements are constants)
or
the diagonal elements depend on an inverse set of functions (so an inverse structure exists so that the [diagonal] system is solvable) which can be continually applied to the local quantitative structure of the system (and/or this inverse function structure must also be consistent with a set of local orthogonal coordinates of the function's domain space [the inverse functions are always defined within an orthogonal coordinate structure]) which are global (and geometrically separable sets of locally orthogonal coordinates)

or
With regard to functions, the idea of commutative (or diagonalization), is related to:
Sets of Operators which act on sets of orthogonal functions (so as to diagonalize the set of operators),
but orthogonal functions are different from locally orthogonal coordinates, where orthogonal functions are assumed to be globally orthogonal.
Thus, sets of operators are less dependent (or they are independent) on the geometry of local coordinates which compose the domain space for the set of functions, and only depend on the "geometry" of the functions as defined by inner products (defined on function space). The geometry of functions seems to be about the relative relation that the function-values of a pair of functions have to one another, and not as much about the shapes of their graphs.
However, partial differential equations are only solvable if they separate in regard to coordinate directions, and which define a continual separable (and invertible) pattern on the global system (or global pattern).
Note: Essentially the only invertible patterns... , which can be found for a geometrically separable pattern... , are the linear relations, ie the diagonal elements are constants. This is because the geometrically separable patterns are local linear patterns which apply to a global shape in a continuous manner, and it is difficult to identify an inverse function at a point which can be both a local inverse and a global inverse as the point moves around a shape, a shape which has no relation to the local inverse function.

Non-commutative implies effectively non-linear which in turn implies an unstable pattern (or system).

For a function space the pattern of orthogonal functions identified as a global property is quite different from a globally orthogonal shape, or a globally orthogonal set of coordinates, since an orthogonal function is mostly about providing a set of significantly different set of function-values at each domain point, rather than being related to the geometry of the domain space.
Thus, since operators on a function space can themselves be functions, if the operator functions are significantly different functions form the types of functions which compose the function space then commutativity of the operators, defined to act on a function space, will be difficult to establish. But partial differential equations can only be solved if the differential equation is separable (geometrically separable).
Whereas, functions, which are simple (spectral) shapes associated to the coordinate set, then commutativity and its relation to the system's properties would be easier to determine and the system properties would also be more related to geometry, and not related to abstract spectral states which have no shape, eg relating wave-structures to a fixed particle-collision pattern of particle-states ie a fixed particle-spectra.
On the other hand, the reason quantum systems are either solvable or not solvable is directly related to geometric properties, namely the 1/r spherically symmetric potential energy structure, or material interaction structure, which has been found to be mathematically impossible to solve, and remain quantitatively consistent.

Abstract math structures which are useless, yet they are the prevalent math constructs

Non-linearity: The set structure is either too general, ie non-linear or non-invertible, (non-solvable), and the idea upon which equations are based is too abstract, ie general covariance of equations defined on arbitrarily moving coordinate frames, does not fit into a quantitative structure in a consistent manner, ie it is in general a non-linear pattern used to define measuring.
Indefinable randomness is about random, distinguishable events defined within arbitrary patterns which cannot be assigned valid elementary event spaces, so that counting of events is not well defined, ie the descriptive construct is not quantitatively consistent. Operators applied to function spaces has not been useful, since mathematically irresolvable geometric patterns of the system, or of the system's components, make the description of such systems, which possess both the property of indefinable randomness and geometric properties, impossible to describe in a valid and/or useful manner.

Alternative

That is, the professional ideas about both shape and randomness should be re-organized about the discrete Euclidean shapes and the discrete hyperbolic shapes, and metric-spaces associated to both physical properties and associated metric-space states which brings the descriptive context into a Hermitian complex-coordinate containment set and the containment set should be many-dimensional.
These simpler math structures should be "what is talked-about" in regard to both
discussions about shape and geometry,
and
this should be the dominant point of
discussion for stable physical systems whose properties are primarily spectral, where these simple discrete shapes should be the basis for the functions which compose a function space, since such functions are both stable, and they carry the structure of simple spectral values on their shapes, and they can be related to one another so as to form commutative patterns between the functions (ie commutative patterns between the shapes of the graphs of the functions).



Scientific dictatorship

A scientific dictatorship is the view of society which is (seems to be) held by intellectuals and the (domineering and controlling) business communities, where the intellectuals whose ideas are allowed to be expressed on the media (including the alternative media), are those who have integrated "within themselves" the key values of the business community, as well as the viewpoints (or rather dogmas) of their, so called, professional peers (note: peer review is about limiting the range of ideas which the science and math community can express, ie Copernicus would still be excluded form the discussion of society's proper authorities).
These dogmatic ideas can seem to be varied, but they are always dense with information and very complicated, and very general and abstract, in their expression.
Thus, the mental characteristics of obsession and obedience can be used as a filter to the expression of scientific and mathematical ideas, ie autism where the autistic still has the use of language.


The principle of propaganda, is to control what is considered to be valid and authoritative thought, where the validity of the propaganda system is that it (the propaganda system ,ie the media) is the one-voice which expresses the authoritative truth, as known by the scientific dictatorship. Thus, the media must control "what is said" within society, and it must control that which is allowed to be considered as a plausible truth.
The authority of the media is based on the authority of science, and the claimed relation that investment brings "to society" the material advantages of science and math, brought to you by the investment class. This, of course is circular, since an equal free-inquiry basis for knowledge, would be full of many new ideas, but investment would then be very risky. In fact, investment should not be determining which ideas are "better" widely applicable (fairly precise) accuracy and a relation to "practical" creative development should be the measures of a carefully considered measurable description's truth, where "practical" may mean "beyond the idea of materialism."

What is the authoritative dogma of the math-science professionals who support the monopolistic business centered scientific dictatorship?
It is a combination of materialism and an arbitrary morality, needed to maintain an arbitrary context for society, where this morality is expressed in a false context of idealism.
This is the basis for the structure of language in society as dictated by the need to have a "solitary voice of authority," which is represented in society as the media.

Abstract language is based on certain sets of opposites, and it is built within the propaganda system to focus social activity, so as to represent the concerns of the business community within society.
This is the basis for the one-voice propaganda system which expresses the views and dogmas of scientific authority, as defined by the business community.
It is based in arbitrariness, ie the arbitrary issues of interest to the business concerns, ie their monopolistic view of how creativity within society is to be centered on materialism... .
(though practical creativity may be the only aspect of language which has meaning, ie is that practical does not necessarily mean materialism, ie existence may be many-dimensional yet higher dimensions have attributes which allow them to Apparently be hidden from a mind focused only on materialism)
... ., furthermore, creativity associated to materialism, is to be organized within society so as to serve the selfish interests of the business community, in a context of (for) language which hides this deception from the science and math communities.

The authority of science encompasses a fairly (apparently) diverse set of interests, but its core is quite traditional and stable so as to maintain the monopolistic businesses. That is, science is given a focus which diverts attention away from the idea of "the nature of existence itself" and "the idea of materialism" is always the fundamental assumption of the authority of science.

To allow arbitrary interests... , rather than the (equal) exploration of precise ideas which might be related to new contexts of "practical" creativity (and the true position [or function] of life within existence)... , the focus of math and science is on quantization structures which are (themselves) within arbitrary contexts, and centered on the idea of randomness
[Instead of going from materialism to something new, the mental state of people is conditioned by repetition, to go from materialism to idealism (or as expressed today "faith"), and that there is no language which can cement the two fundamental opposites of existence, in regard to the material world and the ideal world. Indeed the "Tao Te Ching" expresses this central idea of empire.]

But math, itself, has many patterns which can be used to describe the nature (and true context) of existence, as well as the "correct" model of life.

On-the-other-hand, the math idea concerning stability in regard to quantities, shapes, set structures and the only valid simple set structures for randomness... ., where probabilities can actually be determined, and "used 'to bet,'" in a consistent manner... ., is ignored.

The material world is considered to be fundamentally random with only a few definite attributes:
1. A singular beginning (big bang)
2. A material interaction structure which is non-linear, in a spherically symmetric, singular context of 1/r potential energies for point-particles, and a point-particle-collision model of material interactions which are also unitary, and non-linear, in regard to the particle-state structure of... the...
3. ... , randomly colliding point-particles, to which it is assumed all material structures reduce, so as to make the descriptive context of the material world far too complex to describe, in a manner which can be practically useful.

Yet, the structures of fundamental material systems are stable and definitive and discrete, this implies (or suggests) a very controlled and geometric context for material interaction and (quantum) system formation.
Yet, these systems have no valid descriptions based on the laws of (quantum) physics.

Where the laws of (quantum) physics are:
1. quantum systems are fundamentally random
2. the exact dividing point between classical and quantum systems cannot be identified, and
3. the states of quantum systems are to be modeled as function spaces, with
4. sets of (commuting) operators applied to the function spaces in ways which allow the equations of a quantum system's physical measurable attributes to be identified and solved, but
5. the singular 1/r properties associated to spherical symmetry, in turn, associated to point-charged-particles, and
6. [how] the non-linear relations of point-particle-collisions, which model the particle-states, affect [{on}] (point-particle-collision) material interactions, and
this descriptive structure keeps this quantitative structure from being of any value in regard to practical creative development of material properties.

Thus, the material world is to be conquered and/or controlled by (big-business) gathering nearly infinite amounts of information to be given (descriptive, but not useful) structure by means of correlations in regard to identifiable features of the material world. The process of identifying distinguishable features of complicated systems is very limited by the context of being able to distinguish a feature especially in a context of indefinable randomness within which the basic structures of material are supposed to reduce.
Furthermore, the reduction is always done to a level of perception which is outside the limits of controllability ie it is out-side the idea of practical creativity and it fits into a realm of irrelevant features which are too distant... ., either too far or too small or too small of a feature in an integrated and apparently complicated system, eg living (chemical) systems, ie they are irrelevant distinguishable features... ., to be useable (in the context of practical development). Yet the information about random particle-collisions is used in regard to the rates of (nuclear) reactions, used in the big-business of nuclear weapons engineering.
That is, the point of authoritative science is to reduce descriptions of the material world to distinguishable features (so that correlations can be considered) which are a part of an arbitrary context.
This is about the least productive context of physical description one could consider.


The current emphasis on randomness and non-linearity allows a wide range of contexts, but no relevance to practically-useful descriptions of existence.
While a descriptive context related to stability and shape provides a more narrow set of contexts (or allowable math patterns) to which measurable descriptions can apply (or can be built), but it allows measuring in a stable context of shape so that the description can be related to control.
That is, stable discrete-shapes in a many-dimensional context, with a geometric context for interactions, allows for materialism to become a subset to a greater descriptive structure, and many new ways in which to model both physical and living systems within a new context for existence, where idealism can be given a context within (of) practical creativity, associated to both living intent and living "material" changes to existing structures.
That is, the, so called, wonders of ancient human life is all about the wonders of the actual structure of life, where there are math descriptions which transcend the idea of materialism, that is, existence is not to be based on materialism, which defines a fixed dimension for existence.


Intelligence as a social tool for the elite


What is intelligence?
Is intelligence a familiarity with the higher aspects of a cultural-truth, by means of a mental model of culture, with an already identified vision of high-value, ie a cultural vision of an absolute truth.
A better definition would be an "ability to discern truth," in which case intelligence would actually be about (or represent) something valid, since truth is the difficult issue.
Intelligence, as measured on an IQ test, is the rate of acquisition of culture, ie it is arbitrary (with culture trumping truth).
So the socially functional idea of intelligence is about measuring "acquisition and adherence to a particular aspect of a culture."
This is used to identify a hierarchy of human value, which has been central to education, but (because cultural acquisition is arbitrary idea) it effectively fixed education as an authoritative vocational institution rather than an institution concerned with developing knowledge
Being able to acquire culture is an arbitrary model of intelligence, affected by subjective judgments, and thus, it is about defining an elite within a social-class structure.
Furthermore, this is how the idea is used, ie to manipulate and entrench a social class structure, similar to how the catholic church used Ptolemy's model of the heavens to express authority and identify social class, or to identify the learned-class.

Furthermore there is an obvious assumption, that the elites in our culture believe in the idea of complexity and the quantization of arbitrary patterns, rather than in the expression of simple well-defined law. This belief in randomness, and subsequently, a deep belief in complexity, rather than well defined laws is expressed by the propaganda system.
For example, Newton's law, a change in a component's motion is caused by surrounding material geometry and the surrounding material's relation to spherically symmetric force-fields, as well as the relation of this force-field to moving coordinate frames of the component.
This is very simple, yet it is still not completely understood, especially now, since action-at-a-distance has been verified by the non-local properties of quantum components.
Thus, Newton's frames are better for the descriptions of inertia than are the general frames of General Relativity.

Nonetheless, there is the implicit assumption, by those who possess elite knowledge, that "if people communicate with simple ideas then such people are stupid."
But good communication is based on expressing ideas in a simple clear manner, this is not evidence of stupidity.

In fact, this expression of ideas about "intelligence," shows the failure of the education-propaganda system, where people's mental models of the world are poorly organized around categories used in language. People use words closely associated to society's "levels of value" and social hierarchy, thus these words are full of emotional content which seems to erase the need for words to have objective meanings.
When communicating one wants outlines which give the simple structure so that the outline is filled-in with supporting details.
Instead the words and "their use," which people learn form the propaganda system, and most often enforced by the education system, are all about fixed notions associated to categories of social-rank, and thus the words often carry with "the use of these words" an emotional content, more than an informational content.

A belief in complexity, rather than a concern to determine (find) a clear descriptive structure for the observed patterns of the world, is based on the characterization of "expert knowledge" by the propaganda system.

According to the elite scientists of our culture, the material world, which reduces to its components, is fundamentally random. Thus, "at best" describing the world's quantized, or measured, properties is very complicated.
Despite such an errant idea, represented as an absolute truth, which has, supposedly, been uncovered by the elite intellectuals of our (extremely violent) western culture, namely, that "the world is fundamentally random," nonetheless, there is attention, by experts, riveted on the sets of correlations, ie sets of possible causes.
If these are correlations which interfere with the interests of big-business, then they are either ignored or manipulated by big business, but if these correlations are of interest to monopolistic businesses then they are feverishly pursued, this is mostly within the expert confines of medical and/or chemical research.
However, medicine and chemistry are driven by extremely primitive knowledge, and primitive sets of rules attached to complicated contexts, which seem to lead away from a valid descriptive language for these disciplines, eg chemistry does not have a valid model of chemical interaction or of molecular shape, and biology (or medicine) does not have a valid model of life and how interactions in biological systems can be organized.


Education

In education one discusses "how to describe 'what is true (or "what has been observed"),'" and then one uses that information (or description, or calculated measurable-values, which are needed) to build some new thing.
If the idea (or description, or calculation, etc) is not useful then one looks for new ideas.
That is, education is about free-inquiry, where the inquirer is considered to be an equal to "the person claiming to describe a useful truth."
This is all about presenting one's ideas in a very clear manner, and assessing the context of "what is being described" in a detached manner so as to determine its practical usefulness.
In this process, it helps to have a sense of "what one is trying to build" and "how its construction might proceed," before one engages in free-inquiry, but this is not necessary.

Unfortunately, in the world of big-business monopolies, "what is created" is determined by the "bosses of the monopolies." Thus, the monopolies come to make the decision about a description's relation to usefulness actually is, within society. This is because creativity within society is being determined by the monopolistic businesses.
This is possible because:
(1) of (or is a result of) a few people owning everything so as to control how money is used within society,
(2) as well as the wage-slave social structure instituted by western governments, and where such a wage-slave organization of society seems to have a strong correlation to the strength of the society's military forces (or simply to violent thuggery), and a corresponding control over the population by the, so called, justice system of the society, which is an arm of militarized state (the same type of state as was the Holy-Roman-Empire).

In the western culture (which includes all of the Abrahamic religions, and apparently Hindus and Confucsians as well), intellectual authority has become equivalent to violent institutional authority, because there is no equal free-speech in regard to the authoritative traditions and dogmas of a science and math community, which serves the interests of monopolistic businesses. That is, "peer-review" demands that science and math be defines as traditional dogmas, which can only serve monopolistic business interests.

The subservience of the institutionally educated experts to authority, and to business interests results in a very poor analysis of the relation that education has to society.
Though, the social affects of education are apparently subtle, education and its structure, and subsequent uses, is central to the issue of equality vs. inequality, and the true state of being human.
Human beings are knowledgeable and creative life-forms and the expression of this natural attribute is best done in an equal society, where education is about equal free-inquiry with an idea to creativity, in a society where all people are equal creators.
Furthermore, people must be careful as to: how they use of resources, where resource-use must sometimes be restrained, and how people live, as creators, must be sustainable by their society, but more significantly it is best to allow the world's forces to sustain human creativity, so that humans live in harmony with the world's forces.

Whereas the idea of equality (everyone is an equal creator) is central to the expressions of Socrates as well as to the formation of the US during the American Revolution.
This support for the idea of equality is an idea which separates "a new culture" from "western culture." western culture has been defined by the social structures put into place by the Holy-Roman-Empire, where holiness allows for arbitrariness, and empire requires extreme violence required to maintain the social structure upon which the society is organized, but those social structures have meant the destruction of the earth.
But those who control money and social value (at the time of Socrates and during the American Revolution) have never taken the idea of equality seriously, because of obvious selfish reasons, and the European public is already being familiar with western culture and how it (a western society) needs to expand and depend on fixed ways of providing public needs, eg cultivating fixed types of plants and animals etc.

The problem, in the education scenario, in regard to "careful (or precise) descriptions and their uses," is that the description, itself, has come to appear to be "the use."
That is, the calculation has "come to be" a "big effort," so that if numbers come-out of a calculation... ,
{no matter how few system to which the calculations actually apply, and they have been adjusted to fit data by means of some very abstract scheme for developing a method of converging a construct (or a concept)}
... , to be a specific desired quantity, then the calculating effort is considered a success. However, this is particularly the case, if the model, no matter how dysfunctional in regard to wide applicability, serves a monopolistic business's interests.

Therefore, the math construct is considered to be useful in the world "of efforts required for calculation," but not in the world "of the description (and its information and its context)" being useful in a practical creative context.

This twist of the idea of usefulness has been instituted as professional scientists and mathematicians were also instituted, and the difficult to understand descriptive structures of Newton, ie the still not understood differential equation, has led to endless confusion facilitated by a set of highly authoritative interpretations and traditional contexts associated to ways to look-at the idea of a differential equation.

Is a function a model of measuring a property and a differential equation a model for local measure of the functions values related to the basic measures of a coordinate system
Or
Is a function space a model of a system's intrinsic randomness, where operators which act on functions, eg df(x)/dx, represent measurable properties, so that the algebraic properties of sets of operators are what solve (or diagonalize) a function space so as to determine the systems very stable spectral properties.
However, the relation of spectra to either randomness or to a system's physical properties, is not sufficiently distinguished in this method of using sets of operators to act on function spaces.
Function space techniques for solving physical systems properties seems to only work for systems where the waves have actual physical properties, eg sounds and electromagnetic waves etc.

Are physical laws, which determine differential equations for physical systems, about the relation that distinguished points have to the general properties of space and time (and energy),
or
Are physical laws somewhat surprising relationships which exist between material components and their spatial-material contexts, where the spatial contexts of the material it contains are "absolute."

Apparently the general non-linear math patterns are not functional in a practical sense, and absolute space required by action-at-a-distance appears to be verified (eg quantum non-locality), thus the simpler structures are supported by either evidence or by a need of curiosity to explore other patterns.

Are quantum systems fundamentally random, which organize themselves around the values of their energy-levels?
or
Does the stability and definiteness and discreteness of these systems imply an underlying geometric-material context?

Since random function spaces seem to not have enough structure in relation to
"sets of operators" used to distinguish (or solve):
a quantum system's observed stable (discrete) physical properties,
from
a quantum system's observed randomness, eg the randomness of a quantum system's components,
it is also necessary to satisfy human curiosity so as to explore the pattern that "quantum systems are fundamentally geometric" in their system-structure.

One way in which to satisfy human curiosity would be the both"
Re-structure the descriptions of both material and its interaction structure to be consistent with the simple discrete geometries of both Euclidean space and hyperbolic space (or equivalently space-time space),
And
To model quantum systems as discrete shapes and to model their containing metric-spaces also as discrete shapes, where one can also require that the functions of the function space used to model a quantum system be functions which are also stable discrete shapes. The discrete hyperbolic shapes have very stable spectral properties associated to themselves.

How does one integrate discreteness and separateness, eg mass separate from space, into a descriptive structure which is based on shape and continuity?
Answer: Well the shapes are discrete, their shapes can be related to operations which are done in a discrete manner, and they can be related to different discrete dimensional levels.