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Commentary :: Education
Creativity and science and math
04 Dec 2010
Linearity, metric-invariance, and separable geometries, defined on a many dimensional containing set, is most likely the best basis for a useful new science, a new science which will open up the realm of meaningful creativity…, not the highly edited and controlled creativity (which serves the interests of the ruling class)…, to all of the public
The current set of topics explored by professional mathematicians are characterized by an inadequate identification of the set of properties which a set of measurable things need to satisfy in order to fit into quantitative descriptive structures properly, ie so that the quantitative sets… (which all together are needed to compose the descriptive structure of a system, or of a thing, which has measurable properties and so that these quantitative sets)… relate to one another in a consistent manner.
There are a wide range of possibilities which are related to (of) the containment of a thing’s description within a math context:
beginning with the idea of set containment,
changing to the set containment of a thing’s set of events (which identify the context of looking for this particular set of observed events) and relating these (random) events to probabilities, (thus it is a matter of distinguishing events and counting their occurrence in relation to the full set of events defined by the thing’s event space, and then identifying relative probabilities for each event of the thing’s event space),
and
identifying measurable sets which contain, or can be related to, the system’s measurable properties.
If the containment set for a system’s properties is composed of two (or more) sets, such as spectral values associated to (apparent) particle points in space, ie both spectral values and spatial positions, then if the spectral values, are physically measurable properties associated to either classical physics or to a geometric property, then these quantitative structures must be simultaneously associated to the properties of geometric measures (associated to the spectral-particle events in space) and related to the spatial events, on the other hand if this is not true (not possible) then the quantitative structures of the description are not consistent with one another, and the description is not a description in which the measurable properties (or measurable sets), used to describe the system’s properties, are consistent with one another.

This (inconsistency of quantitative structures between either the eigenvalues or the function’s values and the geometric measures of the domain space) is proved by “a form of induction” where the techniques of quantum physics assume that spectral values and the values of the coordinates (within which the quantum system is contained) are not consistent with one another and subsequently the operator techniques of finding a complete set of linear, commuting, Hermitian operators to act on a quantum system’s (harmonic) function space so as to determine the function space’s spectral functions and subsequently the quantum system’s spectral values, ie the elementary random event space of the quantum system, has not worked for general quantum systems which are observed to have stable, definitive, discrete spectral properties, ie it has not worked for: nuclei, high atomic number atoms, molecules (where straight-out statistical fitting information and techniques work better than the techniques of quantum physics at identifying the geometric structure (or shape) of (a few) molecules), and the addition of a non-linear connection term to the derivative and making the description discrete on all of space and introducing a hidden particle-state space by pushing the description into a set structure which may be “far too big” to make any mathematical sense, only makes things (in regard to useful descriptive capabilities) worse, as in the case of crystals (where the BCS superconducting theory predicted a critical temperature which has been exceeded), as well as using quantum techniques to describe living systems (eg Penrose‘s attempt at describing the mind [at least he sticks his neck out]). Furthermore, large scale systems such as the apparently very stable solar system goes without valid descriptions, and there is no reason to believe that gravity (or gravitational collapse) is ever reducible to a single point within a context in which the description of the singular gravitational point has a continuous relation to spherical symmetry, ie the “big bang” is not a valid theory, as well as the (dark matter) motions of stars in galaxies (which shows how particle physics functions as an epicycle structure for all the observed mysteries), and then the motions of galaxies are still a mystery.
That is, of the fairly well documented (by observation) stable system structures, be they small discrete or large continuous (yet the planetary orbits also have discrete properties), where the descriptions range from linear quantum physics, to non-linear (due to the non-linear particle-state connection operator) particle physics, to non-linear gravitational as well as particle techniques, are not being described in an adequate or useful manner.
On the other hand, when function space techniques are applied to electromagnetic systems, where continuity and consistency of the function values with the geometric measures of the domain space (of the domains of the spectral functions) are assumed to be true, then the function space techniques work, [and when they are not pushed into a set structure where the size of the sets is too big for them to have math validity, then function space techniques work] for electromagnetic spectral systems, where the spectra can be either discrete or continuous. That is, function space techniques do not work for finding the spectral sets of quantum systems where spectral values and geometric measures of the functions’ domain spaces are not consistent with one another, yet they (the function space techniques) do work for finding the spectral properties of electromagnetic systems where the geometric measures on the domain space of electromagnetic waves (or system) are consistent with the function’s (wave amplitude and spectral) values.

Thus there is the idea of set containment, and quantitative containment, and an identification of what the measuring process actually is. There are the: rods, balances, clocks, temperatures, and brightness of light which determine basic measures (of physical systems) which relate to: geometric measures, measurements of motion, a physical system whose material properties are relate to a measurement with a balance, as well as thermal properties, and the idea of the existence of a continuity of the descriptive context, ie the subsystems of a descriptive context have a relative stability in order for the description to exist.
The quantitative descriptive structure for transitions between states of relative stability is most often not a quantitative description whose quantitative sets, involved in the description of (measurable) properties, are consistent with one another. This is the context in which non-linear chaos manifests and the descriptive structure of probabilities of particle collisions is valid, but such a context has very few practical applications, with the exceptions of systems with feedback, and the descriptions of explosions in both the chemical and nuclear contexts.

The quantitative description of sets which possess relative stability depend on what math structures?
What bounds and what centers and what quantitative sets (or what set of measurable properties) define the properties of a stable system’s measurable description?
Fundamental to describing relatively stable material interactions and the properties of measurable systems so that the descriptions provide useful information…
(outside of the context of continual measurement of a system’s descriptive context and continual feedback of measured information to the system, where the external measured context is what one is trying to control with the feedback) which can be used in controlling the measurable properties of the system (for a material system in space),
….are the math properties of differential equations which identify the local measurable properties of the system and which must be linear, and furthermore, the geometric context is both metric-invariant and geometrically separable (natural) coordinates, where separable means that at each coordinate point the local directions of the set of (natural) coordinates through that point are always pair-wise perpendicular to one another.
That is, the geometric measures of the domain space are consistent with the local coordinate measures and the local coordinate measures are related to the function’s values (or the system’s measurable properties) in a linear pattern, and thus the function’s values and the domain values are quantitatively consistent with one another. When this is the case a system’s differential equitation can be solved and its solution provides a great deal of valid stable information which can be used to control the system in relation to another system or another set of properties contained in the geometric domain space.
Where it should be noted that measuring is not (mainly) about verification, rather it is about coupling the system and its properties to some greater set, or to some greater (creative) context.

A further development in the set structure of the descriptive context involves the linear, metric-invariant and (geometrically) separable context for description of existence to be many-dimensional, where the material geometry of adjacent dimensional levels are independent of one another, ie any particular dimensional level forms into an independent space-form model of a metric-space which exists as a stable material space-form in a higher dimensional metric-space, this means that new material types (different from mass and charge) can be added to the higher dimensional metric-space levels, where each (added) material type is also associated to a new dimension time subspace, ie a new type of signature for the metric-function, many metric-space states where each type of material is associated to pairs of opposite metric-space states. On each dimensional level in a metric-space in which the metric-function has a particular signature a particular material-type is defined. Furthermore, in the different dimensional levels there are (can be) many mixtures of quantitative fields, where the fields have both the properties of continuity and smoothness as well as having (there being) a smallest measurable limit associated to the quantitative field, where such a limit is a natural consequence of the spin rotation between metric-space states which takes place within some smallest time interval for the measurement of time in a particular dimension and particular signature metric-space.

The varied field structures, associated to the existence of several metric-space states, on (or between) the different dimensional levels, can in turn, be associated to algebraic structures which separate the metric-space states so as to mix the different quantitative structures together in relation to both the coordinate and “vector spaces” associated to the different algebraic structures used to separate the various different types of metric-space states. For example, the spin-rotation of time-states in three-spatial dimensions is related to the opposite time states and thus each state is associated to an equal and opposite dynamical displacement in the two different time-states of the metric-space. These time-states can be contained as independent structiures in the real and “pure imaginary” subsets of C^3 space. These time-states can be harmonically mixed in the full C^3 space, ie f( C ) has two opposite states in its real and pure imaginary subsets. Similarly there can be an f( Q ), where Q represents the quaternions, and four distinct metric-space states, this would represent the four metric-space states where two such states will exist in one dimensional level and the other two metric-space states will exist in the other adjacent (say higher) dimensional level. The octions can be used to relate the metric-space states of three different dimensional levels etc.

Note: If in 3-Euclidean-space…, the shape of space in 3-spatial dimensions (or in 3-Euclidean-space), wherein mass and dynamics exist…, for energy (or mass, equivalence) then the shape of space for moving material, which has no mass (but only properties of energy), is seen to be spherically symmetric. Thus, within some radial distance around a (the one) gravitational mass the shape of space is spherically symmetric, eg for the path of light, or for the path of a planet with zero mass. But such spherical symmetry does not continue (in a continuous manner) down to a single point. Rather it must become, at some size scale, related to the separable geometric shapes of space-forms. This is because the spherical symmetry is not an attribute of Euclidean space but rather it is a result of the interaction-dynamic process which depends on the geometry of the local coordinate transformations of the fiber group in relation to the geometry of the interaction space-form.


What is being talked about here? (1) this is a relatively simple math structure with which the stable definitive discrete spectral-orbital properties of material systems at all size scales can be described, and which is consistent with both classical and quantum descriptions, (2) by extending the description to higher dimensions (so that these dimensions are not adjusted to maintain the idea of materialism) this results in the idea of materialism being discarded. The verification of such a description is determined by its wide applicability and its very useful relation to creative development. It provides a map for determining the geometric-spectral properties of higher dimensions. (3) It provides a simple model for life, mind, perception, and intent, ie a possibility for a new understanding of life. (4) it implies that the context for life is creativity, ie useful knowledge and the creation of the patterns upon which a math description can be built, and upon which existence depends, where a math description is a description based on quantities and shapes depending on clearly defined sets, and where the sets are not “too large” so that the determination of a set’s element is not too difficult to ascertain. When elements of a set require too much information with which they can be identified then it is not clear as to what properties these elements might have, so the description would become ambiguous and the descriptive words might become related to structures of illusions (in relation to useful creativity).
There is “the world as it really is.” Some “early” native Americans (to some extent) perceived the world as it really was and from these perceptions developed their knowledge. This knowledge has been passed down. It is a knowledge which bridges both science and religion, ie it deals with the material world and it transcends the material world.

Quantities or measurable systems and operators

Is the measurement of a thing, or a system’s properties related to locally measuring a system’s properties with a derivative in a linear relation to its domain space, ie where the domain space is the space of measurements (of measurable quantities) from which all other measurable properties, in relation to the description of the system which is contained in the domain space, are derived?
If a thing (or a system, or object) is a quantity then the operation of addition and the process of counting provides the “proper” context within which to interpret (or view) the idea of quantities, and their relation to comparing (or measuring) the relative size of things, which can, in turn, be related to quantities.
That is, an operator focuses attention on the local (or detailed) functions and actions, or the active context, of the thing one is describing or measuring, and thus placing a thing (or a system) in a context of many distinguishable relations, placing the thing, which is to be described, within a containing set so as to identify other relations, and the full set of relations that the thing has to other properties, or other quantitative sets.
There exist quantities but defining a uniform unit and the operation of addition (and the subsequent idea of counting, successively adding units) focuses attention on quantities and their limited context.
However, there is the question as to whether a set is “too big” and subsequently the set must have attention focused on its structures, and these structures do not relate such a containing set to a valid description of a given system.

An operator which acts on a function space to represent a model of measuring has not worked when the function space values are not (always) consistent with the geometric measures of the functions’ domain space.
The set of operators is too large of a set, if the operators are not consistent with the geometric measures on the domain space. For example, an uncertainty principle forces this to be the case when momentum and position operators together cannot be consistent with the geometric measures on the (quantum system) containing coordinate space.
That is, this is the case when the functions of the function space represent probabilities so that dual function spaces (such as the dual function space which has been Fourier transformed) can be defined with which an uncertainty principle between the function space and its dual function space and the definition of this uncertainty can affect the (valid) consistency of a function’s values with the domain space values, where a function might be energy (or frequency) and the domain space is time, so that energy and time now have uncertainty inter-relationship which negates the meaning of a local linear relation which might exist between the two sets, ie time and energy…., or a momentum and position uncertainty principle where the uncertainty relations imply that material geometries (where the material has well defined positions) must fly apart due to the subsequent uncertainty of the material‘s momentum.
That is, such uncertainty relations imply that there does not exist a relative stability between the descriptive sets which is necessary for descriptive consistency, or descriptive continuity does not exist in these cases.
Though operations, and operators, tend to define the local or immediate context of a well defined (and hence constrained and limited) set, the operators themselves need to be placed in a constrained context so that the containing set of descriptive structures, ie domains functions and operators, are consistent with one another.
A space-form which is defined by lower dimensional material space-forms, which identify some of the higher dimensional space-form’s faces, identifies an operator which defines the actions (and functional relations) of the lower dimensional material space-forms, ie the higher dimensional, interaction space-form can be used to define the material dynamics between lower dimensional material space-forms.
Space-forms are differential-forms which have a real structure, but they have associated to themselves two-real structures due to the existence of a opposite metric-space state structure. Thus, mixtures of these opposite states can be used to define a Hermitian-invariant complex space-form structures in a context of harmonic functions, which are averages defined about the Hermitian space-form structures composed of opposite real metric-space states.
If the system is composed of two-different (geometrically independent, but spectrally inter-related) dimensional levels then the field would no longer be the complex numbers but rather the quaternions. Then one can consider a system which inter-relates three different dimensional levels, in which case the field would be the octions and the object of interest would be harmonic functions defined around the different octionic-subsets and subspaces. etc.

That is, very abstract and mathematically ideas…, which are more valid than what is being preached in the academic and industrial institutions today…., can be realized within the mathematically consistent context of linearity, geometric separability, metric-invariance, and many dimensions, and many material types, many metric-space states, and many mixtures of metric-space states defined by harmonic functions (averages) about the core separable geometries defined over various types of number-fields over various dimensional levels, eg the real numbers, and the complex numbers, and division rings (quaternions), and octions etc.

Yet these ideas are not considered by the professional community despite how simple their structure is and how abstractly complicated the contexts which they describe actually are.
These new math structures deal with deep ideas about many dimensions, ie material structures in many dimensions, and life, and perception, and intent, so that the math context is easily manageable.
Instead the professional math and scientists prefer to put together sets of math entities which are not compatible, nor consistent, with one another, in a math context which has no intended meaning, ie operators on function space defining measurable properties which only reference (or revert back to):
(1) math properties, eg symmetries,
(2) geometric properties, spin rotations for which there is no valid geometric model spin rotation of states, where the idea of a particle-state is represented as something from a higher dimension, but it is a higher dimension which is repressed by the notion of materialism, while on the other hand the (apparent) geometric properties of the system have not been relatable to the observed spectral properties of the system where the spectral properties (values) are placed into incoherent probabilistic structures, eg the elementary space is not fully defined and its elements are unstable and further elements are added to elementary event spaces as Ptolemy added epicycles, and
(3) to classically measurable properties.

Then much attention is placed, by the professional community, on non-linear theories, such as general relativity, where the properties of a solution to a non-linear differential equation only have validity for a short while. This is because of the essential randomness (of chaos), caused by incompatibility of the quantitative structures between the domain space and the solution function’s values. For such systems, guided by non-linear equations, their solutions must be related to feedback, which addresses the geometric context of the non-linear differential equation, so that the feedback can be used to correct for randomly introduced chaos, due to quantitative incompatibility between the domain space and the function’s values.
Much time in professional math is related to addressing the issues of non-linearity in relation to
(1) topology, which addresses geometry in a general (but classical) context, but topology’s most prominent set of geometric relations are those which relate topological geometry to separable geometries (this “in itself” should push interest into the linear, separable, metric-invariant, many dimensional context of precise mathematical description, especially since the abstract questions which can be identified in this context are so fundamental), and
(2) algebraic geometry, which defines the precise properties of (mostly) non-linear geometries, but in this case it is describing unstable geometries which cannot be related to local measures and thus these algebraic geometries are still related to chaos.

Furthermore, there is a lot of interest by professional math in probability defined in its incoherent context, where elementary event spaces are either not finite, not stable, or not defined.
That is, applying probability to cases where the elementary event space is stable and events can be counted to determine probabilities, seems to not be considered to be a useful context of probability description by the professional community, unfortunately it is the only valid context in which to apply probability.
This failure in scientific development due to statistics shows, since successes in the sciences which are dominated by using probability and statistical techniques are usually at a lower probability level than the fraction of beneficial affects related to placebos. That is, most things determined to be useful by statistical methods are usually no more useful (or valid) than is the placebo.

Nonetheless, this failure of the math and professional science communities to provide a basis for useful development, but what “development” which is done, is given to the world in the same sense that the entire population is now treated as the guinea pigs or test animals for the arrogant and criminal experiments of many scientists, experiments and processes which are based on partial knowledge, which they do not fully understand, and the professional scientists have not put their partial knowledge into a context in which it can lead to a more complete understanding before they act. Nuclear energy has been a disaster, domination by oil-energy has been a disaster, genetically modified plants have so far been a failure, and may be very large scale disaster, the chemical-agriculture-business is destroying the ecosystem upon which growing foods depend (making ecosystems and the soil sterile), and medical research is mostly about making money off of the population as the population is being used as test animals for the mostly incompetent ideas of medical researchers, who are incompetent because their knowledge is only partial.



Space-forms are about the statement that stable things which are measurable fit into quantitative containing spaces such as integer lattices, ie checker-boards, but this is basically the Euclidean case, while in the (real) hyperbolic case the “checkerboards” become “lattices” which fit into the circle (or spheres) where there is also a rotation at vertices of the lattice elements so that the “lattice blocks” must fit together but at vertices there is more variation than simply 90 degree rotations so that the “blocks” can still fit into a lattice (space-filling lattice) or discrete regional structures which fit together without over-lapping so as to fill the space as a lattice of separate blocks (or checker-board). Lattices are associated to discrete isometry or unitary subgroups.
This structure can be placed in the context of SO(2) [SO(3)] rotations, or when the base space is turned into a “complex number” coordinate space so that an analogous SU(2) acts (as a local transformation group) on the complex upper-half-plane in relation to a SU(2)/(discrete subgroup) action (group action) on the complex upper half-plane, or equivalently to act on a space-form, so that this space-form is also a model of a metric-invariant metric-space. In this context the hyperbolic space is associated to space-time as a metric-(base)-space where the types of quantities which compose the hyperbolic space are the quantities of a velocity-space, where the hyperbolic space satisfies the velocity properties of special relativity.
This process can continue to higher dimensions but it is limited by the types of lattices which each dimensional level and each metric-function signature allows on the coordinate base-space (or metric-space).
This process can form either bounded or infinite extent space-form geometries on the various dimensional metric-spaces, where the metric-functions on the different dimensional metric-spaces can have different signature representations.



Referencing two articles (Notices (AMS) Dec 2010, K Ono, and A Folsom) The modular forms are lattices on the upper half-plane defined in relation to 4-dimensional space-time and its spin covering group [SU(2) + i SU(2)], group. This can be interpreted to mean that complex 2-space has 4-real-dimensions, where one-real-dimension (ie time) is divided out so as to form something similar to hyperbolic 3-space. That is, modular forms are defined in relation to the discrete groups in [SU(z) + i SU(z)], where here z is either a “real” or “pure imaginary” integer.
This will have analogous constructions in relation to SO(3) the group structure of Euclidean 3-space and [SO(3) + i SO(3)]…,
or [Spin(3) + i Spin(3)]=[SU(2) + i SU(2)], ie SL(2,C) is the spin cover of SO(3,1),
…the group structure of 4-dimensional space-time coordinate space (or base space).
Clearly an isomorphism can be identified between dimensions on the different base spaces.
Conjecture: In the different dimensional contexts of the Euclidean or Hermitian cases the modular functions (or modular forms), if parameterized by t, can identify either periodic (or analytic) functions or approximately periodic functions which are not analytic, whereas in the hyperbolic case only the curves defined on the boundary of the lattice will be periodic (and analytic), while the other curves will quickly converge to the curves of the analytic case, though the dynamics may appear to have several loops associated to its structure, due to non-linear randomness near the distinguished (solitary vertex) point of the space-form geometry. Thus in the hyperbolic case the (few) analytic modular forms define the stable geometric structures associated to the hyperbolic lattices (or the hyperbolic space-forms, ie associated to (real) linear, separable geometries defined in a metric-invariant context).
That is, the fairly complicated context in which one considers the properties of modular forms, can have a more geometric interpretation which leads one to a very simple interpretation of the analytic case and subsequently the more complete analytic and non-analytic structures which are related to the space-form geometries. (This interpretation might be quite wrong.) But in this simpler interpretation one sees that the analytic case contains the more fundamental information about the geometric structure upon which the quantitative structure is defined, while the non-analytic case is about a quantitative structure which does not quite fit into the fundamental geometry upon which the quantitative structure is dependent for its definition. (if it is a valid interpretation…, one might find modular forms an overly complicated structure upon which to base descriptive structures)

(Hypothesize)

If a system is defined in relation to several dimensional levels and one considers a harmonic function defined to oscillate about the stable space-form geometry, then on the lowest dimensional level the harmonic functions which are defined about the real and “pure imaginary” subsets of the complex coordinate space must average to opposite metric-space states in each respective subset, which in hyperbolic space this opposite state is simply the opposite dynamical directions due to material interactions. However, in the next dimensional level the two different dimensional states in each separate level are defined by the basis to the quaternions, just as in the case of the real and “pure imaginary” subsets of the complex numbers, ie the two different dimensions that define the complex numbers, identify the subsets in which the two (opposite) metric-space states exist, that is there are four different metric-space states in which the system at the higher dimensional level can exist, but the quaternions, Q, form a division ring thus they have zero dividers, thus in the fiber group SO(Q^n), ie the Euclidean rotations over quaternion n-space, it is conceivable that the Euclidean rotations over quaternion n-space (or local transformations of coordinates related to the description of the system‘s properties, eg dynamic properties and its opposite state), near the “pure state subsets” of the coordinate space, Q^n, could result in a state, eg in a particular dimensional level, being cancelled to zero (by the local coordinate transformations and the existence of zero divisors in the quaternions) (similar to destructive interference in wave phenomenon), thus the harmonic functions defined about the “pure state subsets” of such a coordinate space do not need to average to opposite metric-space states, thus giving a greater range of possibilities in regard to the (say) complex harmonic structures about the space-form geometries (and subsequent metric-space states) of the other dimensional level. Thus, the geometric constraints associated to harmonic functions which average the space-form geometries of the different dimensional levels might be liberated from one set of geometric constraints (defined about the “pure state subsets” of the coordinate space and its constraining space-form structures), thus leading to the possibility of jumps in geometric conditions on one of the dimensional levels (ie the dimensional level which averaged to zero) during one of the discrete dynamical changes (due to discrete spin rotation of metric-space states) in the other of the dimensional levels, for (in regard to) an interacting system which depends on two dimensional levels for its “full” description.
Note: Discrete spin rotations of metric-space state are necessary to describe the dynamical processes of interacting material in any dimensional level. Mixtures of opposite metric-space states are part of the dynamic process associated to interacting (material) space-forms. (If a dynamical process appears to harmonically average to zero then the constraints of such a dynamical process can be ignored thus liberating the descriptive structure of one of its constraints.)
That is, deformations of shape can be defined in a continuous context in which geometric measures are consistent with both the structures which are being described and the descriptive context but discreteness (discrete jumps of geometric state) can still enter the descriptive structure.

If one considers the interests of professional mathematicians and scientists, where Godel’s incompleteness theorem in fact requires that mathematicians and scientists be classified in the same category of those people trying to determine a useful truth in the context of precise descriptive languages, then they are identified in (Notices (AMS) Dec 2010, article by J Grcar). One sees that about 70% of all math research goes into subjects which deal with non-linearity and function space techniques, where in more than 85% of the research on function spaces, the function values and the domain values are not geometrically consistent with one another. This research is mostly about describing patterns which only have relationships to illusions rather than patterns which are associated to useful creativity. 10% goes into research on statistics and probability, which is mostly dealing with the cases where the elementary event spaces are: not finite, not well defined, ie the actual events are not identified, and/or the elementary events are not stable in their properties, eg deciding between republican and democrat can change from one trial to another (even for trials only separated by a few minutes, thus counting is not a valid operation).
15% is research on computers. This is understandable since it is only the computer and the TV which have been developed for the last 100 years (as well as the A-bomb which used the same particle-collision probability model of an explosion which A Nobel used to develop dynamite).
So about 5% deals with other (proper) math issues, where 3% is about number theory. (Though there can be identified many mysteries about quantities, eg primes, many of these mysteries may not have any structure associated to themselves.) The remaining 2% is about pure math, where often the complexity of the (“newly”) described patterns becomes overly complex.
Higher refinements in knowledge should be easier to describe and use, so as to make relationships to other topics easier to understand. But these higher refinements are mostly “more highly refined abstractions” which are (most likely) describing patterns which are related to illusions, rather than being related to patterns, which in turn, are related to usefulness (which the conclusion of Godel’s incompleteness theorem requires). On the other hand one never knows what “well identified” descriptive pattern will turn out to be useful, yet evaluating the usefulness of the currently considered set of authoritative descriptive structures one might (should) be led to consider developing and using new math patterns. But such patterns cannot be peer reviewed, there does not exist experts for new ideas. That is, peer review is opposed to the conclusion of Godel’s incompleteness theorem which requires that math be useful, thus creating new math ideas should be the main activity of a math community, not competing in peer review journals so that the rulers of society can select a competent professional to do their creative work for them, where in dogmatic structures the creative work is the work of engineering, it is not about developing new knowledge.

This is about a story in which it has been identified (above), namely, that much of professional research does not deal with valid math interests where it is assumed that math…, because its descriptions may be descriptions of illusions which are not helpful in the development of knowledge…, should be related to the true place where the development of society can take place, through new avenues of creativity, (ie useful precise descriptive structures of language) (where the useful-ness of a descriptive language should be a main consideration in relation to deeming a descriptive language’s truth. This idea about math truth is based on the conclusion one should come to in relation to Godel’s incompleteness theorem, where the conclusion is that precise descriptions based on well defined assumptions have limitations as to what patterns they can describe.
That is, all Platonic truths are not equal, the utility of a descriptive language is (should be) associated to its truth [by the people of society].) and what opposes this natural drive for the development of usefulness…, in relation to (useful) creativity…., is elite domination, where an elite adheres to its authoritative truths and which serve….
through the social structure of being wage-slaves and its subsequent relation to personality cult which in turn serves the structure of illusions which are associated to the mechanisms and methods of using the mass media for tight social control
….the narrow interest of industry and business. The Manhatten project and E Teller’s H-bomb project have linked professional physics departments of all universities to a particle-collision model of bomb engineering which is useless in regard to practical physical knowledge (since it only deals with transitional-states and has nothing useful to say about relatively stable physical systems, which are such a prevalent a part of our experience), and a set of non-linear relations as well as function space techniques which have no useful relation with quantitative descriptions.
In fact, the economic collapse has some relation to the descriptions of (random) patterns which are claimed to be based on complicated math techniques, but the math is fundamentally invalid, where its invalidity is based on elementary grounds related to invalid non-linear patterns (which do not allow quantitative sets to be consistent with one another) as well as descriptions of probabilities which are not based on valid elementary event spaces, but nonetheless these are patterns which math professors at universities are most concerned (see above).
The only technical progress in society is related to the development of the TV (invented 1910) and the programmable computer (invented 1936) in the communication industry, while the interests of oil, the chemical-agri-oil-industry, and the military industrial complex, keep all other knowledge held to a static set of authoritarian truths which are helpful (and necessary) to the stability of these industries.
All technical development in society is based on either classical physics (where solution functions to differential equations are consistent with the geometric measures which are defined on the function’s domain space) or ideas about biology and life which are not developed enough to be helpful (useful) except the bacteria, virus model of disease.
Because of the partial knowledge which exists and the arrogant way in which the elite sector of society can do as it pleases despite the extreme short-comings in regard to (full, useful) knowledge, has resulted in the extreme destruction of the earth and the society of people which live on the earth.
The religious community (along with their rich funders and organizers) demand that their religious beliefs be upheld by everyone in the community in the abortion and stem cell issues, but the educated class does not demand that the knowledge, which corporations use, be complete and related to all external relations in a safe manner, and this is where free speech and freedom of religion in this authoritarian dogmatic culture, where dogmatic science is really state funded religion, as opposed to an enlightened and knowledgeable culture that corporate and societal actions be based on what is truly known, not based on some the hyped model of public relations communication misinformation. In all cases it is the totalitarian and dogmatic sides which are organized and given voice within society, while the fundamentals of American law: equality and freedom based on equality to seek and to speak about the truth as one sees truth, are eroded and destroyed. The only place where the issue of certainty of knowledge comes up is in regard to public safety and burning carbon fuels, where (if the state was truly concerned about national security and public safety) the policy should be that if there is a possibility (an outside chance) that the use of resources is detrimental to the society, and to future generations, then the questionable practices concerning the use of resources should be stopped. Nonetheless, armed with a dangerous amount of partial knowledge corporate powers are using this incomplete knowledge to destroy the world, all based on the icon of superiority which is associated to those who control property and money.
The core of the social problem is that law should be based on equality and freedom to believe and freedom to have meaningful speech, but instead it is based on property rights and the letter of the law. Those who control property and money and subsequently they control how language is used in society, are allowed to mire society based on their own selfish interests, it is the same as communism on steroids, where totalitarian China is raising to challenge such a (oligarchical) system, and this is possible since the development of scientific knowledge is being mired by an unnatural focus on descriptions of illusions (rather than useful descriptive structures, which arise when freedom of thought is based on equality) by the society’s arrogant intellectual elites (who have no concept of equality and freedom of speech in regard to the Socratic method of free inquiry, the idea of “superior teachers” within an authoritarian education system is a contradiction in terms, Socrates was the best model of a superior teacher and he had no measure of value associated to himself, the society was glad to put him to death. Only if a society has high ideals can it develop new knowledge. America has those high ideals, but the structure of power within society opposes them, where politicians serve those who fund their public relations campaigns for office and their political careers are defined by how much they want to be helpful to the ruling class.).

An attempt to describe the failings of the intellectual elite…
(an inability of the intellectual elites to describe the stable, definitive, discrete spectral-orbital properties of physical systems of all size scales, in a manner in which the descriptions are useful in relation to creative activity dependent on either information or control over (or of) the orbital systems properties)
…and a subsequent description of an alternative descriptive math structure which is capable of succeeding where the current descriptive math structures are failing, apparently cannot be heard (understood) or cannot be believed by the public, or by the scientists who only take seriously their peer reviewed journals (but this requirement of peer review is like requiring Copernicus to begin expressing his new ideas by first accepting the assumptions of Ptolemy and then based on these assumptions subsequently proving the new ideas which Copernicus described), or by the elite voices of dissent, ie those few dissenters who are allowed a marginal voice in the media (a large market exists for such voices because there is a lot of people who should be in opposition to the beliefs and social and institutional structures which uphold the current structure of society), but only a few carefully selected voices are allowed to have a marginal voice, which results in (does) a bad job of expressing a valid opposition to the beliefs and institutional truths of society, nor are these ideas considered (or even heard) by some of the more articulate dissenters such as (the late) H Zinn, T Ali, and N Chomsky a celebrated Linguist who should be familiar with the limits of precise language which Gödel’s incompleteness theorem implies, but academic people tend to be distracted by the technical aspect of the incompleteness theorem’s statement and they do not pay any attention to what it implies, since “if they did “take to heart” its conclusions then math would not be as ridged and as oppressed by its technical abstractions whose usefulness is questionable,” indeed that the intellectual elites are those who both believe the ideas placed before them by (mostly) corporate interests, and (who) compete to be the most adept at these ideas, that is ideas which most serve our society’s oligarchs of creativity, ie those who fund that which “gets built” by society, though one would think that this idea would be an idea which has already been expressed by some of society’s more articulate (but marginalized) dissenters, and wikileaks does not consider the expression of these new ideas as well kept secrets which could have a cataclysmic affect on society, though they are.
These new ideas and the (new) criticisms of science and math based mainly on (both) the ineffectiveness of current science and math and the natural limitations of descriptive capability which are associated to precise languages based on fixed assumptions, where this criticism is based on the example of the failing capability of a precise language is given in relation to how the ideas of Ptolemy, whose ideas were measurably verified, in turn were abandoned for the more useful ideas of Copernicus.
In a similar way today the experts, the intellectual oligarchs play a coercive game where one plays the game of science by their rules (where their rules are analogous to the rules of Ptolemy) or one does not get into the game. But clearly this is not science, as the example of Copernicus and Ptolemy so clearly show. Rather it is the same as the dogmatic authority of a religion. Thus this action by the peer review journals, which define the authoritative “science of society,” is an example of not only denying the right to free speech, but such a dogmatic authoritarian vision of science is also an example of a state sponsored religion, and thus it denies a dissenting voice, in today’s dogmatic and fixed idea about science, the right to the freedom of religion.
These ideas come from the voice of a highly educated, highly disciplined, independent, creative being which opposes and criticizes the authorities of our science institutions. It is a Socratic voice of free inquiry which also presents deeply considered alternative ideas.
If fake math, which cannot be related to any useful applications, is taken seriously then alternative voices….,
which express a simpler math structure to be used for physical description, that is, a math structure which clearly accounts for the stable orbital-spectral properties of material systems at all size scales and is consistent with classical physics and the “apparent property of quantum randomness” can be derived from its math structures,
…..most definitely should have a voice within the math and science communities of professionals.
The experts of science and math need to pay attention to these criticisms, they are failing, but like (the economic guru) Greenspan they retain their arrogant aloofness and remain pleased with their social positions as servants for the oligarchs in our failing oligarchy.
Science is based on free inquiry (the inquirer is the authority) natural curiosity, and personal integrity. Today, science is about arrogance, authority, and being a member of an in-group (being in the club). Today science is about distinguishing high value, with iconic hints provided by the media as to what has high value in the eyes of the ruling class, in relation to an (absolute) authoritative truth and thus it is not about seeking a useful description of the observed patterns of the world, but rather it is about using the language which those in the “in-group” use to write peer reviewed articles which make no sense and have essentially no uses. Thus today science is really about religion and belief in relation to the “club” of personality cult, and thus it opposes dissenting voices, where dissenting voices are those voices which oppose the religion of science which serves the military businesses, so that science is not about seeking a new route to ever more interesting creations outside the reach of oligarchical interests

This work is in the public domain

Comments

comment
05 Dec 2010
The fact that many (if not most) physical systems have stable, definitive, discrete, orbital-spectral properties at all size scales and because these systems are consistently measurable means that these systems are fitting into a context of linear, metric-invariant, separable geometries at each of the various dimensional levels which define the true containment set of existence and its space-form based system and space structures.