Partitioning a Many-Dimensional Containment Space

By Dr. Martin Concoyle

This book is an introduction to the simple math patterns used to describe fundamental, stable, spectral-orbital physical systems (represented as discrete hyperbolic shapes). The containment set has many dimensions, and these dimensions possess macroscopic geometric properties (which are discrete hyperbolic shapes). Thus, it is a description that transcends the idea of materialism (i.e., it is higher-dimensional), and it can also be used to model a life-form as a unified, high-dimension, geometric construct, which generates its own energy and which has a natural structure for memory, where this construct is made in relation to the main property of the description being the spectral properties of both material systems and of the metric-spaces that contain the material systems, where material is simply a lower dimension metric-space and where both material components and metric-spaces are in resonance with the containing space.

• Language: English
• Publisher: Trafford Publishing
• Release date: Jan 16, 2014
• ISBN: 9781490723716

Dr. Martin Concoyle

Martin Concoyle has a PhD in mathematics and has written extensively about the fundamental issues in math and physics that are confronting our society in regard to our great limitations in describing the physical world, as well as writing about the social conditions that cause our society to possess and maintain such limitations in regard to our cultural knowledge.

Book preview

PARTITIONING A

MANY-DIMENSIONAL

CONTAINMENT SPACE

DR. MARTIN CONCOYLE

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© Copyright 2014 Dr. Martin Concoyle.

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Contents

Preface

PART I

A BOOK OF ESSAYS I:

MATERIAL INTERACTIONS AND WEYL-TRANSFORMATIONS

(ORIGINALLY PUT ONTO SCRIBD.COM, 2013, PUT, M CONCOYLE,

INTO THEIR WEBSITE SEARCH-BAR)

Chapter 1       About math and physics

Chapter 2       Life

Chapter 3       Self-similar patterns eg (Mandelbrot sets)

Chapter 4       New knowledge and rigorous proof

Chapter 5       Review of science IV

Chapter 6       General Relativity and Quantum Physics

Chapter 7       Quantum physics

Chapter 8       Remedy for physics

Chapter 9       New ideas vs. a social structure which opposes new ideas

Chapter 10       Beyond non-linearity and indefinable randomness

Chapter 11       New ideas about math

Chapter 12       Physical description and spectral connections (or spectral derivatives)

Chapter 13       Weyl-transformations

Chapter 14       Math 1

Chapter 15       Creativity and science and math

Chapter 16       Discrete mathematics implies smoothness… ,

Chapter 17       Language and truth

Chapter 18       Arbitrary quantization vs. Stable math constructs

Chapter 19       Mixture

Chapter 20       Connect the spiritual with the material worlds

Chapter 21       Failures of the modern world

Chapter 22       Description based on fundamental indefinable randomness is invalid

Chapter 23       A new language for physical description

Chapter 24       Writing about magic (or Writing about science fiction)

PART II

A BOOK OF ESSAYS III: ELEMENTARY TOPICS

(ORIGINALLY PUT ONTO SCRIBD.COM, 2013, PUT, M CONCOYLE,

INTO THEIR WEBSITE SEARCH-BAR)

Chapter 25       Algebra

Chapter 26       Elementary math

Chapter 27       Language of math

Chapter 28       Language

Chapter 29       Knowledge

Chapter 30       Math 2

Chapter 31       Math 3

Chapter 32       Philosophy

Chapter 33       Problems in math

Chapter 34       Measuring

Chapter 35       Metric-spaces

Chapter 36       Lattices

Chapter 37       Signatures (of metric-functions)

Chapter 38       Geometrization

Chapter 39       Finite spectra

Chapter 40       Function spaces

Chapter 41       General relativity

Chapter 42       Existence

Chapter 43       Entropy

Chapter 44       Discrete shapes

Chapter 45       Dimensional levels

Chapter 46       Derivatives

Chapter 47       Continuity

Chapter 48       Constant curvature

Chapter 49       Classical physics

Chapter 50       Problems in science

Chapter 51       Problems with science

Chapter 52       Physical law

Chapter 53       Probability

Chapter 54       Set size

Chapter 55       Stability

Chapter 56       State of man’s knowledge

Chapter 57       What is material?

Chapter 58       Spin-group

Chapter 59       Spectra

Chapter 60       String theory

Chapter 61       The number of subspaces

Chapter 62       Non-linear math

Chapter 63       Life

Chapter 64       Mind (consciousness)

Chapter 65       Bosons and Fermions

Chapter 66       Action-at-a-distance

Chapter 67       Indefinable randomness

Chapter 68       Measuring

Chapter 69       Summary

References

Index

Appendix I

This book is dedicated to my wife M. B. and to my mom and dad.

Copyrights

These new ideas put existence into a new context, a context for both manipulating and adjusting material properties in new ways, but also a context in which life and creativity (practical creativity, ie intentionally adjusting the properties of existence) are not confined to the traditional context of material existence, and material manipulations, where materialism has traditionally defined the containment of material-existence in either 3-space or within space-time.

Thus, since copyrights are supposed to give the author of the ideas the rights over the relation of the new ideas to creativity [whereas copyrights have traditionally been about the relation that the owners of society have to the new ideas of others, and the culture itself, namely, the right of the owners to steal these ideas for themselves, often by payment to the wage-slave authors, so as to gain selfish advantages from the new ideas, for they themselves, the owners, in a society where the economics (flow of money, and the definition of social value) serves the power which the owners of society, unjustly, possess within society].

Thus the relation of these new ideas to creativity is (are) as follows:

These ideas cannot be used to make things (material or otherwise) which destroy or harm the earth or other lives.

These new ideas cannot be used to make things for a person’s selfish advantage, ie only a 1% or 2% profit in relation to costs and sales (revenues).

These new ideas can only be used to create helpful, non-destructive things, for both the earth and society, eg resources cannot be exploited to make material things whose creation depends on the use of these new ideas, and the things which are made, based on these new ideas, must be done in a social context of selflessness, wherein people are equal creators, and the condition of either wage-slavery, or oppressive intellectual authority, does not exist, but their creations cannot be used in destructive, or selfish, ways.

Note: This book is equivalent to other books; which were originally put onto Scribd.com

Where one of the old books was:

A book of essays I

Material Interactions and Weyl-transformations

(Various essays about stable math constructs, material interactions,

and finite quantitative structures)

By M Concoyle

Copyright 2012, Martin Concoyle,

(1st put onto Scribd.com, put, m concoyle, into their website search-bar)

And the other old book was:

A book of essays III

Elementary topics

(Various essays about stable math constructs, material interactions,

and finite quantitative structures)

By M Concoyle Ph. D.

Copyright 2012, Martin Concoyle,

(1st put onto Scribd.com, put, m concoyle, into their website search-bar)

It could be said that these new ideas about math descriptive context are so simple that the main ideas presented in this book are presented by the handful of diagrams about these simple shapes and how they are folded which are provided at the end of the book.

This book is pieced together from over 100 essays. There may be repetitions (sorry) but they are titled differently so the repetitions are hard to detect and eliminate.

This book is an introduction to the simple math patterns used to describe fundamental, stable spectral-orbital physical systems (represented as discrete hyperbolic shapes), the containment set has many-dimensions, and these dimensions possess macroscopic geometric properties (which are discrete hyperbolic shapes). Thus it is a description which transcends the idea of materialism (ie it is higher-dimensional), and it can also be used to model a life-form as a unified, high-dimension, geometric construct, which generates its own energy, and which has a natural structure for memory, where this construct is made in relation to the main property of the description being the spectral properties of both material systems and of the metric-spaces which contain the material systems, where material is simply a lower dimension metric-space, and where both material-components and metric-spaces are in resonance with the containing space.

Notes:

Double spaces can mean a sudden new direction of the discussion without a new paragraph title.

The *’s represent either favorites (of the author) or (more likely) indecision and questions about (logical) consistency. Information and discussion about ideas is not a monolithic endeavor pointing toward any absolute truth, the wide ranging usefulness, in regard to practical creativity, might be the best measure of an idea’s truth, it is full of inconsistencies and decisions about which path to follow (between one or the other competing ideas) are either eventually made or the entire viewpoint is dropped, but this can occur over time intervals of various lengths.

The main idea of thought (or of ideas) is that it is about either sufficiently general and sufficiently precise descriptions based on simple patterns, or it is about developing patterns (of description) which lead to particular practical creativity, or to new interpretations of observed patterns, or to directions for new perceptions.

Preface

T hese essays span 2004 to 2012 and some old ideas (along these same lines) expressed around 2004 may not be ideas considered correct by myself today (2012), but I have not re-edited them.

Ideas are worth expressing, and the development of ideas can have interesting histories, and old ideas can be re-considered.

Today there exist experts of dogmatic authority who are represented in the propaganda system (as well as in educational institutions which also serve the interests of the owners of society, ie the modern day Roman Emperors) as being always correct, yet they fail to be able to describe the stability of fundamental physical systems, and their descriptions have no relation to being related to practical creative development, since they are descriptive constructs based on probability and non-linearity, and deal with systems made-up of only a few components which possess unstable properties.

Peer review checks for the dogmatic purity of its contributors. However, such a situation in science and mathematics does not express the (true) spirit of knowledge. Knowledge is related to practical creativity and knowledge is about equal free-inquiry with an eye on what one wants to create. In this context knowledge should be as much about re-formulating, and re-organizing technical (precise) language as about learning from the current expressions of knowledge [with its narrow range of creativity associated to itself].

A community of dogmatically pure scientists and mathematicians is not about knowledge, but rather about the power structure of society (a society with a power structure which is essentially the same as that of the Holy-Roman-Empire, ie fundamentally based on extreme violence) and the scientists and mathematicians are serving the owners of society (the new Emperors) by competing in a narrow dogmatic structure of authority, so as to form a hierarchical array of talent to be selected from by the Emperor, and then used within the narrowly defined ranges of creativity, about which the owners of society want attended.

That is, scientists function in society as elite wage-slaves for the owners of society, and they are trained experts, similar to trained lap-dogs.

This structure of knowledge is the opposite of valid knowledge, which should be related to a wide range of creative efforts, by many people, expressing many diverse interests.

It is good to express a range of ideas.

Whereas, being correct is associated to a false, or at best, limited knowledge, which serves the owners of society and is mostly used to express in the propaganda system, the (false) idea, that people are not equal. It is this type of idea which the Committee on Un-American Activities should investigate, since the US Declaration of Independence states that all people are equal, and this should be the basis for US law, and not: property rights, and minority rule, which is the same basis as for Roman-Empire Law.

Preface

T he math descriptions, about which what this book is about, are about using math patterns within measurable descriptions of the properties of existence which are: stable, quantitatively consistent, geometrically based, and many-dimensional, which are used to model of existence, within which materialism is a proper subset.

In regard to the partial differential equations which are used to describe stable material systems they are: linear, metric-invariant [ie isometry (SO, as well as spin) and unitary (SU) fiber groups], separable, commutative (the coordinates remain globally, continuously independent), and solvable.

The metric-spaces, of various dimensions and various metric-function signatures [eg where a signature is related to R(s,t) metric-spaces] have the properties of being of non-positive constant curvature, where the coefficients of the metric-functions (symmetric 2-tensors) are constants.

That is, the containment sets and material systems are based on (or modeled by) the simplest of the stable geometries, namely, the discrete Euclidean shapes (tori) and the discrete hyperbolic shapes (tori fitted together), where the discrete hyperbolic shapes are very geometrically stable and they possess very stable spectral properties.

One can say that these shapes are built from cubical simplexes (or rectangular simplexes).

Both the (system containing) metric-spaces and the material systems have stable shapes of various dimensions and various metric-function signatures, where material interactions are built around the structures of discrete Euclidean shapes (sort of as an extra toral component of the interacting stable discrete hyperbolic shapes), within a new dimensional-context for such material-interaction descriptions, and there are similar interaction constructs in the different dimensional levels. The size of the interacting material from one dimensional level to the next is determined by constant multiplicative factors (defined between dimensional levels) which are (now) called physical constants.

Furthermore, the basic quantitative basis for this description, ie the stable spectra of the discrete hyperbolic shapes, forms a finite set. The quantitative structure is, essentially: stable, quantitatively consistent, and finite.

This descriptive construct can accurately, and to sufficient precision, and with wide ranging generality, describe the stable spectral-orbital properties of material systems of all size scales, and in all dimensional levels. It is a (linear, solvable) geometric and controllable description so it is useful in regard to practical creativity.

The many-dimensions allow for new high-dimension, well organized, controllable models of complicated systems, such as life-forms. These ideas provide a map to help envision these geometric structures.

These new ideas are an alternative to the authoritative (and overly-domineering) math patterns used by professional math and physics people which are based on non-linearity, non-commutativity, and indefinable randomness (the elementary event spaces do not have a valid definition), where these are math-patterns, which at best, can only describe unstable, fleeting patterns, which are unrelated to practical creative development, and whose measured properties can only be related to feedback systems (whose stability depends on the range of validity of such a system’s differential equation).

That is, it is a math construct which is not capable of describing the stable properties of so many fundamental (relatively) stable physical systems, eg nuclei, where within this authoritative descriptive context it is claimed that these stable fundamental physical systems are too complicated to describe.

There are many social commentaries, in this book, this is because such a new context of containment, in regard to measurable descriptions, which possesses so many desirable properties, one would think that such a descriptive language should be of interest to society. But inequality, and its basis in arbitrary (and failing) authority, and the relation which this authority has to extreme violence (in maintaining its arbitrary authority, and in maintaining a social structure (as Mark Twain pointed-out) which is based on: lying, stealing, and murdering) have excluded these new ideas from being expressed within society.

People have been herded, and tricked, into wage-slavery, where deceiving people is easy with a propaganda system which allows only one authoritative voice, and that one-voice is the voice of the property owners (with the controlling stake), and the people are paralyzed by the extreme violence which upholds this social structure, where this extreme violence emanates from the justice system, and whereas the political system has been defined as politicians being propagandists within the propaganda system (politicians sell laws to the owners of society, for the selfish gain of the politicians, and then the politicians promote those laws on the media).

Part I

A book of essays I:

Material Interactions and Weyl-transformations

Chapter 1

About math and physics

T he value (of a culture) is (partly) determined by what is created, and what can be created depends on what is known about existence. Is truth determined by science and the identified objective material truth of actual events, where journalists also try to report in the context of material objectivity, but the reports of journalists have many assumptions about value built into their reports, and it is these assumptions through which the material events are interpreted. Are there other assumptions and other interpretations of observed events or observed geometries? Answer: There are always other ways in which to organize one’s descriptive language. This can have an affect on what it is that we believe is true about existence, both in journalism and in science.

Is scientific truth simply a measurably verified authoritative description of actual material events, or is it also about the context and the descriptive language through which events and processes are interpreted, along with having a relation to not only measurable verification, but also having a relation to the wide applicability and great usefulness of the descriptive language which is chosen to be the descriptive language that one uses to describe observed patterns of existence.

If the fixed authoritative language is not widely applicable and very useful then a new descriptive language needs to be created and considered. This is what Copernicus did in relation to the measurably verified and authoritative descriptions of Ptolemy. Thus, finding a new more useful language than the fixed, authoritative and non-functional language of currently accepted science is, in fact, the central endeavor of science.

Are differential equations the central idea concerning measurable physical properties which can be precisely described, or are classical differential equations organized around another more fundamental idea (or pattern)? Answer: Differential equations are organized around discrete isometry subgroups. What differential equations really identify, in relation to widely applicable, and controllable, and very useful descriptions of physical properties, are the stable and very controllable systems which are linear and/or separable, ie the tangent directions to the coordinates are always pair-wise orthogonal. That is, either (linear) differential equations whose coefficients are constants, or the more difficult geometric (linear) differential equations whose natural coordinates are separable are the types of differential equations whose solution functions result in the greatest number of useful applications. The more difficult to describe geometries, which are also separable, are exactly those geometries defined by space-forms.

That is, the stable, definitive, and controllable physical systems which underlie how material is organized within existence (or within our experience), are either to be modeled as linear differential equations with constant coefficients, or (linear) differential equations related to space-forms. That is, understanding the structure of existence in terms of space-forms in a multi-dimensional containment space is the primary descriptive context for understanding the stable, controllable, and definitive properties of material, or more generally of all existence.

Under the assumption of materialism, if material events were mainly random caused either by the chaos of non-linear systems or by the intrinsic randomness assumed by quantum physics, then there would be no way in which to have stable definitive material structures, ie all organized structures would (at best) be temporary. However, General: Nuclei, atoms, molecules, crystals, material fields, interactions, planetary orbits, as well as planets, stars, and life all have stable definitive (either) properties, (or) defining principles, which in the current paradigm are determined primarily by both chaotic non-linearity and intrinsically random quantum physics, and subsequently the current paradigm has not been successful in describing these general but very stable systems or properties (Are force fields determined by geometry or by random particle collisions?).

Abstract

Illusions about culture are (unfortunately) upheld by the pride that people have for their society’s high culture.

For the many to support (or to believe) scientific experts is the same as supporting the oligarchic structure of society, with some exceptions.

Materialism as a foundation for physical description has not worked in regard to describing in a useful manner the stable, definitive spectral properties of quantum systems.

Alternative: The description of existence should be based on using the mathematics of discrete isometry subgroups, which are built from cubical simplexes, which in turn, can be made into space-form geometries, by quotient topology, where now both material and space are to be modeled as space-forms which exist at different dimensional levels in a multi-dimensional context.

Note: It cannot be proved that this new model of material and space is wrong, and measurements already made verify its truth.

The description of existence should be based on using the mathematics of discrete isometry subgroups, built from cubical simplexes (by quotient topology) so as to form space-forms, (as well as being based on more general unitary groups, more general in the sense of being Hermitian invariant (or an invariant measure of length on complex coordinates)) in a multi-dimensional, many signature metric-function context (where real metric-spaces [of opposite states] fit into the real and pure imaginary subsets of Hermitian space), where both material and space are modeled as space-forms in different but adjacent dimensional levels, so that this description is placed within a general, yet pragmatic, context which is associated to a true description of existence.

It is a description which is not based on materialism, yet it describes the observed material properties as a subset structure of a more inclusive description. In particular it describes the stable, definitive spectral (or orbital) properties of quantum systems (as well as macroscopic systems) of all size scales.

It is a new description based in mathematics, a description which is about material, space, and time (so that it transcends these properties as we know them (in our usual materialistic interpretation of our experience)), so that it is a measurably verifiable description. However, as a description its validity is based on it being both widely applicable and very useful, as opposed to being dogmatic and authoritative descriptions which are only measurably verifiable (as both Ptolemy’s descriptions were, and the currently accepted descriptions are also only measurably verifiable).

Note: It is only associated to prize mathematical problems by accident.

The mathematical structure of space-forms can also be based on differential-forms, so its mathematics will be consistent with classical physics, where the descriptions of classical physics can also be based on differential forms.

Classical physics is about the containment of the material properties (of position, velocity, etc) within coordinates, which form the domain space for the functions, which in turn, represent the physical properties so that the locally measurable (or differentiable) physical properties, represented as derivatives of functions, are set equal to an equivalent geometric representation of the same property type (or quantitative type), so as to define a differential equation. The solutions to these differential equations identify the measurable properties, position, velocity etc, of a classical system. For most physical systems these differential equations are non-linear. Non-linear differential equations are difficult to solve and when there are solutions these solutions most often are characterized by chaos, where slightly different initial conditions lead to quite different solution function properties (occasionally solutions to non-linear differential equations are associated to well defined geometries). The types of differential equations which have led to technical development are the (quite controllable) linear differential equations and when the differential equation has many variables, it is the separable (see next paragraph) differential equations which are solvable and hence useful.

Are differential equations the central idea concerning measurable physical properties which can be precisely described, or are classical differential equations organized around another more fundamental idea (or pattern)? Answer: The most useful differential equations are organized around discrete isometry subgroups. What differential equations really identify, in relation to widely applicable, and controllable, and very useful descriptions of physical properties, are the stable and very controllable systems which are linear and/or separable, ie the tangent directions to the coordinates are always pair-wise orthogonal. That is, either (linear) differential equations whose coefficients are constants, or the more difficult geometric (linear) differential equations whose natural coordinates are separable are the types of differential equations whose solution functions result in the greatest number of useful applications. The more difficult to describe geometries, which are also separable, are exactly those geometries defined by space-forms.

That is, the stable, definitive, and controllable physical systems which underlie how material is organized within existence (or within our experience), are either to be modeled as linear differential equations with constant coefficients, or (linear) differential equations related to space-forms. That is, understanding the structure of existence in terms of space-forms in a multi-dimensional containment space is the primary descriptive context for understanding the stable, controllable, and definitive properties of material, or more generally of all existence.

By arguments about Brownian motion (provided by E Nelson [Princeton 1950’s]) the new description provides a geometric-interaction model of atomic (size) scale systems so that these interactions identify the small scale properties of Brownian motion, which in turn, forms the basis for the apparent random, wave-like quantum properties of (microscopic) material. That is, the new description is consistent with the probability wave-functions of quantum systems, but the probabilistic properties of quantum wave-functions are derived from a more fundamental geometric structure of existence.

Quantum physics is about representing what are considered to be the intrinsically random spectral-particle events of quantum systems as function spaces and then identifying a set of operators (a complete set of commuting [Hermitian and adjoint] operators) which can be used to identify the spectral set of the quantum system’s function space, so that the energy operator identifies unitary invariance for the quantum system’s wave function. The quantum system’s spectral set of functions are supposed to be used to identify the quantum system’s observed particle-spectral random event-set in space and time, but such a complete spectral sets for general quantum systems have not been found using these techniques.

Note: Low dimensional unitary invariance (of wave functions) is used to identify both internal particle structure, eg quarks composing neutrons, as well as general derivatives (or connections) which are used to model elementary particle collision interactions (so as to remain unitarily invariant in terms of equivalent connections) in relation to perturbations of a quantum system’s wave-function, within the mathematical structure of curvature on a principle fiber bundle (acting on the quantum system’s wave-function). This descriptive structure (or process) claims to identify a global wave function’s properties by point-like particle (collision or connection) interactions which take place at exactly one point, where the connection is not a tangent to a curve but rather a term which represents a particle collision (or interaction) at a point. This methods has such limited uses that such a claim should be seriously doubted.

However, this description is (still) not capable of identifying the full set of spectral-particle events for a general quantum system.

A probability based system needs to have a well defined elementary event space, but such elementary event spaces within the quantum descriptive language seem to be subjective sets made up of either incomplete spectral sets or based on unstable elementary particle events (with a limited range of applicability) whose properties are continually adjusted, ie so as to form an inconsistent language.

Yet it is the stable, definitive orbital (or spectral) properties which are most fundamental to the properties of material systems and quantum description has not been able to describe these properties. Though the inconsistent language of quantum physics may be good for fitting data, it has not shown itself to be widely applicable nor all that useful.

Whereas stable, definitive orbital properties of material systems at all size scales are always described by hyperbolic space-forms which descend from the properties of discrete isometry subgroups. The spectral set of a particular dimension spectra at a particular dimensional level has resonance relations to similar spectra which descends from higher dimensional structures which are not directly associated to the particular metric spaces within which our material spectral structure is contained.

Are elementary particle collision models of material interactions within the context of a hidden higher dimensional space necessary (string theory curls up the higher dimensions, which are not supported by the idea of materialism, into small geometries which are in accessible to our experience)? Answer: No. Elementary particles are really distinguished points of space-forms, where the higher dimensions of high dimensional discrete isometry subgroups also appear to be hidden, but these higher dimensions can be macroscopic, and these higher dimensions have properties which can be described and used.

Under the assumption of materialism, if material events were mainly random caused either by the chaos of non-linear systems or by the intrinsic randomness assumed by quantum physics, then there would be no way in which to have stable definitive material structures, ie all organized structures would (at best) be temporary. However, General: Nuclei, atoms, molecules, crystals, material fields, interactions, planetary orbits, as well as planets, stars, and life all have stable definitive (either) properties, (or) defining principles, which in the current paradigm are determined primarily by both chaotic non-linearity and intrinsically random quantum physics, and subsequently the current paradigm has not been successful in describing these general but very stable systems or properties (Are force fields determined by geometry or by random particle collisions?).

Sometimes (or often) when (often times small) material systems interact (where the interaction is modeled as higher adjacent dimensional space-forms whose spatial faces are tangent to the [interacting] material space-forms) the interaction leads to stable, definitive spectral (or orbital) systems, eg stable quantum systems. The (hyperbolic) space-form provides models for both the stable properties of these stable new systems as well as for the interaction structure. The space-form provides a geometric-spectral basis for both the structure of the interaction as well as the stable, definitive orbital (or spectral) properties of both quantum systems and macroscopic systems, eg the solar system is apparently stable.

The main attribute of physical systems (in relatively low temperature thermal systems) at all size scales are their stable, definitive spectral-orbital properties. For example: nuclei, atoms, molecules, crystals, and planetary orbits; all have stable, definitive orbital properties (as well as the intermediate sized systems such as life, clouds [lightning], perhaps mountains, and planets etc). These fundamental stable orbital attributes of physical systems currently go without adequate descriptions in the currently accepted descriptive language, and furthermore, the current descriptions have not been shown to be either widely applicable nor useful.

It must be noted that nearly all of the stable, definitive orbital properties of physical systems go unexplained in the current descriptive structure. Quantum physics, particle physics, general relativity, and string theory do not work for the purpose of providing useful, widely applicable descriptions of existence, and classical physics has clear limitations (eg the apparent stability of the solar system is not understood).

However, in the new descriptive language, the stable orbits of quantum systems are not related to a probability (or function space) based descriptions, rather they are related to the geometry of (hyperbolic) space-form (orbital) flows, where space-forms are models of material systems which are contained within spatial sets, or metric-spaces, which in turn, also have space-form (or spectral) properties, thus the stable definitive spectral systems, which exist at one dimensional level, have relations of resonance with their (complete higher dimensional) containing set.

The new description provides a context for both the orbital geometry of quantum systems which is consistent with:

• the Bohr-Somerfeld orbital model, and

• unitary complex coordinates, (ie coordinates which contain dynamic-systems), and

• spin rotation of material-particle components (spin rotations between orbital flows of opposite states on the system’s space-form), and

• 3-dimensional spherically symmetric inertial properties of quantum-spectral systems in general,

• . . . . as well as the spherically symmetric inertial properties of interacting 3-dimensional macroscopic systems, and specifically (because of the above list) the new description is consistent with the H-atom, so that it also provides the correct context for atomic spectra in general (where [in the new description] there exist more spectral constants than the Planck constant, h, in a (new) multi-dimensional-spectral context), . . . . the new description also provides a space-form context for the existence of greater ranges of dynamic stability for inertial tori of (big) macroscopic (planetary) systems, where these inertial tori are related to (but not the same as) Arnold-Moser (CAM) toral stability for macroscopic systems.

That is, the new description is already a verified theory, with greater range for identifying (observed) stable material orbital properties than the current (dogmatically-authoritative-[materialistic]) descriptive language allows.

In the new descriptive language, both space and material are modeled as space-forms, where a material space-form exists in a metric-invariant metric-space of an adjacent (higher) dimension. However, since the metric-space can also have the structure of a (higher dimensional) space-form, the metric-space will also have spectral properties. The material contained in a metric-space must resonate with its (full) containing space of all higher dimensions which all have space-form structures.

The new description is a multi-dimensional theory such that the 4th spatial dimension (ie not space-time) is apparently not experienced; both because (1) of the size-scale of 3-dimensional interaction space-forms (which are contained in four spatial dimensions) and the relation of interaction 3-space-forms to both the sun’s and the solar system’s space-form structure, so that because of a general relativistic property (of a natural ridged space-form reference frame) the large scale inertial properties which might exist within the four spatial dimensions, that we inhabit, are hidden… . (this is also related to dark matter), and (2) that interactions in 4-space do not have radial direction within a context of spherical symmetry, which can be associated to a radial direction, rather interactions in 4-space have a direction which is tangential to a higher dimensional sphere’s radial directions, thus higher dimensional interactions have a relation with rotational motion (or rotational inertia). Note: This lack of a radial direction (of force) associated with spherical symmetry for material interactions in higher dimensions than three-spatial dimensions is another reason why higher dimensions are not experimentally detected in an obvious manner, ie we only observe an inverse square functional (or geometric) form for force, since spherical symmetry with a well defined radial direction only exists in 3-space.

This new description places great concern about the validity of the structure of the elementary event spaces of the quantum description, both in relation to regular quantum wave-functions, and in relation to particle-physics, where in both cases the probability language of these two descriptions is not consistent with the needed fundamental properties of elementary event spaces for a probabilistic descriptive language (ie elementary events must be complete and concrete [ie do not decay, or change]). However, instead of random events, the new description provides a definite geometric model of both spectral orbits, and particle properties, ie elementary particles are distinguished points on (small) space-forms.

The geometric structure of true existence (and of this new descriptive language) is more consistent with the more fundamental topological relations to geometry which is concerned with the holes that exist within a space (or within a function’s domain space) (and co-homology’s [smoothness] and homotopy’s [continuous] relation to holes in space) which were (better) identified by the properties of discrete isometry subgroups (which are emphasized by W Thurston), than are the relations that the geometric properties of existence have to the less fundamental diffeomorphism-related geometric properties of general relativity, where general relativity only seems relevant to (or primarily to) the 1-body problem in 3-space that has spherical symmetry, or to the less fundamental (smooth) function space properties of a general function space description of geometric properties, or harmonic properties, where harmonic functions relate the general function space descriptions to probability. Note: Such harmonic relations to probability work in classical physics but they do not seem to work in quantum physics because functions’ different relations to various types of geometric properties can be very complicated, so as to make the descriptive language of geometry based on the properties of function spaces more complicated than it needs to be.

Because the large scale properties of the universe seem to be characterized by their flatness, general relativity only seems to be valid in 3-space where the isometry group for Euclidean 3-space is spherically symmetric, so that this (local) coordinate transformation group property descends to the property of spherical symmetry for Euclidean 3-space (the new description claims that this is the origin of spherical symmetry in regard to inertial interactions on Euclidean 3-space, where Euclidean space is the space within which spatial displacement and subsequently inertial properties are naturally defined, where this spatial displacement is done in complex coordinate space, where in turn, mixtures of different metric-space states are a fundamental aspect of the spatial displacement process).

It should be noted that general relativity can only deal with the 1-body problem in the context of spherical symmetry on Euclidean 3-space, where Euclidean space and spherical space are metrically consistent with one another.

The new description provides a greater more general context for all of existence (all the many dimensions and the many different signature metric functions defined for these various dimensions so that physical properties are associated with specific dimension and specific signature metric-function metric-spaces). The material properties of 3-space, both Euclidean (inertia, displacement) and hyperbolic space, ie equivalent to space-time, (charge, time), form a descriptive subset, so that the new descriptive language is (can be shown to be) consistent with all the known, and useful properties of material that have so-far been observed (and/or described). Note: New material types can be defined in higher dimensional spaces so that this new material is associated to the signatures of metric-functions in these higher dimensional spaces.

Note: It cannot be proved that this new model of material and space is wrong, where proofs must be based on the assumptions of the new descriptive language.

It is not the scientific properties of being a: (1) measurably verifiable, (2) widely applicable, and (3) very useful, descriptive language which opposes this new descriptive language, ie the new descriptive language represents the very best methods and standards for determining truth in science, ie changing the descriptive language so as to have a more useful description in relation to creating and controlling new systems, rather what opposes this new description are the illusions of a pre-existing authoritarian-dogmatic truth which is supported by the, currently used (and fixed) scientific language, where scientific description is verified by the thinly identified validation property of a being measurably verifiable (the same verification condition which upheld the science of Ptolemy).

This absurd criterion for scientific truth, which invites descriptions of illusions (just as Ptolemy was describing illusions), is a property of the oligarchic structure of society, where a few socially powerful people can uphold illusions so that the few can dominate the many in a selfish manner.

Illusions about culture are (unfortunately) upheld by the pride that people have for their society’s high culture.

Supporting scientific experts is the same as supporting the oligarchic structure of society, with some exceptions, such as global warming, where the correlations are too significant to not be taken seriously. Society should take all issues related to public harm seriously.

Chapter 2

Life

I n this is a new math-model of existence, which includes materialism as a subset, the math is consistent with all the (actually verified) observed properties upon which the currently accepted dogmas of physics are based, but it gives these observed properties both new contexts and new interpretations.

Yet, it extends the set containment structure up to higher-dimensions, where the higher-dimensions within this extension have the form of macroscopic-geometry, but in the new language (of the new ideas) these higher-dimensions have a naturally hidden structure, which is caused by the (newly provided) geometric structure of material interactions.

However, the description gives a map into those higher dimensions and it identifies the properties to look for, as well as providing a surprising high-dimension model of life.

That is, life is connected to the higher-dimensions where intentional actions can be placed into the new map of the higher-dimensions of existence wherein new (hidden higher-dimensional) material also exists (for example, the higher-dimensional material may be the size of the solar-system).

This new math context is a new structure within which life has an active creative relation to that existence, because the essence of life exists in the higher-dimensions, ie life is an odd-dimensional (in the hyperbolic dimensions of 3, 5, 7, 9) discrete hyperbolic shape; whose genus is an odd-number. The mind (or its memory) is the spectral properties contained on a maximal tori of an SU(11) Lie group.

Assumptions

This paper is science, in the spirit of the scientific revolutions of Copernicus, which explore new ways to use math patterns (measurable patterns) to describe existence, so as to remain consistent with current observed scientific patterns (but placed within new interpretive models), eg as well as for those few physical models of material systems which actually provide practically useful information, but the new theory is based on new interpretations of the data, eg stable, definitive, and discrete properties which have been observed for quantum systems, and these properties require a stable, geometric math structure as the basis for their description… , as opposed to indefinable-randomness, with its close connection to non-linearity, as its basic assumption (ie the currently held assumptions of physical science).

The failings of current authoritative science and math,

and its relation to religion

Having complete faith in materialism is an example of how the corporate propaganda system (which includes the education system) has so effectively turned the narrowly defined, authoritative science of nuclear weapons (based on the idea of materialism) into a religion (ie faith in high-intellectual-value), and this new religion is created in such a way so that the two religions (of faith in meaningless words vs faith in the authority of material based science) are in opposition.

However, an inability for material-based science to both

1.   accurately describe the properties of (general) material systems at a precise enough level, and

2.   To frame these descriptions in a way which applies to a wide range of general (quantum) systems as well as

3.   the language structure of current physical description being almost completely unrelated to practical technical development, . . . , so that these three failings of the current scientific descriptions now imply that:

faith in the authority of material based science is equal to faith in meaningless words, but now faith in meaningless words, in regard to currently accepted authoritative science, is considered to be (believed to be) based on complicated abstractions about the material world.

That is, if science was not supportive of the idea of materialism then the main properties of (absolute) language, to be used in the propaganda system for social control, would no longer exist ie abstractions about the spirit would no longer be in opposition to the idea of a material based science.

If you critically analyze the effectiveness of modern science in regard to technical development you should conclude that modern science is irrelevant to further technical development (see J Horgan, The End of Science, 1995. He re-iterated this belief in a Discovery interview in 2005 or 2006.), [but the statement needs to be even stronger; modern science is unrelate-able to further technical development because its descriptions (its calculations based on its own laws) do not demonstrate sufficient consistency with the observed patterns for any general quantum system, and the careful descriptions do not provide an acceptable level of precision. That is, (based on science’s own standards for validity) modern math and science (2012) is wrong].

This should be a sign to consider new ideas, new ways in which to use math patterns, organized into new descriptive languages.

Horgan is a journalist, who has taken a step-back to observe and assess what is being accomplished based on modern science, and when he did this, he has correctly assessed that black-holes, big-bangs, dark energy, and elementary-particles etc, are irrelevant to further technical development.

The statement of this paper is stronger, physics is unrelated-able to further technical development because it is fundamentally wrong, and logically inconsistent. That is, this paper is challenging the authority of those socially unchallengeable intellects, who espouse a claim that they possess an ‘absolute truth’ (or are progressing toward realizing an absolute scientific truth) based on both materialism, and their inconsistent models of abstract complicated-ness, eg based on non-linearity and indefinable randomness.

That is, this paper challenges the idea that… , only the ideas of the designated authorities are to be expressed within all of society, or equivalently, only a propaganda system is to be allowed to have a (meaningful) voice.

. . . , because it can be seen in a simple, clear manner that the authorities are wrong, and their errors are all about how they use the patterns of indefinable randomness and non-linearity, which are quantitatively inconsistent and logically inconsistent, where these ideas are being used to try to describe measurable patterns of the world, but they are failing at trying to do this.

Instead math descriptions of measurable properties need to be based on stable math structures (linear, metric-invariant, geometrically separable, spaces, and spaces of non-positive constant curvature) placed in new contexts, such as a many-dimensional context in which these stable shapes are central to the descriptive structures, geometry are central to identifying the math formulas which describe material interactions and the stable properties of stable systems (within a containing space which is fundamentally about shape).

How to understand opposition to new ideas, (an opposition which is expressed by every person within society) in the context of science; this is the same model of Copernicus having to oppose the authority of the faithful (in his age), ie only the ideas of the designated authorities are to be expressed within all of society. But Copernicus only dealt with the authority of one institution (called religion, where scientific authority had been integrated into religious authority, in his day), while today material based science has also become a narrowly defined absolute truth, whose ideas cannot be questioned (by ordinary people) and for which (perhaps) one-half (or all) of the public have complete faith in its authority.

The propaganda system has taught the public to have faith in a fixed (material based) authoritative science, and the key to tricking the public into believing in this new religion, the worship of the authority, is to make the knowledge of high-value and exclusive.

That is, new ideas about science are placed into a context in which the new ideas are represented as being opposed to the authority of science, and this is because the propaganda system has successfully turned science into an authoritative religion of materialism which defines the high-value of the authoritative truth about material properties within society, and defines the high-value of a few gifted intellects, whose authority cannot be questioned. And science is framed as being in opposition to religion.

Note: Yet big-oil, the military, the justice system, and big-banking can dismiss this authoritative truth, eg they can dismiss the idea that global warming as being caused by concentration of CO2 in the atmosphere, where this dismissal is based on selfish interest, and on how the political-justice-propaganda-education system protects these selfish interests of oil, military, and banking, (this should be called corruption, but it is called politics, and marketing).

That is, a main issue in regard to the propaganda of science, is that the authority of science remains based on materialism.

This need to base the meaning of science on materialism and in opposition to religion, is done because the propaganda system is based on the high-value of authority, in a manner similar to how the Roman-Catholic-Empire was based on the high-value identified by the authority of religious virtue, ie the arbitrariness of absolute morality.

Thus, if science is based on materialism then the authority of religion, which defines the non-material spirit, can remain unchallenged.

However, the intellect can consider many different ideas, it is only in the context of wage-slavery where one must be true to (or must believe in) the authority of material based science, in order to get a job in the military-industrial-complex, where the military-industrial-complex happens to also include the education system, since education is about memorizing authoritative ideas which are of interest to big-business, eg physics is now (2012) nuclear weapons engineering (thanks to J Oppenheimer and E Teller**, this transformation of physics took place in the 1940’s and 1950’s as the US became militarized under Truman and J. McCarthy).

This paper is about a new mathematical model concerning new interpretations of the observed patterns of the physical world.

Mathematical models should imply measuring, verifying, and using measured properties for building and practical creativity (but in quantum physics, particle-physics, general relativity, and string-theory etc it means mathematical abstractness, with only a few correlations with cherry-picked data selections, but with very little (if any) relation to practical creativity). Note that particle-physics is being used in regard to nuclear weapons engineering, since probability of particle-collisions is related to rates of (nuclear) reactions.

These new ideas about math are about modeling a measurable existence which contains the idea of materialism as a subset, but it is not the subset which people expect.

People are taught to both memorize certain ideas, and remain true to traditions, where both of these actions serve a social hierarchy, so as to try to be creative in that narrow context, so as to serve the social hierarchy.

If the material and the spiritual are not separate and distinct ideas then one could say that the spiritual is about being practically creative within the context of what really exists.

That is, religion would no longer be about arbitrary absolute laws about virtue, as defined by the oligarchs, which are used in the propaganda system in regard to protecting the selfish interests of the oligarchs, because statements about the spirit would have to become consistent with useful mathematical descriptions of existence. However, as in the case of Martin Luther, one would want all people to be taught to read the new scared text, concerning the modeling of existence in regard to practical creativity (in higher-dimensions).

Our social condition (tries to trap) traps us so as to serve that social context, but the point of good education [which should be based on equal free-inquiry, which questions any authority which no longer functions in the context of practical creative development], is that we can invent new contexts within which further creativity is allowed.

This would especially be true if the new context is correct for a particular (new) creative processes (the point of science is to find a context which applies to a very wide range of creative processes).

The new descriptive structure is quite similar to classical physics ie it is practically useful, and it places quantum patterns into a (concrete) geometric context, yet it can also derive the property of quantum randomness.

This is sometimes interpreted to mean that there is to be one-equation which unifies all material processes, but it is more likely that it is, a particularly simple geometric structure which provides the structure for a containment set within which stable (valid) math is (can be) defined, and within which material processes are assigned to independent dimensional levels (where the different dimensional levels have different structures, ie not one equation but rather a geometric principle used to determine the sets of equations for each dimensional level), where these dimensional levels also seem to be associated to physical systems which have a characteristic size, where such a characteristic-size is brought about by the values of physical-constants eg the speed of light etc, which are defined between the different dimensional levels (as well as between different [independent] subspaces of the same dimension, ie in an 11-dimensional space there are [11 chose 3] = 15 x11 = 165 separate 3-dimensional subspaces).

The current math and physics authorities do not want new ideas interfering with their authority [in fact, because they see their authority as defining truth (an idea given to them by the propaganda system) there can be no other truth but theirs, they have faith in their religion (which is based on their own authority)] . . . , (they are personalities who seek dominance, but who are obedient to the interests of the owners of society, they are as scheming as are the politicians and judges) . . . , or interfering with the processes by which authority is to be judged, ie an idea which is actually foreign to the true science, [where true science is to be based on equal and free-inquiry, in turn, related to a description’s relation to both its assumptions (and contexts) as well as to its practical creative developments, which, in fact, is the correct interpretation of Godel’s incompleteness theorem, which also is a claim that the measurable descriptions of the patterns of both math and science are essentially trying to do the same thing].

The new authorities must be willing to express their beliefs at the level of assumption and interpretations, otherwise they get trapped in a realm of abstract meaninglessness, and their rigorous patterns end-up describing an illusionary world, with no practical value.

Monopolistic businesses do not want this type of competition (of new ideas) interfering with their process of vocational training, a process which enforces the idea that only a few people can be judged to be superior, and those people are the few who can earn large salaries with monopolistic businesses, they are of value to the business’s ability to produce a particular product, ie business does not want wide-ranging creative possibilities, it prefers people who are narrowly focused.

That is, knowledge with narrow applicability, fits the propaganda system well, for a propaganda system whose main messages are that

1.   people are not equal and

2.   you need to be afraid, so that superior corporations can protect you, but you need to trust the monopolistic businesses.

If these authorities were anything other than dogmatists, and arrogantly oblivious to valid criticisms, and who serve a social hierarchy (which protects their arrogant ways), they would be responding to these new ideas.

What is being claimed, in this paper, is that the authorities are wrong, their errors (basing their descriptions on non-linearity and indefinable randomness) are explained, and an alternative mathematical model is provided, which contains much their set-context (of both materialism, as well as some of their other math structures of non-linearity, and an explanation of indefinable randomness [the fundamental assumption of quantum physics]) as subsets (materialism and some of the other math structures are subsets of the new math structures).

The new math context is an attempt to place the descriptions of math patterns in a stable and consistent context, the fundamental math structures which do this are the (very stable) discrete hyperbolic shapes and discrete Euclidean shapes can also be used, thus one wants to consider the discrete shapes which can be derived from the classical Lie groups, where the discrete hyperbolic shapes are very stable.

Place these discrete shapes in a dimensional hierarchy, where each dimensional level is itself a discrete shape.

Given an open-closed, bounded discrete metric-space… , contained in a metric-space whose dimension is at least one-dimension higher than the dimension of the (original) given metric-space, . . . , (it) is also the model of material.

Interactions are modeled by means of the relation that a 2-form of a Euclidean torus has to the geometry of the (Euclidean) fiber group, and follow the math patterns of discrete hyperbolic shapes which were uncovered by D Coxeter, where discrete hyperbolic shapes only exist up to 12-dimensional space-time. [Note: n-hyperbolic space is equivalent to (n+1)-space-time.]

This provides a natural dimensional cut-off.

Material is modeled as the open-closed, bounded (or unbounded) discrete hyperbolic shapes from (hyperbolic) dimension 1 to dimension 10, and which are also the model for metric-spaces which contain the material.

If a material interaction, eg a material collision, is within an energy range and the original spectra are consistent with a new system then a new system can form if the interacting structure begins to resonate with the spectra of the containing space, which has spectral properties since each dimensional level as well as all the subspaces are stable shapes which themselves possess spectral properties.

Their errors:

There is a change of context of the derivative and integral operations, when on-the-one-hand one relates a derivative to measurable properties defined on a domain space, where a causal relationship between geometrically measured properties is determined by equating two representations of equivalent measurable geometric properties which is used to define a differential equation for a physical system, which has measurable properties measured within the domain space, And on the other hand one changes over to: a context in which sets of operators (representing global measurable properties of a spectral system) are being related by a function space to measuring a system’s spectra, where the spectral values of the system are attached to random (local) particle-events, which in turn, are randomly related to positions on the domain space.

A global (linear) representation of a wave-function by its expansion in a basis of spectral functions is related by derivatives of the wave-function’s wave-phase… , (which is formally allowed because the wave-length and the (time) period of the wave can be related to momentum and energy respectively) . . . , to global physical properties of a spectral system, thus an artificial physical relation of global values being related to local spectral identification is identified between differential operators and global properties of the spectral system, and with a global (linear) expansion of a wave-function in its spectral basis elements, where local spectral measuring (at spectral-particle locations in space) is supposed to justify such an artificial relation.

The [complete sets of commuting, Hermitian] differential operators act on (the phase aspect of) the global wave-function so as to identify, not local, linear, measurable properties, but rather, this set of operators identifies global system properties for a wave-function, whose spectral basis elements are only related to local random particle-events which have only one spectral value, whereas the spectral system has many spectral values associated to itself. The operators identify global properties of the quantum system only vaguely related to the spectral expansion of the system’s wave-function (and) whose spectral values are always local.

This is (sort of) incoherent, all the relations that the operators have to global properties imply a global (or system-wide) spectral measurement value.

Although many of the equations of quantum physics are linear, the main casual relationship is not about local measures defined on functions, ie measurable values, rather it is about fitting spectral data of the system with the equation (or with a set of operators).

Systems with more than two particles cannot be represented in this way.

The (new) function space model for a spectral system’s differential equation has no motivating structures needed to limit a system’s spectral set, where the measurement of spectral values depend on local measurements, but the derivative is not related to a local structure of these spectral measurements.

Furthermore, the system either has no geometric relations or very limited geometric constraints defined on the domain space.

The math structure is incoherent, where the differential operators are unrelated to their math-structure as a (local) tangent to a function’s graph.

Note: these spectral (function-space) methods work for the electromagnetism model where the wave is physical, and the physical structures which affect the wave are either geometric or are an intrinsic geometric (loop, or node) structure of the electric system, and the conservation laws are (may be) applicable, eg conservation of energy.

This math structure, of function spaces used to fit spectral data, changes the notion of linearity so as to no longer be about a function’s relation to local linear measures (which relate function-values to domain values), and only vaguely relates the spectra to a linear operator, but the spectra do not identify a linear property on the function space but rather identify