The Structure of Existence

The Structure of Existence

If you enjoy this book, show me! Any contribution would be greatlyappreciated.

-Dan.

Table of ContentsThe Structure of Existence .............................................................................. 4

Introduction .............................................................................................. 4 Where the reader is familiarized with the background, nature, and origins ofthis book. .................................................................................................. 4

Formidability test ................................................................................... 4 Difficulty ................................................................................................ 4 Self evident ........................................................................................... 5 No Math ................................................................................................ 5 Science ................................................................................................. 5 Read in order ......................................................................................... 6 No histories ........................................................................................... 6

The universe as a wave .............................................................................. 7 Big bang ................................................................................................ 7 An opposite reality ................................................................................ 10 Divisions .............................................................................................. 11 Local density fluctuation ........................................................................ 12 Particles are waves ............................................................................... 14 Waves are surfaces .............................................................................. 14 Particles are surfaces ............................................................................ 15 Waves on a wire ................................................................................... 15 A wave is a wave is a wave ................................................................... 16 Properties of waves .............................................................................. 16 Standing waves .................................................................................... 17 Resonance ........................................................................................... 18 Standing wave resonance ..................................................................... 20 A standing wave is an entity .................................................................. 20 Interacting waveforms are all that there is. ............................................ 21

Process omnipresence .............................................................................. 23 A fish is unaware of water ..................................................................... 23 Facets of the whole .............................................................................. 24 The seamless universe .......................................................................... 24 Being ................................................................................................... 25 Congruous imagery .............................................................................. 25 Irrelevance of scale .............................................................................. 26 A closing Hindu quote ........................................................................... 26

Models and abstractness ........................................................................... 27 No one model ...................................................................................... 27

All rights reserved Dan Echegoyen 11/3/2003 1


Objects have facets .............................................................................. 29 The medium is the message .................................................................. 29 Each part is a whole ............................................................................. 30 Abstract generality ............................................................................... 30 Learning .............................................................................................. 31 Dreams ................................................................................................ 32 Awareness ........................................................................................... 33 Opposites ............................................................................................ 34 Summary ............................................................................................. 36

The abstractness of unity .......................................................................... 37 Indivisibility .......................................................................................... 37 Cause .................................................................................................. 37 Disunity ............................................................................................... 38 Koans .................................................................................................. 39 Godel .................................................................................................. 39 Flatland contradiction ........................................................................... 40 Self-contradiction ................................................................................. 40 Distinction ............................................................................................ 42 Description ......................................................................................... 43 Representation ..................................................................................... 43

Tangentiality ............................................................................................ 47 Indirectness ......................................................................................... 47 Enlightenment ...................................................................................... 48 Tangent ............................................................................................... 48 X and Y coordinates .............................................................................. 50 Plank’s constant ................................................................................... 51 Three from four ................................................................................... 51 Convergence ........................................................................................ 54 Tiling the plane .................................................................................... 62 Circumference ...................................................................................... 65 A Point ................................................................................................ 69

Self similar patterns .................................................................................. 71 Self reference ....................................................................................... 71 Reflection ............................................................................................ 71 Projection ............................................................................................ 75 Fractals ............................................................................................... 76

Feynman diagrams ................................................................................... 76 Interference patterns ............................................................................ 76 Placeholding ....................................................................................... 78 Reproduction ....................................................................................... 79 Summary ............................................................................................. 79

Local and global ....................................................................................... 82 Perspective .......................................................................................... 82 Wave expansion ................................................................................... 82 Cone, sphere and cylinder ..................................................................... 84



Conic sections ...................................................................................... 86 Ant Colony ........................................................................................... 87 Slime mold ........................................................................................... 88

A model of the universe ............................................................................ 89 Gravity ................................................................................................ 89 Black holes ........................................................................................... 89 Quantum reality and relativity ............................................................... 91 Schrodinger’s cat .................................................................................. 91

I and not-I ............................................................................................... 93 Experience ........................................................................................... 93 Perspective .......................................................................................... 93 Many answers ...................................................................................... 94 Self modification ................................................................................... 94 Both and neither .................................................................................. 94 Self reflection ....................................................................................... 94 Group process ...................................................................................... 97

Rules of being .......................................................................................... 98 Topology ............................................................................................. 98 Change in change ................................................................................. 98 Similar and different ............................................................................. 98

Action ..................................................................................................... 99 Recap .................................................................................................. 99 Nodes .................................................................................................. 99 A constant ......................................................................................... 100

Cycles of being ....................................................................................... 102 Recap ................................................................................................ 102 Expansion .......................................................................................... 102 Having ............................................................................................... 102 Actions of existence ............................................................................ 102 Relations ............................................................................................ 105

Unity ..................................................................................................... 106 Recap ................................................................................................ 106 Numerical relationships ....................................................................... 106 Many answers .................................................................................... 106

Duality ................................................................................................... 107 Heaven and Earth ............................................................................... 107 Alignment .......................................................................................... 107 Both and neither ................................................................................. 107 Branching of Objectivity and Subjectivity .............................................. 107

Trinity .................................................................................................... 108 Quaternity ............................................................................................. 109 Phive ..................................................................................................... 110



The Structure of ExistenceBy

Dan EchegoyenEchegoyen at StructureofExistence.com

3176 N. Mtn. ViewSan Bernardino CA 92405

(909) 204-0201

Introduction

Where the reader is familiarized with the background,nature, and origins of this book.

Formidability test

Understanding the structure of existence can seem an impossible task until theunderstanding of that structure is achieved. The transition to suchunderstanding cannot be forced. There is no logical path or deductive process tothis higher perspective of reality. Glimpses of this higher perspective can,however, be induced indirectly.

Difficulty

This enlightened understanding does not come directly. All truths arecommingled and conventional logic alone simply does not complete the job.Apparent contradictions abound. Zen truths of illusion are real, directexplanation is impossible. The deeper the truth, the more indirectly that truthmust be shown.

Very little in this book is new, but familiar models on the nature of reality areseen anew from a higher perspective. The language already exists to describethe nature of things. A deeper understanding of reality comes from seeing thesubtler embedded message in the words and images that describe things. Eachprecept is part of a greater idea that unfolds gradually. Comprehensive re-examination of understood concepts from this higher perspective leads to newunderstanding.

Although explicit model descriptions are necessarily of one topic at a time, theimplicit information addresses all topics at once.

Early chapters will introduce topics that will later receive more attention. As thefoundation of ideas is built, new courses will return and build on the old, with



topics oriented to bolster each other. The structure is not the bricks, but thebuilding.

Every idea is worked with care, though necessarily imperfectly. A word mayhave many meanings. Semantic parallels are intentional and meaningful.Assimilate each idea fully on its own. Disparate ideas will eventually merge.

Self evident

This work is no invention. It is a discovery and observation of what is, andintegrates conflicting ideas in every area of understanding. Once understood, itspeaks for itself on relevance and scope.

Although formal scientific models (along with other kinds of models) will be usedextensively, this book is not an attempt to prove anything. Scientific models arehelpful because of their consistent and definitive nature and imagery, but thesole intent of this book to help the reader to perceive a higher perspective ofreality. This perception requires not proofs, but internally consistent images ofrelationships to gain understanding on the deeper workings of reality.

This integrated understanding includes non-linear considerations and is onlyunderstood all at once. This understanding is not achieved directly by any oneline of reasoning. It is induced indirectly.

No Math

The interaction matrix of existence is a dynamic structure, like an engine. Justas equations are not needed for a practical understanding of the internalcombustion engine, there will be almost no explicit mathematical equations inthis explanation of the nature of things. Examples of topology and geometry,however, are integral to model imagery and will be used for extended dynamicmodeling. Equations will be rare, but most models will have a mathematicalbasis for the imagery described.

Science

Science and mathematics are wonderful. The truths that are found throughquantification form a most reliable base for the extended examination of reality.Science and math have succeeded tremendously well in the objectification ofreality. They are valid and robust, self-consistent and meaningful. I grew upwith science, gravitating to the hard sciences with their abstract models andstructures. Then I read GODEL, ESCHER, BACH; AN ETERNAL GOLDEN BRAID.In this Pulitzer winner, Douglas Hofstader pointed out the structural similaritiesand parallels of interpretation in different systems such as mathematics, art andmusic. He made his point so well that I started to see many connections he hadnot even mentioned.



Objectivity has its limits. A complete picture of the universe must also includesubjective reality. This dual reality includes facts that seem to contradict eachother. Things exist that cannot be proven, and the non-linear implicationschallenge understanding. Objective science itself points to the fact that scienceis incomplete. Still there is rationality in the conflict. The new perspectivepresented here resolves and integrates even the seemingly contradictory facts ofreality. Logic shows the linear extension of reality. A lateral extension alsoexists that is contrary to (but not contradictory to) linear extension.

Read in order

This work contains many different kinds of understandings, ideas, and truths.They have all been used in a higher self-consistent paradigm on the nature ofreality.

A model on one level may be used to parallel a model on a very different level.The intent is not to prove a point, but to show a way to see the nature of theparallels and relationships of the holistic structure that allows different things toboth be viewed as somehow similar. This new perspective on reality camequickly, but is so vast that new insights and connections happened daily foryears. They still continue to this day.

The task of organizing the ideas of this new understanding was slow andresistant. A linear presentation of inherently non-linear information is a distinctlyabstract interpretation of this understanding. The intent of making this workmeaningful requires that it be read in the order presented. Ideas are introducedat their proper time. This book is a lattice of inference with a broad base ofideas and abstruse spans of continuity. Everything is relevant. There are fewwasted words. The information is densely packed.

Repetitions of a theme are to introduce new lines of thought from commonfoundational information. The reader’s progress through these ideas shouldcreate mental echoes to points made earlier. Each specific observation is anadditional perspective of the whole.

No histories

There will be few attributions. This work is of general knowledge, seen againfrom new perspectives for a grander view of things.

Summary

Experiencing this higher reality can only be accomplished by indirect means. Thevarious imageries of reality can show a silhouette of the higher reality when themodels are properly positioned. Linear extension and lateral extension togethercreate a higher reality that is truly both and neither of the lower descriptives.



The universe as a waveAll the entities of existence participate in this universe by interacting in a waythat makes them both particles and waves. These opposing views are bothcorrect, but incomplete. Anything may be described either by its wave-likeattributes or its particle-like attributes. All things can be seen as waves. All waves have fundamental similarities. Allthings can be seen as particles. All particles aslo have fundamental similarities.All things share unifying wave-like and particle-like properties and arecomparable to all other things, no matter the case. Models of the nature ofindividual things are partial models of the collective nature of all things, and areall comparable to each other.

Big bang

The universe began with the big bang, a commencement of the process ofbeing. The scientific term for the big bang is a local density fluctuation, atechnical name for a unit wave pulse. Everything imaginable or unimaginable isa single unit quantum wave pulse, a resonant group of wave pulses, or aharmonic fraction of a wave pulse. One is the same as another. A significantconnection between one wave or particle and another is the scale of the two,relative to each other. The outcome of wave amd particle interactions dependsupon the scale of one relative to another.

The medium is the message. To understand the wave is to understand thesurface that the wave travels on, for, as this chapter will show, wave and surfaceare the same.

A quantum pulse is a wave, and a quantum pulse is also a particle. Everything inexistence is both a wave and a particle on all its levels and scales of being. Eachthing expresses the wave/particle duality. The wave/particle duality also holdsup on the macroscopic scale. Lifeforms exist in quanta, and have both waveproperties and particle properties. Although everything is actually both a waveand a particle, things are always observed as either one or the other. The typeof observation determines the type of characteristics observed. If one looks forthe particle, one finds a particle. If one looks for the wave, one finds a wave.There are then two different perspectives on the nature of a thing. Anything canbe seen as a particle or a wave, but to ignore either aspect is to give anincomplete description. All locally consistent descriptions of reality areincomplete descriptions of the whole of reality.

Consider the properties of an entity as a wave. As a wave passes any point,some density change (like pressure density) will occur. The density, or pressure,of a medium will fluctuate commonly in the fashion of a sine wave.



The points on the surface that carries the wave go through a change during thetransmission of the wave. The surface moves through the wave just as much asthe wave moves through the surface. Motion along with the wave is motionacross the surface. The wave’s general motion is linear. The propagation ofenergy within the wave is circular (or lateral).

Any bang can and does create a local density fluctuation wave front, a place ofconstant change. This wave is seen in any ripple on the water caused by the‘bang’ of a tossed in rock. The straight nature of a wave travels straight out theradials from the source point of the wave. The circular nature of the waveprocesses the wave laterally across the direction of motion.

Everything appears as a particle or a wavepulse. Every ripple on the water, theentire universe, and everything physical and non-physical in between can beseen as either a wave or a particle. A wave continues to exist by its effectivepropagation, and a particle continues to exist by its inertial persistence. Everywavefront is a quantized local density fluctuation for all other wavefrontfluctuations to interfere and interact with. Each wavefront can have othersmaller wavefronts on it. A lesser wavefront can be part of a greater wavefrontwhere it can interact interdependently with other lesser wavefronts. Groups ofsmaller particles can interact together to make larger individual particles. Theuniverse, a ripple on a pond, and every entity in between are all abstractly thesame in their structures and processes.

As an expanding wavefront, the pond ripple is just as much a universe as theexpanding big bang universe in which we exist. The difference between thewavefront circular ripple of everyday experience and the Big Bang wave front ofbeing is that the external expanding everyday water ripple is outside of us andapart from us, while the Big Bang wavefront is inside of us and a part of us. Toexist in the pond surface universe, an entity must travel along with that ripple.For us to continue to be, we must continue to propagate along within theuniversal wavefront, at rest in the local here and now.

In mathematics a function is plotted as change, graphed by holding one variablestill and observing the changes in another variable. Changing the variable that isheld still changes the image to that of the other plotted changing variable’sperspective.

This is like the difference between keeping still with the water, or keeping stillwith a wave that travels across the water by surfing so as to keep still on the



face of the wave. These are two different views of stillness. We exist by movingalong with and keeping still with the dynamic yet unchanging Big Bangwavefront of being.

As two waves cross each other, an entity can propagate across both of thewaves simultaneously by going at a diagonal to both.

Such an entity’s progress could be influenced alternately by the two waves that itfollows.

What is a perpendicular frame of reference from one perspective can be aparallel frame of reference from another perspective. As example, consider theopposing edges of a rotated tetrahedron.

What is along a direction of motion from one perspective is across that samedirection of motion from another perspective. There is stillness relative the bodyof water, and stillness relative to a wave upon the surface. These are justdiffering perspectives of the same thing. Each perspective is a particular localview of reality, like space and time each being a local perspective of the greaterfield of space-time.

Although we perceive space and time as separate, existence actually occurs inspace and time together. Existence processes through both space and timesimultaneously. We objectively experience one axis of time and three axes ofspace. Every action or event of existence occurs at a particular time and place.Space-time is a continuum of potential being, expressing the unification of twoopposing perspectives of potential change; change in time and change in space.



Within the space-time continuum exist mass and energy, which are known to bedifferent forms of the same thing. Mass and energy are the complementaries ofa dichotomy, either one or the other.

Our universe is that of a dichotomy within a continuum. The universe iscomposed of various combinations of one or the other expressed in both andneither as a diagonal simultaneously of both, until squared to one dimension byobservation and measurement. Differing quantities of space-time can be seen asdiffering quantities of space and time. Differing ratios of space to time yieldvarious masses and energies at differing angles of slope. Whole number ratiosare all real numbers, and all such rational slopes can cross any point in thecontinuum.

A line that intersects a ninety-degree grid-point can be reflected directly back inthe direction from which it came. When the slope for a whole number ratio isprojected on a Cartesian grid, then the rays implied by such slopes, reflectedwithin the first square, will always eventually be reflected back to the origin. Anyrational slope through a point is both a projection to that point and a reflectionfrom that point. Reflection and projection are the actions of a wave interactingwith a surface in the rational continuum.

An opposite realityTo stretch the mind, consider the following. It is commonly agreed that theuniverse is expanding. That is a valid perspective, but there is another. Rarelyentertained is the notion that instead of space-time expanding, mass and energyare contracting. Consider a finite circle. From outside of the circle, space



expands out towards infinity, and the finite circle quickly becomes point-like incomparison. From inside the finite circle, space may be subdivided ever morefinely as it approaches the center of the circle that now becomes, by comparison,infinitely far from the edge of the circle. The finite circle itself can be seen asinfinitely small or large relative to external expansion or internal contraction.Although expansion of space-time seems more reasonable than contraction ofmass/energy, the dynamic relationships inherent in these two perspectives ofchange are equivalent. Local measurement and mathematics can hold mass andenergy still to measure space and time, or hold space-time as fixed to measuremass and energy. Both views are valid in expressing a single process of change.Contrary perspectives can model complementary images of the same reality.

DivisionsAll of existence was originally a single thing. That one thing became divided.The differentiation of the parts is either along or across the extension ofdimension implied by the division. This image can be seen in the lines of forcewithin a magnet. Iron filings are attracted to both poles of the magnet, and willalign themselves to reach along the lines of force. Objects that do not conductelectricity and are repelled by both poles of a magnet will align themselvesacross the same magnetic lines of force. These are two contrary perspectives ofone division.

The kind of divisions of the whole depends upon the number of divisions of thewhole. Quality is related to quantity. Every entity is in itself a whole withdivisions. Every division is in itself a whole. Two-dimensional divisions have two-dimensional interactions, like along and across. Three-dimensional divisions havethree dimensional interactions, etc. (A dimension is an axis of potential or actualextension)Every member of any divided set (both of two or all three of three) each canitself be divided by any number, again showing the kind of division based uponthe number of parts in the division. This is a fractal relationship between theentities of existence.Even though objective separations between all things now appear to exist, asubjective connection exists between all things as well. Although all things areseparate, all things are also connected in this abstract relationship betweenquantity and quality.Quantum reality is expressed mathematically in both matrix mechanics and wavemechanics. Matrix mechanics is a system of mathematical expression similar tothat of equations except that changing the sequence of operations can yielddiffering results. In matrix mechanics, AB does not equal BA. The direction of



the process has meaning in the outcome of the process. A time space slope oftwo to one is different from a space-time slope of one to two. Wave mechanicsis another mathematical system expressing orderly process, and a great triumphof quantum mechanics was to prove that these two different systems expressedthe same relationships. The matrix of structural being in a particle is equivalentto the wave of process being in an energy pulse. The structures and flows ofbeing in the divisions of all things are different ways of seeing the same thing.Waves and particles are the same as each other.

Local density fluctuation

A local density fluctuation is a common sight. It is a ripple in a pond where astone is tossed in. It is also the spherical shock wave from a bomb blast. Thewaves themselves occur on the surface of a higher dimensional field ofexpression and are of a lower dimension than the field that carries them. Asexample, the pond ripple is an expanding circular one-dimensional line on a two-dimensional surface, and the expanding bomb blast is a spherical two-dimensional surface moving through the three-dimensional surface (field) of theair. This is a simplified description of the objective process. Such a wave pulse object has both a linear and a circular direction of motion.One-dimensional flows, like time, can be expressed as continuous change inslope (like the radius of trigonometry), or in linear demarcation (like the X or Ydimension). These two directions of motion correspond to the two kinds ofinertia, linear and rotational (or angular).

In describing this expanding wave pulse, the linear motion is projected straightoutward through the field and away from the relatively motionless source. Thecircular dimension curves back around onto itself, supporting the perpendiculardynamics of wave precession.

As example, the water ripple, moving straight out from the origin, sends thatsurface stretching up away from its stable energy position between water and air(increasing the density of the fluid below), then dips down below the stable levelof the surface (decreasing in the density of the fluid below). The densityfluctuates across every wave point on that surface. The wave moves out alongthe surface in one direction expressing linear momentum, and around across the



surface in two directions back and forth (up and down), expressing angularmomentum.

This wave, propagating in a straight line past a point, moves none of the fluidalong with the wave, but moves all of the supporting fluid below the wave (andsupported fluid above) through a full circle during the passage of the wave.

The linear motion of the wave is straight. The lateral motion of the wave iscircular. Any mini wave upon that expanding pond wave must also have straightand circular properties. Since we (all things) exist on the wavefront of theuniversal here and now, we all possess linear and circular aspects on all levels ofbeing.

A function that plots circular motion against straight-line motion is the sine curve.Trigonometry has no scale. The nature of waves’ interactions is not determinedby size, but by one wave’s size and resonant complexity relative to anotherwave. No matter the size of the wave, its complexity, or the number ofdimensions in the wave, any wave is still similar to all other waves. All wavescarry energy and follow similar structures of interaction and processes ofexchange. All particles contain the properties of mass, inertia, and spin.

In this deeply abstract sense, all things have a fundamental similarity to all otherthings. No one model describes the whole of existence any more than one facetof a crystal describes the whole gem. Each model describes only a facet ofexistence indirectly and only tangentially the whole.

Just as similar facets may describe similar crystals, similar numbers of dimensionsin various models may be abstractly paralleled for symbolically similar



perspectives of the divided whole. All dualities can be compared as parallel to allother dualities, etc. Through this qualitative symbolism, a higher reality may be

seen.

Particles are waves

In the completely abstract subjective mutually connected way that all waves(things) are the alike, everything is the same as everything else. Each thingabstractly and indirectly reflects the unity in all things. Particles and waves seemto be opposites, yet we know them to be the same stuff. When energy isbundled up in the confines of a particle, it exchanges its linear momentum for acircular or angular momentum. Whether straight or curved, the dichotomousentities of mass and energy exist as either one or the other in the space-timecontinuum of both and neither.

Particles are equivalent to waves. The double slit experiments of physics revealwavelike interference patterns even in objects normally thought of as particleslike electrons and protons. Real particles can be observed really being waves.

Waves are also particles. Energy is ultimately the same as matter. A wave maydescribe probabilities of location along its length, but what is located is a particlepoint. Even complementaries like figure and ground are really the same. Onlythe perspective changes. The perception can be of figure or ground.

From one perspective, particles interact through wave exchanges. From anotherperspective, waves interact through particle exchanges. The breeze waves in theflag just as the flag waves in the breeze. Particles and waves exist throughexchanges with each other. Particles exchange waves, and waves exchangeparticles.

Waves are surfaces

Normally, a surface and a wave would not be thought of as the same thing, yetthey are. The surface that carries the wave is everywhere static and still, whilethe wave that moves upon a surface is moving and dynamic, first one place,then another, yet one can be seen to be the same as the other.

As example that a wave is a surface, imagine a craft that can surf along onocean waves. It is possible to see the ocean wave act like a surface while thesolid craft acts like a wave. The craft may interact with the wave in the sameways that a light wave can interact with the surface of a pane of glass. The craft



might pass over the wave like a light wave passing through a pane of glass. Thecraft might be reflected back from the wave like a photon reflected off the paneof glass. The craft could even be absorbed into the wave and carried along withthe wave like a light particle being absorbed by, and thereby warming the paneof glass. By existing in the pane of glass, the energy of the photon becomes apart of the energy of the pane of glass, changing the whole by that much whilebeing a part of the whole.

The same actions could be paralleled with a ball rolling over a ridge. The ballcould roll back to the starting side of the ridge, the ball could roll over and pastthe ridge, or the ball could just come to rest on top of the ridge. The rollingenergy of a ball resting on top of the hill has been transformed into potentialenergy of a rolling ball absorbed by the now larger ridge.

The lateral, all at once surface is the same as the linear moving wave.

Particles are surfaces

This is common and straightforward. Individual air particles gathered in largenumbers conduct themselves as a single three-dimensional surface (a field) thatcarries sound waves. All particles carry waves and thus are surfaces. Everyparticle is a point-like part of a dimensional field that can carry a wave.

A surface is also a particle. A wave surface gives resistance to entry or passagethrough the surface. There is a tendency for an oncoming wave to reflectfloating objects back away from its progress. The spherical bomb blast surfacegives a powerful resistance as it passes each observer. Waves, surfaces, andparticles are all just different ways of seeing the same thing.

Waves on a wire

A single taught wire can hold any wave. A perfect wire could hold all waveimages. Objective models displayed in many dimensions may break out andshow each separate dimension of complexity more clearly, but a single one-dimensional wire can hold all the information.

The number of dimensions used to model a point is meaningful in its ability torepresent different kinds of changes separately along each dimensional axis, butthe total process can be performed on a one-dimensional surface. The numberof divisions of the whole shows the kind of divisions of the whole. The kind ofdescription sought determines the number of dimensions perceived. Unity,duality, trinity, etc., each describes a different aspect of reality. The number ofdivisions speaks to the nature of the divisions and the resulting array of itsmembers. This insight comes not by contrasting the differences between partsin a model, but by comparing abstract parallels between differing models ofsimilar numeric aspects.



A wave is a wave is a waveThere are many different kinds of waves. There are sound waves and sonarwaves, shock waves and solitons, square waves and sine waves, water wavesand waves of probability. There are electromagnetic waves and gravity waves,standing waves and waves of change. Each wave (which is also an object) hasits own individual properties and is some way different from every other wave,even of its own kind. This valid perspective is counterbalanced by the equallyvalid perspective that all these different waves have a unifying similarity to eachother. Waves (all things) are different from each other, and contrarily, wavesare all similar to each other as well. The difference is one of perspective in theobserver.

Properties of waves As just shown, an actively being entity can be seen to be the wave itself,a surface that carries a wave, or an object particle that interacts with a wave oranother particle. Waves as particles acting as surfaces carry other waves andinteract with other particles, all co-mutually. Each wave pulse may be a particlehere or a surface there, and may be either one depending upon the perspective.While the linear propagating motion in the expansion of a wave appears flat andstraight, the concurrent lateral particle motion is circular. Energy not expressedalong one dimension will be expressed along another dimension. An object's size, rigidity, and transparency relative to the size, energy andwavelength of a passing wave determines whether the interaction will be one oftransmission, reflection, refraction, absorption, emission, or whatever. One wayor another, all objects interact with all others. The electromagnetic andgravitational forces in each atom interact with the electromagnetic andgravitational forces in all other atoms in its visible universe. Distant interactionsare interminably weak (infrequent) but real. Interactions are exchanges ofenergy and information. Interactions include the collapse of potentiality intoactuality and the directions of the collapse. The action binds energy andinformation.All interactions have a two-directional component. In electronics, the flow ofnegative charges that move in one direction is much the same as a flow ofpositive charges that move in the other direction. Just a point going from A to Bexchanges the point in one direction and not-the-point in the other direction.Information is an exchange of states from before to after in an observer/observed event.Energy and information exchanges within quarks create atoms. Exchangeswithin atoms create molecules. Exchange within molecular genes creates life.Each level is a lath in the lattice of potentiality. The actions of a wave on onelevel are abstractly parallel to the actions of a wave on any other level.All waves contain a linear objective component and a lateral subjectivecomponent. These are the external physical component and the internal non-physical component. All waves contribute to the ultimate expression of the



totality of being. A wave model can be divided any number of ways. Each sub-model resonates to the whole. Each specific division and parallel illustrates aparticular perspective of the pattern of reality that is found uniformly in allthings. Objectivity sees the varying quantities related to distinct events, and subjectivity sees similar unifying qualities in all entities and events.Objectively, every event of being is different from every other event. Each eventoccurs in either a different time from all others, or a different place from allothers, or both. If two things happen at the same place at the same time, thenthey are two parts of the same event. Although every event is objectivelydifferent from all others, a particular set of different events may collectively bepart of a single greater event of being.Subjectively, every event of being is similar to all others. The sheer fact that oneevent can be compared to another implies some perspective from which acommon ground of similarity exists. The adage that conjures dissimilarity is oneof apples and oranges, yet both are fruit.Objectivity is found in the changing differences between things, Subjectivity isfound among the unchanging similarities between things.All events, things, structures, and processes are the same in the totally abstract.All patterns, from sub-nuclear interactions to structures of consciousnessabstractly follow the same relationships of being.

Standing wavesThe process of existing or being reinforces the actions that allow for continuedbeing, creating a positive feedback loop in existence. As the structural flows andforces of reality interplay, this feedback process supports the growth ofstructures and flows of interaction that themselves are self-reinforcing. Thismakes recurring self-reinforcing interactions more likely. The process of beingproceeds along and across a continuum of self-reinforcing vibrational ratioswithin the differing structural dimensions of exchange.Resonant structures that can successfully create more extensive structures willcontinue to propagate even higher levels of interaction. Existence is acosmological survival of the fittest. To persist through space and time, resonantfeedback structures and processes interact (interfere) with all other entity’ssimilarly resonant feedback structures. Patterns of inflow and outflow mayharmonize or be in disharmony. They are both and neither until resonantreflection points are created by observational exchange. Memory is a similarresonant structure.A self-reinforcing structure (made up of lesser self-reinforcing structures) is anobject that interacts internally with the parts of its group-self and externally as apart of larger groups. Each part of an integrated structure supports the otherparts of that structure. When a structure is self-supporting, it stands alone. Aself-supporting wave entity stands alone. Every entity is a self-supportingstanding wave.



The agents of consciousness follow the same natural self-reinforcing flows andstructures of similarity and difference found in all of creation.A standing wave is often thought of as being of a particular wavelength and ofbeing reflected back and forth in a straight line between two reflectivelysurfaces. Actually, the reflectors (which can become transparent and projective)are part of the standing wave group that is the self-reinforcing resonant entity.A standing wave is finite in size. (There are a finite number of wave iterationsstanding between the reflectors) A standing wave can be reflected and/or projected straight back and forth or reflected and/or projected around ina circle from the point of projection and reflection back again to that point. One-dimensional projective repetition gives the extension of a number line. Two-dimensional projective extensions create a Cartesian coordinate grid.The standing wave’s opaque endpoints (that would hold a wave in one segmentof a line or one square of a grid) can instead become transparent and allow thestanding wave to traverse the number line or grid, either parallel to one axis orat a diagonal to more than one axis.

A standing wave can also be thought of as a circular wave, curving back on itselfand being projected through a transparent surface at the same point on eachcycle.

ResonanceAll entities are standing waves that resonate against all other standing waveentities and continuously feed back actions creating the continuing exchanges ofexistence. As particles and waves each interact through the other, self and not-self both emit and absorb waves and particles. Resonant groups of standingwaves can create a single higher standing wave. Syntropic forces can crystallizeenergy resonances into higher beings through all dimensions. Higher structuresexist exactly as the lower structures that comprise it, but from a differingperspective.There are differing perspectives of stillness and motion. A standing wave canappear to vibrate in one place, or to move along at the speed of the wave in



either apparent direction of its motion. Reinforced standing waves occur only atwhole number harmonic divisions of the wavespace. Whether the wavespace isreflected or projected is a matter of perspective.

A standing wave’s surface can be of a multitude of different single frequencystanding waves upon it. At one extreme is a wave frequency so high that eachwavelength becomes vanishingly small and the amplitude barely deviates fromzero.

The wave appears to coincide with the unwaving surface that carries the wave.An intermediate example of wavelength is a single wave filling the entirewavespace.

This one-to-one ratio of wave to wavespace is the simplest of harmonic ofexchanges. As a single full circle representation of the wave process, thisdemonstrates single spin exchange physics. Other ratios of wave to wavespacedepict half spin exchanges or two spin exchanges. Any segment of a whole-number ratio wave can exist on the same quantity of surface.The other extreme of wave to wavespace is such a small fraction of a wave thatno deviation from zero amplitude can be seen, and no harmonic gleaned.

An infinitely high frequency wave and infinitely low frequency wave both appearto coincide with the flat surface that carries the wave. Harmonic resonanceoccurs between the extremes of no change and nothing but change, which arethe same as each other. These objective and subjective extremes exemplify theopposites to a single unity of both and neither both and neither.



Standing wave resonanceStanding waves have regular beats. They can appear as reflecting back andforth on a flat surface, or as going round and round on a curved surface. Wavesthat resonate at harmonic divisions of the wavespace will be reinforced tocontinue resonating. Resonant energy exchanges occur at harmonic divisionsbetween interacting waves. The effect is strongest at the simplest ratios. Theeffect is subtler in the more complex ratios between waves. The resonantexchanges within a conscious mind are subtle indeed. Waves of energy move on a surface capable of transmitting that energy to otherplaces. On a piano, if the low C is held down gently, making no sound, and themiddle C is struck and released, sympathetic vibrations travel along the surfacesof the air and the piano holding and having the wave. The low C will gain someof that energy and make the piano’s low C sound the middle C note because ofthe simple 2:1 ratio between its natural rate of vibration and the sourcefrequency. This resonant exchange would not occur of low D were held downwhile the middle C was struck. Standing waves occur in natural whole number(real) divisions of the whole.A standing wave can accumulate great amounts of energy from the events inwhich it interacts. The original Tacoma Narrows Bridge was dubbed GallopingGertie when it caught a continuing gentle crosswind of just the right speed andthe whole suspension span acquired a twisting resonance along its length until itcollapsed from structural distress. In simpler structures, objective energy andinformation is dominant over subjective energy, but in the human mind,subjective energy and information dominates the objective exchange…that is ifwe imperfectly see the unity as containing a duality to observe.

A standing wave is an entityEnergy exchange is by way of harmonic resonance between and within the I andthe Not-I. Everything exists as wave. Each part or division of a thing exists asan entity on its own. The only requirement for the separate existence of anentity is the distinctions of the newly discerned entity by its observable parts andactions. Each part in the collection of parts of any entity is a system ofrelationship structures and feedback processes each with their own sub-systemsof structures and processes, which are subjectively similar to the processes ofthe higher structure.As above, so below.A more complex system will support a more complex mix of interactions. Life ismore complex than non-life. More complex life has more complex interactionsthan simple life. In man, emitted energy bundles (like words and phrases) haveobjective and subjective components, as do all energy and information packetsof communication. At the level of conscious beings’ interactions, the subjectiveeffect of the words (the meaning) can be much greater than the objective effect(the sound waves).



A standing wave will feed back to itself the outcome of its own processes. Anywave feedback that terminates the wave process will not be carried forward.Waves that persist will carry a patterned tendency to persist. The characteristicof a wave to persist is the tendency to continue to create new change. Thesepersisting waveforms are the entities of existence.

Interacting waveforms are all that there is.Clumpings of wave groups are as varied as from galaxies to gnats to gluons, orfrom matter to emotions, but the variety belies the unified actions of the processof existence. The act of participation in existence as an entity is the action ofbeing a standing wave on the surface that contains all waves. The feedback ofpersistence in an entity is toward increasing the amount of being or action alongthe various dimensions. Each interaction dimension has its relationship to theother dimensions, whether it is at a parallel or perpendicular, a diagonal, or afunction of some curvature. Each being interacts with all others in their processof interaction. Being means change. To continue to be means to continue tochange. More being means more change.This drive toward increase in change and being creates ever more complexinteractions. Objectivity and subjectivity, each in opposition to the other, feedback to the other increasing potentials for exchange. More potential interactionmeans more potential information. The objective increase in information meansmore objective information, or more truth. The subjective increase ininformation means more subjective information, or more beauty.Objective and subjective processes are towards more objective and subjectivepropagation or growth. These conditions are observed by the entities that theseenhancements’ extended implications create. We are created by the universe,and the universe is created by us. Also, we create the universe, and theuniverse creates us. Both and neither both and neither.

It is not so much that the universe has intention toward the creation andobservation of truth and beauty, but that the conditions of existence providecontrary linear and lateral extensions for propagation. We created observersdefine the pre-existing extensions by our own perception of their meanings. Thegame, the action, of existence is to create more truth and beauty. These are theyin and yang of subjective quality.



Truth and beauty exist in separate realms, yet they are found in each other.Even so, there are times and places where truth seems ugly and beauty is adeception. Truth and beauty are subjective. Position and momentum areobjective, the yin and yang of objective quantification.Opposing facts can both be true, depending upon the perspective. The view of adiagonal hypotenuse, when seen from a distance along the X-axis appears togive the diagonal a value of Y. Viewing the same diagonal from a distance alongthe Y-axis appears to give that same diagonal a value of X. Both views arecorrect, depending upon the point of view. Only from a higher perspective is theapparent contradiction resolved. The diagonal is both and neither X and Y.

Belief, the objective upshot of subjective reality is required for truth. Knowledge,the subjective measure of objective reality, is required for factuality. Feelings, anemotional resolution of experience and reality are required. What is important isnot just what the facts are, but also how they are related to each other.Relationships exist as cases of agreement and disagreement. The world is seenin cases of similarity and difference. Everything is compared to everything else.In some ways everything is the same as everything else, (along the objectivelyunchanging subjective axis), and in other ways (along the subjectivelyunchanging objective axis) everything is different from everything else. Allthings are both the same and different from all other things.The organization of forces and objects needed for life to exist are inherentlyparallel in structure to the organizations that create all levels of existence. It isthrough their similarities and differences that forces of attraction and repulsionare expressed on different levels.



Process omnipresence

A fish is unaware of waterWe pay little attention to the air we breathe. It is just there. We are too busylooking at trees to see the forest. It is just there. We are too preoccupieddealing with the parts of reality to become aware of the whole of it. We are soclose to our reality that we lose our detached external objectivity relative tothings, and just become a part of it. It is just there.Atoms emit and absorb photons that propagate in a self-perpetuating Electro-magnetic induction field that potentially fills all of space. The photon emitted byone atom may be absorbed by another atom at any distance. At the speed of aphoton, Rest mass would be infinite. The photon has no rest mass and existsonly in motion. A photon has no stillness in space and instead is still withrespect to time. From the photon’s point of view, no time passes during theexchange, and everything is all at one time. To a photon, all things areimmediately connected to all other things.Every individual entity’s existence must have context. A particle alone in auniverse would have no motion or inertia. An entity exists by the relationshipbetween itself and the rest of the universe. The existence of every entityproceeds through being harmoniously resonantly reflective and projective. Theexistence of an entity is in the ‘I’ and the ‘not I’ both reflecting and projectingupon their mutual opposites as real. Every particle has the potential ability to have exchanges of photons at anydistance and occupies virtually all of space. Each particle in the universe is ascompletely a part of each of us as our own bodies are. Propagation of a photonis across a constructive interference pattern between two atoms’ infinite energyshells. All atoms interfere with all other atoms gravitationally and electro-magnetically. The interference potential between all things binds all thingstogether. All things are one. Still we perceive separation.In this mortal existence, we are not directly aware of our connection to thewhole of all things. The entities of concurrent local existence exist directly asthemselves and indirectly as the universe around them. Positive and negativefeedback create resonant structures, each perspective through the other. Eachentity’s existence is in its interactions with itself and the universe. Each entityhas its own level of attention that it pays to the universe, and the collection of allother things as a single entity has its level of attention it pays to the entity. Wedo not see our connection as part of the whole. Our attention is on ourselvesand not ourselves. We seem disconnected from the nameless whole, and areonly aware of our connection with the parts. We have all disconnected fromourselves and become lost in a book, a play, or a movie. The greatestathleticism occurs when a player forgets the self, and becomes the game.Disconnecting from the whole world is natural. Being disconnected from the



unity is the method by which we create and gain a local perspective to interactfrom. The disconnection continues and changes in every part of our experienceand in each particular focus. Our personal experience of self is a particulardisconnected highly reflective perspective of the whole through all its parts.Even as we remain ourselves, unchanging, our awareness is constantly changingfocus, topic, and level. Whatever our attention is on, in reflecting upon it webecome that object or idea, and it, to a degree, becomes us. To interact withanother entity is to reflect upon a duplicate image of that other entity, bothobjectively and subjectively.The structures and processes in our bodies have their own individual actions, andthe work of them individually is to achieve their own particular goals. Successesat achieving these goals are synergistic wins on that level of the game of being,allowing greater being. In this sense, we are the things we do. When themembers win, the team wins. Higher games exist as games about other games.Everything is a game. The goal is persistence, survival. Consistently winninglower games allows striving for wins at higher games. We even make gamesmore difficult intentionally, just to be challenged by the game, and make thegame new again. Thus we create ever-greater levels of tension and release,dissonance and resolve. Whether a game is seen to be a game in its own rightor a sub-game to some higher game is just a matter of perspective. Abstractly,all games operate by the same set of rules. Winning at the game of existence isgaining an opportunity to continue to exist. The universe that exists is the onethat contains entities to observe and be observed by that universe.

Facets of the wholeIf reality were described in terms that might describe a crystal, the best attemptwould be in terms that describe the facets of that crystal. The description ofeach facet might be quite detailed, but what is more important than the featuresis knowing that the image is only an indirect description of the higherdimensional reality.

The seamless universeThe universe of all things is an indescribable seamless whole without feature ordivision. The more direct the explanation of the universe, the more indirect thedescription. The only thing that can be said about the unity is that nothing canbe said about it, ironically saying something about the unity. The unity is without parts, but when parts of the divided whole are observed,both the quantities and the qualities of the parts are relevant to an indirectperspective of the whole. Quality and quantity are complementary objective andsubjective parts of the information that indirectly describes a seamless unity.



BeingThe universe and all things in it proceed through existence according to thesubjective and objective processes of being. Being is the action that occurscontinuously, maintaining an active feedback loop of persistence. Being is theaction of persisting. We live in a universe of action and interaction. The onlyconstant is change. By continuing to change, an entity continues to exist. The nature of reality may only be expressed indirectly. Even though surfaceappearances may show only objective differences between things, indirectly, theabstract similarities in different things may become apparent.Rene Descartes, one of the greatest thinkers of all time, made majorcontributions in both the objective and subjective study of reality. He developedthe Cartesian coordinate system, providing a framework for quantifying physicalmeasurement. Descartes also said ‘cogito, ergo sum’ (‘I think, therefor I am’),providing a framework for qualifying the subjective existence of consciousness.He believed that the universe, although experienced subjectively, could bedescribed in physical terms. In his eyes, the purpose of science andmeasurement is to gain verifiable understanding on the patterns of reality thatreflect the subjective nature of mankind. To Descartes, studying the physicalwas the means to the end of understanding the non-physical. He was convincedthat all things are related to each other. Since then, science has become an endin its own right, no longer a means to an even higher end. The narrowed viewof science now broadens again through the many models of objective reality toshow that subjective reality is an equally necessary part of the accurate depictionof this universe.

Congruous imageryEvery part of everything is related to all the parts of all other things. Just aspartial models reflect indirectly upon the whole, so do the ways that the modelsare created. Our senses interpret the constantly changing feedback of realityinto comparable distinctions. We reason, evaluate, feel and decide, all throughthe higher order feat of reflecting on how each experience is similar to andsimultaneously different from all other experiences. Any interaction eventrepresents itself in terms of similarities and differences to other interactionevents.Any directly described relationship of being or action can be seen as a metaphorfor a relationship that is not directly describable. Common parallels ofdescription may be seen for very different actions.As example, consider a heart with blood being pumped in and out over and overwith each passing heartbeat. This image parallels a city with freeway arteriesallowing cars to come in and out of the city, over and over with each passingday. This analogy runs well. The city is like the heart. Freeways are likearteries and veins, streets are like capillaries, and houses are like individual cells.Even though the two systems are quite different, there are definite similarities.



This concrete example proves nothing directly. It is merely an image of theparallels that occur everywhere in existence.Another analogy of similar concrete structures on different scales is astronomical.Saturn with its moons and rings directly parallels the Sun with its planets andasteroids.

Concrete objectivity shows individual distinctions. Abstract subjectivity showsgeneral similarities. Objectivity is found in the perpendicular, where one linecrosses the other. Subjectivity is found in the parallel, where the two lines donot cross. Everything is both objective and subjective. Parallels exist in themost concrete of examples, and differences exist in the most abstract of cases.

Irrelevance of scaleThe size of an entity does not matter in the abstract similarities of the process ofexistence. From the smallest scale to the largest, the universal subjective rulesof existence are unchanging. The template for the common actions of existenceremains the same. As above, so below. The differences in attributes lie only inthe particulars of each individual case of existence, and how that case ofexistence differs from all other cases.

A closing Hindu quote“The whole universe, from Brahma down to a blade of grass is one form oranother of Him”



Models and abstractnessThis chapter examines perspectives and relationships that show a connectednessbetween the parts and the whole. These models are not parts of a proof, butexamples of a method of perception.

No one modelReality cannot be described directly by any one model, but is seen in howdifferent models are similar, indirectly. Objective models are comparable tosubjective models, with a difference.By using a proportional array, objective concepts are seen to be modeled byequation.

The same proportional array shows how subjective concepts are modeled byrelation.

Quantitative relationships use objective equations, and qualitative relationshipsuse subjective relations. They can both be represented by a proportional arraythat separates each element of interest from the others. This array is the divisionof the unity into four parts, seen in two dimensions. Each new overlay ofconcrete existence adds new information for further parallel correlations ofsubjective existence. The better understood each model is, and the greater thenumber of parallel correlations made between models, the clearer an actualindirect perspective of the whole of all things becomes. By aligning severalcontrasting patterns out of the vast array of existent models, a higherperspective may be perceived.Einstein’s famous equation relates the four components of the physical universe;mass, energy, space, and time. Einstein’s said that in cases where the atomsemitting and absorbing photons are at rest relative to each other, E=mc2. E isenergy, m is mass, and c is the speed of light. All motions (including that oflight) are expressed in a rate of distance per time. Distance is the one-dimensional expression of space. (Area would be the two-dimensionalexpression of space.) The equation E=mc2, in this form, does not show the proportional array itnaturally contains. Simple algebra will suffice to restate the equation as theparts of a proportional array. Divide both sides of the equation by m and the result is E/m=c². The crepresenting the speed of light (which is squared) can be rewritten as (s/t) ²,which is equivalent to s²/t², so the equation now reads E/m=s²/t².



The proportional array is now evident. Energy is to mass as space squared is totime squared. It is also evident from this array that energy is to space squaredas mass is to time squared.

E=mc² E/m=c²

E/m=s²/t²The relationship between the four components of the physical universe can beseen to parallel the relationship between the four components of formal linearlogic; the A, E, I, and O propositions.These four propositions are assertions about a relationship between things andthere is a relationship between the four different kinds of assertions and thepossibility of each to exist in the case of the others.The A proposition is ‘All A is B’The E proposition is ‘No A is B’The I proposition is ‘Some A is B’The O proposition is ‘Some A is not B’

These propositions can be visualized topologically.

The relationship between the possible truth of one formal proposition inrelationship to the possible truth of another formal proposition parallels thepossible case of one kind of physical existence for an entity in the presence ofanother kind of physical existence for that same entity. The array of formalpropositions in logic parallels the array of physical components of objectivereality.



Each term of reality is defined by the others, and is a term used to define theothers. This array is a difinative study on the relationships between matter,energy, space, and time.

Objects have facetsA difinative study will encompass all the parts that make up that whole. Eachpart is a term in the display of relationships within tht whole. Each term of adefinative set describes a facet of that object. Facets are not only abstractlydescriptive of models, but are objectively descriptive of physical objects as well.Atoms accumulate into groups by bonding and linking to other atoms in regulargeometric patterns. The patterns involved create defined ends and edges to thereal physical extensions of the object. Even the attributes of sub-atomic particlesare arrayed as polyhedrons when their measurable properties are quantitativelyextended along the three mutually perpendicular axes of the Cartesiancoordinate system. Facets bound the extension of space used for an object’srepresentation. A facets’s boundaries are the edges of the polyhedron where the facets ofthe object intersect. The area of the facet is functionally proportional (as withthe cube/ square law) to the volume of the object, and is inversely proportionalto the number of facets of a polygon with a constant amount of surface area.An object may have only a few facets and be some simple polyhedron, or theobject may be full of many tiny facets that are so smoothly angled as toresemble a perfect sphere. Infinitely many small flat facets on a polyhedronmake it indistinguishable from the smooth curved surface of a sphere, yet alwaysthe object is a polyhedron with facets.In any regular polyhedron, every facet is perpendicular to the object’s center andwill reflect that center point back to itself. As the number of facets grows towardinfinity, the object nears spherical perfection, having every point on the spherereflect the center point back to itself.Objective facets (surfaces) and subjective facets (surfaces) both reflect andproject waves.

The medium is the messageThe whole can be divided into any number of parts. Parts are indirectdescriptions of the whole. Since each model is a qualitative representation of



some quantitative aspect of the whole, each model is a useful representative fora description based on the common feature of the number of facets in theobject. The overlay of model upon model allows differences and distinctionsbetween models to be filtered out, leaving bare the generalized abstract base.That which cannot be described directly can be indirectly seen in the abstractparallels of reality. Detailed lists of parallel models for different numbereddivisions are in later chapters.

Each part is a wholeEach part is, in its own way, a whole with parts. Each whole is, in a way, a partof a greater whole. Each thing is connected to all other things. Each of us is inthe universe and the universe is in each of us in a two-way relationship with atwo-way flow of objectivity and subjectivity across and through each other.Whether any particular entity is seen as part of a whole, or as a whole in its ownright, is only a matter of perspective or context. As example, a heart is one partof the circulatory system, but as a whole, the heart has its own parts like valvesand chambers.

Abstract generalityGenerality relates to abstractness just as specificity relates to concreteness. Asexample, imagine describing a transport device by its parts. In the abstract, theparts are not specified, just as a “transport device” is not specific, but rathervague.Such a list of parts might include such vague descriptives as power source,support structure, amenities, and modes of operation.If the transport device’s parts are given more specifically, the examples becomemore concrete. The transport device includes among its parts such things asradial tires, an internal combustion engine, automatic transmission, bucket seats,and stereo cassette player. The transport device is a car. This more concretedescription is still somewhat vague. A more concrete description of the carmight yield a specific model and year. An even more concrete description wouldinclude all the embellishments that describe an individual vehicle.Each new level of objective information creates a more concrete specificdescription of reality. Even more concretely, one could describe a specific car ata specific time or place. Concrete objectivity is the explicit.In the totally concrete objective, everything is different from everything else.Every concrete event is specific and separate from all other events. Objectivelyevery moment changes the world. As the saying goes, “You can’t step in thesame river twice.”Abstractness is the vague and subtle world of the indirect, the implicit. To begrouped only by a common feature is to be abstracted. In the totally abstract,no specifics are available at all because all things are abstractly part of the one



indescribable unity. In the totally abstract subjective, everything is part of thesame thing that everything else is. While objectively, all things are changing constantly, subjectively, everything isthe same as it has ever been. As participating entities in the existence of allthings, we can view other entities and be viewed by other entities in the abstractand in the concrete. Our surface facets of interaction reflect and projectsimilarities and differences both at the same time. Everything is related toeverything else by their similarities and differences. Both dimensions are neededto create and describe the field. All items have their specific resonant similaritiesand resonant differences as well. Mutual reflective resonances interfere bothconcretely and abstractly. Awareness is of the similarities and differences of perceived events. An event isregistered in the abstract as similar (or parallel) to other events. The sameevent is registered in the concrete as different from (or perpendicular) to otherevents. These two views are in opposition to each other, and expected conflictsof agreement between the two views are reconciled to differing ways of seeing(perspectives of) the same thing. This is the holographic record of the past thatevents and patterns of events resonate against into conscious awareness andmemory. Experience occurs on a lattice of similarities and differences and is onthe diagonal of both together and of neither one alone. Non-linear systems donot require a condition to be either/or, and instead can be somewhat so andsomewhat not-so.

LearningWhen we observe some new event, we notice that in some ways it is similar toother events of experience. We also notice that in other ways this event isdifferent from the previous events of our experience. By aligning the similaritiesand difference, we describe and relate things to create meaningful expressionslike analogy, simile and metaphor. Our language uses many different parallels ofdescription. These distinctions are used tp describe how one thing is related to another. Ineach case, some level of similarity is expressed. In language, words are justsounds, which are auditory parallels of ideas that we have and know about. It is our ability to create these parallel comparisons in a world of manydifferences, (and differentiations in a world of similarities) that makes theuniverse comprehensible. Our experience of each moment is in similarities and differences as compared towhat we already know and feel. A current event will resonate against thememory of past events. Each current event is observed in the context of thereflected resonances relative to past events already experienced and theprojected resolutions likely to occur in the future, from the observer’s point ofview.An event follows a path through time and space, as the flow of energy and theinformation of mass, from the beginning of its occurrence to the end of its



occurrence. In this perspective of our universe we experience one timeline andthree perpendicular spacelines for the past events to reflect against and resonatewith. Deeper representations are illustrated as higher dimensional perspectives.Reflected patterns in memory will resonate positive or negative reinforcementdepending upon the feedback from previous outcomes.Knowing the history of past paths and comparing them to new paths, similarbeginnings can project similar future outcomes or resolutions. Subjectively, alloutcomes are possible. Objectively, some outcomes are just more probable thanothers.Objectve equations and subjective relations can both be expressed asproportional arrays. Equations link physically oriented entities and events andquantitatively express an objective perspective of reality. Relations link non-physical entities and events and qualitatively express a subjective perspective ofreality. Our level of self-awareness is attributable to the extreme resolution ofour projections into the future and the depth and subtlety of our ability to detectresonances to the pattern of reflections of the past.

DreamsThought is along a line of reasoning, or many. Awareness of an event is thetaking of a position, (a perspective), that includes the knowledge and belief thatcertain futures to occur are more probable than others. Choosing actions to alterthe probabilities of events is a process of consciousness. Points of resonancewhere the actions in one dimension can influence the actions in another can begraphed in space on harmonizing, interfering grids. Events are described aspatterns of resonance and patterns of patterns.The process of consciousness propagates through resonance points of being.Exchange is two-directional. That which occurs moves in one direction along thegrid. What does not occur travels along the grid in the opposing direction.Consciousness creates order in the subjective direction, and therefor, it createsdisorder in the objective direction. Order and disorder are subject to a point ofview. From different perspectives, order and disorder can each be the other.That which changes is the arrangement within ordered groups.@Sub-atomic particles are described by their ordered groups of properties.Exchanged particles are themselves properties of higher ordered groupings ofproperties. An exchange of properties is an exchange of one order for anotherorder. Similar particles may decay and give up their properties into differinggroupings of particles. Similar events may have differing possible outcomes.The outcome of one possibility is the non-outcome of all the other possiblepossibilities. Patterns of emitted decay (into one event or another) are paralleled on the levelof human consciousness interactions. As events occur and are registered intoconsciousness, other events of non-occurrence are also registered intoconsciousness. This is like the weaving of a tapestry creating an opposing weave



in the threads yet to be incorporated into the work. The weaving work cannotcontinue unless the future threads are unwoven regularly. In this same manner,dreams allow consciousness to unweave the events and non-events in the futurethreads of awareness. These dreams may be processed in images that aresimilar to and/or different from experienced events.

AwarenessDeductive reasoning goes from the general cause to the specific effect.Deduction determines the various reasonable effects concurrent with a set ofcausal facts, and is an objective perspective. As example, we know that runningheats the body and makes one sweat. Also, running consumes oxygen, leavingthe body starved for air. Now, if a running person covers a distance of two milesin less than nine minutes, we can predict that the runner will be hot, sweaty andbreathing hard, even if the race is unseen. This process is of logical linearreasoning that projects inevitable effects from accepted premises. This is formallogic.Inductive reasoning goes indirectly from the specific effects to the general cause.Induction looks for the most common causes for a concurrent set of facts and issubjective. (When an African hears hoofbeats, the thought is less likely ofhorses than of zebras.) As example, One enters a stadium to see people dressedfor running and standing on the track beyond the finish line. They are bentover, breathing hard, and sweating profusely. Inductive reasoning concludesthis to be the end of a race where the participants were running at a furiouspace. This is lateral, non-linear reasoning and reflects a probable cause for thecase at hand.Our level of consciousness is a function of our ability to compare similaritiesbetween different things, and contrast differences in similar things.Consciousness reflects upon current events and resonates the relevant harmonicssignificant to events of the past. We analyze for patterns, and project a realisticprobable perspective of futures events. Our brains are designed to make senseof conflicting information. In fact, the two hemispheres of the brain view thingsin two different ways and presume a conflict. One half of the brain comparesdifferent events of the past and present for similarities that might have somecommon cause, while the other hemisphere contrasts similar events of the pastand present for differences that might create some expected effect. These arethe two reasoning systems: induction and deduction.Linear deductive thought is direct problem solving. It is A to B, and as such,finite. Deductive reasoning works only as well as the considered propositionsagree with reality.Lateral inductive thought is indirect feeling about the problem. There areinnumerable paths of thought around a problem, and as such is infinite.Inductive reasoning (deciding how one state was brought on by another) accepts



all cases as possible, and judges in the moment as to which process is mostprobable.The similarities and differences in all things are unending. No two things are anymore similar than different, nor more different than similar. As example, onecannot say that men are more similar to women than different from them, ormore different than the same. Men and women, like all paired object ofcomparison, are both incomparably similar to and different from each other.One can say that object A is more like object B than it is like object C, but themanner of comparison must be expressed. As example, compare a 200-poundrock, an ant, and a man. The man is more similar to the rock than the ant if oneis comparing mass, but a man is more similar to an ant than a 200-pound rock ifone is comparing complexities of feedback systems.With sub-atomic particles, the manner of comparison equates to the properties ofthe particles. Similar times and spaces are as valid a basis of comparison assimilar masses and energies.

OppositesOpposites exist in all things. The yin and yang each have the other’s opposite atits center. One would not experience darkness, except for the existence of light.A push in one direction is a pull from the other direction. For one person to havemore than another, the other must have less. For good to exist, evil must alsoexist. Good and evil, God and devil, perspectives of opposition are universal.The simplest extension of space is a one-dimensional representation, (a taughtwire representing a line), that involved two opposing forces for the extension ofspace to exist. One force is the tension that pulls the two endpoints of the wireapart, the force of expansion. The other force is the tension that holds the wiretogether, the force of contraction. Each force has its own positive or negativeresonances, depending on the feedback response of the other.Surfaces are stable places between levels of opposing forces, whether the stablesurface is found in the layer between fluids of different densities, isometric linesof force, or in the harmonic geometric node set of a taught vibrating wire. Pushand pull together define extension into space. The tension between two forcescreates the surface for waves to travel through space on. Two tensions feedback to each other, together creating surfaces of vibrational stability and a placefor constant change. Each entity supports opposing tensions to hold standingwaves. When opposing forces are out of balance, disease occurs. As example,growth and no growth are at odds with each other. If no growth is undulydominated by growth, cancer can result. If growth is unduly dominated by nogrowth, a vital organ might fail.What exists in the one-dimensional universe is the line, which is between twopoints. The two endpoints of a line are opposite each other. Any choice ofmotion along the line is one way or the other. There are two directions forpotential flow. Every point on a line is at a unique and complementary set ofdistances from the opposing end points. Each point on the line exists in two



ways. A point exists both as a potential non-moving nodal surface point fixedharmonically between two endpoints and a point also exists as a part of thetransitional wave moving across the surface of tensions, (position andmomentum).As a standing wave vibrates on a wire, oscillating on a motionless surface. Awave moving resonantly along the vibrating surface will eventually also bereflected back in a standing wave manner and so also be a surface. Wave projections and reflections move through each other across every point onthe line. The motion of the line is the sum of all the waves on the line. Eachpoint on the line boasts a unique position, making the points on the line all partof a single complete set of points having uniqueness as their common feature.Each person is an individual, unique unto that single self. In some way, each ofus is special and like no other. But since everyone is special, no one is special.We are inescapably similar, bound by our common differentness. We are alldifferent in the same way.For good to be possible in life, bad must also be possible. Both must exist foreither to exist.Agreement and disagreement both exist in all compared things. No two thingscan be in complete agreement or disagreement. If they both register completedisagreement with the other, then on that disagreement they agree. If twoentities were in complete agreement, they would have to be in the exact sameplace and time, and there would be only one entity, not two.An entity exists by its interactions with the rest of the universe, with the not-self.To interact with the universe, an entity creates a model of the universe inside ofitself. Entities exist by interacting as the self and by being the image that is notthe self.For an entity to be what it is, it must also be not what it is. Two contradictoryassertions that come from this are; This is this, and this is not this. Thesestatements are icons of similarity and difference. Being and not-being areintegrated onto the consciousness of each entity.Expanded, these two contradictory expressions are stated more fully. This is thisand this is only this. This is the deductive linear perspective. Freud cautioned inhis dream therapy that sometimes a cigar is just a cigar, and not necessarilyrepresentative of something else in contrast to a cigar.This is not this, but all things like this. This is the inductive lateral perspective.Magritte spoke of this in his painting of a pipe with painted words asserting it (inFrench) not to be a pipe. Instead, the painting is representative of things thatare comparable or similar to a pipe.The first statement is exclusive, projective, objective, and left brained. Thesecond statement is inclusive, reflective, subjective, and right brained.Consciousness integrates linear and lateral opposites to diagonally represent bothand neither.



SummaryLinear thought is one axis of understanding. Objective reasoning is required tocreate objective models, but one who is to firmly grounded in objectivity seesonly the trees and misses the forest. Restated, one can mistake the examplesfor the pattern. Lateral thought is the other axis of understanding. Subjective reasoning isused to give meaning to the patterns, but subjectivity alone fails to justify themeta-pattern by using only objective verifiable examples for comparison.An integrated perspective sees the examples as the pattern, and not the pattern.The higher truth is not one or the other; it is both and neither. Whether twolines are parallel or perpendicular, (whether the lines cross or not) is dependentupon perspective. The two lines can exist in more than two dimensions. Thesimplest three-dimensional structure is the tetrahedron. From differentperspectives, opposing edges of a tetrahedron can be seen as either parallel orperpendicular. From differing perspectives, a particular set of opposing edgescan be seen to cross or not cross.



The abstractness of unityThis chapter focuses on the challenges involved in directly experiencing unity.

IndivisibilityAll that exists is the whole of all things. This is the universe of existence. Allthings have the potential to exist. Everything is possible; some things are justmore likely than other. What varies is the probability of that existence tomanifest. Possibility is lateral. Probability is linear. We (all things) exist hereand now only probably. If causality were broken and the past were altered, thecurrent present would never have existed at all. Everything that has everhappened (and not happened) in the entire universe has led to the presentmoment being exactly as it is. All things are a part of the whole. Divisions of the whole may appear to be opposites, or complements, but thewhole is not the divisions. The whole is without distinction and can only bedescribed as indescribable, a description nonetheless. Thus the highestdescription of the universe is silence.

CauseThe universe, originally all one thing in one place at one time, maintains forevera connectedness in all its parts as that one thing. This is an acausal connection-one without cause. There is no first thing causing any second thing. No partcomes first or second. There is no linear sequential connection. Instead, theconnection is lateral. Time, as a continuous now, laterally passes through allentities at the same time, like a circular water ripple passes through the cornerpoints of a surrounding polygon, or like a spherical expanding wave passingthrough all the points of the surrounding polyhedron- all at one time.

The points on the polygon that the circular line passes through all at the sametime are acausally connected. The passage of the line through acausallyconnected points happens all at the same time.Causal connection across a polygon is seen in two expanding polygons expandingthrough each other from beginning to the end of the process of expansiveinteaction..



A plane passing through a three dimensional crystal shows a three-dimensionalstatic as a directional two-dimensional process. Action in three dimensions (thedirectional flow of time) is similarly viewable as passing a three-dimensionalplane across a four-dimensional static crystal.

From the point of unity, all things happen at once and all of time and space is anunmoving higher-dimensional crystal. Through the geodesics of this four-dimensional crystal passes a three-dimensional plane of dynamic action.In a two-dimensional universe, the axis of time and the axis of space may beseen as separate dimensions for the diagonal process of both at once as two-dimensional space-time. On the diagonal, passage through space also meanspassage through time. A photon passes through space but does not pass through time.On the higher crystal of unity, all points are but one point, and what ishappening to any one thing is happening to all other things at the same time.We all exist in one higher dimensional place, experiencing the same acausalconnection of a single moment. All things exist simply in the here and now. Allthings started out together, and are still together. There is no division. In thisuniverse of action, all entities are doing the same thing. In this universe, allthings exist through a common set of actions necessary for persistence, theobjective and subjective propagation through space and time.

DisunityOur everyday experience is of disunity and does not directly reflect the abstractunity of existence. Our discrete experiences process a linear flow through time.One basic division of the whole of all things into parts is the dynamic division ofbefore and after. This is another perspective of cause and effect, the subjectacting on the object, the interaction of the observer and the observed. Eachevent observed (physically recorded) is similar to, and different from, otherevents observed. The observer is not separate from the observed. Each one changes theother during the mutual act of observation. In unity, the concept of distinction,as in similar or different, does not exist. There is no exchange; there are nothings. The distinction of differentiation does not exist. In this ‘place’ things



that are different are also not different. This is a contradictory notion and isbeyond linear objective reasoning. In unity there are no objects or subjects.There is no cause or effect, and no flow of time or position in space. There justis.

KoansNon-linear abstract thinking is perhaps best seen in koans. The classic koan is‘What is the sound of one hand clapping?’ Such koans have no linear logicalanswer. The purpose of a koan is to circumvent the linear avenue of thought.This leaves lateral non-linear thinking, an all at once arrival at a conclusion. Theconnection is induced, not deduced. A Zen Master would say that thisunderstanding comes not from words or things, and cannot be described. Theimagery of the unity is described as indescribable.

GodelKurt Godel, a 20th century mathematician proved something so earthshaking tothe world of mathematics that it rivals any scientific revolution for loss offoundation and a need for a new perspective. His work was in non-linearequations.Godel proved that any finite mathematical system capable of meaningful processwould be unable to prove all of the mathematical statements of that system tobe true or false. Such unprovable statements can also be expressed in spokenlanguage. (Another system of meaningful process) As example, such astatement in English would be “This statement is false.” This self-contradictorystatement possesses neither truth nor falseness. If the statement is true, then itis false. If the statement is false, then it is true. The statement just is.The variety of these unprovable statements is unending, and their formulationcan be quite intricate and insightful. What makes these statements so importantis their implications in the description of formal systems. These unprovablestatements are self-contradictory. The paradox of self-contradiction has beenknown for millennia. Some mathematicians have explored it, most have ignoredit, but Godel’s work is definitive. Mathematics and linear objectivity are nothing if not self-consistent. Paradoxand self-contradiction have no place in linear reasoning. One counts on gettingthe same answer to the same equation every time the numbers are calculated.An electron always has the same charge. Besides self-consistency, the other expectation of mathematics was self-completeness; the potential resolution of the truth or falseness of any statementpresented. This completeness is what Godel destroyed. What Godel actually proved was: Any finite self-consistent system ofrepresentation must be incomplete.



What Godel did not state, but what follows logically (and linearly) from thisproven fact is that: Any finite system of representation that is completemust be self-inconsistent. A complete description of the universe, in any language, must be self-contradictory.

Flatland contradiction Edwin Abbott envisioned a universe of two dimensions with ensuingdimensional limitations. These Flatland creatures are aware of only twodimensions and not three as we are. These two dimensional creatures have noawareness of a third dimension running perpendicular to Flatland’s two-dimensional world, as we are unaware of a fourth dimension runningperpendicular to the three dimensions that we experience. Flatlanders would know only the two-dimensional X, Y coordinate system. If aFlatlander were to become enlightened of the existence of this ‘third dimension’,the description would be in two-dimensional terms. A partial description of thistheoretical Z-axis, a ‘third dimension’ would place it at 90 degrees to the X-axis.To Flatlanders, this would seem to be a description of the only other axis, the Y-axis. The enlightened Flatlander’s further attempt to describe this ‘thirddimension’ would also fix the new axis at 90 degrees to the Y-axis. To theunenlightened Flatlander, these two depictions obviously contradict each other.Perpendicular to X is Y. Perpendicular to Y is X. To a two-dimensional being,the Z-axis exists only as a contradictory reality and cannot be experienceddirectly. It is a meta-experience of contradictories in agreement. A similarlogical limitation exists in our own three-dimensional quest for a higherdimensional perspective on reality.

Self-contradiction Our universe is one of self-contradiction, and not. The convolutions of anon-linear self-contradictory system include agreeing and not agreeing withitself. Quantification and measurement describe objective reality, but leavesubjectivity unaddressed. The complete set of rules for existence, despiteapparent self-contradiction, includes both the objective and the subjective in alltheir opposing manifestations. Since objectivity and subjectivity innatelycontradict each other, the expression of both in a single self-contradictory beingprovides a point of perspective where contradictory facts can both be locallycorrect. (A photon is correctly, if narrowly, described as a particle and alsocorrectly described as a wave. A higher description of a photon sees it as bothand neither a particle and a wave.) It is from a higher perspective thatcontradictories can be in agreement. Contradictory statements like ‘this is this’and ‘this is not this’ (or ‘this equals this’ and ‘this does not equal this’) can both



accurately describe contradictory aspects of the lower three-dimensionaluniverse, which in four dimensions would not be contradictory. From differing perspectives, what is parallel from one perspective can beperpendicular from another perspective. Valid opposing statements of a lowerperspective’s contradictory viewpoints can be compared using a mathematicalnotation for ease of expression. To simplify the assertion ‘this is this’ and ‘notthis is this’ (or ‘this is not this), the expressions ‘A’ and ‘~A’ will also be used.The following expressions of contradictory assertions about assertions show theexpanded relationship between two contradictory statements. To see therelationship as one way or the other is to have a perspective. To see bothopposing perspectives as the same as well as different is to take a higher moreglobal perspective.

(A), (~A)This is this, this is not this

(Linear deduction), (Lateral induction)

((A)=(~A)), ((A)~=(~A))‘This is this’ equals ‘this is not this’, ‘This is this’ does not equal ‘This is not

this’

(((A)=(~A))=((A)~=(~A))) , (((A)=(`A))~=((A)~=(~A)))‘This is this’ equals ‘this is not this’ equals ‘This is this’ does not equal ‘This is

not this’,‘This is this’ equals ‘this is not this’ does not equal ‘This is this’ does not equal

‘This is not this’

The self-contradictory nature of reality is evident on all levels of being. Mutuallyexclusive statements are just differing perspectives on the same reality. Howone looks at a thing is just as important as any intrinsic properties a thing mayhave. The observer effects the observed. The orientation of a tetrahedron tothe observer provides the kind of symmetry an opposing pair of edges mightdisplay,

Perspective also decides the kind of symmetry exhibited by a plane’s passageacross the tetrahedron, whether triangular, square, or hexagonal.



DistinctionThe observation of the properties of an entity (or event) can be of the wholeentity or of the parts of the entity. The view of a part or set of parts of an entity is a view of a divided thingwith distinct describable attributes observed. This is a self-consistent localperspective.The view of an entity as a whole is of the entity as an undivided undescribedself-contradictory single thing. This is the perspective of the unity of a thing,and is self-contradictory global perspective.In this image, each end is internally consistent, but as a whole, its parts areinconsistent with each other.

The change from a perspective of the unity (or the whole) to aperspective of the parts and differentiation is the change that allows fordistinctions to be observed. This is a transition from a global perspective to alocal perspective - not of the whole, but of the parts. Locality is seen in the physical closeness that allows increasingly minutedistinctions to be made from increasingly narrow observations, that is; less ofsweep resonates around the circle. To observe locally is to perceive the flatfacets of a polyhedron, to be too close to see the smooth curved surface of asphere. A global perspective takes in the whole, at the expense of being aware ofthe details of the parts. A local perspective focuses on the parts, making aglobal view impossible. The transition from a global view to a local view allowsthe parts of the whole to be seen. These parts themselves are seen as wholesthat can be approached even more closely for an even more local, less globalview.There is a relationship between local-global interactions at different scales, andthe energy level in the system. It turns out that a thimble of liquid helium, nearabsolute zero, when placed on a turntable, does not spin slowly first, then faster,but instead spins first not at all, then all at once. At extreme low temperatures,angular momentum is quantized in the entire thimble of liquid, and angularmomentum is more global. It also turns out that the winds of Neptune travelmuch faster than on any of the warmer planets. Again low energy is the causeof such global motion. Where atmospheres are warmer, there is moreturbulence, which causes local distortions. This local action prevents theswiftness of the global wind motions on the colder planet.



Description The differentiations and distinctions of the local parts indirectly describethe global unity. Different sets of distinctions describe different kinds of parts,but the patterns found when comparing one set of parts to another set of partsshows the abstract parallels for the indirect understanding of the common unity.These abstract parallels are seen in structures of correspondence and relationalarrays like tables of correspondence, geodesics, and mathematics.

OBJECTIVE SUBJECTIVELINEAR LATERAL

STRAIGHT CURVED ALONG ACROSS

ENERGY MASSSPACE2 TIME2

Representation The described parts of the whole are like the described facets of a crystal.They are tangential to the central object, and are only indirectly representativeof the whole. A crystal’s facets reflect some objective waves back out to interactwith the outer world, and the same facets also reflect some subjective wavesfrom the object back to itself. The surface that is the facet is the interface between the outside and theinside of an entity. Facets are bordering structures for the whole of three-dimensional space, just as lines are the boundaries of two-dimensional space.Surface facets reflect and project objective and the subjective projections,reflections, absorptions, and emissions. Just as polygons reflect around inside acircle, creating differing reflecting reinforcing circular resonant structures, thefacets of a solid are reflecting reinforcing two-dimensional structures of resonantsymmetry within a sphere. The universe is expanding. Waves can expand as they propagate. If thesurface and the wave both expand at the same rate, the resonant symmetrybetween them remains constant. If the wave expands faster than the surface,each wave will transition the origin of other waves and two waves are groupedas one. If the surface expands faster than the waves, overlaps dissociate andassociations decay. Between integration and disintegration lies the structures ofstillness.



In this passage of waves through each other, interferences, (both positive andnegative) come into being and mark the expanding node points in space thatshow the geometry of the changing yet unchanging relationship between waves.

In an expanding universe, a standing wave moves its reflective facets intonew space. This motion creates a continuously changing matrix of before andafter relationships as the facets continue to pass through new and greateramounts of space. Expanding objects interfere with each other as they passthrough each other.

Wave motion contains linear and circular aspects. An object expandingaway from a point displays linear motion out from the center.



The circular or angular motion around the point is called spin, and goesaround the center. If spin is included with the outward expansion, the cumulative path of theobject’s expansion through space will allow a potentially reflecting facet from anearlier time to become parallel to an adjacent facet of the crystal at a later time.This is a spiral expansion.

The rates of expansion and spin create specific distances and frequenciesbetween earlier and later parallel reflecting facet positions. Different distancesbetween an expanding crystal’s reflecting surfaces allow specific wavelengths tofeed back and resonate harmonically with the parts of itself over time. Differingspin rates permit differing rates of propagation to be timed into self-reflectivefeedback. Past wave pattern engrams can remain in existence and resonate againstnew wave patterns, creating interference pattern projections that predict andsupport the probabilities of future outcomes. We compare and contrast the patterns projected. Similarities anddifferences lie within the particular local patterns focused on for comparison. Imagine a triangle, a two dimensional crystal. There are three points.There are also three lines. There are three axes of symmetry, two differentways. These two ways to show symmetry both divide the object into three equalparts. The triangle is either three lines, each with two end points, or threepoints, each between two lines.

Another symmetry found in a triangle (or other polygon) is its direction ofspin, or chiraltry. This is either clockwise or counterclockwise. There is also thesymmetry of before and after (or inside and outside) found in expansion. In the symmetry of lines with endpoints, the interaction is along the lineand across between the endpoints, which do not move. Points along the line areall potential nodes, which in turn are potential surfaces for projection orreflection. The node points do not move in the direction of the wave or itsenergies. The node points are the surfaces that the waves move upon andacross. Node points on a standing wave are points across and through whichenergy travels during an exchange. Although node points do not move alongthe line, they do change actualized location on the line with changing harmonic



divisions of the line. The various energy resonances of opposition in standingwave harmonics can change the tensions and divisions of the surface.



TangentialityIn the sense that all things are perpendicular to the unity, they are similarlyparallel to each other.

Indirectness All attempted descriptions of the model of existence are tangential yetparallel to the higher description of the meta-model. All that exists is theuniverse of all things. This is a logically contradictory concept. Any universethat contains all things must contain all things that are not in the universe of allthings, for they too are things. All experience is of the universe, in all its forms, experiencing itselfthrough being dynamically interactive with the rest of its universe self. Eachentity experiences being as both itself directly, and as not-itself indirectly. Theuniverse’s experiences of the self and the not-self are through its interactionsand relationships, every part with every other. The part(s) of the universe that is (are) the self is (are) in all things andinteract(s) with the part(s) of the universe that is (are) not the self and is (are)also in all things. All things are both the self of the universe and the not-self ofthe universe, depending upon the perspective of that thing. All interactions areof the universe experiencing existence as itself and as not itself. The separateexperience(s) of the entities of existence is (are) both direct and indirect formsof self-experience.Every entity exists as both a particle and a wave. The higher perspective seesexistence as both and neither the particle and the wave. Not only is this universe one of both and neither, it is actually both andneither both and neither particle and wave.Objective and subjective dimensions both have the tendency to persist andexpand. Each separate dimension has an interest in its own benefit andincrease. Objectively, energy flows downhill in entropy during an exchange.Subjective information flows uphill during an exchange. Objective and subjectiveflows are in opposite directions, and the flow of exchange is each through theother. On one level, increase or benefit to one group may reduce or reversebenefit to the other group. On another level, benefit or loss is shared by allmembers of the group. These distinctions create the basis for cooperation andcompetition. The dynamics of persistence are of hierarchical feedback from levelto level as precipitated into existence. The game is to persist and propagate. Allpaths are explored. The opposition of cooperative and competitive intents in an exchangesystem can create tensions of expansion or contraction. There is plenty of spacefor expansion and contraction. An attractive exchange moves objects together,and repulsive exchange moves objects apart.



A new and higher level of response to the competitive drives ofpersistence is to see how there is a way to benefit the self by benefiting othersthat are the not self. This is a conceptual inclusion or grouping of disparatethings into a greater group. This action of inclusion integrates the members of agroup as a higher-level entity. Enlightened self-interest occurs when members ofa group see how helping the other members is an indirect way of helping theself. This mutual altruism promotes the survival of a group as a higher entity. Contrarily, the mere creation of a new group creates another division ofthe unity. Another collection of things that are not in the self-created group nowexists. The existence of another group of separated things, not the self, iscreated when any grouped thing is created. To the extent that entities are in the same group, they collectively benefitby cooperation. To the extent that entities are in different groups, theyseparately benefit by competition. Entities work toward the same purpose assome other entities, and against the purpose of other entities.In the genetics of humanity, two similar chromosomes create a woman, and twodifferent chromosomes create a man. The nurturing female nature of humanityis exhibited in cooperative similarity, and the aggressive male nature of humanityis exhibited in competitive difference. An entity can exist in groups that are at cross-purposes with each other.To do this, the entity is not directly aligned with either group directly, but is at adiagonal to both groups. All things are both objective and subjective and so areon a diagonal to the field of both and neither. Higher levels of tangential self-contradiction lead to increasingly subtle and indirect expressions of reality.

Enlightenment Buddhists say that enlightenment cannot be sought or found directly. Itcomes not from words or learning, and is not an outcome of logical thought.Enlightenment cannot be described directly. Since enlightenment can be experienced, and since that enlightenmentcannot be experienced through direct description, all that is left are indirectmeans, which are not at all to the point.

Tangent When getting to a point, or attempting to, one follows a line of thought ora physical line. A line that is not to the point will, by default, miss the point.Such a line can only indicate the point attempting to be made indirectly. On an indirect line there is a point that is perpendicular to the pointattempting to be made. The indirect point actually made is where the point tobe made is reflected back from the indirect line. The closest point on the indirectline is where it is at a tangent to the circle that exists around the point at thatdistance. An indirect point on a line may be tangential to many circles



surrounding many points that can be made, and one indirect line by itself is notspecific about which point is intended indirectly.

The line of thought reflects upon some point. From the perspective of thepoint that might actually be implied, a reflection from a line can come from anydirection.

All models of reality are tangential to the unity and therefor can be seen asabstractly parallel to each other from a higher perspective. The direct and theindirect are perpendicular to each other from the lower perspective. Indirect linesare tangential to the point not directly made. Two related indirect lines miss thepoint less vaguely than one line.

The hypotenuse line of a right triangle (as on an X, Y graph) will alwayshave a point upon it that is tangential to the origin.



X and Y coordinates A wave in a two-dimensional field (a flat surface) has two axes, X and Y.The two components are one wave.

The hypotenuse of Pythagorus is the mirror image of the unit circle length ofTrigonometry. Both are indirect expressions of the two original axes, both andneither.

No matter what the angle of the unit circle around the point, the radialline always points away from the center. No matter what angle the hypotenuse, there is always a point on the linethat reflects the center back to itself.



The hypotenuse is a constant value (one, like the unit circle) for acontrasting pair of perpendicular dimensions to share a functional relationship.The total squared areas of the two perpendiculars are constant across all angles.

Plank’s constant Space and time are linked components of the continuum of the universe.They can be seen as similar to (and different from) each other. They can also beseen as a single higher dimensional meta-object of space-time. The hypotenuse of X and Y is a meta-object for both X and Y separatelyand is thus both consistent and contradictory with itself from the perspectives ofX and Y. A fixed length hypotenuse of space-time is the fundamental unit ofmeasure for the opposing forces linear and lateral, (or angular) propagation, andis called Plank’s constant after its discoverer, Maxwell Plank. With the hypotenuse length remaining constant, the values for X and Ymay vary. As X grows longer and closer to the length of the hypotenuse, Ygrows shorter. Heisenberg showed that in complementary sets of information, X and Y,knowledge of the two kinds of information (like position and momentum) aremutually exclusive. The kind of knowledge available is based on whether thehypotenuse is more nearly parallel with X or Y. The greater the certainty ofhaving one kind of information, the greater the certainty of a having a lack ofthe other kind of information. A hypotenuse yields two opposing perspectives onreality from one ambiguous tangent.

Three from four One hypotenuse traverses one quadrant of the X, Y graph. Left / rightsymmetry and top / bottom symmetry provide three more hypotenusessurrounding the graph origin with an infinite set of parallelograms of fixed lengthdiagonal hypotenuses, one side for each quadrant of the graph. Two sets ofreflecting parallel lines exist regardless of the quantities in the relationship.



In trigonometry, the unit radius line of the circle changes direction around theorigin. The reflective hypotenuse for each potential radial has its centercollocated with the center of that radius line. The center of the hypotenusemoves in the same direction as the center of the radial, but the angular changesof the two lines are in opposite directions. As the center of the trigonometric pair (the radius and hypotenuse) movesaround in a circle in one direction, The reflection back to the center from thehypotenuse line moves around the center in the opposite direction. While oneperspective shows a constant angular motion in one direction, the reflection ofthe center (from the hypotenuse) moves around the circle in the oppositedirection through each of the four quadrants.

The natural motion of the fixed length hypotenuse though a full fourquadrant circle traces out a hypocycloid.



The co-located midpoint of the hypocycloid hypotenuse and the unit circleradius both trace a circle with a radius of half the length of the original unit. Thearea inside the inner circle is one quarter of the total area, leaving three quartersof the area on the outside of the inner circle. The relationship of X, Y space across two dimensions, (across and along),creates the basis for a third dimension, around. The range of a new dimensionis all of the perspectives from the original lower domain. A circle needs a two-dimensional field to exist in.There is the unit circle, and collocated within the unit circle is the midpoint ofcoexistence circle halfway out from the center. The inner circle can have atangent to it. When the inner diameter is half the outer diameter, the tangentline reflects around inside of the outer circle exactly three times making exactlythree tangents around the origin.The area of the outer ring half of the unit circle is three fourths of the totalinternal area. Three fourths of the area is in the outer ring. This tangentreflects around within the circle three times creating a three dimensional radialdivision of space.

The ratio of straight space to curved space in angular divisions of the circledepends on the number of harmonic divisions created around the circle.



The repetitive flow around a point is a feedback system for resonantpropagation. In these flat examples, the circular two-dimensional motion can beseen as moving through one axis of time and one axis of space. One view of ourfour dimensions sees a similar repetitive motion through one axis of time butthree axes of space. A triangle inscribed in a circle, itself describes an inner circle at half theradius of the outer circle. One quarter of the outer circle’s total area is found inthe inner circle. A square inscribed within a circle has its own inner circle with half the areaof the outer circle. If another square is inscribed, and then another inner circle,the second inner circle of the square has the same area as a single inscribedcircle from an inscribed triangle.

Halving the area of circle twice with a square is equivalent to halving thelength of the hypotenuse once with a triangle.

Convergence As shown above, self-reflection from the center origin of a graph occurswith each of the four hypotenuses at any slope around a point. Everyperpendicular line pair rational position on the grid acts as a direct reflector forevery radial from that point.

Self-reflection within a grid square occurs from four directions from anyposition within the square. The four 90 degree corners are natural directreflectors.



Exterior reflection of space and interior reflection of space are differentperspectives of the same geometry of linear process.

Divisions of the whole circle other than four 90-degree radials can also mark outequal angles of radial sweep around a point. 60, 90, and 120-degree rotationsallow unit length extensions into space to continue self-similar patterning on theplane.

Any number of radials around a point can divide the circle. The orientations andextensions of dimension in being, in space-time, are at a stable balance whenopposing forces receive equal uniform resistance.

The more radials around a point, the less the angle of sweep exists around acircle between radial lines. The occupation of space can occur with any polygon.

The number of corners in a polygon is same as the number of sides of thatpolygon. Since the number of sides of a polygon is always the same as thenumber of corners of that same polygon, every polygon is its own ‘dual’. That is,



every polygon can be rotated half way out of phase with itself and have a one toone correspondence between sides and corners of the two positions of thepolygon. Two regular identical polygons, rotated out of phase with each other,can be of a relative size that their edge lines will cross. Each polygon has itsedgelines lines crossing the lines of the (by its perspective, out of phase) otherpolygon.

Every point in space has an infinite number of radials through it. Every point inspace also has an infinite number of circles surrounding the point.

All expressions of space are perpendicular to all expressions of time. Every pointon the tangent line (where the circle and radial meet) is at a given distancefrom, and at a given angle to the central point. At specific ratios of uniformlengths and angles, a plane is covered with three self-perpetuating, resonant,geometric organizations of space and time. These arraingements are seen asthe triangle, square, and hexagon. The intersections for each of these repeatingpatterns of extension into space are motionless node points. Flat planar spacecan be seen as a grid with uniform divisions or patterns of potential runningacross it. Three dimensions of space are more complicated than two dimensions. Athree dimensional dual has the number of corners of one polyhedron matchingthe number of facets of the other polyhedron. The cube and the octahedron areduals of each other. Only the tetrahedron is its own dual.There are at least four ways to describe the point location of an object in two-dimensional space; the Cartesian X, Y two-distance coordinate system, the tworadial coordinate system, the single radial-distance coordinate system, and thethree-distance coordinate system, where the intersection of only two circleswould leave uncertainty.



Lines can be reflected and projected by other lines. Radial lines comefrom a point. Lines are of reflections and projections from one point to another.

Tangent lines miss the point. Tangent lines reflect and project relative tothe circles radius around a point. A radial line from one perspective can be atangent line from another perspective.

Memory traces are enduring wave interference patterns of projections andreflections whose resonant vibrations have caused recognition in consciousness.Pattern recognition is being able to resonate against past patterns to comparefor such things as harmonic tensions, stress relationships, and classes ofresolution, seeking the higher pattern.The resonance traces can be seen in the infinite set of tangents of the circularexpansion from a point. The resonant echo can be seen in a particular radial’sset of tangents in a particular reflective or projective pattern, or it can be seengoing around or through divergent radial lines. The resonant pattern can besimple or complex.



This trace is a sequence of points patterning specific times and spaces. Patternsequences from one point to another can occur along an infinite number of pathsthrough an infinite number of points, but the most direct route is therenormalized general description. From one point on an X, Y graph to another,motion can be in either direction.A line can be a tangent to a circle around a point or a radial away from a point.The tangent line is perpendicular to the radial line, and one is the same as theother. Angular motion of the tangent line is the same as linear motion awayfrom the radial point. Slope change in the tangent line is only a considerationwhen the origin of the tangent line is local.Sequential motion of a point strictly in a radial direction will have tangent lines tothat point that are all parallel to each other, never crossing, with a given linearquantity between any pair of points on the line of motion. Motion of a linestrictly around a single point will have radial lines that all meet at a single point,with a given angular quantity between any two lines.

No line is just a tangent or just a radial. Every line is both a tangent and aradial. Perspective allows a line to be seen as one or the other.



All flows are not just X or Y, but X and Y. The line of flow will be at somediagonal slope to the X, Y coordinate system.

A two to one slope has a wave’s line of travel going twice as far along one axisas the other axis while the line moves but the slope is still. This straight-line flowof slope can be in flat space or in curved space. Curved space comes backaround to repeat a flow across the same space. If the curvature is just X or justY, the resulting objects are cylinders. If both X and Y curve around to allowangular flow along both axes, the resulting shape is a torus.

If the line of flow along a curved space appears to be nearly exclusively alongone axis, it can be seen to curve back around and be parallel to itself on its nextcycle, and the next. The line itself is always at some diagonal, but may appearto move almost exclusively along one dimension. If the cycle is observed formay similar passes of adjacent parallel lines along one dimension, a timed pointalong that cycle will show fixed a set of points at the same place in the cycle toall describe a single line nearly lateral to the original flow. The marked repetitionof an explicit linear line of thought along one direction of motion will yield alateral line of implicit inference in the across that same direction of motion. Atrue perpendicular to the rotating spiral is a spiral in the other direction aroundthe closed surface. The closer one direction gets to being completely across theflow in one direction, the closer the perpendicular gets to being completely alongthat same direction of flow.



This same lateral direction of patterned flow exists even when the linear slopeacross the grid is greater and the lateral line is less obvious. Every rationalharmonic of X and Y has a related lateral structure existing along with andagainst the objective structure. When a straight line passes across the plane, the repeating change inquantities of X and Y define the slope ratio for that rational pattern. There existswithin the parts of the ratio, dimensional extensions where a standing wavemight develop. Such a repeating pattern of X and Y is an object. A given slopeis of a particular object. The more subtle the ratio between X and Y the morecomplex the object created. A two-dimensional pattern may appear to repeatover and over on a flat surface, or the two-dimensional surface can be reflectedback to the origin within a single grid square.

Passage of a line across a two dimensional geometric figure is analogous topassing a plane across a three-dimensional geometric figure, as is the passage ofa three-dimensional surface through four-dimensional object. Exchanges arealong the geodesics between node points, whether in some sequence, or all atonce.

The facets on a high order polyhedron (one that looks like a sphere) whenviewed locally appear to be a grid on a flat surface. Exchanges across the highorder polyhedron’s surface then appear to be motion from node points to nodepoints on the grid. Quantum exchanges along node points can be betweenindividual nodes or groups of nodes that are collectively a single node, or groupsof groups of nodes, etc… Geometry is the study of angles and distances on surfaces. Topology is thestudy of the curvature of surfaces. The relationship between geometry andtopology is that a topological object, like a sphere, is a high order geodesic and ageometric object, like a cube, is a low order geodesic shape. Both sphere andtetrahedron possess qualities of topology and geometry. The differentattributes, though the same, have differing influences on differing scales.



A wave traveling on the surface of a topological object is via the geometric nodepoints of the geodesic surface. Both actions are that of a lower-dimensionalsurface passing across a higher-dimensional object.

When viewed from a global perspective, a high order polyhedron surface iscurved. When viewed from a local perspective, the surface is flat.

An expanding ripple can be on a curved or flat surface. The perpendicularsine wave travels along the radial lines of the origin point. The circle’s sine waveexpands away from the center. Globally far from the center, a local radialsection across the front of the wave will be flat and perpendicular to thedirection of travel. The sine wave itself is time invariant. That is, the image of the wave looksthe same forward or backwards. What is not time invariant is the wavefront’scurvature across the local part of a full circle. One direction is positive, The otheris negative. No matter how little curvature there is, the curvature is in thedirection of the original point, the direction of probable cause. The other side ofthe wave of passage is the direction of probable effect.

If the wave, starting at a point, travels completely across the polyhedron, theenergy of that wave will meet again on the other side of the polyhedron at apoint. This processes is time invariant. Sub microscopically, it happenscontinuously. Quantum particles are completely time invariant. In themacroscopic world, however, a wave will lose or transfer its energy beforereaching the other side of the geodesic, and time-flow cause and effect becomesdirectional.



Tiling the plane Only three regular polygons will tile the local flat surface without gap oroverlap. These are the triangle, the square and the hexagon. A flat tilingaround a single point will use three hexagons, four squares, or six triangles.

With these three polygons, points at the corners of the tiles define the plane’snodal geodesic surface. Intersecting planes describe edges. Edges describeboundaries. The new points in the tiling infer new points of resonance for moretiling of the plane. From each extension of a tile, more tiling extensions of spacecan be described. Waves travel along a surface through its potential divisions ofthat surface. The potential node points pass energy as slope exchange in bothdirections at once. Old to new, and new to old; the tile node points areterminals of harmonic exchange. To gain curvature on the tiled surface, affecting the topology throughgeometry, the number of polygons around a point can be reduced. Four squaresaround a point are flat, but three squares around a point make the corner of acube.

Angling and reducing the number of facets around a point can create objectsthat are (in the simplest regular form) the five platonic solids. The lines connecting corner points on the polyhedron carry wave exchangesaround the object in three dimensions instead of two. More dimensions allow formore complicated exchanges. The shape of the polyhedron shows the wave setsit will carry.The cube and octahedron are a pair of expressions for one symmetry of space.They are each platonic solids and duals of each other. Polyhedron pairs that areduals of each other have the corners of one object radially collocated spatiallywith the facets of the other object.

The cube has eight corners and six facets, while the octahedron has sixcorners and eight facets. Both objects have twelve edge lines. An edge line on



one object matches perpendicularly to a corresponding edge line of its dualobject. Duals have all the edges on one object each perpendicular to acorresponding edge on the other object. The other platonic dual set is the dodecahedron and icosohedron pair, withfacet counts of twelve and twenty each, respectively. They both have thirtyopposing edge lines. The fifth and simplest platonic solid is the tetrahedron. This is a four-sidedfigure with four corners. The tetrahedron is the only solid that is its own dual. Atetrahedron has six edge lines to interact with another tetrahedron. On a tetrahedron there are six paths of exchange between four points ofreflection and projection. Each corner point has three lines going from it to the three other points. Each facet centerpoint is surrounded by three lines that go around the facetsand are tangent to the center of the facet and tangent to the center of thetetrahedron. When two same sized tetrahedrons are placed out of phase with the other, allsix lines of exchange on each tetrahedron cross all lines of six lines of exchangeon the other tetrahedron. No matter the orientation of one tetrahedron to theother, the two sets of six lines can always cross and touch. The point where twoedge lines cross and touch each other are the node points of stillness for bothpolyhedrons.

The tetrahedron structure depicts the tensions of a three dimensional standingwave object. The lines of the tetrahedrons can resonate harmonically. Still nodepoints on one line can change location along that line and influence still nodepoints on the dual line that crosses it through indirect mutual reflective feedback. Harmonic progression nodes in the lines on each tetrahedron indirectlyinfluence the other tetrahedron’s harmonic progression nodes, and as thecrossing nodes move, so does the spatial orientation of one tetrahedron to theother. This is the dynamics of the four-dimensional crystal.



Observed properties of a tetrahedron are quite instructive. The closest packingof spheres is in a tetrahedral array. A tetrahedron is the simplest and moststable three dimensional object. Two opposing tetrahedrons form thecrossmembers of a cube, which has six single surface reflectors, twelve twosurface reflectors, and eight three surface reflectors.

A tetrahedron shows the symmetries that tile the plane: From oneperspective, perpendicular to two opposing edges, a tetrahedron has thesilhouette of a square. From another perspective, perpendicular to a facet, atetrahedron has the silhouette of a triangle. Crossing diagonals on the facets ofa cube are made of two crossing tetrahedrons, and the diagonal silhouette of thecube as a whole is a hexagon when seen perpendicular to any of the cube’s fourthree dimensional opposing corner diagonals.

The passage of a plane through a geodesic plots not just the parts, but also theperspective of organization. For that pattern to exist, its parts must each havean exchange in sequence discovered by the passing plane’s perspective.Exchanges between the parts can be seen from different perspectives.A plane, passing through a tetrahedron perpendicular to its square perspective,maintains a constant length perimeter as the ratio of height and width exchangequantities. A plane passing through a tetrahedron perpendicular to its triangularperspective maintains a constant ratio of area to height as the volume changes.These are different resonance structures in the tetrahedron.

Four spheres pack into a tetrahedron. By the two symmetrical ways to pass aplane across the tetrahedron of spheres, four is counted two plus two, and also



counted as one plus three. The exchange arrangement goes in both directionsfrom both perspectives.The tetrahedron can grow in the number of spheres needed for its creation. Thenext higher order tetrahedron has three spheres in a row along the edges.There are three layers to pass through, two different ways. That is three plusfour plus three, or one plus three plus six.

From the perpendicular perspective, this higher order tetrahedron makesexchanges from three spheres in a line to a two by two arrangement, and thento three spheres in line at ninety degrees to the first line. The six new spheresneeded for this tetrahedron exist in two different symmetries. One additionalsphere occurs between each of the two opposing perpendicular lines of spheres,and the other four spheres form the square of equal perimeter interface betweenthe two perpendiculars lines of spheres. The primary addition was two plus two.The next level of addition goes three plus four plus three. From the triangular perspective, the old tetrahedron makes exchanges from oneto three and back. The new tetrahedron goes from one sphere to three spheresto six spheres. All six new spheres occur in one plane together, and have theirown internal perpendicular planar symmetry of one plus two plus three.Triangular three-dimensional addition is one plus three plus six.

Circumference Every point in space is surrounded by an infinite set of circles, radials, andtangents to circles. Every radial has an infinite number of perpendiculars from asinfinite number of directions.



A point in space may have two circles expand out away from it starting atdifferent times. There may be, then, an outer circle and an inner circle that bothexpand away from the center. This expanding set of circles will be called a circlepair. Within a circle pair, a line that is tangent to the inner circle will be a secant orchord line to the outer circle.

If the inner circle diameter is near zero, the length of the inner circle tangentline that is a chord to the outer circle approaches the diameter of just the outercircle.

If the center circle expands relative to a fixed outer circle, the chord betweenthe two circles grows shorter. As the inner circle approaches the outer circle, thetangent approaches zero.

Now, if these two circles both expand at a rate that leaves a constant lengthtangent chord between them, then the area between the two circles remainsconstant. The area between any pair of concentric circles is a function of thetangent chord length between those two circles.



This fixed length tangent of a circle pair is the fixed length hypotenuse unit ofquantum measurement. We see the universe as expanding. We see bothcircles as expanding. If the tangent length stays the same between the circlesthen the area between the circles stays the same. What we see is a fixed lengthtangent, the basic quantum of measurement and exchange. A fixed two-dimensional area also represents this fixed one-dimensional length. The areathat is the square of the hypotenuse remains constant and equal to the sum ofthe squares of the X and Y quantities that describe that hypotenuse, and pi isthe factor of rotational extension around a point. This relationship betweenlength and area aids in understanding the relationship between rolled upmembrane surfaces and unit length strings in superstring theories.What changes, along with ratio of radii to chord lengths, during the expansion ofa circle pair, is the number of tangents that reflect around the circle. At specificratios of radial length to tangent length the reflections around a point arereinforced by whole number harmonics. This allows for a set of circularlyreflected standing waves.

A disk rolling on a surface remains upright, holding a resistance to the force ofgravity to lower the disk’s center of gravity. If the disk is spun backwards to thedirection of motion across the surface, the disk remains upright as the frictionalforces of rotational deceleration and linear deceleration compete. When thefrictional forces equalize, either the direction of spin in the wheel will havechanged or the direction of travel across the floor will have changed. On aspinning turntable surface, a disk spun backwards will reverse both its directionof spin and direction of travel continuously around the spinning center of thissurface, with a circle as the limit of the disk’s travel. Different size disks havedifferent size patterns around a similar sized limit circle for a given speed ofrotation around the center of rotation.



Entities are standing waves with any and all number of divisions of the whole.Entities’ different numbers of divisions resonate against each other by one facetfrom each of the two entities being a single composite pulse that is some fractionof one entity and some other fraction of the other entity. The ratios of one tothe other can vary vastly. Changing the ratio between interacting circle-pairschanges the resonance of the interactions between them.

Common resonance structures for standing waves include the circle diameter,inscribed triangle, square, pentagon, pentagram; all self-reinforcing inscribedpatterns. All regular polygonal structural lines of flow can be reflected around bythe outer circle back onto itself, as long as the inner circle does not interfere. Asthe circle-pair expand, first the simplest geometries are blocked, then higherresonances. At great expansions, only the highest resonances endure. A wavetraveling around inside the outer circle interferes with itself for feedback andpersistence. All possible ratios of radius to tangent occur in the fixed area of an expandingcircle pair. When the inner circle starts at zero radius, the internal fixed area ofthe circle pair is the same as the area of the whole outer circle. The tangentbetween the circle pair is then equal to the diameter of a single circle with thesame radius. The tangent equals one and the outer radius equals one half. Theinner radius is zero. The ratio of radii to tangent is one half to one for the outercircle, and zero to one for the inner circle.

As the circle pair expands, the radii of the two circles successively becomelarger than the tangent chord length. With enough time, the radii become solarge that the unit length of the tangent becomes virtually zero in relation to



either radii. The difference in length between the two radii has shrunk tovirtually zero. The radii to tangent ratios become nearly infinite.

Local closeness of a tangent to the center of the circle is in relationship to theswept angle of that single segment around the point. The greater the tangentlength in relation to the radius length, the closer the tangent line is to the center,and the fewer tangents it takes to go around the point. Everything is a wave. The wave circle can be seen as an expanding surfacepulse flowing away from a point. This circular wave that is the outer circle canreflect back into the circle. Even though the wave is circular, the paths ofexpansion on the wave are all straight. The flows of the inner wave go instraight-line reflections around the inside of the outer circle. Any point inside theouter circle provides a starting point for a circular wave to find straight geometricreinforcement at any angle. Wave starting points near the edge of the outercircle only allow for iterations around the circle that do not cross.

The simplest two-dimensional geodesic is the triangle. Next simplest is thesquare. Two circle inscriptions of the square are the same as one inscription ofthe circle in a triangle.

A Point All lines of discourse on the nature of things are at a tangent to the truepoint of unity’s singularity and will miss the mark. In Olde England’s archery, to



miss the mark is to ‘sin’. The first circle was sin one, and the next circle was sintwo, etc. The vocabulary of King James colors modern terminology for wrongdoing.Biblically we all fall short of the aim of being a squarely centered reflection ofGod. To face self-reflection directly as the godly unity is beyond mortal abilities,as we exist on the diagonal and experience God only indirectly. Some peoplefind it difficult just to meet the reflective gaze of another person squarely. We are made in the image of God, abstractly, but so are all things. No matter how precise a description of the unity is attempted, it willfail to hit the mark exactly. Even the closest imagery is at a tangent tothe truth and will, by its nature, miss the point.... And this great truth of the certainty of any description of reality tomiss the point, itself completely misses the point.



Self similar patternsEverything is abstractly the same as everything else. Self-similarity has manyforms and is seen in all things. This chapter is an overview of many of themechanisms of self-similarity in our universe of existence.

Self reference The point of the previous chapter’s description of ‘missing the point havingmissed the point’ is that being is a self-referential action. Godel’s proof ofunprovability is of equations that are self-referential and contradictory. A self-contradictory being, as surreal and ambiguous as that seems, creates a feedbackimage of itself by objectively being indirectly subjective and subjectively beingindirectly objective. Actions and reactions are conducted ion a common field ofindirect play, each axis through the other. This continuously reflected feedback pattern, on every level, leads tocommon kinds of distinctions and differentiations through harmonic dynamicsand a drive for truth and beauty. These are the goals of the forces of objectivityand subjectivity.

Reflection Another way of seeing self-similar patterning is by simple reflection. Thereflected image is the same as the original object image of the self, onlydifferent. Two-dimensional reflections of an image are all different from theoriginal object in the same way. The direction of spin (a quality also known aschiraltry or handedness) in a reflection is opposite to the spin in the projectedobject being reflected.

Each reflected image has the same quantity of information as the objectof reflection, but the quality of the information has reversed. The images aredifferent yet the same. A reflected image of an object usually appears to belocated in a virtually projected place; not where the actual self is, but on theother side of the reflecting surface, where it appears with a reversal ofhandedness. The surface of a flat reflector gives an undistorted image of self-reflection.The image of the self is on the other side of the reflecting surface from the self,and at equal and opposite distance from the surface of reflection. The



cumulative point of direct self-reflection on the surface is perpendicular to thereflecting surface. A curved reflecting surface will make the reflected image of the self seemcloser and smaller or farther and larger, depending upon whether the curvatureof the surface is convex or concave to the object of reflection.

If instead of central self’s eyes looking out at larger or smaller reflections, theself were the smallest eye, then the central eye that was the self before is now aconcave reflection. This relationship of size, distance, and curvature exists fromlevel to level regardless of which perspective is that of the self. The greater isthe same as the lesser. A two-dimensional reflector has a two perpendicular dimensions to curvethrough, X and Y. The two axes may be flat or may curve independently intothe third dimension either toward or away from the object being reflected. Thetwo axes can each curve in separate and opposite directions. The flat surface isone example of the class of reflectors that places the virtual image on the otherside of the reflector from the object.

There are three possible positions for the reflected image of the self,depending on the class of curvature observed in the reflector’s surface. The flatreflector is an open or hyperbolically curved (like a saddle) reflecting surface. Ina reflector that is hyperbolic, the observer sees the image of the self on theother side of the reflector, in at least one dimension. The closed reflector (like acircle) is an elliptical curve, and the reflected image is focused inside the sameellipse (or circle) as the object being reflected.

Between the two broad classes of curvature, (hyperbolic and elliptical),lies the fine line of parabolic curvature, where the image focuses at infinity inboth directions.



(There is another entire way of describing the properties elliptical, hyperbolic,and parabolic. Here, though, the distinction is whether the two axes both curvein the same direction, different directions, or have at least one dimensionremaining uncurved.)

A reflecting surface can have any number of dimensions. When a surface curvesaway from the observer with one axis and toward the observer with the otheraxis, the curvature of the two-dimensional surface is hyperbolic. Euclideansurfaces are flat and open in at least one dimension. A surface curved the sameway in both dimensions is closed elliptically.When the observer is very close to any reflective curved surface, the image is so

nearly flat that its reflection appears to be off of a Euclidean surface. Theapparent amount of curvature can change with distance. Increasing curvatureindicates greater distance from the reflector. Local surfaces are flat while more

distant global surfaces are curved, either towards the hyperbolic, or the elliptical.

If the reflecting surface curves away from the self, then one’s reflectionwill seem, from any distance, to appear smaller and smaller as the surface’scurvature increases. Although the reflected image looks farther away (is smaller)on such a convex surface, the reflected image will actually focus closer to thereflecting surface as its curvature away from the reflected object increases. Acurved surface might also curve toward the self being reflected, making theconcave reflection look larger and causing the image to focus farther and fartheraway with increasing curvature. As long as the image of the self appears to beon the other side of the surface, this concave reflector is in the same class ofreflectors (relative to an observer) as the flat and convex curved reflectors.



The flat reflection, all convex reflections, and cases of reflective curvature towardthe self that still leaves the reflection on the other side of the reflecting surfaceare all open reflectors of the self being reflected.

Any whole dimensional surface (not a fractal dimension) is flat, smoothand open if seen from close enough. As distances from reflective surfaceincrease, making the image reflect off a more global surface, increasing orders ofcurvature become apparent. Curvature is a feature of globality. Locality, or thelocal perspective, is flat.As the curvature of the reflector towards the self continues to increase and theimage continues to grow larger and focus farther away, eventually the recedinglines of focus will not converge at any distance beyond the reflector. When thelines of reflection all become parallel, the image is resolved only infinitely faraway. In this case of reflection, the image is at infinite resolution in bothdirections at once and is just as much on one side of the reflector as the otherside.

This is a parabolic reflector and is neither an open reflector nor aclosed reflector. This curve is the division between open and closed curves. The third class of curvature is elliptical. In this class of curvature,an object’s image of reflection is formed not on the other side of the reflector,but on the same side as the object being reflected.

This reflecting surface curves back on itself into a closed loop calledan ellipse. Inside the ellipse are both the object being reflected and the imageof its reflection. Planets orbit the sun in an ellipse, with the sun at one focalpoint, and no object at the reflection point. A special case of the ellipse is thecircle, which alone has the object and the focus of reflection in the same spot inspace at the center of the reflecting circle. These three types of curves; Hyperbolic, parabolic, and elliptical,are the kinds of curves that can occur when a plane is passed through a cone.



Projection A surface that reflects an image of the self might also allow the realimage of the self to be projected through to the other side of that surface.

This transmissibility of a surface allows for variations in the patternsequence of projections and reflections of the wave that resonates and reflectsinto the set of surfaces that make up the past history of an entity. Moments ofexperience are sequenced by time and space pattern characteristics. Additionalsurfaces of reality are created by each new moment as it occurs.

The sequence of reflections and projections may reveal complex interferencepatterns to resonate possible and probable futures. A real image that is areflection on one side of the surface is a projection on the other side of thereflector. The surface reflecting an image might also be the surfaceprojecting an image. A surface can do both at once. Confusions can occur. Wehave all looked into a mirror from an angle and thought it to be a window. Insuch a mixed-use medium, it can at times be difficult or even impossible to tellwhether an image is a projection or a reflection. An excellent example of this effect is at the Haunted House ride atDisneyland. There is a ballroom where the ride-goer looks down ontomechanical men waltzing around without partners. Ghostly images of dancingwomen then appear in the arms of the dancing men. The effect is seamless.

In actuality, the suddenly appearing ghosts are below the ride-goer, on the same side of a large glass surface as the ride-goer. The ghosts arereflected on the large glass surface that the mechanical dancing men were seenthrough. The men are projected to the observer and the ghosts are reflected tothe observer. The reflected images of the ghosts seem co-located with theprojected image of the men when a light is shined on the ghosts making themvisible and reflecting their image up and back to seemingly merge with the men.



Projections and reflections are both equally real. Each can influence the otherindirectly. Reflections and projections generate a being and are generated by abeing.

Fractals Fractals are self-similar structures of infinitely fine detail. A fractalpattern looks self-similar at different scales of magnification. Magnification of apart of a fractal does not materially change the amount of relative detail in thefractal image. An example of a regular fractal is the Koch curve.

The triangular image of the Koch curve shows finer and finer detailas one looks closer and closer. In a fractal, scale is irrelevant. Fractals dimensions exist between whole number dimensions like aone-dimensional line or a two-dimensional plane. Instead Fractals exist in2.45536 dimensions, or whatever portion of dimension is defined by the initialparameters and particular equation of feedback that defines that fractalstructure. A fractal image is self-referential in that it uses its own value onone scale to compute the value for its modified image on a closer scale.

Feynman diagramsFeynman diagrams show the explicit observed relationship between interactingparticles. They also show the unobserved, infinitely complex self-similar potentialinternal matrix of relationships that are implicit in any observed relationshipbetween particles. The infinite complex of unobserved interactions that equateto the simple observed interaction are of the same type, but at a shorter scale oftime.@

Interference patterns When two or more waves interfere, opposing constructive and destructiveconditions can form a standing wave higher order interference pattern. Placetwo flat combs together and the interference pattern will be straight linesbecause the combs’ teeth are straight. A pattern can even interfere with its ownprojected shadow or reflection. An interference wave pattern is formed from two or more similar patternson another scale and orientation., and is similar to the lesser resonant structuresAn interference pattern contains properties of scale larger than any of thecontributors, singly.



Harmonic resonance patterns depend on similar magnitudes or scales ofcurvature for interfering interactions to occur. A common example of an interference pattern in seen when traveling alongfreeways. Overcrossings for pedestrians are fenced on both sides. Both fenceshave a similar pattern. When two fence patterns are viewed, one throughanother, a higher order interference pattern is formed. The interference patternis larger than the pattern of a single fence’s pattern alone, but the interferencepattern is the same shape as the pattern in each of the two similar fences. Ifthe pattern in the fence is of round holes in a hexagonal array, then, the largerinterference pattern of both fences together will be of round holes in ahexagonal array. An interference pattern is the same shape as its constituents, but on adifferent level. The figure and ground relationship of the interference patterncan be reversed from the figure and ground image of the separate fences. When two fixed patterns are superimposed on the same plane, then theinterference pattern is as fixed in space as the contributing patterns. If there is a third dimension of expression in the interference pattern (ifthere is a perpendicular space between the patterns), then the interferencepattern is not fixed In space relative to the fixed original patterns. When an observer passes by the separated fences that make up theinterference pattern, that observer will see the positions of the fences (relative tothe observer) to change, just like the positions of every object the observerpasses by. But as the observer moves by the fences, the interference patternmay be seen by the observer to move in a direction independent of themotionless fences. The interference pattern may move in the same direction asthe observer, in the opposite direction as the observer, and can even display twodifferent interference patterns moving in opposite directions at different speedsthrough the unmoving fences. .

Stillness or motion for these two levels of being relative to an observermakes two frames of reference. There is stillness or motion relative to thepattern, or relative to the interference pattern. These are two opposingperspectives of stillness and motion.Resonance of one structure with and against another structure creates a similarstructure on another level. The composite structure occupies a given amount ofspace in a similar number of dimensions. There is a ratio between the low andthe high, cause and effect, the parts and the whole, the matrix of existence.This ratio is the diagonal slope which is altered in two different ways. First, twocontributors can be brought closer together to change the ratio between them



and the combined whole. The other method of changing the ratio is bychanging the rotational orientation between the contributors. This also changesthe ratio between the greater and the lesser structures. The two ways to makechange are by changing distance and by changing orientation. Change isstraight or curved. The interference pattern found in any repeated pattern is strongest whenthe two patterns are of the same apparent size. When the patterns become outof scale with each other, the interference pattern changed resonancesdrastically..A hologram is an interference pattern. Moving the point of view across theholographic plate can be seen as viewing an image at the same time fromdifferent places, or viewing an image at different times from the same place.

Placeholding In our numbering system, there are symbols that stand for amounts, (1,2, 3, 4...) These symbols may be arranged in an incremental order according togradations in amount, a numerical sequence. Placeholding was developed torepresent new levels of magnitude of the same relative quantities. We use thenumber ten as the base for our numbering system, but placeholding will exhibita self-similar pattern in any base. A coloration method of notation allows forhierarchical self-similarity to be seen on different levels of magnitude for anybase’s placeholding of a numeric sequence. Each base has a different pattern seen in its placeholding. Within eachbase, a new order of magnitude shows the same pattern, only on another scale.As in fractal structures, we see similar patterns at different levels of order. Asthe number of terms grow, so do the number of possible states. As a staticimage, this structure displays exclusively linear and lateral components. Adynamic system would include both components and be on the diagonal.



Reproduction Life reproducing life is an example of self-similar patterning. Each newgeneration is the same as the old one, yet different. As a dynamic structure, lifeflows on the diagonal, with levels of stillness and columns of motion interactingto create the rational slope of change. Any life flow that fails to propagatethrough change like its predecessors will go out of existence. New life recreatesthe potential for new changes that keeps life continuing to exist. Simpler lifereproduces simpler relations. The more complex the relationship for comparedpotential states, the greater the range of options between the entities ofexchange. Even non-life objects continuously reproduce themselves at lower levels ofsimilar kinds of action. The atomic particles themselves recreate their ownopportunities and conditions for continued existence. Mass creates the space forthe mass to exist in. The abstract process of existence is one of continuing self-reproduction,or continued propagation as a wave. It is the process of allowing of a continuedbeing by continuing to be.

Summary Exchange and feedback are parts of awareness, being, and consciousness.Each entity operates in a relationship with all entities, including itself. There are four types of relation between the self and the not-self. Theself and the not-self can each interact with the other directly and indirectly. The



four paths of exchange are; Self to self, self to not-self, not-self to self, and not-self to not-self. The objective axis and the subjective axis each have a self and anot-self as their parts

A newborn child is not aware of the self and the not-self, there is justbeing. Everything is a part of the experience, which is being. Soon the infanthas learned many new things and compares each new thing to those things thathave been previously learned. Each new thing is compared to all other things ina process of pattern recognition. Each new thing learned is similar to thingslearned in some way or ways, and different from things learned in some otherway or ways. This every increasing ability to make distinctions gives the child anawareness of the self and the not-self. The grouping of things as ‘similar to self’and ‘not similar to self’ is analogous to grouping them as similar to each otherand different from each other, or parallel and perpendicular. Contradictory perspectives are processed diagonally as both and neither bothand neither. Objective and subjective awareness creates a potential slope ofopposing tensions and flows. Time and space flow through each other with regularity of repetition.There are two beats to keep, a time axis beat, and a space axis beat. Thediagonal flow of reality goes through both axes. A change in slope changes theratio of the two beats on the line’s perpendicular passage across the X and Yaxes.The objective feedback of the world is the physical universe, including the body.This is a description of the outside of the self. Subjective feedback of the worldis the non-physical universe, the spirit. This is a description of the inside of the



self. The first division of the unity is into two: the physical and the non-physical,the objective and the subjective. The one way to see duality is to see that duality may be seen in either oftwo ways: either as a single thing seen from two different perspectives, or as asingle perspective of two different things. The observer and the observed arenot truly separate. The objective universe and the subjective universe are interwoven. Theforces of objectivity and subjectivity work together and apart to follow thedictates of persistence. Each contains the other, always. Escher’s work on self-similar contradictory imagery is unmatched. A diagonal can have a right hand twist from one perspective and a lefthand twist from another perspective



Local and globalThis chapter will examine scale and grouping, the whole relating to the part, andthe unchanging rules of existence.

Perspective A local view is to and from a particular point that views back locally. Aglobal view is to and from all points, which also look back globally. When veryclose to the surface of an object, it appears flat. The local view of a wavefront,(even a circular one), is one of no curvature. Local flat observations can bemade at any scale with an appropriate observer or probe that can get closeenough in size or wavelength (frequency) to observe (interact) locally inharmonic resonance with the observed wave. The Earth is flat or round, depending on a local or global perspective.Space is flat or curved, depending on perspective. One can be too ‘close to a topic’ to be objective about it. A moreremoved global perspective objectifies and diminishes individual objects ofprojection and reflection, and their influences. Local objects strongly locallyreflect each other, and suffer reduced amounts of direct reflection as moredistance between them and a more global perspective is achieved. For a moreglobal focus, the individuals are all considered parts of a single group. The moreglobal the perspective, the more curvature and a contradiction of perspectives isresolved and embraced. With all local images minimized, a higher globalstructure emerges as a reinforced interference pattern in the same image as itsabstract origins. This higher global pattern and others like it will interferetogether on a higher local level and become part of some even greater pattern.

Wave expansion The depth and range of an entity’s resonant structures’ abilities to interactand be locally or globally co-observed may become unendingly subtle andcomplex, but their simplicity is finite. Most objects are complex compositeinterference pattern objects and are made out of somewhat less complexcomposite objects. Each interference pattern object is composed of lower interference patternobjects, themselves interfering to create the higher being. Layer upon layer oflower complexity becomes and supports higher complexity. After factoring out the interference patterns down through each level ofexistence, the remaining patterns are simple propagation objects with nointeractions or overlap of waveform to create a higher-level interference object. There are three simple propagation waveforms. They can be illustratedby two-dimensional or three-dimensional models. All three shapes depict anaspect of change and represent different traits of a wave and of being. Theirstructure is the shape of their different propagations.



In these propagations, the waves continuously actively maintain theirspecific shape. There is an actual force holding these waves in specific shapes.Waves that hold their shape as they propagate are called autocatalyticwaveforms. The first of these autocatalytic waveforms is that of the expanding sphereor circle, propagating directly out away from a central point in every direction.

This is seen in three dimensions as the shock wave of an explosion in theair or in two dimensions as a ripple on the surface of a pond. This wavefluctuation comes from a single pulse origin. Continuous pulses from a relativelystill point creates an unending set of concentric wave circles surrounding thatpoint. The wave pulse travels out and away from the origin in all directions atthe natural speed of a wave in that particular medium and environment. The second waveform is the propagating cone. The source of this wave isa point that continuously moves faster than the wave it creates.

This waveform itself propagates diagonally, perpendicular to its conicsurface. The shock wave cone seen in two dimensions is the V-wake of aspeedboat. In three dimensions, this cone is seen in the sonic boom of anaircraft traveling faster than sound. The third autocatalytic waveform in three dimensions is the torus or smoke ring.The torus is generated by a single pulse in a single direction.

The smoke ring travels slower than the natural speed of a wave in itsmedium. It is also seen in two dimensions as the twin vortices of an oarstrokeon the surface of the water. The difference between two dimensions and three in all these examples isone additional axis of rotation perpendicular to the direction of motion.While the sphere and the cone expand over time, the torus does not. Instead,the torus propagates only along one dimension. While the waveform of theexpanding sphere (expressing position) and cone (expressing momentum) willeventually pass across and transition all observers, the torus, exhibiting bothangular and linear momentum, expresses a direct exchange from one point toanother.



Cone, sphere and cylinder Each of these three autocatalytic waveforms may be seen as a dynamicwave in motion, or as a static object. When a plane is passed though eachwaveform as a static three-dimensional object, a lower-dimensional section isdescribed. Passage of a plane through a sphere creates only an expanding and thencontracting circle in any case.

Plane passage through the cone and torus are more complex. A plane will intersect a cone in an ellipse, as long as the plane crosses therotational centerline of the cone and does not become parallel to the edge of thecone.

Any cone, no matter how narrow or wide, can be sectioned congruent toany describable ellipse, no matter how elongated or round the ellipse may be.An ellipse is a closed curve within which there exists two points such that, fromall points on the ellipse, both internal points can see only the reflection of theother point.

If the plane is perpendicular to the centerline of the cone, the sectiondescribes a special case of the ellipse, the circle. In this case, the two points ofmutually observed reflection in an ellipse become one point.

If the sectioning plane does become parallel to the edge of the cone, thenthe curve described is the parabola. Of the two reflecting points, one is nowinfinitely far away from the closed side of the curve, and the open ends of thecurved line eventually approach straight and parallel to each other at infinity.

If the sectioning plane cuts the cone at an angle beyond the parallel ofthe cone’s edge, then the two open ends of the sectioning curve will be straight



but diverging at infinity. This is the hyperbola. Here the point of focus is notresolved even at infinity, but is only inferred abstractly as a virtual image on theother side of the reflector.

These three possible ways to section a cone correspond to the threeclasses of reflector. In the ellipse, the focus of a reflection is within the sameclosed loop as the object. In the parabola, the focus of the object is at infinity(in both directions). The hyperbola shows the local reflection of an object to befocused on the other side of the reflector. The three conic sections also define the three types of paths of motionthat may occur for two objects moving with respect each other in space, whereone relates gravitationally to the other either elliptically, parabolically, orelliptically. The waveform of the torus needs conceptual clarification. Space can beseen as curved or flat. If one were to look into a strong enough instantaneoustelescope, one would see the back of one’s head. A torus is the curved versionof the flat expression that is a cylinder. What is a cylinder in a flat space can bea torus in a curved space.

There are two axes that a flat surface can curve through, X and Y.Either axis alone leaves the surface flat if it is unchanged. For a surface to beclosed, both axes must be curved.

A surface closed along one axis and flat along the other axis is acylinder. The torus, curving along two axes at once, is a surface closed in twodifferent directions. In sectioning a cylinder with a plane, only an ellipse or a circle canbe described, depending on the angle of the sectioning plane.

The eccentricity of this ellipse is limited to the length of thecylinder, relative to its radius.



It is more than interesting that the cone, sphere, and cylinder havean integral volumetric relationship. The volume of a cone with a height on oneand a base diameter of one plus the volume of a sphere with a diameter of oneequals the volume of a cylinder with a height of one and a diameter of one. Ifthe cone has a volume of one, then the sphere has a volume of two, and thecylinder has a volume of three. 1+2=3

If all the common factors are reduced out of the equations for theirvolumes, the basic relationship between the height and radius of these solids isexposed. H=2R

Conic sections A fuller description of conic sections needs additional comment. For thesections of a cone that are the ellipse and the parabola, nothing more is needed,but the hyperbola includes another cone for a full description. In a sectioningplane that is angled beyond parallel to the edge of the cone, the plane willintersect a second cone that is inverted, relative to the first cone and extends up,tip down, from above the first cone. The two cones meet at their points.



A hyperbolic section will cut through both cones, but the curvedintersection of the conic and a plane (nearest the apex) may be closer to themutual apex in one cone than in the other cone.

Both sections are more curved when closer to the apex, and more nearlystraight when away from the apex. As the curved closer part of the sectionreaches the apex, the section curve can only appear to be two diverging straightlines going directly away from the apex point.

When the intersecting plane actually crosses the apex of the cones, thethree varieties of curve define either an elliptical (or circular) point, a parabolicpair of straight lines running down the edge of one cone infinitely close togetherand up the other cone similarly, or a hyperbolic pair of lines diverging from theapex of each cone in opposite directions and at similar angles. When the section of a cone is visibly away from the apex, the view is alocal one of the curvature of the section. When the sectioning plane is infinitelyclose to the apex of the cone, the view is then one of a more distant globalperspective. The sectioning plane being close to the apex is the same as anobserver being far from the apex. Local and global differentiates between twostraight lines moving away from a point and two curved lines that tangent thepoint. One thing can be seen as two different things, and two different thingscan be seen as the same thing.

Ant Colony Existence as a single thing on one scale does not preclude existence aspart of a greater whole on a more global scale. An ant is an animal by all counts, doing ant-like activities. A more globalview sees the ant as just a part of a larger entity, the ant colony. On this largerscale, the ant is just a part of a greater living entity that exists independently ofthe existence of any particular ant member. The goals of the ant colony aresimilar yet different from the goals of any individual ant. Gaia, a name for the living mother Earth, is seen this way. We currentliving species are only a temporary part of the greater global creature.



Slime mold A slime mold is a single celled creature, much like an ameba. The slimemold culture shows a complete transition in its member cells from individuality toall cells becoming assimilated parts of a single greater whole. A culture of slime mold cells will grow and divide in a normal single celledmanner at first. Then a transformation begins. At some point, the entire cultureof cells will begin a pulsation. This pulse starts in the center and pulses outwardto the edge of the culture, moving the cells themselves toward the outer edgeand into a ring. This pulsing continues, and then starts to pulse around in acircle through the ring of slime mold cells, around and around over and over. Asthe pulse circles the ring of cells, a beginning edge and a trailing edge of thepulse become defined. Now the circling pulse has a beginning and an end. Thecircling pulse then slows and stops. The culture of mono-cellular individuals hasnow self-organized to the point that they behave as a single multi-celledcreature. The beginning and the end of the ring of cells are the head and tail ofa new higher creature. It just uncurls itself from a circular position and movesoff in an inchworm style, looking for its greener pastures. Finding a goodlocation, the slime mold changes again, this time stretching way up as a lifelessstalk with a spore sac at its top, ready to propagate again.



A model of the universe

Gravity An excellent model of gravity is that of a spherical weight rolling on a flatstretched rubber sheet. The model is a three-dimensional model of agravitational process that actually happens in four dimensions. The weight of thesphere distorts the rubber surface, curving (creating areas of acceleration upon)the two dimensional elastic surface. Smaller objects rolling along and creatingtheir own little distortions are curved in their paths of distortion by the largerobjects distortion. These paths can be seen as straight lines in curved space, orcurved lines in flat space. This elastic surface model can be extended from a flat local part of spaceto a global curved whole wavepulse surface. Stretched elastic sheets and autocatalytic waveforms both hold theirshapes forcefully, just as space maintains its shape. Existence is persistingpatterns in patterns in wave pulses. The surface of the smoke ring, which is anactual universe, is neither the smoky inside, nor the non-smoky outside, but isinstead the surface that divides the inside from the outside. A smoke ring is asmall simple wavepulse. The universe is a big complex wavepulse. The smokering is a small simple universe. The dynamic smoke ring torus, although of lowerdimensions, is a real universe nonetheless. As the torus propagates in a straight line, any given area of the dynamicsurface is moving in a circular fashion. The torus as a whole is moving in astraight line, but every individual point on the surface is moving in a circle.Einstein showed that gravity is indistinguishable from acceleration. Acceleration(which is gravity) may be linear or angular. In the torus, angular (circular)acceleration expresses gravity in the positive feedback and locally cumulativemass distortions of the dynamic surface of propagation.One view of the force of gravity is of masses moving in straight line throughcurved space. Another way of seeing the force of gravity is as an attractiveexchange of graviton particles in flat space. The view that incorporates boththese perspectives is that of an interference pattern between sub-light speedobjects moving on an elastically distorted surface with the interference pattern’sinteractive nodes of mutually reflective diagonal exchange expanding at thespeed of light. The converging lines of space in one gravitational object interferewith the converging lines of space in another gravitational object.@

Black holes The two dimensional universe of the torus is finite and unbounded.Though the actual elastic surface area has a quantitative limit, a linear motion



upon that curved surface will not ever be hampered. Any rational slope can bemapped out on a torus. Our own expanding universe is also finite andunbounded. The wave propagation forms of the cone and sphere each havetheir own versions of finiteness, boundedness and curvature.@ The surface tension of the torus, cone, and sphere are unified in theirpropagation, even though each kind of shape is experiencing its own kind ofaccelerations. The relationship between the opposing tensions holds the surfacezero energy surface in its particular shape. Eventually, some portion of the torus’s surface becomes slightly pushedoutward by accruing wave fluctuation distortions of the field. All objects (waves)create gravity and are drawn together. As the local spot on the propagatingtorus gathers more mass/energy and bulges out, that spot tends to gather evenmore mass/energy in a process of positive feedback. More mass attracts evenmore mass. The accruing mass and gravity at that spot in the torus eventuallyovercomes the tension force of the surface to hold the torus together, and thefield collapses. When this happens, the smoke ring bulge stops spinning aroundthe original torus and shoots out in a straight line a new smaller smoke ring,straight along in front of the generating torus smoke ring, still connected to thefirst by a fine line of smoke surface. This string is the connection between oneuniverse and another. This second smoke ring is a black hole to the first smokering, and is a new universe. In the new universe, the directions of X and Y havereversed. The smoke ring demonstration can easily be performed. It is best tomake big slow smoke rings in a room with very still air. The torus’s black hole isnot created until most of the energy of the original smoke ring is lost and thesmoke ring is moving quite slowly, barely moving. The torus is the basic shape of exchange. The dynamic torus is found inevery energy exchange. The torus is found in the photon exchange, with itsperpendicular oscillating electric and magnetic fields. The torus is found intornadoes and hurricanes, in neuron impulses, everything. Matter is the processof the torus in along three mutually perpendicular axes. While the sphere ofpotentiality expands outward as a probability wave going in all directions, thetorus is the collapse into the actuality of a single direction. The cone depictswhere along the diagonal a measure could be taken, and when.

HUH?

This light cone, and its hyperbolic reflection, expand at their opposing bases asslope and time increase. This process goes from a line to a plane. @ In this ordinary universe, there is freedom of motion for masses andenergies in space. Motion (momentum) is through three axes of space. Flowthrough time, however is restricted to a single linear dimension with threelocations (position) ; past, present, and future. There is freedom in motion



through space, and no freedom in motion through time, objectively. Space is onthe outside, and each entity moves through space. Time is on the inside, andtime moves through each entity. In a black hole, matters are reversed. Inside a black hole, time andspace mathematically switch places. Instead of an entity being locked in a linearmotion through time, in a black hole, travel through time is possible. Past,present, and future are all available axes of motion. Motion through space,however, is restricted to a linear one dimension as the point of the singularitymoves through the three axes of ordinary space. All times are available to be atalong that line of travel. All points on a line are potential nodes.

Quantum reality and relativity Quantum reality and relativity are opposing views, either local or global,of the same thing. When quantum reality describes a single unit exchange particle, like atorus, relativity describes both the curvature of the space-time that the toruspropagates through and the curvature of the surface that is the torus itself. When relativity describes the curvature of space, quantum realitydescribes both the nature of objects propagating through space-time and theunity of space-time as a single propagating entity.

Schrodinger’s cat On all levels and to all degrees, all things interact with all others. Eachentity exists by its own ability to perform the actions needed for it to continue toexist. During this activity of experiencing our common reality, each entity is atthe cause of some events and at the effect of other events. In this interactiveprocess each entity is an observer and is observed. Entities include such thingsas people, cats, bacteria and air molecules. Nothing is realized (made real) until it is observed. That is where thechange in reality occurs, in the observer. As people, the continued life or deathof Schrodinger’s cat is not real to us until we observe it. Until then, there arejust probabilities of outcomes. In quantum mechanics, an event does nothappen until it is observed. Without observation, there is no existence. It is the case, however, that we, as people, are not the only level ofexisting things capable of observation and interaction. The cat in the boxobserves the world and can thus be affected by the potentially activated poisonin the box with the cat. The bacteria in the box with the cat also observe theworld. If, in their world, the bacteria observe the cat to no longer fight off theirinvasion, bacterial growth and cat decay are inevitable. Although the cat is somepercentage alive and some percentage dead to us, to the bacteria, (and the cat),the matter is settled. Air molecules will observe and interact with a rotting cat/ growingbacteria amalgam, dispersing concentrations of vapors. If we could only observe



directly with our eyes, we would never know if the cat still lives. With noinformation, there is no change within the observer. A human observer, usingonly the eyes, might never actually see the cat as living or dead in a light proofbox, but the smell would eventually be a dead giveaway. We observe with allour being, and so do all things. In this way the world progresses even when we are not observing it.We can gain information with all observations. The world is always observingitself on all levels. Our observations include observing the other entities thatobserve each other and each of us in their interactions of the world. The feedback process of the projections and reflections of awareness istoward ‘making a difference’ and resolving conflict to harmonic resolution. Theseare the basic crossed-purpose processes of objectivity and subjectivity. These two processes are parts of one thing in every action of existence.Together they create a higher level to have distinctions made of, or be seen in aparticular way. A new perspective of truth and beauty, that ultimately is twodifferent views of the same thing.

Objective and subjective models can both be displayed by proportional arrays toillustrate the similarity of traits found in all facets of reality.The forces extant in this universe can also be aligned in an array correspondingto the four components of the physical universe. This alignment starts with areexamination of the nature of the forces of existence.At higher temperatures and earlier times, before the spontaneous symmetrybreaking occurred, the forces were unified. In the cooler broken symmetry ofnow, forces are more distinct. The forces to reexamine include the strongnuclear force, the color force, the weak force, gravity, quintescence, andelectromagnetism. All these forces can be grouped in a manner that allows themto exactly parallel the physical components of the universe. The weak force is taken out of the group altogether; it is the only force that isnot conserved. The weak force comes into existence and goes out of existence.The function of the weak force is to bring higher groupings of entities intoexistence and take them out of existence. The strong force and the color force are the same single force, either inside oroutside the proton or neutron.Gravity and quintessence are different aspects of the same phenomenon, eitherlocal or global. While the global torus exerts energy to keep a field flat, anindirect effect is a local accumulation of energy to flow across the field.And there is electromagnetism. As temperatures cool, unified forces separate.Electromagnetism can be separated into the electric force and the magneticforces.The forces that parallel mass, energy, space, and time, are; gravity, the strongforce, electricity and magnetism.



I and not-IThis chapter deals with different views of the same thing.

Experience We each experience the world alone in our own personal universe of theinternal ‘I’ and the external ‘not-I’. All of one’s personal experience of self, andone’s personal experience of the not-self are together one duality perspective ofall things. This experience is part of the universe of experience of all things.Each entity experiences one part of the totality of all experience. Self and not-self both occur in, by, with, and for that higher level of mutual reality we allshare, the common reality of both and neither . All things exist in terms of the self, the not self, and both and neitherboth and neither. These paths of existence are static perspectives on a dynamicmerging of the three into one interaction terminal. This can be seen with thesubjective right brain as the same as me, the objective left brain as the same asnot me, and the integration of the two different views by the corpus callosuminto both perspectives of the same thing. Awareness processes similarities anddifferences. Being is an active process that integrates opposing internal and external flows ofimagery, each feeding back to the other. Doing is the action of controllingmotion and stillness. Having growth is completing the cycle or moving on to thenext node in an expanding pattern.

Perspective To see things as different and similar at the same time is to see howcontradictories can actually be in agreement; a significant step towards anenlightened perspective. The hypotenuse is a representation of both X and Y. In one way, thehypotenuse is the same length as the X value, and in another way, thehypotenuse is the same length as the Y value.@It is obvious that locally, the hypotenuse is neither parallel nor the same lengthas either the X axis or the Y axis. The place from which to view the length of the X axis (and one view ofthe hypotenuse) is from some great distance along the Y axis. By extending thedistance along the Y axis that the X value and the hypotenuse are viewed from,the X value and hypotenuse can reasonably be seen to be the same length andparallel to each other. From a point an infinite distance along the Y axis, there is no angulardifference between the hypotenuse and the X dimensional value, so they seemto be the same length.



Also, at this infinite distance, the greater distance to the far end of thehypotenuse does not seem farther than the closer end of the hypotenuse or anypoint along the X axis. It is the same distance to the points along the X axis as itis to the points along the hypotenuse. From infinitely far away, the hypotenuse and the X axis appear to be thesame length as each other and parallel to each other. The same process holdsfor viewing the Y axis from a distance along the X axis. An infinite depth of fieldis created. From two opposing infinite perspectives, the hypotenuse, at allslopes, is parallel to and the same length as both X and Y.

Many answers There can actually be many different right answers to the same question.If a juggler does one trick in one hand, and simultaneously does another trick Inthe other hand, the juggler can be said to be doing one, two, or three tricks.One trick is two things at once, two tricks is one in each hand, and three tricks istwo tricks and both of them at once. Perceptions are not right or wrong, theyare similar or different.

Self modification Our continuing drive to exist includes modifying ourselves to continue toexist. We perform the changes that alter things so that we may persist, and weperform the changes that keep things the same so that we may persist. Doingone is the same as doing the other, and not. As new and different changes to seek persistence are attempted,differing results will reinforce the changes or not. New changes do things thathave not been done before. Reinforced new changes are kept and becomeentrenched. Entrenched changes do the same things repeatedly to support anever more enhanced persistence. An enhanced stable base of change supportsyet a higher subtler level of even newer changes to be tested. Changing change is the same as unchanging change. Motion andstillness are relative to each other.

Both and neither All that exists is the universe of all things. All of experience is of theunity indirectly. This experience is of the self, the not-self, and both and neither.On the abstract plane of unity, concepts of ‘me’ and ‘not-me’ vanish. We are stillall part of the same thing. Parts of ‘me’ are not me. (I am not my body.) Partsof “not-me” are me. (My family is a part of me.)

Self reflection The slope of the hypotenuse passes at a diagonal through the X,Y grid.Where this line can be seen as a rational fraction that passes through a specific



number of units of distance X for each specific number units of distance Y, thenthe slope can also be seen to be reflected within a single rectangular unit of XYeventually back to the origin. Reflecting around within a geodesic is similar toprojecting across a similar flat grid.@In our three dimensional view of the world, locally observed object’s surfacesoften reflect waves directly back to an observer object, but as distance grows, sodo the misses to direct reflection. A truly global perspective has a real butextremely remote chance of a mutual reflective gaze. @Direct self-reflection with the point of higher dimensional unity is not a linearpossibility. We focus our attention on one thing at a time. To reflect on thehigher reality, we would have to see ourselves reflected in all things at once.

Indirect self-reflection is the nature of experiential existence. It is theperpendicular tangent to a slope that indirectly represents the direct reflection tothe point of unity. Indirect self-reflection can be an explicit perpendicular to aslope line between two separated points, or implicit, from the self, reflected backto the self. One is the same as the other. As simple ratios of indirect self-reflection are established, subtler ratios of slope become the new levels ofreality. These higher harmonics of self-reflection are the subtler levels of being. Through opposing structural tension (along the grid of nodes) andharmonic resonance, each level of an expanding wave entity participates inmutual process of cause and effect with all other entities. Reflective and projective exchanges are the interactions of reality.These interactions, all real, can be objective or subjective. Two people whoreflect each other’s gaze well can connect in a very real but subjective way. Each entity is a wave and a surface of projections and reflections,absorptions and emissions, pushes and pulls. Some exchanges can be created,blocked, focused or intensified by specific materials and configurations. Thiswould include the forces of electricity and magnetism. Other exchanges (like gravity) are transparent to any interruption andact directly, each entity to every other entity. The gravitational exchanges ofeach particle are its interference interactions with every other particle. The fieldsof each particle are reach virtually infinitely far reaching into space and arevirtually infinitely weak at those near infinite distances, but real. In three dimensions, the forces of exchanged for electricity, magnetism,and gravity all decrease or increase as the inverse of the square of the distancebetween each set of reflecting objects. This relationship can also be seen in theview of the self in a flat reflector. The size of a reflected image grows as theinverse of the square of the distance between the object and its reflection. Eachgravitationally reflecting object forms a flat reflecting surface directly to everyother gravitationally reflective object. Every object sees itself in every otherobject. A three dimensional flat reflector is created by three flat mutuallyperpendicular planes.@



Attraction and resistance follow cube / square laws and limits the scalability ofspecific structures, which is why there are no twenty foot tall people or neutronstars over a given mass. Three dimensional space is not delineated by the three axes of space,X,Y, and Z. Space is divided by the planes that are perpendicular to those threeaxes. Space is occupied by three pairs of planes limiting space in threedimensions. This shape is the cube. The opposing diagonals of these parallelsets of three perpendiculars are a pair of tetrahedrons. @ A three dimensional point of reflection (where three mutuallyperpendicular planes intersect) directly reflect all objects in three dimensions,back to each object of reflection. This point of reflection in space integratesthree two-dimensional reflectors into one three-dimensional reflector. Thereflected image in the three dimensional reflector is seen as if having beenpassed through a single point at the intersection of the three planes andprojected onto a plane equidistant beyond the reflector. The difference betweena three-dimensional direct reflector’s image and a one-dimensional flat directreflector’s image is that the three dimensional reflection is rotated 180 degreesaround the axis of direct reflection. This is the same relationship between objectand image as is found in a pinhole camera.Whether an object sees its own reflection inverted or not depends upon the kindof reflector. Different reflectors (objects) give different kinds of reflections atdifferent ranges and perspectives of symmetry. Reflective surfaces are groupedby curvature, topology, and by the number of dimensions involved.@ A wave pulse can be an expanding sphere that is hollow in the inside.Whether the hollow is virtually all or none of the sphere’s volume, the wave, (ormass), of the sphere interacts gravitationally with other spherical objects / wavesas if all the individual mass points of each spherical object were located at apoint of omnidirectionally direct reflection at the center of that sphere. Thecumulative effect of the forces of the individual members in a group sphere isgravitationally equivalent to the same amount of mass all at a single point in thecenter of the objects. As a massive wave sphere expands toward an observer,the gravitational attraction to that observer remains constant and unchanged.The reflected image of the observer, however, seen on such an expandingsphere would increase from virtually nothing at a point sized sphere to completeflat local reflection where the sphere touches the object.@ Once an expanding sphere has surrounded another sphere, thegravitational force between the two bodies falls to zero. Any increase in theforce of gravity, caused by a greater closeness to one part of the larger sphere’smass, is offset by a greater amount of mass therefor remaining on the other sideof the internal object. The magnified image of the self is reflected back insidethe sphere. Direct reflection happens one of two ways. Either the internalobject is offset from the center, or it is centered. If it is centered, there is a



direct reflection in every direction. If the object is offset, there will be twoimages, opposing in direction and orientation along the axis of the center andthe object.@ Other forces in our universe do not follow the inverse square of thedistance laws. The strong nuclear force is much stronger than other forces atvery close distances and much weaker at greater distances. The strong forcefalls off at the 7th power, not the 2nd power like gravity, electricity andmagnetism. The strong force is virtually zero at just a few nuclear diameters ofdistance. This can also be explained in terms of self-reflection. This enormouschange in attraction over distance will not change with only three flatdimensions. Instead of using flat reflectors, however, curved reflectors can beused. Imagine the smooth curved surfaces of two spherical nucleons. As theyapproach each other, the two curved surfaces that face each other can get soclose together that, when and where they touch, the curvature of the surface isvirtually flat and the strong force is fully reflected back and forth.@ At this very close local distance, little image reduction occurs betweenreflections and the full strength of the reflective interaction is felt. As the twonucleons move apart, curvature becomes apparent. The size of the reflectedimage on the spherical reflectors falls off quickly as the objects get just a fewdiameters apart and a reflectively diminished global curved perspective isacquired. At large distances, only the most infinitesimal virtually image isreflected, and the strong force would be negligible. This fall off effect can beincreased to greater powers of magnitude by multiple reflection iterations backand forth between curved reflectors.The number of dimensions on the reflecting surface changes the rate ofreflective fall off. The reason sounds can carry so well on the surface of a bodyof water is that the sound energy falls off more slowly when it expands smoothlyacross two dimensions instead of out into three dimensions.@

Group process All objects are physically linked by the interactions of their mutuallyreflected images and interactive exchanges. Different combinations of reflectionsand projections give an array of cumulative attractions and repulsions. Globalopposing forces may effectively cancel each other out, leaving a locally neutralinteraction for particular force combinations. The process of being the ‘I’ and‘not I’ as interactors, group within group, level after level, layer upon layer, is theself supporting process of existence. @



Rules of being

Topology All causes and effects feed back in a continuing resonant reflection of theharmonic progressions of existence. As form follows function, structure followsprocess. A particular group of structures coincides with a particular group ofprocesses or actions Each action or entity could again be divided onto groups.Groupings of such abstractions of entities can be sorted topologically. Theactions of an entity place that entity into a group of things with some particulardynamic feature. All the members of that group are doing some common action.To be so grouped by that action is to be topologically placed into that group. Anentity ‘comes into existence’ and ‘goes out of existence’. Existence, the processof being, is a common process for all things grouped as existing.

Change in change New things are created or brought into existence by an entity makingchanges in other things that already are going through many changes to bewhat they already are before they are changed again. All entities continue tomake the changes that continue to contribute to their remaining in existence.Being is change. Change is inevitable in existence. Change is constant. There is changing change and there is unchanging change. Once a newunstable changing change has established itself into a pattern of change, itbecomes stable and changes to an unchanging change. An entity willcontinuously require new new changes that themselves will get old andestablished. This need for continuing newness itself changes from a new needto an old need being needed anew. So changing change in change becomesunchanging change in change. Even an entity that had been changing and thenstops changing, changes. Every level of changing change can be meta’ed to another level ofunchanging change. With the needs of change to go ever further, a continuingmeta’ing of meta change makes the whole cycle virtually endless. Change andno change simply exist together in harmonious contradiction; motion andstillness, yin and yang.

Similar and different Each thing changes like all other things change, and all things change,each in their own way. The whole is all those changes and not those changes.Change is existence, existence is change. The question is whether theperspective is one of similarities that are different or differences that are thesame, or both and neither.@



Action

Recap All that exists is waves in action, a wavefront of change where there isexchange. Change is in incriments of objective change along the wave andsubjective change across the wave. Each direction of change (quantitivly andqualitativly) indirctly influences the other. Smaller wavefronts may becomeunified into a larger more complex wavefront with properties contained and notcontained in the smaller waves alone; a coherent supposition, where a higherlevel of indirct influences may resonate and persist. Each wave, whetherstanding or moving, large or small, is still a wave and is abstractly the same asall other waves. The rules of existence are the same on all levels. As above, sobelow. In the two-dimensional division of existence, the two perpendicular axesof reality, (objective and subjective), together create a diagonal unifiedexpression that is neither yet both X and Y. The actions of existence allpropagate a continuing possibility for further action and thus are the same, yeteach wave front culminates in a separate and distinct event in space-time andthus each wave is different.

Nodes A one dimensional surface, (a wire), can hold the waves of any numberof dimensions. The wire has two unmoving endpoint nodes and a geodesic ofnode points between the ends. Node points on the wire do not move as astanding wave passes across the wire. Standing waves on the line have awavelength that is an integral division of the distance between the nodes. Thewave oscillating on the line may absorb and emit energy . Resonant energyexchanges may be transmitted as change in amplitude or frequency. A changein amplitude or frequency can each be exchanged for the other. As thefrequency of a segment’s waving increases, new nodes of stillness and motioncome into existence between the endpoint nodes. All nodes in a line segmentare evenly divided between the endpoints of the line. The ratio of distancesfrom a node to its two endpoints is always a rational fraction. Wavelength,frequency, and nodal spacings are in the realm of harmonic rationalities andresonant energy exchanges within an entity. While the node points do notmove, they do change angular orientation back and forth. Midway between anytwo node points is a part of the line that moves but does not change its angle.Between these extremes lies a continuum of exchange between the concepts ofdistance and angle. The numbers of geodesics in a polygon or a polyhedron represent thenumber of combinations between a given number of reflective endpoints. Oneendpoint holds no describable geodesic lines. Two endpoints hold one geodesic.Three endpoints will support three geodesics. Four endpoints will have six



geodesics, etc. The number of potential lines of interaction is the descriptive forthat geodesic. The geodesics in a polygon can be arrayed perpendicularly around apoint in a circle. In such a circle, the first and last endpoint overlap as all thesegments overlap. With three geodesic segments, the circular representation isa triangle. Because each geodesic segments overlaps the next, circular flow in onedirection goes continuously downhill in an Escheresque spiral. This direction isseen as objective entropy. The opposing direction is then seen as subjectivesyntropy.@ Many geodesics may share a common endpoint. Geodesics representpotential exchange pairs. The lines are paths of exchange between endpoints.More dimensions mean more potential symmetries and paths of exchange. Two-dimensionality limits higher order geodesics to representation ashigh order polygons. A third dimension allows four geodesic points to all interactdirectly in three dimensions without overlap as a four sided polyhedron, atetrahedron. A tetrahedron can be described as either; four co-mutually reflectiveendpoints, six geodesics, each connected to two endpoints directly andconnected to the other two other endpoints indirectly, or four planes withmutually non-parallel intersections. A tetrahedron is also one set of diagonals fora cube. The geodesic lines of a polyhedron can be seen as straight or curved.@

A constant As the surface of space-time carries projected and reflected waves tointerfere and interact, the surface processes the masses and energies of theuniverse through each other. New things are created, simultaneously changingand not changing the materials, like knitting yarn into a sweater or reorganizingatoms into a new molecule. The physical state of existence is a harmonicextension of all realized probabilities to date. This resonance state is a dynamicobject. The present moment is the culmination to date of a complex harmonicchord progression with a correspondingly complex system of nodes andgeodesics. The actualization of exchange, (the actual change in being), isbetween and among motionless changing node points that the waves generate.Nodes come into existence and go out of existence as the energies of persistencepropagate. Interference patterns are geodesically related to their subpatterns.

There are nodes of stable intervals set at established positions along theline. There are also nodes that transition across stable established nodes. Fromwhichever level is defined as still, theire is a higher level that moves upon itsprogenitors. The motion of an object is relative to the other objects on that same



level. The goal of creating, exchanging and absorbing harmonic tensions is tocreate a beautiful and logical progression of events. All points in space arepotential node points. Constant motion of the time axis changes the angle of theconstant length hypotenuse of self-contradictory extensions which existsbetween node points,

An entity is described in terms of stillness and motion, change and no change,similarity and difference, parallel and perpendicular. These are the things thatchange in an entity and that are themselves subject to change. Change occursin intervals from one node to another. Intervals and cycles overlap and interact.

These intervals are described differently from different perspectives andlevels of interaction. Scale is meaningless in the abstract perspective, allinteractions are abstractly the same. The interval of comparative change has nosingle quantitative description or measure. This quantity I call ECHEGOYEN’SCONSTANT, the interval from one point to another, and not.



Cycles of being

Recap

Being is existing is surviving is continuing to continue. An entitycontinues to exist by the continued existence of its parts and the continuedstanding wave resonant exchange feedback among those parts. Each part itselfpersists by its own parts also persisting. External feedback and internal feedbackboth are needed for persistence. Feedback is against a reflected changeableresonance state between interacting outputs and inputs.

Expansion

The spherical bomb blast explosion creates an actual universe. Thewave front expands uniformly until the entropy drag of molecular observations(exchanges) reduces and consumes the existence and observability of the wave.Other smaller waves may exist and expand across the larger wave surface. Inan expanding wave universe, only an expanding wave entity will persist.Expansion is motion into more space. Different wave groups, each in their ownhierarchy of interaction, interfere constructively or destructively in the process ofcooperation and competition. Each wave group feeds back reflections andprojections to other wave groups seeking resonant support. This cosmic naturalselection determines the persistence of groups that will persist and expand.

Having

Even among expanding survivors there is gain and loss. To gain is tohave greater expansion and have more space. The process of being is to havemore expansion. More having means more being.

Actions of existence

The specific divisions of a two-dimensional field can be viewed in manyways; Left and right, X and Y, yin and yang, information and energy, positionand momentum, distance and angle, etc. One tremendously powerful division ofduality is into the objective and the subjective. This parallels the external andthe internal, the physical and the non-physical. Objectivity and subjectivitytogether describe a definitive two-dimensional division of the whole of reality.

Each axis, both objective and subjective, is a partial contributing factorto the diagonal flow of the meta-wave that is both and neither. Eachcontributing axis is one of the actions of that particular division (and axis) of thewhole. Even though the two are part of the same thing, they are different fromeach other.



When the diagonal of change is broken down into explicit X,Y values,the actions along each dimension bear the characteristics of that dimension.There are objective actions and subjective actions that correspond to theobjective dimensions and subjective dimensions both in the diagonal. All two-divisional examinations of reality can be aligned to all other two-divisionalexaminations. A dualistic parallel will always exist between any pair of two-dimensional model concepts. There is always some meaningful way to alignthem. The symbolic array of such paralleled concepts is a table ofcorrespondence.

objective subjectivedeductive inductive masculine feminine

outside inside Left-brain right-brain

direct indirect explicit implicit

There are also tables of correspondence for three-dimensional divisionsof the whole, four-dimensional divisions, etc.

Each process of existence, both objective and subjective, can itself bedivided again into further objective and subjective components, just as allmembers of all numbers of divisions of the whole can be further subdivided. Anydivision is an entity. Any entity can be described by its two-dimensionalfeatures, its three-dimensional features, or any number of divisions into which itis broken down. Any specific feature in any subdivision of an entity is itself anentity that can again be sub-divided by any kind of division or feature. This is aproperty found in regular fractals, where each part looks like the whole at anyscale.

The division of the whole into three parts introduces the actions ofexistence. There are three objective actions and three subjective actions.

The three objective actions of existence are being, doing, and having.These actions are detailed in various religions, and can be seen in Englishgrammar. The part of speech describing action is the verb. There are threekinds of verbs that parallel the three kinds of objective actions. There are beingverbs; am, are, is, was, were, be, being, been. There are doing verbs; hit, run,throw, etc. There are having verbs; have, having, has, had.

The three subjective actions of existence are feeling, knowing, andcommunicating. These non-physical actions of the entity have analogousrepresentation in studies of the brain. The right brain is the feeling, lateral,emotional side. The left side of the brain is the knowing, linear rational side.Conflict resolution between the two sides of the brain is expressed through thecorpus callosum communicating a diagonal resolution between two opposingperspectives.



A triangle with mutually overlapping endpoints can have a continuingcircular downhill flow from one perspective and a continuing circular uphill flowfrom the other perspective. The objective actions of existence and thesubjective actions of existence flow, two sets of three things as one, in oppositedirections around the triangle of indirect higher action.@

The A.T.P. molecule, vital to the creation of work energy in living bodies istriangular and spins like a top continuously around the molecules central axis,doing the work of entropy and syntropy@

‘Having’ in an expanding universe is the expanding of a wave. What ison the inside of the expanding circle is what is ‘had’ by the wave as a whole.Two expanding waves are needed for overlap, interference, and interaction.Two expanding interfering waves cooperate as part of the same thing andcompete as things that are different from each other. They are both the sameand different. They push and they pull in dynamic tension.

Expansion means having. For one wave to have another wave, the onewave must surround the other wave. The actions of being, doing, and havingcan all be represented topologically by the various aspects of wave expansionand overlap.

Being is seen in the topological relationship afforded groups in formallogic; All A is B, Some A is B, Some A is not B, and No A is B. @

These logical grouping allow rational analysis to prove or dispute anassertion from facts and inferences.@

Doing is seen in the interference transitional exchange of one wavegoing from being inside another wave to being outside of that same wave.@

Having is seen as one wave simply being around another wave. Onewave ‘has’ the other.@

Being, doing, and having are all different perspectives of the sameprocess. These three actions are different yet the same. They are a naturalprocess of expansion and interactions with interferences.

The three objective actions of existence and the three subjective actionsof existence flow through each other in opposing directions, (linear and lateral)and interfere with each other, creating the here and now. The higher levelinterference pattern of the two contributor waves is similar in shape to thecontributors themselves, and so are all patterns, high and low. We are all made



in the same image, the abstract pattern of the creation, which builds upon itselfin ever greater iterations of interacting interference patterns.

These two abstract sets of three actions conform to the two concretesets of three axes for action In our universe. These are the three axes of space;X, Y, and Z, and the three axes of time; past, present, and future. Extensionand propagation through space and time are the physical manifestations of thethree dimensional process(es) of action and being.

Relations

In the parallels of all things being similar and different, tables ofcorrespondence align things that seem different so that the similarities may beseen. Concrete examples of everyday existence vary extensively, but abstractcomparisons always show common parallels. When such parallels arequantitative, the array is a proportion and equations are produced. When suchparallels are qualitative, relations are produced. Relations and equations both fitinto arrays of correspondence. Subjective arrays are just as valid as objectivearrays, but qualitative instead of quantitative.@



Unity

Recap

Our local perspective of global unity (or any higher level meta-system),will be tangential, indirect, and self-contradictory.

Godel proved that any finite consistent system is incomplete, and ittherefor follows that any finite complete system must be inconsistent, meaningself-contradictory.

Numerical relationships

The only thing that can be said about the unity is that nothing can besaid about it, but that is saying something about it. It is a self-contradictorysomething, but still something.

Observations of the unity are of the parts and only indirectly reflect uponthe whole. A description of the whole of anything is a description of the parts ofthat thing.

The simplest division for descriptive observations is a division of thewhole into two parts. This could be the objective and the subjective, the left andthe right brain, etc. This divided pair is linked by the relationship between them.The relationship between X and Y is itself a third division with distinct separatelinks to each of the other two parts. A fourth division would be the common linkbetween itself and the first three parts, etc. Unity has no links.

Many answers

Great philosophers have long debated whether the universe is correctlydescribed as one thing (great unity), or two things (great duality). Both answersare correct., Higher numbers of division are also applicable to the nature ofthings. Just because one answer is right doesn’t mean another answer is wrong,just different.



Duality

Heaven and Earth

The Judeo-Christian bible opens with an enlightened symbolic description ofduality;

In the Beginning, God created the Heavens and the Earth. The Earthwas without form, and void; and darkness was on the surface of thedeep. And the face of God moved upon the surface of the waters. Theheavens are the subjective reality (the kingdom of heaven is within you),and the Earth is the objective reality. The formless objective universe (theEarth) was void of interaction. The surface of interaction was only stillness.God’s face upon the waters’ surface allowed for self-reflection, and God’s motionupon the surface of the water created waves of interaction.

AlignmentDuality is easily the most commonly understood and agreed upon metaphysicaldistinction, and is quite well represented with meaningful examples. Dualisticpairs match their two parts easily to one specific side of division or the other.Some pairs obviously complement each other, but there may be confusion as towhich side each member belongs, be it the objective or subjective. Often,members of such pairs can be seen as properly belonging to one side or theother depending upon the particular perspective taken. What is more importantis that the alignments can be seen at all. As Einstein said, “The mostincomprehensible thing about the world is that it is so comprehensible”.

Both and neitherWave/particle duality is quite telling. When experiments are performed on anelectron, the test will detect either a particle or a wave, depending on what isbeing looked for. If a particle is being looked for, a particle is found. If a waveis being looked for, a wave is found. The electron, and every other entity, isboth and neither a wave and a particle. When observed, the entity is either oneor the other. When unobserved a particle is both and neither.

Branching of Objectivity and SubjectivityWhen an entity is divided into its subjective and objective components, each ofthe two parts may still be divided into further objective and subjective parts. Asexample, speech may be divided into objective words and subjective meaning ofthe words.



Trinitythe nature of three



QuaternityNature of four



PhiveNature of five


Documents

The Structure of Existence