PART IV: Circular Unity

TRIAXIAL RETROGRADE INTERFACE

SYNDEX AXIS = SYNTAX

Frame of Reference
Six as the First Perfect Number
Circular Unity
T.R.I. as a  Model of Sacred Space
Critique of Euclidean Geometry
Toward an Ideal Syntax

CIRCULAR UNITY 
&
THE TRIAXIAL RETROGRADE INTERFACE

"There is no such phenomenon in Universe as 'One,' the lone observer."
"There are no indivisible points."

                                                                         Fuller, Cosmography

FRAME OF REFERENCE

Any experience, event modelling, or orientation in spacetime requires a frame of reference to distinguish the event or scenario from irrelevant factors.  Traditionally, the rectilinear XYZ system of defining points in 3D space has been used since ancient Greece.  But what is a point?

Since the birth of quantum mechanics the meaning of the supposed three-dimensionality of space has come into question.  The best answer to what a point is in physical terms is the elementary atomic particle such as an electron.  But on closer examination, it has no discernable physical structure and exhibits wave-like properties.  Three coordinates are too few to describe the state of the electron.

However, Fuller reminds us that "nature is not using the strictly imaginal, awkward and unrealistic coordinate system adopted by and taught by present-day academic science."

Synergetic modelling is fundamentally different in its entire approach: "The synergetic hierarchy provides a description of all omnitriangulated polyhedral systems exclusively in terms of points and prime numbers."

Fuller's critique of Euclidean geometry comes from it deficiency in modelling holistic and energetic processes:  "The XYZ coordinates of parallels and perpendiculars have nothing to do with the way the Universe is operating.  Universe is operating in radiational-divergence and gravitational convergence.  Events in parallel never get resolved; convergent events become exquisitely resolved.  You cannot have a nucleus in a perpendicular or a parallel system.  You can have nuclei  only when you have symmetrical tetrahedral convergence."

He outlines the self-organization inherent in nature: "Nature's continuous self-regeneration is 100 per cent efficient, neither gaining nor losing any energy.  She grows outwardly by omnitriangulated structuring from nuclei."

As a frame of reference, the cube or hypercube is inherently unstable.  A vectorially-edged cube collapses without triangulation.  Six end-interconnected diagonals form the six edges of a tetrahedron.  The most efficiently stabilized cubical form is accomplished with the prime structural system of Universe, the tetrahedron.

Squares and cubes may have been fine for dividing up fields after floods or carving stone.   But they are not the best model for curvilinear reality.  Without diagonal stabilization, a nonstructurally triangulated cube is a topological self-deception.  XYZ as a frame of reference or orientation is obsolete.

Fuller clued us in that, "Synergetics is not a frame at all, but a pattern of most omnieconomical (ergo, spontaneous) interaccomodation of all observed  self-and-otherness interexperiencing, (ergo, geodesic--geodesic being the most economical interrelationship of  a plurality of events)."

He further states again that, "All structures are tetrahedrally based."

Six vectors provide minimum stability, therefore the synergetic model far exceeds the simple cube in defining a volumetric, energetic entity.  The cube is still part of the intertransformations.  It can contain or be contained by a sphere, and is part of the reciprocation of the vector equilibrium (cuboctahedron) with its geometric dual--the octahedron within a cube.

Therefore, it is infinitely superior as a frame of reference, even though it is no frame at all, but an energetic system.

CIRCULAR UNITY

The full definition/description of circular unity begins first with the definition of the word unity.  As defined by Fuller in Synergetics II:  "Unity is plural and at minimum sixfold."

Drawing from a variety of Fuller's sources, we find that, "A point is not a relationship...for every point in Universe, there are six uniquely and exclusively operating vectors...There are six vectors or none."

"Every event is six-vectored.  Six unique vectors constitute a tetrahedral event.  Each vector is reversible, having its negative alternate.  There are no straight lines, physical or metaphysical.  There are only geodesic, i.e. most economical, interrelationships (vectors)."

"It takes a minimum of six interweaving trajectories to isolate insideness from outsideness, ergo, to divide all Universe systematically into two parts--macrocosm and microcosm...Unity, as represented by the internuclear vector modules, is of necessity always of the value of two; that is, unity is inherently two, for it represents union of a minimum of two energy centers."

Imagine two ping pong balls kissing.  Imagine a line connecting their centers (vector).  Half of the vector forms the radius of one sphere, while the other half forms the radius of the other sphere.  Unity is dualistic in this sense, of uniting two singularities.

"There may be no absolute division of energetic Universe into isolated or noncommunicable parts.  There is no absolutely enclosed surface, and there is no absolute enclosed volume.  Universe means 'toward one-ness' and implies a minimum of twoness....Our modern concept of Universe is a comprehensive system of energy processes.  Universe is a non-simultaneous potential vector equilibrium...The vector equilibrium is the minimum operational model of happenings."

Vector Equilibrium is a sublime state which energetic processes constantly pass through, but never stop at.  It is where interference patterns can pass through one another in energetic changes, without interference.

Vector Equilibrium is the common denominator of tetrahedron, octahedron and cube.  It is the prime nucleated system.  It is omnidirectional equilibrium based on the closest packing of spheres of equal radius.  The nuclei of atoms are based on this close packing.  In this model, physical and metaphysical reality share the same ideal design.

"All experiences are omnidirectionally oriented.  Omnidirectional experiences resolve themselves scientifically into discrete angle and frequency patterns.  That is life!  Relations are local to pattern.  Patterns are comprehensive to relationships...In considering a total inventory of the relative abundance of different patterns, it becomes apparent that patterns are reciprocal."

"There are six positive and six negative degrees of fundamental transformation freedoms, which provide 12 alternative ways in which nature can behave most economically upon each and every energy-event occurrence.  You have six vectors or none for every energy event ... For every event-fixed locus in Universe, there are six uniquely and exclusively operative vectors. Every vector is reversible.  Every event is six-vectored.  There are six vectors or none."

In sections 537.10 and 537.14 of SYNERGETICS I, Fuller reiterates these basic truths:

"Each of the six positive and six negative energy lines impinging on every nonpolarized point ("focal event") in Universe has a unique and symmetrical continuation beyond that point.  The six positive and six negative vectors are symmetrically arrayed around the point.  Consequently, all points in Universe are inherently center of a local and unique isotropic vector matrix domain containing 12 vertexes as the corresponding centers of 12 closest- packed spheres around a nuclear sphere."

Hopefully, these reiterations of the geometry are helping the reader to visualize this system more clearly, and energetically.

"Experiments show that there are six positive and six negative degrees of fundamental transformation freedoms, which provide 12 alternate ways in which nature can behave most economically upon each and every energy-event occurrence.  Ergo, there is not just one  "other"; there are always at least 12 "others...We find that in the 12 degrees of freedom, the freedoms are all equal and they are all realizable with equal 'minimum effort'."

"The six vectors represent the fundamental six, and only six, degrees of freedom in Universe.  Each of these six, however, has a positive and a negative direction, and we can therefore speak of a total of 12 degrees of freedom."

In 2D, circular unity can be graphically demonstrated by a circle divided into six individual but interdependent sections.  The color wheel is a good graphic example of circular unity, and represents six discrete qualities of six individual but interdependent quantities represented by each section of the wheel.  A circle can be divided into six distinct quantities, each with  individual but interdependent qualities, i.e. unification of number and geometry.

In that six is the sum and/or product of the first three numbers, 1 + 2 + 3 or 1 x 2 x 3, it contains a harmonious whole number relationship with them, and is thus called the first "perfect number".  The first instance of the harmonic synchronization of number and geometry (quantity and quality) occurs in the number six.

However, this prescription for circular unity is two-dimensional.  The three pairs are each separated by the centerpoint which has no dimension.  In order to formulate a spatial abstraction of circular unity, we draw three lines that interconnect the six face centers of a cube and enclose that cube within a sphere.

Doubling this two dimensional circular unity produces the first true Holotome (A), which is predicated on number twelve.  This three dimensional holotome of six positive, and six negative symmetrical retrograde event identity axes is then also represented by the closepacking of twelve spheres about a thirteenth nucleus sphere.  This produces the dodecahedron, (the primitve non-pi spherical module).

Synergetics modelling of space has radically departed from the XYZ models of Cartesian description.   As we have pointed out, though it has been the standard in science, the cubic model does not model the architecture of creation nor the energetics within systems.  In COSMOGRAPHY,  Fuller restates his premise:

"There is no such thing as a primitive cube, because it is impossible to find any position in which the three edges convergent at each of eight corners will interstabilize themselves at an omni 90 degree position.  The way in which human society became academically hooked on the cube was by carving out rectilinearly dimensioned wall building blocks of marble while misassuming an inherent solidness to be demonstrated by the marble."

"Despite its universality and elegant economy, the tetrahedron has been all but ignored on planet Earth.  Academic science references all its physical mensuration to the XYZ-three-dimensional coordinate system and all of its energetic phenomena to the c-g-s system, which represents the amount of energy required to lift 1 cubic centimeter of water to a given temperature 1 centimeter in 1 second of time.  The cube is the chosen geometrical unit of volume measure, and the square is the geometrical unit of areal measure in all of today's world-around, state-of-th-art scientific activity, not to mention everyday use."

The Triaxial Retrograde Interface, however, contains the graphic capability to represent a virtual spacetime object.  Nature's rules for assembly are based around the principle of tensegrity, tensional integrity.  Every geometrical structure is a tensegrity. According to Ingber (SciAmer, Jan. 98, p. 48):

That nature applies common assembly rules is implied by the recurrence--at scales from molecular to macroscopic--of certain patterns, such as spirals, pentagons, and triangulated forms.  These patterns appear in structures ranging from highly regular crystals to relatively irregular proteins and in organisms as diverse as viruses, plankton, and humans.  After all, organic and inorganic matter are made of the same building blocks of carbon, hydrogen, oxygen, nitrogen, and phosphorus.  The only difference is how the atoms are arranged in three-dimensional space.

Geodesic structure is the guiding universal pattern, the building code of nature.  We invoke Dr. Fuller's entire body of work to clarify the preceding remarks.

Ingber is still arguing against the old paradigm for acceptance of his theories about geodesic forms in biological systems, even though they are readily visible.  He states:

"The geodesic structure found  within the cytoskeleton is a classic example of a pattern that is found everywhere in nature, at many different scales.  Spherical groups of carbon atoms called buckminsterfullerenes or buckyballs, along with viruses, enzymes, organelles, cells and even small organisms, all exhibit geodesic forms.  Strangely, few researchers seem to have asked why this is so.  My view is that this recurrent pattern is visual evidence of the existence of common rules for self-assembly.  In particular, all these entities stabilize themselves in three dimensions in a similar way: by arranging their parts to minimize energy and mass through continuous tension and local compression--that is, through tensegrity.

...More broadly, all matter is subject to the same spatial constraints, regardless of scale or position.  Thus, given these constraints,  tensegrity is the most economical and efficent way to build--at the molecular scale, at the macroscopic scale and at all scales in between.  It is possible that fully triangulated tensegrity structures may have been selected through evolution because of their structural efficency--their high mechanical strength using a minimum of materials.  ...geodesic forms, such as hexagons, pentagons and spirals, predominate in natural systems."

The basis of geodesics is circular unity.  Circular unity is conserved through the fundamental increments of the Holotomic Sequence.  Circular unity is conserved by the employment of prime numbers only.  No redundant multiplexing is required by numbers that contains factors of division, as is the case of the factorials.  Thus, the holotomes are the minimal numerical magnitudes to accomodate the maximum amount of consecutive factors of division.

When mapped out in a circular array, each of these mathematical entities produce a half-positive, half-negative, symmetrical retrograde mandalog.  This is the direct, visual, graphic syntax of a Holotome.  The Holotomes are non-arbitrary numerical moduals (dualistic unities).  They coherently describe the interrelationships between numbers, particularly the primes.  Ideal syntax has been hidden from view due to unconscious disregard of retrocity in at least one of the three primary axes of qualification.

"Ideal syntax" becomes possible through the concept of word contexts that derive from a rational correlation between quantitative notation and geometrical notation.  This graphic syntax is embodied in the Holotomes as rational arrangements of numbers, words, and geometry.  By them, we can access or convey information not available within our imperfect literary syntax.  As whole systems, the Holotomes contain a definite structure which may be described in words, geometrical structures, graphs, diagrams, etc.

The Triaxial Retrograde Interface is the basic imaginary foundation for the descriptive mechanism of human language.  All languages have this fundamental idea event in common, but this has yet to be fully explored through physiomathematical epistemography.  Even though words fail to fully explain the many scenarios that abound in nature, they do point to possibilities and potentials.  This is perhaps the archetypal basis of alphanumerics in  protolanguages and ancient, classical languages.

Models of Sacred Space

We have shown how six was considered the first perfect number.  The results of multiplying or adding the first three integers produces six.

In the scientifically systematic discipline of numeronomy, the step from the first perfect number of six (which also represents the second form of unity as sixfold plurality) to the second form of plural unity (twelvefold), represents a step from a plane to a 3D volume.

Even though the T.R.I. is presented on a flat 2D surface, it can rationally represent or model the equation of a cube or sphere with its three ambidirectional axes, representing the six directions of spatial orientation.

Archetypally six represents spatial orientation  in spacetime (four cardinal direction, plus a vertical dimension).   In ancient times, this comprehension of one's position in spatial reality was essential to survival and renewal by contact with the spiritual dimension.  Thus, many rituals and conceptual ideas arose around this recurrent theme.  Geometry was always fundamental in this process.

The oldest models of this so-called sacred space were cubic, (quadratic magic circles and abstract cubes).  The energetic component of geometry was not understood.  The crux of the Syndex perspective centers on an energetic version of the cubic model and its geometrical duals, the octahedron and vector equilibrium.  We might refer to this model as a cubic non-linearity.

Creation of such models revives the archetypal notion of primal creation, the emergence of something from "nothingness."  Jungian, Mircea Eliade spoke of such creation myths in his book The Sacred and the Profane, stating:

"The creation of the world becomes the archetype of every human gesture, whatever its plane of reference may be.  Every construction or fabrication has the cosmogony as paradigmatic model."

Even in our modern scientific thinking, this archetypal background is fundamental to our paradigmatic notions about reality.  We cannot escape it, even if we try, since it is intrinsic to our being.  Techniques of orientation, (aligning oneself to the directions), are designed for the construction of sacred space.  The model for the creation of sacred space always begins from a center and projects horizons in the four cardinal directions.  Psychologically, we always reside at the center of "our world."

The quadrated circle sets up the conditions necessary for us to enter into sacred time.  Then, traditionally, we may contact higher forces through the medium of the sacred pole or cosmic pillar, the vertical dimension.  Eliade points out the great importance of the notion of retrocity in this process.

"Sacred time appears under the paradoxical aspect of circular time, reversible and recoverable, a sort of mythical eternal present that is periodically reintegrated by means of rites."

When we enter this space, in a ritual or even in a thought-experiment, we experience the feeling of immortality, the sense of the presence of Truth, we feel "centered".  Sacred space is equivalent psychologically to the "beginning."

The principle characteristics of sacred space are:

1).  A break in the homogeneity of space;

2).  This break is symbolized by an opening where passage from one cosmic region to another is facilitated (i.e. between heaven and earth; earth and the underworld);

3).  Communication with heaven is expressed by variants of the Cosmic Pillar, which stands at the Center of the World.

In Ego and Archetype, Jungian, Edward Edinger has identified this Pillar as a useful symbol for what he terms the Ego-Self Axis.  It forms the link between ego-consciousness (or personality) and the Higher Self, or cosmic Truth.  This represents both the conscious and subconscious mind working together in harmony on the transpersonal level.  It is true perception of nature and reality in the timeless sense, or insight.

The old mythic models helped establish our relationship to the cosmos and our conscious relationship to totality.  It is fundamental to our way of thinking, and explains why metaphor is an important aspect of scientific discovery.  Our modern myths are couched in scientific language, mathematics, and geometry.  Science has become our most believable "religion."

We therefore suggest the T.R.I. as a modern, paradigmatic representation of this ancient means of apprehending Reality.  If, as Jung and Pauli have suggested, there is unity between psychological and physical realities, they share the same underpinnings.  This commonality  between psyche and matter (physics) can be expressed geometrically much better than through words alone.

An example from Physics is a six-vectored model for discovering Truth and manipulating alternative realities.  This is a scientific, practical application of the cosmic model.  For the first time, we can violate Heisenberg's Uncertainty Principle, regarding position and velocity of subatomic particles.  By condensing atoms from photons,  the quantum mechanics of the microcosm become visible in the macrocosmic.  An atomic trap is created using six lasers focusing on a single point.  According to Cornell and Wieman, SciAmer., March 1998, p. 40-45:

"The Bose-Einstein condensate [formed at the nexus point of the lasers] ...can be thought of as the matter counterpart of the laser--except that in the condensate it is atoms, rather than photons, that dance in perfect unison."

"Einstein showed that if a sample of atoms were cooled sufficiently, a large fraction of them would settle into the single lowest possible energy state in the container.  In mathematical terms, their individual wave equations--which describe such physical characteristics of an atom as its position and velocity--would in effect merge, and each atom would become indistinguishable from any other...the condensate offers a macroscopic window into the strange world of quantum mechanics, the theory of matter based on the observation that elementary particles, such as electrons, have wave properties."

"But in the Bose condensation, the wave nature of each atom is precisely in phase with that of every other.  Quantum-mechanical waves extend across the sample of condensate and can be observed with the naked eye.  The sub-microscopic thus becomes macroscopic."

Thus, quantum physics transcends its microcosmic bounds into the classical realm of mechanics.  There is a break in the homogeneity of space.

"Einstein's theory requires that the atoms in the condensate have energy that is as low as possible, whereas Heisenberg's uncertainty principle forbids them from being at the very bottom of the trap."  [We can't know their position and velocity simultaneously].

"Quantum mechanics resolves this conflict by postulating that the energy of an atom in any container, including our trap, can only be one of a set of discrete, allowable values--and the lowest of these values is not quite zero.  THIS LOWEST ALLOWED ENERGY IS CALLED THE ZERO-POINT ENERGY, because even atoms whose temperature is exactly zero have this minimum energy. [vector equilibrium] Atoms with this energy move around alowly near--but not quite at--the center of the trap.  The uncertainty principle and the other laws of quantum mechanics are normally seen only in the behavior of submicroscopic objects such as a single atoms or smaller.  The Bose-Einstein condensate therefore is a rare example of the uncertainty principle in action in the macroscopic world."

Toward an Ideal Syntax

The three ambidirectional axes of the Triaxial Retrograde Interface represent the six directions of spatial orientation: up and down; right and left; fore and aft.

On the plane, in the form of the color wheel, we may regard it as circular unity represented by the six qualities or values of red, orange, yellow, green, blue, and violet.  Note the three dipoles as harmony, complimentarity and concommitance.

In the volumetric or 3D mode, we can regard the 12-fold unity as spherical or cubic and refer to Fuller's model of Vector Equilibrium with its 12 universal "degrees of freedom," representing nature's most economical movements of energy.  The 12 closepacked spheres around a thirteenth nucleus form the facets of a dodecahedron with its 8 triangular windows and  6 square windows, which yields 14 windows in all.

At this point we have a symmetrical and harmonizing synchronicity of quantity, quality, and form which also includes structure.  These are the ingredients of a compound syntax.

The T.R.I. does not just deal with a special and isolated case of dynamic retrocity,
but with the three basic pairs of opposing qualities that form the basis of generalized description.  It is a graphic means of "holding the tension of the opposites," in a unified model.  Such as thinking/feeling; sensation/intuition; judging/perceiving.

The Syndex perspective is not only about the intrinsic nature of number, but also the specific way in which number relates to the descriptive mechanism of human languages.  The crux of the descriptive mechanism of language revolves around the Greek prefix QU as in WHO and HOW MUCH (identity and plurality) and of course, quantity and quality.  This preceded the English prefix WH (as in WHO, WHAT, WHEN, WHERE, WHICH, and WHY).

This yields a sixfold coordinate system of the descriptive mechanism:

1    WHO           Identity         person              A
2    WHAT         Identity         object               E
3    WHEN         Time             duration            I
4    WHERE       Space            extension          O
5    WHICH       Plurality        number            U
6    WHY           Causality       and/or HOW   Y

Note also that the six vowels are all accounted for and figure qualitatively in the six primary axes of description.  The fact that unity is plural and at minimum sixfold gives added credibility to the T.R.I., which is the fundamental paradigm upon which rests the symmetrical unity of the Holotomes.

The Sumerian alphabet contained exactly six vowels, three primary and three secondary, which suggests an interesting correspondence between ancient descriptive syntax and the T.R.I. in the color wheel.

In a nutshell, this is the epistemographic syntax found in the Holotomic Sequence through the multiplication of the twelvefold spherical unity of Holotome A.  We multiply the higher moduals of spherical unity by the prime numbers in their natural order of occurence.

The T.R.I. does not just deal with a special and isolated case of dynamic retrocity, but with the three basic pairs of opposing qualities that form the basis of generalized description.  Keep in mind that the term WHICH is the only direction of the six that refers to plurality.  The other five deal with ideas that could be seen as qualities.

WHO and WHAT are qualities that deal with identity (person, object), WHERE with space (extension), and WHEN, with time (duration).  WHY refers to the quality of questioning.  The first four qualities may refer to something that can be exclaimed, but the term WHY cannot be followed by anything but a question mark.

In the case of WHICHness, we mean the first instance of plurality or the number two.  The second degree of plurality does not occu until the T.R.I. has itself been doubled into the form of twelveness, which involves three dimensional space, (in the form of the dodecahedron).

In other words: WHY, HOW, and WHICH are the only ones of the six that can be followed by a question mark.  WHO, WHAT, WHEN, and WHERE, can be followed by an exclamation point and/or a question mark.  The only exceptions are in exclamations such as:  "That's why!" or "That's how!" or in any context where the WHY and HOW have been qualified.

In the case of the color wheel, we have the six qualities of visible light: Red, Orange, Yellow, Green, Blue, and Violet, which consist of three primary and three secondary colors, that is:  three discrete pairs, or, a quantity of qualities.

Since the color wheel is represented on a two dimensional plane, it is not a plurality in a volumetric sense.  We must fold (double the plane) in order to bring plurality into a three dimensional entity.  The twelve spheres of the dodecahedron surrounding a thirteenth nucleated sphere is then a 3D representation of the Zodiac.

The most effective way to understand the quality of six is as the nave of the first holotome with 12 as the node.  This also makes the node of Holotome B (24), and its nave would then be the node of Holotome A.

Each true Holotome can be represented as a circular unity, but may refer to a spatial or spherical unity.  We find that this specific sequence of numerical quantities are the series of minimal magnitudes which accomodate the maximum amount of consecutive factors of division.  When represented on a plane as a spiral, they are graphic depictions of symmetrical half positive, half negative retrograde octave cycles.

What may be deemed the foundation for an ideal syntax must produce a synchronetic interface between words, numbers, and geometrical forms.  This graphic form of syntax which is in total synch with numerical notation produces the only valid presentation of physiomathematical epistomography.  It even yields another quality of semantics, fulfilling the classical suggestion of a truly mathematical language.

All Holotomes are examples of circular unity in terms of four positive and four negative event octaves in a retrograde cycle.

The alphanumeric system of notation occupies such a closed loop cycle of 24 signs (Holotome B), 18 consonants and 6 vowels.  Working alphabets may employ more or less signs but an ideal syntax requires the perfect symmetry of a Holotome.

The Sumerian cuneiform alphabet consisted of 21 letters (six of which were vowels) plus maybe 6 dipthongs making 27 letters.  It was possibly formulated from information surviving the deluge, and we can speculate that its loss was involved in the confusion of the tongues (loss of ideal syntax).

Anthropologists regard language not just as vocabulary and syntax, but as a cultural phenomenon.  The anthropology of rhetoric includes the social use of metaphor.

According to Colin Renfrew's theory, (SciAmer; Oct.98, pp. 106-114), the ancestral languages of the Indo-European, Afro-Asiatic and Dravidian groups originated  quite close together in the Near East about 10,000 years ago.

"The people who built Stonehenge and the other great megalithic monuments of Europe were Indo-Europeans who spoke a form of Indo-European ancestral to the Celtic languages of today...In much of  northern Africa the dominant linguistic group is the Afro-Asiatic, which includes ancient Egyptian and the Berber languages as well as the Semitic group.  The Dravidian languages of India, and later proto-Dravidian tongue would have been displaced by the Indo-European languages that are now spoken in India."

It has been proposed that, "a number of Eurasian language families, including among others, the Indo-European, the Afro-Asiatic, and the Dravidian, are related in a "superfamily" they called the Nostratic.  The recognition of such superfamilies, which may represent a breakthrough in linguistics, is still regarded as controversial."

These studies have indicated that there is a close genetic relationship among the speakers of the Afro-Asiatic, Indo-European and Dravidian languages, among others.  In southern India, Dravidian influence still prevails, while northern India is Aryan (Indo-European) influenced.

Researchers link the coming of agriculture to the formation and distribution of present-day languages.  "Protolanguages and language groupings as far back as 10,000 B.C. may ultimately open the way to a better understanding of the whole phenomenon of human linguistic diversity."  Renfrew.

According to Berendt, "The old concept of relationships existing solely between languages of the so-called "Indo-European family" cannot be upheld any longer.  As the new science of paleolinguistics has shown, there is only one language family, the family of human languages--period.  Like so many other myths, the myth of the Tower of Babel is true: In the beginning, there was only one language!"

When linguists trace word sources back along etymological lines, they call the process "feedback," because it is a recursive movement.  Linguists have also shown that many primal roots have a so-called mirror root, which does not simply negate the meaning of the primal root but rather reflects it into new dimensions.   Consider the derivation of the western Amen from the eastern OM, when it moved from India to the Near East and into Europe:

"The change of sound from OM to Amen reveals two totally different kinds of existence.  Amen is a subdivided OM, partitioned into O and M, with each of these parts being further embellished.  This happened when OM migrated west, first to Israel and then into the Christian world of Europe.  Along this route it was subdivided into its component parts--just as everything that comes to the West is divided and taken apart, analyzed and dissected.  It all seems like the opening move of a truly royal game of chess, like an overture for everything that was yet to come, when one realizes that this process of taking apart and subdividing was heralded thousands of years ago--back when OM became Amen...Indeed, the change from OM to Amen in this way becomes a formula for what separates the East from the West."

Alphabet is a finite closed loop of holotomic character (numeracy preceded literacy).

Ideal syntax depends on the logic contained in the structure of the holotomic sequence.    The possible restoration of prediluvial science proceeds from an understanding of number behavior in terms of geometrical form.

Graphic synchronicity of quantity and quality occurs in the context of the T.R.I.  It dovetails with the Pythagorean 3:4:5 triangle as the fundamental protothing which projects its image in an omnidirectional retrograde octave unity of harmoniously polyaxial integrity.  It synchronizes geometry, number, and the two ambidirectional operations of arithmatic.  As Fuller noted, addition is reverse subtraction and you cannot multiply anything without dividing something.

CONCLUSIONS

Numeronomy, or the laws governing the behavior of the continuum of quantitative notation is the natural result of numerology, the study of number, with or without the "woo-woo" number mysticism which degrades its historical reputation.

Numeronomy is the outcome of the right quality and quantity of successful cogitation and proper insight.  The numbers speak for themselves through structure and behavior.  Each flash that went into the discovery of this grand nexus of synchronetic complexes was beatific joy.

The six key discoveries of the Syndex Theory have always been available to everyone.  However, in my own life journey, they emerged through my self-reflexive dialogue with nature and the nature of reality.  On the chance I have been understood by the reader, I hope I have been able to impart some choice tidbits.

It was my truly mystical luck to meet and talk with some of the most signficantly accomplished beings in the modern world.  I had to go after these giants, but I wanted to get right to the source, rather than simply reading books.  Kinesic sign language delivers the gist of a subject which might otherwise require tomes.  Once Bucky Fuller indicated the two four-vertexed-each tetrahedra with three fingers of each hand.  That graphic gesture imparted a profound insight, a preverbal communique.

When we talk about number, we are also talking about talking.  Number/geometry is the fundamental cornerstone of human communication and specifically the alphanumeric principle of descriptive notation.  The T.R.I. reduces thousands of words down to a principle that contains the fundamental elements of the descriptive mechanism of language in general.  It simplifies the numerical/geometrical essence of language, which is primarily a way of describing the empirical scenarios of something we call nature.

Ultimately nature and universe may be unknowable.  But arguably, truth is born of arithmatic because two plus two is definitely four.  In itself number, the source of truth, means nothing.  But how we apply it to theory is science which distinguishes us from most other creatures.  But not enough to count much in the vast panorama of evolution!

The T.R.I. represents the geonumerical basis of the sequence of minimal pluralities that accomodate the maximum amount of divising factors.  This special series is terminologically designated as the Holotomic Sequence (holo- as in holistic; tome as in book or information containment module).

The holographic aspect of this sequence is that each member or tome contains all of the geometrical qualities and numerical quantities of the previous holotome, plus the added degree of data content over the previous module.

A major feature of these data modules is a retrograde symmetry in the form of a half positive and half negative octave system predicated on the octave nature of the so-called base ten system of number.

The full signficance of this most simple observation has escaped the understanding of all previous number theorists.  The base ten system of number is an octave system, where either one or nine can be seen as a null value event.

Furthermore, this octave can be regarded as a cyclic function.  The zero, one, or nine can function as the null event which acts as the null value gap between the beginning and ending of the octave retrograde cyclation, due to its half positive and half negative symmetrical cycle (which may negate the numerical value of one or nine just as if they were of the same nature as the zero).

A good example of the symmetrical retrograde octave cycle can be seen in the multiples of nine, where the nave of the retrograde reversal occurs between 45 and 54, or precisely at 49.5:
 

9      18     27     36     45     54     63      72     81     90
                                      49.5

        half forward                            half reverse

                                  full octave
 

Due to the octave nature of the eight true numbers, no transpalindromic sequence can exceed an octave cycle.

As simple as this is, the greatest math experts in modern times have totally overlooked this crucial element to the proper comprehension of number behavior.  The very phrase "Number One" is self-contradictory.  No wonder the ancients designated zero or one as Aleph--THE FOOL....

This overview led Marshall to the epochal rediscovery of the 99 CYCLOFLEX, an abbreviated term for octave cycloscillation, which is the long sought exemplary base wave that continues indefinitely through the continuum of the base ten system of quantitative notation.

We have adopted this valid term to help clarify the behavior of the cyclic and reciprocating nature of the interaction of nine and eleven in the exemplary 99 wavecycle.  Further abbreviation of cycloscillation is the shorter term, cycloflex.  In each cycle we have a full oscillation: one up and one down (or fore and aft).  The cycle to wave ratio in the holotomes is that a whole number series of oscillations can occur in one complete 360 degree cycle.

In the 99 CYCLOFLEX, we have 49 1/2 numbers that are either palindromes or transpalindromes.  There are in fact twelve discrete classes of number, determined by whether a number reversed falls in the same class or is a combination of two classes.  An example is number 16, the only two-digit square that is a prime when reversed as 61.

The retrograde symmetry of the 99 CYCLOFLEX is  complex and cannot be seen without the adoption of the TWELVE GLYPHS described at length elsewhere, (Part Three).

The step from circular unity described in the color wheel to the cubic or spherical unity of the T.R.I. is accomplished by doubling the first perfect number which then may be expressed as the 12 spheres all touching a thirteenth nucleus sphere producing the triangle/square surface of the dodecahedron.

Altogether, this in effect establishes the synchronicity of number and geometry on a plane and then produces the first instance of spherical and cubic synchronicity of number and geometry in 3-dimensional space.

The triangle is an expression of number three as a minimal plane synchronicity, and the tetrahedron a minimal expression of 3-D spacetime and number four.  By forming the dodecahedron, we archieve a spherical symmetry which begins the sequence of hotomoic close packing which can also be represented on either the surface of a plane, or the volume of 3-D space.  An analogy can also be made between the point, the line, plane, and cube.  Number is just another name for geometry.

Throughout recorded history, the Auric Key is manifested in myriad ways and under a wide variety of titles:  THE PHILOSOPHER'S STONE; the white stone, the holy chalice, the Emerald Tablet, etc.

The esoteric traditions of the Sufi masters and the basic tenets of all major religions dealt exclusively with these universal laws of nature, which may only truely be expressed in the universal nature of number/geometry.

But for the most part, the true understanding of these laws have remained dormant in human understanding, due to the inclinations of human avarice, greed, and hate in the interpretation of the most ancient and holistic meaning contained in the original notations from deepest antiquity.  In other words, at various times, they were intentionally concealed from the profane for a variety of self-serving purposes.

This is why, as we approach the Millennium, Syndex offers a radically new perspective--one open to all who would understand.  This is not the threshold of the Apocalypse and destruction, but the threshold of the new Epoch, the Epochalypse, a bold new era for mankind, based on fundamental harmony and understanding of nature and nature's laws essential to our continuing survival.
 

(Editorial Note:  Unscanned graphics include Triaxial Retrograde Interface; general alphnumeric correspondences; alphnumeric corr. with zodiac signs; corr. of colors and vowels; tables of foreign alphabets; Cube of Space, etc.)