SYNDEX: Theory & Practice

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As  per  M.-L. vonFranz's suggestion in our opening quote, we choose an interdisciplinary, general systems theory approach, finding common patterns of methods employed in a wide range of theories.  We can use ontological (the science of reality; that branch of metaphysics which deals with the essential nature, properties and relations of things) and epistemological metaphors ("how we know what we know") from physics, music, and psychology to explore the relationships among numbers.  We shall do that here, also adding a fourth art - metaphysics.

However, the primary mode of Syndex transmission, its SYNTAX, is GRAPHIC DEPICTION.  Its philosophical basis is minimalism, minimism (maximal information in a minimum number of graphic elements).

From the dawn of history our species has always carefully, thoughtfully, and systematically observed nature and modelled nature.  Our general world view, including our attitude to physical and mathematical aspects of basic concepts is very important.  The essential truth lies in mathematics.  The physical universe is an aggregate of frequencies.  Mathematics has penetrated sociology, psychology, and linguistics, as well as many other fields.

In Questioning the Millennium, Stephen Jay Gould says, "My argument for the origin of our fascination with numerical regularity closely parallels my claims about our affinity for dichotomous classification.  In part, we latch on to numerical regularity, and seek deep meaning therein, because such order does underlie much of nature's patterning.  The pperiodic table, after all, is not an arbitrary human mnemonic, and Newtonian gravity does work by a law of inverse squares.  But our search for numerical order, and our overinterpretations, run so far beyond what nature could possibly exemplify, that we can only posit some inherent mental bias as a driving force...Our searches for numerical order lead as often to terminal nuttiness as to profound insight."

Without equations there is nothing to talk about.  Or, more properly, the mathematics enables us to talk about physical concepts more precisely.  Mathematics is a form of language, a very precise form of communication.  These extremes usually compliment one another and our thinking process can move back and forth between them.  Physical concepts can guide the development of new equations as well as visa versa.

SYNDEX is primarily a form of insight that arises through our attempts to obtain a perception of a deeper nature of reality as a whole. Its imaginative qualities are as important a feature as precise math concepts.  Imagination helps further the development of holistic concepts.  Even in physics, play and speculation are part of the legitimate process of discovery, and in fact essential to it.

These dynamic connections are a fact of nature provable by experiments; but to explain them philosophically is difficult, or rather complex.  Demonstrable evidence cannot be found in a conceptual vacuum, therefore a testable theory must  be assumed.  Theory is a perspective, a "Way" of seeing.

SYNDEX THEORY assumes along with R. Buckminster Fuller that unity is plural, and also that nature manifests only  in a  +4,  -4  wavecycle with the ninth null event.

If you don't understand this, or you disbelieve it in relation to prime  number dynamics, we suggest you temporarily suspend disbelief.  If you don't like metaphors go directly to the number proofs and graphics.  If you are math phobic, try the metaphors before tackling the math.  Hopefully, one of our metaphors  will speak to you.  Let the experimental facts, as displayed in the graphics, speak for themselves, creating a new frame of reference.  These pragmatic, positivistic (what is physically observable is real), operational assumptions suggest a deeper connection.

If nature behaves in certain fundamental ways, we can expect the dynamics of natural number, which describe those processes, to do the same.  In seeking greater control over nature and a wider glimpse of cosmos man forges his thoughts into concepts.  Among the vital concepts realized so far, number and its chief mode of expression geometry, coupled together, play the most crucial role in man's technological development.

Space and time can be quantified, their mutual relationship described more objectively and less arbitrarily with a firm grasp of geometry and numbers, and the subsequent description of space and time in exact terms, allows us to examine our world more thoroughly and tap the cosmic forces which govern our very lives and future.

Megalithic structures, such as Stonehenge and the Great Pyramid of Cheops, show the great extent to which our ancient ancestors already achieved this, thousands of years before modern technology.  The functions of these and other examples of ancient technology varied from sophisticated calendars and celestial gauges, to temples of worship and dwellings.

One common feature of them all was concise geometry and direct reference to numbers in their very structure and dimensions.  Apart from these essential outgrowths of reliable calculating techniques, man has sought to harmonize the systems of mathematical insights into a single whole.

Ancient mathematicians also sought to understand number on their own terms with results which often seem vague or arbitrary to the modern mind.  Consider astrology, Qabalism, numerology, etc.  In ancient times, numbers were also letters.  The continuum was  indivisibly ALPHANUMERIC  (ref. Hebrew, Greek, and Latin systems, which form the basis of the modern western occult tradition).

But regardless of the conclusions drawn from these ancient systems, geometry and numbers are vital to their inner workings.  And despite enormous variances in time, place, and culture, certain numbers recur so often that they cannot be dismissed  as coincidence.

Why does Plato relate 5040 to his ideal city-state?  Why is 1260 referred to five times in the Book of Revelations, and so prevalent in music theory?  Why did the Babylonians base their number system on 60 and have 360 degrees in a circle, when they knew the sun took more than 365 days to complete a yearly cycle?  And further, why does 12 abound everywhere from the western zodiac, to calendars and clocks?  Why are there 56 Aubrey Holes in the outer circle of Stonehenge?  And why is 7 considered a sacred number in many religions?  We hope to convincingly, empirically, answer some of these points.  Others you may work out for yourself.

The fact that these numbers relate to THE AURIC KEY may be significant.  Could it be that the systems from which these numbers derived had a common origin or basis, which is cross-cultural?  There is an indication of this, founded on NUMBER LAW in itself, i.e. Numeronomy.

Plato and Pythagoras both dealt with the nature of the perception of reality by using geometry as an aspect of number.  Plato taught that there are changeless, eternal forms on which existing things are modeled.  "The theory of forms" is the most famous of all Platonic doctrines.  It asserts that any object's true reality is found in its RATIONAL FORM or structure, rather than its material appearance.  Philosophy begins in the sense of wonder coupled with the discipline of reason; its pre-geometric forms describe changes from one state to the next.

THE SYNDEX PERSPECTIVE regarding the geometry of number, and visa versa, or the interrelationship of plurality and form, including structure, is predicated upon a series of geometrical moduals (dual modules) that involve a discrete plurality determined by the natural order of prime number occurrence.

These moduals, designated as HOLOTOMES, are the minimal plural quantities that accomodate the maximum amount of consecutive factors of division.

The two-dimensional representative of HOLOTOME A is a circle divided into 12 radial sections just as the Zodiac divides the celestial sphere into 12 radial constellations of thirty degrees each.  Twelve also reflects the 12 Buddhist links in the chain of causality.

The present document provides conclusive proof that this ancient system of a twelvefold classification of primary qualifications was by no means an arbitrarily invented system but a clearly logical discovery of the qualities and quantities of nature's actual scenarios.

The 360 degree cyclation of this archaic celestial roadmap is also both a logical and rational quantity and quality of nature and was by no means arbitrarily determined by the processes of human cognition and conceptualization.

The array of cleavage possibilities that result in the growth of crystals follow structural laws.  Likewise, the pre-geometric structural design of the atomic configurations of  individual  elements also conforms to structural qualities that over the centuries have been identified and labeled according to the systematization of description we know as the alphanumeric principles of notation.  Remember, in ancient times letters were numbers,  although they never reached a level of universal tabulation fully translatible linguistically.

In a very legitimate sense the revelations contained in this writing provide the means of a basic and universal system of describing the structural and topological characteristics of matter which makes no distinction whatever between inert and organic, dead or living.

The observations to be revealed declare that the universe in its so called "infinite entirety" is a living being only separated from itself by the limits we impose on our imagination, which if not hindered by a misunderstanding of itself has no limits.

Henceforth regarded as the SYNDEX PERSPECTIVE, the present document begins with a graphic gesture which acts as a primal foundation for an IDEAL SYNTAX which, when seen in the light of its own vision, arguably abolishes the two arch-enemies of truth: paradox and chaos.  Neither of these can exist in nature, except in the province of language and modelling itself, which of course is a variable aspect of nature.

The graphic gesture just mentioned is entitled the TRIAXIAL RETROGRADE INTERFACE or T.R.I., for short.  It idffers from the Cartesian XYZ in that it is based on the tetrahedron, rather than cube.  The purely imaginary geometrical figure denotes the 3 ambidirectional axes of spatial description.  But these are not the XYZ of Cartesian coordinates, but represent a dynamic tertahedral tensegrity.  Altogether, these vectors represent the six minimal ways that one may move in the omnidirectional options of spatial tropism: up/down; right/left; fore/aft.

Since we cannot visit the past by the expedient of walking backwards we must concede that time is not a direction.  And since we could not know if everything is expanding as space time passes, we have no reason to regard time as either a direction or dimension.

Time, then, being an empirical assumption based on what we recognize as spatial movement (the past is 3D, at least we remember it that way) is a complete mystery.  Due to the nature of human language, specifically the descriptive mechanism of language, time can only be regarded as the duration of whatever scenario we are concerned with at the moment of concern:  TIME IS A DURATION OF CONSCIOUSNESS.

Einstein's suggestion that time is the fourth dimension implies that past and future are separated from the here-now by the insertion of a hyphen between space and time.  In reality,. these are only words and words always refer to something else.  No amount of semantic trickery can change the fact that the cosmos is not constructed of alphanumeric imagery.  Only our apprehension and consideration is thus fabricated.  It's the old saw:  THE MAP IS NOT THE TERRITORY.

The essence we are dealing with is tripolar with three degrees of ambiretrocity -- i.e. the cosmos is 100% omnidirectionally retrogradient, following the third law of thermodynamics.

Even though the enigma of temporality has its only solution at the instant of our personal death we may speculate upon its nature by dismantling a clock and observe the cause of its ticking.

Note that a coil spring loads the escapement mechanism with a reserve of kinetic energy stored up in the elastricity of the spring.  If the spring happens to break due to molecular flaw, the universe goes on down the road without it.  Time does not depend on how it is measured, but is measured by how it depends....beginningness is absurd in regards to matter.

"Most people believe that time passes.  In reality, it stays where it is.  The concept of passing time is false, because man, limited to experiencing time only as passing, does not understand that it stays where it is."  Dogen, Zen Master.

"To put it differently, we do not live in time, but time lives within us...Space is externalized, objectivated time, time projected outward. internalized, subjectivated space...Time and space are related to each other as the inside to the outside of the same thing."   Lama Govinda.

The universe depends totally upon time which stops when we die.  Therefore time is life.  The universe is a cycloscillating complex of events that was never born and can never die.


In thermodynamics, an ideal process is called a reversible process, defined as a change in the state of a system which goes through a continuous succession of equilibrium states.

The full definition/description of circular unity begins first with the definition of the word unity.  As defined by  R. Buckminster Fuller in SYNERGETICS II: "Unity is plural and at minimum sixfold."  Circular unity, then, can be graphically demonstrate 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 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.  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 primitive non-pi spherical module).

This TRIAXIAL RETROGRADE INTERFACE then, contains the graphic capability to represent a  virtual spacetime object.  One example found in nature is the primary cleavage planes of crystals.

We invoke the entirety of Dr. Fuller's master work, SYNERGETICS II to clarify the preceding remarks.

The following shows the fundamental platform from which the Holotomes evolve:

Perfect number (Unity)   = 6  Nave of Holotome A
Doublation produces       =12  (Zodiac) or Holotome A
       times two                  =24   Holotome B
     times three                 =72   Holotome C
     times five                  =360   Holotome D
  times seven                =2520  Holotome E
In this way,. circular unity is conserved by the employment of prime numbers only.  No redundant multiplexing is done through numbers that contain factors of division as in the case of the factorials.

It is easy to tell, at least with very high probability, whether or not a large integer is a prime.  If it is not a prime, then it can be written as a product of two or more factors.  For instance the integer 146,527,939,199 is the product of  the two primes 1,445,599 and 101,361,401.  There are no methods currently known for efficiently determining factors of large nonprime integer.

An important scheme for secret codes, developed in the last decade, relies for its security on the difficulty of factorization.  As a result, the U.S. National Security Agency is interested in factoring.  The coding scheme has also caused a strong surge of interest among mathematicians in the problem of designing well-defined proceedures, or algorithms, to factor integers.

The Holotomes are the minimal numerical magnitudes to accomodate the maximum amount of consecutive factors of division.


The baseten concept of quantitative notation consists of a sign denoting nothing, 0 (zero), a sign denoting singularity, I (one), and eight other signs denoting eight discrete degrees or ratios of plurality: 2, 3, 4, 5, 6, 7, 8, and 9, altogether representing a cyclic continuity of plural members we call numbers.  This continuum must be regarded as an endless series inasmuch as there can be no such idea-entity as a highest or top number.  Because of this open-ended nature of numbering this continuum is said to be infinite, that is, without an end.

Because of this infinite quality of the numeric continuum, we cannot speak of number as having a definite structure, however, if we choose to regard any particular numerical event beyond duality, then we have a finite series which is then a closed system.  Such a system then contains a definite structure which may be described in words, geometrical structures, graphs, diagrams, etc.

To arbitrarily choose a number (amount) for the purpose of establishing a finite and therefore describable system of numbers will provide only one of very many possible systems and/or structures; (the term "infinite number" is meaningless).

The foregoing proposition contains the reason for the need of a non-arbitrary numerical modual that renders possible a scientifically systematic method of describing members in terms of structure and behavior.

Such non-arbitrary numerical modules now exist.  They are called Holotomes: a discrete plural quantum of coherently describable interaction, i.e. a finite unity of a plural componentry.

For those readers who may think that a Holotome is something new, or recently invented, there is indisputable evidence from existing records that clearly indicate that the Sumerians understood the discrete series of Holotomes over 6000 years ago.  That their knowledge of the Holotomes was still clearly remembered as late as 1900 years ago is evident in the writings of the New Testament.

The information contained in the ensuing pages is instrument not only to the intrinsic nature of number, but also to the specific way in which number relates to the descriptive mechanisms of human languages, that is, to the exact and actual structure of an ideal, non-paradoxical syntax.

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, Quality and Quantity.  This preceded the English prefix WH (as in WHO, WHAT, WHEN, WHERE, WHICH, and WHY).  This yields the full 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

These relate to eternal questions of our orientation in the cosmos:  Who am I?  What is the object and source of being, and limitations?  When will I die?   Where do I come from?  Which is my path in life?  For what purpose?  How am I related to it?

In the table, 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 concept of the TRIAXIAL RETROGRADE INTERFACE, which is the fundamental paradigm upon which rests the symmetrical unity of the Holotomes.

Marshall asserts that 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.

These comments suppliment the intended meaning of the phrase, "IDEAL SYNTAX," which should clarify the idea that paradox results from 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 may be understood as a GRAPHIC SYNTAX.

The sequence of mandalogs that represent the Holotomes is an example of this graphic syntax: a rational arrangement of numbers, words, and geometry, by which to convey information not available to the imperfect literary syntax of modern scientific philosophy or what is otherwise termed physiomathematical epistemography.

When Sir Isaac Newton formulated the third law of motion, he could have been much more general and stated that for every axiom there is an equal and opposite reaxiom.  The third law of motion is as much a statement about descriptive language as it is about any intrinsic behavior of physical law.  The concept of action and reaction occurring on a straight line is not stated but is unconsciously accepted.  We know that in modern dynamics, curves and vectors are fundamental, since spacetime is curvilinear.  A vector is a line of force aimed in a known angular direction in respect to an axis of reference.  The length of the vector is the product of its mass multiplied by its velocity.

Number is not at all what we think but how we think.  Remember, the alphanumerical aspect of language in ancient times.

Language, both oral and written is the result of the ideas evolving from plurality on the neurological level.  Civilized culture could not exist without the subliminal notions occuring beneath the words, each, every, any, many, both, all, and either/or, etc.

Up/down, right/left, and front and aft are cognitions that precede conceptions and symbols in the matrix of the mind.  Number and geometry are quantity and quality on the prelinguistic level.

The T.R.I. depicts six forward and six reverse quantity quality event scenario data events on the non-semantic level.  It is another way of demonstrating that within the context of oral tradition the roots of written language reach in six directions.

An example is the Qabalistic meditation device known as THE CUBE OF SPACE, also known as the Key of the Cosmos.    In it, each direction and vector is assigned an alphnumerical glyph from the Hebrew alphabet (See Part Four).  The T.R.I. provides conceptual orientation in imaginal space in much the same way.  The six directions stem from three ambiconceptual axes of spatial cognition.  Time, which we do not directly perceive, is totally conceptual.

Number/geometry is the preverbal mind-scape from which we derive our picture of the so-called real world.  The mind's eye sees very differently than in our familiar three-dimensional world.  Geometry lets the inner eye visualize such spaces as if they truly existed.

Mathematics teaches us this art and at the same time protects us from illusions.  For to understand these spaces, we must first rely upon the exact symbolism of formulas.  Only then can we stand aside and give free reign to our imagination.  The most fundamental geometrical concept is the idea of dimension. Number/geometry is the foundation of the conceptual world, not real at all.  We perceive plurality without resort to number, just as we perceive qualities without the words that refer to them.

Numbers, letters, and symbols are devices of utility in themselves and are only required to suppliment the utility of our legs, arms, hands, fingers, and cerebral activity.  Social order can exist without language but language only exists because there is an innate order in our interpersonal concerns.

The archives of antiquity speak of many disciplines predicated on the metrologies peculiar to all successful technological cultures.  The number twelve (12) and its multiples stand as an exemplary statement of number utility.   They range from the signs of the Zodiac, the labors of Hercules, the hours in the day, the months of the year, the planets of the Sumerian solar system, the stones of Aaron's breastplate, birth stones, the tribes of Israel, the twelve spheres around the 13th nuclear sphere of Fuller's Vector Equilibrium Matrix.

By SYNDEX definition, one is a singularity, not unity, and therefore not a number in the sense that the other eight base numbers are unifications of a plurality of singularities.  This misunderstanding was acknowledged in the Qabala by stating that Aleph is the first letter, but it does not count.  This story is in accord with the legend of Lord Krishna who lost one of his ten fingers on the last day of creation, but still considers one as a number or digit.

The ten number signs only contain eight true numbers: 2 - 3 - 4  - 5 - 6 - 7 - 8 and 9, as an octave.  No transpalindromic sequence can exceed four forward and four reverse number event identities.

                              Multiples of nine:     18

Thus, the retrograde cycle of number is an octave cycle, with a ninth null event, as  stated by Bucky Fuller, the first modern number analyst to recognize this crucual aspect of number behavior.

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