SYNDEX: Preface, Foreword

SYNDEX 2 Foreword Introduction Synchrograph C Base Ten Study Sheets Glossary Bibliography What's New

SYNDEX: Preface, Foreword



Certain it is on my own part
That I have made several mathematical discoveries
Of a fundamental unexpected and unpublished nature.
As I realized my discovery
I always have had
The same strange sensation
That this newly realized conception
Previously unknown to terrestrial humans,
Had been known
To the human mind
Sometime vastly long ago.

                                                                --Buckminster Fuller, Intuition (1970)

This sentiment of Fuller's echoes Bob Marshall's own feelings of discovery during his 30 year pursuit of the revisioning of number dynamics and the synergetic number field through Numeronomy and Synchrographics.  He could not help but feel that even though he was finding seemingly undiscovered properties of numbers that these revelations were, in fact, the recovery of a lost wisdom whose traces are found in ancient natural sciences.

The primary subject of this book, the Hindu divine numberword Om/108, is called the number of the Universe.  The graphic enspiralment of the natural number continuum into a mandala or mandalog (based on 108 axes) formed Marshall's crucial tool for investigation of hidden properties of numbers.  Multiples of 108 form the basis of Indian time measurement, the Yugas and Ages.

Cosmology, horizon-based astronomy, astrology, architecture, navigation, geography, geometry, mathematics, timekeeping, writing, proportion in art, and musical notation were all related to numerical canon .  The ancients encoded their knowledge of the world in their sacred monuments and texts as an esoteric code of numbers, formulas, and proportion.

Ancient state temples may have functioned as permanent repositories of standards of measures.  Gods, (to whom the temples were dedicated) had characteristic numbers, from which they were indistinguishable.  (In our example, 108, the Universe is also the god Brahma.)  Numbers expressed qualities, not just quantities.

In the old beliefs, this code, (whose true source is lost in prehistoric antiquity),  is always alleged to have a divine origin, from the gods or a god-like man.  Lore relating to sacred words or phrases arose, because letters and numbers were interchangable or alphanumeric. The code arises naturally from the inherent structure of arithmetic.  This code emphasized certain key numbers, which were seized upon by different cultures.

Prime numbers figure prominently in the measuring and numerical canons of ancient and modern times.  Ancient metrology is the science whose evidence is encoded in the sacred dimensions of such cosmic image models as the Pyramids and Stonehenge, earthly monuments oriented to the heavens.  The numerical code lies behind the layouts of temples and cities and systems of measuring time.

In fact, metrology was the basis for development of both philosophic and scientific attitudes.  The divine order of the universe was the central idea of the ancient world, and all belief-systems were enmeshed with it.  Metrology provided the foundation of the systematic rational vision of the world.  Cosmic order embodied in metrology was the fundamental aspect of ancient thought.  Number mysticism was the essential basis of most of their knowledge.

Of course, information about the Universe has always been there, but its availability is limited to those prepared to receive or decode it.  Ancient cosmologies were not only models of the physical universe, but representations of a universal mathematical archetype.  The numerical canon revealed correspondences between different orders of natural phenomena.  Metrology included sacred units for measuring the Universe, units of time, space, weight, and mass (or volume).

The ancient sacred units of measure come from the principle dimensions of the earth (geodesic or geodetic) and astronomical (or cosmological) constants, such as the Precession of the Equinoxes, and the orbital periods of the observable planets.  Geography developed from metrology.  Traders and navigators needed to calculate distances and time for travel.  This link between measures of length and time united metrology and astronomy, and led to astronomical navigation.  Ancient navigators used a sexigesimal method of dividing the horizon, using six (rather than four) cardinal directions.

Ancient linear measures expressed fractions of the earth's dimensions (polar diameter, circumference, radius, meridian circumference), generally in units of 12.  Thus, we have 360 degrees of latitude, each of 60 minutes of 3600 seconds.  Cross-culturally, ancient units of measure relate proportionately to each other, because the old units (whether Mesopotamian, Greek, Egyptian, Roman, Chinese, etc.) represent fractions of the earth's dimensions.  Russian archaeologist Bieliaev, points out that the same weights with the same subdivisions are found in early Rome and India of the third millennium B.C.  He traced connecting links to Sumer and Egypt, and found the same units used in medieval Russia.

In ancient times, the Universe meant the observable Universe. For Pythagorean and Platonist thinkers, the patterns of numerical relationships which occur in the processes of arithmetic and geometry were considered the formative influences behind all of nature's phenomena.  Numerical patterns were detected in the manifestations and dynamics of nature. Behind this is a philosophy of numbers which express universal relationships.

Although usually superceded by practical arithmetic, there is much to learn from the study of the relationship of number and form.  The essence of all matter is dynamic relationships.  Number is the 'first paradigm,' the basic ordering principle of nature.

Curiously ancient metrology, synergetics, and Syndex number dynamics all share certain key numbers in common.  They have been enshrined in monuments, cosmologies, philosophies, calendars, measurement, and number theories throughout recorded history.  Any numerologist (you know who you are) can find many of his "favorite" cosmic code or cyclic numbers here, but that is not what this is all about.  For the skeptics, we hope to present some facts about the number continuum.  These facts stand on their own, even if we disagree about what they might mean.

Many so-called "key numbers of the Solar System" are involved, because key numbers have always stood out for their unique properties.  The ancients discovered them through aeons of empirical observations of cosmic cycles.  They were capable of observing long-term effects, (such as the precessional cycle), with horizon-based astronomy.  Their observations of the divine order were central to the core of their civilizations.

Ancient metrology does provide a clue to what numbers might be interesting to investigate.  Syndex II follows the clues by using direct observation, rather than interpretation of what is there to be seen.  It requires no ancient, alien, or mystical source, no occult doctrine or arcane secret, no ideology.  It predicts no "end time."  It is simply a graphically revealed "truth."

In Syndex, numbers do not have values according to historical significance or preconceived ideas.  Rather, numbers speak for themselves since numerical progressions are often related by geometry and can graphically display their own qualities.  The synergetic aspect of Syndex is showing how the first perfect number six interacts with the prime numbers, and how numbers relate to one another in discrete systems, which have relationships to one another.

Synergetics suggests nature transforms in rational whole number increments (no fractions, no pi) related to prime numbers.  According to Fuller, reality consists of whole numbers of energy events.  By modeling an energetic reality, and helping us coordinate our senses with reality, synergetics reaquaints us with Universe.  Synergetics helps us see the principles which govern the relationship of parts to whole systems.  There is a fundamental geodesic design in nature.  Synergetics models this otherwise invisible phenomena.

Synergetic geometry is a study of relationships and systems, based on the minimal system--the tetrahedron.  Six connections between four events defines the tetrahedral system as the basis for modeling reality.  It is the simplest way to enclose space, and the most economical.  All systems are necessarily polyhedral, (interrelated events).  All polyhedra are multiples of the tetrahedron's six connections.  Fuller's mathematics is based around thinking in terms of systems to describe local processes and relationships.

Syndex reveals how the key numbers of both ancient metrology and synergetics are related together in the Holotomic Sequence (circular unities) and 9/11 Wavecycle, a synergetic +4, -4 basewave running through the continuum of natural number.

In modern times, our vision has been extended from the sub-atomic realms to intergalactic levels, but the same functioning of prime numbers in whole increments is still the principle basis for describing nature's transformations.  In Cosmography, R.B. Fuller details just how synergetics relates to the underlying principles of the Universe.

#108 = OM = UNIVERSE

A. Universe is inherently resonant.  Resonance is a complex of intertransformative frequencies of miniintertensioned systems.

B.  The inherent resonance of Universe is caused by nature's never pausing at, and only forever transiting, exact equilibrium.

C.  The union of Universe is differentially complementary regenerative-production wedding of inherently, uniquely prime numbers 1, 2, 3, 5, 7, 11, 13, and all of their successive primes.  The prime numbers are divisible only by themselves and by 1, representing in synergetics unique system behaviors.

D.  The prime numbers imposse an eternal disquietude--transformative adjustings and omniintertensional resonances eternally interaccelerating.

                                                                        R. B. Fuller, Cosmography (1992)

The most important starting point of Fuller's work is that he reveals a basic error in the foundations of classical philosophy and natural science.  Namely, that the Greek mathematicians made the mistake of opening the wrong door into physical reality by adopting the square and the cube as their prime modules of reality.  They took a 90 degree wrong turn.

He models synergetic reality with the dynamic, rather than static model, of the tetrahedron.  The axes of a cube are not inherently stable unlike the four centrally coordinated planes of the tetrahedron, which nature actually employs to create material reality.  There are no 90-degree angles in nature and no perfect spheres (only geodesic polyhedra), according to Fuller.

A summary of this viewpoint of philosophical geometry or geometrical philosophy can be distilled from Cosmic Fishing (1977), by E.J. Applewhite:

"The essence of Fuller's synergetic geometry is to advance a single model to describe the shape of the physical universe, the shape of energy's behavior, as well as the shape of metaphysical universe, which is the shape of our thinking...If the notion of measuring all experience in terms of tetrahedra seems unduly perverse and abstract, it is really no more so than our familiar and unquestioned employment of the cube for the same purpose."

Fuller employs nature's matrix, based on the closest packing of spheres to demonstrate energetic forces.  It is the geometry of the subatomic realm and therefore of the universe.  It echoes the ancient dictum, "As Above, So Below."  In this matrix (Vector Equilibrium Matrix), the direction from the center of closest packed spheres to the neighboring centers is 60 degrees, not 90.  Vectors of equal length radiate omnidirectionally in 12 directions.  He argues that nature and the universe are best modelled by omnidirectionally intertensioned, nested tetrahedrons and octahedrons (Isotropic Vector Matrix).

But vector equilibrium is not a structure, since energetic motion never ceases. There is always motion in real systems, even at the so-called "zero-point energy," there is a gradiant, (the vacuum potential).  All physical reality consists only of energy.  In the multidimensional IVM, the vertices are all equidistant from one another, and the center of a local vector equilibrium.

This IVM provides an alternative frame of reference to the traditional XYZ coordinates, the building block through which we have tried to understand space.  There is a great advantage to using the tetrahedron rather than cube as the basic volume unit, or way of orienting oneself in space.  Cubes are inefficient, require three times the space, and don't reflect nature's own self-organization.

"He concedes that the square and the cube do work in their awkward way, but he argues that their adoption as modules was misguided and erroneneous because they have nothing to do with nature's own coordinates.  Height, length, and width simply do not exist for him independent of the observer.  Thus the observer always inadvertently provides the fourth (or tetrahedral) point of reference.  In his synergetics, height, length, and width exist only as aspects of polyhedra.

"With the cube and the square the ancient Greek mathematicians entered the world of nature by the wrong door, eschewing the more elegant triangle and tetrahedron which were so easily available and have been so ignored.  Fuller regard the XYZ coordinates as the accidental result of man's choosing the wrong tools for calculation, spawning irreducible fractions and irrational numbers like pi--with unresolved odd numbers to the right of the decimal point.

He regarded "the XYZ system as an aberration of man and not as a reflection of nature's own most economical coordination, which is in triangles and tetrahedra rather than squares or cubes...Fuller claims not only to have discovered nature's coordinate system--to which all history up to now has been blind--but to have revealed how Einstein's relativity and quantum mechanics can be demonstrated to popular understanding in simple geometrical models...the fourth dimension became visible in his topological accounting."

"...Three dimensions can be modeled with perpendiculars in the cube.  Four dimensions can be modeled with equiangularity in the tetrahedron.  What the three axes of the cube do for three dimensions, the four axes of the tetrahedron do for four dimensions.  The tetrahedron provides for the convergence and divergence of four centrally-coordinate planes."  [Cosmic Fishing].

The simplest arrangement of closest-packed spheres is the four whose centers define the tetrahedron.  Subsequent researchers have shown that the natural structure of the universe and life cannot be explained without this geometry.  It is fundamental to the structure of everything in the microcosmic, meso- and macroscopic universe.

"In synergetics, number is not an abstraction: each number has a geometrical identity as well as a numerical identity.  The two are intertransformative so that the number measurement of  areas and volumess always comes out even, without fractions or odd numbers left over.  No pi; nothing to the right of the decimal."

Thus, Fuller created the first explicit formulas for the area of a circle in triangular modules and for the volume of a sphere in tetrahedral modules--all without pi, but based on prime number dynamics.  This made him a mathematician of singular distinction.  He proved and demonstrated that the tetrahedron is not merely an object, but the minimum structural system in our synergetic Universe.  As it turns out, his philosophical universe accurately models the modern scientific view of the Universe.

But he also acknowledged that metrology and ancient monuments enshrine ratios from closest-sphere-packing hierarchies.  When he saw Baalbek, he declared that the Phoenicians knew his principles.  These principles included circular unities, finite discontinuities, the three-way great circle grid, the tetrahedral matrix, tensegrity, and synergetic mathematics.  It is through this towering intellectual achievement that we revision the nature of the synergetic natural number continuum.


"Jung suggested coining the term 'synchronicity,' so that certain aspects of reality which are not included in the causal description of nature can be interpreted as synchronistic events without the necessity of regressing into an archaic form of magical-causal thinking.  Similarly, it seems to me desirable to introduce a new qualitative concept of number to complement our hitherto prevailing quantitative number concept, without falling back into magical-numerological speculation on this account. . .Mythological images and numbers have always been associated with each other." --M. L. von Franz, Number and Time

ABSTRACT:  Syndex II is about the processs of discovering synergetic, rhythmic symmetries on a graphic enspiralment called Synchrograph C.  On this number wheel, the natural numbers are spiralled 60 times around a radial array of 108 increments to the number 6480.  Contemplating the C-graph over the years has produced several revelations, including the following Holotomic Sequence, (12, 24, 72, 360, 2520, 27720, 360360, 6126120, etc.) created by prime number multiplexing, and the exemplary 9/11 wavecycle, discovered by Bob Marshall.

This book is not about number mysticism, or numerology.  No occult theory of numbers is presented, no cosmic code of alien descent, no ideologies.  Rather, it outlines the history of numbers and writing and the ancient science of astronomical measurements.  Classical cultures are characterized by certain general basic ideas, of which metrology is foremost.  We show why certain cultures considered certain numbers "divine," and why we should turn our attention to them in modern times.

Most of these numbers seem to have originated in Sumerian culture and are the result of geodesic and cosmological measurements (such as the Precession of the Equinoxes) discovered thousands of years ago, in the mists of prehistory.  These numbers are important in certain inherent rhythms in the base-10 system of numeration.  These synergetic qualities have hitherto remained unnoticed in classical number theory.

In antiquity, knowledge of an alphanumerical canon spread throughout the Middle East, to Greece and India, back to the Moslem Empire, and from there into medieval Europe to catalyze the Renaissance.   India raised mathematics to a high art, and the most revered of numbers was 108, the number of OM and the Universe, the number of Brahma.

This number formed the basis of the Ages and Yugas, which are all multiples of this sacred numberword.  Yugas include 432, 864, 1296, 1728 and add to 4320.  Ages include 648, 1296, 1944, 2592 and add to 6480.

108 is itself  3 x 36--part of the Sumerian sar, 3600, also dubbed the number of the Universe, a unit of Divine Time, a year of the gods (3,600 earth-years).  The number of zeros tacked on the end of these cosmological numbers is almost irrelevant, and merely emphasizes their vast importance.

Inasmuch as 108 is 3 x 36 and both systems mutually include the square of 36 (1296), it becomes evident that the classic 360 degree circular unity is the common denominator of these separate systems (360 degrees of 60 minutes or 3600 seconds each).

According to Neugebauer (1952), "the division of the circumference of a circle into 360 parts originated in Babylonian astronomy of the last centuries B.C.  The sexagesimal number system as such is many centuries older and has nothing to do with astronomical concepts."

However, in a far newer work, Sumerian scholar Zecharia Sitchen (1993) differs in opinion, attributing both mathematical astronomy and  360 circular unity to the Sumerians, based on his own cuneiform translations.  He also refers to "the role that the key number 12 played in Sumerian science," and the "celestial 72," which comes from the precessional shift of 1 degree.  He notes that 120 sars equals 432,000 earth-years.  This is the number of the Great Yuga.

On Synchrograph C all the numbers that represent the two Hindu astrocalendaric systems fall in the same zero axis.  The sum of the Yugas falls at 2/3 of this axis.  6480 divided by 3 = 2160, the Platonic Month:  12 x 2160 = 25920, Platonic Year.

Contemplating the  C-Graph led Marshall to deduce Sumerian origins for the holotomic sequence of circular unities, and the source of ancient Hindu cosmology.  The Yugas fall in perfect tertiary symmetry, while the Ages assume a perfect quadratic symmetry.

The Yugas can be generated as 36 x 12 = 432; 36 x 24 = 864; 36 x 36 = 1296; 36 x 48 = 1728.  Likewise, the Ages: 18 x 36 = 648; 36 x 36 = 1296; 54 x 36 = 1944; 36 x 72 = 2592.

360 is divisible by all eight base digits except prime number 7.  To include 7 as a divisor, the prime circular module must be raised to 2520, the Auric Key, and smallest number to accomodate the greatest amount of factors of division, the lowest number divisible by all base digits.

The key to Sumerian metrology is not as simple as the sexigesimal 6 x 60 = 360.  Even in Sumeria, the sexigesimal system (60-division) was only applied in strictly mathematical and astronomical contexts.  The sexagesimal numerical system had a decimal substratum (36 x 10 = 360).  In other matters they used 24-division, 12-division, 10-division, and 2-division.

The real key involves the sequence in which prime numbers naturally occur in the baseten continuum.  This is demonstated by multipling the third and fourth Holotomes together: 72 x 360 = 25920, a number given for the Precession of the Equinoxes in Sumerian cuneiform records.  This number relates directly to Yugas and Ages.

              72 x 36 = 25920 divided by 2 = 12960; divided by 3 = 8640
by 4 = 6480; by 6 = 4320
72 + 360 = 432

Contemplation of the numberwheel 108 discloses the complete menagery of "sacred numbers."  864 is 12 x 72, holotomes A and C; 1728 is 24 x 72, holotomes B and C.
Both systems share 362  = 1296.

The key numbers of ancient metrology and the Holotomic Sequence are found in positions that issue a perfect symmetry (such as the quadratic array of the four-digit palindromic sequence: 1881, 2772, 3663, 4554) where only chaos exists in classical number theory.  Nature's behaviors coincide with the most crucial divisions of the synergetic continuum of baseten number.

Prime numbers figured prominently in metrological and numerical canons of ancient times, a system of interlinked measures, numeration, astronomical cycles, and geodetic standards.  They also figure prominently in the graphic symmetries of synchrographics and the wavecycles of numeronomy.  The same functioning of prime numbers in whole increments is still the principle basis for describing nature's transformations in synergetics.

Jung asserted that number forms the particular element which unites the realms of psyche and matter.  It is real in an archetypal, qualitative sense and a quantitative sense, uniting the imaginal and physically knowable.  The psychic dynamics of the concept of number appear archetypally as its "transgressive" aspect in the realm of matter.  Numbers above the threshold of consciousness appear as quantitative discontinuities and qualitative individual numbers.  But according to the Jungians, in the unconscious they interpermeate and overlap participating in the one continuum that runs through them all.  Thus, we find certain synchronicities in the Syndex numberwheel mandalas, creating metaphysical and empirical harmonies.

Certain authentic mathematical structures can originate in the unconscious even though Western number theory has traditionally followed a very different path.