## Archetypal Integers

SYNDEX: THE AURIC KEY

Synergetic Synopsis of the Geometry of Number

by Iona Miller & Bob Marshall

Number Harmonics, Resonance & Dynamics

Full story and illustrations at

http://syndex.weebly.com/

**"Your cyclic synchrographing work clarifies and simplifies this whole matter to an epochal degree.**

**At any rate, your work fills me with joy.**

**Would you be willing to have me publish this work in another edition of SYNERGETICS with full credit to you?" --Buckminster Fuller to Bob Marshall, 1981****"...**

*I would conjecture that the task of future mathematicians will be to collect their characteristics and analyze, when possible, every number in its logical relationship to all others. This research should be undertaken in collaborations with physicists, musicians, and psychologists who are conversant with the empirical facts about the structural characteristics of numbers in different mediums*."**--M. L. von Franz, Jungian Analyst, NUMBER AND TIME**

**Syndex is an approach to the natural number sequence, rather than a theory. Its models are inherent in nature and can be graphically displayed by circular arrangements of the number sequence is about the intrinsic structural patterns that appear in the baseten continuum of number A main feature of number theory has been the absence of any noticeable pattern of regularity among prime numbers. Reversal is the key to number law. Prime numbers play a fundamental role in the construction of geometrical form, and in turn of structures. The Holotomic Sequence produces a graphic syntax that displays all the structural intricacies of the continuum of baseten numbers. Syndex theory can graphically show 100% symmetry of prime number distribution within the context of its finite series of geometrical modules. These mandalic modules are the minimal amount of consecutive factors of division. Syndex is not number mysticism, but a non-reductive holistic way of viewing obvious realities about the continuum through "circular unities." Number is not an abstraction in synergetics. Rather, each number has a geometrical identity plus a numerical identity, which is inter-transformative.**

**(c)2010, All Rights Reserved; Use with Permission Only**

There is a relationship between number dynamics and geometry that is pre-arithmatical. SYNDEX encodes the maximal amount of information in the minimal amount of graphic elements, disclosing circular unity in the natural geometry of number and a base-wave in the natural number system. Circular Unity is the basis of Ancient Metrology & Number Dynamics.

**"...the powers of human reason could not be limited to any accepted prearranged system of formalized rules. What Godel showed was how to transcend any such system of rules, as long as those rules themselves could be trusted." --Roger Penrose**There is a relationship between number dynamics and geometry that is pre-arithmatical. SYNDEX encodes the maximal amount of information in the minimal amount of graphic elements, disclosing circular unity in the natural geometry of number and a base-wave in the natural number system. Circular Unity is the basis of Ancient Metrology & Number Dynamics.

**Abstract: SYNDEX identifies and demonstrates various properties of the base ten number field, such as the symmetrical distribution of prime numbers. The continuum can be viewed as both progressive and regressive. The key to the comprehensive analysis of general number behavior is found in the concept of "circular unity." Synchrographics has been systematically contrived to formally illustrate behavioral patterns that have successfully led to a general understanding of the fundamental elements of the geometrical nature of the base ten system.**

**The graphic importance of the Holotomic Sequence is that circular symmetry is being conserved and may be enlisted as the fundamental reference key in the graphic investigation of number behavior. The primes are deployed in symmetrical interface only within these specific Holotomic domains. Here, the enigma of prime number distribution has been solved.**

**Synchrographics regards symmetry as a primary analytical aspect of reference, making the Syndex archetypal system of classes of numbers possible. The foundation of this system is palindromes and transpalindromes, yielding 12 classes of number. Palindromes, or binomial reflection numbers are neither purely accidental nor without significance. Transpalindromes are the reversal of any particular number exceeding a single digit (for example, 16 and 61).**

**Numeronomy, the laws relating to the essential structure and dynamics of number, is a new word for an extremely ancient science. This science, (based on the knowledge that the continuum contains a definite structural order with general laws that describe the nature of that order), has laws that relate to the general behavior of nature itself. Each number has both a geometrical and numerical identity. It is the outcome of Synchrographics: numbers speak for themselves through structure and behavior. The first concern of Synchrographics is maximum information expressed via minimal graphic elements. Correspondences, such as those between geometry, numbers, colors, and frequency of divisibility form an integral part of the system.****All mandalogs (number wheels) are the product of the systematic generation of the exact sequence of minimax factorization. They have the perfect retrograde feature by which the patterns generated in the first half of the spiral are reversed at midpoint and are reflected as a mirrored image in the second half of the spiral. Comprehending the universal nature of the transpalindromic function of number behavior is not easy. We tend to see the number chain as a unidirectional continuum, which is too linear for a synergetic perspective.****Revisioning the number continuum with the concept of simultaneous counterflow yields a more accurate picture. Remember, this is also happening in Post-quantum Physics under the rubric of quantum backflow. With large spans of number, the complex interrelationships become difficult to visualize without good graphics. Because of the octave nature of the base cycle there cannot be more than four consecutive transpalindromic pairs in a single symmetrical sequence, regardless of the amount of digits in each individual number.****We cannot contemplate numeracy without an automatic involvement with geometry. A triangle is an expression of the number three and a square is an expression of number four, i.e. number and geometry are two sides of the same coin. Therefore, Synchrographics was contrived to analyze the geometrical properties of number and conversely the numerical properties of geometry. In the proceedures that will be explained in the text, we discovered the key sequence (Holotomic Sequence) which consists of a series of key numbers or circular unities in the rhythmic wave.****Buckminster Fuller was very excited, and "filled with joy" over these revelations, and we hope you will be also. After all, numbers are what they are, not what we wish them to be. They will not do what they cannot do, i.e. show symmetries where none exist. Nor can they hide their inherent qualities forever from the astute devotee. Using a general systems theory approach, we employ metaphors from many disciplines to demonstrate how this perspective can be employed in other fields of investigation.****BOB MARSHALL SAYS: "I boast of entitling myself as the world's leading numeronomist. But no longer the ONLY numeronomist. Iona Miller, who has written the first literary account of numeronomy under the title A NEW PERSPECTIVE ON NUMBER DYNAMICS has over the past decades developed a perspective of the tenets of this science that to me is astonishing in its depth of proper assimilation. She transliterates my awkward and illiterate work notes, which are highly redundant and confusing, even to myself. I'm often inclined to think that Iona has usurped the title of 'Master' and made me the apprentice. Perhaps the only way that I excel is in my ability to spontaneously identitfy the ambidirectional nature of any specific integer, i.e., to read numbers backward with the same facility as reading numbers in the classic unidrectional mode."**

**2520: Reflexive patterns inherent in natural number mirror one another on both halves of the wheel.**

**Summary: SYNDEX 1 & 2**

This concrete form of philosophy was determined by the nature of Greek mathematics. These philosophies seek to reconcile the actual condition with a hypothetical distant ideal, which expansively incorporates both personal and universal dimensions. It is an inward-oriented epistemology. By intuitive perception we can consciously reiterate the laws of Nature and mind which are equivalent to the archetypes themselves. Belief in the essential aspect of the mathematical as a real world, a "last reality" underlies the surprising efficiency of mathematics in the natural sciences and technology. But are numbers really abstract entities existing independently of the human mind?

*Syndex I & II*are about the spiritual and universal beauty of numbers. They reflect the order and beauty of nature, but also of psyche. According to Jung, number unifies the physical and psychic (as in "realm of the psyche", not fortunetelling) worlds through synchronicity. Jung's basic ideas about the unity of knowledge and existence are in principle synonymous with the Platonic tradition, alchemy, Qabala and Gnosticism. Plato treated the end product of the evolution of mathematical concepts, (a fixed system of idealized objects), as an independent beginning point of the evolution of the "world of things."This concrete form of philosophy was determined by the nature of Greek mathematics. These philosophies seek to reconcile the actual condition with a hypothetical distant ideal, which expansively incorporates both personal and universal dimensions. It is an inward-oriented epistemology. By intuitive perception we can consciously reiterate the laws of Nature and mind which are equivalent to the archetypes themselves. Belief in the essential aspect of the mathematical as a real world, a "last reality" underlies the surprising efficiency of mathematics in the natural sciences and technology. But are numbers really abstract entities existing independently of the human mind?

**What is the nature of mathematical truth, and how is it translated into mathematical knowledge? If it exists in another "ideal world", how can we know anything at all about the subject-matter of mathematics? What collective criteria determines the nature, terms and rules of this world?**

**In the Jungian view, numbers (like other archetypes of the collective unconscious) are contents and patterns of behavior which are not personally acquired in experience but are inborn.**

**The**

__Platonic Forms__are the objects of knowledge, which is regarded as innate. They can emerge dynamically as well as imagistically. The essential nature of the Forms is dual: unity and multiplicity, finitude and infinitude. "The One" is the origin of Forms in the same way that the psyche is the origin of the archetypes.**Because they form a primary conceptual language, numbers have heavily influenced the development of culture, philosophy and myth as well as sciences such as cosmology.**

**'Number is All' was the Pythagorean motto. Numbers were symbols representing cosmic principles. The whole philosophy of numbers came from distinctions created by the primordial division of the One into multiplicity. Because of their archetypal essence, their mode of articulation is essentially mythic and radically symbolic.**

**Mathematics, by the very nature of its method, is an essentially Platonic pursuit. Mathematicians treat the objects of their investigations as real objects in a hypostasized space,**

*as if*they existed independently in some pure world of their own. Thus, they reason that the amount of prime numbers is "infinite."**Discussing the amount of prime numbers, mathematicians believe that they are discussing objects as real as collections of things in their everyday life.**

**We use numbers casually and rigorously as a language to order space. Since ancient times, their archetypal dynamics have been the foundation of philosophy, religious, and artistic thought. Patterns of dynamic energy in numbers reflect patterns of nature--the order of the universe. Whether they actually**

*form*the basis of the universe is the subject of ongoing debate among many schools of mathematicians. The qualitative distinctions we make between phenomena are fundamentally numerical.**We still don't know why the universe appears to follow mathematical laws. However, as Hilbert has suggested, we do know that the idea of the Infinite deviates significantly from the situation in the physical Universe.**

**Are numbers and functions the inventions of mathematicians, or do they exist independently of us? Just because a mathematical object can possibly exist doesn't mean it actually**

*does*exist. Yet, mathematicians imagine they are talking about real objects, when they may be talking about stabilized concepts.**The new direction in the**

__philosophy of mathematics__is a "quasi-empirical approach that treats mathematics as just another messy experimental science." A partially unconscious process of idealization ends in the stable concept of numbers, points, lines, spheres.**When working in geometry, a mathematician does not investigate the relations of real things. He investigates some idealized, fixed notion of these relations. This notion is subjectively treated as "reality" without any fundamental reality behind it. It can, therefore, arguably be considered art as well as science.**

**In practice, mathematicians jump to conclusions, and after the jump has been made begin the labor of proving the theorem or constructing a coherent theory. This involves subconscious reasoning, tenacity, focus, judgement, concentration, elementary intuition, free association, and conceptual visualization.**

**Some say mathematics is a purely human construct, an artifact of our nervous systems and culture. Others attest that even chimps and infants are hard-wired by evolution for arithmetic to deal with real objects in the real world.**

**Numbers are not Platonic ideals but neurological creations. Integers, like colors, are artifacts of our sensory processing mechanisms. Dehaene traces the arithmetical model to the inferior parietal cortex. This poorly understood location is where visual, auditory, tactile signals, and language processing converge. Mathematics, or at least mathematical notation, is another human language. It also appears to be the language of nature, and therefore physical reality. Of the infinite range of mathematical creations, scientists keep those that help explain and predict reality.**

**The concept of natural numbers is a fixed model, an idealization of quantitative relations which ends in stable concepts of numbers. The dynamics of those numbers are described in**

__number theory__. Number theory, one of the oldest branches of pure mathematics, concerns elementary properties of primes, divisibility among integers, the existence of greatest common divisors, the study of specific families of numbers, simple recurrent relations, factorization, and more. Syndex addresses these aspects with easy to state conjectures which can be understood and observed in graphics without any particular mathematical training.**Mathematical Platonism concerns the investigation of fixed or self-contained models. The Platonic Idea or Form is essentially an unchangeable form.**

**As symbols, numbers express the particular in the universal, the eternal in the finite. They express the ordering function of their archetypal nature. The Neoplatonists assumed an a priori structure of knowledge grounded in archetypal forms and directed toward a unification of the ultimate principle of "the One" with the diverse phenomena of "the Many." This could also apply to the number field.**

**We contend that the Holotomes are such self-contained models of holistic, self-reflective, finite portions of the number continuum. Holotomes are geometrically symmetrical, modular unities, based on the minimal numbers divisible by the the maximal factors of division. Each holotome adds an additional factor of divisibility to its circular unity. All base digits are captured by the number 2520.**

**Every subsequent holotome retains a copy of the initial data plus an additional factor. Each holotome contains a rational section of a complete cycle. In these geometrical entities, the prime numbers are distributed in perfect radial symmetry within the context of every holotome. Such closed loops of causation are 'objective,' i.e. considered legitimate objects of scientific scrutiny.**

**Number and geometry are two ways of expressing the same set of ratios or relationships.**

**The Exemplary 9/11 Basewave (Cycloflex) is also a synergetic, dynamic representation of objective closed loops of causation. They can not only be described, but also graphically displayed. This is a reflexive +4, -4 ambidirectional base wave with a ninth null event, (as per Buckminster Fuller), forming a series of octaves running through the continuum.**

**This octave is a cyclic function. This base wave can be faithfully mapped into a single coherent syntactic time frame. The base wave is highlighted by palindromes and transpalindromes (the reverse identity of any number over a single digit, i.e. 16 - 61).**

**Syntactic objects, which clearly exist represent similarly "real" objects--objects of investigation.**

**Syndex is a method of mapping number structure and dynamic, synergetic behavior making number theory visibly coherent It geometrically paraphrases the elements of numeric progression.**

**Syndex reveals the self-reflexive, synergetic properties of the base-10 natural number continuum or field. It simply exists at the level of nodes and mappings in the Syndex diagrams.**

**Syndex graphically displays formerly undiscovered symmetries in the natural number sequence and distribution of primes. It is based on a series of circular unities (self-contained objects), the results of prime number multiplexing, from whose factors cascade the whole panoply of ancient “sacred numbers” of many diverse cultures.**

**These sacred numbers come from the ancient wisdom traditions, including those of Sumeria, Babylonia, Egypt, the Bible, Plato, Pythagoras, ancient India, Stonehenge, the Mayans, and Qabala. Their importance to human culture echoes down to us from the past, not in any occult way, but by disclosing an ancient number canon that conceals and reveals inherent rhythms in the base-10 continuum. It reveals a synergetic relationship between number and geometry, which can be displayed graphically and easily understood even by the nonmathematical.**

**These circularities are based on prime number multiplexing.**

**Within each circular number wheel, the primes are dispersed in rational, symmetrical deployment. This mandalic science helps us visualize facts about dynamic aspects of the interaction of numbers and their families. This fact remains undiscovered in classical number theory, and is discussed under the rubric of the**

__prime number enigma.__**The Auric Key to this enigma is the rediscovery of the original program of the alphanumeric system of notation and the fundamental platform of general science, the history of which began with horizon-based astronomy and cosmology in Sumeria. The Auric Key excavates many vital properties of numbers.**

**Classical cultures are characterized by certain basic ideas, of which metrology is foremost.**

__Ancient metrology__was a system of interlinked measures, numeration, astronomical cycles, and geodetic standards. We can find the most often cited numbers of ancient metrology extrapolating out of a certain numerical sequence, (The Holotomic Sequence).**We begin with the question of why some unknown and ancient geometer selected 360 degrees for dividing the celestial sphere and the circle. The division of 360 by 12 produced one of the first historical cosmologies--the Zodiac.**

**The basis of this standard of circular unity can be deduced.**

**360 is divisible by all eight base digits except the number 7. To include 7 as a divisor, the prime circular module must be raised to 2520, the Auric Key, the lowest number divisible by all base digits. From this clue, we can destrapolate and extrapolate an essential sequence, a family of numbers.**

**It turns out that 360 is but one in a strategic series of circular unities based on prime number multiplexing. Numbers 2, 3, 5, 7, 11, and 13 are the first primes. By starting with 6 (the first perfect number) and multiplying by the primes in their natural order, we get the sequence 12, 24, 72, 360, 2520, 27720, 360360, 6126120, etc.**

**Each of these numbers forms a geometrical entity, a circular unity, (Holotome). These numbers just happen to be the exact sequence of minimal sums that accomodate the maximal amount of factors of division. Their synergetic qualities have remained unnoticed in classical number theory.**

**This minimalism is reflected in Syndex number theory.**

**The first concern of Syndex method is to encode the maximum information expressed through minimal graphic elements. Therefore, we employ correspondences between numbers, colors, and frequencies of divisibility to integrate the system.**

**The number 2520 is the Auric Key. It,**

*not*360, is the first number divisible by all nine base digits. It is exactly twice the number 1260, a number referred to cabalistically five times in the Book of Revelations (12:6 and 12:4). It is half of the number 5040, which figures prominently in Plato’s “Laws” regarding his ideal city/state.**This number 2520, more than 360, captures nature’s cyclic behaviors. And the graphic number wheel (synchrograph or mandalog) based on this number reverses to form a mirror image of itself at the midpoint of 1260. The real key involves the sequence in which prime numbers naturally occur in the base-10 continuum.**

**This synergetic effect is demonstrated by multiplying the third and fourth Holotomes together: 72 x 360 = 25920, a number given for the Precession of the Equinoxes in Sumerian cuneiform records.**

**In Sumeria, mathematics was based on a sexagesimal system (60s) with a decimal substrate (10s). The Sumerian**

*sar*was based on multiples of 36, 360, 3600; it was known as the number of the Universe (36 x 10 = 360). Imagine a circle for space of 360 degrees x 60 minutes x 60 seconds = 1,296,000 seconds.**The real key to this system involves the sequence in which prime numbers naturally occur in the base-10 continuum:**

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

**The precessional number, 25920, can also be arrived at by 432 x 60 = 25920, employing the Sumerian sexagesimal system.**

**This number relates directly to ancient Hindu cosmology and divine time measurement as the Ages and**

*Yugas.*Their numbers (without the cosmological zeros) include 432, 864, 1296, 1728, 4320 for the*Yugas*, and 648, 1296,*1944, 2592, 6480*for the Ages.*Both Ages and**Yugas*share the number 1296 (362).

*The Hindu systems are based on multiples of #108 (3 x 36), the divine numberword OM, also known as the number of the Universe. The Yugas and Ages can also be generated on multiples of 36. Multiply by 12, 24, 36, and 48 for the Yugas; and 18, 36, 54, and 72 for the Ages.***12960 (half the Precessional cycle) is a numerical basis for astronomical measures and played a role in Plato's mystic symbolism: 12 x 2160 (Platonic Month) = 25920 (Platonic Year).**

**In all cases, the historical precedent for this system comes from Sumeria, and its ancient cosmology inspired by horizon-based astronomy. These numbers and their importance come from direct observation of the precessional cycle and orbital times of the planets.**

**Ancient India raised mathematics and astronomy to a fine art. In medieval times, it gave the west its system of so-called Arabic numerals, the base-10 system, place value, and the zero, and created a Renaissance in art and science. It is within this system of mathematical notation that the +4, -4 basewave inherent in the continuum can most easily be seen through the mechanism of palindromes and transpalindromes.**

**SYNDEX I identifies and demonstrates the various properties of the base-10 number field, such as the symmetrical distribution of prime numbers. The continuum can be viewed as both progressive and regressive, or self-reflexive. The key to the comprehensive analysis of general number behavior is found in the concept of "circular unity." The graphic importance of the Holotomic Sequence is that circular symmetry is being conserved and may be enlisted as the fundamental reference key in the graphic investigations of number behavior.**

**The primes are deployed in symmetrical interface only within these specific Holotomic domains.**

**Synchrographics regards symmetry as a primary analytical reference, making the Syndex archetypal system of number classes possible. The foundation of this system is palindromes and transpalindromes, yielding 12 classes of number. Palindromes, or binomial reflection numbers are neither purely accidental nor without significance.**

**Transpalindromes are the reversal of any particular number exceeding a single digit.**

**Numeronomy, the laws relating to the essential structure and dynamics of number, is a new word for an extremely ancient science. This science, (based on the knowledge that the continuum contains a definite structural order with general laws that describe the nature of that order), has laws that relate to the general behavior of nature itself. Each number has both a geometrical and numerical identity. The outcome of Synchrographics is that numbers speak for themselves through structure and synergetic behavior.**

**All**

**Syndex mandalogs (number wheels) are the product of the systematic generation of the exact sequence of minimax factorization. They have the perfect retrograde feature by which the patterns generated in the first half of the spiral are reversed at midpoint and are reflected as a mirrored image in the second half of the spiral. Revisioning the number continuum with the concept of simultaneous counterflow yields a more accurate picture. This revisioning is also happening in post-quantum physics under the rubric of**

__quantum backflow.__**With large spans of numbers, the complex interrelationships become difficult to visualize without good graphics.**

**Because of the octave nature of the base cycle, there cannot be more than four consecutive transpalindromic pairs in a single symmetrical sequence, regardless of the amount of digits in each individual number. The Holotomic Sequence consists of a series of key numbers or circular unities in the rhythmic wave.**

__Buckminster Fuller__was very excited and "filled with joy" over these revelations, when the Syndex discoveries were shared with him before his death. He wanted to publish them in a subsequent edition of__Sy__*nergetics**.*And why not, since they shed light on old enigmas. After all, numbers are what they are, not what we wish them to be. They will not do what they cannot do, i.e. show symmetries where none exist.**SYNDEX II is about the process of discovering synergetic, rhythmic symmetries on a graphic enspiralment called Synchrograph C. It is based on the Hindu number of the Universe, 108. 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 Holotomic Sequence, created by prime number multiplexing, and the exemplary 9/11 wave cycle (a +4, -4 base wave).**

**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. On this graph the four-digit palindromic sequence (1881, 2772, 3663, 4554) appears in quadratic array, where only chaos exists in classical number theory.**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 the 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 number wheel 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, using its accepted, formalized rules.**

**On rare occasions graphical architecture combines with the data content to yield a uniquely spectacular graphic. Such entities can be described and admired but there are no compositional principles on how to create that one wonderful graphic in a million.**

**The ultimate Platonic ideal was that of Beauty. The most beautiful graphics do not traffic with the trivial. Graphical elegance is often found in simplicity of design and complexity of data. Visually attractive graphics also gather their power for content and interpretations beyond the immediate display of some numbers. The best graphics are about the useful and important, about life and death, about the universe.**

SYNDEX 2: number mysticism and alphanumeric writing; cosmic cycles of creation and destruction (

*Yugas*and Ages); ancient Hindu mathematics & astronomy; mandalog #108; the Sumerian legacy; models of sacred space; milestones in the evolution of the number concept; Syndex number theory; metrology; cosmography.

**http://syndex2.iwarp.com/**

**http://syndex1.iwarp.com/**

**http://ionamiller.iwarp.com**

SYNCHROGRAPHICS & THE AURIC KEY

SYNCHROGRAPHICS & THE AURIC KEY

**--***"Beauty--art is largely a matter of the unification of contrasts. Variety is essential to the concept of beauty. The supreme beauty, the height of finite art, is the drama of the unification of the vastness of the cosmic extremes of Creator and creature."***Author Unknown****That which we call Truth, or Reality is metaphysically dependent on whose truth and which reality. Quantitative notation and geometry are the conceptual tools by which we formulate our standard of physical description and dialogue, i.e. systematic science.****The first concern of synchrographics is maximum information expressed via minimal graphic elements. Correspondences, such as those between geometry, number, and color, and frequency of divisibility form an integral part of the system.****There is some agreement among astro-archaeological historians that the earliest evidence of technological civilization is a mere 6000 years old. The author is concerned here with the original metrological formula (founded upon measurements of the earth and precession of the equinoxes). Our present technological situation is founded on these systems of measurement and their geodesic bases..****Reflecting on his thirty year study of the synergetic interaction of number and geometry via synchrographics, Marshall (as author of the Auric Key) realized that the system of number regard he had investigated for half his lifetime produced the exact same system of metrology that had initiated and proliferated industrial technology, during the historical era.****THE AURIC KEY is the rediscovery of the original program of the alphanumeric system of notation and the fundamental platform of general science.****Whether the Auric Key is of local or extraterrestrial origin (as Zecharia Sitchen might argue for Mesopotamian number wisdom and astronomical knowledge), is open for further inquiry. Radical discoveries are a source of continual reevaluation of historical opinion.****The Auric Key is a remedy for verbal deficiency in describing how a cyclic base evolves to cyclic accumulation of quantitative notation, in a +4, -4 octave wavecycle.****The scientifically systematic principle which synchrographics rests upon is of such simplistic design that we cannot help but wonder why such an obvious psychological tool was not used through the centuries for teaching. All of the individual elements that comprise this discipline were well known from deepest antiquity.****What we call numbers are a continuum of a finite set of graphic signs which form a cycle which is determined by the quantitative amount of the base set or primary individual signs. Inasmuch as neither zero nor one are numbers in themselves divisible, that which we call baseten is actually an octave set of actual numbers (members). Pythagoras also did not consider the duad (dyad) a true number.****In regards to the cyclation of number, only an octave can progress in what would be termed an exemplary cycle or a cycle that may progress in an unbroken compounding of cycles. The exemplary wave is an escalation of null event lapping of each cycle to the next.****In our usual regard of the base ten number we see the addition of each digit as the point at which the cycle begins anew.****It is at this very point where serious confusion occurs in that this "point" is being counted as a member. It is merely a position upon which the cycle revolves and therefore may not be included in any terminal tally of quantitative magnitudes, i.e. 100 equals 99.****R. Buckminster Fuller treated this problem by calling base ten an octave with a ninth null event. The null event was regarded as nine being the proxy of the one that he counted as a legitimate number.****I show this octave cycle in a very different way: when one considers the multiples of nine and disregards the initial none, the octave cyclation becomes quite clear:****Between 45 and 54 a reversal occurs and the four following multiples are retrograde companions of the prior four multiples, i.e. four forward and four reverse event octaves.****This shows that base ten is actually base eight, an octave loop.****In view of the foregoing, the nave or turnaround point of the octave is at 49.5. It is NOT 50, as claimed by Fuller, and never subsequently corrected in SYNERGETICS III, as he would have liked.****The symmetrical perfection of synchrographics results from the expedient of reversing the octave between numbers, instead of upon a number. Turnaround is at 50, between 49 and 50.****THE AURIC KEY****2520 is the first and lowest numerical sum which is divisible by all eight basic numbers.****By the simple expedient of de-strapolation by the first 4 prime numbers, we discover the Holotomic Sequence:****2520 - 7 = 360 - 5 = 72 - 3 = 24 - 2 = 12**

E D C B AE D C B A

**By extrapolation of the Zodiac (#12) by the prime numbers in their natural order of appearance, we produce the sequence of discrete quantities that are the minimal sums to accommodate the maximum amount of consecutive factors of division.****This presents the maximum data in a graphic context with minimum elements of informational referencia.****Each subsequent Holotome retains all of the data of its father plus one added degree of data content, retaining coherency of the interrelationships existing in and between the members of the primary series.****This natural system of coherent number behavior/structure was know to those who programmed the infrastructure of the Sumerian culture 6000+ years ago.****The most direct association of the work of Zecharia Sitchin and the Auric Key is his notation (translated from cuneiform) of the Sumerian knowledge of the exact duration of the precession of the equinoxes as only recently confirmed by state-of-the-art astronomical tooling. It indicates a source in prehistory for all the key numbers of the Auric Key: 72 (C) x 360 (D) = 25920**

**Prelude to Terms and Proceedures of the Auric Key****The term AURIC KEY, chosen for the prefix AU which in Latin forms the word audio as in sound, while in Greek forms the word aura as in light, suggests the relationship between the eyes and the ears or seeing and hearing. It also derives from***aurum*, or gold, implying a golden key.**The term Numeronomy derives from a concept requiring a trifle more explanation: as a term of scientific validity, it refers to the interdependence of geometrical and numerical notation, neither of which could produce valid equations without the existence of each other.****These two disciplines, quantitative notation and qualitative notation are in essence two sides of the same coin. The first Pythagorean rectangle, 3 measures by 4 measures, produces a hypotenus (diagonal) of 5 measures which affirms a synchronicity of the quantities 3, 4, and 5 with the quality of rectangularity, which in effect produces a synchronetic unity of number and geometry.****3 + 4 + 5 produces the quantity of twelveness, which is so fundamamental in Syndex Theory, as Holotome A. There are many ways to describe the synchronetic quality of a circle divided into 12 thirty degree sectors. For the purpose at hand, we prefer to draw attention to a square divided into a grid of sixteen subsquares which when enclosing a circle of 12 thirty degree sectors shows the grid lines intersecting the circle at exactly thirty degree intervals.****Sequence of Discovery****The semi-arbitrary answer to the question of why some unknown and ancient geometer selected 360 degrees for equating a circle has been that 360 has more than the usual amount of divisors for its size. This is far from a complete, specific, and logical answer.****As a matter of fact 360 is divisible by all base digits except prime number seven and when we multiply 360 by prime number seven, we produce 2520 which is the first and lowest number divisible by all base digits.****This odd result might make us stop and think:****Since by multiplying 2520 by the next prime we receive another palindrome followed by a zero, i.e. 27720, we naturally decide to destrapolate this sequence to see where it begins:****27720 - 11 = 2520 - 7 =360 - 5 = 72 - 3 = 24 - 2 = 12****Since these are the exactly most often cited numbers of ancient metrology, we have arguably discovered the long lost key to the basis of ancient metrology or numeronomy.****To amplify this claim, we have only to note that 12, 24, 72, 360, 2520, 27720, etc. are the exact sequence of minimal sums that accomodate the maximum amount of consecutive divisors (factors of division). Because to my knowledge, no one else has discovered the complete and rational answer to the selection of 360 degree circular unity, I claimed the right to entitle this the Holotomic Sequence.****In the Holotomes and Holotomic Sequence we see that the more-than-the-sum-of-its- parts quality of natural numbers emerges. They reveal the higher complexity integrity of the newly emerging system. This complexity system preserves in its integrity-memory a complete history of self-organizational instruction. Its success and longevity can be anticipated by the great degree of economy which it expresses with the least of resources.****In synergetics, the components and aspects of synergy do not work separately, but function together as a single systemic event: The Auric Key. Thus, the Auric Key functions as quasi-intelligence informing rational number; this holonomic instruction gives any system its inherent intelligence to find its place and function in continued self-organization of its evolution.****Shortly after this revolutionary observation, I realized that #6 is exactly half of the first true Holotome. This makes the first perfect number the nave of Holotome A (i.e. 12).****The complete role of geometry and numbers in our grasp of reality and nature has been for centuries only partially acknowledged. A comprehensive system that coherently reveals the transdisciplinary relationships between music, ancient pyramids, esoteric numerology, astronomy, chemistry, physics, and architecture has until recently remained virtually ignored.****Marshall's vision provides the basis for a common vision: a key that unlocks conceptual doors and enables us to regain the vantage point our ancient ancestors presumably once possessed.**

**The Structure of Number****The Auric Key excavates many vital properties of numbers. The frequency of synchronicity is any whole number factor and factors of divisibility within the limiting range determined by the base digits. One (1 = singularity) is regarded as a special case.****Number One is an indivisible integrity. Singularity is operationally irreversible. Number Two is an affinity-evolvable informational duality; self-generated reciprocity.****In our investigation of the creation of matter during the birth of the Universe, we have begun at singularity. While at singularity, the point of integrity has no physical dimension, it has metaphysical dimension and content of potentiality. In other words, we can consider potentiality as the content of integrity-singularity in the metaphysical dimension once-removed from physical reality.****The number field is holonomic, containing all things, encoded in the simplest and purest metaphysical pattern of informational potentiality. Numbers are a projection of evolving, expanding potentiality. We can go backwards toward the point of integrity/singularity into the evolution of its potentiality, which has no physical properties, but which is a seed potential. This is relatively easy to illustrate with tetrahedronal geometry.****Singularity is irreversible. The sign, [***insert symbol]*, represents a reflectional transaction, or the reversing of a function that passes through the infinitesimal, yet omnipervasive site between every numerically relative symbolic event. In the empirical sense, it means the inversion or reversal of the image; that transaction which occurs to images reflected from a mirror or the surface of a dark pool of still water.**In respect to the behavior of numbers, we know that reversal is a basic element to any system employing zero as a null state between plus and minus, for plus and minus are essentially the opposite or reversal of each other.****, then, is the zero with an extra quality decreed by Syndex routine. That quality is the direction of positive quantitude. For even though zero is void of quantity itself, it still contains which way the quantity/unquality is relayed through its situation. That is, where zero is merely a location, is a situation for it incorporates direction.****Thus, as a mathematical entity, (incorporates and) involves aspects of number structure that are otherwise not considered by the classical definition of the zero expression.****Our usual regard for one (1) as a number also creates a logical omission. This is likewise considered in the use of the Syndex character .****Two (2), then, is the minimum element of reflectivity for each side (site); it is the essential twin as it can be divided and multiplied by itself, whereas one (1) cannot.****Example: 2 x 2 = 4**

1 x 1 = 11 x 1 = 1

**Meaning plus two (2) is the first full positive, divisible and multiplicable unit and minus two (2), its reverse mate.****In view of the foregoing considerations, we must allow that singularity is not reversible and polarity (2) is the minimum experience of numericity.****Thus, frequency is the amount of base digits that evenly divide any given number, (1 excluded). Synchronicity is the specific combination (array) of base digits that dictate the frequency. The higher the frequency, the greater the universality of the number. The term "fold" indicates the specific incidence of divisibility.****On the right hand side of the composite graph is a coded strip that shows visually the frequency of synchronicity of numbers 2 through 144. To the right of the number column are the eight color-coded tracks isolating the synchronicity of these numbers. For example, the number 72 is evenly divisible by 2, 3, 4, 6, 8, and 9. It thus has a six-fold frequency of synchronicity and has six white spaces to its right in the corresponding number tracks, which start at the base of the coded grid.****Note that since every other number is evenly divisible by 2, there is a white space in every other position in the 2 (red) track. The same principle applies to subsequent tracks; there is a white space every third position in the three (orange) track, etc. The term "null frequency" is used in conjunction with the incomplete concept of a prime number.****The colors chosen to represent the right frequencies are of two kinds: chromatic and metallic. The first six refer to the natural chromatic spectrum, while the seventh and eighth refer to the metallic colors of silver and gold. One, (singularity, not an operational number at all), is white and has no set frequency since it is a special case. It can, in fact, be said to occupy all positions.****To the immediate left of each number on the column is a corresponding horizontal tag that is coded to show the frequency of that particular number. The frequency of numbers is regarded essentially as their degree of primeness and..."non-primeness." A null-frequency number, 23 is designated with a black bar to its left (11, 13, 23, 97, 121, 137) and generally those numbers classically referred to as prime. Notice that 121 is not prime, as such, being divisible by 11.****There is a crucial distinction between the null frequency and the prime, one of conceptual essence. By standard definition, a prime number is divisible evenly by itself and one only. On the other hand, a null frequency number is divisible evenly by itself, one, and a limited set of primes that exceed the range of the base digits.****To the left of the strip is a series of horizontal bars whose color and length correspond to the frequency of a given number. A mono-frequency number is designated with a red bar to its left, a two-fold orange, three-fold yellow, four green, five blue, six violet, seven silver, and eight gold. All of the primes collectively constitute a subset of null frequency numbers, where the set of "nulls" is determined by the base.****The higher the base, the closer the set of nulls is to becoming identical with the set of primes, though they never totally coincide. In this context, the Auric Key shows the spectral relationship between high and low frequency numbers, and between null frequency and prime numbers. This eliminates a deeply rooted "either /or " dichotomy prevalent in the current notion of prime numbers, and basic assumptions regarding (or disregarding) the structure of number.****The first number that is evenly divisible by all nine base digits is 2520. This is the auric (golden) node (knot) that ties ancient wisdom with modern data. The pyramids, standing stones of Stonehenge and calendars of the Mayan and Egyptian civilizations are with us no less than our personal computers and atomic clocks.****2520 is exactly twice the number 1260, a number referred to cabalistically five times in the Book of Revelations (12:6 and 12:4). It is half of the number 5040, which figures prominently in Plato's "Laws" regarding the architectural implications of his ideal city-state (and/or Atlantis).****These and other key sacred numbers (identified with intervals along the coded strip) reveal the unifying elements of the major religions. They frequently recur throughout diverse sacred literature, music and architecture. Stonehenge is a very special example containing a comprehensive collection of these special numerical ratios in a supereconomic context. All convey similar information that relates words with numbers, and numbers with the operation of the cosmos. Another example of this is the Hebrew Qabala.****The specially coveted numbers of each religion are crucial to the understanding of their esoteric teachings. They come from a time when guild secrets were defended to the death. More important, however, is the perception of the matrix from which they derive, the OMNIT.****If we spiral the nine tracks forming the coded strip, (extended to 2520), into seven bands of 360 places each, signficant patterns inherent in numeric structure are clearly revealed. This is the prime form and function of Synchrograph A (Holotome E, 2520), the prime reference key to the lost doctrines of the neolithic and pre-classical eras.****The synchrograph A shows a split pentacle in the center. It is an extended translation of the coded strip in that each of the 360 places of each band (rotation) are designated with color where there would be voids in the coded strip. In spiraling the coded strip, both the coded number column and frequency codification were deleted.****Notice that at the midpoint of 1260, the configuration of digital formation begins to reverse, or mirror itself until it is perfected at 2520, the last number of the seventh band, and the first omnit of the base ten system. This, in addition to 2520 being the exact product of 360 and 7, strongly indicates that the selection of 360 by ancient geometers and metrologists as a basic circular system of reference was neither arbitrary nor the result of bad astronomy, as some have suggested.****The nine tracks, which the numbers make as they spiral outward in the synchrograph, form a pattern that visibly divides itself into twelve sections (termed synchrostats) of 210 numbers each (indicative of the criteria of 12 zodiacal signs). Common to the synchrostats is that they alone are divisible by 5, 6, and 7 (see chart regarding these) and these numbers are at the core of the twelveness that informed the ancient world of law, religion, commerce, etc.****When Fuller saw the hexagonal court at Baalbek, he remarked that the ancient Phoenicians had recognized his principles of tetrahedral synergetics.****Relationships with astrology (planets whose position lie in "trine," "square," "opposition," etc.) and chemistry are shown by meditation on the auric key. Spiralling the chemical elements of the periodic table shows some interesting groupings. A version of this table is included in the composite graph. (insert THE CHEMISTRY PAGE).****Many common spacetime measurements (Metrology) that people take for granted, such as the division of space into miles, feet and inches, and time into hours, minutes and seconds, derive from unknown antiquity. Yet these unite into place within the seven-banded spiral, creating a symmetrical and satisfying sense of harmony.****To elucidate, when the second band ending number is added to 144, 864 is derived. Odd, indeed, that there are 86,400 seconds in a day and that the current astronomical measurment of the sun's diameter is 864,000 miles! 2160, the sixth band ending number, has long been taken to denote an "age of years," i.e. the Age of Aquarius, Pisces, etc., and is likewise close measurement of the moon's diameter in miles. Thus, space and time become equilibrated in a most mysterious, yet pleasing, fashion.****The Auric Key reveals discrete levels of finitude, a series of holistic, circular unities within the number field. Infinity, an often misunderstood word, cannot be classified. Lord Bertrand Russel pointed out the great paradox of analytical systems when he said:***"That class which includes all classes cannot be considered a class inasmuch as it is the only member."***As a compliment alternative to infinity, the Auric Key points to the omnisynchronistic module, a crucial concept dealing with the expansive limitations of any finite quantitative system. It can briefly be defined as the number that accomodates (synchronizes) the maximum amount of consecutive numbers from one onward possible. It is thus the most universal number of all (a common denominator to all real numbers). There are larger numbers, but none with as high a factor of divisibility.****So, to repeat, the Auric Key shows relationships of finite, discrete levels of relationship as they are signified by numbers. Synergetics prefers the maximum information containment with the greatest economy of terms, and the Auric Key fills this requirement.**

**The Study of Synchrographics****Synchrographics emerged from the notion that geometry and numbers are interwoven disciplines emerging from a mysterious but unified source. By isolating basic relations between number and geometry something may be learned about that source.****Holotome E (2520) may be considered the cornerstone to the various mandalogs that comprise the Auric Key and reveals the pattern of compound synchronicities that occur in behavior of the base digits in all their permutations, which end at 2520. It begins near the center and spirals outwards, a process which reveals even more inherent symmetry and produces tantalizing rays. There are seven spiral bands, each divided into 360 subsections.****The conceptual discipline of synchrographics is both simple and complex. The many levels of graphing the relationships that exist between interdependent events and functions are possible.****A simple biaxial grid consisting of vertical and horizontal rows qualifies as a synchrograph of the initial order. Gregor Johann Mendel is noted as employing this graphic technique, extensively in his botanical investigations concerning hereditary transmission, which actually layed the groundwork for the modern scientific theory of heredity. This work formed the first step to the DNA logistic.****What might be called the second order of synchrographics consists of a TRIAXIAL GRID or radial/axial configuration of three axes of interreference. This mode consists of a finite 360 degree radial quantum (Circular Unity). We cover it fully in PART FOUR as its own chapter.****Here it is enough to say that it is a finite axial extension that represents an ambidirectional continuum of reference. It is a tridirectional continuum in the form of an ambidirectional or counter-spiral that formulates the triaxial web of interdependent geometry of data which is otherwise referred to as the sunflower matrix, which encodes 618034.****( insert GRAPHIC OF SUNFLOWER)****By the simple addition of spiralic axes all of which share a whole number comensurate synchronicity, we explicate the full band continuum of synchrographics, in two dimensions.****The present investigations (of Neil Sloane at Bell Labs) that deal with the ideal distribution of points on the surface of a sphere is an intuitively misguided idea. His idea of multiplexing axes of interreference with the intention of creating additional axes of rational interaction only serves to protect intelligence by antiquated Euclidean absurdities based purely on Greek mythography.****A serious review of SYNERGETICS II shows that Fuller clearly discredits the idea of perfection of the sphere. Fuller has clearly demonstrated through various expressions of geodesic rationality that Nature does not provide us with even one example of a perfect sphere. The only exception is the idea of a perfect circle or sphere suggested by Plato.****Let us examine the seemingly perfect glassine soap bubble in terms of the surface "skin" on a coloidal level. Since triangular deployment of coloids cannot closepack on a curved surface only on a surface that is flat, our perfect bubble will by nature of space be a geodesic deployment of hexagons and pentagons .****In view of this, and Fuller's "twelve universal degrees of freedom" (which determine the perfect interaction of triangle-square interface of the dodecahedron and Vector Equilibrium Matrix.) we are forced by the laws of number/geometry to disregard ideal sphericity on any cosmic level other than imagination.****So quasi-sphericity is what we and nature have to deal with. Since we can deal with that in terms of quantitative notation, which does not and will not lie, we have what is required of super science. Some might contend that such science is a religion.**

**THE AURIC KEY****(A Poemgraph on the Nature of Number)****All SYNDEX mandalogs (or number wheels) are instrumental in the description of a system of number regard that is here termed Numeronomy. Links in ancient texts, sacred geometry, architecture, and the use of precessional “divine” numbers indicate that the use of such a system may have been known in ancient times, perhaps even before the dawn of written history in Sumeria. After all, mankind had already been surveying the heavens for some 50,000 years.****Syndex reveals the nature of number, which nature reveals so beautifully in the synergetic structure of the natural world, which is based on the tetrahedron as the minimal structural form in nature and the Universe.****The primary tool of inquiry into this system is the synchrograph or mandalog. Mandalogs are composed of the graphic enspiralment of numbers about circles divided into differing axial allotments. A few discrete examples of the synchrograph have been selected as the most prolific in exhibiting special data arrays displaying the geometrical nature of number. Primary among these number wheels are the spiral of 2520, known as the Auric Key; and the spiral wheel of 108, the Hindu number of the universe, the number of Om and the numerical basis of the Yugas and Ages. Scientific process depends upon numbers as legitimate tools regardless of what is recognized about their nature.****Synchrographics emerged from the notion that geometry and number are separate yet interwoven disciplines emerging from an essentially unified source. By isolating basic relations between them something may be learned about the nature of the source. Fuller discovered that, in synergetics, number is not an abstraction: each number has a geometrical identity as well as an inter-transformative numerical identity. This means that the number measurement of areas and volumes always comes out even, in whole rational numbers, without fractions or odd numbers left over.****Attending synchrographics is a formal discipline resulting from the requirement to simplify an otherwise too complex model. The model employs a color code index to redefine numbers graphically. Any given number has a “frequency of synchronicity” which is determined by how many of the base digits will evenly divide a given number. And this is color coded in the number wheels.****Synchrograph A (#2520) consists of a nine-banded spiral that progresses seven times around a disc divided into 360 axial increments. Each of these nine bands are coded to shown the occurance of a base digit which is assigned a color in the place of the numerical figure itself.****Thus, the first band, representing base digit two has a red space at every second position and the second band has an orange space at every third space, etc.**

**Red 2**

Orange 3

Yellow 4

Green 5

Blue 6

Iron/Violet 7

Copper 8

Silver 9

Gold SynchOrange 3

Yellow 4

Green 5

Blue 6

Iron/Violet 7

Copper 8

Silver 9

Gold Synch

**Once this color code is assimilated, one may easily refer to any number and visually determine the frequency of synchronicity of the numbers by merely noting how many spaces are filled with a color. If no space is filled then the number is null frequency and has a black label.****0 space = null frequency Black**

1 space = mono frequency Red

2 2 fold Orange

3 3 fold Yellow

4 4 fold Green

5 5 fold Blue

6 6 fold Violet/iron

7 7 fold Copper

8 8 fold Silver

9 9 fold Gold1 space = mono frequency Red

2 2 fold Orange

3 3 fold Yellow

4 4 fold Green

5 5 fold Blue

6 6 fold Violet/iron

7 7 fold Copper

8 8 fold Silver

9 9 fold Gold

Synchrograph A, 2520, ends at 2520 and has all nine spaces filled at that final station, completing a module of circular unity, a mandalog or holotome. Note that at 1260 (3 1/2 turns, or the auric nave) all spaces are filled except the one (number 8) and at this location the sequence reverses and begins to mirror itself.

Synchrograph A, 2520, ends at 2520 and has all nine spaces filled at that final station, completing a module of circular unity, a mandalog or holotome. Note that at 1260 (3 1/2 turns, or the auric nave) all spaces are filled except the one (number 8) and at this location the sequence reverses and begins to mirror itself.

**(insert color graphic of 2520)**

**Synchrograph B consists of enspiraling 108 labels around a circle divided into six axial stations. By regarding these labels as numbers, we find that the multiples of six always fall on the sixth spoke, but the multiples of five and seven fall into counter-rotational spirals that synchronize at 35, 70, and 105. By extrapolating beyond number 108, we find how these spirals will only synchronize with the number six spoke at 210.****This (210) is the first synchrostat, i.e. the first number divisible by 5, 6, and 7 (12 synchrostats comprise the auric node (12 x 210 + 2520). Or, if we regard the 108 labels as the chemical signs, we find that the inert gases alway lie in trine, as will the best electrical and thermal conductors, etc. In effect, this arrangement is symmetrically consistent in its graphic regard of chemical classification.**

**(insert color graphic of wheel 108)**

**Synchrograph C consists of enspiraling numbers around a circle divided into 108 axial positions for 60 turns - or to number 6480, an ancient Hindu divine number derived from the Precession of the Equinox. This mandalog, like synchrograph B has two counterrotating spirals. A red spiral denoting multiples of 105 (multiples of 35) and a green spiral that denotes multiples of 111 (multiple of 37) and the engulfing number 108, is the third multiple of number 36. It has been found that the red spiral and green spiral will not meet at the engulfing axis until number 279720 is reached. This number is the key to the hypersynchronetic series.**

279720 - 105 = 2664

108 = 2590

111 = 2520 Auric Node279720 - 105 = 2664

108 = 2590

111 = 2520 Auric Node

**279720 - 35 = 7992**

36 = 7770

37 = 756036 = 7770

37 = 7560

**279720 - 5 = 55944**

6 = 46620

7 = 399606 = 46620

7 = 39960

**Synchrograph D is a combination mandalog and synchrograph. Its configuration is result of comparing and analyzing the Stonehenge ground plan with the proven results of the synchrograph’s mechanism. Thus synchrograph D is a radial array of 56, keyed to the 56 “Aubrey Holes” at Stonehenge.****When numbers are enspiralled around 56 axial positions, we find that the synchrostats fall only in the perfect axial quadrants, or east, west, south and north.****(Stonehenge groundplan, annotated)****The Auric Key as an Outgrowth of Synchrographics****As discovered by Robert Marshall, the Auric Key began as a modern day effort to illustrate the unique symmetry of numbers themselves. The graphic "rituals" culminated in the synchrograph we now know as Holotome E (2520). In this graph every second square of the inmost spiral is highlighted, as compared to every third in the next, and fourth in the next, and so on.****Viewing the spirals additively (from inside outwards), the formation begins at one and continues until a number is reached where an additional track synchronizes, producing a number of higher frequency than any previous one.****For example, three tracks synchronize at #6, four tracks at 12, 5, and 24, and six tracks synchronize at 72. Close inspection of these positions, called synchrostats, show a reflective pattern that pivots at half the number being considered. These numbers already cited are, in fact called Holotomes. The only exception is the first, 6, which is the nave of the first Holotome (A).****The next synchrograph (Holotome F: 27720) has an 11 band spiral divided into 2520 sections. The pattern then perfects at 27720, a binomially reflective number which is the next Holotome after 2520. This pattern could be despiralated and extended vertically, but in so doing it would stretch to more than thirty feet! This shows the usefulness and economy of Synchrographics, which condenses otherwise extensive patterns while having other obvious advantages over row and column configurations.****As an alternate to infinity, the Auric Key points to the omni-synchronistic module. It depicts a crucial concept dealing with the expansive limitations of any finite quantitative system. It can be briefly defined as the number with the greatest amount of consecutive divisors from one onward and is the most "universal" number of all.****The omni-synchrononistic module is a web of relationships that exist in the first 28 Holotomes. A compounding of the relationships that occur, for instance in Holotome E (which deals with the permutation possible with the eight base digits), is shown by the fact that 2520 is the smallest number divisible by all eight base digits. The number 2520 is a common denominator of several religio-mathematical systems.**

**The following is a list of historically important numbers prevalent in the Auric Key:****5040 - found in Plato's "Laws" describing the dimensions of his ideal city/state.**

1260 - referred to five times in the Book of Revelations and prevalent in ancient music theory.

360 - the number of degrees in a circle; 360 x 7 = 25201260 - referred to five times in the Book of Revelations and prevalent in ancient music theory.

360 - the number of degrees in a circle; 360 x 7 = 2520

**60 - basis of the Babylonian number system; is evenly divisible by 2, 3, 4, 5, and 6.****12 - the twelve signs of the Zodiac, months in the years, hours on the clockface, etc.****The Auric Key unites these seemingly disparate entities under a single graphic theory.**

In a letter to Robert Marshall, Buckminster Fuller comments on Plato's use of the number 2520:

In a letter to Robert Marshall, Buckminster Fuller comments on Plato's use of the number 2520:

*"Plato does not say why he is concerned with the number 2520, but it is easy to discover as the product of the conventional 360 degrees of a circle being multiplied by the prime number seven, the circle's 360 degrees having included the first three primes to wit, two, three, and five, wherefore omission of the seven in the inherenly octaved Pythagorean physical demonstrations of musical note progressing of tensed strings rendered inherently all irrational. The cyclic calculating referenced to the Babylonianaly adopted 360 degrees as the comprehensive quotient of nature's cyclic behaviors..."*

Also prevalent in the Auric Key is the number 56. The architecture of Stonehenge is based on a circle divided into 56 sections. 56 x 45 = 2520, and 45 and 56 appear in the exact middle of a list of the factors of 2520 (Holotome E).Also prevalent in the Auric Key is the number 56. The architecture of Stonehenge is based on a circle divided into 56 sections. 56 x 45 = 2520, and 45 and 56 appear in the exact middle of a list of the factors of 2520 (Holotome E).

**Could it be that those unknown architects who built Stonehenge used 56 as a practical reduction from an ideal circle of 2520 subsections? The relationship between the Auric Key and Stonehenge does not appear to be coincidental. That Stonehenge probably served as a gauge of celestial phenomenon is well known.****But is there yet another element pertaining to this megalithic structure? Because of its ruined state, it is difficult to know what the exact dimensions of Stonehenge were when it was built. As a result, different theories have arisen as to its possible uses. The discrepancies in its dimensions allow for varying interpretations. Questions arise as to just how precise a celestial gauge Stonehenge was. Its configuration has an elegance which rules out its inadvertent construction.****In light of Synchrographics, Marshall has propounded a basic theory which states essentially that Stonehenge was a device for optimally expressing several mathematical relationships, as such.****The distinct possibility exists that the Stonehenge architects purposely sacrificed a certain degree of accuracy in describing specific phenomena, in order to accommodate the expression of several unique phenomena and relationships. Were this the case, and there is supporting evidence, then the Stonehenge architects were concerned as is Synchrographics, with the optimum expression of information within a given confine.****The geometry of Stonehenge consists of whole numbers. The description of nature and the cosmos in terms of whole numbers was a concern not only of the Stonehenge builders and Pythagoras and his followers. Syndex has rediscovered a comprehensive system which shows numbers as they truly appear in nature, apart from our useful but somewhat arbitrary mathematical practices.****SYNERGETICS, the revolutionary system of mathematics, formulated by the late Buckminster Fuller, emerges directly from the geometry and numbers employed by nature. Fuller contends that nature uses only whole rational numbers, and his geodesic modelling never requires resorting to irrational, unresolvable sums, such as pi. Synergetics deals only with experientially demonstrable phenomena.***"Synergetics uses simple geometrical models based on a few basic modules that fit together in the most logical possible ways. Synergetics uses whole numbers, completely eliminating all irrational, imaginary, and irresolvable numbers and complex formulae...Synergetics, alone among general systems theories, models Universe using only frequency and angle."***After Marshall's conception of Synchrographics, certain interesting correlations arose between these two disciplines.****One common feature of both systems is the definition of large multi-divisible numbers. These include the super-Scheherazade number of Synergetics and the omni-synchronistic module of Synchrographics.****In reference to numerical structure, and particularly to the super-Scheherazade number, Fuller states:****"There is a basic wave running through the second powering of all number up to 50 and returning to zero. The wave series is 24 integers long. I'm confident that the circle consisting of the 71 integer number****616,494,535,0,868,49,2,48,0,51,88,27,49,49,00,6996,185,494,27,898,13,35,17,0,25,22,73,66,0,**

864,000,000864,000,000

**is the number employed by universe as the comprehensive circular unity by virtue of which all interoperation of all numbers will always come out in whole rational results."****Elsewhere (Cosmography, 1992), Fuller tells us that this number can be used as the number of divisions of circular unity.****"This number embraces a minimum n number of all the prime numbers involved in evolving all trigonometric functions and all the surface and volumetric spherical system intertransformings of synergetics."****Multiplying the fourth, fifth, and sixth prime numbers-- 7, 11, 13, which superstition labelled "bad-luck" numbers--produces the 1001 Nights.****As Dr. Fuller suggests, the occurrence of a basic wave is significant. It shows that despite their discrete nature numbers-as-integers have wave-like properties. Not only is there a basic wave running through the second powering of numbers, but there is an abundance of waves occurring on all levels of numbers. The super-Scheherazade number in it's finite aspect shares identical properties with the Holotomes previously described. What they share precisely is that both represent discrete levels of finitude.****As previously stated, Bertrand Russell spoke of the paradox of referring to infinity:***"That class which includes all classes cannot be considered a class inasmuch as it is the only member."***The omni-synchronistic module helps resolve this deeply embedded paradox. It allows us to graphically, and directly perceive the number behavior of the universe.****As Dr. Fuller continues in a letter to Marshall,***"Nature is always operating in her own modular system of four progressively additive then progressively subtractive event octaves, with a ninth null event altogether constituting an octave nine system, all of which relate physically to two, four-vertexed each tetrahedra, as the tuned in tuned out, minimal structural experience of universe."***To understand this more thoroughly, bear in mind that the tetrahedron is a solid made up of four equilateral triangle faces. It contains the least amount of volume per unit of surface area and is considered by Fuller to be the basic building block of universe.****The Auric Key excavates many vital properties of numbers. It's very existence and ultimate form hinges on numbers which occupy space. By arranging numbers in synchrographs, a number matrix or field is formed. Regarding numbers in terms of matrices and fields is important, and acknowledging that numbers have spatial qualities is vital to fully appreciate their significance.****Each track in a synchrograph depicts the occurrence of certain events, i.e. the dividing of any given number by specific base digits. These events are not causally related to each other; the repetitious patterns of each track occur independently of each other. Nonetheless, important relations between them occur. Synchronicity as herein described stems from a numerical context. However, it closely parallels synchronicity as first propounded by the late Dr. Carl Jung, an acausal connecting principle.****Jung sought to account for people's collective behavior and perceptions which could neither be explained by causation or purposivism. Causation explains behaviors as caused by past events, while purposivism explains behavior as determined by seeking future goals.****To these Jung added a third principle called synchronicty for explaining those events which occur together in time, but do not cause each other. They are events which are nonetheless related. Jung realized the physical significance of synchronicity and concurrently renowned physicist Wolfgang Pauli was developing comparable ideas in his theories. In the mid fifties, they collaborated in an effort to describe their mutual concept of synchronicity.****In light of their results, and in light of the specific nature of synchronicity we describe, it appears that the Auric Key constitutes a precise mathematical model of synchronicity, as described by Jung and Pauli. Their work together centered around finding a unified view of psyche and matter.****A desirable feature of synchrographics in general is that their very configuration allows one to cognize several different patterns and relationships concurrently if not simultaneously.****This is conducive to a far greater understanding of numbers and their over-all implications. By spiraling the periodic table into differing axes forming synchrographs, specific relationships between the various elements are accentuated. For example, the inert gases will lie only in trine or opposition to each other. This has precedent in modern chemistry and shows another application of synchrographics.****Prime numbers play a vital role in the construction of geometric forms, and in turn of structures. These structures range from the microscopic to the macroscopic. They comprise our physical reality. In classical mathematics, the order of prime number occurrence is submerged by the orderly progression of cyclical nine and predictable squares.****Here again is the classical example of how context determines coherency. The way we have been looking at numbers has scrambled our vision of how they ultimately behave. In the graphic rituals of Syndex numeronomy, the order of prime number distribution is for the first time described in an intelligent manner.****The frequency of numbers is essentially their degree of "primeness" or "non-primeness" with respect to the base numbers. The true set of primes is a subset of the "nulls" where the set of nulls is determined by the amount of columns under consideration (base numbers).****In this context, the frequency graph shows the spectral relationship between high and low frequency numbers such as 2520 and 26 respectively. This extends beyond a deeply rooted "either/or" dichotomy prevalent in the current notions of number and basic assumptions regarding (or disregarding) the structure of number.****The myriad implicit patterns in the synchrographic rituals are staggering. Chief among them is the perfectly symmetrical arrangement of marked squares which occurs regardless of how many columns are considered. Halfway between zero and every holotome is a mirror; a location where every marked position on one side is replicated on the other, only reversed; an exact reflection.****For example, Holotome A is evenly divisible by the base digits 2, 3, 4, and 6. Notice how this elegantly simple pattern progresses to the mid-point (or nave) at 6, and is perfected at 12. This general pattern recurs throughout all of the true holotomes, which are all divisible by 12.****In fact, Holotome E, at its mid-point of 1260, symmetrically reverses direction and is perfected at 2520. It is divided into 12 synchrostats. The number 210 happens to be the lowest number divisible by 5, 6, and 7, and 5 x 6 x 7 = 210. This symmetry reveals the structure of number, which in it's utter simplicity and clarity can serve as a valuable and stimulating educational aid in mathematics.****Synchrographics can also be explained in terms of Modulo Functions, which have widespread application in computer science. Readers familiar with the modulo (MOD) function will notice that each track is counting in MOD X, where X is the number associated with that track. Since even divisibility is what is being stressed, highlighting those segments of the track which correspond to a zero remainder (or modulo result) displays the juxtaposition of even divisibility.****To be sure, holotomes are simple mathematical entities, for 2520 is nothing more than the smallest number to be evenly divisible by all base digits. To the ancients, numbers such as 60 and 2520 possessed seemingly mystical abilities to describe the exact order and limits of their universe. Perhaps the Auric Key will help us appreciate more the role of astrology, numerology, etc. as the evolutionary predecessors to our contemporary science and mathematics.****The highlighted tracks in the Auric Key can be translated into corresponding sounds or notes showing the numerical basis of music. The coded strip in itself is an inverse representation of the harmonic series which is basic to all music and physical vibrations in general.****The numbers 2520 and it's half, 1260, permeated music theory long before Pythagoras. The reflective patterns of which these two numbers are a vital element, closely parallel the reflective patterns in J.S. Bach's Retrograde Fugue. Fellow musicians and musicologists may find these correlations worth investigating.****Using both colors (light) and music (sound), the Auric Key clearly approaches a universal language, synthesizing these into a coherent non-arbitrary mathematical structure. The Auric Key is an outgrowth of synchrographics.****Synchrographics is a methodology which can be successfully employed in broad areas of study and merges with general systems theory, which finds common patterns of methods with a wide range of theories. Interdisciplinary exchange is vital to fully integrate, synthesize, and use our accumulated knowledge and information. Synchrographics represents an important application of general systems theory.****The Auric Key is among the first applications of modern synchrographics. Apart from its parallels to many specific sciences, the Auric Key is a visual reminder of the on-going search for a synthesis of our ever-increasing specializations and stands for the basic methodology with which we seek to close the arbitrary lacunae between psychology and physics, indeed between science and religion. The Auric Key is a genuinely interdisciplinary unifier, one whose power is at once startlingly elegant and harmonizing.**

TETRACTYS

The tetractys is a symbol composed of ten dots in an upward-pointing triangular formation. It was a sacred pattern for the school of philosophers who followed the teachings of the Greek sage Pythagoras (lived 6th century BC). They used the tetractys to swear their oaths upon, in much the same way that modern Christians swear oaths upon the Bible.

The Pythagorean oath, as quoted by the Renaissance magician Cornelius Agrippa, is as follows:

Some authorities claim that the oath was sworn to the "one who bestowed the tetractys to the coming generations," which might be interpreted to mean the Monad, or the teacher Pythagoras. Probably all three -- God, Pythagoras, and the tetrad -- were in the mind of the individual taking the oath. However, I believe that the oath was primarily focused upon the tetractys itself, as the symbolic blueprint of creation.

Pythagoreans possessed two tetractys, the tetractys of addition (1 + 2 + 3 + 4 = 10) and the tetractys of multiplication (1 + 2 + 3 + [2x2] + [2x2x2] + [3x3] = [3x3x3]). It is easier to understand the tetractys of multiplication by means of a simple diagram.

The 1 at the highest level of the tetractys of multiplication is the Monad, symbolic of perfect unity. According to Theon of Smyrna, it contains the principles of

Usually when the tetractys is written about, the tetractys of addition is intended. In order to understand why the tetractys was held to be so sacred, you must know that the Pythagoreans believed the entire universe to be composed of numbers, specifically the numbers from one to ten, upon which all higher numbers are based in our familiar decimal system. For Pythagoreans, numbers were not merely indicators of aggregate amounts of things, but living deities, each with its own unique personality and occult powers.

For example, the number five was held to represent the sacred principle of justice, because it occurs in the exact center of the tetractys of addition, as well as in the middle of the single-digit numbers from one to nine, and therefore symbolizes balance and equality. But to the Pythagoreans, five was not merely a symbol but a living being, a spiritual intelligence embodying the active principle of justice wherever it found expression on earth or in heaven. The number five was regarded in a way somewhat similar to the way we look upon the graphic symbol of the scales held in the hand of the goddess Justice, except that five was the goddess herself, not merely a symbol for the goddess.

The number six was looked upon as the principle of holy marriage, since it contained within itself the mathematical formula 2 x 3 = 6. Two was considered the first feminine number, and three the first masculine number. Their sexual union was expressed by the process of multiplication, since by multiplying more is brought forth than the original amount, just as in sexual union, children exceed the natures and abilities of their parents.

The first true number in the Pythagorean system is the number three. Pythagoreans referred to the number one as the monad, and to the number two as the duad. The monad signified perfect unity of all, the duad was the root of all diversity throughout the universe:

Thus the tetractys of addition contains within itself the monad, the duad, the first odd true number, and the first even true number. Odd numbers were held by Pythagoreans to be masculine, and even numbers to be feminine, for reasons which should be obvious upon consideration (evenness was represented by the two legs, oddness by the two legs plus the male penis). The number four, or tetrad, contained within itself all of the principles of the tetractys (1, 2, 3, 4). It is the smallest number that embodies all parts necessary for manifest existence, and for this reason four is the number of the material world.

Musical theory played an extremely important role in the philosophy of the Pythagoreans. The tetractys symbolizes all of the classical tonal divisions of music.

When the tetractys of addition was considered in company with the tetractys of multiplication, both combined were held to represent the musical, geometric and arithmetic ratios upon which the entire universe was structured. Man was viewed by Pythagoreans as a full musical chord in the harmony of the music of the spheres. For the benefit of any musicians who may be reading, the chord of man is a fundamental or tonic, its major third, its just fifth, and its octave.

Jewish Kabbalists were strongly influenced by Greek philosophy. They created their own version of the tetractys using the Hebrew letters of Tetragrammaton (IHVH), the divine name of four letters. When these letters on the tetractys are written out in a line and added together, they number ten, and compose a Ten-letter name of God that Agrippa called

The ten-letter name, translated into Latin characters, is: I + IH + IHV + IHVH.

(Kabbalistic tetractys of the letters of Tetragrammaton)

The meaning of Tetragrammaton in the Kabbalah is similar in many respects to the meaning of the tetractys. The Hebrew letters in the name were linked to the four elements -- together, they express manifest existence. The letters are both three and four in number, three distinct letters, yet four letters numerically. In this way they express the first two true numbers of the Pythagoreans. The tetractys is also three and four, in that it has three sides, yet four levels.

The numbers of Tetragrammaton also represented the ten Sephiroth, the emanations of God by which the universe was created. Each Sephirah has its own divine name of power. In a mystical sense, the ten-letter name of God embodies the powers of all those names. When counted together, the letters of the Kabbalistic tetractys total 10, yet when the numerical values of the Hebrew letters are added, they total 72 (10 + [10+5] + [10+5+6] + [10+5+6+5]), an extremely significant number in the Kabbalah. There are 72 divine names in the Shemhamphoresch, and 72 demons were imprisoned by Solomon in a vessel of brass. The 360 degrees of a circle, when divided by 5 yield divisions of 72 degrees.

At first consideration, the tetractys of the Kabbalah appears more complex than that of the Greeks. This is an illusion caused by the modern tendency to regard numbers as all more or less the same, apart from their numerical values. To the Pythagoreans, each number had its unique identity, just as to Kabbalists each Hebrew letter has its unique vital energy and nature. Since both tetrads express the same fundamentals of the process of emanation, there is naturally a great deal of correspondence between the two. Indeed, I have found that the study of the Kabbalah leads to a much deeper understanding of Pythagorean number mysticism, and I recommend the Kabbalah to anyone seeking to learn Pythagorean philosophy.

**SYNCHROGRAPH C:**

#108, OM, THE NUMBER OF THE UNIVERSE#108, OM, THE NUMBER OF THE UNIVERSE

**In a gestalt approach to the study of the concept of number or the field analysis of number behavior, any specific number is considered in terms of the neighborhood in which it dwells, instead of by some individual feature which it may share with some other family member.****Graphic aesthetics are useful in revealing certain features of the number behavior which remain couched in linguistic terms. There are certain typical elements which constitute elegance in graphic depiction.****Number Mysticism reached a zenith in ancient Greece, since the Greeks were fascinated with the essence of the integers themselves to the point of worshipful devotion. etc. But after the burning and plundering of the Library at Alexandria, Egypt (the repository of all extant knowledge at the time), the exact science of ancient mathematics was lost to the west.****We attribute our present system of so-called Arabic numerals to those near-eastern cultures which preserved them through Europe's Dark Ages. However, this system of numeration originated in India and was one of the many kinds of knowledge translated into Arabic during the cultural flowering of that area. The numerical characters and such notions as the zero came directly from India.****Yogananda and other Hindu sources cite #108 as a divine number, "the number of the Universe." It is said to be the number of Om, the universal sound which underlies all creation. It is fundamental in two Hindu astro-calendaric systems, the Ages and Yugas. Both the so-called Ages and Yugas are all multiples of #108 (see tables which follow).****The Hindu religion is a vast ocean of religious thought, springing as it does from the earliest times, long before the dawn of history, and comprises in its multi-colored texture shade after shade, an endless variety of design and pattern as it grew in the human mind; from animism to Nature worship.****The worship of the sun was common in antiquity. There is a famous sun temple in Konark in South India, and in the historic town of Mooltan or the land of the Sun, in the North. And #108 has to do with the numbers of revolutions of sun in the various epochs.****Not only sacred to the Hindus, this number also reappears in Tibetan Buddhism, where it is considered highly auspicious, being the number of beads on each strand of the**

or Tibetan roasary beads. Therefore, it reveals its character as an ancient form of circular unity.*malla,*or Tibetan roasary beads. Therefore, it reveals its character as an ancient form of circular unity.

**The Hindu calendar is of an amazing antiquity. Its starting point is the divine beginning of Brahma, the first one of the Holy Triad of Brahma, Vishnu, and Shiva. Its unit is the Kalpa, equivalent to one day of Brahma's life (4,320,000,000 years). Brahma's allotted life span is 100 years of 365 Kalpas each. The present epoch is the Kali Yuga and this Hindu year exceeds the figure 155,521,972,849,000 and counting...****In most Hindu systems, certain points of time back are fixed on as epochs. They each begin when the planets are assumed to fall into a line of mean conjunction with the Sun in the beginning of Aries.****In the***Surya Siddhanta*(the classic text of Indian astronomy), the least cycle of years in which the Sun, Moon, and planets are supposed to return to a line of mean conjunction at the beginning of Aries is 1080,000 years, of a fourth of a Maha Yug of 4320,000,000 years or revolutions of the Sun (Surya). The revolutions given in the Surya Siddhanta must always be divisible by four, or no mean conjunction could take place at the beginning of the Kali Yuga.**The Holotomic Sequence was discovered through a systematic graphic analysis of the enspiralment of number 108 or 3 x 36.****There are two primary astrocalendaric systems in India: Yugas and Ages denoted by metals:****FOUR YUGAS****Kali 432 (108 x 4)**

Dvapara 864 x 8)

Treta 1296 x 12)

Krita 1728 x 16)

Maha 4320 x40)

Dvapara 864 x 8)

Treta 1296 x 12)

Krita 1728 x 16)

Maha 4320 x40)

**FOUR AGES****Iron 648 (108 x 6)**

Copper 1296 x 12)

Silver 1944 x 18

Gold 2592 x 24Copper 1296 x 12)

Silver 1944 x 18

Gold 2592 x 24

**sum 6480 x 60****The synchrographic structure of these two ancient Hindu modules of circular unity disclose that the Yugas fall into a perfect tertiary symmetry. The Ages assume a perfect quadric symmetry when spiralled along 108 axes of a number field, array, or matrix. The final number of this synchrograph is 6480. The glyph unifies the two ancient systems.****These high factorial number arrays preceeded modern forms of circular unity, even perhaps the Babylonian adoption of 360 as circular unity in that 108 is 3 x 36.****The number wheel, Synchrograph C, enspirals the natural number series around a field divided into 108 radial increments from zero to 6480. Since #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 two separate systems. Note also that the numbes that represent these two systems all fall in the same zero axis. Also note, the sum of the Yugas (4320) end at two thirds of this axis: (6480 - 3 = 2160: Platonic month: 12 x 2160 = 25920).****In the configuration of this mandalog, the four-digit palindromic sequence "1881, 2772, 3663,4554, 5445," etc. fall in a quadric array, and the turnaround or nave of transpalindromicity (49.5) synchronizes the corner of the square with the side of the triangle, i.e. the nave between 45 and 54 (which added together equals 99).****Contemplation of this wheel discloses the complete menagery of "sacred numbers," the key numbers of ancient metrology and the Holotomic Sequence in positions that yield a perfect symmetry where only chaos exists in classical number theory.****Nature's behaviors coincide with the most crucial divisions of the continuum of base ten number. This wheel reveals a rhythmic series of revelations that are otherwise not available for contemplation.****(Editor's Note: See the entire text of SYNDEX II (A Revisioning of Number Dynamics in Light of Ancient Metrology and Modern Cosmography) for a complete explication of this Synchrograph based on #108. This work includes ancient milestones in the history and development of the alphabet and number concepts: Number Mysticism & Alphanumeric Writing (the Origin of Divine Number Words); Cosmic Cyles of Creation & Destruction (The Hindu Doctrine of Yugas); The Hindu Concept of Number; The Surya Siddhanta, History of the Development of Indian Mathematics, the Sumerian Legacy, etc.)**TETRACTYS

The tetractys is a symbol composed of ten dots in an upward-pointing triangular formation. It was a sacred pattern for the school of philosophers who followed the teachings of the Greek sage Pythagoras (lived 6th century BC). They used the tetractys to swear their oaths upon, in much the same way that modern Christians swear oaths upon the Bible.

The Pythagorean oath, as quoted by the Renaissance magician Cornelius Agrippa, is as follows:

*"I with pure mind by the number four do swear;*

That's holy, and the fountain of nature

Eternal, parent of the mind..."That's holy, and the fountain of nature

Eternal, parent of the mind..."

Some authorities claim that the oath was sworn to the "one who bestowed the tetractys to the coming generations," which might be interpreted to mean the Monad, or the teacher Pythagoras. Probably all three -- God, Pythagoras, and the tetrad -- were in the mind of the individual taking the oath. However, I believe that the oath was primarily focused upon the tetractys itself, as the symbolic blueprint of creation.

Pythagoreans possessed two tetractys, the tetractys of addition (1 + 2 + 3 + 4 = 10) and the tetractys of multiplication (1 + 2 + 3 + [2x2] + [2x2x2] + [3x3] = [3x3x3]). It is easier to understand the tetractys of multiplication by means of a simple diagram.

The 1 at the highest level of the tetractys of multiplication is the Monad, symbolic of perfect unity. According to Theon of Smyrna, it contains the principles of

*"ratio, of limit and of point."*The 2 and 3 on the second level are*"prime, incomposite numbers, and measured only by the unit, and are consequently linear numbers."*The third level contains the numbers 4 (2 x 2) and 9 (3 x 3), which are the first square numbers (numbers created by the multiplication of a number with itself). They represent the geometric surface or plane. The fourth level contains the numbers 8 (2 x 2 x 2) and 27 (3 x 3 x 3), which are the first cubic numbers (numbers created by the multiplication of a number with itself, then with the number again). Cubic numbers represent the geometric solid. It was held to be of the highest significance that all of the numbers that compose the tetractys of multiplication sum 27, the final number of the symbol (1 + 2 + 3 + 4 + 8 + 9 = 27). Theon remarked that it was with these numbers that Plato constituted the human soul.Usually when the tetractys is written about, the tetractys of addition is intended. In order to understand why the tetractys was held to be so sacred, you must know that the Pythagoreans believed the entire universe to be composed of numbers, specifically the numbers from one to ten, upon which all higher numbers are based in our familiar decimal system. For Pythagoreans, numbers were not merely indicators of aggregate amounts of things, but living deities, each with its own unique personality and occult powers.

For example, the number five was held to represent the sacred principle of justice, because it occurs in the exact center of the tetractys of addition, as well as in the middle of the single-digit numbers from one to nine, and therefore symbolizes balance and equality. But to the Pythagoreans, five was not merely a symbol but a living being, a spiritual intelligence embodying the active principle of justice wherever it found expression on earth or in heaven. The number five was regarded in a way somewhat similar to the way we look upon the graphic symbol of the scales held in the hand of the goddess Justice, except that five was the goddess herself, not merely a symbol for the goddess.

The number six was looked upon as the principle of holy marriage, since it contained within itself the mathematical formula 2 x 3 = 6. Two was considered the first feminine number, and three the first masculine number. Their sexual union was expressed by the process of multiplication, since by multiplying more is brought forth than the original amount, just as in sexual union, children exceed the natures and abilities of their parents.

The first true number in the Pythagorean system is the number three. Pythagoreans referred to the number one as the monad, and to the number two as the duad. The monad signified perfect unity of all, the duad was the root of all diversity throughout the universe:

*"The all-perfect multitude of forms, therefore, they obscurely signified through the duad; but they indicated the first formal principles by the monad and duad, as not being numbers; and also by the first triad and tetrad, as being the first numbers, the one being odd, the other even..."*(Thomas Taylor,**Theoretical Arithmetic**).Thus the tetractys of addition contains within itself the monad, the duad, the first odd true number, and the first even true number. Odd numbers were held by Pythagoreans to be masculine, and even numbers to be feminine, for reasons which should be obvious upon consideration (evenness was represented by the two legs, oddness by the two legs plus the male penis). The number four, or tetrad, contained within itself all of the principles of the tetractys (1, 2, 3, 4). It is the smallest number that embodies all parts necessary for manifest existence, and for this reason four is the number of the material world.

Musical theory played an extremely important role in the philosophy of the Pythagoreans. The tetractys symbolizes all of the classical tonal divisions of music.

*"The importance of the quartenary obtained by addition (that is to say 1, + 2, + 3, + 4) is great in music because all the consonances are found in it"*(Theon of Smyrna).When the tetractys of addition was considered in company with the tetractys of multiplication, both combined were held to represent the musical, geometric and arithmetic ratios upon which the entire universe was structured. Man was viewed by Pythagoreans as a full musical chord in the harmony of the music of the spheres. For the benefit of any musicians who may be reading, the chord of man is a fundamental or tonic, its major third, its just fifth, and its octave.

Jewish Kabbalists were strongly influenced by Greek philosophy. They created their own version of the tetractys using the Hebrew letters of Tetragrammaton (IHVH), the divine name of four letters. When these letters on the tetractys are written out in a line and added together, they number ten, and compose a Ten-letter name of God that Agrippa called

*"the name of Jehovah with ten letters collected"*(*Three Books of Occult Philosophy*, Book II, Ch. 13).The ten-letter name, translated into Latin characters, is: I + IH + IHV + IHVH.

(Kabbalistic tetractys of the letters of Tetragrammaton)

The meaning of Tetragrammaton in the Kabbalah is similar in many respects to the meaning of the tetractys. The Hebrew letters in the name were linked to the four elements -- together, they express manifest existence. The letters are both three and four in number, three distinct letters, yet four letters numerically. In this way they express the first two true numbers of the Pythagoreans. The tetractys is also three and four, in that it has three sides, yet four levels.

The numbers of Tetragrammaton also represented the ten Sephiroth, the emanations of God by which the universe was created. Each Sephirah has its own divine name of power. In a mystical sense, the ten-letter name of God embodies the powers of all those names. When counted together, the letters of the Kabbalistic tetractys total 10, yet when the numerical values of the Hebrew letters are added, they total 72 (10 + [10+5] + [10+5+6] + [10+5+6+5]), an extremely significant number in the Kabbalah. There are 72 divine names in the Shemhamphoresch, and 72 demons were imprisoned by Solomon in a vessel of brass. The 360 degrees of a circle, when divided by 5 yield divisions of 72 degrees.

At first consideration, the tetractys of the Kabbalah appears more complex than that of the Greeks. This is an illusion caused by the modern tendency to regard numbers as all more or less the same, apart from their numerical values. To the Pythagoreans, each number had its unique identity, just as to Kabbalists each Hebrew letter has its unique vital energy and nature. Since both tetrads express the same fundamentals of the process of emanation, there is naturally a great deal of correspondence between the two. Indeed, I have found that the study of the Kabbalah leads to a much deeper understanding of Pythagorean number mysticism, and I recommend the Kabbalah to anyone seeking to learn Pythagorean philosophy.

*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 interchangeable 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 superseded 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 impose 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 erroneous 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 volumes 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.**

FOREWORD

*"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 accommodate 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 demonstrated by multiplying 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

72 x 36 = 25920 divided

**by 2 = 12960; divided**

**by 3 = 8640**

by 4 = 6480; by 6 = 4320

72 + 360 = 432

by 4 = 6480; by 6 = 4320

72 + 360 = 432

**Contemplation of the number wheel 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 number wheel 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.**

**METROLOGY & ALPHANUMERICS**

*"Number makes its appearance in this context as the*__vinculum amoris__, the bond of love which unites the two principles [psyche and matter] by jointly ordering them. In its profoundest sense number thus possesses the significance of an all-uniting Eros, although it connotes something different from the usual sense of the words love and Eros...Because there seems to exist such a clear spiritual "objective" order at the base of Eros, it is expressed in the seemingly abstract, feelingless, impersonal order of numbers, as a clear, immutable factor free from illusions...this cosmic ordering of the Self constitutes the ultimate mystery behind all human desire and behavior, an unfathomable and fearsome mystery."**-- M.L. von Franz,**

*Number and Time*, p292-3

*"The unexpectedness of a mathematical result gives us the feeling that it is not our own creation, that the world of number exists in its own right, while its necessity and symmetry are balm after the ragged edges of life, or pure joy to those who do not yet know them. The appeal of mathematical form reaches deep into human character."***--L. L. Whyte**

*"Very vigorous applause your very intelligent, scientifically systematic synchrograph evolved elucidations binomial symmetries, tantalizing manifestations...which to me clearly related several fundamentals...Your cyclic synchrographing work clarifies and simplifies this whole matter to an epochal degree...your work fills me with joy."*--B. Fuller letter to Bob Marshall, 3/3/81

**NUMBER MYSTICISM & ALPHANUMERIC WRITING**

**Number mysticism reached a zenith in ancient Greece, since the Greeks were fascinated with the essence of the integers themselves to the point of worshipful devotion. The relation between numbers (and number words) and magic remained alive throughout the ages. It is visible in Pythagorean and Platonic philosophy, the Qabala, and various other forms of religious mysticism.**

**The Pythagoreans believed that numbers were the key to understanding the order of the universe, and to them numbers meant whole numbers or integers. They believed that the soul could ascend through the spheres, to eventual union with God, by means of mathematics. This peculiar fascination with numbers as individuals created an obstacle to developing a collective theory of numbers, i.e. arithmetic.**

**The main thread of the number concept in the crossroads cultures passed from Sumeria-Akkadia-Babylonia to Phoenicia to Hellenistic (and Hebrew), to Indian to Islamic to European cultures. Key numbers, cosmic cycles, and divine numbers permeate the number concepts of all these cultures. The Greeks and Hebrews had alphanumeric systems which developed into numerology and numberword mysticism.**

**Number mystics from the Pythagoreans onward considered number 'one' as the Infinite God, the First Cause, the One who transcends all multiplicity. To the Greeks, numbers were divine concepts, ideas in the mind the god who had fashioned the world. God was a great mathematician. In the Hebrew Qabala, the world is made with numbers and letters. In more accurate terms, the characters representing manifestation were alphanumeric.**

**Whether 'one' was actually a number at all was answered by the concept that it is the essence or underlying principle of number. All the numbers are made of it. In the West, ten (10) is the number of completion and perfection which returns the essential numbers back to unity. In China, eleven is the number of Tao, but not in the quantitative sense of ten plus one, but signifying the unity of the decade in its wholeness.**

**Jung echoes these ancient sentiments in**

*Memories, Dreams, and Reflections*(pp. 287 f.) by stating:

*One, as the first numeral, is unity. But it is also "The unity,": the One, All-oneness, individuality and non-duality--not a numeral but a philosophical concept, an archetype and attribute of God, the monad.***In**

*Number and Time*, M.L. von Franz carries this thought further:

*The number one possesses these unique qualities to a particular degree...it does not multiply by itself, or reduce itself by division because it is a divisor of all other numbers...It is the first triangular and also the first square number...it has no predecessor. In this sense it does not yet "count"; if it did it would be the first uneven prime number...in mathematics the number one is not reckoned among prime numbers.***This is supported by experimentation: "**

*dealing with the wave configurations of sand vibrations on thin plates of metal, all prime numbers figure with the exception of the one."***Influenced by Pythagorean ideas and Qabala, in which 10 Sephiroth (Spheres) emanate from God, the occult tradition asserts that the succession of numbers 1 through 10 symbolizes and is, in fact, identical with the emanation of the manifest Universe. The 22 letters of the alphanumeric Hebrew alphabet contained and created the secret structure of all things.**

**The**

*SEFIR YETZIRAH*, the Book of Creation or Formation (300-600 AD) describes how God created the manifest universe by means of letters and numbers which are the foundation of all things. The letters are part of '*one body*,' the alphabet which is an extension of God's own being. All created things, made by means of the letters, are also parts of the one body which is God.**True being for the Hebrew is the 'word,'**

*dabhar*, which comprises all Hebraic realities: word, deed, and concrete object. Non-being, nothing (no thing) is signified correspondingly by 'not word,'*lo dabhar.***In European magical tradition, the most important of all alphanumeric alphabets is the Hebrew which had 22 letters, all of which were consonants. Vowels were inferred from context. Contemplation (theory) and application (practice) is the mystical tradition of Qabala. In this alphabet there are no vowels (our a,e,i,o, and u) represented. The same is true of the older Phoenician (Canaanite) alphabet, from which our own alphabet is descended--by way of the Greek, Etruscan, and Latin alphabets.**

**All over the ancient orient, in Assyria and Babylonia, as well as Egypt, the word and particularly the word of God, was not only nor even primarily an expression of thought; it was a mighty and dynamic force. The Assyrians and Babylonians conceived of the divine word under the image of a physical-cosmic power.**

**In Egypt, the power of creating and sustaining everything was traced back to the divine word, the ever-active fluid or ethereal divine substance proceeding out of the mouth of divinity. For example, in Memphis,**

*Ptah*is the Creator of the world. The specific organ of creation is '*the mouth which named all things*.'**ALPHANUMERIC WRITING**

**All things nameable can be recorded or counted by symbols for things. Writing (like naming) is an ancient, magical art, assumed to have been invented by the gods. Emerging around 3200 B.C., writing contained mysterious, hidden, even divine Wisdom, for those contemporary minds. The archaic history of writing records its evolution from pictographs and ideograms, to phonetic and syllabic cuneiform, and the alphabetic form, whose sequential letters are also used as numbers.**

**Certain milestones in the development of alphanumeric characters have been documented archaeologically. Interaction along trade routes in crossroads cultures contributed both to the development (from syllabic hieroglyphics and phonetic cuneiform), and dispersal of a letter sequence which could be adapted to the phonetics of local dialects.**

**A tablet has been found from the 14th Century B.C. showing Ugaritic letters arranged opposite a column of known Babylonian syllabic signs, which supplied the sounds for the characters a, be, ga---and so on---in basically the same order and roughly the same sounds that would appear 300 years later in the Phoenician alphabet. By 1000 B.C., the Phoenician alphabet had come to full flower.**

**According to Isaac Asimov (1989), this is why the alphabet was never invented independently by any other society:**

*"Between the Egyptians and the Babylonians were the Canaanites, inhabiting the eastern shore of the Mediterranean Sea, (the Greeks called them the Phoenicians). They were traders who acted among other things, as intermediaries between the Egyptians and Babylonians. It was necessary for such traders to know both the Egyptian and Babylonian languages, and that was a hard chore indeed."*

*"It occurred to some nameless Canaanite to simplify writing by adopting a kind of shorthand. Why not give a separate symbol to each of the common sounds made by human beings in speaking a language? You could then build up any words of any language by using those sound-symbols. Sound-symbols had, in fact, been used by the Egyptians, but they also preserved symbols for syllables and for whole words. The Canaanite inventor had the notion that the sound symbols should be used exclusively and that words should be built up out of them."***That same alphabet could be used as numerals.**

(scan alphanumeric table)

(scan alphanumeric table)

**TIMETABLE**

**The Ancient Development of Alphanumeric Characters:**

**2800-2600 BC Sumerian cuneiform; pictographs, ideograms**

**2500 BC Cuneiform spreads through Near East; adapted**

Sumerian signs to the

phonetics of local languages (Akkadian 2300-2150)

Sumerian signs to the

phonetics of local languages (Akkadian 2300-2150)

**2100-1300 BC Syllabic cuneiform (Semitic style 2500-2000)**

**1800-1600 BC Old Babylonia**

**1500-1400 BC Ugaritic cuneiform of 30 characters; first ABC letter sequence;**

phonetics of a Canaanite dialect corresponding with

Babylonian syllabic signs; precedes alphabetic cuneiform

phonetics of a Canaanite dialect corresponding with

Babylonian syllabic signs; precedes alphabetic cuneiform

**1400-1300 BC ALPHABETIC CUNEIFORM from Babylon**

**1100- 900 BC Phoenicians spread precursor of modern alphabets; script of 22**

characters, no vowels; rise of Assyria

characters, no vowels; rise of Assyria

**800 BC Greeks and Hebrews adopt Phoenician alphabet;**

Greeks add first vowels;

Babylon rebuilt; ALPHABETIC NUMERALS

Greeks add first vowels;

Babylon rebuilt; ALPHABETIC NUMERALS

**500 BC Sanskrit alphabet and grammar codified**

**1000 AD Hindu-Arabic numerals and decimal system introduced into**

Europe by Pope Sylvester II

Europe by Pope Sylvester II

**It is now generally agreed that all existing alphabets as well as those no longer used, derived from one original alphabet (Paleo-Sinatic, Syria and Palestine 1750-1500 BC). There is obviously a real advantage in the use of single symbols for single sounds, compared with thousands of symbols for representing things or ideas (pictograms). The simplicity of alphabetic writing removed the monopoly on learning. The alphabet expanded literacy.**

**But all alphabets are inherently flawed, or at least limited. The shortcoming is that it lacks the delicate variations necessary to indicate all the subtleties of the human voice. So perfection has eluded any alphabet for that would mean the accurate rendering of every speech-sound.**

**In an ideal alphabet each sound would have to be represented by a single letter, and each letter would be limited to one sound. Every alphabet so far has omitted symbols for some sounds, and most have contained redundant letters. The adaption of a script to a language is not easy when it contains sounds not occuring in the speech from which it was borrowed.**

**In any event, the prototype of alphabetic writing was spread by the Phoencians. Local scribes embellished it, or pared it down and evolved local variations. Historians and linguists cite four main branches of the Original:**

**1) North Semitic, included Canaanite, ancient Sinatic Hebrew, and Phoenician;**

**2) Aramaic includes Persian, Syriac, Mongolian, Armenian, Georgian alphabets, and the Indian main branch with 200 offshoots of Sanskrit; also the square Hebrew alphabet;**

**3) South Semitic is mainly Arabic;**

**4) Greek main branch includes all European alphabets: Etruscan, Cyrillic, Slavonic.**

Romans adopted only 21 letters from the early Etruscan alphabet, as well as their

names for letters, which were different from the ones Greeks derived from Semitic

letter names.

Romans adopted only 21 letters from the early Etruscan alphabet, as well as their

names for letters, which were different from the ones Greeks derived from Semitic

letter names.

**It made writing far easier to learn with its economy of symbols, and its direct relationship to the sounds of spoken languages and numbers. Literacy spread dramatically.**

**COSMIC CYCLES OF CREATION & DESTRUCTION**

**THE HINDU DOCTRINE OF YUGAS**

**After the burning and plundering of the Hellenistic Library at Alexandria, Egypt, the exact science of ancient mathematics was lost to the west. The vanguard of mathematical discovery passed to medieval India.**

**Hindu mathematicians had little direct influence on Europe. But it is certain that the Arabs got their arithmetic and algebra from Brahmin knowledge. Caliphs entertained Indian mathematicians in the ninth and tenth centuries. Both Sansrit and Greek classics of science were avidly translated into Arabic during the Moslem Empire.**

**The Crusaders were exposed to this Arab knowledge in the Holy Land, and their knowledge gradually penetrated Europe also through Islamic Spain (Toledo). This led directly to a revival of European learning after the Middle Ages.**

**Therefore, we attribute our present system of so-called Arabic numerals to those near-eastern cultures which preserved them through Europe's Dark Ages. However, this decimal system of numeration originated in India and was one of the many kinds of knowledge translated into Arabic during the cultural flowering of that area. The numerical characters and such notions as the zero and place valuation came directly into modern society from India, even though they had been tentatively used in older societies.**

**Prior to the introduction of Hindu numerals, the alphanumeric characters developed by the Phoenicians predominated. Numbers were represented by the letters of an alphabet in their spoken succession. Both the Greeks (800 B.C.) and the Hebrews adopted this principle. Not only the alphabet, but the sounds of the letters were retained.**

**This adoption of an alphanumeric model led to the mathematical backwater of Gematria where every sum was a word or many words, and every word had a numerical equivalent. Number mysticism then concerned itself with various cryptographic messages and numerical codes. While good for mysticism and possibly promoting superstition, it was no favor to the advancement of mathematics. The old Phoenician "acrophonic" numerals were abbreviations of number words. Alphanumerics permeated the crossroads cultures.**

**Cultural concepts of time, real and divine, differ dramatically and underlie and condition each culture's worldview. The background of Hindu cosmology and science has its roots in the crossroads cultures. It involves notions of time and history, astronomy, and the idea of the Divine Word.**

**Ethnopsychology, psychology of language, philosophy of language, logic of language, semantics and comparative linguistics show that, relatively speaking, Hebrew thinking is dynamic and temporal, while Greek thinking is static and spatial--even the Greek conception of time is spatial--boundless.**

**The concept of number can be understood either as spatially quantitative or dynamically qualitative quantities. For the temporally-oriented Jews, there is an inner connection between plurality and intensity. Hebrew thinking moves in time, while the Greeks employ space as their thought-form. Hebrews used a lunar calendar, while Greeks used the solar year.**

**Both Indo-European and Semitic languages reveal a cross-cultural ambiguity when using spatial expressions to designate tempral notions. "Before" and "behind" can mean "future" and "past." This double temporal meaning of the same words reveals two different notions of time, as eternal rhythms. In Semitic languages, the notion of recurrence coincides with that of duration. Time is the stream of events, the historical content of occurrence.**

**The European sense of time is a confused mixture of time and space, a legacy of Greek thought. The Indo-Germanic framework of past, present, future is foreign to Semitic thinking where tense comes principally from the dynamic of completed or incomplete action.**

**Our modern concept of time is spatialized. For us actions are oriented objectively, impersonally and spatially; the ancient Hebrews thought subjectively, personally, and temporally. Europeans got both space/time views mixed together as Bible cosmology.**

**These notions came down ambiguously because the Hebrews had no notions of firm boundaries to objects, while the Greeks delighted in thinking geometrically. They relate to quantity and number as spatially quantitative (Greek) and dynamically qualitative quantities (Hebrew).**

**The Hebrew language has no expressions for the simplest geometric figures such as the triangle, quadrilateral, or square, nor the corresponding adjectives. Numbers are distinguished qualitatively as rhythms, each with its own peculiarity.**

**The form and syntax of the Hebrew numbers two to ten indicate that the smallest and basic numbers were thought of as qualitatively different totalities. From there it was just a step further to the conception of holy numbers...concrete numerical gestalts, an intuitive quality adhering to a totally unarticulated general impression of quantity. Hebrew plural forms are preferably designated as intensive.**

**God revealed himself to Israel in History, not Ideas. Therefore, the Israelites developed no mathematical science, though it flourished in neighboring Phoenician and Mesopotamian cultures.**

**The mathematical ideas of the Greeks cannot be comprehended without bringing geometry into the inquiry. The Greek Ideas were geometrical basic forms, the eternal blueprint of reality.**

**Space perception is the given thought-form of the Greeks, and the visible form of things occupied their attention. Geometry for them was the most important branch of mathematics.**

**The Greeks, including Euclid, thought geometrically even when they dealt with numbers. The square was a visual representation of the second power and the cube of the third. For the Greeks, the concept of large, quantity (largeness) was mostly a spatial idea.**

**The Indian concept of time has differences and similarities with the Greek and Hebrew notions revealed by linguistics of their respective languages. Language (syntax, grammar, verb tenses, etc.) displays the basic worldview of a culture, notions about how real-time experiences are processed and conditioned by the basic philosophy of a culture. Linguistic perculiarities come from the underlying assumptions about existence in time and space, perception, being and becoming, active/passive, etc.**

**Like the Greeks, the Indian view of time is static, that is it is conceived statically rather than dynamically, as the Jews also do. The early Greek, Heraclitus posits that flux and becoming aloneare real, permanence and constancy are merely apparent. The Hindus believe the exact opposite.**

**Indians recognize, of course, that the things of this world are always moving and changing. But the substance of things is seen as basically unchanging; its underlying reality is unaffected by the ceaseless flux. Indian thought places a high value on universality, and the connection between this, and the static conception of phenomena, is of course not accidental. "The one remains, the many change and flee."**

**The static conception of time permeates Indian thought. It could hardly fail to do so, for it is present in the very forms of language itself, conditioning all philosophical thinking. In classical Indian languages, there are no words corresponding to the concept "to become." "To become" is "to exist."**

**"Being born" and "existing" come from the same root. So to become is to be born. Indians express change at all as "being otherwise." Becoming is expressed in terms of being; dynamic is seen as a phase of static. This point of view permeates the language and conditions the philosophy.**

**The classic Western expression of the sense of flux uses a vivid and specific verb: "All things flow." The corresponding idea in India is expressed in Sanskrit as sarvan anityam, "all existences are impermanent." It always directs the attention away from the action to the stable state of the actor, from the changing aspect of the action to the unchanging universal: "to appear" does not equal "appearance;" nothing can disappear or arise. The adverb isn't even a part of speech in Sanskrit.**

**In Indian philosophy, the Absolute is a Being beyond all temporal appearances. These exist and change in time; the Absolute is essentially static. The great unborn Self is imperishable, incorruptible, eternal, fearless Brahman, which is coequivalent with Atman.**

**Indian philosophers replaced the concept of Becoming with three aspects of temporal existence: Appearance, Extinction and Continuance, which are fundamentals in their cosmology. All three states are clearly conceived as static.**

**Here is a similarity to Platonic thought: Plato formulated the antithesis between Being and Becoming with the true essence of reality consisting of changeless, timeless Forms. This is why geometry was important, but Greek physical sciences only developed statics. Modern scientific thought, in contrast is concerned with kinetics, dynamics, synergetics.**

**Preoccupied with a more metaphysical time-sense, the numbness to the passage and flow of specific events makes non-Indians regard Indians as lacking in common sense. They simply do not seem to have a clear awareness of discrimination of "real time," historical time, and it shows in their language through the discrimination of tense. Children in India will ask you, "What is time?," not "what time is it?"**

**The difference between absolute past and relative past is not clearly made in the Indian language. Terms can be determined only through context. They don't grasp time quantitatively, and with historical accuracy. They exist through multiple lives repeated in limitless time: appearance, extinction, continuance, over and over through cosmic cycles of creation and destruction.**

**According to the Indian worldview, the universe, the world and social order are eternal. The personal is fleeting, and the basic assumption of transmigration is pervasive in language, thought, and philosophy. So, passing phenomena have no real significance, and no importance is given to providing them with accurate dates. In quasi-historical fashion they resort to hyperbole, idealization, and exaggerate to astronomical proportions. Therefore, much of Indian so-called history is confabulated, the product of pure imagination.**

**They are more interested in religion and poetry than historical documentation. Proper observance of ancient precepts is stronger than the regard for historical accuracy. They contemplate eternal paradigms of human experience which are by their nature timeless and in that sense, outside history.**

**This is a contemplative orientation and worldview, expressed in the forms of Sanskrit itself. In sanskrit, it is "effect and cause" syntactically, rather than the Western "cause and effect." The Western order of thought is to proceed temporally from cause to effect; the relationship is seen in time.**

**In Sanskrit, progressive phenomena are seen as already complete. Rather than "the relation of the knower and the knowable," it is "the relation of the knowable and the knower."**

**This way of thinking is retrospective and different from the approach which starts from the cause. Things are evaluated in terms of a final cause or aim, a teleological relation. But Indians do have a concept of abstract time and changing phases of the world. They just adhere to the universal principle that whatever is subject to organization is subject also to destruction, in lesser or greater duration.**

**There is no substance which abides forever. All matter is force; all substance is motion; every individual is unstable; all things pass away. Modern physics, the bastion of science's "cause and effect" confirms this curiously enough through inductive and deductive reasoning which would be alien to Indian thought.**

**All this is the essential background on Indian language, thought, and philosophy which provides the fertile matrix from which their cosmology of cosmic cycles of creation and destruction arose. In fact, the philosophy conditioned the language and vice versa.**

**And the nutshell of this philosophy and language is contained in the divine rootsyllable, the sacred numberword AUM, the sound of the mystery of the Word everywhere, whose personal realization is a peak experience.**

**Joseph Campbell explains AUM in THE POWER OF MYTH(1988):**

**AUM is a word that represents to our ears that sound of the energy of the universe of which all things are manifestations. You start in the back of the mouth "ahh," and then "oo," you fill the mouth, and "mm," closes the mouth. When you pronounce this properly, all vowel sounds are included in the pronunciation. AUM. Consonants are here regarded as interrutions of the essential vowel sound. All words are thus fragments of AUM, just as all images are fragments of the Form of forms. AUM is a symbolic sound that puts you in touch with that resounding being that is the universe. To be in touch with that and to get the sense of that is the peak experience of all.**

**A-U-M. The birth, the coming into being, and the dissolution that cycles back. AUM is called the "four-element syllable." What is the fourth element? The silence out of which AUM arises, and back into which it goes, and which underlies it. My life is the AUM, but there is silence underlying it too. That is what we would call the Immortal.**

**As well as philosophy, Hindu cosmology also mixed space and time concepts derived from astronomical and geodetic measurements. They were influenced by the ancient Sumerian lunar reckoning which came with the Aryan invasion, and is, in fact, the legacy of all neolithic cultures. Later Hellenistic notions permeated their astronomy.**

**The figure the ancients used to define the circumference of the earth came from their foot and their cubit. These two numbers, 1296 and 864, are basic to many ancient systems of measure.**

**Is it a coincidence that a circle of 1,296,000 units has a radius of 206,265 units, the length of both an English and Egyptian cubit? The Hebrew shekel weighs 129.6 grams, and the English guinea 129.6 grains. The measure of the Holy of Holies in Solomon's Temple was 1296 inches.**

**129600 is the numeric basis for astronomical measures and played a role in Plato's mystic symbolism. Multiples and submultiples of 12960 are easily memorized: 1728, 864, 720, 432, 360, 216, 180, 90, 40, 36, 20, 16, 10, 8, 5, 4, 2. These sacred numbers were used everywhere in the building of sacred temples. The Babylonian Tablet (Igi-Gal-Bi) uses all of them, plus 144, 162, and 810.**

**In IDEAL METROLOGY, W. H. Wood points out the meaning of these figures in the East: "In the law of the yoga, all periodic actions developed under the inspiration of The Invisible are measured by ideal cycles, expressed in geometric form by the number 1296 in thousands or thousands of thousands. The third stage of Yoga is represented by the third of 1296 or 432, which is considered the symbol of consecration, or standing in harmony with nature's beauty and order. The exalted life of a disciple of Buddha called for a cycle of 4320 million years."**

**In his classic, THE BOOK, Alan Watts points to the Hindu myth which says that as time goes on, life in the world gets worse and worse until at last the destructive aspect of the Self, the god Shiva dances a terrible dance which consumes everything in fire. There follows, says the myth 4,320,000 years of total peace during which the Self abides in itself and does not play or hide. Then the game begins again in a universe of perfect splendour which begins to deteriorate only after 1,728,000 years.**

**In ANCIENT CULTURAL ANTHROPOLOGY, Dr. Charles Muses wrote on the origin of certain Babylonian numbers. He noticed embedded in cosmic structure certain deeply fundamental numbers, which constitute an "alphabet" of sacred numbers. Among those still used today are 360 degrees of a circle; 60 minutes for an hour; 60 seconds for a minute and 24 hours for a day; 7 days a week; 12 months a year. Muses makes a list of 1, 3, 4, 5, 7, 12, 24, 60, and 360. He proceeds to show how all these numbers are related to patterns of circular arrangement.**

**Twofold twelveness, or 24 comes from uniting the 12 signs of the Zodiac with 12 hours of the day. Thus, from 360, 60 and 24 came a circle of time of 24 x 60 x 60 or 86,400 seconds. And a circle for space of 360 x 60 x 60 or 1,296,000 seconds.**

**Another research project of mathematician Dr. Muses is even more stunning in its results. He discovered that the roots an ancient Tantric lunar meditation practices were timed to certain anomolies in the moon's orbit. The Satapatha Brahmana and the Taittireya Sanhita recount the proceedures for a Tantric Lunar Resonance Meditation, associated with the Indo-European soma saccrifice. They are linked to the phases of the moon, but not the obvious points. The practice specifically divided the lunar month into 9 special days in both the waxing and waning halves, a cycle composed of 18 days total.**

**There is a striking correspondence between the two-fold cycle of lunar phases (9 + 9 = 18) each month and the hypernumber w, a lunar elliptic orbit function developed by NASA for the space program.**

**This hypernumber w and it's phases of the elliptical orbits provide the only available mathematical paradigm corresponding to the anomolies distinct to the waxing and waning lunar fortnights. It is amazing that they could be known through some unknown form of calculation in pre-Vedic times.**

**It is not necessary to describe the source and functions of hypernumbers here. It is enought to know that the hypernumber w has the remarkable property that, when multiplied successively by itself, all the resulting numbers lie on a certain ellipse. The number resulting from multiplying the square root of w successively by itself also lie on the very same ellipse. Exactly 12 distinct points are generated by both these processes.**

**There are three principle irregularities in the lunar orbit known since Ptolemy of Alexandria, but this cannot be the Vedic source, since it came later. Together these irregularities furnish a set of eight places in the lunar orbit where these reflecting configurations of force are maximum. These eight places map on the eight points furnished by the integer powers of the hypernumber w. W was conceived by 20th century mathematicians to describe these irregulartities of the lunar orbit.**

**In ancient Indo-Iranian tradition the holiest time of the month is the dark of the moon, where it is conjoined by the sun itself.**

**The sun travels through the celestial sphere of 360 degrees. Multiples of 360 reveal a cascade of ancient sacred numbers, which are instrumental in the arithmetical construction of Divine Ages of the Hindus.**

**1 x 360 = 360**

2 x 360 = 720

3 x 360 = 1080 - OM

4 x 360 = 1440

5 x 360 = 1800 - half circle

6 x 360 = 2160; age of years

7 x 360 = 2520; Auric Key

8 x 360 = 2880

9 x 360 = 3240; x 2 sum of ages 6480

10 x 360 = 3600; Sumerian sar

11 x 360 = 3960

12 x 360 = 4320 Maha Yuga div by 4 = 1080

x 2 = 8640 (4320 + 6480) Yugas + Ages

2 x 360 = 720

3 x 360 = 1080 - OM

4 x 360 = 1440

5 x 360 = 1800 - half circle

6 x 360 = 2160; age of years

7 x 360 = 2520; Auric Key

8 x 360 = 2880

9 x 360 = 3240; x 2 sum of ages 6480

10 x 360 = 3600; Sumerian sar

11 x 360 = 3960

12 x 360 = 4320 Maha Yuga div by 4 = 1080

x 2 = 8640 (4320 + 6480) Yugas + Ages

**Hindu cosmology mixed time-space concepts derived from solar and lunar calendars with holy number words. The Hindus had their own numberwords, called mantras. These words held mystical and numerical values. They were based on metrological and cosmological constants as well as ancient mythology, and therein lay their sacredness or divinity.**

**Yogananda and other Hindu sources cite #108 as a divine number, "the number of the Universe." It is said to be the number of AUM, or OM, the universal sound which underlies all creation. OM or AUM is the Word of the creator of universe, Brahman, who is associated with number 43200.**

**This notion is fundamental in two Hindu astro-calendaric systems, the Ages and the Yugas, which delineate the number of divine years in different Epochs. Both the so-called Ages and Yugas are all multiples of #108 (see Tables which follow).**

**The Hindu religion is a vast ocean of religious thought, springing as it does from the earliest time, long before the dawn of history. It comprises in its multi-colored texture shade after shade, an endless variety of design and pattern as it grew in the human mind, from animism to Nature worship to number mysticism.**

**DIVINE AGES**

**FOUR YUGAS FOUR AGES**

Kali 432 (108 x 4) Iron 648 (108 x 6)

Dvapara 864 x8) Copper 1296 x 12)

Treta 1296 x12) Silver 1944 x 18)

Krita 1728 x16) Gold 2592 x 24)

Maha Yuga 4320 x40) Sum 6480 x60)

**36 x 3 = 108**

**36 x 36 = 1296**

**1296 x 2 = 2592 - 4 = 648**

**10800 x 4 = 43200**

CREATION OF THE WORLD

**According to Hindu cosmology, the world is created from an embryo, a "center," which also implies the construction of cosmic Time. This center concept is the root notion behind the**

**mandala, a term which itself means "a circle."**

**Like our Synchrographs, the mandala represents a whole series of circles, concentric or otherwise, inscribed within a square. It is a symbol of the rite of penetration, which places the neophyte in a sort of labyrinth as an initiatory process. Mandalas clearly have a labyrinthine character, and so do mandalogs if viewed from that perspective. They help us to concentrate and find our own center in the microcosm.**

**This can lead directly to a more authentic and deeper personal experience and understanding, if traditional ritual has become fossilized; the need of a personal experience is for reactivating certain primordial symbols in our consciousness. The purely mental constructions act as a support for meditation.**

**The Hindu notion of deep time is revealed when Indra hears from the mouth of Vishnu the true story of the eternal creation and destruction of worlds, the Great Time, mythic time in which we find the true source of all beings and of all cosmic events. This helps us pierce the veil of illusion created by profane time and our own history, and like Indra cures us of our pride and ignorance. It is a redemptive function.**

**To transcend profane time and re-enter into mythical Great Time is equivalent to a revelation of ultimate reality--the reality which is strictly metaphysical, and can be approached in no other way than through myths and symbols.**

**The conception of cyclic and infinite Time, Presented by Vishnu is the general Indian conception of cosmic cycles. Though this belief is found in all archaic societies, it is first espoused in the**

**Atharva Veda.**

**India elaborated the doctrine of cosmic cycles by amplifying the number of periodic creations and destructions of the Universe to ever more terrifying proportions. The transition of each age marks the beginning of a regression. The decreasing length of each**

*yuga*marks this durational degeneration toward the present*Kali Yuga*. It is so called for the "black" goddess*Kali*or (**Shakti, the Great Goddess), whose name is akin to the Sanskrit**

*kala*, or "time." She is the personification of time.**Number 108 is also said to be the number of names of the great Mother Goddess.**

**The 12,000 years of one**

*mahayuga*has been counted as "divine years" of 360 each, which gives a total of 4,320,000 years for a single cosmic cycle. This is all we need to retain with the cyclic character of cosmic time. The life of Brahma comprises 2,560,000 of these*mahayugas*, each going through the same stages concluding with a*pralaya*, and grand dissolution.**THE HINDU CONCEPT OF NUMBER**

**Indian Philosophy, Cosmology, and Science**

*"The Hindu traditions were brought to the Indian subcontinent by 'Aryan' migrants from the shores of the Caspian Sea, cousins of the Indo-Europeans who were the Hittites of Asia Minor (today's Turkey) and of the Hurrians of the upper Euphrates River, through whom Sumerian knowledge and beliefs were transmitted to the Indo-Europeans. The Aryan migrations are believed to have taken place in the 2nd millenium BC and the Vedas were held to be 'not of human origin,' having been composed by the gods themselves in a previous age. In time the various components of the Vedas and the auxilliary literature that derived from them (the Mantras, Brahmanas, etc.) were augmented by the non-Vedic Puranas, and the great epic tales of the Mahabharata and Ramayana. In them, ages deriving from multiples of 3600 also predominate, [and the Divine Cycle of 432,000]."***--Zecharia Sitchen,**

*When Time Began***In the Bronze Age, the Indus Valley of Pakistan and Northwestern India was one of the cradles of civilization. Their lost language was proto-Dravidian. The**

*Vedas*were written in the Indo-European predecessor of the Indian root-tongue Sanskrit.**The two main cities were Mohenjo-Daro in Sind, and Harappa in the Punjab. Its original civilization, the Harappan, emerged about 2500 B.C. This was a sophisticated urban society with pictographic systems of writing and measurement (metrology). A thousand years later, Aryans brought cultural influences from the north with rituals that formed the foundation of Hinduism. These traditions apparently included number mysticism, but one of astronomical numbers, not integers..**

**Beginning with the**

*Brahmanas*, and even the*Puranas*, the Indians developed the doctrine of the four Yugas, the four Ages of the World. The essence of this theory is the cyclical creation and destruction of the World and the belief in "the perfection of the beginnings." As the Buddhists and Jains hold the same views, this doctrine of the eternal creation and destruction of the Universe is a pan-Indian idea.**In Indian cosmogony, the complete cycle is terminated by a dissolution (**

*pralaya*), with a great dissolution (*mahapralaya*) at the end of the thousandth cycle.**The names of the four Yugas first appear in the**

*Aitareya Brahmana,*VII, 14. In India, time is not a measure of quantity, but a means of expressing universal relationships. This doctrine of ages is a variation on the Myth of the Eternal Return, a primal conception of periodic renewal of the World.**In Hinduism, man plays no part in this re-creation, but desires to escape from the cosmic cycle. There is no final End of the World, just intervening annihilations of one Universe and the appearance of others.**

**In every age there is a turning-point, a new way of seeing and asserting the coherence of the world. Each culture tries to fix its visionary moment, when it was transformed by a new conception either of nature or man.**

**When seeking the roots of ancient sciences, it is important to remember that a language system may persist in the religious or sacred arena long after it is superceded by a more popular dialect. This has been the fate of Sumerian (which ceased to be spoken around 2000 BC), but was the language of sacred liturgy and divine knowledge for fifteen more centuries.**

**Other liturgical languages with a similar destiny include Sanskrit, Hebrew, and Latin, (as well as Old Slavic). The Akkadians preserved old Sumerian religious structure of a supreme Triad, and this reflected into India as Brahma/Vishnu/Shiva and the west as the Trinity.**

**The Akkadians promoted the Sun god over the Supreme Triad, and the Triad gradually lost cult supremacy to the sun as unrivaled universal divinity whose primary quality is the emanation of numinous light.**

**Another creation of Akkadian religious thought is divination. They multiplied magical practices and developed occult disciplines including astrology, which later became popular throughout the Asiatic and Mediterranean world. They added the personal experience to religious life and exalted certain divinities to supreme rank.**

**Astrology, a late development, was originally practiced primarily by the royal entourage. Over time, the ideas, beliefs and other techniques of Mesopotamian origin circulated from the western Mediterranean to the Hindu Kush. The Mesopotamian discoveries always emphasized a direct correspondence between heaven and earth, or macrocosm and microcosm. Contact with Sumerian culture mutated other civilizations, including the Egyptian.**

**The first cities of India, the indigenous Harappan civilization, were overrun by the Aryan warlords, who deplored writing and had no cities of their own. Their characteristic feature, before they settled down, was oral tradition, since after their encounter with the Near Eastern civilizations, they prohibited using writing.**

**This mixing of cultures led to a religious syncretism or mixing of the mental concepts of both groups, which very shortly spread Hinduism through the subcontinent. The Harappan religion provided the prototype of the Mother Goddess and her consort, the phallic**

*Shiva**Shiva/Shakti*). They echo Mesopotamian mythology. (**Around 1750 BC, the Indus civilization was on its deathbed, and the Indo-Aryans gave it a mortal blow. But this happened progressively, over centuries of intermingling. Aryanization of the Punjab launched the movement of the synthesis that became Hinduism.**

**In the west, the Hellenic culture and religion was the result of the symbiosis between the Mediterranean substratum and the Indo-European conquerers from the north. Then Hellenism sent its roots into Egypt and Asia on the tide of Mycenaean conquerors.**

**Despite symbiosis with countless pre-Hellenic traditions, the Aryan-speaking conquerors succeeded in imposing their pantheon and in maintaining their specific religious style. The original home of the Indo-Europeans is the region north of the Black Sea between the Carpathians and the Caucasus.**

**The Indo-Europeans had elaborated a specific mythology and theology (pantheon headed by a storm god and Mother Goddess). They practiced sacrifices and knew the magico-religious value of the Word and of chanting.**

**They possessed concepts of rituals that enabled them to consecrate space to "cosmicize" the territories in which they settled, and enabled them to "periodically renew the world." 10800 bricks in the fire altar = recreating universe in a ritual imitation of creation.**

**The Indo-European tribes called themselves Aryan, "noble man." They progressively assimilated the survivors of the Dravidian Indus civilization, as shown by language. Vedic Sanskrit has a series of phonemes, especially the cerebral consonants, which are found in no other Indo-European idiom, not even in Iranian. Very probably these consonants reflect the pronunciation of the aborigines trying to learn the language of their masters. Similarly, the Vedic vocabulary preserves a large number of non-Aryan words.**

**The time of the**

*Asuras*preceded the present epoch, ruled by the*Devas.*In India as in a number of archaic and traditional religions, the passage from a primordial epoch to the present epoch is expressed in cosmogonic terms: passage from a state of chaos to an organized world, a cosmos.**The**

*agnicayana*ritual was an imitation of the creation which sacralized a locality, making it the local center of the universe. The altar was built with 10,800 bricks piled up in five courses, sometimes taking the form of a bird, symbolizing the sacrificer's mystical ascent to heaven.**Originally, it involved human sacrifice, repeating the self-sacrifice of Prajapati. The building of the altar symbolized the creation of the universe, which consecrates any land. The cosmologies, like so many other religious ideas and beliefs, represent a heritage transmitted from prehistory everywhere in the ancient world. The Indians revalorized and reinterpreted many cosmogonic myths.**

**In the most famous hymn of the**

*Rig Veda*, the cosmogony is presented as a metaphysics, revealing how Being came out of Non-being. There was an undifferentiated principle called "One" (neuter): "*The One breathed from its own*i*mpulse, without there being any breath*." Aside from that "nothing else existed."**Heat gave birth to the "One" potential and this potential developed desire which became Consciousness. The first seed then divided itself into genders, and the gods were born afterwards. The "One" transcended both Gods and Creation. The One precedes the universe and creates the world by emanation from his own being. Both consciousness and the universe are the product of procreative desire.**

**The**

*Rig Veda's*notion of the "One" is continued in the identity of*Purusha/Prajapati*. In the beginning Prajapati was the nonmanifested Unity-Totality.**The triple identification of Prajapati with the universe, with cyclic time (the year) and with the fire altar constitutes the great novelty of the Brahmanic theory of sacrifice.**

**They contain the thought that the world and life exhaust themselves by their very duration.**

*Satapatha Brahmana*states that, "*This Prajapati, the Year, is made up of 720 days and nights; that is why the altar comprises 360 enclosing stones and 360 bricks.*" In short, every sacrifice repeats the primodial act of creation and guarantees the continuity of the world for the following year.**In the**

*Brahmanas*, sacrifice recreates the cosmos that has been exhausted by cyclic time (the year). This later becomes the conceptual basis of creating the*atman*, or indestructible spiritual being.**The self (**

*atman*) is equated with Brahman. The Brahman knows the structure and origin of the universe, because he knows the Word that expresses all that; for*Vac*, the Logos, can transform any person into a Brahman.**The identity atman-Brahman leads to the experience of "inner light." This spiritual exercise reflects the Vedic tradition that the sun and light are regarded as epiphanies of Being, of Spirit, of immortality and procreation. According to the**

*Rig Veda*1.115.1, the sun is the life or atman--the Self--of all things. The atman is a form of "light in the heart." That Immortal, fearless being is atman. That is Brahman.**The identity brahman-atman constitutes the most important discovery of the**

*Upanishads.***The**

*MAHABHARATA*, with 90,000 verses is the longest epic in world history. It recounts the conflict between two lines of Bharatas. By the fifth book of the series, they are preparing for battle, which is recounted in the sixth book--the Bhagavad Gita.**This monstrous war was decided upon by Brahma, to relieve the earth of a population that did not cease to multiply. Therefore, Brahma convinced a certain number of gods and demons to become incarnate in order to provoke a terrifying war of extermination.**

**Thus, the**

*MAHABHARATA*describes the end of a world (*pralaya)*, followed by the emergence of a new world. The poem has an eschatological structure revealing a gigantic battle between good and evil. There is destruction on a cosmic scale followed by the resurgence of a new and pure world. It is the conclusion of a cosmic age.**The cyclical theory was popular from the earliest times of the**

Even though the eschatological myth is not documented in the Vedic period, this doesn't prove that it did not exist. The

*Puranas*. The eschatological myth is older than Hinduism; it is archaic and widely disseminated among crossroad cultures. The myth of the end of the world was known by the Indo-Europeans.Even though the eschatological myth is not documented in the Vedic period, this doesn't prove that it did not exist. The

*Mahabharata*contains Vedic and pre-Vedic notions. It is an epic transposition of an eschatological crisis, which Hindu mythology called the end of a yuga. It is a grandiose synthesis, much richer than the Indo-European prototype. In this cycle of the eternal return, Krishna reveals himself to Arjuna as an incarnation of Vishnu.**Vishnu is the author of catastrophic destructions and resurrections. This is as much to say that Vishnu, as a supreme being, is the ultimate reality. He governs both the creation and destruction of worlds. He is beyond good and evil, like all the gods.**

**But the poem also glorifies the complementarity of**

*Shiva*and*Vishnu*, the Aryan/Harappan synthesis. These gods, together with the Great Goddess (*Shakti, Kali, Durga)*have dominated Hinduism from the first centuries of our era to the present. Understanding the creative/destructive aspect of divinity is equivalent to a revelation and also constitutes a model to follow in obtaining deliverance.**Deliverance involves comprehension of the relations between the two modes of the real: immediate--that is, historically conditioned--reality and ultimate reality.**

**Curiously, this paradoxical work about a frightening war of extermination and the end of a**

*yuga*is the exemplary model for every spiritual synthesis achieved in Hinduism, especially the tendency to reconcile contraries. It justifies a certain mode of existing in time; it valorizes the historicity of the human condition. Arjuna's existential crisis ends with his exemplary revelation concerning the human condition and the "ways" of deliverance.**Like the Greeks and the Jews, the Hindus faced the dilemma of time's meaning:**

**In the**

*History of Religious Ideas*, Eliade puts it succinctly:

*"How is it possible to resolve the paradoxical situation created by the twofold fact that man, on the one hand, finds himself existing in time, condemned to history, and, on the other hand, know that he will be 'damned" if he allows himself to be exhausted by temporality and by his own historicity, and that consequently, he must at all costs find in the world a way that leads to a transhistorical and atemporal plane."***Since the whole univese is the creation, (or even the epiphany of**

*Krishna-Vishnu)*, to live in the world, to participate in its structures, does not constitute an evil act. The "evil act" is to believe that the world and time and history posses an independent reality of their own, that is, to believe that nothing else exists outside of the world and temporality. The idea is certainly pan-Indian, but it is in the*Bhagavad Gita*that it received its most consistent expression.**It is still Vishnu who periodically destroys the universe, at the end of each cosmic cycle. All is created and governed by God. Cosmic life, individual existence and history receive a religious meaning. The periodic destruction of the universe is a theophany...the resacralization of life and human existence.**

**In Hinduism, man plays no part in this re-creation, but desires to escape from the cosmic cycle. There is no final End of the World, just intervening annihilations of one Universe and the appearance of others.**

**In every age there is a turning-point, a new way of seeing and asserting the coherence of the world. Each culture tries to fix its visionary moment, when it was transformed by a new conception either of nature or man.**

**Hindi Baseten Numerals**

**The history of our base ten system emerges from this Hindu cosmogony and astronomy. Hindi-Arabic numerals penetrated into Europe beginning in the 12th Century. A unique property of Hindu numerals is that (unlike Hebrew, Greek, Roman, Mayan, Chinese, or other characters) the numerals are REVERSABLE and hold place value.**

**Without resorting to graphic depiction to reveal inherent symmetry and rhythms, they allow for the symbolic representation of palindromes and transpalindromes, the emergence of classes of numbers.**

**This is a singular property of this base ten system of notation, even though the Hindus were influenced by Hellenistic culture as well. Greece and the Near East still employed alphabetic numerals, with no place values. With the advent of positional numeration and its universal acceptance, the decimal cryptogram of a number automatically provided it with a name.**

**According to the Hindu view, all the aspects of the manifest world spring from similar principles. There is a correspondence or equivalence between sounds, forms, numbers, colors, ideals, as there is also between the abstractions of subtle and metaphysical worlds on one side and the forms of the perceptible universe on the other. Astronomical phenomena form the basic symbols of universal principles.**

**According to the Nondual Principle, the Supreme Cause must be beyond Number, otherwise Number would be the First Cause. But one is considered a number just like two, or three, or ten, or a million. If "God" is one, he is not beyond number any more than if he is two, three, or a million. But, although a million is not any nearer to infinity than any number, it seems to be so. The number one is in a way the number farthest removed from infinity, so divinity is best represented by an immense number of different gods.**

**In the**

*Puranas*, it says,*"The nature of illusion (maya) is [represented by] the number one."***To speak of the manifest force of a unique God implies a confusion between different orders. God manifest cannot be one, nor can the number one apply to an unmanifest causal aspect. At no stage can unity be taken as the cause of anything, since the existence implies a relation and unity would mean existence without relation.**

**Divinity as ultimate essence, is neither one, nor two (dual), nor many. The nondual principle transcends all forms of manifest divinity. This nondual Immensity is the Brahman, on a plane different from that of existence. Existence is multiplicity.**

**The identity of the macrocosm and microcosm can be observed in the permanence of the relations found as the substratum of all the aspects of the perceptible universe. These relations can best be expressed in terms of number. Hence NUMBER is easily seen as the common element of all forms, the all-pervading unity of all substance. Modern physics reflects and confirms this philosophy.**

**The creative or revealed Word of Brahm in the Vedas is**

*AUM*, or*OM**.*It is the first manifestation of articulate language, the root monosyllable, which includes all language and meaning. It is the seed syllable of all human speech, a nutshell containing the whole of wisdom. The four Vedas are merely comments on and amplifications of this infintely meaningful syllable. It is more than past, present, and future; it is an indestructible Immensity

*AUM*is said to issue through a process of MULTIFOLD REFLECTION.**Taken as a symbol of divinity,**

*AUM*appears as the form from which the universe develops; the first thought-form of Brahman, the Creator. From this basic syllable spring forth all the elemental sounds, the roots of manifestation, keys of all language.**The number 4,320,000 (108 x 40) has a very ancient symbolic or "divine" meaning. It came to India with the Aryan migration and became codified in the**

*Rigveda, Book of Sacred Verses*. Among other things, it is the number of syllables in the*Rigveda*, which has 40 syllables per stanza, (10800 stanzas x 40 syllables = 432,000).**Hindu tradition associated the "divine" number 432,000 with the Brahman and the**

*Yugas*and Ages. This number of the*catayuga*divided by four yields ages of diminishing length.**Golden Age = 4 x 4,320,000 = 1,728,000**

Age of Knowledge = 3x =1,296,000

Age of Sacrifice = 2x =864,000

Age of Discord = 1x =432,000

Age of Knowledge = 3x =1,296,000

Age of Sacrifice = 2x =864,000

Age of Discord = 1x =432,000

**Ten eons = 1000 cycles of caturyuga = 4,320,000,0000 years; "Day of Lord Brahman," This is a close estimate to the age of the Solar System, 4.5 billion years..**

**These are divine, not human years...the corresponding duration for the**

*Kali Yuga*is 36,000 mortal years. 32 x 12.**Indian Science and Cosmology**

**The Golden Age of Indian science came to medieval India during the Gupta Empire (320-647 AD) when culture and the arts flourished. The most famous scientist of the period was the astronomer and mathematician Aryabhata. He discussed, in verse, quadratic equations, sinces, the value of pi, eclipses, solstices, and equinoxes, and the spherical shape of the earth, and its daily revolution on its axis. His successor, Brahmagupta, systematized the astronomic knowledge of India.**

**Other Indian astronomers made up a calendar of 12 month, each of 30 days, each day of 30 hours, inserting an intercalary month every five years. The Buddhists still use a lunar calendar. They also predicted eclipses accurately, calculated the moon's diameter, and expounded the theory of gravity.**

**Indian astronomy and mathematics were unequaled (except in geometry) by those of any ancient western people. Our Arabic numerals and decimal system which come from them are far more fluid and versatile than any before them. The numerals can be found on the rock edicts of Asoka (256 BC), while the scientists used the decimals system long before the Arbs, Syrians, and Chinese had a chance to borrow them. The mathematicians also created the concept of a negative quantity (without which algebra could not exist), and found the square root of 2, and solved complicated equations.**

**The discovery sometime in the first centuries of our era of the Principle of Position became a world-wide event. It was a radical departure in method, which in Syndex Theory makes reciprocity possible. Without this principle of position no progress in arithmetic was possible.**

**Place position probably was inspired by the use of counting boards. ZERO was probably conceived this way also from an empty column, and became the Indian SUNYA. It reprents a turning point for modern science, industry, and commerce. It paved the way to a generalized number concept, and plays a fundamental role in nearly every branch of mathematics. It is one of the single greatest achievements of human thought.**

**There is an ancient code of numbers and proportion based on metrological standards of measure. Such constants as astronomical Precession, and geodetic measures such as polar diameter provided the basic context. Fractions of the earth's principle dimensions mirrored numerical patterns in the appearance and movement of nature.**

**These numbers are the vestiges of the Sumerian sexagesimal system and calendar. Earlier measures of astronomy, astrology, and cosmology were usually in units of 12, as were various ancient units of measurement of time.**

**Mankind counted days and the changing of the moon and seasons for millennia before recorded history. As early as 3760 BC, the Sumerians created a lunar calendar. By 2800 B.C., they had worked our a cycle of 19 years which kept it synchronized with the solar year and seasons. Certain years had 12 lunar months, while others had thirteen. This lunar calendar was adapted by the Akkadians, Babylonians, Assyrians, Greeks and Jews. The Nippur calendar is still the basis of Jewish religious ceremonies.**

**Sumerian astronomy included the concept of "deep time," as recounted in the**

*Enuma Elish, the Epic of Creation*. Ancient texts known as the Sumerian King Lists describe the settling of the divine Anunnaki on Earth before the deluge. They list the governorships of the first 10 leaders which lasted a total of 120*sars*, or 432,000 Earth-years.**This is a direct source for divine eras in Hindu lore, but they expand the vastness to an overall time span of 4,320,000, and then to a Divine Year or Day of Lord Brahma--4,320,000,000--a thousandfold great**

*yugas.*The Sumerian formula is echoed in the Hindu traditions.**From Sumeria comes the ubiquitous concept of a sky divided into 360 degrees of Latitude, 60 minutes of 3600 seconds; 12 month years beginning on Spring Equinox; 12 hours of day and night (2x12=24); 12 signs of the Zodiac, etc.**

**Sumerian fractions were geared to the principle of repeated halving. Whole unit or natural fractions are important in arranging metrological units. The system based on 60 is evenly divisibly by 2,3,4,5,6,10,15, and 30 eliminating the frequent need of fractions. This naturally leads to grouping higher units in 12, 30, or 60. All these ratios occur in one or another of the parallel systems of units in Mesopotamian metrology. 4320 is one such number; so is 108000.**

**The Greek astronomers adopted this system, and so did their followers in India, the Islamic Empire, and Europe. Much of the mathematical knowledge commonly ascribed to the early Greek philosophers was already known to the Egyptians and Mesopotamians centuries before the rise of Greek civilization. However, the Greeks preserved and spread this knowledge. They were the first to consider mathematical concepts as abstractions not part of the real world, but of the idealized "sacred space" of the human mind.**

**There is some evidence of ancient India having direct contact with Sumeria around 2500 B.C. This is difficult to document, but not to deduce. However, nevertheless, Hindus contributed the final step to mathematical astronomy, namely, the use of the place value notation for the smaller decimal units. This is where we get our divisions of 60, 24, 12, and 2.**

**AS WE HAVE SHOWN ELSEWHERE, THESE ARE CLOSELY ALLIED TO THE HOLOTOMIC SEQUENCE: 12 - 24 - 72 - 360 - 2520, ETC.**

**These numbers are the vestiges of the Sumerian sexagesimal system and calendar.**

**ROOTS OF**

**THE NUMBER CONCEPT IN INDIA**

**2500-1500 BC Contact with ancient Sumerians. Indus civilization; proto-Dravidian language; pictographic script; no firm evidence of separate numerals. Pre-Vedic**

*PURANAS*, "Ancient Writings."**1500-1001 BC**

*UPANISHADS*: Vedic period begins;*RIGVEDA*, Sacred Book of Verses.**1000-801 BC Pantheistic religion develops; Brahmanism; astronomy; lunar year adjusted to correspond with solar year; In Greece, alphabetic number system.**

**700-600 BC Indian**

*VEDAS*completed; doctrine of transmigration.**585 BC In Greece, Thales uses Babylonian methods to predict eclipse of sun.**

**500 BC Era of Buddha; Sanskrit alphabet and grammar codified.**

**500-451 BC**

*RAMAYANA*text.**326 BC Alexander invades India; Greco-Indian kingdoms established; Greek influence on art and science. Hellenistic culture flourishes. Barrier between East and West broken.**

**300 BC**

*MAHABHARATA*text.**250 BC In Greece Erathosthenes sieve reveals distribution of primes among first 100 integers.**

**Early centuries AD Invention of the Zero (Sunya) & negative numbers in India.**

**150 AD In Greece, Ptolemy's**

*ALMAGEST,*a unified method for representing celestial phenomena, circular cycles and epicycles.**300-400 AD Christians vandalize Library at Alexandria, Egypt.**

**375-413 AD Astronomical and mathematical advances of medieval India; Aryabhata,**

Brahmagupta.

Brahmagupta.

**400 AD**

*SURYA SIDDHANTA,*classical astronomical text; spherical geometry; epicycles; formula for length of day; solar velocity; earliest place value; #108 = numberword AUM (OM) = Universe.**500 AD Aryabhata argues for a moveable and rotating earth.**

**505 AD**

*PANCA SIDDHANTA*, by Viraha Mihira, summary of five classical astronomical treatises; sine tables.**595 AD Powers and roots of numbers; first recorded decimal reckoning.**

**600-700 AD Moslem Empire; Moslems burn Alexandria Library, ancient exact science lost to west.**

**760 AD Hindu numerals known in Bagdad; Arabs bring decimal system from India.**

**810 AD Al-Khwarizmi uses zero and positional notation to create algebra.**

**814 AD Arabs adopt Indian numerals, including zero to multiply by 10.**

**850 AD Mahavir, Indian mathematician; Pythagorean triplet construction known in India.**

**975 AD Present arithmetical notation taken into Europse by Arabs, Jews, and Crusaders; penetrates by 12th century.**

**1000 AD Sridhara recognizes the importance of zero; present version of**

*SURYA SIDDHANTA.***1030 AD al-Biruni's report on Hindu astronomy and astrology derived from Viraha Mihira.**

**1100 AD Europe begins adopting Hindu-Arabic numeral system from Jewish scholars who learned it in Babylon, Jerusalem and Islamic Spain. First brought to Europe by Moors; introduced by Gerbert of Aurillac (Pope Sylvester II), about 1000 AD.**

**1202 AD**

Leonardo Fibonacci, who derived it from Al-Khwarizmi during his North African travels. Introduced Arabic-Hindu numerals to Europe in Latin translation.

*Liber Abaci (Book of the Abacus)*written by Italian mathematicianLeonardo Fibonacci, who derived it from Al-Khwarizmi during his North African travels. Introduced Arabic-Hindu numerals to Europe in Latin translation.

**THE**

*SURYA SIDDHANTA*THE CLASSIC OF INDIAN ASTRONOMY**--**

*"The time by which the worlds come to an end is different from the time which measures life. Time is thus of two kinds, gross and subtle, manifest and unmanifest."*

*Surya Siddhanta*1.10 [371]**The worship of the sun was common in antiquity and India was no exception. There is a famous sun temple in Konark in South India, and in the historic town of Mooltan or the land of the Sun, in the North. The sacred wordnumber 108 had to do with the numbers of revolutions of the sun in the various epochs, which are all multiples of #108.**

**The Holotomic Sequence was discovered through a systematic graphic analysis of the enspiralment of number 108 (or 3 x 36).**

**Not only sacred to the Hindus, this number also appears in Tibetan Buddhism, where it is considered highly auspicious, being the number of beads on each strand of the malla, or Tibetan rosary beads. Therefore, it reveals its character as an ancient symbolic form of circular unity.**

**The Hindu calendar claims an amazing antiquity. Its alleged starting point is the divine beginning of Brahman, the first god of the Holy Triad Brahman/Vishnu/Shiva. Its unit is the**

*Kalpa*, equivalent to one day of Brahma's life (4,320,000,000 years--a close estimate to the age of the Solar System). Brahma's alloted life span is 100 years of 365 Kalpas each. The present epoch is the*Kali Yuga*and this Hindu year exceeds the figure 155,521,972,849,000 and counting.**In both solar and lunar calculations, the ancient Hindus fixed certain points of time back as epochs. They each begin when the planets are assumed to fall into a line of mean conjunction with the Sun in the beginning of Aries. In the classic astronomical text, the**

*Surya Siddhanta*(400 A.D.), the zodiacal signs are used to denote arcs on any great circle.**In the**

*Surya Siddhanta*, the least cycle of years in which the Sun, Moon, and planets are supposed to return to a line of mean conjunction at the beginning of Aries is 1080,000 years, a fourth of a*Maha Yuga*of 4,320,000,000 years or revolutions of the Sun (*Surya*). The revolutions given in the*Surya Siddhanta*must always be divisible by four, or no mean conjunction could take place at the beginning of the*Kali Yuga.***There are two primary astrocalendaric systems in India, solar and lunar:**

*Yugas*and Ages denoted by metals:**According to Neugebauer (1952), the sixth chapter of the**

*Surya Siddhanta*deals with a graphical representaion of the different phases of an eclipse; the thirteenth chapter deals with the construction of a celestial globe. These mysteries were reserved for initiates: "*This mystery of the gods is not to be imparted indiscriminately: it is to be made known to the welltried pupil, who remains a year under instruction."***Spherical astronomy methods are characterized by the use of the interior of a sphere for determining the length of circular arcs on the sphere. This method was used in the**

*Surya Siddhanta*to determine the length of daylight from the shadow of a sundial of known height.**Another astronomical text, the**

*Panca Siddhanta*(505 A.D.), written by Varaha Mihiri is a summary of five great classical astronomical treatises. It reveals a close relationship in methods of calculation to the Babylonian linear (arithmetic) method. This method of determining the position of the sun works with zigzag functions or step functions which approximate greatest and smallest solar velocity. There is no direct evidence for a direct link from Babylon to India, but it cannot be ruled out. However, the Hellenistic influences in the texts are obvious to scholars.**Despite its origin, the apparently Babylonian knowledge was passed back to Asia Minor in an improved form by al-Biruni, who reported on Hindu astronomy and astrology in 1030 A.D. The**

*Panca Siddhanta*also contained rules for computing lunar motion based on processes now known to us from Greek sources.**But the**

*Surya Siddhanta*arguably remained the main canon of Hindu astronomy. It was allegedly revealed by the Sun (Surya) at the end of the Golden Age (2163102 B.C.) to a Maya Asura. Its contents, however, reflect the Hellenistic influence.**While the original may be dated to 400 A.D., the consistently-modified present version may have been written as late as 1000 A.D., long after the conquests of Alexander the Great (356-323 B.C.), and his death in Babylon. From that point forward, Hellenistic and Mesopotamian sources are definitely mixed.**

**The terminology and methods of Hindu astrology are certainly of Greek origin. For example, the names of the zodiacal signs are Greek loan-words. Similarly, the basic concepts of the planetary theory of the**

*Surya Siddhanta*are influenced by the Greek epicyclic models and not by Babylonian linear methods.**In the chronology of Hindu astronomy, linear methods as well as trigonometric models point to the early centuries AD, not BC. Babylonian methods and concepts reached India either via Persia or Roman/Greek sea routes to Pondicherry where these methods first surface in the subcontinent. They appear only in the form of Hellenistic astronomy and astrology.**

**The**

*Surya Siddhanta*combines older, very primitive sections with the Greek theory of epicyclic motion. But even though this Greek influence is apparent, it has obviously undergone a quite independent transformation in many details of the general theory.**Modifications of certain types, such as the values of numerical constants, went on almost continuously. They moved closer into accord with the Hellenistic sources. The time of the**

*Surya Siddhanta's*origin and this cultural contact is the same--about 400 AD.**The source book of the**

*Panca Siddhanta*is the*Paulisa Siddhanta*which contained the earliest documented sources on place value notation. Hindu astronomy reflects here the oldest strata of Greek astronomy, without Ptolemaic theory's refinements, (150 BC-150AD).**Latin translations of the astronomical tables of Al-Khwarizmi are a curious mixture of the Hindu and Greek methods. He translated**

*SLOKAS,*or Hindu sacred verses, for the west. Another Arab scholar, Al-Biruni translated an astrological work of Varaha Mihiri's into Arabic.**According to Neugebauer:**

"There are many evident indications of a direct contact of Hindu astronomy with Hellenistic tradition, e.g. the use of epicycles or the use of tables of chords which were transformed by the Hindus into tables of sines. The same mixture of ecliptic arcs and declination circles is found with Hipparchus and in the early Siddhantas, [where they referred to polar longitude and polar latitude]." The extensive use of the sexagesimal system is common in both Greek and Mesopotamian astronomy.

"Indian asterisms appear in Abu Ma'shar, and their source is found in the astrological writings of varaha Mihira, the same author of the sixth century AD in whose astronomical work we found the use of the linear methods for the lunar motion, otherwise known to us from Greek papyri and finally from cuneiform tablets. Following the unmistakable traces of very specific astrological doctrines, one can reconstruct the road which connected Hellenistic Mesopotamia with Hellenistic Egypt, with pre-Islamic Persia, and with India."

**The lunar theory presented in the**

*Panca Siddhanta*is essentially the same step functions described in Babylonian texts. In the*Surya Siddhanta*, the zodiacal signs are used to denote arcs on any great cicle, as did the Greek Hipparchus. In the*Surya Siddhanta*, lunar months are described of fixed length, but later in Hindu astronomy they are of variable length as in the adjusted lunar calendar. Decimal place value notation probably was a modification of the sexagesimal place value notation with which the Hindus became familiar through Hellenistic astronomy.**So, it appears that even in the ancient world, "there is not much new under the sun." Concepts travelled along cultural exchange routes, and were widely shared and modified, then recycled back to where they came from...in the so-called beginning.**

**However, for the case of the Hindu calendar systems, this is hardly as far back as their huge cosmolgical epochs would have us believe. Even though the**

*Maha Yuga*is a good pre-scientific guess for the age of the Solar System, (4.5 billion years), there is another, symbolic meaning to these great sums. The key numbers' importance comes from basic metrological constants. 25,920 = 2160 x 12 is the formula of the "Great Year" or or Precessional Cycle. 500 such cycles 500 x 25920 = 12,960,000.**The Aryan, or pre-Vedic**

*Puranas*derived ages from multiples of 3,600: 3600 x 3600 = 12,960,000. The globe is divided into 360 degrees of latitude, each degree containing 60 minutes of 3,600 seconds. 3600 = 602 . 3168 - 1008 = 3.1428571. #1080 is a cross-cultural lunar number, and close to the radius of the moon in miles.**Haraclitus spoke of 10800 years between successive destructions of civilizations. Its Aryan roots show in the Germanic 1080 pillars of Valhalla. In oriental astronomy, it is an important metrological unit (1080): divide a circumference of 3393 by 108 = 3.1416666.**

**60, 602 , 603 , 604 , = 12,960,000**

**(c) 2010-2014 Iona Miller, All rights reserved on all graphic and written content.**

If you mirror my works, plus include the credit and URL LINK for reference.

This site is a natural product made from recycled electrons.

If you mirror my works, plus include the credit and URL LINK for reference.

This site is a natural product made from recycled electrons.