## The Auric Key

**The Auric Key**

**Prelude to Terms and Proceedures of the Auric Key**

**Sequence of Discovery**

**The Structure of Numbers**

**The Study of Synchrographics**

**The Auric Key: A Poemgraph**

**The Auric Key as an Outgrowth of Synchrographics**

SYNCHROGRAPHICS & THE AURIC KEY

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*"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 A

E 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 = 1

1 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 Synch

Orange 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 Gold

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 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 Node

279720 - 105 = 2664

108 = 2590

111 = 2520 Auric Node

**279720 - 35 = 7992**

36 = 7770

37 = 7560

36 = 7770

37 = 7560

**279720 - 5 = 55944**

6 = 46620

7 = 39960

6 = 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 = 2520

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 = 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 accomodate 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,**

864,000,000

864,000,000

**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 occcur 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 implicite 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.**

**SYNCHROGRAPH C:**

**#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 24

Copper 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:

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 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

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.

*"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.