THE MANDALOG OF THE UNIVERSE
"In India, where the first form to appear in the lotus of Vishnu's dream is seen as Brahma, it is held that when the cosmic dream dissolves, after 100 Brahma years, its Brahma too will disappear--to reappear, however, when the lotus again unfolds. Now one Brahma year is reckoned as 360 Brahma days and nights, each night and each day consisting of 12,000,000 divine years. But each divine year, in turn, consists of 360 human years; so that one full day and night of Brahma, or 24,000,000 divine years, contains 24,000,000 times 360 or 8,640,000,000 human years, just as in our own system of reckoning the 24 hours of a day contain 86,400 seconds--each second corresponding to the length of time, furthermore, of one heartbeat of a human body in perfect physical condition. Thus it appears not only that the temporal order written on the faces of our clocks is the same as that of the Indian god Vishnu's dream, but also that there is built into this system the mythological concept of a correspondence between the organic rhythms of the human body as a microcosm and the cycling eons of the universe, the macrocosm."
Joseph Campbell, The Mythic Image
As such, Marshall was a seer when he conceived Synchrograph C or Synch "See," as a mandalog of concentric circles, in the tradition of the mantras, mandalas, and yantras (graphic mantram).
In a gestalt approach to 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 displays can reveal certain features of number behavior which remain hidden in numerical or linguistic terms. The neighborhood of special numbers can be revealed by certain spiralic displays of circular unity (mandalogs).
#108 as the Hindu number of the Universe is one such circular totality which encodes the structure of Epochs or Divine Ages. Since the incremental numbers of the ages are multiples of #108, when enspiralled along 108 axes, the characters 0 - 6480 all align along the zero/108 axis -- they share the same neighborhood.
The synchrographic structure of the 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 number of zeros at the end of any astronomical Hindu number is nearly arbitrary. 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 #108, 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.
"The word OM," said Ramakrishna to his friends, "is Brahman. Following the trail of OM, one attains Brahmin." The vowel O in Sanskrit is regarded as a fusion of A and U.
Note also that the numbers 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, Precessional numbers).
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.
Prior to this development, there were no most useful base ten Hindu characters with place valuation which makes the retrocity of the base wave visible. But since Sumerian times, there were Tables of Multiplication which clearly demonstrated the factors of divisibility of even astronomically large sums.
The certain numbers which stood out for their special properties came to be recognized as sacred or divine. As we have seen elsewhere, these are closely related to the Holotomic Sequence, which has its nave in the perfect number 6.
12 - 24 - 72 - 360 - 2520, etc. are all key numbers in the Sumerians so-called sexagesimal system. It was not beyond the Sumerians to determine their factors of divisibility even when they had no concept of the unique properties of prime numbers.
SIX, not sixty, is the key to the original system, which much later influenced the development of Hindu numerals and Divine Ages. There was a decimal subtext to the original Sumerian sexagesimal system.
Numeronomy is naturally based on six, not sixty. The assumption of sixty as the number on which the Sumerians based their system of calculation creates a difficulty in seeing how the number six, by itself, gives the foundation for the synchronization of number and geometry.
Six as the first perfect number denotes circular unity in planal geometry and accomodates Synergetics requirements for wholeness. By doubling six, we involve spherical unity represented by the close pack of 12 spheres around one. The number 60 shows no such harmony. Symmetry and synchronicity of planal and spatial systems of geometry and number share a basic unified interface.
60 is not a Holotome, and does not represent a symmetrical retrograde unity when mapped out in the synchrographic discipline.
It does however contain a unique nature in that it is the lowest number to accomodate 2, 3, 4, 6, and 8. ITS MISSING DIVISORS, FIVE AND SEVEN are conspicuously absent in either the Yugas or Ages.
NO FIVES EXIST IN THE YUGAS; NO SEVENS OR THREE EXISTS IN THE AGES. 2, 3, 5, 7, 11, and 13 are the first primes.
The absence of these specific primes in these modules holds an important key to the preBabylonian use of number thirtysix. 3 x 36 = 108, the Hindu number of the Universe, another form of totality. In each block of the divine epochs, the sum number of each block is tenfold the initial number. These calendaric values could have been discovered by contemplation on multiplication tables, and observational astronomy.
12 x 3 = 36 x 3 108 62 = 36
All numbers divisible by Holotome A: #12
432 = 12 x 36 648 = 12 x 54
The Sumerian calendar was based on the 25,920 Precession cycles. While the Platonic Year was based on the divine number 2160 (1080 x 2). Plato mentions another divine number in his Republic, 5040 (2520 x 2).
12 x 2160 = 25920
20 x 108 = 2160
36 x 60 = 2160
2160 + 360 = 2520
2160 + 432 = 2592
So, the crucial key to the anatomy of BASETEN NUMBER BEHAVIOR lies in the special series of number modeules referred to as the Holotomic Sequence.
It represents the ordinal series of those minimal numbers that accomodate the maximum amount of consecutive factors of division from one onwards. The first nine members of the sequence include these symmetrical entities.
The first four numbers are recognized as numbers frequently used in prebabylonian times as metrological modules--the zodiac, 24 hours of the daily cycle; 72 = 1 degree of arc every 72 years; 360 degrees in a circle.
The next number (2520) is not commonly recognized, but 5040 was held in importance by Plato and alluded to in Revelations through the number 1260 (1260 x 2 = 2520).
THE MAJOR SIGNIFICANCE OF 2520 IS THAT IT IS THE FIRST NUMBER DIVISIBLE BY ALL NINE BASE DIGITS. FOR THIS REASON WE CALL IT THE AURIC KEY, for it made numeronomy graphically visible.
The next number 27720 of course is divisible by the first palindromic prime which is eleven and through its intimate connection to number nine is instrumental in the cycloreflexive wave that both separates and connects the Holotomes from and to each other. That is, it preserves the logical continuity of the transfinite chain of number. Each holotome retains and builds on the image of the one that precedes it.
The semiarbitrary answer to the question of why some unknown 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 not necessarily 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.
Since by multiplying 2520 by the next prime and receiving 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 exactly the most often cited numbers of ancient metrology we have arguably discovered a long-lost key to the basis of ancient metrology or numeronomy.
To amplify this claim, note that 12, 24, 72, 360, 2520, 27720, etc. are the exact sequence of minimum sums that accomodate the maximum amount of consecutive divisors (factors of division). #SIX was exactly half of the first true Holotome, making the first perfect number the nave of Holotome A (12).
The Holotomic Sequence was discovered through the systematic graphic analysis of the enspiralment of number 108 (AUM), and so was the 9/11 Cycloflex.
Multiples of 360, show the linkage between 360 and 2520 by prime numbers 7 and 11; this table yields interesting results.
1 x 360 = 360
2 x 360 = 720
3 x 360 = 1080; OM
4x 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 - 4 = 1080 x 2 = 8640
12,000 years of mahayuga x 360 "divine years" = 4,320,000
To summarize the Hindu translation of the divine years into human we arrive at the following:
4,800 x 360 = 1,728,000 human years
3,600 x 360 = 1,296,000 "
2,400 x 360 = 864,000 "
1,200 x 360 = 432,000 "
12,000 divine = 4,320,000 human years = 1 Great Cycle or Mahayuga
1,000 Mahayugas = 1 daytime (or 1 night) of Brahma (1 kalpa):
i.e. 12,000,000 divine years or 4,320,000,000 human years.
360 days and nights of Brahma (720 kalpas) = 1 Brahma year:
i.e. 8,640,000,000 divine or 3,110,400,000,000 human years.
100 Brahma years = 1 Brahma lifetime:
i.e. 864,000,000,000 divine or 311,040,000,000,000 human years.
THE SUMERIAN LEGACY
The Sumerian legacy is an integral aspect of Synchrographics. Historically, the first synchrograph could be considered their division of the sky into the 12 divisions of the Zodiac.
Zecharia Sitchin concludes that Sumerian science originated with the "gods from outer space." But it is not as mind-bending to imagine some more plausible alternatives to this "channelling." An ancient "Newton," "Leonardo," or "Einstein" could have bootstrapped his mathematical system from ages of pre-historical experience, 50,000 years of human observation of the heavens and earth.
Just like the nameless creator of the Phoenician alphabet, the name of the source was lost, but the useful knowledged retained. Steeped in legend and myth by Babylonian times it was attributed to a divine source just as we attribute our own moments of inspiration or genius to a higher source, beyond our ordinary selves. This nameless genius created an oral tradition whose tables and methods were eventually written down. At first, one had to be an initiate (priest or scribe) to use the methods. Later they were adopted in everyday life.
The ancient systematic observers noticed the regularity of the passages of the planets through the constellations of the fixed stars. They conceived the grandiose idea of a mathematically determined cosmic order of greatness with lesser ever-evolving cycles of celestial manifestation, disappearance and renewal. Man sought then to harmonize with these cycles through the timing of religious festivals and astronomically based calendars in imitation of heavenly circumstances.
The Precession of the Equinoxes was first noticed as a slow but steady slippage through the Zodiac of 1 degree every 72 years. To complete one cycle of the zodiac--a "Great" or Platonic Year--requires 25,920 years. Dividing this sum by 360 yields the number 432, the root of the mythological count of 432,000 years. However, it is not only mythological, or archetypal--it was discovered by centuries of controlled astronomical observation, even prior to written record-keeping.
In India, the Kali Yuga is supposed to have begun on February 17, 3102 BC. The astronomical aspect of a yuga begins with the sun, moon, and planets in conjunction in the initial point of the ecliptic. Everything returns to the same point at the end of the age. This belief originated way before Hindu astronomy and is cross-cultural. But 3102 BC is a good approximation of the invention of the arts of writing, mathematics, and astronomy--all of which are a remarkable effort at translating celestial mathematics into the ordering principle of life on earth.
This is the echo of the old Mesopotamian doctrine which reverberated through Greece and Rome (Berossos to Seneca) as well as India (Yugas). It spread all over the known world into Egypt, the Zoroastrians, and traces are even found in China, Mexico, and South America. The old Sumerian tradition of astronomical observation was the basis of all intellectual culture, and originator of the myths of eschatology, or end times.
The Sacred Portal
The sacred place, the center of transformation, has always been a refuge from the laws of the temporal world. Sacred space is the visionary gateway which opens communication with the transcendental reality of the divine. Here, as Jung states, "man is no longer a distinct individual but his mind widens out and merges into the mind of mankind--not the conscious mind, but the nconscious mind of mankind, where we are all the same.
When the concept of such a holy site or center is joined with a mathematically structured universe, derivation from ancient Mesopotamia must be suspected. It is the archetypal source, the navel of the world. In many cases, the center is conceived as an axis extending vertically upward and downward, with the center at the conjunction of the four cardinal direction.
This is the ancient model of sacred space, which corresponds in Synchrographics with the form of the T.R.I., the Triaxial Retrograde Interface. The three intersecting axes of Euclidean space with a shared coordinate.
The Hindus had a version of this centering mechanism called the regents of the directions. Brahma was in the overhead position, Vishnu below, with Shiva as the vertical axis. Each directions is attributed to a god and quality.
The essence of this image of the axial point or pole is that it symbolizes the way or place of passage from motion to rest, time to eternity, separation to unity; but then also, conversely rest to motion, eternity to time, unity to multiplicity. The realization of the nonduality of heaven and earth--even of being and nonbeing--is assimilated in the sacred center. The ego is sacrificed in the primal waters of deathlessness, and released to be carried in all directions. This is the mystical-psychological sense of sacrifice in all great religions.
A solar hero is the most frequent embodiment of this process of purgation, illumination, and unification. He unites the religious significance of the sun, the zodiac, and the seasons with circular or cyclic determinism. Man sought to rise and share the great cycle with the sun and stars, to climb beyond the material universe to the immaterial realm of the world-sustaining sun. The ageless concept of the new dimension transcending linear, historical time echoes Mesopotamian cosmology. We ourselves are already that light of consciousness, that ground of being.
THE JUNGIAN APPROACH TO NUMBER
Jung revealed how mythological images and numbers have always been associated with each other. Here, we find a correspondence between the Universe, #108, and cycles of the Sun.
Von Franz summarizes her Jungian view:
"The concept of natural numbers rests on an archetypal foundation. It represents a preconscious pattern of thought common to all human psyches, and therefore constitutes the basis for transmitting knowledge to a greater degree than mythological images, which exhibit more ethnological variations.
"Those aspects of the number archetype which present-day Western mathematics has made conscious in no way exhaust all its aspects...The preconscious aspect of natural numbers points to the idea of a numerical field in which individual numbers figure as energic phenomena or rhythmical configurations. The "field," which we take to represent the structural outlines of the collective unconscious, is organized around the central archetype of the Self (which corresponds with the Sun, which corresponds with 108, and Brahma). For this reason historical mandala structures deserve particular attention. In corresponding "cosmic models" and mathematical representations of God, the first four numbers predominate to an exceptional degree.
"...These synchronistic and parapsychological aspects of number...can only be fathomed when we take into account the unconscious emotional setup and preconscious fantasies of the abserver along with his conscious mental situation and outlook. The description of such phenomena will of course no longer produce universally valid theories, but rather transmittable realizations that can exert a mind-releasing, community-building effect, just as scientific advances did in the past. The common denominator in mankind's cognitive processes thereby shifts from the level of doctrinaire intellectualism onto another plane. It centers instead on the realization of an a priori psychic structure common to all men. Depending on the epoch and an individual's creative abilities, the basic substratum becomes clothed in the most varied shapes and conscious formulations, progressively transforming 'ancient, eternal truths' into more highly differentiated conscious patterns of realization.
"As the ultimate verification of these processes stands the objective psyche and its synchronistic manifestations, which contain the mystery of the sporadic conjunction of psychic and physical events, revealing a common 'meaning.' . . .When we take into account the individual characteristics of natural numbers, we can actually demonstrate that they produce the same ordering effects in the physical and psychic realms; they therefore appear to constitute the most basic constants of nature expressing unitary psychophysical reality."
The Development of Mathematics
According to Singer's A Short History of Scientific Ideas, something of the nature of mathematics must be much older than the earliest documented examples. In tribal pre-history mankind watched the movement of the heavens and kept tallies of the passage of cycles of both lunar and solar nature. The importance of the Sun grew with the rise of agriculture and the importance of dating planting and harvest times accurately.
By Sumerian times, numbers were represented in a system which combined a decimal with a sexagesimal notation. It embodied the principle of place-value, but not as we now know it. Shifting a number one place to the left multiplied its value sixty-fold, successive shifts to the right corresponded to repeated divisions by sixty to form sexagesimal fractions. In later Babylonia of the Seleucid period, the texts employ a 'zero' to indicate an empty sexagesimal place between two other figures. Remnants of the sexagesimal system survive with us in the 360 degrees of the circle, etc.
The mathematical texts usually consist either of tables for multiplication, squaring of numbers, etc. or of worked examples illustrating the solution of elementary geometrical or algebraic problems. The geometry amounts to little more than estimations of the areas of fields, though the special property of the right-angled triangle was known. The ratio of the circumference of a circle to its diameter, pi, was taken as equal to 3. This is the value adopted in the Old Testament, perhaps under Babylonian influence.
The algebra of the Old Babylonians could solve quadratic equations by a procedure equivalent to evaluating the modern formula, which gives the roots in terms of the co-efficients, thought the known texts nowhere quote or prove this rule. They also handled linear equations in several unknowns and even attempted to solve cubic and biquadratic equations.
The Old Babylonians astronomy amounted to little more than recognition of bright stars, arbitrary demarcations of the heavens, and often undated observations of striking celestial or atmospheric phenomena. There are also records of omens drawn from these, whose significance marks the beginning of astrology. Originally used to predict the fortunes of contending kingdoms, horoscope astrology subsequently developed into complex procedures for foretelling the destinies of individuals.
The later or Seleucid texts, on the other hand, embody complicated systems of theoretical astronomy. These were elaborated by the temple priests who observed the heavens from characteristic stepped watch-towers or temples, of which the Tower of Babel is a reminder.
The periodicity exhibited by the planets, and more particularly the revolutions of the sun and moon, were utilized for the measurement of time. The monthly changes of the moon are more obvious than the annual travel of the sun. So the lunar calendar was retained for religious purposes, while the solar was adopted for agriculture.
No natural numerical relation exists between the lunar month and the solar year. But by the fifth century BC, it was established that 19 solar years are equal to 235 lunar months (125 of 30 days and 110 of 29 days each) to within a fraction of a day. These 19 years, comprising 12 of 12 months each and 7 of 13 months each, were combined in a certain order to form what has been called, after the alleged Greek inventor Meton, the Metonic Cycle. The sequence in which 29-day and 30-day months followed one another was seen to be affected by the variations in the rates of motion of sun and moon, by the latitutde of the moon, and by the inclination of the ecliptic to the horizon.
In the tables for predicting the dates of successive new moons, separate columns indicated the corrections to be separately applied for these various factors affecting the length of the month. They represented fluctuating discontinuity between upper and lower limits in a characteristic manner. The Babylonian tables, which extended also to the prediction of planetary phenomena, have been classified into two main systems, according to the mthods employed to represent the variation of the sun's rate of motion through the course of a year. (adapted freely from The Short History of Science).
The Indus civilization also learned its first lessons in mathematics from astronomy, the gateway to time reckoning and temple building. In the arithmetic of trade, the merchants of India were the equals of those of Mesopotamia.
Until about 2000 years ago, they probably used numerals made up of horizontal strokes. When they began to use dried palm leaves as writing material and developed a flowing style of writing, they also began to join up these strokes, so that became and became .In this way they gradually built up different signs for each number up to nine. Each sign could be conveniently used to indicate the number of pebbles in any groove of the abacus.
The Indians learned how to tell not only how many pebbles are in a groove, but also which groove they are in. The far right stood for units, the next to the left for tens, then hundreds, and so on. An empty column used a dot, as we now use zero. Thus each value meant only that one figure.
This system does away with space-consuming repetition. We can record the same number on any groove of the abacus by using the same sign. Saving space is only a small advantage. The great advantage of the Hindu system is that it enables us to calculate with numbers.
Other ancient systems of writing all relied on the use of different symbols for the same number of pebbles in different grooves of the abacus. Before you could do written or mental calculations with them, you would need to learn a different table of addition and multiplication for each groove. When there are only nine different signs, each of which can show the number of pebbles in any groove, and a zero indicates empty grooves, you need learn only one simple table, once and for all. You can carry over in your head because there is only one simple table to remember.
The Hindu number language quickly led to a revolution in the art of calculation. The mathematicians of India began to think in fractions and write them in the modern way. By 500 AD, Indian mathematicians had solved problems that baffled the greatest scholars of antiquity. The mathematician Varahamihira calculated how to forecast the positions of the planets; Aryabhata wrote a rule for finding square roots and gave the value for pi as 3.1416.
Around 800 Ad, this numerical system was exported to Baghdad on the age-old caravan route. The Muslims used trigonometry. Because they had mastered the new arithmetic of India, they could make much fuller use of the geometry of Euclid. Improved navigational equipment emerged from the observatories which also had improved equipment. Knowledge took a big leap forward between 800-900 AD, when East met West in Baghdad, and the baseten system became the standard..