*

THE PULSE OF BEINGAt what period and in what part of the archaic world did the number 432,000 become attached to the system of signs symbolic of the predictable renewals after periodic dissolutions of a living which in the iconography of Old Europe had been is the body of its Creator? The datings recognized by Gimbutas for the relevant regions of the Old European Neolithic are as follows:(

26)

l. The Aegean and Central Balkan AreaNeolithic, ca. 7000-5500 B.C.

Chalcolithic, ca. 550-3500 B.C.

ll. The Adriatic Area

Neolithic, ca. 7000-5500 B.C.

Advanced Neolithic-Chalcolithic, ca. 5500-3500 B.C.

lll. The Middle Danube Basin

Neolithic, ca. 5500-4500 B.C.

Advanced Neolithic and Chalcolithic, ca. 5000-3500 B.C.

lV. The East Balkan Area

Neolithic, ca. 6500-5000 B.C.

Chalcolithic, ca. 5000-3500 B.C.

V. The Moldavian-West Ukranian AreaNeolithic, ca. 6500-5000 B.C.

Chalcolithic, ca. 5000-3500 B.C.7000-3500 B.C. are then the bounding dates of this epoch in the chronology of the evolution of consciousness in Old Europe. Engraved signs which have been interpreted as giving evidence of a old "linear old European script" have been identified on as many as one out of every hundred of the Chalcolithic statuettes, as well as numerous plaques, dishes, spindle-whorls, and other objects from ca. 5500 B.C., as votive offerings to the Goddess.(

27) No signs have yet been reported, however, of a knowledge at that time of any such order of mathematical symbolics as the recognition of cycles of 43,200 or 432,000 years would have required.The earliest recognizable mathematical documents known to archeology are from Sumer, third millennium B.C., and their system of numeration is sexagesimal (base 60). As interpreted by

:KramerThe mathematical school texts which have come down to us are of two types: tables and problems. The former include tabulations of reciprocals, multiplications, squares and square roots, cubes and cube roots, the sums of squares and cubes needed for the numerical solution of certain types of equations, exponential functions, coefficients giving numbers for practical computation (like the approximate value of the square root of 2), and numerous metrological calculations giving areas of rectangles, circles, etc. The problem texts deal with Pythagorean numbers, cubic roots, equations, and such practical matters as excavating or enlarging canals, counting bricks, and so on. As of today, almost all problem texts are Akkadian, although they must go back in large part to Sumerian prototypes since nearly all the technical terms used are Sumerian.(

28)Indeed, a Sumerian tablet of about 2500 B.C. from the ruins of Shuruppak, home city of the Flood hero Ziusudra, already contains a table for the calculation in sexagesimal terms of the surfaces of square-shaped fields.(

29)In what period this method of mathematical calculation was first applied to measurement of the movements of the celestial lights, no one has yet determined. However, as a moment's attention to a calculator will demonstrate, 60 X 60 X 60 X 2 = 432,000, while 60 x 60 x 60 x 60 x 2 = 25,920,000; 25,920 being the number of years required in the precession of the equinoxes for the completion of one full circuit of the Zodiac, since, as already remarked in discussion of Julius Oppert's observations touching the relevance of the biblical sum of 1656 years to Berossos's 432,000, the advance of the equinoctial points along the Zodiacal celestial way proceeds at the rate of I degree in 72 years. And 360 degrees X 72 years = 25,920 years, for one completion of a Zodiacal round, which period has for centuries been known as a Great or Platonic Year. But 25,920 divided by 60 equals 432. And so again this number appears, now, however, in exact relation to a scientifically verifiable cosmological eon or cycle of time.

Moreover, as I learned some years ago from a popular hand-book on physical fitness,(

30) a man in perfect condition, at rest, has normally a heart rate of approximately I beat per second: 60 beats a minute; 3,600 beats an hour; in 12 hours 43,200 beats and in 24 hours 86,400. So we hold this measure in our hearts, as well as in the manufactured watches on our wrists. Can it be that the Old Sumerians, ca. 2500 B.C., might already have had some notion of the relevance of their sexagesimal system to the mathematics of any such macro-micro-meso-cosmic coordination?From an authoritative work on Indian tantra yoga I learn that, according to the

and other related Upanishads, all living beings inhale and exhale 21,600 times a day,(Dhyanabindu31) this being in evidence of their spiritual as well as physical identity in the nature of the universal, the Great Goddess who in India is celebrated in a litany of her 108 names. 21,600 X 2 = 43,200. But 108 X 2 = 216, while 108 X 4 = 432, and 432 X 60 = 25,920.maya-sakti-deviIt was

in Philadelphia at the University Museum in 1905, poring over literally thousands of cuneiform clay fragments upon which mathematical reckonings were inscribed, who first recognized this last figure, which is of the Great or Platonic Year, among remains of such early date. In his report, published 1906, he wrote, "All the multiplication and division tables from the temple libraries of Nippur and Sippar and from the library of Ashurbanipal are based upon 12,960,000." And as he there pointed out, 12,960 X 2 = 25,920.32H. V. Hilprechtwas inclined to accept this discovery as indicating the likelihood of a recognition of the precession in Mesopotamia as early as the third or perhaps even fourth millennium B.C. "If this interpretation is correct and the figure really does refer to the precession," he wrote, "then it proves that before Hipparchus an exact reckoning of the precession had been achieved, which later was forgotten."(Alfred Jeremias33) And he wrote "again," It is, in fact, incredible that the Babylonians, experienced as they were in the observation of the heavens, should not have deduced from the difference between earlier and later observations a shift of the equinoctial point. . . . As soon as the position of the sun at the time of the spring equinox became a point of observation, the precession during centurieshave been noticed . . . Indeed in the course of one year it comes to 50 seconds, and during longer periods cannot possibly have been ignored."(must34)It is generally held that an Asiatic Greek, Hipparchus of Bithynia (fl. 146-128 B.C.), in a treatise entitled, "On the Displacement of the Solstitial and Equinoctial Signs," was the first to have recognized the precession of the equinoxes and that it was then not until A.D. 1526 that the exact reading was announced of 1 degree every 72 years. Yet the Chaldean priest Berossos, a century and a half before Hipparchus's time, had already taken seriously the number 432,000, as had, also at that time, the compilers of Genesis 5-7, whose antediluvian cycle of exactly 1,656 years shared as factor with Berossos the critical processional term 72. The still earlier possibility suggested by Hilprecht and Jeremias of a Sumerian anticipation of all this in the third or fourth millennium B.C. has not, as far as I know, been further examined or even seriously discussed.

So that, although it is reasonably certain that it was in Sumer, ca. 3500-2500 B.C., that the figure 25,920 divided by 60 equals 432 first became associated with the order of a universe, which in the Neolithic period had been revered as the body of a goddess, we know little or nothing of the stages and processes by which these two distinct traditions — the earlier of mythology, folklore, mysticism, and legend; the later of mathematical logic, cosmological inquiry, rational and speculative thought — were brought together and conjoined. All that can be confidently said is that by the sixth century B.C. at the very latest, in the mathematically formulated speculations of the mystical, secretive brotherhood founded by the Samian sage Pythagoras (born on the island of Samos in the Aegean, ca. 580 B.C.; died in Metapontum, Italy, ca. 500 B.C.) — whose fundamental dictum, "all is number," had opened the way to a systematic study of the mathematics of form and harmony which united, as of one transcendent science epitomized in music, the laws at once of outer space (cosmology), inner space (psychology), and the arts (aesthetics) - the two, apparently contrary approaches of the visionary and the empiricist were brought and held together as substantially in accord.

Reconstruction of the scientistic

of Pythagoras has been rendered for scholars problematic by the fact that the master himself (like the Buddha, his oriental contemporary, ca. 563-483 B.C.) left no writings. Furthermore, the mystical brotherhood that he founded in southern Italy not only was governed by rules of secrecy but in the middle of the fifth century B.C. was forcibly disbanded and its membership dispersed. Sources purporting to represent the movement go back at best to fourth-century sources, which are already uncritical in character and often amalgams of Pythagorean, Orphic, and Neo-Platonic information.(mythos35) Hence, it is impossible to determine how much of what has come down to us can be attributed to Pythagoras himself, how much may have been derived by him from the general body of mystic lore already shared by the numerous gurus of his day throughout the Near, Middle, and Far East, or how much of this esoteric learning may have become assimilated to the movement centuries later.The idea, for example, of sound (Sanskrit

) as generator of the perceived universe is fundamental to the Vedas and all later Hindu thought.sabda, in hisAlain DanielouIntroduction to the Study of Musical Scales, quotes from a commentary on a Sivaite Sutra:The initiating point (

bindu), desirous to manifest the thought which it holds of all things, vibrates, transformed into a primordial sound of the nature of a cry ().nada. That is to say, it thinks it. Hence the term,It shouts out the universe, which is not distinct from itself, "word." Meditation is the supreme "word": it "sounds," that is to say, "vibrates," submitting all things to the fragmentation of life. This is how it issabda, "vibration." This is what is meant by the saying: "Sound (nada), which is of the nature ofsabda, resides in all living beings."(nada36)Likewise, in the Chinese "

,"Book of Rites, which, as Danielou reminds us, was edited by Confucius (ca. 551-478 B.C., again a contemporary of Pythagoras), we are told,Li ChiMusic makes for common union. Rites make for difference and distinction. From common union comes mutual affection; from difference, mutual respect. . . .

Music comes from within; rites act from without. Coming from within, music produces serenity of mind. Acting from without, rites produce the finished elegance of manner. Great music must be easy. Great rites must be simple. Let music achieve its full results, and there will be no resentments. Let rites achieve their full results, and there will be no contentions. The reason why bowings and courtesies could set the world in order is that there are music and rites.(

37)

, a later Confucian scholar, second century B.C., expanded upon these thoughts:Tung Chung-shuTuned to the tone of Heaven and Earth," he wrote, "the vital spirits of man express all the tremors of Heaven and Earth, exactly as several citharas, all tuned on

(the tonic), all vibrate when the noteKungresounds. The fact of the harmony between Heaven and Earth and Man does not come from a physical union, from a direct action, it comes from a tuning on the same note producing vibrations in unison. . . . In the Universe there is no hazard, there is no spontaneity; all is influence and harmony, accord answering accord.(Kung38)A characteristic Pythagorean symbolic diagram cited by all authorities as in some way epigrammatical of an essential doctrine of the movement is the so-called

, or "triangle of fourness," which can be viewed either as an equilateral triangle of 9 points composed around a single central point or as a pyramid of 10 points arranged in 3 expanding stages of descent, respectively of 2, 3, and 4 ( = 9) points, unfurling from a single point at the summit.tetraktys

*

* *

* * *

* * * *The Pythagoreans, by all accounts, regarded even numbers (2, 4, 6, and so on) as female; uneven (3, 5, 7, and so on), as male; interpreting 1 as neither even nor odd but germinal of both series, corresponding thus to the Indian tantric

, "desirous to manifest the thought which it holds of all things." Asbindu, vibrating, transformed into primordial sound, this initiating impulse "shouts out the universe, which is not distinct from itself"; that creative "shout" being in modern terms the Big Bang of creation, whence from a single point of inconceivable intensity this entire expanding universe exploded, flying into distances that are still receding.nadaIn Indian mystical utterance this universal Sound is announced as

. In oriental model music it is represented in the tonic in relation to which the melody is heard. And in Pythagorean thought it was identified withOM, the supporting ground tone, A, which thereby was considered to have 432 vibrations (whereas the pitch in modern tunings is raised to around 440). Musically, as Danielou points out, the primal sound given measure yields first its octave (2/1), after which a third tone, the fifth (3/2), is heard, in relation to which the others then find place.(Proslambanomene39) And in this regard he cites a verse from theTao Te Ching: "The Tao produced One; One produced Two; Two produced Three; Three produced all things."(40)In Indian thought the first characteristic of

(from the verbal rootmaya, "to measure") is duality; and for the Pythagoreans, likewise, the world-process was a complex of dualities sprung from the imposition of "limitation" or "measure" (=ma) upon the "unlimited" (maya); the "unlimited" and its "limitation" then being the first of a series of nine further pairs of opposites: odd and even, light and dark, and so on, essentially the Chinesebrahmanandyang.yinOut of the stress of such a context of universal polarization, the Indian (Sankhya) philosophers recognized as arising three "qualities or characteristics" (

), through the interrelation of which all of "nature" (gunas) was seen as motivated; namely, "inertia, mass, or heaviness" (prakriti), "energy and vitality" (tamas), and the "harmony or clarity" (rajas) of any balanced relationship of the opposed two. In Pythagorean terms, the same three would correspond, respectively, to (1) the "unlimited," (2) the "limiting," and (3) the "harmony" or "fitting together" (sattva) of any "beautiful order of things" (harmonia), whether as a macrocosm (the universe), microcosm (an individual), or mesocosm (ideal society or work of art). And the number representative in that system of such a visible order is 4.kosmosAnd so now, counting the number of points of the Pythagorean

, from the base upward to the creativetetraktys(beyond number) at the top, the sum of their sequence, 4-3-2, is of course 9; as is that, also, of 2-1-6 (which is half of 432); as well as of 1-0-8 (half of 216); which last is the number of her names recited in worship of the Indian Great Goddess, Kali, Durga, Uma, Sita, Sati (pronounced Suttee), and Parvati ("Daughter of the Mountain"). Moreover, the total 9 is implicit, also, in the sum of years of the biblical 10 patriarchs, from the day of Adam's creation to that of the end of the antediluvian age in Noah's Flood, since 1+6+5+6= 18, while 1+8 = 9. And finally, most remarkably, in the course of the precession of the equinoxes the number of years required for the completion of one circuit of the Zodiac at the rate of 1 degree in 72 years (noting that 7+2 = 9), is 2+5+9+2+0 = 18, where again, 1+8= 9.bindu