Grid of the Gods

by Farrell, Joseph P.

  The musical metaphor of the circles also lies behind the “churning of the Milky Sea”, for the diversity of the universe, as we saw at Angkor Wat, arises from the tension created by Vishnu’s original “tripartation” or differentiation. Rotation, understood in musical terms, in the terms of frequencies, is the key.29 It goes without saying that spin and rotation moment are crucial concepts in distinguishing sub-atomic particles; thus as we shall see in chapter 13, there may be even deeper meanings to these ancient metaphors. There is even a dimension of Vedic teaching which relates all this cosmological topology and music to consciousness itself, for Soma, the magical food and drink of the gods that confers expanded consciousness, does so first of all by bringing insight into the musical experience as being comprised of the theory of numbers.30

  From the musical point of view, however, the Vedic philosophy never completely reconciled the two cycles arising from unity, namely, the cycle of thirds, and the cycle of fifths. To put it differently, it never completely integrated the “female” octave with the “male” notes within that octave, and thus, any number of types of scales could be generated, all of which were, from the Vedic cosmological standpoint, equally valid.31 The task of effecting that union and taking the first steps to our modern system of “equal tempering” or tuning was taken in Mesopotamia, and with its sexagesimal system of arithmetic.

  D. The Sexagesimal System, Music, and Cosmology

  It was in fact the famous Sumerologist Samuel Noah Kramer who located the fabled Sumerian “land of the gods,” Dilmun, with the “Harappan culture of pre-Vedic India.”32 By the time of the high Mesopotamian cultures, however, Vedic mathematical prowess had grown to enormous sophistication.

  It is startling to learn…that the art of calculation in the third millenium (sic) Babylon — before the time of Abraham — was already comparable in many aspects with the mathematics “of the early Renaissance,” thirty-odd centuries later. Computation was made easy by the possession of tables (of which we have many copies) of “reciprocals, multiplications, squares and square roots, cubes, and cube roots, the sums of squares and cubes… exponential functions, coefficients giving numbers for practical computation… and numerous metrological calculations giving areas of rectangles, circles,” etc. The Pythagoran theorem was known in Babylon “more than a thousand years before Pythagoras.” The foundations were laid for the discovery of the irrationality of √2 “exactly in the same arithmetical form in which it was obviously re-discovered so much later by the Greeks.” Traditional stories of discoveries made by Thales or Pythagoras must be discarded as “totally unhistorical”; much of what we have thought was Pythagorean must now be credited to Babylon.33

  The implications, for McClain, are enormous, for this means that

  The Hebrew Bible is thus the product of a Semitic culture which had mastered the fundamentals of music and mathematics a thousand years and more before its oldest pages were written. The stage was set for mathematical allegory on a grander scale than the relatively late Christian civilization has ever realized.34

  Indeed, as will be seen, the Hebrew version of this mathematical and musical metaphor constitutes a step of trying to edit and invert the inherited Mesopotamian musical and mathematical metaphors of the “god of the mountain.”

  In this musical mathematical allegory, McClain notes that its sexagesimal system of whole number integers was “probably the most convenient language for acoustical arithmetic the world ever knew” until the rise of logarithmic computation introduced in the nineteenth century of our era.35 Here we must also pause to note something that was observed in the previous book in this series, Genes, Giants, Monsters, and Men, namely, that the ancient systems of measures, and in particular, the Sumerian sexagesimal system, were also based on astronomical and geodetic measures,36 in other words, one is not only looking at a musical system of numbering, but on a cosmological and geodetic one. Quite literally, the three cannot be disentangled; one is literally looking at the music of the planets, the music of the medium itself. The musical advantage is that it allows one to retain the uses of the “female” even numbers generating the octave matrix and the male numbers, based on powers and multiples of 3 and 5, generating the rest of the twelve tones, as in the ratio 30:60, a ratio that is based on multiples of 2, 5 and 6. Note also that the ratio can be reduced to 3:6, which can be reduced to the female number of 2; and that 60:5 is, of course, 12, giving the 12 tones of the chromatic scale, and, for the Mesopotamians, the 12 houses of the Zodiac. Succinctly stated, it is in the sexagesimal system that cosmology, music, number theory, and physics all meet in a harmonious whole.37

  But what of the “gods” themselves, and our formula “Mountains ≈ Planets ≈ Gods ≈ Pyramids ≈ Music?” Why did the gods become associated with mountains and music?

  It so happens that within Mesopotamia numerological mythology, that the three principle gods, Ea-Enki, Enlil, and Anu, are all numerically, and therefore, musically related, Ea-Enki having the value of 40, Enlil the value of 50, and Anu the value of 60, which, in the sexagesimal system, is also representative of the primordial unity, or 1. In musical terms, if one assigns a fundamental tone — say in this case, the note D — to An, then Enlil represents a third up or down from that (f or b), and Ea-Enki a fourth down or up (A or G), and from Enki, then, the entire circle of fourths and therefore all twelve tones, would be generated.38 Note that the ratio of these three gods is 40:50:60, or 4:5:6. From them, the whole modern twelve-note chromatic “tonal universe” is generated, as in our circle of fourths example above.39

  If all this seems dense and obscure, it’s about to become even more so, for in the ultimate example of the “unified intention of symbol,” the numerical-musical allegory is reproduced in Berossus’ version of the Kings’ List of kings before the Flood:

  Note that the total, when divided by the quintessential Mesopotamian sexagesimal number of 3600, is 120, a harmonic of 12, our twelve chromatic tones once again.

  In order to understand how all this relates to our musical tone circles, we have to look closer at Ea-Enki, whose numerological value is 40. To understand how this is so, it is important to remember that every whole number, when viewed musically, is viewed in some ratio to the number sixty, but the Mesopotamians do not actually write that second number. Thus, Enki’s number, 40, is really the ratio 40:60, or 2:3, an essential musical relationship in generating the twelve tones, for as such, he is the “first born son” of Anu, that is, “the first odd, hence male integer.”41 As god of the “sweetwaters,” Enki is also “the Sumerian counterpart to the Greek Poseidon” and thus intricately related to the myth of Atlantis.42

  E. Music and Higher-Dimensional Geometries:

  The Musical Gods of the Musical Mountains

  Enki, with 2:3 as his numbers, thus is a metaphor for the powers and multiples of 3 and 5, and here we come to the crux of the matter, for when these powers are graphed, a “numerical mountain” results, which we have followed by showing McClain’s graph of the “irreducible” integers and the tonal “zigurrats,” as McClain calls them, or mountains that result.

  McClain’s “Tonal Zigurrats”43

  Similarly, Enlil, whose number is 50, that is to say, 50:60 in the Mesopotamian scheme of ratios, and Marduk, laying at 25, both generated their own numerical tonal mountains.

  McClain’s Babylonian Gods of the Mountain44

  Note the “Pickax” form of tones and their reciprocals (represented by the dotted “upside down ’mountain’”), for if one does a rotation of that mountain on its side so that the numbers on Marduk?s Mountain, which represent the tones generated in the pickax, can a common shared generating point in the number one, we get this:

  McClain’s Diagram of Twin-Peaked Mt. Mashu45

  Note that on the horizontal line extending in each direction we have the initial unity, its first “tripartation” represented by 3 and 5 on the horizontal and diagonal, and on the horizontal, powers of three extending into infinity, and on the
diagonal, powers of 5 extending into infinity, and between them, multiples of 3 and 5.

  If we overlay the extended version of these tonal mountains over each other, we obtain an analogue of a familiar, and very Babylonian, figure, the “Star of David:”

  Musical Brahmins and Babylonian “Star of David”46

  The significance of all this is that music and its mathematical codes, in McClain’s view, played an inevitable role in the emergence of monotheism:

  Monotheism took as its God not the Great God 60(actually written in Babylonian-Sumerian as a large ONE), but the irreducible unity itself, that is, the unity whose multiplicity creates all the diversity of number, that unity which alone can subdivide prime numbers, the active agents of all creation.47

  And of these, as we see from the previous page, the numbers 3 and 5 are the first two and most important prime numbers in the musical metaphor.

  In other words, the ancient mathematicians performed what geometers would call a rotation, revealing a connection to another metaphorical mountain, the sacred tectratys of Pythagoreanism:

  McClain’s Musical Evolution of Monotheism48

  We will reserve comment on all the esoteric and physical principles embodied in the Pythagorean tectratys for chapter twelve. For now, it should be noted that, like the musical circle of tones itself, we have returned to that musical-topological metaphor that began the process we discovered at Angkor Wat, but now the metaphor has taken on an added richness, for specific numerical and musical functions have now been ascribed to the original primary “tripartition” or differentiation.

  1. Babylonian and Hebrew Flood Chronologies

  There is another backdrop against which the ancient physics of the grid must be viewed, and that is the Platonic allegory of Atlantis and of the Flood itself, an account that McClain, with much humor and accuracy, says is a “kind of Pythagorean Grand Opera, complete with an all-star cast, a water show, dazzling scenery, and a tragic finale.”49 Yet, even here one finds that there are codes within the texts.

  For example, there are hidden correspondences between the Hebrew and Babylonian chronologies of the Flood, correspondences that point to deeper numerical codes. McClain observes that the famous scholar of comparative mythologies, Joseph Campbell,

  … discovered a correlation between the 432,000 years from the creation to the flood in Babylonian mythology and the 1,656 years from the creation of Adam to the flood in the Hebrew account. Campbell points out that these numbers have a common factor of 72, and that 1656/72 is 23. Now 23 Jewish years of 365 days plus five extra days for leap years equals 8,400 days or 1,200 seven-day weeks; multiplying by 72 to find the number of Jewish seven-day weeks in 1,656 (= 23 x 72) years yields 86,400 (1200 x 72). But the number 86,400 is 432,000/5, i.e., the number of Babylonian five- day weeks to the flood. Thus there is no necessary contradiction whatever in these different flood chronologies.50

  To put it differently, it is possible that the standard views of conservative biblical scholars as to the relative recentness of the Deluge are thrown into a cocked hat, and that the actual meaning of the biblical numerical codes is that the Deluge occurred much farther back in time, in a context or chronological framework commensurate with its antiquity in Mesopotamian myths.

  2. Babylonian Mathematics: Clues to a Higher-Dimensional Physics?

  In this context, a closer look at the sexagesimal system of ancient Sumer and Babylon are in order, for as has been seen, various numbers are ascribed to various gods in the pantheon. But there is another clue in Mesopotamian numbers, a clue that, oddly, resembles the modern numerical notations for higher-dimensional geometric objects: “In the sexagesimal system, 450,000 would be written as 2,5, meaning 2 x 603 + (5 x 602), perhaps a pun on Marduk = 25.”51 Note that in this system of notation, each number in {2,5} stands for that number in connection with some function that is a power of 60. One can, notes McClain, have a series of such numbers, such as {8,0,0} and so on.52

  It is important to note what this notation means, for cubing and squaring a number — e.g. x3 and x2 — are, of course, geometrical functions describing objects in two or three spatial dimensions. Thus, the notation {2,5} mentioned above could be written this way more abstractly as {x, y}, and since the first number is multiplied by the cubic power of 60, and the second by the squared power of 60, the notation really would look like this:

  We can therefore imagine extending this notation to {x,y,z}, and extending the powers of 60 with which each number is multiplied, e.g. {(x ⋅ 604) + (y ⋅ 603) + (z ⋅ 602)}; in other words, notations such as {8,0,0}, which are also within the realm of possibility in ancient Mesopotamian notation, conceivably may be understood as representing powers of 60 greater than the cubic, that is to say, as geometric and numerical representations of objects in four or more dimensions.

  To state it as succinctly as possible, the very structure of ancient Mesopotamian numerical notation implies a basic familiarity with hyper-dimensional geometries and the basic mathematical techniques for describing objects in four or more spatial dimensions. Indeed, as we shall discover in chapter 13, the exact same notation convention began to be used in nineteenth century geometrical techniques for describing objects in four or more dimensions!53

  This contains a further, and very suggestive, implication, for it is to be noted that the Sumerian-Babylonian gods may be described by such notation. In other words, the gods were being described peculiar union of physics and religion, as hyper-dimensional entities or objects.54 This new twist upon the “unified intention of symbol” we will encounter again in the next part of this book in conjunction with the Egyptian interpretation of this paleophysics of the physical medium, and its conjunction with religious cosmology. It is, however, a heritage that we have discovered is common to ancient Vedic India as well as Mesopotamia, and we have encountered suggestive parallels between Mesopotamian myths and those of Meso-America. It was, to paraphrase McClain, in India, Mesopotamia, Egypt and even Meso- America, that one is able “to watch the birth of the gods in the minds of musical poets and discover that continuity of tradition which maintains a perfect unity between music, mathematics, and metaphysics.”55 With Plato, the final step was taken, as the physics of the celestial harmonies and the gods was transformed into a technique of social engineering and political theory.56 The ancient classical world had, in other words, moved quickly to outline all the implications of this musico-physical-metaphysical legacy that it had inherited, even though it may not have fully understood those implications, nor raised the technology to match in deed what its mythologies recorded.

  3. Mesopotamian Music and the Fine Structure Constant

  But does all this musical numerology actually contain any clue that the ancients were passing on a legacy that contained within it the seeds of a lost knowledge of a much deeper physics?

  There is indeed one such clue, and it’s a whopper.

  The Greeks, as noted above, inherited this musical-metaphysical legacy from Plato, who in turn gained it from the Pythagoreans and Mesopotamia. One may also point out that Plato was clear — in his “Atlantean dialogues,” the Timeus and Critias — that there was also an Egyptian influence at work. All this was in turn encoded by Plato in many dialogues as a political theory, as a means of social engineering. Various “cities” are worked out — including Atlantis and Athens — along different numerical lines. In these attempts to divine the musical proportions of the “best” city, Plato proposes the city Callipolis, his

  ‘absolutely best’ city — his ‘celestial city,’ the diatonic scale sung by the Sirens in his planetary model — seven numbers required for the diatonic scale produce all eleven tones.

  McClain observes that within this octave-numerical scheme, that the largest “genetic element is 36, or 729.58

  That number — 729 — may be one of the most significant in all of physics, for it is the decimal coefficient of the Fine Structure Constant, typically given a fractional value of 1/137 and usually denoted, coinci
dentally, and perhaps ironically enough, by the Greek letter alpha, α, for when one carries out the function of dividing 1 by 137, the result is .00729927007, an approximate harmonic of 729.59

  Of course, the presence of only one occurrence of this coefficient does not mean that the Greeks — or for that matter those from whom they inherited their knowledge — were aware of this significance of this number. But as we shall discover in the next section on Egypt, there is strong and suggestive evidence that whatever Very High Civilization as preceded those cultures of the classic era(i.e., the Vedic, Mesopotamian, Egyptian and Greek civilizations), that civilization did know of the existence of these and other constants of modern physical mechanics, millennia before their (re-)discovery in our own era.

  Why would the preservation of the numerical value of the fine structure constant, particularly in a musical-political context, be so significant? The answer lies in the deeply mysterious nature of the constant itself. First discovered in 1916 by physicist Arnold Sommerfeld, the constant is essentially a dimensionless constant — effectively, a scalar in mathematical terms, or a “pure magnitude” — possessing the same value in all systems or units of measure, and measuring the strength of electromagnetic coupling. But the problem is, while the constant “fits” the rest of physics like a glove, its own origins are so unique and inscrutable that it has puzzled physicists ever since. No less a physicist than Feynmann felt compelled to comment on its almost mystical nature and attraction for physicists ever since its first discovery: