evolutionary process of the cosmos. Without conscious human

action, the whole of creation cannot complete itself."

It is interesting that with the transposition of a single letter or two a word can take on heightened meaning. For example, the word “sacred” can, with the alteration or substitution of letters, become “secret” or “scared.” There is perhaps more to this letter-juggling than meets the eye. The Bible tells us that the fear of the Lord is the beginning of wisdom. When Mary saw an angel, she was “sore afraid.” The sacred brings fear upon us because it brings to remembrance huge secrets which have been kept hidden from the beginning of the world.

We study the writings of Gurdjieff from the attitude that we have been given sacred laws, laws which have been purposefully concealed from the profane, laws which instill in us the awesomeness of the cosmos in which we live. As Dorothy Dooling points out, this knowledge brought by Gurdjieff is in grave danger of disappearing because the very thing which claims our attention - the hugeness of its scope - makes it ungraspable in its entirety. It is only on this scale, which we are loath to confront, that a perspective can be opened in which it seems our lives might begin to make sense. How is it possible that we are so brave at one moment, so cowardly the next; then so eager, and now so indifferent?

Our bravery remains intact so long as we rest content in the ordinary world of the known. Gurdjieff’s teachings, however, make the insistent demand that we step into the Unknown. We are required to glimpse other planes of existence, not look away, even when our cowardice and unknowing makes us feel “sore afraid.” Without this transforming ladder of knowledge work on oneself is reduced to mere "self-improvement" - more and better of the same thing. Transformation, actual change of being, which is the goal of all true teachings is forgotten. Gurdjieff calls this transformation evolution, and it is the foundation of the structure of his doctrine.

The word evolution, in Gurdjieff's teaching, is used to mean the opposite of what is mechanical and unconscious. Evolution cannot be the result of things which “happen.” On the contrary, mechanical evolution is not possible. According to this teaching, the individual human being plays an important part in the evolutionary process of the cosmos. Without conscious human action, the whole of creation cannot complete itself. The idea is astonishing! What possible human action, conscious or not, can be so important as to affect the workings of the entire universe? A crucial piece of information is being transmitted here, if only we can get it. With some fear and trepidation, I set forth the rather scary idea that the responsibility of humans is to alter a piece of the harmonic series. By means of this conscious action, a triad can be created. What formerly was disconnected and mechanical and unconscious can become a sacred trinity of forces enabling interaction and relationship: a real cosmos.

The legendary Pythagoras was, for western minds, the first to speak of a cosmos, the well-ordered scheme of sun, moon, and planets, fixed by certain boundaries and organized according to universal laws. What he termed the “music of the spheres” was represented on earth by the ladder of musical scales which were constructed upon the same laws and moved with the same motions. Whether the discovery that musical pitches depended upon numerical proportions led, in its turn, to the analogy of a similar harmony in the heavens; or whether, instead, the observation of the heavens led to musical discoveries is still being debated. What remains an astounding fact, to those who contemplate its significance, is that from the musical pitches derived by Pythagoras over two thousand years prior, Johannes Kepler discovered the laws of planetary motion which are still valid today.

It is sadly ironic that while scientists have found the Pythagorean musical mathematics valid for astronomical calculations, present-day scholars of ancient Greek music are still unable to come to any agreement concerning what “the music of the spheres” might mean in terms of musical scales and harmonies. While anecdotal stories have been preserved throughout historical times which tell of music’s heavenly powers, its curative effects, its magical properties, its power to inspire or degrade, and even kill or bring to life, there is apparently very little information extant revealing how the interlocking structure, harmonia, actually sounded or what gave it its power. Although a substantial body of information has been conjectured about the music of the ancient world, the actual basis and knowledge of its construction have apparently been lost forever to the modern world. Or has it?

As pupils of Gurdjieffian cosmology, the reason for our interest in the harmonia is the deep and important relevancy it bears to the idea of the soul. What we must understand, from the beginning, is that the Work, above and beyond anything else it may purport to be, is really a mystery school. Historical evidence from various writers in ancient Greece attested to the fact that what the mystery schools taught was a science of the soul. Although the nature of a secret society rendered it impossible for outsiders to become acquainted with the inner teachings, there have been men like Plutarch, Porphyry, Iamblichus, and Proclus, to name a few, who “had partaken of the sacraments of the Mysteries and expressed the religious ideas of those Mysteries in their philosophic teaching without disclosing the details of initiation.” From their writings and others, we can assume that the ancient injunction “Man, know thyself” meant “Man, know thy soul.” How can man know his soul? The very word “soul” brings with it the feeling of mystery, of a secret and sacred principle. The soul is unknown and unknowable; unmeasured and unmeasurable. Or is it?

The means of transmission of the knowledge of the soul was through the teaching of the harmonia. In fact, the word harmonia, according to extant texts, first appears in the writings of the Pythagorean brotherhood during the pure modal period in ancient Greece.

It was around this time, as legends tells us, that Pythagoras brought back to Greece from his twenty-two year sojourn in Thebes the musical proportion, 6:8:9:12. Those Greek pupils fortunate enough to be schooled under his tutelage, the Brotherhood of Harmonists, were taught that the underlying principle of harmonia is a numerical system bound together by interlocking ratios.

A huge amount of occult information lies buried under these words. The word “occult” simply means “hidden, concealed from view.” To uncover what is buried below the obvious, however, is not so simple.

For the empiricists - those scientists who deal with the natural world of phenomena; and whose sole practice is to rely upon observation afforded by the subjective senses for verification - the interlocking harmonic ratios have an obvious meaning: simply that the octave (6:12) is separated into two equal tetrachords (6:8 and 9:12) divided by the tone (8:9). The idea is set out in an ancient mathematical treatise written by Sextus Empiricus.

"Harmonia is a systema of three concords, the fourth, the fifth, and the octave; and the proportions [analogiai] of these three concords are found in the four numbers preciously mentioned, in one, two, three and four."

Sextus Empiricus (Adv. Math. vii.94-5)

The empirical musicologists, intent upon the obvious meaning, have overlooked two simple and obvious clues: (1) the “harmonia” implies the harmonic series, and (2) the “concords,” in the order stated (that is, the fourth 6:8, the fifth 6:9, and the octave 6:12), do not make their appearance in the harmonic series until the sixth tone, the G6.

“Sextus Empiricus” seems to suggest that we look at the empirical evidence inherent within the harmonic series, and that we pay particular attention to these interlocking ratios starting from the sextus tonos, the “G.”

I set forth the further possibility that this “G” may be the real reason that Ouspensky, throughout **In Search of the Miraculous**, shortens Gurdjieff’s name (presumably for convenience) to “G.”

In Masonic lore, the letter G signifies the animating principle, the ever-present emanation of God, who watches over a universe no longer held to be simply an Automaton, but is the essence of harmony and order: in other words, a “cosmos.”

For a scientist, the letter “G” refers to gravity. Scientists say that gravity, and its corresponding particle termed the “graviton,” did not exist at the very beginning of the formation of the cosmos, although they themselves are admittedly puzzled by its absence. Looking at the harmonic series, the reason becomes glaringly obvious: the “G6” does not occur until the sixth tone.

The force of “one G” is defined as the amount of pull exerted by gravity on bodies on the earth, and is measured as 30 rpm (revolutions per minute). One “G” of thirty spins occurs during one “minute” of time. If, instead of 6, we assign to “G” its “spin number,” 30, then our “harmonia” (that is, 6:8:9:12) begins spinning out corresponding accelerating proportional values: 30 spins, 40 spins, 45 spins, 60 spins.

According to Einstein’s “principle of equivalence,” acceleration and gravity are the same. Scientists don’t really know why; they only know that gravity and spin are somehow intimately connected, and that spinning brings “time” into the picture.

Now things really start to get interesting. In the cosmic scheme, one revolution of the earth on its axis is the measure of the “day,” and thirty such revolutions give us our month of 30 days. The month is a lunar measure: the approximate time for the moon to make one revolution around the earth. Thus one “month” is the cosmic equivalent of “30 rpm’s” (revolutions per month), or “one cosmic G”! It might also be mentioned, in passing, that recent discoveries suggest the theory that the moon did not exist from the beginning of the solar system; rather, it was a later development. The harmonic “module,” 6:8:9:12, which does not begin spinning until the G6, would appear to give some credence to that theory.

The moon exerts its gravitational force upon the earth. Gurdjieff likens the moon to the weight on a cosmic clock. “The gravity of the weight, the pull of the chain on the cogwheel, set in motion the wheels and the hands of the clock. If the weight is removed all movements in the mechanism of the clock will at once stop. The moon is a colossal weight hanging on to organic life and thus setting it in motion.”

Put in the language of the philosophers, the moon is the “prime mover.” The Freemasons say the “G” is the animating principle. In the ancient Mysteries, it is the soul. Gurdjieff puts the three ideas together: “Everything living,” he says, “sets free at its death a certain amount of the energy that has ‘animated’ it; this energy, or the ‘souls’ of everything living - plants, animals, people - is attracted to the moon as though by a huge electromagnet, and brings to it the warmth and the life upon which its growth depends.” The vibratory composition of these souls - plants, animals, people - is measurable. It can be weighed.

The measure of the soul, its weight, according to metaphysical teachings, is the measure of the man. The soul of a real man, that is a “man-not-in-quotation-marks,” is composed of three complete parts. Each part is a particle of the whole; each part has its own scale and is subject to different orders of laws. The three parts are measurable as the intervals of fourth, fifth, and octave, respectively. If the measure of the soul reveals an insufficiency in any of its three parts, then the man is considered an incomplete specimen.

Gurdjieff strongly states that of the several categories of “souls,” only one can truly be called by this word. The true Soul is the integrated Trinity, the three-in-one, indivisible, individual “I.” Of all living things, man alone has the possibility of attaining “I.” It is only a possibility, not a fact. The soul must be acquired during the course of life. Even then it is a great luxury and attainable only for a few. Most people live all their lives without a complete soul, and for ordinary life it is quite unnecessary.

At death, it is another story. Jesus may have been hinting of the idea when he said “I am the way, the truth, and the life; no one goes to the Father except by me.” The “Father-I” is the completed soul; one cannot get to the whole without the full complement, the “sum of the parts.”

Here we already have, by the definitions accorded it, the mathematical calculations for the determination of the true Soul, or harmonia.

At the most fundamental level of nature, harmonia and all its parts are constituted out of the natural principles of the unlimited, the limiting, and the even-odd. The harmonia as a whole is even, since it has four terms: whereas its parts and ratios are even and odd and even-odd. Its nete is of 12 units and is even, its paramese is of 9 and is odd, its mese is of 8 and is even, and its hypate is of 6 and is even-odd. Since harmonia and its parts are naturally related to one another in this way through their excesses and ratios, it is concordant with itself as a whole and with its parts.”

For a musician of Gurdjieffian persuasion, the harmonia (6:8:9:12) is a perfect manifestation of the tertiary dynamics of that one “common-cosmic Unique-Crystallization” called the Omnipresent-World-substance Okidanokh. This crystallization has three absolutely independent parts which in their manifestation have nothing in common, the particularities of which are “the chief cause of everything existing in the Universe.”

In my book, Nearly All and Almost Everything, I show how the three independent parts of the harmonia form the outlines of that figure brought into the modern world by Gurdjieff, commonly known as the enneagram. My figure is reproduced below.

The nine iterations of the harmonia (6:8:9:12) create the nine colored “concentrations” around the circle. There are two distinct colors: the green (at the 8s) depicts the “inner circulation”; the orange (at points 3-6-9) describes the outer triangle. A geometer might recognize this picture as one method for “sectioning the canon.” In fact, in some ancient treatises, the word “canon” is indistinguishable from “harmonia.”

If we carry the investigation only a little further, we see another interesting numerical division. As shown below, this one cosmic crystallization, the Omnipresent Okidanokh, is actually the unique representative of the three forces, here depicted in the three colors of red, blue, and green.

Look closer. The six concentrations of 8’s (red) occur only at 40 degree points: 40 80 160 200 280 320. Beginning with the first red box at 40, and moving clockwise around the circle to each successive red box, we realize that the numbers occurring within each box at these six “red” points of concentrations add, by theosophical addition (or gematria), to 4, 8, 7, 2, 1, 5, respectively. Don’t believe me. Do the numbers yourself. See how, using theosophical addition, every number within the red box at 400 loci adds to 4. Then add the numbers in the red box at 800 and see how they all add to 8. And so on, around the entire circle.

Now see how the number 6, and its octave double 12, occur solely at loci of 120 and 240 degrees, which are points 3and 6 on the figure of the Enneagram (the exceptions being in the first two iterations of 6:8:9:12, where the two numbers first appear at 30 and 60 degrees). Again applying gematria, at point 3 each of the numbers in the box adds to 3; at point 6, each adds to 6.

There is something rather peculiar regarding the numbers 6 and 12 of the musical proportion. The “iterations” themselves, one segment following another, produce a kind of blending of the numbers 6 and 12. Like Machaut’s Mass, “My End Is My Beginning,” the last term 12 invariably transforms into the first term 6, and the pattern thus continuously iterates itself. Thus, although 6:8:9:12 is really a four-term proportion, practically speaking it contains only three terms. The numbers which occur only at points 3 and 6 are shown on the figure of the Okidanokh in blue boxes.

Of the nine concentrations in the boxes around the circle, only one box remains yet to be considered. Representing the number 9, it stands alone. As expected, all sets of numbers within the box of this ninth concentration add to 9. Its first three appearances are at 45, 90, and 180 degree arcs, after which it settles down to remain always at the apex of the circle, at the locus of 360 degrees. The number 9 is shown on the Okidanokh figure in the green box.

Thus, by cutting the circle into the requisite aliquot parts as decreed by the harmonic proportion (the degrees measured at 30 40 45 60), we have managed to make manifest that one common-cosmic Unique-Crystallization, called the Omnipresent-World-substance Okidanokh.

In addition, during the process of this investigation into the soul, we have also understood objectively, mathematically, what Gurdjieff meant by the “three absolutely independent parts which in their manifestation have nothing in common, the particularities of which are “the chief cause of everything existing in the Universe.”

It is not surprising that the geometrical enneagram figure would have direct links with the new discoveries in science called Chaos Theory and Complexity Theory.

**THE INFLATIONARY BODY**

The square root of 2 is the geometric function which represents the universal metaphor of the root and root systems. The square root of 2 is an irrational function. As such it symbolizes the archetypal realm, referred to by the Pythagoreans as “the unutterable” (i.e., unspoken, wordless). This speechless wordless irrational part, in psychological terms, represents the unconscious mind. Depth psychologists say that the first thing to be grasped is that the form of representation peculiar to the unconscious is not that of the conscious mind at all. The unconscious does not define its objects by logical (logarithmic, logos) analysis. The way of the unconscious is different. It explains more by equivalence than equation, and weaves its threads together, combining each with each, into a fine garment, a tapestry or net. In ancient Egypt the unconscious was the feminine principle personified as the goddess Neith, the cosmic Weaver, who clothed the material universe by the warp and weft of her spinning loom. On the charts, the “warp and weft” is represented by the crossing of the horizontal and vertical lines that form the matrix, while “spinning” itself is apparent as the turnings along the right-hand vertical axis.

This spinning produces the specific intervals that form the invariant ratios of the “harmonic series.” However, it was quickly becoming apparent that these were no “ordinary” ratios, like the ones produced by the ordinal horizontal numbers. No, indeed, these special vertical ratios were “superparticular.” And now I knew why the ancients deemed them so. It was not because they were simply “one above the one before,” as the scholars would have us believe. Rather, it was because these superparticular ratios, unlike their ordinary numerical counterparts, define specific pitches. Another word for “pitch” is “note.”

As I wrote in my book, Aristoxenus’s Ghost, a note is the third of Aristoxenus’s seven categories of elements. In his Elementa Harmonica, he describes a note as “the incidence of the voice on one pitch.” Aristoxenus is at pains to suggest to his readers that the category of “notes” is more advanced than the category of “intervals” (which is the second category, the first category being “genera”). The word “note” does not necessarily have to be music-related, however. It can mean “that by which anything may be known;” and in fact is originally derived from the Latin pp. fem. of noscere, “know.” Notes, it would appear, give a higher type of knowing than mere intervals.

Looking at notes, I suddenly realized why the physicists were disenchanted with their “String Theory.” No wonder, since they were content to treat the “string” as simply the horizontal line of ordinary integers: 1:2:3:4:5, and so on. They were stuck in the second category, “intervals,” and had utterly failed to notice the importance of “notes.” While an interval is “generic,” a note has a “specific gravity.” In fact, the definition of “pitch,” relative to music, is: “The gravity of all the notes of an instrument with reference to some standard.”

For a Western musician, standard pitch frequency is expressed as the vibrations per second of one of its notes, generally specific to middle C or middle A. However, according to Chinese scholar Joseph Amiot, the fundamental standard pitch of the ancient Chinese pitch pipe (called “lu”) was F# (he estimated it at approximately 708 cps). This fundamental, called the huang chung, represented the “eleventh month” of the calendar. I think it very likely, given the importance of harmonics in ancient cultures, that the huang chung may very well be the eleventh harmonic (taken from the fundamental C):

Now see how the number 6, and its octave double 12, occur solely at loci of 120 and 240 degrees, which are points 3and 6 on the figure of the Enneagram (the exceptions being in the first two iterations of 6:8:9:12, where the two numbers first appear at 30 and 60 degrees). Again applying gematria, at point 3 each of the numbers in the box adds to 3; at point 6, each adds to 6.

There is something rather peculiar regarding the numbers 6 and 12 of the musical proportion. The “iterations” themselves, one segment following another, produce a kind of blending of the numbers 6 and 12. Like Machaut’s Mass, “My End Is My Beginning,” the last term 12 invariably transforms into the first term 6, and the pattern thus continuously iterates itself. Thus, although 6:8:9:12 is really a four-term proportion, practically speaking it contains only three terms. The numbers which occur only at points 3 and 6 are shown on the figure of the Okidanokh in blue boxes.

Of the nine concentrations in the boxes around the circle, only one box remains yet to be considered. Representing the number 9, it stands alone. As expected, all sets of numbers within the box of this ninth concentration add to 9. Its first three appearances are at 45, 90, and 180 degree arcs, after which it settles down to remain always at the apex of the circle, at the locus of 360 degrees. The number 9 is shown on the Okidanokh figure in the green box.

Thus, by cutting the circle into the requisite aliquot parts as decreed by the harmonic proportion (the degrees measured at 30 40 45 60), we have managed to make manifest that one common-cosmic Unique-Crystallization, called the Omnipresent-World-substance Okidanokh.

In addition, during the process of this investigation into the soul, we have also understood objectively, mathematically, what Gurdjieff meant by the “three absolutely independent parts which in their manifestation have nothing in common, the particularities of which are “the chief cause of everything existing in the Universe.”

It is not surprising that the geometrical enneagram figure would have direct links with the new discoveries in science called Chaos Theory and Complexity Theory.

The square root of 2 is the geometric function which represents the universal metaphor of the root and root systems. The square root of 2 is an irrational function. As such it symbolizes the archetypal realm, referred to by the Pythagoreans as “the unutterable” (i.e., unspoken, wordless). This speechless wordless irrational part, in psychological terms, represents the unconscious mind. Depth psychologists say that the first thing to be grasped is that the form of representation peculiar to the unconscious is not that of the conscious mind at all. The unconscious does not define its objects by logical (logarithmic, logos) analysis. The way of the unconscious is different. It explains more by equivalence than equation, and weaves its threads together, combining each with each, into a fine garment, a tapestry or net. In ancient Egypt the unconscious was the feminine principle personified as the goddess Neith, the cosmic Weaver, who clothed the material universe by the warp and weft of her spinning loom. On the charts, the “warp and weft” is represented by the crossing of the horizontal and vertical lines that form the matrix, while “spinning” itself is apparent as the turnings along the right-hand vertical axis.

This spinning produces the specific intervals that form the invariant ratios of the “harmonic series.” However, it was quickly becoming apparent that these were no “ordinary” ratios, like the ones produced by the ordinal horizontal numbers. No, indeed, these special vertical ratios were “superparticular.” And now I knew why the ancients deemed them so. It was not because they were simply “one above the one before,” as the scholars would have us believe. Rather, it was because these superparticular ratios, unlike their ordinary numerical counterparts, define specific pitches. Another word for “pitch” is “note.”

As I wrote in my book, Aristoxenus’s Ghost, a note is the third of Aristoxenus’s seven categories of elements. In his Elementa Harmonica, he describes a note as “the incidence of the voice on one pitch.” Aristoxenus is at pains to suggest to his readers that the category of “notes” is more advanced than the category of “intervals” (which is the second category, the first category being “genera”). The word “note” does not necessarily have to be music-related, however. It can mean “that by which anything may be known;” and in fact is originally derived from the Latin pp. fem. of noscere, “know.” Notes, it would appear, give a higher type of knowing than mere intervals.

Looking at notes, I suddenly realized why the physicists were disenchanted with their “String Theory.” No wonder, since they were content to treat the “string” as simply the horizontal line of ordinary integers: 1:2:3:4:5, and so on. They were stuck in the second category, “intervals,” and had utterly failed to notice the importance of “notes.” While an interval is “generic,” a note has a “specific gravity.” In fact, the definition of “pitch,” relative to music, is: “The gravity of all the notes of an instrument with reference to some standard.”

For a Western musician, standard pitch frequency is expressed as the vibrations per second of one of its notes, generally specific to middle C or middle A. However, according to Chinese scholar Joseph Amiot, the fundamental standard pitch of the ancient Chinese pitch pipe (called “lu”) was F# (he estimated it at approximately 708 cps). This fundamental, called the huang chung, represented the “eleventh month” of the calendar. I think it very likely, given the importance of harmonics in ancient cultures, that the huang chung may very well be the eleventh harmonic (taken from the fundamental C):

C C G C E G Bb C D E F#

1 2 3 4 5 6 7 8 9 10 11

**Huang Chung**

1 2 3 4 5 6 7 8 9 10 11

Let us assume that is the case. Then, by the usual convention of octave multiplication, at the fifth power this eleventh harmonic becomes 352 (11 x 25 = 352), which is indeed very close to the number of days in the lunar year, usually counted as 354 days.

However, let us take our supposition further. What if the eleventh harmonic was slightly sharped, so that instead of 11 it is 11.25? There are several interesting things to notice about this sharped F#. For one thing, as the number 1125, it represents the speed of sound in feet per second. For another thing, 1.125 is the decimal ratio for the major whole tone, 9/8, the primary interval used around the world in musical scales. Third, this sharped F# may correspond to what the Greek’s termed the “sharp harmonic fourth” (the F is the interval distance of a fourth above the tonic C) and may be the musical representative of the devilish tritone, the diabolos in musica. Fourth, the word for “sharp” is “diesis,” and as I have demonstrated in Aristoxenus’s Ghost, the dieses provide important tools in ancient musical systems of measure. Last, but not least, the multiplication of 11.25 x 25 gives 360, the number of days in the ancient solar year. Given the importance afforded by the ancients to the pitch of notes and their relationship to calendrical measures, perhaps it would behoove us to look further into this topic.

Simply by beginning from 360, and adding 360 to the one before, the harmonic series from 1 to 12 comes into focus, as shown in the set of numbers below:

360 + 360 = 720 2/1

720 + 360 = 1080 3/2

1080 + 360 = 1440 4/3

1440 + 360 = 1800 5/4

1800 + 360 = 2160 6/5

2160 + 360 = 2520 7/6

2520 + 360 = 2880 8/7

2880 + 360 = 3240 9/8

3240 + 360 = 3600 10/9

3600 + 360 = 3960 11/10

3960 + 360 = 4320 12/11

If we stop for one moment and really think about this, we see that the information provided by the numbers is astonishing. Rather than one single universe (uni one, versa turn) now there are “multiverses” evidenced by the many turning cycles: the worlds whirled into being. Beginning with the first cyclic number, 360, every succeeding ratio is indicative of yet another spinning cycle. Adding 360 to 360 gives one spin, 720; adding another 360 gives two spins: 720 + 360 = 1080; adding another 360 gives three spins, or 1440; and so on. As shown in the series above, the twelve ratios from 360 to 4320 mark the completion of twelve spinning cycles. From spinning around, one’s consciousness became attuned to the “music of the spheres.”

A cycle is the measure of Time. The most natural cycle of Time is the year, measured by the number of days (turnings on its axis) for the Earth to make one full revolution around the Sun. The ancient value was taken as 360. The division of the circle into 360 degrees (attributed to Hipparchus) supposedly comes from this ancient tradition. In ancient Greece, the exquisitely beautiful celestial music of the spheres was said to come from the lyre of the Sun god, Apollo, whose time scale was vastly different than that of the paltry Earth’s. In “The Arousing of Thought” (p. 40), Gurdjieff asks: “Can I confine myself merely to this, in the objective sense, paltry Earth of ours?” Directly following this question, he writes about his beloved grandmother who, disapproving of such a thing would turn in her grave “so many times that she would almost be transformed into an ‘Irish weathercock.’”

Apollo himself was the god of divine harmony, and was the leader of the nine Muses who were well known for their “spinning about the peak of the cosmic mountain.” In Greek mythology the nine Muses were the goddesses of music and song. In fact, our word “music” derives from the Greek mousa, “a Muse,” from which we get our word “muse,” meaning “to ponder, to think deeply.” This “cosmic mountain” appears now to be the set of numbers above that begin at “Apollo’s peak,” 360. From the peak of this “cosmic mountain,” every single individual number adds, by gematria, to 9 (3+6+0=9; 7+2+0=9; 1+0+8+0=9; 1+4+4+0=9; and so on).

Now, certain things in ancient Greek writings that were formerly obscure begin to make more sense. For example, almost two thousand years ago, the Greek musician Aristides Quintilianus, who lived around the first century CE, wrote that “they [the ancients, the astute scientists who lived long before his own day] called the number 9 music,” the reason being that “it alone displays the harmonia of the universe.” The enigmatic word “harmonia,” so puzzling to today’s scholars, must refer to the harmonic series itself, beginning at 360.

What we seem to have here is the “earthly” scale producing squares by powers of 2 (the octaves of C’s); and the “divine” heavenly scale based upon the circular number 360, the sharp F#.

In hermetic Freemasonry, the two instruments used to lay out these two figures are the square and the compass. The compass measures the intellect, the spiritual and moral part, in contrast with the square, which measures the foundational physical body. The compass’s two legs, hinged at the top by a pivoted joint, draw the circular arcs adapted to spherical trigonometry and the measurement of orbiting heavenly bodies. In terms of mathematics, trigonometric calculation, the calculus, demands a higher reasoning power than that of plane geometry: in short, a “higher education,” one proper to the higher intellect.

Not only in Freemasonry, but in other traditions as well, the square symbolizes the Earth, the bounteous Mother, described geometrically as a plane figure. From her ample bosom come the limitless profusion of bounteous gifts of fruits and grains and flowers; and her opulent sensual nature ministers to the needs and comforts and luxuries of her children. The circular or spiral aspect, on the other hand, symbolizes the Father in heaven, ministering to the finer, sharper aspects of mind. The male, acting with appropriate jurisdiction and discretion, is responsible; the discrete intervals; the female, whose proclivity is to flow out unhesitatingly, acts without discretion.

Thus the hermetic symbol of square and compass is actually musical in nature, and concerns the two notes, C and F#. The “female” number, the powers of 2, by gematria, produces a repeating set of six numbers: 1 2 4 8 7 5. These six numbers, the octaves of C’s, form the figure known as the “lemniscate,” which is symbolic of the “eye” and “seeing” (8). Quite literally, the power of octaves produces the “horizontal 8.” On the other hand, the “male” number, the “divine 9,” the second power of 3, produces itself alone (9, 27, 81, 243, 729, and so on, all add, by gematria, to 9). The number 9, its shape, is symbolic of the “ear” and “hearing.”

The number 8 is 2 cubed (2^{3}). The number 9 is 3 squared (3^{2}). The male above the female, or 32/2/3, generates the musical “whole tone,” 9/8. Mounting evidence from our study appears to indicate that this specific ratio, the musical whole tone, is “the unit of vibrations of sound.” Carrying the speculation even further, it appears that this unit is what Gurdjieff termed “the Nirioonossian world sound.” Significantly, he connected it to the ear. As he put it, the Nirioonossian-crystallized-vibrations “arise in the completed formation of every being as a result of the process of all kinds of perceptions of their organ of hearing.” Somehow, this “sound” is extracted out of the harmonic series and emitted into circulation. And what this circulation produces is the sensation of Time!

What we perceive consciously as sound is really only the vibration of air that, touching our ear drums, forces them to vibrate. This secondary phenomenon, relating to touch, actually pertains to sensation. It is this cool sensation that gives us our perception of “passing time.” Gurdjieff goes on to say that the functioning of the perceptive organ of hearing, by the action of vibrations obtained from the sequence of sounds, evokes associations in one or another of the three brains at the moment called “the-momentum-of-what-was experienced;” and the sequence of experiencings proceeds in automatic order. Yes, the automatic and invariant order of the harmonic series.

While it is admittedly a bit interesting to notice that the word “emit” spelled backward is “time,” and while it is equally interesting (at least to this writer) that “emit” and “emission” relate to “emissary,” which means “secret agent;” such curiosities are not really convincing. What is convincing is the fact that every number in the harmonic series originating from 360, without exception, by the process of gematria, adds to 9. (The reader is invited to calculate for himself this astonishing fact). That is certainly not the case in the “primal series” that begins at the number 1. What information can be gleaned from this data?

For one thing, we must admit to the fact of two different harmonic series. One series issues naturally from unity, “1,” and follows all-universal purposes. The other, being unnatural and “artificially contrived,” issues from 360. (How intriguing that the numbers 3-6-0 look similar to the letters in E-G-0, and the word “ego” is another word for “I”). Gurdjieff said that human life in general can be compared to a large river which, at a certain point, becomes divided into two streams. Here, at the branching of the two streams, the waters no longer mingle. “Individually the life of every man up to his reaching responsible age corresponds to a drop of water in the initial flow of the river [from unity, 1], and the place where the dividing of the waters occurs [360] corresponds to the time when he attains adulthood.” “A man who has in his common presence his own “I” enters one of the streams of the river of life; and the man who has not, enters the other.” Is it mere coincidence that the letter “I” is the ninth letter of the alphabet?

Gurdjieff writes: “Although the real man who has already acquired his own “I” and also the man in quotation marks who has not, are equally slaves of the said ‘Greatness,’ yet the difference between them, as I have already said, consists in this, that since the attitude of the former to his slavery is conscious, he acquires the possibility, simultaneously with serving the all-universal Actualizing, of applying a part of his manifestations according to the providence of Great Nature for the purpose of acquiring for himself ‘imperishable Being,’ whereas the latter, not cognizing his slavery, serves during the flow of the entire process of his existence exclusively only as a thing, which when no longer needed, disappears forever.”

There is the implication that “Being” has to do with a second system that goes beyond ordinary harmonics.