Appendix Four
Expounding Upon
Liber Trigrammaton
sub Figura XXVII
By
Frater Centaurus
3°=8□
Preface
By
Greatly Honored Frater
Zoel Dana Kaim/Caim
Reading Frater Centaurus’ commentaries caught me a bit by surprise as I remembered my own contemplations when I first read Trigrammaton. Crowley didn’t write much on this holy book and I agree with Paul’s commentaries as they are what I am inclined to say myself. The diligent student should be able to create an interpretation based upon defining different sephirothic correspondences for the starting points. These commentaries are a new ‘classic,’ raising the bar to a new and rare development in Qabalistic thought.
As a project, Trigrammaton is made to stir minds in the time to come, and seeing it again, I wonder what did Crowley really did with the trigrams? Trigrammaton is a sequel, which is a prelude to the classic eight trigrams of I Ching. In the first nineteen trigrams of this work, there appears a void symbolized by an asterisk. What is this? The asterisk is bound to be called something like: the source, the unknown factor, zero, or the harmonized but alien fundament. The use of this symbol changes the interpretation of the components of the trigram, the Yin and Yang. The trigrams are composed of what we can see as a binary code ; zero & one, and Crowley changes this by recreating this scheme into the classic Egyptian triadic way, of which we find again in Hegel’s dialecticism. As the asterisk is a balanced nihil, the broken line now truly becomes a negative zero, a real minus.
As the Ogdoad and the processes within Ain Soph Aur become more known, it would seem reasonable to ascribe more of Trigrammaton to that which is beyond Kether. The transition between Trigram Nineteen and Trigram Twenty could be used herein, as this is where the use of the unknown factor is omitted. To describe the processes beyond, the school of Hermiopolis used the same as in the Ennead. The Ogdoad counted one less, as its final outcome, the ninth was the first of the Ennead, and the first was quite unknown, thus it had the structure of the Ennead implicit.
Liber Trigrammaton
sub Figura XXVII
Although the main body of this Liber is Class A, the attribution of letters to the English Alphabet is not of that level. These letters were added at a later date by Crowley, and with the later revisions of Liber DCCLXXVII, form one approach toward an English Qabalah. Commentary by Crowley is in brackets; commentary by Centaurus in italics, just below it. The appendices are from other sources.
Being the Book of the Trigrams of the Mutations of the Tao with the Yin and the Yang
This is certainly a unique concept; a mutating Dao, and it extends the idea of a trinity. We see the Dao interacting with its two manifestations, the Yin and the Yang. There is also a certain corollary that can be drawn with Madame Helena Blavatsky’s Book of Dzyan and as well, this work can be seen as a strong appendage to the Chinese wisdom of the Yi Jeng and the Dao De Jing.
0/1 (Number Zero/First Trigram)
*
*
*
Here is Nothing under its three forms. It is not, yet informeth all things.
[‘I’ Narrowed breath. Represents concentration, including aspiration.]
The three asterisks represent the Ain Soph Aur. But a hint of Kether is here in that all things are informed therefrom.
1H/2
*
*
—
Now cometh the glory of the Single One, as an imperfection and stain.
[‘L’ Passive undulation, without effort, unchecked.]
The top two asterisks represent Harmony and Purity. The dash below them represents disruption by way of the quest for selfhood. As per the myth of Qabalistic generation, the Ain Soph Aur formulates a center. This center is the first hint of manifestation and represents a disturbance in the Dao. The momentum is downwards as any disturbance carries weightiness, much the same as the emotional baggage that humans carry. The quest for selfhood is an emotion in the form of desire; the bud-will. And as the Supernal Sephiroth are really one and the same, the allusion to Chokmah is here suggested. Also, regarding the “Single One,” there is recursive detail in that Liber Cordis Cincte Serpente provides more on the nature of this “imperfection and stain.” Cf. Liber LXV:II.5-6[1]
2A/3
*
*
- -
But by the Weak One the Mother was it equilibrated.
[‘C’ Vide ‘S’ and ‘K’]
Equilibrium is the action here; as if the Mother is generated from the disturbing quest for self-awareness. The reflection cast becomes the awareness of selflessness. This is the nature of not only Kether but in the arrival into the City of the Pyramids. The now broken line shows the feminine or passive nature. The Mother is Nuit (All/Yin), equilibrating the single Yang. Cf. the Dao De Jing, Cap. 52, vs. 2.[2] And we may also juxtapose the “Weak One” with the “Strength” in the verse connected with the next Trigram. But the interesting thing here is that we have moved from the present tense in the first two verses to the past tense. The first two verses then, seem to present the idea of consciousness and being;
the ‘here and now.’ An inference may then be drawn that due to a previous equilibration, consciousness becomes possible; as if to show the Ain Soph Aur formulating its center so that it might know itself.
3D/4
*
—
*
Also the purity was divided by Strength, the force of the Demiurge.
[‘H’ Forcible addition of pure breath to other sounds. Represents effort.]
The Demiurge is the false God of Genesis that separates the Waters. This is the assertion of selfhood into Da’ath. The asterisks now represent the waters, separated (above and below) by the dash, as the dash becomes Choronzon.[3] The net result is the assertion of the identity of the Universal Mind.
Considering the juxtaposition, mentioned above, “purity” is a reference to the female “Mother” of the previous verse, whom is also confused by the Christists into the image of a Virgin with the resulting horrors that accompany such a false morality. This morality is a blind in much the same way as the demonization of Choronzon (the Demiurge) is a blind…as much as the “shame of Khem.”
Graphically, this trigram identical with the division sign used in mathematics.
4T/5
*
- -
*
And the Cross was formulated in the Universe that as yet was not.
[‘X’ Combines ‘K’ and ‘S’]
The broken dash is again, the female symbol considering selflessness in relation t the ‘waters.’ The broken dash with the top asterisk then represents the Supernal Triad with the bottom asterisk representing Da’ath, which is then, a reflection of Kether. The broken dash as Chokmah and Binah are negatively charged in relation to Kether, as the generating force.
We may also draw from this, a certain reference to the formula of Liber XXXVI; therein, the appearance of Set in the Circle annihilates the operators (2=0). Set becomes the imperfection, the “shame of Khem” and the stain in the tomb. Cf. AL:III.34.[4]
That the cross is formulated in the Universe as a result of the force of the Demiurge associates the cross with the Demiurge.
5E/6
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*
*
But now the Imperfection became manifest, presiding over the fading of perfection.
[‘T’ the sexual onslaught. A less responsible form of D.]
The Demiurge asserts its dominance over both waters, whose preeminence it denies and covers up. This is the One becoming the All and suffers the “shame of Khem” as per Liber LXV:I.5-6. Set is then the Prince. We see here also, the Ain Soph or even the Soph Aur brought down into the Ruach & Assiah as the manifestation of Fermions in the electromagnetic Aethyr. The transition back, from the past to the present, shows the “shame of Khem.” This is the “imperfection” of the One becoming the All. Notice in the next verse, the woman (the All) connected to this by use of the word “Also.”
Graphically, the solid line indicates a cloud hanging over perfection; hiding perfection in its shadow.
6M/7
- -
*
*
Also the Woman arose, and veiled the Upper Heaven with her body of stars.
[‘Y’ when distinct from ‘I,’ dignifies the vowel to which it is prefixed.]
Nuit becomes the Daughter, awakening the Eld of the King (Cf. the Signs of N.O.X. in Liber V vel Reguli). Nuit as consort of the Demiurge (Pan/Choronzon=Demiurge?)[5] dwells in his same place as she lay with him and is one with him. Considering Crowley’s teaching in the footnote below, it should be obvious that a study of the Starry Gnosis and the role of both the Redeemer and the Leviathon will provide greater insight into the importance of this. Also note Liber CCXXXI and Kenneth Grant’s work on this.
7N/8
*
—
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Now then a giant arose, of terrible strength; and asserted the Spirit in a secret rite.
[‘P’ As to ‘B’ as ‘K’ is to (hard) ‘G.’ Bursting of a bud as against that of a fruit.]
The two dashes are the Annunaki and the Nephilim[6] having fallen from the heavens, with the asterisk representing the star, Lucifer, the Guardian Angel of humanity as per the ancient Hebrew legend. The “secret rite” is the Sons of God mating with the Daughters of Men. The spirit asserted is the dot on top as the bottom line is the imperfection and stain per the second trigram.
Two states of time, “Now” and “then” are given with the first two words of the corresponding verse to this Trigram. But it may be seen as a story telling convention, making it obvious that this is an historical account of creation; not unlike Blavatsky’s Secret Doctrine, but with greater succinctness.
8I/9
*
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And the Master of the Temple balancing all things arose; his stature was above the Heaven and below Earth and Hell.
[‘A’ Open unmodulated breath. (ah.)]
The dash becomes the firmament (per the second trigram) as the Abyss, between the Ruach and Supernals, with the star(s) above that the Magister Templi casts as he or she successfully traverses the Abyss and simultaneously reflects down into the Ruach. The broken dash is then the Ruach (Earth), being dual-natured; with Hell being it’s nightside. Notice also that this symbol is the exact reverse of that of the Black Brothers, symbol 18 (numbered 17) and that the Master is referred to in the singular as the Black Brothers are referred to in the plural.
9F/10
*
- -
—
The dash is the Black Brother; he seeks to rule the world; to generate order in Assiah.
By putting the astral body of the dual-natured Ruach, into the Abyss (indicated by the broken dash taking the place of the line of the firmament in the previous trigram) as in the Christian mystery with the bodily assumption to Heaven, the key to the working of the Tree-of-Life is confused. Therefore, they present the perversion of the MT formula; they are Qliphotic and blind forces that would bring the ego into the Abyss and find the false crown.
Against him the Brothers of the Left-hand Path, confusing the symbols. They concealed their horror [in this symbol]; for in truth they were
[‘J’ Like soft G.]
- -[7]
—
*
This is an inversion that hides the light of the stars, as if trapped in matter; this being also an illusion. And we can deduce from this an allegory of the Night of Pan. The “Brothers” (plural) being the “Master” (which we can deduce from the stature of the Master), must be One. This is perhaps, why it is said that there is no Black Lodge, from which we can infer that they ultimately are destroyed and absorbed into the body of the “Master.”
10S/11
*
- -
- -
The master flamed forth as a star and set a guard of Water in every Abyss.
[‘W’ When distince from ‘U’ represents the operation of choice. ‘U’ does this to some extent. (Will, word, way.)]
“every Abyss” would seem to refer directly to Da’ath, and Qesheth. They enclose the Ethical and Astral Triads, being the ones that have the apex of their triangles pointing downwards, as is drawn the Alchemical symbol for water.
We might also state that as the “master” sets a “guard,” that this “water” or emotion is that of fear; a blind cast forth by the Guardian of the Threshhold who is also the “giant” that “arose” in a preceding verse.
The traversal of the Abyss of Da’ath is shown by the solid line of the last trigram being broken; as if broken through or busted through. These two abysses are also the two entrances to the nightside of the Tree-of-Life.
11O(20)/12 [EQ value in parentheses]
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*
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Also certain secret ones concealed the Light of Purity in themselves, protecting it from the Persecutions.
[‘O’ The breath concentrated and directed. Is to I as magic is to mysticism.]
The secret ones are the Secret Chiefs on the one hand, but it’s interesting to note that Moses persecuted the Nephilim. The light hidden in these Sons of Light is the light hidden in the Ruach with it’s 5th Dimensional[8] nature being as if passive or negative to the waters; normally shown as broken dashes, indicative of their feminine nature.
The light of purity (the 1st Trigram, numbered Zero; the AIN, which is also NOT and Silence) is that ineffable secret that can’t be communicated. It is represented by the dot, and is concealed between two walls, indicated by the dashes. These also serve as counter-charged poles with the dot transcending this polarity. The dot is also the spark of the Pleroma, the light of consciousness and being.
12U(30)/13
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*
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Likewise also did certain sons and daughters of Hermes and of Aphrodite, more openly
[‘G’ (hard) Opening as if to devour. (Soft?)
The Starry Gnosis showing itself more plainly in Greek mythology. And so the revelation of the sky is Yang or male, as indicated by the unbroken dash. Note also, that the Greeks worshipped the male form. But the Nephilim were men and women, being the sons and daughters of the mating of the Sons of God with the Daughters of Men. The lower pole of the last trigram is the world of duality, the microcosm; indicated by the broken dash.
13V(40)/14
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*
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But the Enemy confused them. They pretended to conceal that Light that they might betray it, and profane it.
[‘Z’ An irritated or excited form of ‘S,’ emphasizing elements of anger and alarm.]
The top dash of the previous trigram is now broken, as if representing the light perspiring upwards. This gives one the impression of being “white and glistening[9].” The buster upper pole represents the macrocosm, which is the starry fabric of the body of Nuit; per seventh trigram. The lower line is that imperfection and stain; per the second trigram.
This should not be interpreted as representing a Manichaean analogy; the Black Brothers serve despite their will. Yet, shown here is a basic deception of the Black Brotherhood. The cloud formed of this deceptive confusion is represented by the unbroken (male) dash. Being opaque, it refracts the light. If we see Jehovah as the Demiurge, Joseph’s coat of many colors comes to mind. In history, the Orthodox priesthood shunned the esoteric side of the revelation; hence a reference to the Templars.
14L(50)/15
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*
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Yet certain holy nuns[10] concealed the secret in songs upon the lyre.
[‘B’ Bursting forth. Phallus and Vulva. Kissing.]
Nuns=none/not/zero; Priestesses of Nuit; Babalon. The Bards sang these songs of love that to this day and as always, have been equated with the stars; represented by the asterisk. It is these “nuns” that have drawn the song from them. These “nuns” may also be the Bacchantes; the priestesses of Eleusis.
The true nature of the light that they draw is the inscrutable secret that cannot be communicated, but is revealed to the wise. It is the key to incredible power. Graphically, the trigram represents the feminine mystery. The broken dash above represents Nuit (the music of the spheres) as the one below, Babalon (the lyre). The star in-between is the light.
15G(60)/16[11]
—
—
*
Now did the Horror of Time pervert all things, hiding the Purity with a loathsome thing, a thing unnameable.
[‘F’ Compound of ‘P’ and ‘H’]
That which is “unnameable” would be Hadit. Cf. AL:II.4.[12] In its loathsomeness, it may then be as the “caress of Hell’s own worm” as found in AL:II.62 or the ‘blind creature of slime.’ With the transition back to the present tense, time may be seen as the source of “Now;” deriding ‘Because,’ which more directly involves consideration of the past and the future.
16C(70)/17
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*
Yea, and there arose sensualists upon the firmament, as a foul stain of storm upon the sky.
[‘S’ Defiance,[13] warning, etc.]
The sensualists are dualists, indicated by the unbroken dash. It is the center line that was the firmament in the ninth trigram. The storm here refers back to the cloud, discussed in my comment, above. But here, on a lower level, it is not the Black Brotherhood, but its dupes. Returning to the past tense, and for the remainder of this holy book, a “storm upon the sky” seems an indication of the lightening flash that created life. It’s as if life is a simultaneous creation of past, and present. Prophecy added into this, includes then, all three tenses brought into the manifested moment called ‘Now.’
17P(80)/18
- -[14]
—
*
And the Black Brothers raised their heads; yea, they unveiled themselves without shame or fear.
[‘M’ The Will to Die.]
The Black Brothers stand between the star (asterisk) and the sky (broken dash). These dupes; false prophets, comprise a false lodge that really doesn’t exist. They pose as intermediaries between the above and below in a denigration of human dignity.
18Y(90)/19
- -
- -
*
Also there rose up a soul of filth and of weakness, and it corrupted all the rule of the Tao.
[‘N’ The vibration which includes Life and Death as complementary Curves.]
The broken dash at the top of the trigram represents the false universe or the Earth out of its proper place; it should be below. The broken dash in the middle represents the false soul, shown by the Black Brotherhood. And the asterisk stands alone to represent the Dao.
19R(100)/20
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Then only was Heaven established to bear sway; for only in the lowest corruption is form manifest.
[‘E’ Softened, but otherwise unmodulated breath. (Phallus.)]
The truth now, is only found in matter, as all three veils are a sealing off of human awareness. The three lines represent the completed ToL and the three triads thereof. The involution is complete and then emanates Malkuthy “the lowest corruption” wherein form is manifest.
20W(200)/21
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Also did Heaven manifest in violent light,
[‘R’ Continuous vibration, like ‘L’ but active. (Air of the Aethyr.)]
Into this depth (matter), the violet light; the light beyond eyesight is discovered by the materialists—modern physicists—the ultra-violet that can destroy eyesight. It is as if the male, solar-phallic light of the previous trigram hides it.
21B(300)/22
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And in soft light.
[‘Q’ Combines ‘K’ and ‘U.’ (The Sun.)
The soft light is the light of individual consciousness, which of necessity asserts itself as a response to blindness. Interpreting the extremely yang nature of the twentieth trigram by its gender, the anima or subconscious is equilibrated.
22K(400)/23
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Then were the waters gathered together from the heaven,
[‘V’ Conscious male will. Manhood, strength, truth, righteousness, immortality, integrity. (Water.)]
And through the violet light and the assertion of consciousness, heaven is rediscovered and the code of the Starry Gnosis is again revealed through those prophets; now emerging from amongst us. The broken line is the Water of Heaven.
23J(500)/24
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And a crust of earth concealed the core of flame.
[‘K’ Opening as if startled. (Earth.)]
The heavens are brought down to the Earth and found hidden in matter. This is the redemption of matter; the resurrection of the body. The “crust of earth” and the firmament is indicated by the dash. The Water becomes the Fire of Earth as shown in the two sets of broken dashes.
The fire shown by the broken dashes, emanates downwards in direct correlation with the 26th Trigram, numbered 25.
24Z(600)/25
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Around the globe gathered the wide air,
[‘D’ The paternal vibration. (The Moon.)[15]
Humanity discovers itself as equal to the Demiurge and takes its rightful place between the above and the below; becoming the crowned Prince. Here again, the firmament is represented by a male dash, surrounded by air as the female or broken dashes. This is Earth in its receptive form receiving the Fire from above[16].
25X(700)/26
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And men began to light fires upon the earth.
[‘U’ Like ‘O’ with added refinement and a tinge of melancholy. ‘O’ is completely self-confident. (Fire.)]
The fiery passion of the human soul, then celebrates the joy of existence. The Fire lifts itself to the sky and the Heavens; both the vaulted one revealed in the seventh trigram and the one beyond it. The two broken dashes over the solid dash graphically depicts fire as if emanating or radiating from a log of wood.
26Q(800)/27
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Therefore was the end of it sorrow; yet in that sorrow a sixfold star of glory whereby they might see to return unto the stainless Abode; yea, unto the Stainless Abode.
[(Vulva).]
The above and below are then united in the Adept, who has mastered the mystery of the Temple, which is life itself. The three broken lines bring us full circle, back to the three dots of the first trigram. Both have a feminine or passive quality. The broken dashes represent the passive spiritual energy and the three dots represent the active spiritual force.
The three triads of Trigram 20; numbered 19, here express the ToL in the world of duality. Assigning the letter Q to this is significant as the letter depicts a completed Universe (the circle) with the attached line as the emanation that points to Malkuth and manifestation.
Appendices
The Hexagram Tables of Trigrammaton
Beginning with the 27 basic Trigrams, there are 729 possible Hexagrams that can be created using the divination method described above. These arrange themselves most naturally into 27 separate groups, or ‘houses’. Each house contains the 27 Hexagrams having the same Trigram in upper position. This classification puts each successive multiple of the number 27 at the head of each house. For ease of reference, a chart is included that shows the numerical value of these Trigrams in the upper position.
These multiples of 27 are significant because they can all combine to form an octahedral matrix that contains the identical numerical characteristics of the original model described above, since every numerical unit of the original octahedron can be replaced by a multiple of 27. They are also significant because each of these Hexagrams acts as a pure Trigram, raised into the upper position; the lower Trigram is the Zero, and does not interfere with the operation of the upper Trigram. These 27 Hexagrams are found in the lower right corner of the page, and their numerical value is also the name of their ‘house’.
Thus the House of 243 contains all those Hexagrams which have a Nine Trigram in the upper position. Conversely, the house of 12, or 19, would be the set of all Hexagrams with those Trigrams in the lower position. These sets do not follow the same numerical order, and it is more difficult to find a particular number when using them, but they do form an interesting classification in their own right. For the present purposes it will be simpler to arrange the houses numerically.
Following the Hexagram tables are charts of inversions, doublings, oppositions, and inverted-oppositions. The chart of the inversions presents the 27 Hexagrams which show the same structure when inverted. This technique of inverting the Hexagram is also used in the arrangement of the chapters of I Ching. The chart of the doublings presents the 27 Hexagrams which have the same Trigram in upper and lower position. This arrangement is also considered in I Ching, where the eight Hexagrams that are doubled are given the same name as their component Trigrams. The chart of the oppositions presents the 26 Hexagrams which have opposite Trigrams in the upper and lower positions. This arrangement is of interest in the study of the polarities of Trigrammaton. The chart of the inverted oppositions completes the pairing of related Trigrams, so that the four charts depict the four basic relationships of Trigrams to each other.
Following the extra charts are two lists of the ‘Antigrams’ of Trigrammaton. The pairs of Antigrams are the numerical values of two Hexagrams whose lines are all changed into their opposites. This chart is meant as a supplement to the Hexagram tables and is therefore written in Base Ten only, rather than in Hexagrams. Finally, there is a ‘master-list’ of all the numbers from 1 to 728. This chart is also in Base Ten, and is intended as a condensed table of the most basic information about any Hexagram. The number in the left column is the root number, and all the other columns have some relation to it, such as opposite, inverse, and so forth.
These several tables form a reference guide for the gematria of Trigrammaton. They can be manipulated any number of ways, both mathematically and structurally, but perhaps the most important concept to bear in mind is that any Hexagram can ultimately transform into any other Hexagram.
The chart of opposite numbers shows three pairs that are essential to this qabala: the numbers 31 & 62, 93 & 186, 333 & 666 are opposite pairs. The first pair represents the formula of LAShTAL; there is a 31, which is the XXXI of the Keys for the Aeon and Lust, opposite its double, 62, which shows the combination of LA and AL. The second pair represents a glyph for the sentence “Love is the Law, love under will”, since both ‘love’ and ‘will’ equal 93 in Greek. The third pair represents the number of Choronzon opposite the number of the Beast. The first and third pair are inversions of each other, while 93 & 186 are the inverses of 111 & 222.
What is truly remarkable is that the Tree of Life can be exactly depicted by the Hexagram of 666, with the Tao lines as the sephiroth of the middle pillar, and the Yin lines as the sephiroth of the outer pillars. An extra Tao can be added for Kether at the crown without changing the numerical value. Thus Kether occupies the 729’s place on the Septagram, but this level is not activated. It is the sphere of Baphomet. The opposite Hexagram of 333 thus shows the Tree of Life with the horizontal paths emphasized. Note that these paths total to 93 in the Golden Dawn Tree. In terms of the obverse and reverse of the Tree, 333 as Choronzon indicates the reverse Tree, while 666 is the obverse Tree.
The inversion of the 333 Hexagram happens to be the 31 Hexagram, while the inversion of the 666 Hexagram is the 62 Hexagram. Together these inversions total 93, and this shows that from the standpoint of Kether, the Tree unfolds as a double-sided glyph which embodies the 93 current. This is further developed by the inversion of the Septagram of 333, which is the 93 Septagram, and the inversion of the 666 Septagram, which is the 186 Septagram. Thus from the point of view of the Ain Sof Aur, the total Tree develops as a double sided glyph of 93 and 186. The following are the Hexagrams in question. The Septagrams are made by including Kether, i.e., by adding Tao at the top.
— — ——— • • • •
— — ——— — — ——— • •
• • • • — — — —
— — ——— — — ——— • •
• • — — ——— — — ———
• • • • — — — —
666 333 186 93 62 31
• • • •
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• • • • ——— — —
— — ——— — — ——— • •
• • — — ——— ——— — —
• • • • • •
666 333 186 93 111 222
Trigram Values in Upper Position of a Hexagram
• I • J — — N
• — — — —
• 0 ——— 189 • 648
• L • W ——— E
• — — ———
——— 27 — — 216 ——— 351
• C ——— O ——— R
• • ———
— — 54 ——— 270 — — 378
• H ——— G ——— Q
——— • — —
• 81 — — 297 ——— 432
• X — — Z — — V
— — • ———
• 162 ——— 513 ——— 594
——— T — — B ——— K
• • — —
• 243 — — 540 — — 459
— — Y ——— F — — D
• ——— ———
• 486 • 324 — — 621
• P ——— S — — U
——— — — — —
——— 108 • 405 ——— 675
• A — — M — —
——— ——— — —
— — 135 • 567 — — 702
• • • • • •
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• • • • • •
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
1 2 3 6 9 18
• • • • • •
• • • • • •
• • • • • •
• • • • ——— ———
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4 5 7 8 10 11
• • • • • •
• • • • • •
• • • • • •
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
19 20 12 15 21 24
• • • •
• • • •
• • • •
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13 14 16 22
• • • • •
• • • • •
• • • • •
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17 23 25 26 0
• • • • • •
• • • • • •
——— ——— ——— ——— ——— ———
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
28 29 30 33 36 45
• • • • • •
• • • • • •
——— ——— ——— ——— ——— ———
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
31 32 34 35 37 38
• • • • • •
• • • • • •
——— ——— ——— ——— ——— ———
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
46 47 39 42 48 51
• • • •
• • • •
——— ——— ——— ———
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
40 41 43 49
• • • • •
• • • • •
——— ——— ——— ——— ———
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
44 50 52 53 27
• • • • • •
• • • • • •
— — — — — — — — — — — —
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
55 56 57 60 63 72
• • • • • •
• • • • • •
— — — — — — — — — — — —
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
58 59 61 62 64 65
• • • • • •
• • • • • •
— — — — — — — — — — — —
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
73 74 66 69 75 78
• • • •
• • • •
— — — — — — — —
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
67 68 70 76
• • • • •
• • • • •
— — — — — — — — — —
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
71 77 79 80 54
• • • • • •
——— ——— ——— ——— ——— ———
• • • • • •
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
82 83 84 87 90 99
• • • • • •
——— ——— ——— ——— ——— ———
• • • • • •
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
85 86 88 89 91 92
• • • • • •
——— ——— ——— ——— ——— ———
• • • • • •
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
100 101 93 96 102 105
• • • •
——— ——— ——— ———
• • • •
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
94 95 97 103
• • • • •
——— ——— ——— ——— ———
• • • • •
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
98 104 106 107 81
• • • • • •
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
109 110 111 114 117 126
• • • • • •
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
112 113 115 116 118 119
• • • • • •
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
127 128 120 123 129 132
• • • •
——— ——— ——— ———
——— ——— ——— ———
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
121 122 124 130
• • • • •
——— ——— ——— ——— ———
——— ——— ——— ——— ———
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
125 131 133 134 108
• • • • • •
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
136 137 138 141 144 153
• • • • • •
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
139 140 142 143 145 146
• • • • • •
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
154 155 147 150 156 159
• • • •
——— ——— ——— ———
— — — — — — — —
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
148 149 151 157
• • • • •
——— ——— ——— ——— ———
— — — — — — — — — —
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
152 158 160 161 135
• • • • • •
— — — — — — — — — — — —
• • • • • •
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
163 164 165 168 171 180
• • • • • •
— — — — — — — — — — — —
• • • • • •
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
166 167 169 170 172 173
• • • • • •
— — — — — — — — — — — —
• • • • • •
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
181 182 174 177 183 186
• • • •
— — — — — — — —
• • • •
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
175 176 178 184
• • • • •
— — — — — — — — — —
• • • • •
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
179 185 187 188 162
• • • • • •
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
190 191 192 195 198 207
• • • • • •
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
193 194 196 197 199 200
• • • • • •
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
208 209 201 204 210 213
• • • •
— — — — — — — —
——— ——— ——— ———
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
202 203 205 211
• • • • •
— — — — — — — — — —
——— ——— ——— ——— ———
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
206 212 214 215 189
• • • • • •
— — — — — — — — — — — —
— — — — — — — — — — — —
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
217 218 219 222 225 234
• • • • • •
— — — — — — — — — — — —
— — — — — — — — — — — —
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
220 221 223 224 226 227
• • • • • •
— — — — — — — — — — — —
— — — — — — — — — — — —
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
235 236 228 231 237 240
• • • •
— — — — — — — —
— — — — — — — —
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
229 230 232 238
• • • • •
— — — — — — — — — —
— — — — — — — — — —
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
233 239 241 242 216
——— ——— ——— ——— ——— ———
• • • • • •
• • • • • •
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
244 245 246 249 252 261
——— ——— ——— ——— ——— ———
• • • • • •
• • • • • •
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
247 248 250 251 253 254
——— ——— ——— ——— ——— ———
• • • • • •
• • • • • •
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
262 263 255 258 264 267
——— ——— ——— ———
• • • •
• • • •
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
256 257 259 265
——— ——— ——— ——— ———
• • • • •
• • • • •
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
260 266 268 269 243
——— ——— ——— ——— ——— ———
• • • • • •
——— ——— ——— ——— ——— ———
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
271 272 273 276 279 288
——— ——— ——— ——— ——— ———
• • • • • •
——— ——— ——— ——— ——— ———
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
274 275 277 278 280 281
——— ——— ——— ——— ——— ———
• • • • • •
——— ——— ——— ——— ——— ———
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
289 290 282 285 291 294
——— ——— ——— ———
• • • •
——— ——— ——— ———
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
283 284 286 292
——— ——— ——— ——— ———
• • • • •
——— ——— ——— ——— ———
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
287 293 295 296 270
——— ——— ——— ——— ——— ———
• • • • • •
— — — — — — — — — — — —
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
298 299 300 303 306 315
——— ——— ——— ——— ——— ———
• • • • • •
— — — — — — — — — — — —
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
301 302 304 305 307 308
——— ——— ——— ——— ——— ———
• • • • • •
— — — — — — — — — — — —
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
316 317 309 312 318 321
] ——— ——— ——— ———
• • • •
— — — — — — — —
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
310 311 313 319
——— ——— ——— ——— ———
• • • • •
— — — — — — — — — —
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
314 320 322 323 297
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
• • • • • •
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
325 326 327 330 333 342
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
• • • • • •
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
328 329 331 332 334 335
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
• • • • • •
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
343 344 336 339 345 348
——— ——— ——— ———
——— ——— ——— ———
• • • •
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
337 338 340 346
——— ——— ——— ——— ———
——— ——— ——— ——— ———
• • • • •
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
341 347 349 350 324
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
352 353 354 357 360 369
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
355 356 358 359 361 362
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
370 371 363 366 372 375
——— ——— ——— ———
——— ——— ——— ———
——— ——— ——— ———
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
364 365 367 373
——— ——— ——— ——— ———
——— ——— ——— ——— ———
——— ——— ——— ——— ———
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
368 374 376 377 351
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
379 380 381 384 387 396
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
382 383 385 386 388 389
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
397 398 390 393 399 402
——— ——— ——— ———
——— ——— ——— ———
— — — — — — — —
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
391 392 394 400
——— ——— ——— ——— ———
——— ——— ——— ——— ———
— — — — — — — — — —
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
395 401 403 404 378
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
• • • • • •
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
406 407 408 411 414 423
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
• • • • • •
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
409 410 412 413 415 416
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
• • • • • •
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
424 425 417 420 426 429
——— ——— ——— ———
— — — — — — — —
• • • •
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
418 419 421 427
——— ——— ——— ——— ———
— — — — — — — — — —
• • • • •
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
422 428 430 431 405
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
433 434 435 438 441 450
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
436 437 439 440 442 443
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
451 452 444 447 453 456
——— ——— ——— ———
— — — — — — — —
——— ——— ——— ———
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
445 446 448 454
——— ——— ——— ——— ———
— — — — — — — — — —
——— ——— ——— ——— ———
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
449 455 457 458 432
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
— — — — — — — — — — — —
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
460 461 462 465 468 477
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
— — — — — — — — — — — —
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
463 464 466 467 469 470
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
— — — — — — — — — — — —
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
478 479 471 474 480 483
——— ——— ——— ———
— — — — — — — —
— — — — — — — —
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
472 473 475 481
——— ——— ——— ——— ———
— — — — — — — — — —
— — — — — — — — — —
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
476 482 484 485 459
— — — — — — — — — — — —
• • • • • •
• • • • • •
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
487 488 489 492 495 504
— — — — — — — — — — — —
• • • • • •
• • • • • •
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
490 491 493 494 496 497
— — — — — — — — — — — —
• • • • • •
• • • • • •
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
505 506 498 501 507 510
— — — — — — — —
• • • •
• • • •
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
499 500 502 508
— — — — — — — — — —
• • • • •
• • • • •
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
503 509 511 512 486
— — — — — — — — — — — —
• • • • • •
——— ——— ——— ——— ——— ———
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
514 515 516 519 522 531
— — — — — — — — — — — —
• • • • • •
——— ——— ——— ——— ——— ———
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
517 518 520 521 523 524
— — — — — — — — — — — —
• • • • • •
——— ——— ——— ——— ——— ———
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
532 533 525 528 534 537
— — — — — — — —
• • • •
——— ——— ——— ———
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
526 527 529 535
— — — — — — — — — —
• • • • •
——— ——— ——— ——— ———
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
530 536 538 539 513
— — — — — — — — — — — —
• • • • • •
— — — — — — — — — — — —
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
541 542 543 546 549 558
— — — — — — — — — — — —
• • • • • •
— — — — — — — — — — — —
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
544 545 547 548 550 551
— — — — — — — — — — — —
• • • • • •
— — — — — — — — — — — —
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
559 560 552 555 561 564
— — — — — — — —
• • • •
— — — — — — — —
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
553 554 556 562
— — — — — — — — — —
• • • • •
— — — — — — — — — —
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
557 563 565 566 540
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
• • • • • •
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
568 569 570 573 576 585
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
• • • • • •
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
571 572 574 575 577 578
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
• • • • • •
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
586 587 579 582 588 591
— — — — — — — —
——— ——— ——— ———
• • • •
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
580 581 583 589
— — — — — — — — — —
——— ——— ——— ——— ———
• • • • •
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
584 590 592 593 567
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
595 596 597 600 603 612
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
598 599 601 602 604 605
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
——— ——— ——— ——— ——— ———
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
613 614 606 609 615 618
— — — — — — — —
——— ——— ——— ———
——— ——— ——— ———
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
607 608 610 616
— — — — — — — — — —
——— ——— ——— ——— ———
——— ——— ——— ——— ———
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
611 617 619 620 594
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
622 623 624 627 630 639
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
625 626 628 629 631 632
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
— — — — — — — — — — — —
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
640 641 633 636 642 645
— — — — — — — —
——— ——— ——— ———
— — — — — — — —
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
634 635 637 643
— — — — — — — — — —
——— ——— ——— ——— ———
— — — — — — — — — —
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
638 644 646 647 621
— — — — — — — — — — — —
— — — — — — — — — — — —
• • • • • •
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
649 650 651 654 657 666
— — — — — — — — — — — —
— — — — — — — — — — — —
• • • • • •
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
652 653 655 656 658 659
— — — — — — — — — — — —
— — — — — — — — — — — —
• • • • • •
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
667 668 660 663 669 672
— — — — — — — —
— — — — — — — —
• • • •
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
661 662 664 670
— — — — — — — — — —
— — — — — — — — — —
• • • • •
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
665 671 673 674 648
— — — — — — — — — — — —
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
676 677 678 681 684 693
— — — — — — — — — — — —
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
679 680 682 683 685 686
— — — — — — — — — — — —
— — — — — — — — — — — —
——— ——— ——— ——— ——— ———
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
694 695 687 690 696 699
— — — — — — — —
— — — — — — — —
——— ——— ——— ———
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
688 689 691 697
— — — — — — — — — —
— — — — — — — — — —
——— ——— ——— ——— ———
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
692 698 700 701 675
— — — — — — — — — — — —
— — — — — — — — — — — —
— — — — — — — — — — — —
• • • • ——— — —
• • ——— — — • •
——— — — • • • •
703 704 705 708 711 720
— — — — — — — — — — — —
— — — — — — — — — — — —
— — — — — — — — — — — —
• • • • ——— ———
——— ——— — — — — • •
——— — — ——— — — ——— — —
706 707 709 710 712 713
— — — — — — — — — — — —
— — — — — — — — — — — —
— — — — — — — — — — — —
— — — — ——— ——— — — — —
• • ——— — — ——— — —
——— — — • • • •
721 722 714 717 723 726
— — — — — — — —
— — — — — — — —
— — — — — — — —
——— ——— ——— — —
——— ——— — — ———
——— — — ——— ———
715 716 718 724
— — — — — — — — — —
— — — — — — — — — —
— — — — — — — — — —
——— — — — — — — •
— — ——— — — — — •
— — — — ——— — — •
719 725 727 728 702
• • • • • •
• • ——— ——— ——— — —
——— — — • ——— — — •
——— — — • ——— — — •
• • ——— ——— ——— — —
• • • • • •
36 72 84 120 156 168
• • ——— ——— ——— ———
— — — — • • • ———
——— — — • ——— — — •
——— — — • ——— — — •
— — — — • • • ———
• • ——— ——— ——— ———
204 240 244 280 316 328
——— ——— ——— ——— ——— — —
——— ——— — — — — — — •
——— — — • ——— — — •
——— — — • ——— — — •
——— ——— — — — — — — •
——— ——— ——— ——— ——— — —
364 400 412 448 484 488
— — — — — — — — — — — — • • ——— ——— ——— — —
——— — — • ——— — — •
——— — — • ——— — — •
• • ——— ——— ——— — —
— — — — — — — — — — — —
524 560 572 608 644 656
— — — — •
— — — — •
——— — — •
——— — — • These are the 27 Invertable Hexagrams
— — — — •
— — — — •
692 728 0
• • • • • •
• • ——— ——— ——— — —
——— — — • ——— — — •
• • • • • •
• • ——— ——— ——— — —
——— — — • ——— — — •
28 56 84 112 140 168
• • ——— ——— ——— ———
— — — — • • • ———
——— — — • ——— — — •
• • ——— ——— ——— ———
— — — — • • • ———
——— — — • ——— — — •
196 224 252 280 308 336
——— ——— ——— ——— ——— — —
——— ——— — — — — — — •
——— — — • ——— — — •
——— ——— ——— ——— ——— — —
——— ——— — — — — — — •
——— — — • ——— — — •
364 392 420 448 476 504
— — — — — — — — — — — — • • ——— ——— ——— — —
——— — — • ——— — — •
— — — — — — — — — — — —
• • ——— ——— ——— — —
——— — — • ——— — — •
532 560 588 616 644 672
— — — — •
— — — — •
——— — — •
— — — — • These are the 27 Doubled-Trigrams
— — — — •
——— — — •
700 728 0
• • • • • •
• • ——— ——— ——— — —
——— — — • ——— — — •
• • • • • •
• • — — — — — — ———
— — ——— • — — ——— •
29 55 87 116 142 165
• • ——— ——— ——— ———
— — — — • • • ———
——— — — • ——— — — •
• • — — — — — — — —
——— ——— • • • — —
— — ——— • — — ——— •
194 220 261 290 316 348
——— ——— ——— ——— ——— — —
——— ——— — — — — — — •
——— — — • ——— — — •
— — — — — — — — — — ———
— — — — ——— ——— ——— •
— — ——— • — — ——— •
377 403 426 455 481 495
— — — — — — — — — — — — • • ——— ——— ——— — —
——— — — • ——— — — •
——— ——— ——— ——— ——— ———
• • — — — — — — ———
— — ——— • — — ——— •
524 550 582 611 637 660
— — — —
— — — —
——— — —
——— ——— These are the 26 Hexagrams with Antigrams
——— ——— in their upper and lower positions.
— — ———
689 715
• • • • • •
• • ——— ——— ——— — —
——— — — • ——— — — •
— — ——— • — — ——— •
• • — — — — — — ———
• • • • • •
45 63 87 132 150 165
• • ——— ——— ——— ———
— — — — • • • ———
——— — — • ——— — — •
— — ——— • — — ——— •
——— ——— • • • — —
• • — — — — — — — —
210 228 245 290 308 332
——— ——— ——— ——— ——— — —
——— ——— — — — — — — •
——— — — • ——— — — •
— — ——— • — — ——— •
— — — — ——— ——— ——— •
— — — — — — — — — — ———
377 395 410 455 473 487
— — — — — — — — — — — — • • ——— ——— ——— — —
——— — — • ——— — — •
— — ——— • — — ——— •
• • — — — — — — ———
——— ——— ——— ——— ——— ———
532 550 574 619 637 652
— — — —
— — — —
——— — —
— — ——— These are the 26 Hexagrams with
——— ——— Inverted-Antigrams in their
——— ——— upper and lower positions.
697 715
Nuclear Hexagrams
The Nuclear Hexagrams of Trigrammaton are derived by the same method found in I Ching. The top and bottom lines of a Hexagram are disregarded, and lines 2, 3, 4, & 5 are used to create a new Hexagram. Lines 2, 3, & 4 become the lower Trigram, while lines 3, 4, & 5 become the upper Trigram of the Nuclear Hexagram. Four lines are used to generate the Nuclear Hexagram, and there are only 81 possible Tetragrams, thus there are only 81 possible Nuclear Hexagrams. Each of these Nuclear Hexagrams is shared by 9 regular Hexagrams, i.e., there are 9 Hexagrams that all have the same Nuclear Hexagram.
Since there are only 81 Nuclear Hexagrams, these can be attributed to the 81 lines that make up Liber Trigrammaton, with some very interesting results. Since the Nuclear Hexagrams occur in 27 groups of 3 consecutive numbers, they are attributed to the Trigram which occurs in upper position of their Hexagram. Thus 30, 31, & 32 are all attibuted to the 1 Trigram, since this is the upper Trigram of Hexagrams 30, 31, & 32. Hexagrams 60, 61, & 62 all have the 2 Trigram in upper position, so they are attributed to the 2 Trigram. But they are also the Antigrams of 30, 31, & 32, thus they are located on the same lines as their opposites. 31 & 62, being Antigrams, are each attributed to the first line of opposite Trigrams. This relationship holds true for all 81 lines, since the Antigram of every Nuclear Hexagram is also a Nuclear Hexagram.
In fact, in the set of the 81 Nuclear Hexagrams, any particular Hexagram of the set also has its antigram, its inverse, and its inverted-antigram as a member of the set, as well as its corresponding Hexagram from the Kamea of Baphomet. This last relationship is represented by the fact that whatever position a Nuclear Hexagram has on the chart of the 81 lines, its magic-square partner, (equidistant from the center), will also be in the same position, on a different Trigram. Thus 31 is the bottom line of the 1 Trigram, and its magic-square partner, 697, is the bottom line of the 25 Trigram.
The sum of the 81 Nuclear Hexagrams is 29,484. This number equals 324 x 91. The Hexagrams attributed to the Tao lines of the chart add to 6552, which is 72 x 91. The Hexagrams attributed to the Yang lines of the chart equal 9828, which is 108 x 91. The Hexagrams attributed to the Yin lines of the chart total 13,104, which is 144 x 91. Thus the Yang lines represent one-third of the total, while the Tao and Yin lines represent two-thirds of the total, with the Yin lines having twice the value of the Tao lines.
Continuing the process of nucleation, we discover that the 81 Nuclear Hexagrams have only 9 possible Nuclear Hexagrams of their own, and these happen to be all the multiples of 91, from 0 to 728. The process stops there, as any further nucleation still results in one of these 9 Hexagrams: 0, 91, 182, 273, 364, 455, 546, 637, 728. While the pure Hexagrams of 0, 364, & 728 can only reiterate themselves, the other six occur as three pairs. The Nuclear Hexagram of 91 is 273, and vice versa. The same is true for 182 & 546, as well as 455 & 637. This last pair is of great interest because not only are they the last two Hexagrams of I Ching, but they are opposites and inverses of each other. See the section on Trigrammaton and Astrology, where this set of Hexagrams is discussed as they relate to the four quarters of the Year. It is noteworthy that the ultimate distillation of the Hexagrams is the number 91 multiplied by the numbers 0 to 8, since these nine numbers are just exactly the value of the 9 possible Bigrams, whose interactions with each other produce the 81 Nuclear Hexagrams. 81 is the value of the word ‘Nothing’, and the central line of Liber XXVII is here attributed to 516, which is the value of verse I:28 of the Book of the Law: “None, breathed the light, faint & faery, of the stars, and two.”
The Trigram Sequence in Liber XXVII
The 81 Nuclear Hexagrams Arrayed by their Upper Trigrams
• 2 • 210 — — 667
• 1 — — 212 — — 668
• 0 ——— 211 • 666
• 32 • 240 ——— 364
• 30 — — 241 ——— 363
——— 31 — — 242 ——— 365
• 61 ——— 273 ——— 393
• 60 • 274 ——— 394
— — 62 ——— 275 — — 395
• 91 ——— 304 ——— 455
——— 90 • 303 — — 454
• 92 — — 305 ——— 453
• 182 — — 518 — — 608
— — 180 • 516 ——— 606
• 181 ——— 517 ——— 607
——— 244 — — 546 ——— 484
• 245 • 548 — — 483
• 243 — — 547 — — 485
— — 488 ——— 335 — — 637
• 487 ——— 334 ——— 638
• 486 • 333 — — 636
• 120 ——— 424 — — 696
——— 122 — — 425 — — 698
——— 121 • 423 ——— 697
• 150 — — 578 — — 726
——— 151 ——— 577 — — 727
— — 152 • 576 — — 728
Transitional Hexagrams
Another phenomenon of interest might be termed the ‘transitional’ Hexagram. The idea behind this derives from some work done on the Trigrams by Fr. RVS, who developed an approach to their structure based on philosophical, rather than mathematical principles. His essential idea is that like plus like produces like, thus Tao plus Tao equals Tao, (which is also true of Zero), and Yang plus Yang equals Yang, (not true of 1), while Yin plus Yin equals Yin, (also not true of 2). This idea, in a reverse sense, sheds some light on the casting of Hexagrams.
Suppose for example that one has cast a Hexagram with certain changing lines, thus resulting in a becoming Hexagram as well. By the use of the above concept, a transitional Hexagram can also be discovered, which is the interval between any two Hexagrams. Now mathematically, it is obvious that the difference between any two Hexagrams is simply the number needed to be added to one Hexagram in order to generate the other as the sum. But philosophically the matter is different. If one sees the Tao, Yang, Yin; Tao, Yang, Yin as a repeating cycle of three entities, always in the same position, then to change from one to the other type of line can be accomplished by going through the third line. So in order to get from Tao to Yin, it is possible to travel through Yang first, and to get from Yang to Yin it is possible to travel backwards through Tao to get there. Thus any one type of line can be the transition between the other two lines. As an example, let us take two of the important cabalistic numbers, 666 and 93:
— — ——— •
— — • ———
• • •
— — • ———
• — — ———
• • •
666 249 93
This shows that to change from 666 to 93 can be represented by Hexagram 249. The 1st and 4th lines are static, thus the transitional Hexagram also has a Tao there. In line 2, the Tao becomes a Yang, and goes through Yin. In lines 3 and 5, the Yin becomes a Yang, and goes through Tao At the top, Yin becomes Tao, and goes through Yang. Note that any of these Hexagrams is the transition between the other two; they are locked into a triangular arrangement. Thus, given any two Hexagrams, there will be one, and only one, transitional Hexagram between them. In the special case where two of the Hexagrams are Antigrams, then the transitional Hexagram will always be Zero.
This is an important tool in the analysis of any divinations that produce mutating Hexagrams. One might also postulate a beginning Hexagram for the present, postulate another for the desired result, and then generate a transitional Hexagram which tells how to get there. In this example, 666 stands for the Great Beast, and 93 stands for Aiwass, his Holy Guardian Angel. Between them is 249, the value of verse I:39, “The word of the Law is θελημα.” The total of all 3 Hexagrams is thus 1008, the value of verse II:55, “Thou shalt obtain the order and value of the English Alphabet. Thou shalt find new symbols to attribute them unto.”
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Appendix
Introduction to 2nd edition of Book Chameleon
by C.F. Russell
[pic]This six-fold figure, called KI TZI, is one of 64 Hexagrams, no two alike, which comprise Text of YI KING, Classic of Changes, initiated system of Chinese Magick. It is esoteric & occult, i.e., hidden from Hoi Polloi, but only as differential Calculus may mystify Hottentots, not otherwise than most college graduates may puzzle over language of Hot Plates. Our Text was brought from sunken continent of Atlantis to a geographical point later ruled by Manchus before Akkadian era. Sealed in this book are secrets never published except by oral communication before end of last century when trend was to reveal to properly prepared what explains weightiest problems of mankind.
Methods of Initiation aim to control contact between cerebrum, main organ of personal consciousness & memory, the cerebellum & other brains in head, along spinal column & all way down to feet. (Don't forget feet!) Types of Divination, Astrology, Tarot, Geomancy, Numerology, etc. promote Initiatory growth by their catalytic action on nervous system. Spirits with whom you converse are connected with specific parts of your brain. (See Goetia.) Cerebrum operates only in sphere of memory & sensation, otherwise it is blind & stupid, cannot perceive supersensible data & is used chiefly to deal with Troglodytes. Initiates have secret script to keep nature of life in higher worlds from becoming common property. Under paraphernalia of robes, rituals & old tortoise-shell games lies what can be explained scientifically by following procedure.
A single line, ---------, whole called YANG, is male, manifestly but occultly female; a double or divided line, --- ---, called a YIN is outwardly female but secretly male, These grams, YAO, stand for the primary sexual elements in macrocosm, universe & microcosm, human being. In YI KING a Yang is often spoken of as a "nine", a Yin , a "six", former odd, latter even. Creation comes from their combination & permutation. Visible
arrangement, however, is less important than invisible -what dwells between lines must never be lost sight of. Two at a time they generate four different HSIANG digrams, to illustrate TETRAGRAMMATON formula -
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See comment under Hex #31. Next step combines Yangs with Yins three at a time, to get Eight Trigrams, KWA, tabulated with names & attributes in the Logical Order. Four & five-fold figures are studied in our TROPERMIC CALCULUS & GRAMMAR OF CHANGES (1944). The six-fold figure, LOOK YAO, is produced by joining Ye Kwa & interpreted by shape & inner configuration & relationships. Besides meaning of two obvious trigrams we get in each case two "nuclear" hexes, first made by counting (up) 2nd, 3rd, 4th grams to combine with 3rd, 4th & 5th. Thus in #43, first nuclear hex combines kwa from grams 5,6,1 with 6,1,2; in #43 this will repeat 3X6; but e.g. in #44, first nuclear hex is #43 & second is 8X8, =#64. In KI TZI, ruler of Hex is 2nd place "six", although weak it succeeds by corresponding to strong "nine" in 5th place. We begin with strong nine in 1st place but 2nd place six yields to it -& so on with the analysis & interpretation which goes on behind the scenes to get the oracles. Correct technic makes Magical the erection & evokes Spirit assigned to Hex.
Prepare two dice with their pips arranged as pictured.
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Consecrate female die with your own feminine potency which proceeds from right hand of man or left hand of woman; for NARM ZHAI use masculine power by holding it always in left hand of man or right of woman. Be careful not to spoil these talismans by contact with wrong hand. Throw them simultaneously upon specially made SQUARE . There the hexes are put in Logical Order -from 1 to 64, figures or tzu wen -#1, Lingam of Lingam, in Magical East whole Square is oriented by this corner pointing usually toward immediate source of fresh water, TSAO. Files, TSUNG each have one & the same upper, Major KWA, respectively; ranks, WANG, same lower or SIAO KWA throughout. From top to bottom & left to right in each case margins or parameters read 1 2 3 4 5 6 7 8, or KHIEN SUN LI KAN TUI KHAN CHAN KHWAN - see Table of FU-HSI by GENESTHAI. p.0. wha shik tzu Alchemical symbols. #43 is in third wang of dai look tsung nai siao fong.
Cast the two dice, pairing them thrice, upon the logical Square to erect Look Yao. Gram is either Yin or Yang as sum of pips uppermost after throw is even or odd. Three throws set up male, or Minor; the three simultaneous YIN ZHAI throws erect Major, TA KWA. Suppose after first throw male shows 3 & female 4; next gives 2&5; finally 1&6; then tzu Hex is LI of KHAN, KHI TZI, always pertinent to circumstances & problems of the moment -it takes the scene & applies to each & every participant in ceremony. Kon p. 43 of Text for verses of the Thwan & Yao -here meaning is Perfected Work, Complete Success. Our friend WAW has composed an Essay on #43 -see Appendix. Since all things necessarily are restricted, we do not rest on our laurels but are aware of being close to frontier of new disorders -as Confucius says, "Superior Man, KIUNG TSZ, thinks of Evil that may come & guards against it beforehand." In #43 yangs &yins all correspond in nature with places they occupy, alternating light & dark, strong & weak, hard & soft. When YAO thus agree with place auspice is best, else vai hiung!
YI KING shows dual cosmic forces perpetuating themselves by unending chain of permutations & combinations. (See our book, COMBINATIONAL ARITHMEMTIC (1944) & MANUAL OF ELECTRO-COMBINATIONAL ENGINEERING (1945). Each Hex shows one unique modus operandi of sexual intercourse -union on man & woman, or intermingling of Heaven & Earth -name of this generative game is "CHANGE." #43 especially symbolizes orgasm expressing perfect harmony of mutual completion, graphically depicted by alternation of yang & yin properly placed & related. Such concord is clue to happy & healthy sex life itself reflected in all environment. CHHING LOI JU YUN. Man's experience in sex is compared to Fire which flares-up but can be extinguished by Water that takes long time to heat over Fire, but cools down slowly. This Hex is virtual image of difference both in pre- & post-orgasmic conduct of man & woman. In the scheme of Otz ChIIM, of holy Qabalah, it exhibits Averse Relation of Tiphareth (Sun) & Yesod (Moon); Sephiroth linked by path of Samekh (see Tarot), referred to Sagittary -see Table of Alphabet of LO, page 000.
No system of Divination merits attention if objective mind be allowed to interfere either in finding or reading the oracle. Furthermore, one must heed divine revelations - then Spirits will reciprocate your confidence & trust by disclosing symbols clearer & clearer in exact ratio to your fidelity & loyalty. Keep records of your Workings. You will find the given Hex is always right, the answers always true, appropriate & suitable to all individuals involved & situation & conditions in increasing proportion as habit is acquired of heeding counsel of the gods & conforming your conduct to offered advice, with firm correctness. Slipshod, careless procedure insults Spirits; operators shall be punished to fit the crime. Use of this Grammar from dishonest motives is likely to lead to serious trouble!
Organ of personality, cerebrum, mammalian brain, sees by reflected light (moon-light). Man is not instinctively intelligent, for little stream of experience flowing into his physical consciousness is not enough to guide him. From the center of Earth to utmost reaches of Space (&beyond) is the Kingdom of Man, the Fourth Hierarchy, (cf. expansion & contraction, Course of Light -NU & HADIT of old Egypt), hence to act intelligently, in accord with totality of all experience, all his bodies (seven) must be coordinated & information from all his senses (twelve). Old Alchemical charts display this beautifully. Cerebrum only shows vanishing point of cosmic understanding -lowest mind that can possibly act on universal scale. Insight, wit, rationality, co-ordination, creative thinking, perception of nature & identities of Things as they Are, of meaning of Life, i.e. Genius or Godhead belongs not to cerebrum but is function of cerebellum whose activity is mostly sub-conscious. Epoch is here to evolve the brains for truly practical thinking -about which pseudo-scientists know very little.
DIVINATION is excellent exercise to this end if done faithfully with right ritual or technic. No guesswork, superstition or psychic speculation is involved. Necromancers, Witches, Fortune-tellers, anyone who deals with Spirits, can make mistakes, but worst error is wrong concept or attitude, failure to understand & obey borderland laws, or possess a clear, level head, self-control, equilibrium & absolute moral integrity. Warnings are heard against spiritism, mediumship, black magic -but aside from obvious validity of caution, yet entities higher in scale of evolution than ourselves must not be imagined more stupid -that is scarcely possible! Malice & falsehood are inseparable -no understanding can receive TRUTH unless it belong to a WILL, receptacle of GOOD. Cosmos contains no really intelligent Evil Spirit. In fact, Evil is merely an event at wrong time &/or place! There is proper time & place for everything. E.g., one mighty Devil named LUCIFER did incarnate in ancient China; other great one called Satan or AHRIMAN is found incarnate during twentieth century -watch out for Him lest He lead you astray! Misunderstanding shall be cleared-up in due time -in meantime regard as absolutely impossible for anyone -human or not- to hate Humanity & at same time develop any adequate faculty of prevision or clairvoyance. Suspect those who gaze in crystals to prate of malevolent monsters -what they see is only themselves! Genuine awareness of nature & powers of their own beings would enable them to pass The Dweller on the Threshold (HUEN). If they remain slaves to Time & Space, Maya & illusions of their shadow personalities it is because in vestibule of Spiritual World, the "Sphere of Three Iron Necessities", there is no pass-key but LOVE! Synonymous with Initiation at some Grade, Genius is to think consciously & voluntarily with Cerebellum. First we must get habit of Faith which is not at all blind belief in unknown, for "Faith is of Truth & Truth is of Faith & Truth before it can become object of Faith must be in its own Light & be seen; otherwise the False may be believed".
FAITH is confidence in promptings, instincts & correlations apprehended by that brain whose processes are foreign & exterior to organ of personality. You need not believe paradoxes, antinomies or absurdities -philosophers, theologians & politicians to the contrary, notwithstanding! Current, established theories in Physics, Biology, Geology, Astronomy & even Mathematics are subject to continual revision, hence if accepted without moral or mental discernment no better than blind leaders of the blind. No class has monopoly of whimsical, puerile & superstitious ideas -such are only natural to Troglodytes, cave-dwellers, dazzled by that Light which can form no image in cerebrum. Divination, POOK, especially YI KING, is safe & sure road leading out of cave. "By eight & by eight shall I learn to count Thy favors, O Thou elevenfold God, Four hundred & Eighteen"! In life there is no higher purpose than to do Good; no guide to gain Divine Favor more reliable than Voice of your own Conscience, pontificating from its throne in cerebellum, by media of trustworthy Messengers -Mercury is Oracle of SOL -Who will resolve correctly your problems if you approach * Them humbly with authentic & authoritative Modus Operandi, Working by the "eight & ninety rules of Art". This Path, TAO, directly & quickly reaches source & center of TRUTH, Itself; of BEAUTY, Itself; of GOOD, Itself; & beyond to the Shrine of HOLINESS! May you find this Sanctity in the Heart of the LORD Who dwells in your own Heart!
* Matthew XXI, 9
John XIV, 13-14
Appendix
Circular Key to the Hexagrams from 2nd edition of Book Chameleon
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Circular Key to the Digrams &Trigrams from 2nd edition of Book Chameleon
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The Table of FU-HSI
from "Book Chameleon"
by Fr. Genesthai
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KHIEN
Meaning: Creative Power
Attributes: Lingam. Creative Impulse, Heaven, The Sky
Sphere: Daath
Force: Saturn, Zodiac & higher
Color: Black, brown, gray
KHIEN is Heaven; the Dragon's Our Friend, The Sage!
Originating, keen, strong to the end, presage!
Deathly still, Dragon, hide in the deep.
In the field, preside; Virtue's harvest reap!
Vigilant as gnomes, be active, even asleep.
In the depth yet, stage the upward leap.
Now fly the sky -crimson comets sweep!
Exceed not -weep not; the Golden Mean keep!
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SUN
Meaning: Flexibility, Penetration
Attributes: Air. Wind, Wood, Mind
Sphere: Hod
Force: Mercury
Color: Orange
SUN warns the Wise -beware the whip!
"Thy will be done"; thou shalt not slip!
Three times I say it, this is my refrain.
Beneath the couch, waiting wizard, stay.
God's Spell & Scourge! take the hint today.
Reiterated, say again & again!
Thy heart is full -maintain the right of way.
Thy heart o'erflows -relax the axe and pray.
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LI
Meaning: Brightness, Elegance
Attributes: The Sun. Spirit-Self, Manas, Realization, Lightning
Sphere: Tiphareth
Force: Sol
Color: Yellow
LI's double brilliance brightens the bright;
Docile like a cow -yet firm and upright!
Thy feet are clean, step on the golden stair.
Firm in place, held by a yellow strap.
Sober Muse, play on my earthenware.
Shun sudden shocks -top-side up with care.
Righteousness pours fortune in thy lap!
Vigorous victor, let every quarter share!
[pic]
KAN
Meaning: Solidifying, resting, act of arresting.
Attributes: Earth. Hills, Mountains
Sphere: Netzach
Force: Venus
Color: Green
KAN's twin peaks mark the stops & goes.
Watchful, notice nothing beyond thy nose.
Firm correctness keeps the toes at rest.
Righteous regulations thighs arrest.
Glowing heart pounds ribs -lull the loins.
Quiescent torso augurs auspice best.
Thy jaw is set -quiet, the noisest.
Acquire peaceful devotion's golden coins!
[pic]
TUI
Meaning: Pleasure, complacent satisfaction. Easy movement
Attributes: Water, collected as in a marsh, lake or pond
Sphere: Chesed
Force: Jupiter
Color: Blue
TUI joins true hearts in Christian Love:
Joy below responds to Joy above!
Be strong in seat of strength, wholly in tune!
Procure ye fresh, Our Wine; pour & commune.
Pleasure's doubled, perfected -hand in hand.
Combine the Two in One -companion's boon.
Let him be "ever a Sun & she a Moon"!
O, Golden Quest! o, Holy Ampersand!
[pic]
KHAN
Meaning: Restriction, fixation, peril, difficulty
Attributes: The Moon. Darkness, Defiles, Caves, Rain, Clouds, Springs, Rivers
Sphere: Yesod
Force: Luna
Color: Violet
KHAN's overflowing heart & piercing mind.
Dare pit after pit, constant, firm & kind!
In the double defile, Our Friend enters the cave.
Environed with peril, make not yet the escape.
Whether He comes or goes He shall behave!
Wine-bottle & rice-basket -sage & suave.
The Moon's not yet quite full -retain thy shape.
No rest for the wicked -in thorny thicket, thrice-brave!
[pic]
CHAN
Meaning: Moving, Exciting Power
Attributes: Fire. The Will, Thunder
Sphere: Geburah
Force: Mars
Color: Red
CHAN encourages; thunders twain entwine.
Ladle tight handle, high hand thy wine!
Meet coming motion soberly with cheer.
Exalted humility sees thy bread return.
Excitement works Righteousness to earn.
Hard pressed between, be firm & preserve.
Moving safely, centered in thy concern.
Proper precautions polish the golden urn.
[pic]
KHWAN
Meaning: Expansion to Infinity, Capaciousness, Submission
Attributes: Yoni, Cup or Chalice
Sphere: Malkuth
Force: The Earth
Color: Pink & flesh
KHWAN doubles the Cube -Big Yin brings
Initiatory Virtue to men & things!
Dancing on dew -later come big rains.
Brilliant results the Way of Earth obtains!
The Servant of the Lord excellence restrains.
The careful sack apples red contains.
Yellow shod the honored spot retains.
Dragons fight; azure and amber stains!
Liber Trigrammaton Decoded
ONE of the most enigmatic of the ‘Holy Books’ written by Aleister Crowley is Liber XXVII, entitled Liber Trigrammaton --- Being the Book of the Trigrams of the Mutations of the Tao with the Yin and the Yang.
This work contains 27 Trigrams formulated by the use of three symbols in groups of three: a Tao, represented by a point; a Yin, represented by a broken line; and a Yang, represented by a solid line.
Crowley notes that Liber XXVII describes the cosmic process, or the course of creation, on the basis of three principles. The present work will show that by using the Base Three system of mathematics, this cosmic process can be decoded, and an entirely new qabalah, or mystical system, can be established from it.
The decoding of the Trigrams is a simple process. In Base Three, there are only three numerals: Zero, One, and Two. These numerals correspond to the symbols for Tao, Yang, and Yin. As with the Hexagrams of I Ching, the Trigrams are analyzed starting from the bottom line and moving to the top line.
In the decoding process, the bottom line corresponds to the first digit of the Base Three system. This digit represents the “Ones” place, inasmuch as 3 to the zero power equals 1. The middle line of each Trigram corresponds to the second digit in Base Three, which represents the “Threes” place, (where 3 to the first power equals 3). The top line of each Trigram corresponds to the third digit in Base Three, which represents the “Nines” place, (where 3 to the second power equals 9).
Each line may be occupied by the number zero, one, or two, which designates how many ones, threes, and nines go to make up the number.
According to this system, a value can be generated for each Trigram by considering which symbol is in which place, and converting those symbols into Base Three. These figures will then be translated into Base Ten for easier comprehension.
For example, the Trigram containing three Yang lines has a value of 1 for the “Ones” place, 1 for the “Threes” place, and 1 for the “Nines” place. The sum of 1 + 3 + 9 = 13, therefore that Trigram is an expression of the number 13 in Base Three. The same method is used for all the Trigrams, with the three symbols of Tao, Yang, and Yin determining how many ones, threes, and nines are involved in each.
After being decoded, the 27 Trigrams are seen to represent all the numbers from Zero to Twenty-six. These 27 numbers are NOT in serial order, making the sequence all the more fertile for creating a new Qabalah.
For example the first Trigram contains a zero value for every digit, and therefore equals 0.
The following six Trigrams all contain two points, and designate this numerical sequence:
1, 2, 3, 6, 9, & 18. The total of all six of these numbers is 39; this is the key number of Liber Trigrammaton.
The next 12 Trigrams all contain only one point, and are in this order:
4, 5, 7, 8, 10, 11, 19, 20, 12, 15, 21, & 24. The sum of this set of twelve numbers is 156.
The final set of eight Trigrams all contain no points, and appear in this order:
13, 14, 16, 22, 17, 23, 25, & 26. The sum of this set of eight numbers is also 156. Note that 156 = 4 x 39.
The sum of all the Trigrams, the numbers from 0 to 26, is 351. This total is split into three sections; the first section of seven Trigrams equals 39, and the following two sections each equal 4 x 39.
Having established a numerical identity for each Trigram, the next step in the creation of a new Qabalah is to attribute various Elements, Zodiac signs, and Planets to these Trigrams.
The initial Trigram, valued at Zero, is attributed to the Element of Spirit.
The next four Trigrams in the sequence are attributed to the four classical Elements:
Fire is 1, Water is 2, Air is 3, and Earth is 6.
This is the Elemental order that forms the basis for Crowley’s Book of Thoth Tarot.
The next two Trigrams are valued at 9 and 18. For reasons that will be clear later on, these two receive no single attribution: they are the neutral poles of the system.
The next twelve Trigrams, containing two Tao lines, symbolize the 12 signs of the Zodiac. These are attributed in the traditional order, starting with Aries.
The final eight Trigrams are attributed to the Planets. In the Book of Thoth, Crowley has placed these Trigrams on the mystical Hebrew diagram known as the Tree of Life. Here, the Trigrams correspond to the Supernal Triad and the seven Sefirot below it. By using the planets associated with these Sefirot in the Book of Thoth, the eight Trigrams are attributed to Saturn, Mercury, Sun, Juppiter, Venus, Moon, Mars, and Earth, in that order.
One of the charts below displays the absorption of the Trumps of the Tarot into the Trigrammaton structure. It is important to note that the Trigrams are not being attributed to the Tarot, it is the Tarot that is being assimilated into the Trigrams. The Trigrams are numbers, and all qabalistic interpretations ultimately refer back to pure number. Not the Zodiac, not the Tarot, not Hebrew letters, but pure number.
Once the qabalistic attributes are determined for the Trigrams, it is a simple matter to absorb the Tarot as well. There are 26 Trigrams with an English letter and a qabalistic attribute, and these are cognate with the 22 Trumps and the 4 Aces of The Book of Thoth Tarot:
The Aces are attributed to the four Elemental Trigrams, having 2 Tao-lines each.
The Planetary Trumps are attributed to the Planetary Trigrams, having no Tao-lines.
The Zodiac Trumps are attributed to the Zodiac Trigrams, having one Tao-line each.
This leaves the Fool, the Aeon, and the Hanged Man, which are attributed to the 0, 9 and 18 Trigrams.
The Fool is attributed to the Zero Trigram according to Crowley’s definition of the card in The Book of Thoth: “The really important feature of this card is that its number should be 0. It represents therefore the Negative above the Tree of Life, the source of all things. It is the Qabalistic Zero. It is the equation of the Universe, the initial and final balance of the opposites; Air, in this card, therefore quintessentially means a vacuum.”
The Aeon is attributed to the 9, the positive, masculine pole of the system, while the Hanged Man is attributed to the 18, the negative, feminine pole of the system
The most controversial step in the qabalistic process is to attribute a letter of the alphabet to each Trigram. This step will create a new ‘gematria’, a technique of translating words into numbers based on the individual values of the letters in that word. In his commentary to Liber Trigrammaton, Crowley has attributed the 26 letters of the English Alphabet to all of the Trigrams, except the final one. Each of these English letters is then given the Base Three value of its associated Trigram.
This fulfills verse II:55 of Crowley’s Book of the Law: “Thou shalt obtain the order & value of the English Alphabet; thou shalt find new symbols to attribute them unto.”
In the Commentary to this verse Crowley states: “The attribution in Liber Trigrammaton is good theoretically, but no Qabalah of merit has arisen therefrom.” I contend that no Qabalah arose for him because Crowley only solved the ‘order’ half of the “order & value” equation. He arranged the order of the letters, but did not decipher the correct values for each letter. It is only by obtaining the correct numerical values for the “new symbols”, which are the Trigrams, that a “Qabalah of merit” can arise therefrom.
The present work follows Crowley’s original letter attributions, as these are the only indication he has left us regarding the basis of an English-language Qabalah. These attributions to Liber XXVII were published in Crowley’s periodical The Equinox Vol. 1 # 7, March 1912, and subsequently in ‘The Law Is For All’ ed. Israel Regardie, and ‘Magical and Philosophical Commentaries on the Book of the Law’, ed. Symonds & Grant.
Liber Trigrammaton is one of the ‘Holy Books of Thelema’, a group of works that are technically known as ‘Class A’ documents. By definition, a Class A document can not be changed, even by one letter; thus the exegesis of the meaning and value of each letter is integral to an understanding of such a document. Since all of the Holy Books are written in the English language, such an exegesis requires a Qabalah and a gematria based on the English Alphabet.
The Trigrams of Liber XXVII
(Numbers are Trigram values in upper and lower positions of a Hexagram.)
• • — —
• 0 — — 189 — — 648
• 0 ——— 7 • 24
• • ———
• 27 — — 216 ——— 351
——— 1 — — 8 ——— 13
• ——— ———
• 54 • 270 ——— 378
— — 2 ——— 10 — — 14
• ——— ———
——— 81 • 297 — — 432
• 3 — — 11 ——— 16
• — — — —
— — 162 • 513 ——— 594
• 6 ——— 19 ——— 22
——— — — ———
• 243 • 540 — — 459
• 9 — — 20 — — 17
— — ——— — —
• 486 ——— 324 ——— 621
• 18 • 12 — — 23
• ——— — —
——— 108 — — 405 — — 675
——— 4 • 15 ——— 25
• — — — —
——— 135 ——— 567 — — 702
— — 5 • 21 — — 26
Further light is shed on these numbers when one looks at the Trigrams in sets of opposite pairs, or Antigrams. A Trigram’s opposite is determined by switching Yang lines to Yin, and vice-versa. The Tao has no opposite.
The Elemental Trigrams as Polarities
• •
• 1 • 2 = 3
——— — —
• •
——— 3 — — 6 = 9
• •
——— — —
• 9 • 18 = 27
• • -----
Total 39
The Planetary Trigrams as Polaritites
——— — —
——— 13 — — 26 = 39
——— — —
——— — —
——— 14 — — 25 = 39
— — ———
——— — —
— — 16 ——— 23 = 39
——— — —
— — ———
——— 22 — — 17 = 39
——— — — -----------
Total 156
The Zodiac Trigrams as Polarities
• •
——— 4 ⊥ — — 8 α = 12
——— — —
• •
——— 5 _€€€€€€ — — 7 ? = 12
— — ———
——— — —
• 10 β • 20 ε€ = 30
——— — —
——— — —
• 11 χ • 19 δ = 30
— — ———
——— — —
——— 12 φ — — 24 ι = 36
• •
——— — —
— — 15 γ ——— 21 η = 36
• • -----------
Total 156
The diagram above demonstrates that all the Fire signs are opposite Water signs, while all the Air signs are opposite Earth signs. This arrangement reflects the polarities of the Elemental Trigrams.
The total value of the six Fire and Water signs is 78, and these are all even numbers, (4, 8, 10, 20, 12, 24).
The total value of the six Air and Earth signs is also 78, and these are all odd numbers, (5, 7, 11, 19, 15, 21).
Of the six Antigram pairs, each possible combination of Cardinal, Fixed, and Mutable Zodiac signs is present: (C-C, F-M, F-F, M-C, M-M, C-F).
The three similar pairs: C-C, M-M, F-F, represent only Water and Fire signs, and their Trigrams total 78.
The Fire signs contain only Tao and Yang lines, while the Water signs contain only Tao and Yin.
The three unlike pairs: F-M, M-C, C-F, represent only Air and Earth signs, and their Trigrams also total 78.
All of the Air and Earth signs have a combination of Tao, Yang, and Yin.
The pairs of opposite numbers also show a unique set of relationships when the difference between two Antigrams is examined. The chart below shows that the 13 pairs differ by each of the numbers from 1 to 13.
The initial set represents the Elemental Antigrams.
The sequence of 1, 3, 9, (the place-values of the three lines of a Trigram), is shown in this set.
The second set represents the Zodiac Antigrams. All the differences in this set are even numbers.
In the third set, the differences between Planetary Trigrams are all prime numbers.
Antigrams Difference Sum Product
1 & 2 1 3 2
3 & 6 3 9 18
9 & 18 9 27 162
4 & 8 4 12 32
5 & 7 2 12 35
10 & 20 10 30 200
11 & 19 8 30 209
12 & 24 12 36 288
15 & 21 6 36 315
13 & 26 13 39 338
14 & 25 11 39 350
16 & 23 7 39 368
22 & 17 5 39 374
135 + 216 91 351 2691
The sum of the numbers 1-26, plus the products of the Antigrams, equals 2 x 39 x 39.
For the pair 22 & 17, the total of their difference, sum, and product is 418.
The sequence of Antigrams, arranged by increasing value of their differences, is a key feature of base 3 mathematics, and will be used below in the attribution of Hexagrams to the wheel of the Zodiac. The reason this feature is so important, is because there is one, and only one, pair of Antigrams that correspond to a unique difference-value. For example, 93 and 186 are the only pair of Antigrams that differ by 93, and so on for every other whole number.
The Four Special Groups of Hexagrams:
These are the 27 Reversible Hexagrams:
• • • • • •
• • ——— ——— ——— — —
——— — — • ——— — — •
——— — — • ——— — — •
• • ——— ——— ——— — —
• • • • • •
36 72 84 120 156 168
• • ——— ——— ——— ———
— — — — • • • ———
——— — — • ——— — — •
——— — — • ——— — — •
— — — — • • • ———
• • ——— ——— ——— ———
204 240 244 280 316 328
——— ——— ——— ——— ——— — —
——— ——— — — — — — — •
——— — — • ——— — — •
——— — — • ——— — — •
——— ——— — — — — — — •
——— ——— ——— ——— ——— — —
364 400 412 448 484 488
— — — — — — — — — — — —
• • ——— ——— ——— — —
——— — — • ——— — — •
——— — — • ——— — — •
• • ——— ——— ——— — —
— — — — — — — — — — — —
524 560 572 608 644 656
— — — — •
— — — — •
——— — — •
——— — — •
— — — — •
— — — — •
692 728 0
-------------------------------------------------------------------------------------------------------------------
These are the 27 Doubled-Trigrams
• • • • • •
• • ——— ——— ——— — —
——— — — • ——— — — •
• • • • • •
• • ——— ——— ——— — —
——— — — • ——— — — •
28 56 84 112 140 168
• • ——— ——— ——— ———
— — — — • • • ———
——— — — • ——— — — •
• • ——— ——— ——— ———
— — — — • • • ———
——— — — • ——— — — •
196 224 252 280 308 336
——— ——— ——— ——— ——— — —
——— ——— — — — — — — •
——— — — • ——— — — •
——— ——— ——— ——— ——— — —
——— ——— — — — — — — •
——— — — • ——— — — •
364 392 420 448 476 504
— — — — — — — — — — — —
• • ——— ——— ——— — —
——— — — • ——— — — •
— — — — — — — — — — — —
• • ——— ——— ——— — —
——— — — • ——— — — •
532 560 588 616 644 672
— — — — •
— — — — •
——— — — •
— — — — •
— — — — •
——— — — •
700 728 0
-------------------------------------------------------------------------------------------------------------------
These are the 26 Hexagrams with Antigrams in their upper and lower positions:
• • • • • •
• • ——— ——— ——— — —
——— — — • ——— — — •
• • • • • •
• • — — — — — — ———
— — ——— • — — ——— •
29 55 87 116 142 165
• • ——— ——— ——— ———
— — — — • • • ———
——— — — • ——— — — •
• • — — — — — — — —
——— ——— • • • — —
— — ——— • — — ——— •
194 220 261 290 316 348
——— ——— ——— ——— ——— — —
——— ——— — — — — — — •
——— — — • ——— — — •
— — — — — — — — — — ———
— — — — ——— ——— ——— •
— — ——— • — — ——— •
377 403 426 455 481 495
— — — — — — — — — — — —
• • ——— ——— ——— — —
——— — — • ——— — — •
——— ——— ——— ——— ——— ———
• • — — — — — — ———
— — ——— • — — ——— •
524 550 582 611 637 660
— — — —
— — — —
——— — —
——— ———
——— ———
— — ———
689 715
-------------------------------------------------------------------------------------------------------------------
These are the 26 Hexagrams with Reversed-Antigrams in their upper and lower positions.
• • • • • •
• • ——— ——— ——— — —
——— — — • ——— — — •
— — ——— • — — ——— •
• • — — — — — — ———
• • • • • •
45 63 87 132 150 165
• • ——— ——— ——— ———
— — — — • • • ———
——— — — • ——— — — •
— — ——— • — — ——— •
——— ——— • • • — —
• • — — — — — — — —
210 228 245 290 308 332
——— ——— ——— ——— ——— — —
——— ——— — — — — — — •
——— — — • ——— — — •
— — ——— • — — ——— •
— — — — ——— ——— ——— •
— — — — — — — — — — ———
377 395 410 455 473 487
— — — — — — — — — — — —
• • ——— ——— ——— — —
——— — — • ——— — — •
— — ——— • — — ——— •
• • — — — — — — ———
——— ——— ——— ——— ——— ———
532 550 574 619 637 652
— — — —
— — — —
——— — —
— — ———
——— ———
——— ———
697 715
[pic][pic][pic][pic][pic][pic]
-----------------------
[1] LXV:II.5 “I suffered the deadly embrace of the Snake and of the Goat; I paid the infernal homage to the shame of Khem.”
Crowley’s commentary:
It accepts the formulae of:
(a) Duality,i.e., life as vibration.
(1) Death.
(2) The illusion of Knowledge.
(b) Exile.
(1) The Hunger of Lust.
(2) Labour.
It acquiesces in the shame of being a God concealed in animal form.
LXV:II.6 “Therein was this virtue, that the One became the all.”
Crowley’s commentary:
The object of this act is to realize the possibilities of one's unity by representing its wholeness as an infinite number of particular cases, just as one might try to get an idea of the meaning of ``poetry'' by studying all available poems. None of these can be more than one imperfect illustration of the abstract idea; yet only through these concrete images can one get any understanding of what it means.
[2] Knowing the Mother, we may know her offspring. He that knoweth his Mother, and abideth in her nature, remaineth in surety all his days.
Motta’s commtary
This verse has nothing to do with genetics on one side, and Momism on the other. Cf. LXV:II.1-6
[3] Crowley writes in Qabalistic Dogma: “It is important to explain the Position of Daath or Knowledge upon the Tree. It is called the Child of Chokmah and Binah, but it hath no Place. But it is really the Apex of a Pyramid of which the three first Numbers for the Base.
Now the Tree, or Minutum Mundum, is a Figure in a Plane of a solid Universe. Daath, being above the Plane, is therefore a Figure of a Force in four Dimensions, and thus it is the Object of the Magnum Opus. The three Paths which connect it with the First Trinity are the three lost Letters or Fathers of the Hebrew Alphabet.
In Daath is said to be the Head of the great Serpent Nechesh or Leviathan, called Evil to conceal its Holiness. (scn = 358 = cysm, the Messiah or Redeemer, and ] t y v l= 496 = t v q l m, the Bride.) It is identical with he Kundalini of the Hindu Philosophy, the Kwan-se-on of the Mongolian Peoples, and means the magical Force in Man, which is the sexual Force applied to the Brain, Heart, and other Organs, and redeemeth him.”
[4] AL III.34: "But your holy place shall be untouched throughout the centuries: though with fire and sword it be burnt down & shattered, yet an invisible house there standeth, and shall stand until the fall of the Great Equinox; when Hrumachis shall arise and the double-wanded one assume my throne and place. Another prophet shall arise, and bring fresh fever from the skies; another woman shall awake the lust & worship of the Snake; another soul of God and beast shall mingle in the globed priest; another sacrifice shall stain the tomb; another king shall reign; and blessing no longer be poured To the Hawk-headed mystical Lord!"
From Crowley’s commentary:
Another sacrifice Love is the Magical Crucifixion, &c., as
shall stain Formula: Sex as the Key to the Magical
the tomb Life. "The tomb" -- the Formula. Death as
temple of Love the Key to Life.
"The tomb" -- the
coffin or grave.
[5] Crowley writes in Qabalistic Dogma: It is important to explain the Position of Daath or Knowledge upon the Tree. It is called the Child of Chokmah and Binah, but it hath no Place. But it is really the Apex of a Pyramid of which the three first Numbers for the Base.
Now the Tree, or Minutum Mundum, is a Figure in a Plane of a solid Universe. Daath, being above the Plane, is therefore a Figure of a Force in four Dimensions, and thus it is the Object of the Magnum Opus. The three Paths which connect it with the First Trinity are the three lost Letters or Fathers of the Hebrew Alphabet.
In Daath is said to be the Head of the great Serpent Nechesh or Leviathan, called Evil to conceal its Holiness. (scn = 358 = cysm, the Messiah or Redeemer, and ] t y v l= 496 = t v q l m, the Bride.) It is identical with he Kundalini of the Hindu Philosophy, the Kwan-se-on of the Mongolian Peoples, and means the magical Force in Man, which is the sexual Force applied to the Brain, Heart, and other Organs, and redeemeth him.
[6] The Nephilim would also be the Titans in Greek mythology. Cf. Reign of the Demiurge.
[7] This is the 18th Trigram, numbered 17.
[8] Cf. Testing the Night of Pan.
[9] LXV.I:18 - So also the light that is absorbed. One absorbs little, and is called white and glistening; one absorbs all and is called black.
[10] Nun=Death Atu=50 or 5(Man)x10(whole ToL or complete creation); hence the complete, manifested being. By complete here, it is meant, fully attained. These are the Secret Chiefs and the bardic songs that hold their secrets.
[11] The two numbers assigned to this Trigram are equal to 31. It’s interesting that the value of G is 60 in the EQ, which is the Art Atu (that which leads to Tiphareth). Not (31) being the Key to AL, is expressed here also as 5th 8th and 12th Trigrams, which together equal 25, the number of Man; note the comment about Hadit; the loathsomeness being Hell’s own worm. Hadit most closely represents then, the Giant of terrible strength discussed in the 8th Trigram. But also the Cross of Light at the intersection of which is the heart and the 5th Trigram (again, 5 being the number of Man); and also the secret one that hides the light of purity (secretion of the light) and that which is not known as per his chapter in Liber AL. Of the lesser numbers of the Trigrams (the ones on the left that start with Zero for the first Trigram, we get the letters EIU. The Manifestation of Imperfection, presiding over the fading of Perfection; the Master of the Temple balancing all things and the Sons and Daughters of Hermes and Aphrodite openly hiding the light of purity in themselves. The Perfection of course is NOT and the MT is NOT with the light of Purity being that NOT that is the Ain Soph Aur or limitless light.
[12] AL II.4: "Yet she shall be known & I never."
Crowley’s commentaries:
DJIERIDENSIS
She is known, as He goeth on His Way, and doth His Will; each Event adds to His Knowledge of Her Nature.
He cannot be known, for He hath no parts whereby to define Him.
THE OLD COMMENT
The circumference of Nuit touches Ra-Hoor-Khuit, Kether; but her centre Hadit is forever concealed above Kether. Is not Nu the Hiding of Hadit, and Had the Manifestation of Nuit? (I later, Sun in Libra, An. VII, dislike this note; and refer the student to Liber XI and Liber DLV.
THE NEW COMMENT
See later, verse 13, "Thou (i.e. the Beast, who is here the Mask, or "per-sona," of Hadit) wast the knower." Hadit possesses the power to know, Nuit that of being known. Nuit is not unconnected with the idea of Nibbana, the "Shoreless Sea," in which Knowledge is Not.
Hadit is hidden in Nuit, and knows Her, She being an object of knowledge; but He is not knowable, for He is merely that part of Her which She formulates in order that She may be known.
[13] Variant reading, “defense.”
[14] This Trigram is also appended to the verse connected with the 10th Trigram, numbered 9. It is the Trigram of the false prophets and gurus, cult leaders and antichrists.
[15] The moon is not considered to be a light, but as a cohesion of the planet’s atmosphere.
[16] Cf. The Golden Chain of Homer.
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