Trigrammaton Qabalah

A Book of Mutations

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Explanation of the New Naples Arrangement
Do what thou wilt shall be the whole of the Law

I have been asked to explain what connections, if any, there are between the New Naples Arrangement and the Holy Books of Thelema. In order to properly answer that question, I will have to explain these arrangements more fully, and touch on their characteristics both within and beyond the scope of the Holy Books of Thelema.

A very lengthy entry follows the cut.

The Naples Arrangement of Aleister Crowley:

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61 +146=0 as Undefined (Space).
61 +146+207=0 as basis of Possible Vibration.

1. The Point: Positive yet indefinable.
2. The Point: Distinguishable from 1 other.
3. The Point: Defined by relation to 2 others.
The Abyss–between Ideal and Actual.
4. The Point: Defined by 3 co-ordinates: Matter.
5. Motion (time)—He', the Womb; for only through Motion and in Time can events occur.
6. The Point: now self-conscious, because able to define itself in terms of above.
7. The Point's Idea of Bliss (Ananda).
8. The Point's Idea of Thought (Chit).
9. The Point's Idea of Being (Sat).
10. The Point's Idea of Itself fulfilled in its complement, as determined by 7, 8 and 9.

The New Naples Arrangement of R. Leo Gillis:

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61 = AIN = Nothing. “61 the Jews call it… but they have the half.”
61 + 146 = AIN SOF = No Limit. 207. The other half of the AIN.

There is no Ain Sof Aur.
There is no Da’at.


1—Space—The Vector manifest, the String, Hadit as the Snake, Length.

2—Angle—Vectors defined by each other, two dimensions, the Triangle or Square.

3—Matter—The vector implied by 0, 1, 2. Third dimension, the Tetrahedron or Cube. Implies 3 other vectors.

4—Gravity—Mass impinging on itself, creating tension via compression, its complement. Insideness.

5—Motion—Objects in space-time are all in motion. Spin. Includes light-speed as the limit of all motion.

6—Charge—Positive and negative electric Charge. Magnetism. Electromagnetic radiation, Light.

7—Resonance—Note at which the entity vibrates. Bliss, harmony, one's Will.

8—Measurement—Consciousness, awareness of otherness relative to an inertial frame, one's Thought.

9—Existence—One's Being, defined by all parameters, the ontological essence, reflection of Zero.

The fundamental feature of this schema is not the point, but the Vector, in agreement with Buckminster Fuller's Synergetic Geometry.

The Zero and the First Triad constitute the four dimensional Timespace continuum, in agreement with Albert Einstein.

Motion and the four fundamental forces of nature appear in the next Triad, (the Strong and Weak nuclear forces being hidden in Tiferet).

The three aspects of Brahman from the Vedanta school are incorporated in the third Triad, in agreement with Aleister Crowley.

This Tree may also represent a version of String Theory, inasmuch as the six spheres numbered 4 through 9 can also represent the six 'folded-up' spatial dimensions of that theory.

The spheres numbered from 3 to 9 also have the traditional planetary associations: Saturn, Juppiter, Mars, Sol, Venus, Mercury, Luna.

The New Naples Arrangement is so-called because it is a refinement of Aleister Crowley's 'Naples Arrangement' of the qabalistic Tree of Life, and was first worked out by RLG while overlooking the city of Naples, Italy

The fundamental difference between these two arrangements is that Crowley defines the series of whole numbers occurring on the Tree of Life in terms of a point-particle, while Gillis considers the vector, and not the point or vertex to be primal, while also modifying the numbering of the Tree of Life to include a Zero. The subtle differences in these approaches may be worked out by the reader if necessary. The similarities include the use of the coordinates of three spatial dimensions, motion, and the three concepts of Sat, Chit and Ananda.

Both of these arrangements utilize the qabalistic Tree of Life as the matrix to explain the sequence of whole numbers as representative of the necessary attributes of conscious substance, so as to create a sort of ‘numerical ontology’. As the whole numbers increase by unity at each step, so these characteristics are aggregated upon one another to reach fulfillment at the end of the Tree.

The overall structure of the Naples Arrangement is three Triads, and a Completion.
The overall structure of the NNA reverses this, and has a Source and three Triads.

In the NNA, the first emanation, or number, on the Tree of Life is Time. Any and every thing that exists and occurs takes place in Time. And this is inexorably wedded to the emergent triad:

The first Triad establishes the 3 dimensions of space, thus Matter.
The next Triad establishes the qualities of Matter via the four forces of Universe, as well as Light and Motion.
The last Triad quantifies the attributes of Consciousness.

Thus the NNA creates a matrix for describing, through Number, the fundamental aspects of Universe: Substance, Attributes and Consciousness. This is essentially what Crowley attempted to do as well. The NNA seeks to update his arrangement, particularly by the inclusion of Zero as the beginning of the Tree, rather than unity.

Before going into more detail about the NNA, I should address the connection with the Holy Books of Thelema.

In the original Naples Arrangement, Crowley never made a claim that his ontology was rooted in the HBOT. If there had been any clear-cut associations with these Books, he would have surely pointed them out to us. This does not mean that there are no connections, only that the Naples Arrangement did not spring fully formed from the basis of any of the HBOT.

But one major reference in the Holy Books seems to have been ignored by Crowley in his formulation, and this is rectified in the NNA. The reference is to the AIN, and is found in Liber AL vel Legis:

“45. The Perfect and the Perfect are one Perfect and not two; nay, are none!
46. Nothing is a secret key of this law. Sixty-one the Jews call it; I call it eight, eighty, four hundred & eighteen.
47. But they have the half: unite by thine art so that all disappear.”

The word ‘sixty-one’ here refers to the Hebrew word AIN, meaning ‘not’, or nothing.
The AIN is one half of the concept of Nothing. Its complement in Hebrew Qabalah is the Ain Sof. Its complement in Thelemic Qabalah is the mysterious 8, 80, 400 & 18.

In a more subtle sense, AIN as 61 is complemented by the number 32, for in the Ternary mathematics of Liber Trigrammaton, the numbers 61 and 32 are Antigrams, and in this case, the 32 represents the 10 Spheres and 22 paths of the Tree of Life. The other sense, that AIN is complemented by 8, 80, 400 & 18, will be left to explore at another time.

The key point for now is that in light of the reference in Liber AL, the NNA does away with the Ain Sof Aur, except in the syncretistic sense that this very Ain Sof Aur is identical with the 0 that is the first Sphere of the Tree of Life.

There are three Holy Books that could be said to refer to the Tree of Life, but only one of these is specific in this regard. Liber Tau organizes the 22 Hebrew letters into seven Triads, and these might be studied in terms of their position on the Tree. Also, Liber CCXXXI details the characteristics of the 22 Tarot Trumps, and likewise these may also be studied in the context of their appearance on the Tree. But neither of these two books deals specifically with the structure and nature of the Tree and its spheres, and it is the spheres that are the real subject matter of the Naples Arrangement and its successor.

Only Liber Ararita could be said to be devoted specifically to the structure of the Tree of Life in terms of its spheres. Each of the 7 chapters of Liber Ararita contains verses numbered from 0 to 13. In each case, the verse numbered 0 refers to the Ain or Ain Sof beyond the Tree, while the numbers from 1 to 10 refer to the classic ten spheres of the Tree itself. Progressing beyond these, each chapter mentions the number 418 in verse 11, a ‘crown of twelve rays’ in verse 12, and a completion in Unity in verse 13, (as the Hebrew word Achad, meaning ‘one’, has a gematria value of 13).

Even within a Book devoted to explicating the nature of this Tree of Life, only one chapter really deals with the same type of subject matter as the Naples Arrangement, namely, the character of each of the successive whole numbers. But before looking at this chapter, we must consider a couple other verses from this Book. The very first sentence of the Book is this:

“O my God! One is Thy Beginning! One is Thy Spirit, and Thy Permutation One!”

Let us note first of all that this verse is numbered 0. We begin the counting process with Zero, as any mathematician would do. In like fashion, the first Tarot Trump is numbered Zero also. (And similarly, Libri Tzaddi, A’ash and Arcanorum begin with a verse numbered Zero).

The beginning of chapter three echoes this idea of unity, again in a verse numbered 0:

“Say thou that He God is one; God is the Everlasting One; nor hath He any Equal, or any Son, or any Companion. Nothing shall stand before His face.”

Contained within this verse is a resolution of the apparent conflict of numbering the first sphere of the Tree as a Zero. This is really no more perplexing than having the Fool of the Tarot numbered 0, while bearing the first letter of Hebrew, the Alef, whose value is 1. You have to start somewhere, and wherever that is becomes the ‘first’ place in the Tarot, or in this case, the first place on the Tree.

God is further described as ‘everlasting’, and this refers to the phenomenon of time. There is no end of god in time. From this idea, a connection is made between the number 0 and the phenomenon of time; this will be further explained in a later verse.

Lastly, it is said that nothing shall stand before the face of god. We may recall that the Tree of Life was often referred to as the face of god, (cf. the terms ‘long of face’ and ‘short of face’, or greater and lesser countenance, in the holy qabalah). We might take this phrase literally and say that nothing, i.e., the Ain, stands before the face of god, or before the Tree. Thus the true nothing of the Ain, rather than the relative nothing of 0, is what exists outside of the Tree. And note also that ‘before’ can mean both spatially and temporally in front of something. Nothing stands ‘before’ the face of god in time; nothing stands ‘before’ the face of god in space. And we shall see later that Time and Space are inseparable.

In chapter five of Liber Ararita, the verse numbered 0 tells us this:

“In the place of the cross the indivisible point which hath no points nor parts nor magnitude. Nor indeed hath it position, being beyond space. Nor hath it existence in time, for it is beyond Time. Nor hath it cause or effect, seeing that its Universe is infinite every way, and partaketh not of these our conceptions.”

The two previous quotes were from chapters headed by the letter Alef, whose value is 1. This chapter’s heading is Yod, which has a value of 10, or the number 1 raised an octave. The letter Yod is but a small speck, one little dot. One might even say that this dot is the smallest conceivable thing. And it appears from the text that this verse numbered 0 is in some ways a comment on, or is inspired by, this Yod, considered as the ‘indivisible point’.

While the NNA does not consider the ‘point’ to be the primal entity, at least not in the same sense found in the original Naples Arrangement, it is still a useful metaphor for the number 0. Consider the attributes this Yod or point is supposed to possess: it is an indivisible atom with no parts or size. It is like a perfect sphere, with an infinite surface, so to speak. And what number can be said to have no parts? Surely not 1; for we can divide 1 into an infinite number of parts; but the number 0 has NO parts. One-half of zero is still zero. And thus this description occurs in a verse numbered 0.

And yet this 0 is the beginning of the Tree insofar as it is a point, just as Crowley first understood the Naples Arrangement. This little Yod can be discerned, or imagined, and this is the sense in which it is the first emergent ‘thing’. The difference in the NNA is that this ‘point’ is really a ‘point-of-departure’.

It is further said that this point is beyond both space and time. In the NNA, time and space are the first emanations of the Tree, so we must understand the implications of this part of the verse, which seemingly makes this ‘point’ a predecessor to the whole Tree.
For this we go back to the first words of the verse: “In the place of the cross…” This point actually occupies the point of ‘crossing-over’ from the Ain Sof to the Tree itself. This is why it can be said to be beyond time and space. It is not really on or off the Tree. It is the threshold. One might even say that, due to its character, it is the very idea of sphere itself, as an atomic, indivisible entity that is infinite every way.

But as soon as anything comes after this point, it is occurring in time and in space, and thus the first spheres of the actual tree are given over to these fundamental forms of existent entities. But time must come first. And this time is said to be ‘unmanifest’ in the NNA, because it is meaningless until there is space involved as well. So Time may be more rightly said to be the vector connecting sphere 0 with sphere 1, but for our purposes, we must give the first sphere numbered 0, some kind of name, and so we call it Time. But this time is not manifest until we try to leave 0 and arrive at the number 1; when we try to get something from our nothing, then we will actually encounter time in the universe.

And how do you get something from nothing? By calling the first something ‘nothing’. And the best we can do in this regard is to give it the number 0. For all the above reasons, the first sphere is numbered 0, and thus the Tree proper begins. And does not the word ‘beginning’ already imply the element of Time? And what sense is there to say that something exists ‘before’ time? The very word betrays the fact that Time is the first of all emanations of the Tree.

At this point, (no pun intended), we might contrast what has been said with the opening verses of Liber XXVII. After the Zero trigram appears, the very first word of the Book is ‘Here’, implying space: “Here is nothing under its three forms, it is not, yet informeth all things.” This is a depiction of the three dimensions of space, indicated by the three lines of the trigram. This is the form that all spatial entities will take in our consciousness, and thus the three dimensions ‘informeth all things’.

The very next verse indicates the Line, the Yang, and says, “Now cometh the Single One as an imperfection and stain.” The first word of the second verse is ‘Now’, indicating Time. From this we might conclude that Space precedes time, but these very words betray the fact that Time must come first. Since Einstein and Minkowski formulated the mathematics of Timespace as a matrix that consists of 4 dimensions that cannot be separated, it may be a matter of choice as to whether we insist that Space comes before Time, or vice versa.

Liber XXVII seems to indicate that all three spatial dimensions are a given, and that these then proceed to manifest themselves in Time. But it should be remembered that Liber XXVII does not deal with the Tree of Life, and this is the concern of the NNA. It should also be noted that the detailed characteristics of these three dimensions are given in the totality of all 27 trigrams, which cohere to make the Cube of Space. So in that regard, it is no surprise that the first word is ‘Here’, indicating space. And note also that the three types of line found in Liber XXVII, (the Tao, Yang and Yin), are the three digits of the base 3 counting system, and are thus identical to the first three spheres of the NNA, whose numbers are 0, 1, & 2.

The three-layered form of Nothing found in Liber XXVII echoes the ‘triple veil of the negative’ of the traditional qabalah, and thus the Ain Sof Aur. But it is important to note that two of these lines are superfluous; to indicate the number 0, we need only the single line of Tao. And it is this line that is the beginning of our Tree of Life; the other two lines indicate the Ain and Ain Sof, the Nothing and the Infinite that precede the Tree, and stand ‘before’ the face of God.

The last section of Liber Ararita to consider, in terms of the NNA, is the entirety of chapter Six, which gives equivalents to many of the numbers assigned to the spheres of the Tree of Life:

“0. Deeper and deeper into the mire of things!
Farther and farther into the never-ending Expansion of the Abyss.

1. The great goddess that bendeth over the Universe is my mistress; I am the winged globe at her heart.

2. I contract ever as she ever expandeth;

3. At the end it is all one.

4. Our loves have brought to birth the Father and Creator of all things.

5. He hath established the elements; the aether, the air, the water, the earth, and the fire.

6. He hath established the wandering stars in their courses.

7. He hath ploughed with the sever stars of his Plough, that the Seven might move indeed, yet ever point to the unchanging One.

8. He hath established the Eight Belts, wherewith he hath girdled the globes.

9. He hath established the Trinity of Triads in all things, forcing fire into fire, and ordering all things in the Stable Abode of the Kings of Aegypt.

10. He hath established His rule in His kingdom.

11. Yet the Father also boweth unto the Power of the Star 418 and thereby

12. In his subtlety He expandeth it all into twelve rays of the Crown.

13. And these twelve rays are one.”

The first verse here could be said to deal with the infinity of Space, in its use of the terms ‘farther’ and ‘deeper’. Yet a prior verse, also numbered 0, showed that we are beyond space and time at this stage.

The second verse personifies this space as a goddess. Note that this space is ‘bent’, which might be considered an adumbration of the curved space of general relativity. The verse continues on to identify the writer, or adept, as a ‘winged globe’, the center of this infinite sphere of space, (infinite in the sense that the curvature returns back on itself, and has no beginning or end). It is curious, and telling, that the heart of the goddess is itself a sphere, or globe, implying that she surrounds it in all directions, and is herself a sphere also.

The third verse shows the dichotomy of expansion and contraction between the goddess and the adept. The contraction of the winged globe (down to a singularity?) is accompanied by the expansion of the goddess. This may be considered a prophecy of the expanding Universe.

And the fourth verse, numbered 3, sums up the previous verses by saying that ‘it is all one’. In the NNA, this is the sphere attributed to the last of the three spatial dimensions. And since these three are intimately tied up with time, to create the 4D Space Time, they are rightfully said to be ‘one’, in the sense that they are all Unified.

Now we continue to the verse numbered 4, which the NNA calls ‘Gravity’, the force which Buckminster Fuller called ‘Love’. And here we find that ‘our loves’ have brought to birth the Creator of all ‘things’. This term ‘things’ refers to the ordinary objects of consciousness, like chairs and stars and snowflakes. They are all 4D ‘things’, and they all possess Gravity. The coherence of the parts into wholes makes realizable ‘things’ in our Universe.

But at the same time, this verse indicates a passage into a new realm, wherefrom the Creator will bring all things into existence. This is now possible because the basic 4D nature of all these things has already been established. This Father and Creator is a turning point, an entity of a different kind altogether, just as Gravity is a universal Force that is different than the other three known to us.

The verses from 5, 7, 8 & 9 all indicate a specific example of that number in the Universe. We begin with a list of the 5 elements. This does not refer to Motion, as found in the NNA. Rather, it refers to an important occurrence of the number 5 in the Universe.
In verse 6, we have no reference to the number 6, only to ‘wandering stars’. This may refer to the sun as a Star, since sphere 6 is the normal place of the Sun on the Tree. But ‘wandering stars’ also refers to planets, as the name originally meant in the Greek, and so this verse may well be indicating 6 of the seven ‘sacred planets’, since the Sun is not a wanderer like the others. Once again, this has little to do with the phenomenon of ‘charge’ that is used in sphere 6 of the NNA.

And also with verse 7, the ‘seven stars of the Plough’ are what we in the West call the Dipper; the constellation that points to the Pole Star. In the NNA, sphere 7 is called Resonance, and the connection here can only be that just as those stars point to the Pole Star, which appears unchanging because the world axis turns around it, so too do all the various frequencies of any entity revolve around one resonant frequency. This is a loose connection with the verse, at best.

In the verse numbered 8, there is reference to the ‘eight Belts’ that girdle the globes. These may be considered as eight ‘great circles’ that would subdivide a globe or sphere and be used as a means of measuring them. Or they may be considered as the eight directions of the compass, which could be attributed to the eight I Ching trigrams, (as in the Sequence of Later Heaven). In either case, the idea of measurement could easily be incorporated into this verse, and thus have an affinity with sphere 8 of the NNA, which is called Measurement.

In the verse numbered 9, there is mention of the ‘Trinity of Triads’, which could be considered a reference to the structure of the Tree of Life itself, which has three Triads in either the NNA, or the original Naples Arrangement. And it is in this sphere that we find the Triads ‘ordering all things’. One can reasonably conclude there is nothing left to put in order after this point.

By the time we reach the verse numbered 10, there is no more mention of numbers directly, just a mention of the Kingdom, which is a common name for the tenth and last sphere on the old Tree of Life. And in like fashion, the NNA does not concern itself with the number 10. The Tree is already completed by the number 9 and the Trinity of Triads.

So in this chapter we find a few references to numbers themselves, but precious little to make definitive connections to either Naples Arrangement. And of course, Liber Ararita is describing the nature of spheres on the traditional Tree of Life; these spheres have been renumbered in the NNA, although the numbers coincide starting with sphere 4, where the character of the Father and Creator is introduced as a key turning point. This Father may easily be connected with Juppiter, the King of the Gods, since this is his traditional sphere on the Tree. All the planetary references to the Tree can be found in the first chapter of Liber Ararita, where the standard order of Saturn, Juppiter, Mars, Sol, Venus, Mercurius and Luna can be seen:

“3. Thou hast appeared unto me as an agid God, a venerable God, the Lord of time, bearing a sharp sickle.
4. Thou hast appeared unto me as a jocund and ruddy God, full of Majesty, a King, a Father in his prime. Thou didst bear the sceptre of the Universe, crowned with the Wheel of Spirit.
5. Thou hast appeared unto me with sword and spear, a warrior God in flaming armour among Thine horsemen.
6. Thou hast appeared unto me as a young and brilliant God, a god of music and beauty, even as a young god in his strength, playing upon the lyre.
7. Thou hast appeared unto me as the white foam of Ocean gathered into limbs whiter than the foam, the limbs of a miracle of women, as a goddess of extreme love, bearing the girdle of gold.
8. Thou hast appeared to me as a young boy mischievous and lovely, with Thy winged globe and its serpents set upon a staff.
9. Thou hast appeared to me as an huntress among Thy dogs, as a goddess virginal chaste, as a moon among the faded oaks of the wood of years.”

These planetary references are exploited in the NNA by the associations of its names and characteristics with the gods whose planetary spheres they occupy. Thus the Sun is the sphere called Charge, which deals with electromagnetism, as light is electromagnetic radiation. And the sphere of Venus is called Resonance, because it deals with harmony and beauty, which are attributes of the goddess of love. And so on for the others, as will be explained below. In this sense, the NNA does have a connection to the Holy Books of Thelema, insofar as Liber Ararita reinforces the connections of the sacred seven planets with the seven lower spheres of the Tree.

In the last of the verses of chapter six that refer to specific numbers, we heard mention of the ‘Trinity of Triads’ as a euphemism for the number 9. This underlines the importance of this number, but also can be cross-referenced to another Holy Book, Liber B vel Magi. In this work, we find the appearance of both a trinity of triads as well as the term Sat-chit-ananda, which may have been a partial justification for Crowley’s inclusion of this Trinity in his original Naples Arrangement.

“15. Now the grade of a Magister teacheth the Mystery of Sorrow, and the grade of a Magus the Mystery of Change, and the grade of Ipsissimus the Mystery of Selflessness, which is called also the Mystery of Pan.

16. Let the Magus then contemplate each in turn, raising it to the ultimate power of Infinity. Wherein Sorrow is Joy, and Change is Stability, and Selflessness is Self. For the interplay of the parts hath no action upon the whole. And this contemplation shall be performed not by simple meditation --- how much less then by reason! --- but by the method which shall have been given unto Him in His initiation to the Grade.

17. Following which method, it shall be easy for Him to combine that trinity from its elements, and further to combine Sat-Chit-Ananda, and Light, Love, Life, three by three into nine that are one, in which meditation success shall be That which was first adumbrated to Him in the grade of Practicus (which reflecteth Mercury into the lowest world) in Liber XXVII, "Here is Nothing under its three forms."

18. And this is the Opening of the Grade of Ipsissimus, and by the Buddhists it is called the trance Nerodha-Samapatti.”

The use of Sat-Chit-Ananda, or Being, Consciousness/Thought, and Bliss
is thus directly related to instructions from Liber B vel Magi. This term comes from the Vedanta school of Hindu thought, and refers to a description of Brahman: “In Advaita Vedanta, Brahman is without attributes and strictly impersonal. It can be best described as infinite Being, infinite Consciousness and infinite Bliss.”

One thing we can glean from this Holy Book is that the first Sphere of the Tree can be numbered Zero, for it states that the ‘opening of the grade of Ipsissimus’ results from incorporating the Triads together and arriving at 'Nothing under its three forms'. This triple formed nothing is the Ain Sof, plus the first sphere of the Tree, all of which are above the sphere numbered 1, which is the place of the Ipsissimus.

Another thing we can gather from this Book is that there are three triads to be incorporated with each other. These triads are:

Sorrow, Change, Selflessness
Light, Life, Love
Sat, Chit, Ananda

These must be combined, ‘three by three into nine that are one’. This indicates that there must be three triads, and these shall constitute a unity, i.e., the coherence of the whole Tree.

Sat, Chit and Ananda are directly referenced in spheres 9, 8 and 7 of the NNA.
Light, Life and Love refer to spheres 6, 5, and 4.
Sorrow, Change and Selflessness refer to spheres 3, 2, and 1.

Sat is Being, the summation of the Tree in sphere 9.
Chit is Consciousness, referred to sphere 8, where Measurement occurs.
Ananda is Bliss, and refers to sphere 7, where the Resonance of the Pure Will is.

Light is electromagnetic Radiation, and refers to sphere 6, the home of Charge.
Life is defined at least in part by growth, metabolism, reproduction, adaptation, etc. There is no definition of life that does not include some aspect of Motion, and so it has its rightful place in sphere 5 of the NNA.
Love is the force of attraction between entities. Bucky Fuller used it as an alternative name for Gravity, and thus it has its place in sphere 4 of the NNA.

The spheres of Sorrow, Change, and Selflessness have been established as relating to the numbers 3, 2, & 1 in Crowley’s formulation, and so they are connected with the spheres of the same number in the NNA.

By the above means, the three triads mentioned in Liber B all appear in connection with the NNA.

There is precious little else in the Holy Books of Thelema that directly bears on either Crowley’s Naples Arrangement, or the NNA. We may summarize the account by saying that although neither arrangement is directly created from any of the HBOT, there is also nothing in these Books to militate against their formulation, as we can find many points of agreement between them and the Holy Books.


The purpose of the NNA is to describe the parameters of energy in the Universe, as well as its evolution, in terms of the 10 Sefirot of the Tree of Life. These spheres are manifested as the numbers from 0 to 9. The NNA is thus a description of the linear progression of the whole numbers as they indicate the attributes of the conscious substances that exist in the Universe.

To begin with, we must discard the notion of the AIN SOF AUR. This so-called 'Triple Veil of the Negative' is no longer valid in its original form. The Absolute Zero, or Nothingness, or the Void, does have three forms, as stated in Liber Trigrammaton, but one of these forms is the Zero that begins the counting numbers on the Tree. The other two are beyond the Tree, and are known as the Ain Sof.

Regarding the enumeration of the Tree from 0 to 9, rather than the traditional 1 to 10, there are two compelling reasons for this; first of all, any counting system must begin with Zero. All number systems require the existence of a Zero, which is just as much a number as 1, 2, or any of the others.

The second reason is that by beginning the Tree with 0, we are following the lead of Crowley, who, in his diagram called The Chinese Cosmos, applied the Chinese Yin-Yang Theory to the Tree of Life. This Tree began with the first sphere as the Tao, the next sphere as Yang, and the third sphere as Yin. The closest numerical analogues of these three concepts are the numbers 0, 1, and 2. Thus, the NNA represents the three digits of Base 3 mathematics at the apex of the Tree of Life. They are the fundamental digits, of which all other numbers are an elaboration or complication.

So the first of three modifications of the original Naples Arrangement is that the Tree is numbered 0 to 9 instead of 1 to 10. The numbers 1 to 10 need not be discarded, however; they may still be considered the ordinal numbers of the Sefirot.

The other modifications are that sphere 0 is identified with Time, which AC identified with sphere 5 despite the fact that Time and Motion are two different things entirely. Also, sphere 6 has been renamed Charge, in order to incorporate electricity into the fundamental attributes of substance.

Whereas Crowley dealt with the spheres as representing point-particles being fundamental, and lines and planes arising from that, the NNA understands the Vector as primal. In this we are in accord with Fuller's Synergetic geometry, which dismisses dimensionless points as being illusory. One might then understand this new Tree as symbolic of String Theory, as opposed to the classical point-particle theories. The String is Hadit as the Snake; the center of the sphere need not be a point, and is never identified in Liber AL as such.

Einstein demonstrated that Timespace is a four dimensional continuum, with one time dimension, and three space dimensions. The spheres 0,1,2 & 3 therefore represent the four dimensions of Timespace. They form the initial Tetrahedron of the Tree. From this we might understand that although 0,1,2 is the ‘Supernal Triad’, since it contains the three digits of Base 3 mathematics, another way of looking at this scheme makes the Zero a form of the Absolute, and the Triad of 1,2,3, (our old supernal Triad), remains the three common spatial dimensions. The grouping of spheres 1, 2, & 3 is therefore mainly to be considered the first of three descending triads.

If one prefers to understand the Tree in terms of String Theory, then the remaining six spheres are spatial dimensions that are 'folded up' into the weave of TimeSpace, and are not normally experienced. For this reason, other attributes are given to these spheres, since we have little to say about these six hidden dimensions, other than to stipulate that they exist.

Once the 4 dimensions of TimeSpace are established, the next sphere, (number 4), represents Gravity, since the 4d Timespace has established the foundation for an object to have Mass. While it is true that there are certain particles, like light, that are mass-less, it is still a requirement for a substance to have mass in order to have Gravity.

The next sphere, 5, represents Motion, since all objects in TimeSpace are moving; they have a velocity, which means they have momentum in a specific direction. Following this is sphere 6, representing Electric Charge, which is a fundamental property of substances in TimeSpace. This sphere includes magnetism as the complement to Electricity, and also includes Light, being Electromagnetic radiation.

While the first Triad gave us the dimensions of space, and the next Triad gave us three properties of objects in space, the final Triad is not concerned with physics. Rather, we follow Crowley's lead, and take the last Triad to represent the 'Being, Consciousness, Bliss' of the Vedanta school. These are said to be the attributes of Brahman, the All-Mind.

And thus sphere 7 represents Bliss, and this is to be understood in the sense of Joseph Campbell's dictum, 'follow your bliss'. This is identical in practice to the phrase Do what thou wilt. One's Bliss is one's state of harmony, one's resonant frequency. Thus we incorporate the idea that all substances have a Will, which might be understood as Velocity, i.e., motion in a specific direction. To fight this current, or attempt to vibrate at anything other than one's resonant frequency, is to expend energy ineffectively.

Do thy will; do that and no other shall say nay.

As Schopenhauer put it, the World is Will and Idea, (or as Gillis put it, Thelema and Ennoia). So the counterpart to the Will of sphere 7 is the Thought of sphere 8, which is called Measurement, for it is here that Consciousness appears, and this is understood as 'awareness of otherness'. Having a resonant frequency means that now there is a vantage point from which all that is the Not-Self can be understood and measured. One must be outside the boundaries of an object in order to measure it. Here is where Thought occurs.

The final sphere, number 9, is thus Being. The conscious substance must exist, or else nothing could be said of it. In a way this is really Crowley's sphere 6, for the conscious entity can now understand itself in terms of all the properties it contains, and it's position relative to all other entities.

In the diagram of the Chinese Cosmos, Crowley of necessity had to put the Trigram of Saturn in the place of Da'ath on the old Tree of the Golden Dawn. In so doing, he actually revealed the structure of the New Naples Arrangement, for Da'ath is a position on the Tree that must be filled and numbered. There may be an Abyss, but there is no Da’ath in the NNA.

By placing the 13 trigram in the correct position, and attributing it to Saturn, the seven lowest spheres make the traditional hexagon-around-a-nucleus. And by attributing the planets to the spheres with the same numbers that they have always had, we have the traditional sequence of Saturn to Moon unchanged, and have the bonus of making an actual hexagon from these, encircling the Sun at the center. Such an arrangement is displayed on the Six of Disks card in the Book of Thoth Tarot.

With these planetary associations in mind, one can see how well the new understanding of the Naples Arrangement resonates with the traditional astrological character of the planets.

Once the third dimension is reached, a substance has volume, and therefore Mass. Mass can be understood crudely as weight, and there is no weightier planet than dull, grey, leaden Saturn.

From this we move on to Gravity, which keeps the planets spinning in their orbits, just as Juppiter represents the Wheel of Fortune in the Tarot. Also Gravity is in a sense the ruler of all the forces in the Universe, for it shows no apparent spatial limit in its function, unlike the other three known forces. Also, gravity has yet to be unified with the other forces in a single, overarching formula.

The next sphere, number 5, is related to Mars. This is the active and energetic planet, and is ideal to symbolize Motion. The alchemical glyph of Mars shows a circle with an arrow erupting from it, and this arrow is the direction of the Motion that any substance has.

In sphere 6 we have Electromagnetism and light; the planetary symbolism of the Sun should be obvious here. Due to the significance of the Sun as a star, which generates power by nuclear fusion, this sphere might also be said to include the Strong and Weak nuclear forces, as modern physics has been able to combine these with electromagnetism into a single unified theory.

In sphere 7 we have Harmony, and this identifies it with Venus, the Goddess of Love, who rules over all that is beautiful and harmonious. The pentagram she creates in her orbit around the Sun is the number 5, which is the antigram of 7. Her alchemical symbol has a circle surmounting a cross. The hash mark on the cross represents the value of the specific frequency that a substance vibrates at, like the mark of a ruler, or the line on a spectrograph.

The sphere numbered 8 is the realm of Mercury, and is associated with the quicksilver thoughts of the mind. Mercury is the Logos, the Word, the left-brain, to compensate for the Sound of the right-brain. His caduceus is the DNA helix, the list of information that creates the living entity's form. This staff is also a symbol of the snake of Kundalini in the spine.

And finally in sphere 9 is the Moon, the receptor of the light from the Sun above, as Being is the receptacle of all the attributes that came before it.


Another means of understanding the New Naples Arrangement is to consider the numbers of the spheres to be exponents, and thus to be describing spatial dimensions.

The initial sphere is numbered Zero. Any number to the Zero power equals 1, and thus in an esoteric sense, this sphere is numbered 1, which is appropriate since it is the first emanation of the Ain Sof.

Zero as an exponent will also indicate the Zeroth dimension. Thus this sphere can be considered the 'indivisible point, which hath no points nor parts nor magnitude'. In Liber Ararita, this point is further explained by saying that it has no existence in time, for it is beyond Time.

And yet, as soon as we move out of this point, we will be involving Time, as all events occur in time, and Space and Time cannot be separated. So calling this sphere 'Time' indicates that it precedes and yet gives birth to time. This sphere will have no meaning whatsoever until there is something that is related to it. Sphere 0 is meaningless in and of itself; it remains inscrutable or ineffable. This is the sense in which it is 'beyond time'. And yet Time will occur as the flow of emanation proceeds from this 'point', a point that in itself is dimensionless.

Now we make the first step forward and go to the second sphere, and this sphere is numbered 1. This number 1, as an exponent, indicates the first (spatial) dimension. This is easily seen by the fact that from our Zero we have extended a vector in order to arrive at Sphere 1. Thus we have generated a line, which is a 1-dimensional construct. So sphere 1 is the domain of the Line, the First dimension.

Also, 1 as an exponent indicates any number itself, i.e., a number raised to the first power is simply that number itself. 5^1 = 5, etc. Any number could be represented here. Having created our first spatial dimension, we refer to this sphere as Space.

Moving on to sphere 2, again we consider the number 2 as an exponent, and thus we must be in the Second dimension, the Plane. This is easily demonstrated by the fact that this is the third sphere to emanate, and thus to join all three we also have three paths, which make a triangle, which is the simplest two-dimensional figure.

Not only did we generate a path from sphere 1 to sphere 2, but by necessity we also generated a path from sphere 2 back to sphere Zero. We have a triangle, and thus a plane, and thus 2 dimensions. We call this sphere Angle, because we have vectors defined by their position relative to one another, and these positions are expressed as an Angle.

Moving on to sphere 3. This is where the Abyss is sometimes attributed. But the New Naples Arrangement has no Abyss, because we are talking about the regular sequence of the integers. There is no break between them; they increase by 1 each time. It is just as far from 3 to 4 as it is from 5 to 6, etc. Thus all paths between spheres are of equal length.
But there is, between 3 and 4, that mysterious number Pi, which goes on to infinity; such would be an example of the 'never-ending expansion of the Abyss'. And since in the traditional Tree the abyss occurs between spheres numbered 3 and 4, we might consider the Abyss to be Pi. But in the NNA, this is not an essential feature.

Once again, considering the number of the sphere to be an exponent, the third dimension is the so-called 'solids'. The simplest 'solid' or polyhedron, is the Tetrahedron, a figure made from four points and the vectors that connect them. This is exactly what we have here so far, and thus sphere 3 completes our four-dimensional time-space continuum, as per Einstein & Minkowski.

For this reason, we call this sphere Matter, as the fabric of our everyday 4-D world is now created. And like the traditional Tree, we begin our Planetary associations here, to supplement our understanding of the numbers. This is the sphere of Saturn, an apt symbol for Matter, as its metal is lead, the heaviest and most stable of the chemical Elements. One might think also of the Tarot card for Saturn, which is the Universe, the final Trump major, indicating that the material world is completed as far as its basic matrix is concerned. This is very Kantian in the sense that the 4-D TimeSpace is a necessary prerequisite to all the experiences of consciousness.

[In these first four spheres of the NNA, we recognize the 4D TimeSpace of Einstein. But we are also justified in considering it as the 4d TimeSpace of Fuller’s Synergetic Geometry. Fuller agreed that the world is a 4d continuum, but he disagreed that Time is a separate dimension. For him, Time was involved in ALL the dimensions of Space. And by using the 60-degree co-ordinates of the tetrahedral matrix, (rather than the 90-degree co-ordinates of cubical Cartesian space), he arrived at 4 spatial dimensions, each of which included Time. Using this perspective, one might just as well call the first sphere, numbered 0, the first spatial dimension instead, and call it TimeSpace – Unmanifest. But in either view, it requires four spheres and 4 dimensions to make up the basis of our physical universe, and these manifest as a tetrahedron. So this choice boils down mostly to a matter of aesthetics.]

All of the remaining spheres can have their numbers considered as exponents, which are then indicating spatial dimensions. But we may ignore these for the time being, as they are not experienced directly in human consciousness. If in fact they do exist, they must be 'folded up', as in String Theory, and inaccessible to normal awareness.

Now that the basic matrix of matter is created, we take the next path to the second Triad and the Sphere numbered 4. This sphere is called Gravity, as all matter has gravitational attraction to other matter. This is also one of the four Forces known in the Universe, and yet it has not been integrated with the other three, (in a manner analogous to the fact that the dimension of time is not exactly identical with the dimensions of space, and yet co-exists with them).

As Bucky Fuller put it, Gravity is Love, the attraction that objects have for each other. In this sense we see a relation to the old Tree of Life, where this sphere was called Chesed, which means 'loving kindness'. And just as Crowley considered law to be established here, so Love is the Law.

Gravity attracts in all directions; it is omni-spherical or circumferential. In this sense we have a connection to the planetary aspect of this sphere, which is Juppiter, the planet of expansive inclusiveness, (a symbol of which can be found in the Tarot in the Trump called the Wheel of Fortune). Also of note is that Juppiter's magic square is 4 x 4, and has 16 cells. The number 16 is 2^4, and is therefore the simplest number, (other than 1), to express the fourth dimension, as in the Tesseract. This being the sphere numbered 4, it thus has a connection to this Tesseract, or any other fourth-dimensional figure.

Moving on to the sphere numbered 5, we already have Matter, and its inherent gravitational attraction to itself and other matter. Such attraction results in movement, and so this sphere is called Motion. The planetary aspect of this is Mars, symbol of dynamic movement. Its alchemical symbol is also apt; a circle, representing the omni-directionality of gravity, with an arrow coming out of it, representing the motion of matter on a line with its gravitational attraction to other matter.

In sphere 6, we continue to progress in the basic attributes of Matter, which include electrical charge. This is the sphere of the Sun, and thus includes Light, which is electromagnetic radiation. Such radiation exemplifies one of the other four Forces, namely electromagnetism. Within this sphere is also hidden the other two universal forces, the strong and weak nuclear forces. These forces control the particles of the atomic nucleus, and sphere 6 is the nucleus of the New Naples Arrangement.

Since we now have radiation in existence, we are also including radioactive decay of elements. Note well that this decay may occur in all directions, but it is blocked from proceeding back to the source by the lead of Saturn, in the sphere above it. Thus metaphorically, the lead of Saturn is in the ‘Abyss’ that absorbs all of the disintegration of the consciousness of identity found in the lowest triad. But this is more esoteric than we need to be at the moment.

Moving on to the last Triad, and sphere 7, we call this Resonance. We have entities in TimeSpace that are subject to the laws of motion and the four forces of the universe. But each such entity will have a particular frequency at which it vibrates. Note that vibration is already accounted for under Motion: here that vibration is moving at its optimum rate. The symbol of this is the planetary correlation with Venus, goddess of Love and Beauty. When all is in harmony, in perfect and thus beautiful proportion, then motion or activity occurs in conformity with the Will.

Such a Will is inherent and instinctual. No entity needs to calculate what this frequency will be for that frequency to be operative. Only when the next sphere is reached do we introduce the idea of Measurement. Such measurement is symbolized by the planetary association with Mercury and the process of intellection. Only here do we begin to have a conscious awareness of otherness. The entity exists in TimeSpace, is subject to the laws of Motion and the four Forces of Universe, and resonates at a particular frequency. Only from this position can any measurements of other such entities begin to occur, and thus consciousness appears here to identify itself relative to the rest of its Universe.

Being in existence, and measuring that existence through its awareness of otherness, consciousness now defines itself by all these parameters in the last sphere, called Being or Existence. In a certain sense, this End is a Beginning, for all along we have only been talking about things which Exist.

Therefore this sphere can easily be the first sphere of another Tree in an infinite chain. The beginning is at an End, and the End is at the beginning. Existence is in Time, and Time is in Existence.

Love is the Law, love under will.
R. Leo Gillis

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I love it! I can't say I understand it all precisely, but I follow it. And it provides much room for exploration.

this quote from the Bagh-I-Muattar is related to the NNA:

"But even the Hebrews acknowledge the superior purity of the 12 system by retaining Hua as a title of Kether, their highest emanation. Unfortunately they seem to have forgotten that Kether should itself be counted as Zero, thereby altering their whole chain of aeons and its symbolism, though it is true that, realizing the necessity of Zero as a starting point for any system, they concealed behind Kether three veils of the negative, culminating in Ain, pure negation."

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