Another Look at the Letters on the Paths of the Tetractys

The big thrust of this whole mathesis thing was to develop a graphical outline of the structure of the cosmos, both macrocosmic and microcosmic, and allow for the use of letters as vehicles of transformation between different states on the cosmic map.  We decided to use the Tetractys as our overall map, and found a set of 24 paths between the ten spheres of the TetractysEach path was then assigned to one of the 24 letters of the Greek alphabet (excepting the obsolete letters digamma, qoppa, and sampi), and boom, we have our graphical cosmic map.  Thing is, all this was experimental and an exercise in logic and extrapolation; it’s been largely untested, but it does provide a neat way to arrange the letters on the Tetractys.

I’ve been feeling comfortable with the assignment of the spheres on the Tetractys to the ten forces: the Monad or Source, light or activity, darkness or passivity, alchemical sulfur, alchemical mercury, alchemical salt, fire, air, water, and earth.  Mapping these forces to their cosmological equivalents, likewise, was fairly straightforward.  What I haven’t been completely comfortable this whole time with, however, was the assignment of letters to the paths themselves.  I’ve guessed from the beginning that, no matter how logical my original assignment was, chances are it wasn’t going to be a permanent assignment.  I all but definitively knew that at least some of the letters on the paths were going to change, and I’d leave it to until I actually got around to exploring the Tetractys through ritual and scrying to change them.

Somewhat ahead of that predicted schedule, however, I asked Hermes and asked for some guidance about the upcoming trips on the Tetractys paths, but unfortunately he was unusually tight-lipped; this was definitely something I would have to explore when the time came.  He did say he’d help open some doors in the meanwhile to help me get a feel for what’d be coming up, however, so I went back and took another close look at what I’ve been discussing since I first laid out how I assigned the letters to the paths.  This time, however, I kept the distinction of direction and the Gnosis/Agnosis Schemata in mind, and started over from there.  I ended up with a wholly new way to assign letters to the paths and, although I’m still feeling a little unsure, this has a much different feel than the first arrangement, and it’s one I conceptually like more.  I warn you, in this post I’m going to be using lots of gaudy color, and since we’ve already been through this kind of analysis once before, I’ll be a little more rough when explaining things.

So, in the Gnosis Schema, we have twelve paths that go around the Tetractys, hitting the sphere of Mercury four times and every other sphere once:

alchemical_planetary_tetractys_paths_circuit1The Agnosis Schema, on the other hand, has the twelve remaining paths that only connect to the non-Mercury middling spheres:

alchemical_planetary_tetractys_paths_circuit2

Consider that the Gnosis Schema is an orderly array of paths, a sequence that follows a strict ordering.  The Agnosis Schema, however, has no such inherent order, and has criss-cross of paths that allow for wandering around without a plan, so to speak.  If we start with these two ideas, we have two sets of twelve paths.  We have 24 letters, which are divvied up between four elements, the meta-element Spirit, seven planets, and twelve zodiac signs.  We can divide the letters and their corresponding forces, likewise, into two groups of twelve: the twelve zodiac signs/simple consonants, and the twelve forces/vowels and complex consonants.  The zodiac signs follow a particular celestial order, and while we can ascribe orders to the elements based on density or planets based on distance from Earth, we also recognize that the elements shift among themselves and the planets move around from place to place.

So, if we assign the twelve zodiac signs to the twelve paths of the Gnosis Schema, in the order that we proceed from Mercury to Air to Fire and so forth, we end up with the paths in the same order as the twelve signs of the Zodiac, as below:

tetractys_paths_gnosis_signs

Alright, easy part’s over.  We still have the twelve paths of the Agnosis Schema to set out, and this is where things get a little more complicated.  First, let’s review what we know about the letters and their stoicheia again:

  • There are two sets of forces: zodiacal and energetic.  Zodiacal forces are the 12 signs of the zodiac, and the energetic forces are the four elements, the meta-element spirit, and seven planets.
  • There are four elements of the forces: fire, air, water, earth.
  • There are three modes of the forces.  In the zodiac forces, these are manifested as cardinal (Aries, Cancer, Libra, Capricorn), fixed (Taurus, Leo, Scorpio, Aquarius), and mutable (Gemini, Virgo, Sagittarius, Pisces).  In the energetic forces, these are manifested as the ideal (the four elements Fire, Air, Water, Earth), the empyrean (the planets of the Sun, Mercury, Moon, and spirit considered as a planet), and the ouranic (the planets of Venus, Jupiter, Mars, and Saturn).
  • We can link the ideal mode of the energies to the fixed mode of the zodiac signs, the empyrean to the cardinal, and the ouranic to the mutable.
  • There are four groups of three zodiac signs and four groups of three energies based on element.
  • There are three groups of four zodiac signs and three groups of four energies based on mode.
  • There are thus six forces (three energetic and three zodiacal) for each of the four elements.
  • There are thus eight forces (four energetic and four zodiacal) for each of the three modes.

Drawn out in tables, we see the following:

Fire Air Water Earth
Ideal Fire Air Water Earth
Empyrean Sun Spirit Mercury Moon
Ouranic Mars Jupiter Venus Saturn
Fire Air Water Earth
Cardinal Aries Libra Cancer Capricorn
Fixed Leo Aquarius Scorpio Taurus
Mutable Sagittarius Gemini Pisces Saturn

We know what the letters and their corresponding forces look like for the Gnosis Schema, and we can use that to help guide us with a bit of geometrical innovation to figure out what the paths on the Agnosis Schema should be based on the geometry of element and mode.

Let’s focus on the elements of the zodiac signs first.  If we divide the twelve Gnosis Schema paths up by element, we get the following four figures: three paths for the Fire signs, three for Water, three for Air, and three for Earth.  Below are the paths color coded such that red paths are Fire, blue are Water, green are Earth, and yellow are Air:

tetractys_paths_gnosis_signs_element_color

The Fire and Water signs both emanate out from the central sphere of Mercury, while the Air and Earth signs emanate out from the three extreme spheres of the Monad, Fire, and Earth.  Note that if we look at the Fire set of signs and Water set of signs separately, we can draw an equilateral triangle that connects the outer points of their paths.  These would give us another three paths for both the elements of Fire and Water to complete the set, which forms the hexagram in the center of the Tetractys, a symbol renowned as the mark of combining fire with water.

As for Air and Earth, on the other hand, it gets a little less clear.  We know from the elements themselves that Air likes to connect and bridge gaps, while Earth likes to close it on itself and separate.  Thus, let’s give Air the three paths in the middle of the outer edges of the Tetractys, trying to reach and form one large triangle, while Earth gets the three paths in the corners of the Tetractys, trying to form three small triangles.  Just as the Fire and Water paths intersect with each other to form a cohesive union, the Air and Earth paths must be joined together (though they don’t intersect) in order to form complete wholes on their own; the triangles that the Earth paths form are completed by Air, and the larger triangle that the Air paths form is completed by Earth.  Thus, we have three more paths for Air and three more paths for Earth:

Note the interplay of elements for the paths with this.  The central hexagram joins Fire and Water together, with one triangle belonging to Fire and the other to Water, and if we include the zodiacal paths that connect the vertices of the triangles, we end up with a 2-dimensional birds-eye look of two interlocked tetrahedrons, one pointing up (Fire) and one pointing down (Water).  The hexagon around the hexagram alternates Air and Earth, and with the six zodiacal paths inside the hexagon, we end up with a 2-dimensional view of a cube facing one of its corners, with its 12 edges bounded by the elements four times each.  Each of the elements comes in contact with all the other elements at least once each by means of the paths on the Tetractys, forming a completely yet regularly mixed whole.

tetractys_paths_gnosis_elements_color

Now we need to figure out the modes of the paths, and this is where things get a little less geometrically clean.  We already know the modes of the zodiacal forces, after all, and if we plot them out by cardinal, mutable, and fixed, we end up with this weird “broken W” shape rotated each way around the Tetractys.  Let’s use orange for cardinal paths, purple for fixed paths, and pink for mutable paths:

Remember, though, that these are for the zodiacal forces on the Gnosis Schema, while we need to figure out the energetic forces on the Agnosis Schema.  Both the Gnosis Schema and Agnosis Schema have four paths for each of the three modes, and we’re trying to divide up the twelve hexagon/hexagram paths of the Agnosis Schema into three groups of four.  We did this a ways back when we were discussing the meditation of the divine name IAŌ on the Tetractys by making three rectangles that orbited the central sphere of Mercury:

We used a similar method to complete the division of elemental forces based on zodiacal mode, but now I think that method was somewhat misguided since it conflated the two, and further it never really resolved the association of the hexagram paths of Air to their forces in a clean way.  Instead, let’s talk about what I mean by the energetic modes of Ideal, Empyrean, and Ouranic:

  • Ideal energies are the pure elements themselves, their most high and abstract concepts and overall form to which the other energies are associated.  These are the four elements of Fire, Air, Water, and Earth.
  • Empyrean energies are the four forces of the Sun, the Moon, Mercury, and Spirit.  The three planets here are those that are those represented by the Triadic rank of the Tetractys, associated respectively with Sulfur, Salt, and Mercury.  These are the high holy forces of Light/Sameness, Darkness/Difference, Motion/Existence, and Spirit/Emptiness.  Although “empyrean” literally means “on fire” and often refers to the abode of the gods/God, I’m using it here to denote a different kind of “heavenly planet” from…
  • Ouranic energies are the four forces of Mars, Jupiter, Venus, and Saturn.  These are the other four planets that are represented in the Tetrad rank of the Tetractys, and associated respectively with Fire, Air, Water, and Earth.  Unlike the empyrean forces, the ouranic forces (also meaning “heavenly” but in a sense closer to “celestial” rather than “divine”) are not planets associated with the process of alchemy, but planets associated with the materials of alchemy, the four elements.  They’re in a sense “lower” than the four empyrean forces.

We have three modes of energetic forces, and we also have three modes of zodiacal forces.  We’ve already established from before that the fixed signs are closest to the elements themselves, so we can associate the zodiacal mode of fixity with the energetic mode of ideality.  Carrying the idea (pun unintended) through, the zodiacal mode of mutability might best be associated with the energetic mode of ouranicity, which leaves us the zodiacal mode of cardinality which can be associated with the energetic mode of empyreality.  This allows us to associate the zodiac forces with the energetic forces quite nicely and cleanly:

Fire Air Water Earth
Primary
Mode
Cardinal Aries Libra Cancer Capricorn
Empyrean Sun Spirit Mercury Moon
Secondary
Mode
Fixed Leo Aquarius Scorpio Taurus
Ideal Fire Air Water Earth
Tertiary
Mode
Mutable Sagittarius Gemini Pisces Virgo
Ouranic Mars Jupiter Venus Saturn

Although my previous attempt to assign the modes to the three elements of Fire, Water, and Earth may have been misguided, I do like how I assigned the three rectangular sets of paths to the three modes.  Thus, the vertical rectangle with short horizontal paths is still given to the fixed/ideal mode, the diagonal rectangle with short down-right paths given to the cardinal/empyrean mode, and the diagonal rectangle with short down-left paths given to the mutable/ouranic mode.  We thus end up with the following combinations of paths based on their mode:

Putting it all together, we now know the mode of every path in the Tetractys:

tetractys_paths_gnosis_modes_color

When we combine our knowledge of what element each path should be along with what mode it should be, knowing already whether it’s a zodiacal force (on the Gnosis Schema) or an energetic force (on the Agnosis Schema), we end up with a new Tetractys of Life with the appropriate letters on each of the 24 paths:

alchemical_planetary_tetractys_gnosis_paths

Overall, I like this version of the Tetractys more; it has a different “ring” to it, something a little clearer and smoother, but I’m still unsure as yet whether it’s the right one.  Only exploration and testing will show that out, and whether any adjustment (or outright rewriting) is needed.  What’s interesting, though, is how this might affect our exploration of the Tetractys in a structured way.  Note that we’ve assigned the Gnosis Schema paths to the twelve signs of the zodiac.  The Zodiac is the belt of stars that the Sun and all the other planets travel through over the course of their orbits, and we make one revolution through the Zodiac every year.  Thus, we have a sort of solar schedule for how we travel through the paths: for instance, we make the trip between Mercury and Air during Aries, Air and Fire during Taurus, Fire and Sulfur during Gemini, Sulfur and Mercury during Cancer, and so forth until we end up back at Mercury while we’re in Pisces.

The association of the Zodiac with the Gnosis Schema paths, further, divides the year up into three periods, one for each of the Initiatory Cycles as mentioned before. the first four signs (from the start of Aries to the end of Cancer) to the Hot Initiation (Mercury, Air, Fire, Sulfur); the second four signs (start of Leo to the end of Scorpio) to the Cold Initiation (Mercury, Salt, Earth, Water); and the last four signs (start of Sagittarius to the end of Pisces) to the Cosmic Initiation.  Of course, this is slightly adrift from our notion of having four seasons of spring, summer, autumn, and winter, but we do go from a period of cold to hot (heating the year), a period of hot to cold (cooling the year), and a period of just cold (darkest and coldest point of the year).  It’s not hard to make associations between these three quasi-seasons with the three Initiatory Cycles, but of course, my living in the Northern Hemisphere is coloring my views somewhat.

Of course, I don’t think we need to follow the Sun in the Zodiac as we follow the paths in the Tetractys, but it does imply that there’s a natural flow, a cycle that’s inherent in the mechanics of the cosmos.  Consider the three empyrean planets of the Sun, Moon, and Mercury: the Sun only ever goes in one direction through the Zodiac, as does the Moon; Mercury does go retrograde fairly often, but its retrograde periods are also extremely short compared to all the other planets, and is so close to the Sun that it basically is taken along with it.  Spirit, the other empyrean energy, is both lower than and amidst the planets themselves, providing the space and nature for them to exist and coexist at all.  Between the Sun, Moon, and Mercury, there’s a natural flow that pretty much only ever goes in one direction, and that’s around the Zodiac in its proper order.  As the Sun and Moon pretty much define nearly all the natural cycles down here on Earth, it suggests that there’s a natural flow and pull for ourselves to be taken along the Gnosis Schema ever onwards towards gnosis and henosis.

However, we get trapped and caught up by the forces of the other planets and elements, which gets us tangled up and going against the natural flow and rhythm of the Gnosis Schema.  We get swept up in a particular planet’s influence, we get brought down by a particular element’s effects, and we generally get caught up in long periods of retrograde motion and muddled manifestation of forces that keep us from flowing naturally with the cosmos as we should.  In aikido terms, the more stressed we are, the less ki can flow through us; in quasi-Thelemic terms, the more we focus on our temporary will, the less we naturally enact our True Will.  If we could simply incorporate the powers of the planets and elements without being subsumed or dominated by them, we could live with the natural flow of the cosmos to attain our true destinations and ends.  Of course, because of the various influences shining down upon us and emanating from within us, we have to struggle to constantly align and realign ourselves with the natural flow of things.  We have to constantly be on guard so that we don’t fall from Gnosis back to Agnosis; we have to constantly keep ahead of the ghost of Argos so we don’t become trapped once more.

From a Gnostic standpoint, this set of paths makes even more sense than the one before.  While we’re trapped in this world, we’re subject to the seven heavens of planets and their associated archons, which clothe us in misunderstanding and agnosis; they give us false notions of how the cosmos works, as well as how we ourselves work.  But, once we break free of them outside the realm of elements and planets, we enter into the realm of the fixed stars, that starry Eighth Sphere, where we proceed into gnosis.  Quoth the Divine Poemander:

First of all, in the resolution of the material body, the Body itself is given up to alteration, and the form which it had becometh invisible; and the idle manners are permitted, and left to the Demon, and the senses of the body return into their Fountains, being parts, and again made up into Operations.  And Anger, and concupiscence, go into the brutish or unreasonable nature; and the rest striveth upward by Harmony.

And to the first Zone [planet] it giveth the power it had of increasing and diminishing.  To the second, the machinations or plotting of evils, and one effectual deceit or craft.  To the third, the idle deceit of Concupiscence.  To the fourth, the desire of Rule, and unsatiable Ambition.  To the fifth, profane Boldness, and the headlong rashness of confidence.  To the sixth, Evil and ineffectual occasions of Riches.  To the seventh Zone, subtle Falsehood, always lying in wait.

And then being made naked of all the Operations of Harmony, it cometh to the Eighth Nature [sphere of the fixed stars, realm of the Zodiac, etc.], having its proper power, and singeth praises to the father with the things that are, and all they that are present rejoice, and congratulate the coming of it; and being made like to them with whom it converseth, it heareth also the Powers that are above the Eighth Nature, singing Praise to God in a certain voice that is peculiar to them.  And then in order they return unto the Father, and themselves deliver themselves to the Powers, and becoming Powers they are in God.  This is the Good, and to them that know, to be desired.

Thus, while we’re trapped in this world, we cycle chaotically and confusedly around the cosmos without real understanding of how it works, no matter how much we jive with the planetary and elemental forces.  It’s only once we recognize them for the powers that they are that we break free of them, traveling among the fixed stars themselves.  Even in agnosis, there is learning; we need to be aware of what the elements and planets do to us before we can truly break free of them and shed ourselves of their influence.  Once we know how to work them and how to get rid of their influence while remaining in control of them, we then proceed to rise above them to gnosis and understand what the whole cosmos is really about.  Planetary and elemental magic can only get us so far; they cannot get us to the most extreme parts of the cosmos (or, in this model, the outermost spheres of the Tetractys) nor can they get us to a point where we’re balanced and able to go in any direction we want (the sphere of Mercury).  It’s only by making the leap from agnosis to gnosis that we can do that, but even then, we must be on our guard; we can slip and fall back into agnosis by dwelling too much on any one energetic force, allowing it to entrap us once more.

Personally, though I don’t expect this to be the final draft of the Tetractys with lettered paths, I think it’s definitely an improvement, and unless Hermes opens up any more doors in the meanwhile, I expect this to be the system of letters and paths that I’ll use.  If nothing else, it goes to show that there really isn’t just one way to attribute letters to the paths; then again, without having come up with the notion of the Gnostic/Agnostic Schemata, this set of lettered paths wouldn’t’ve been possible.  Still, even using the Schemata as our base, we could still attribute each cycle of Initiations to one of the three groups of energetic forces instead of the zodiac signs, perhaps by giving the empyrean energies to the Hot Initiation, the ouranic energies to the Cold Initiation, and the ideal energies to the Cosmic Initiation.  There are many ways to arrange the paths systematically, so it’s unclear without testing it to see which one works best, if any at all even really matter.  To that end, let’s see how well this particular system can be used.

Tying the Tetractys to the Qualities of the Numbers

This post is going to be a little winding and wending around several topics we’ve gone over recently about the Tetractys, paths, and the like, so I apologize if it’s not as coherent as the others; this is half-exposition, half-exploration, so I hope you have some caffeine handy.  Not too long ago, I had an idea of analyzing the internumeric/arithmetical relationships of numbers as presented by collections of the Monad, Dyad, Triad, and Tetrad in the Tetractys.  This was combined with a geomancy-influenced approach to analyze specific combinations of these numbers which resulted in a deeper understanding of the principles and qualities of the numbers 0 through 10:

  1. Emptiness
  2. Individuation
  3. Relation
  4. Harmony
  5. Form
  6. Growth
  7. Order
  8. Essence
  9. Mixture
  10. Realization
  11. Wholeness

Each of these has a whole explanation about how they’re arrived at and what they mean on a deeper level, but the one-word name for each works pretty well.  However, we could link pairs of these principles or qualities together, balanced around the number 5.  In a deep sense, both the upper number (less than 5) and lower number (more than 5) reflect the same attribute, with the upper qualities reflecting more of an internal nature and the lower qualities more of an external nature.  Those metaqualities are:

  • 0/10: Being
  • 1/9: Becoming
  • 2/8: Variation
  • 3/7: Accordance
  • 4/6: Structure
  • 5: Growth

The diagram illustrating this from before can serve as a good reminder of how these things are all linked together:

tetractys_decad

In a deep sense, the ten qualities described by the ten numbers of the Monad up through to the Decad can be described in another Tetractys: instead of eleven qualities (Monad through Decad plus Mēden, or Nothing/0), we end up with six metaqualities: Becoming, Variation, Accordance, and Structure, preceded by Being and succeeded by Growth.  However, I personally feel that Being and Growth themselves, as metaqualities, are the same: one cannot be (being) without coming to be (growth), nor can one become (growth) without existing enough to become (being).  So, in reality, we have four qualities assigned, yet again, to the Monad, Dyad, Triad, and Tetrad, with another quality given to the “hidden pentad” which forms the threshold between one iteration of the Tetractys and the next.  In essence, we end up with a fractal of meaning for the Tetractys, with tetractyes within tetractyes, tetractyes all the way down.

Anyway, backing up again to the Decad from the Tetrad, I think I figured out a connection between these qualities and the order of the sphairai established from the Gnosis Schema discussed from before.  In case you’ve already forgotten and don’t like rereading old posts, the Gnosis Schema is a series of 12 paths that lead to every sphaira on the Tetractys, first starting at Mercury, then Air, then Fire, then Sulfur, then down to Earth and back to Mercury, then up to the Monad and back again to Mercury.  It’s like the Lightning Bolt Path on the Tree of Life in qabbalah/kabbalah, although this Gnosis Schema is cyclical instead of linear.  This is in contrast to the Agnosis Schema, the set of twelve paths formed by the hexagon and hexagram in the Tetractys that eternally circle but never connect to Mercury, as well as the extreme sphairai of the Monad, Earth, and Fire.

Looking at the Gnosis Schema, the sphairai can be uniquely numbered in the same order as the paths lead to them, skipping over Mercury as it’s repeated:

  1. Mercury
  2. Air/Jupiter
  3. Fire/Mars
  4. Sulfur/Sun
  5. Salt/Moon
  6. Earth/Saturn
  7. Water/Venus
  8. Light/Fixed Stars
  9. The Monad
  10. Darkness/World

The only annoying thing is that the numbering in this manner isn’t contiguous; you can’t go from 4 to 5 without passing over 1 again.  It’s not ideal, but it’s one possible system all the same, and I make no claim to any of this being ideal or correct right out of the gate of development.

So, here’s a different idea.  Instead of just limiting ourselves to counting the sphairai uniquely, why not count them contiguously?  In other words, on the Gnosis Schema, after we go from Mercury (1) to Air (2) to Fire (3) to Sulfur (4), we go back to Mercury (5) to Salt (6) to Earth (7) to Water (8), then back to Mercury (9) to Light (10) to the Monad (11) to Darkness (12), then return to Mercury (13) to begin another cycle.  Since we like numbers 10 and less, let’s reduce them all by taking the remainder of a number larger than 10 when we divide it by 10.  So, if we have the Monad given the number 11, the remainder of 11 ÷ 10 is 1, the remainder of 13 ÷ 10 is 3, and so forth.  So, when we started out with Mercury at 1 when we began our first pass through the Gnosis Schema, we ended up with Mercury at 13 (3).  If we try it again, we end up with Mercury at 25 (5), and again at 37 (7), again at 49 (9), and the next schema would start it at 61 (1).  It takes five complete passes around the Gnosis Schema for us to return to the same number (or reduced number, which is the same in this line of thinking).

So, if we were to chart out a comparison between the schematic numbering of the spheres compared to the pass number of the spheres, we’d end up with the following chart (ignore the System column for now):

Sphaira Schema Continuous Passes System
Pass 1 Pass 2 Pass 3 Pass 4 Pass 5
Mercury 1 1 13 (3) 25 (5) 37 (7) 49 (9) 1
Air 2 2 14 (4) 26 (6) 38 (8) 50 (10) 2
Fire 3 3 15 (5) 27 (7) 39 (9) 51 (1) 3
Sulfur 4 4 16 (6) 28 (8) 40 (10) 52 (2) 4
Mercury 1 5 17 (7) 29 (9) 41 (1) 53 (3) 1
Salt 5 6 18 (8) 30 (10) 42 (2) 54 (4) 2
Earth 6 7 19 (9) 31 (1) 43 (3) 55 (5) 3
Water 7 8 20 (10) 32 (2) 44 (4) 56 (6) 4
Mercury 1 9 21 (1) 33 (3) 45 (5) 57 (7) 1
Light 8 10 22 (2) 34 (4) 46 (6) 58 (8) 2
The Monad 9 11 (1) 23 (3) 35 (5) 47 (7) 59 (9) 3
Darkness 10 12 (2) 24 (4) 36 (6) 48 (8) 60 (10) 4

Incidentally, as it takes five complete passes around the Tetractys for us to reach the same number we started at, I had suggested earlier that we go through Four Initiations (Hermetic, Hot, Cold, Cosmic) that would collectively focus on each force within its own system, or a tetrad of forces extending from the Mercury sphaira out to one of the outermost sphaira:

  1. Hermetic Initiation
    1. Hot System (Mercury → Air → Fire → Sulfur)
    2. Cold System (Mercury → Salt → Earth → Water)
    3. Cosmic System (Mercury → Light → the Monad → Darkness)
  2. Hot Initiation
    1. Hot System with a focus on Mercury (e.g. a deeper acquaintance of the Hot forces)
    2. Hot System with a focus on Air (e.g. seeing Air and how it relates and acts throughout the Hot forces)
    3. Hot System with a focus on Fire (e.g. same as above but with Fire)
    4. Hot System with a focus on Sulfur (e.g. etc.)
  3. Cold Initiation
    1. Cold System with a focus on Mercury
    2. Cold System with a focus on Salt
    3. Cold System with a focus on Earth
    4. Cold System with a focus on Water
  4. Cosmic Initiation
    1. Cosmic System with a focus on Mercury
    2. Cosmic System with a focus on Light
    3. Cosmic System with a focus on the Monad
    4. Cosmic System with a focus on Darkness

In other words, the Hermetic Initiation would be one whole pass through the Tetractys (12 sphairai).  The Hot Initiation would cycle through the first third of the Gnosis Schema four times (4 sphairai × 4 = 16 sphairai, 12 + 16 = 28); the Cold Initiation would cycle through the second third of the Gnosis Schema four times (another 16, so 28 + 16 = 44); the Cosmic Initiation would cycle through the last third of the Gnosis Schema four times (another 16, so 44 + 16 = 60).  All told, we’d hit sixty sphairai before returning ultimately to the Mercury sphaira at 61, itself reduced to 1.

However, notice that as we’re undergoing the Hot, Cold, and Cosmic Initiations, we’re simply looping around four of the sphairai four times, always starting at and passing through Mercury before going to the next set of initiations.  We can assign the numbers 1 through 4 to each of the spheres within each system, which is what the System column in the table above shows.  And, if we can assign certain groups of sphairai to a certain number, then we can see what comparisons and qualities come out of that analysis:

  1. Mercury
  2. Air, Salt, Light
  3. Fire, Earth, the Monad
  4. Sulfur, Water, Darkness

It’s interesting to note that, although Mercury is central to the Gnosis Schema and the Tetractys generally, it forms its own group, always in the worlds but never of the worlds; this, to me, only reinforces its liminal nature as both abyss/boundary and bridge/transformation even more.  The second and fourth groups should look similar to us: they’re the paths we’ve assigned to the letters associated with Air, based on planetary, elemental, or zodiacal symbolism.  The Dyadic systemic group is connected by Air, Jupiter, and Spirit; the Tetradic systemic group is connected by the zodiacal signs of Libra, Aquarius, and Gemini.  Since the Dyad is more about relation/mixture (which speaks to me more strongly of the fixed stars and the zodiac signs) and the Tetrad more about form/structure (more about discrete forces that constitute bodies and action), I question now whether I should swap these associations so that that the Dyadic system is given to the signs of the Zodiac and the Tetradic systemic group is given the forces.

The Triad systemic group, however, is composed of the three outermost and extreme sphairai of the Monad, Earth, and Fire.  They cannot be connected to each other without going through either Dyadic or Tetradic systemic sphairai, nor can they be connected to central Mercury.  However, the Triad is based on harmony and essence, and if nothing else, these three sphairai represent the ultimate foundations (in their own ways) of the cosmos: pure active manifesting force (Fire), pure passive manifested matter (Earth), and the Source of everything and everything in between (the Monad).

Anyway, all this is getting away from the main point I wanted to make: is there a way to link the ten sphairai of the Tetractys with the qualities of the Decad?  Well, the straightforward way would be to associate the ten qualities with the ten sphairai as we numbered them uniquely based on the Gnosis Schema:

  1. Mercury — Individuation
  2. Air/Jupiter — Relation
  3. Fire/Mars — Harmony (??)
  4. Sulfur/Sun — Form (?)
  5. Salt/Moon — Growth (???)
  6. Earth/Saturn — Order
  7. Water/Venus — Essence
  8. Light/Fixed Stars — Mixture (?)
  9. The Monad — Realization
  10. Darkness/World — Wholeness

Some of these make sense, and some really don’t.  I mean, what really catches my eye that sets me off is the association with the Pentad (Growth) with the sphaira of Salt.  I mean, sure, in its astrological sense of the Moon, this sphaira can reflect the notion of growth as much as it would atrophy, increase as well as decrease.  However, the alchemical notion of Salt is not what I’d consider resonant with growth; on its own, Salt is fixed, stable, and dead.  Without either Sulfur to cause change or Mercury to receive it within the vehicle of Salt, growth is simply a moot point.  Then again, without the body provided by Salt, growth can’t happen, either; growth can only happen after a body is present.  And, as our Tetractyean studies indicate, growth (Pentad) can only arise in things with bodies made from the four elements (Tetrad).  So maybe this does make sense.  Maybe the other sphairai with question marks have similar occult reasons as to why they can correspond to the quality of their numbers, but it requires some thought.

Another way to consider the qualities as related to the sphairai is not the “essential quality” of the sphairai (based on their unique schematic numbering), but based on the number we arrive at a sphaira based on the passes through the Tetractys using the Gnosis Schema.  For instance, on our first pass through, Mercury is sphaira #1 and thus associated with Individuation; on the second pass, it’s #3 and associated with Harmony; on the third, it’s #5 and associated with Growth, and so forth.  After five passes, we start over again.  Note how the sphairai of Mercury, Fire, Earth, and the Monad (the Monadic and Triadic systemic sphairai) only ever receive odd (active) numbers in this method, while the middling sphairai (the Dyadic and Tetradic systemic sphairai) only ever receive even (passive) numbers.  This system is much more complicated than the straightforward one we just discussed, but it also reflects a system of constant evolution and development that requires several passes through the Tetractys in order to fully grasp the entirety of each sphaira, both in terms of its alchemical/planetary force as well as its numerological qualities.  I might contrast this with the preceding method as how a planet in astrology has both essential dignity (determined solely by its degree in the Zodiac) and accidental dignity (what else is going on around the planet relative to itself).

Well, if we were to use the essential qualities of the sphairai, we also know that we can combine pairs of the qualities into metaqualities that subsume them, like how Relation and Mixture are both aspects of Variation.  In that sense, we can combine pairs of the sphairai as below:

  • 1/9: Mercury/The Monad — Becoming
  • 2/8: Air/Light — Variation
  • 3/7: Fire/Water — Accordance
  • 4/6: Sulfur/Earth — Structure
  • 5: Salt — Growth
  • 10: Darkness — Being

Thus we have four pairs of sphairai and two sphairai left over.  Coincidentally, these leftover ones have the qualities of Growth (Pentad) and Being (Decad), and I mentioned above that I feel like these two numbers (with Mēden/Nothing as 0) could be paired together as well as one metaquality, say “Reality”.  Of the other four pairs, only one pair has a path between themselves (Air and Light); as both these sphairai fall under the banner of Variation, it could indicate that it is by means of Air (which gives sense to sound, distance, and sight) and Light (by which we see, are seen, and Work) that such variation can be reckoned and worked with.  The other three pairs (Mercury and the Monad, Fire and Water, Sulfur and Earth) lack such a path.  Moreover, these three pairs lack a path in different ways:

  • There’s a clear space for a connection between Mercury and the Monad, but this connects the central sphaira with one of the outermost, which is not allowed.  However, the geometry of this path would mimic that between Darkness/Water and that between Light/Air.  I interpret this to indicate that although the motion needed is possible to make for this path (geometry exists elsewhere), the “distance” to the Monad from Mercury is too far to make.  They’re both Becoming, but at such different stages; one is conception, the other manifestation.
  • Fire and Water are on the same rank of the Tetractys (within the Tetrad), but are separated from each other by the sphaira of Air between them.  No direct connection can be made; either one goes directly through Air, or rises to and falls from Sulfur to get to the other.  Both these forces represent the metaquality of Accordance, and thus need something else to accord with, since these two forces are diametrically opposed to each other.
  • There’s a clear space for a connection between Sulfur and Earth, but this would connect one of the outermost sphaira with one of the middling ones on the far side of the Tetractys.  No other path like this exists, and the disparity between the two is great enough to be geometrically disallowed.  This indicates that, although they both represent Structure, they represent them in two completely different and unrelated ways, an internal, dynamic, and spiritual way (Sulfur) and an external, static, and material way (Earth).  I’d compare these two things to the cardiovascular system and the skeletal system; both are needed to organize and arrange the human body just so, although the former is fluid and quick while the latter is fixed and solid.

alchemical_planetary_tetractys_paths

While I’m not sure how far to take this analysis of numerological qualities/metaqualities and the sphairai on the Tetractys, it does offer me more food for thought as I explore them and the paths that connect them more.  Besides, these give me interesting ways to think about the sphairai on the Tetractys; it’s not inconceivable that these qualities can be used as names for the sphairai themselves, much as the qualities of God are used as names for the sephiroth on the Tree of Life; instead of Victory, we have Essence (or, in Greek, Ουσια).  Alternatively, they could just be called by their force (Water, Υδωρ) or their systemic number (Heptas, Επτας).  While this post seems, in retrospect, to be more mental exercises in analysis rather than digging out occult secrets, there’s still plenty here to chew on as I contemplate and delve deeper into this system-in-development.

Traversing the Paths on the Tetractys of Life

There hasn’t been much talk here about the paths themselves on the Tetractys since we figured out a way to associate letters to them.  Largely, this is because I’ve had a hard time figuring out where to start.  I mean, I developed the whole mathesis thing out of a need to work with a Greek system of paths between the spheres on the Tree of Life, yet never actually did much pathworking or meditation on the paths themselves on the Kircher Tree (which, though it goes against my usual advice, I think was justified here).  I know that the paths describe a means of change and evolution from one emanation to the next, yet beyond that…it was hard to say.  Since then, I’ve been looking at the Tetractys and trying to figure out where to start.  Unlike the Tree of Life in qabbalah that so conveniently gives us Malkuth as the starting line for our Work, the Tetractys doesn’t have anything so readily apparent.  Then again, the answer was literally staring out at me from the middle of the whole thing, and it’d be a shame for me to ignore my own patron god Hermes at this point.  Starting with that brief moment of inspiration, I started from the middle of the Tetractys and worked my way out, and now I’ve ended up developing a way to traverse the sphairai on the Tetractys of Life in an ordered and coherent way.  Bear with me guys, because this post is going to be a little lengthy to get all my thoughts out.

So, we have our Tetractys of Life.  For simplicity’s sake, let’s ignore the letters on the paths and focus just on the existence of the paths:

alchemical_planetary_tetractys_paths

First, let’s talk about having a single “path” (really, a network of paths between individual sphairai) that traverses the whole Tetractys sphere by sphere.  I propose the following schema:

  1. Mercury
  2. Air/Jupiter
  3. Fire/Mars
  4. Sulfur/Sun
  5. Mercury
  6. Salt/Moon
  7. Earth/Saturn
  8. Water/Venus
  9. Mercury
  10. Light/Fixed Stars
  11. Monad
  12. Darkness/Earth

Graphically, the paths on the Tetractys selected between these sphairai look like this:

alchemical_planetary_tetractys_paths_circuit1

I’ll bet you’re confused.  For one, we have twelve spheres listed, with Mercury being listed three times; shouldn’t we have to go through each sphere only once?  Second, we’re starting with Mercury and not the Monad; shouldn’t we start with the Monad being the All and the Source of all?  Well, sorta.  I’ll admit, my background in qabbalah was inhibiting me from running with this sequence of paths, but then, mathesis is not qabbalah, and the Tetractys is not the Tree.  In Hermetic qabbalah or Jewish kabbalah, we have a clearly defined start and end, a Source and a Destination, and either of them will be Kether or Malkuth depending on whether you’re going up or down the Tree.  However, while the Tree is like an elaborate map, the Tetractys presents us with something different, like a blueprint.  Instead of showing how things come to be in a linear fashion, the Tetractys shows the presence and building blocks of life present in all things; the Tetractys shows how things come to be in a nonlinear fashion.  There is no single end goal with the Tetractys; the Monad descends into the Tetrad, not any one of the four elements alone.  All the parts of the Tetractys must be constantly and repeatedly traversed to become complete both of ourselves and of the cosmos, encompassing all aspects of the act, process, and result of Creation.

As for passing through the sphaira of Mercury, let’s talk about what we’re doing on the paths first.  We start with what looks like the Mitsubishi logo around the Tetractys: three rhombuses each with one acute corner at the Mercury sphaira and the other acute corner at one of the distant corners of the Tetractys.  I’ll call each of these three sets of four sphairai a system, and each system focuses on a particular theme:

  • The Hot System involves the active principles of Air, Fire, and Sulfur.  Processes of power, actively causing change.
  • The Cold System involves the passive principles of Salt, Earth, and Water.  Processes of reception, passively receiving change
  • The Cosmic System involves the encompassing principles of Light, the Monad, and Darkness.  Processes of cosmic stasis and unity.

In each case, we both start and end at Mercury, both astrologically and alchemically, being the center and present in nearly all things except the purest and most extreme of all elements: Earth, Fire, and the Source itself.  Everything else is connected with Mercury, so it makes sense that it’s the only one that can reasonably allow us to translate between the three systems. Yes, we can go from Water to Air (traversing the Cold and Hot Systems directly), Sulfur to Light (Hot and Cosmic), or Salt to Darkness (Cold and Whole), but a better balance can be preserved and future progress can be assured by always returning to Mercury.  If we spend some time in the Hot System, we should pass from Sulfur through Mercury to Salt, because Mercury is what naturally balances the two forces.  At the end of the Cold System, we pass from Water/Venus to Light/Stars; though it’s not immediately apparent how Mercury balances these two, consider the myth of Aphrodite being born from Ocean (Water) from the remains of Ouranos (Sky); the ability to create physically comes from supercelestial impetus and the latter is accomplished by the former, but also consider the endless horizon is the meeting point of the two realms.  At the end of the Cosmic System, we proceed from Darkness to Air; again, an awkward comparison to make, but recall that in the Poemander myth of creation, air is what separated the heavens from the mixed mass that would eventually become the Earth, and the ability to begin the process of rising and falling through the spheres is accomplished by means of air as an intermediary.  Mercury is a symbol of strong change, but not in a way that changes something into its direct opposite; rather, Mercury changes something into its complement, something that completes and links the two systems together.

The use of systems here isn’t just to provide a way to go through all the sphairai of the Tetractys in one go.  Rather, within each system are four sphairai and four paths, forming a kind of mini-tetractys within each system in a mini-cycle.  While one can traverse each system once to complete the whole Tetractys, I see it being worthwhile to cycle through each system several times to really grok and complete the work that needs to be done in each.  If we consider the three phases of alchemy (nigredo, albedo, rubdeo), then each system can be viewed as one of these stages, and it may take time for the Work from each phase to settle in.  Going through each stage of the work thoroughly requires several iterations; for instance, cycling through the Hot system four times would yield a pass each to focus on the ideas of Hot, Hot-Air, Hot-Fire, and Hot-Sulfur.  By cycling not only through the Tetractys as a whole but within each system on the Tetractys, we can begin to fully understand each force in its entirety and on its own terms.

All this leads to the cycle of paths that this “Mitsubishi” arrangement forms.  We start with Mercury then descend into the Hot System by progressing to Air, drying ourselves into Fire, and rarefying ourselves into Sulfur.  From there, we return to Mercury, cooling down and becoming pure Salt, degrading into Earth, then quickening into Water.  After that, we return to Mercury, ascend into the Light, achieve union or the image of the Source, then descend back down to Darkness.  From there, we repeat the process over again, returning to Mercury and heating up again into Air, cycling through the Tetractys infinitely and repeatedly, each time becoming more powerful with each sphaira and each time achieving more and more of the henosis that is the Great Work.  So, a full set of iterations to proceed throughout the whole Tetractys in this manner would involve a total of four stages that I tentatively call Initiations, progressing through the different systems or within the same system to obtain a deeper understanding of each force.  Keeping the same order within each system, the whole schema looks like this:

  1. Hermetic Initiation
    1. Hot System (Mercury → Air → Fire → Sulfur)
    2. Cold System (Mercury → Salt → Earth → Water)
    3. Cosmic System (Mercury → Light → the Monad → Darkness)
  2. Hot Initiation
    1. Hot System with a focus on Mercury (e.g. a deeper acquaintance of the Hot forces)
    2. Hot System with a focus on Air (e.g. seeing Air and how it relates and acts throughout the Hot forces)
    3. Hot System with a focus on Fire (e.g. same as above but with Fire)
    4. Hot System with a focus on Sulfur (e.g. etc.)
  3. Cold Initiation
    1. Cold System with a focus on Mercury
    2. Cold System with a focus on Salt
    3. Cold System with a focus on Earth
    4. Cold System with a focus on Water
  4. Cosmic Initiation
    1. Cosmic System with a focus on Mercury
    2. Cosmic System with a focus on Light
    3. Cosmic System with a focus on the Monad
    4. Cosmic System with a focus on Darkness

And, after this, we’d repeat the whole thing over again as many times as desired or as necessary until we achieve the Great Work.  Besides, by completely cycling through the whole Tetractys (at least in the Hermetic Initiation) starting and ending with Mercury, we hit Mercury four times, and four is a number mythologically sacred to Hermes.  And, if we consider all the Initiation passes together, we pass through the entire Tetractys a total of five times.

So, in this manner, we have a set of twelve paths traversing three systems within the Tetractys.  Each system is composed of four sphairai, all starting with and ending with Mercury; Mercury is then a liminal point between the three “worlds”, both starting and ending each set of paths within an system.  We constantly proceed from and return to Mercury as a central hub or nexus.  However, with our twelve Mitsubishi paths, we leave another set of twelve paths unused.  What are these paths?

alchemical_planetary_tetractys_paths_circuit2

These twelve paths never touch central Mercury or the extreme Earth, Fire, or Monad sphairai at all, but instead connect the six “middling” sphairai of Darkness, Salt, Water, Air, Sulfur, and Light.  Two cycles are presented here, shown by the hexagram paths (inner cycle) and hexagon paths (outer cycle).  Instead of having systems, we have one group of six sphairai that are each connected to everything but their complement (e.g. Salt and Sulfur, Water and Light) and four leftovers that are unconnected which would link everything else together.  Rather than getting us to henosis and the Monad, or alternatively to a fundamental understanding of how our cosmos works through Earth and Fire, these cycles keep us trapped, never able to each any extreme and never having the ability to reasonably transform ourselves into anything we need to progress.

Between the Mitsubishi paths and hexagram/hexagon paths, I think we have a distinction of how things progress within the cosmos as shown by the Tetractys.  The hexagon and hexagram paths indicate a cycle of reincarnation, always stuck hovering around and just under the things that truly break them out but never quite within reach; the one thing that can do that is Mercury, which they constantly rely on but never call upon. We’ll call these set of paths the Agnosis Schema, as opposed to the Mitsubishi paths which I’ll call the Gnosis Schema.  The Gnosis Schema connects all the sphairai together and in a way that encourages, well, enlightenment in almost a Buddhist sense of extinguishing the process of forced rebirth and reincarnation, freeing ourselves from the trap of maya or ignorance that keeps us in the cycle of being reborn without our control.  In other words, the Gnosis Schema allows us to be reborn by choice and free ourselves from this Hermetic samsara, which is a world of difference from the Agnosis Schema; we can deliberately choose to go to places that we’d never end up in involuntarily or by accident.  We continue around the Gnosis Schema as long as we need or desire to until that last iteration where we go to the sphaira of the Monad and stay there, never returning to Darkness to continue the cycle.  (And, of course, metempsychosis or reincarnation was indeed a belief of Pythagoreanism and Neo-Platonism, so I’m in the right here to bring that beast of a topic into this.)

So, going back to the Gnosis Schema of paths, we can use the order of them to figure out a numerical assignment from 1 to 10 of the sphairai on the Tetractys of Life.  Again, if we start with Mercury as the start, we assign it the number 1 and proceed along the Gnosis Schema paths in order, skipping over where Mercury is repeated:

  1. Mercury
  2. Air/Jupiter
  3. Fire/Mars
  4. Sulfur/Sun
  5. Salt/Moon
  6. Earth/Saturn
  7. Water/Venus
  8. Light/Fixed Stars
  9. Monad
  10. Darkness/Earth

This system of numbers is grossly different from that of the qabbalistic scheme of things, and rightly so.  We’re not describing a path of linear descent from the Source to the World, but a means of cyclical progressive process that continually builds one up further and further until they reach the Highest without having to go down lower anymore.  Described numerically, the Tetractys looks like the following:

numerical_tetractys_gnosisBear in mind that, although each of the sphairai are associated with some celestial heaven (from the Prime Mover to the World we live in), these numbers do not describe their level.  The celestial numbers of the heavens stay as they are, such that Saturn is still the third heaven (from the Top), and so forth.  If we were to compare the cosmological number of each of the sphairai (based on their planets) with the Gnosis Schema numbering (based on their alchemical force), we end up with the following table (which is an exercise in polyvalent thinking):

Sphaira Gnosis Schema Cosmological
Alchemical Planetary
Mercury 1 8
Air Jupiter 2 4
Fire Mars 3 5
Sulfur Sun 4 6
Salt Moon 5 9
Earth Saturn 6 3
Water Venus 7
Light Fixed Stars 8 2
The Monad 9 1
Darkness The World 10

Note that two of the sphairai, the Monad and Mercury, are essentially the same when it comes to what their force is: the planetary force of Mercury and the alchemical force of Mercury are so close that they’re conceptually synonymous.  Likewise, the Monad is…well, the Monad.  There’s literally only one Monad in any system of thought here.  However, look at the numbers: we see two of the sphairai, those of Venus/Water and Darkness/World, have the same number in both systems.  While these are the exceptions to the rule, they’re exceptions worth noticing.  That Darkness/World is 10, the final stage in the emanatory process, is unsurprising; it is completion, it is the ending, it is the goal of creation to create the World.  Although it is present in the Dyad in contrast to Light/Fixed Stars and thus “comes first” before anything lower, the entirety of the World can only exist when all the other forces are present to give it life, animacy, and agency.  As for Water/Venus, it’s interesting that it’s kept the number seven between the two, that of essence and quality of life.  It’s low down on the Tetractys as part of the Tetrad, but all the same it’s vital to giving things animacy, as opposed to Darkness/World which is what is given animacy.

Personally, I feel it appropriate to comment on what the Gnosis/Agnosis Schemas mean for the individual letters of the paths themselves.  For instance, note that all the Air paths (letters Υ, Φ, Ψ, Σ, Δ, Μ) are all part of the Agnosis Schema, as well as the other fixed signs (letters Φ, Κ, Ν) as well as the other elemental paths (letters Χ, Ξ, Θ).  The twelve letters that belong to the Gnosis path are Ο, Ζ, Π, Ε, Η, Λ, Τ, Ω, Α, Β, Ρ, and Ι, which are the six non-fixed non-Air signs and the six non-Jupiter planets.  However, all I’ve done so far is figure out which abstract paths to take regardless of their letters; I fully expect my Tetractys of Life to have its letter-path assignments change over time as I fine tune and explore the system deeper.  The system, as of now, is coherent and structured, which I like, but who knows whether it’s actually valid and practical to use.  That’s what further writing and scrying is for, and now that I have an actual path to pathwork, I think that process should begin soon.

Towards a Greek Kabbalah: Letters on the Paths of the Tetractys

Where do we stand on our system of kampala, or Greek kabbalah?  We have letters, we have spheres, we have paths.  We’ve combined the paths with the spheres, and now we need to combine the paths with the letters.  This is the last big thing we have yet to do in order to fully develop our use of Greek letter-number-stoicheia mysticism into a full-fledged theurgic framework, turning simple grammatomancy into grammatotheurgy.  Last we checked in on our Tetractys of Life, we have the following ten spheres linked together with a set of 24 paths: alchemical_planetary_tetractys_paths Each sphere is associated with a particular alchemical concept as well as a cosmic heaven, all coming down from the single, divinely simple, undifferentiated, all-generating Monad.  Seven of the ten spheres are moderate enough in their forces to be connected as completely as they can, while three are too extreme to be connected to any except their closest two forces.  So far, so good.  Now, let’s talk about the letters of the Greek alphabet.  It’s hard to assign the letters to these 24 paths based on their symbolic looks alone, and although the Greek letters are number, it’s also difficult to assign pure number to the paths by virtue of their cardinality, parity, or magnitude.  However, we have another route: using the stoicheia, or occult associations, of the Greek letters, which provide many more qualities and concepts on their own which can help us to figure out which path might best be represented on our Tetractys of Life.

Recall that the practice of stoicheia assigns one of the 12 signs of the Zodiac, one of the seven planets, or one of the five elements to each letter of the Greek alphabet.  After all, 12 + 7 + 5 = 24, so this can easily be done.  And, lo, it is!  Recall that there are three groups of letters in the Greek consonants: vowels, simple consonants, and complex consonants.  There are seven vowels (Α, Ε, Η, Ι, Ο, Υ, Ω), twelve simple consonants (Β, Γ, Δ, Ζ, Κ, Λ, Μ, Ν, Π, Ρ, Σ, Τ), and five complex consonants (Θ, Ξ, Φ, Χ, Ψ).  In that case, our division has already been made for us.  We give each of the vowels to one of the seven planets, starting with Alpha as the Moon and Ōmega as Saturn; we give each of the simple consonants to the twelve signs of the Zodiac, starting with Bēta as Aries and Tau as Pisces; we give each of the complex consonants to one of the five elements from most dense to least dense, from Thēta as Earth to Khi as Fire and Psi as Spirit.

The simplest way to assign these forces and their corresponding letters to the Tetractys of Life would be to base the selection on the geometry of the paths itself.  For instance, in the Jewish kabbalah’s Tree of Life which uses the 22 letters of the Hebrew alphabet, there are three sets of paths: twelve diagonal paths, seven vertical paths, and three horizontal paths.  The diagonal paths are given to the zodiac signs; the vertical paths are given to the planets; the horizontal paths are given to the elements (Hebrew mysticism recognizes only Air, Fire, and Water as elements, with Earth and Spirit not being considered).  Kalagni over at Blue Flame Magick describes how he developed his own set of qabbalistic correspondences between the paths and the Hebrew letters based on their stoicheia, finding a closer resonance to the Jewish practice using the Hermetic Kircher Tree, which is different from the traditional Jewish kabbalah Tree of Life.  The Golden Dawn’s use of the Tree simply plots each path in a particular order from 11 at the top to 32 at the bottom, and gives each path a letter based on its order in the alphabet.  Kalagni and I agree in that this doesn’t suit the actual significance of the letters, so I should find some way to assign the Greek letters to the Tetractys of Life based on the geometry of the paths themselves.

Unfortunately, the 24 paths on the Tetractys don’t split up well into groups of 12, 7, and 5, so of course I’m going to have to think about this and figure out deeper connections that aren’t immediately apparent.  However, 24 is a nice number and can be easily and evenly divided into many smaller numbers: 2, 3, 4, 6, 8, 12.  Is it possible to use any of these factors to devise a scheme to divide the zodiac signs, elements, and planets into even groups?  And, if so, is there a coherent way to assign these groups to different groups of the paths? Recall from our meditations on the Greek divine name ΙΑΩ that we were able to divide the paths up into four groups of six: horizontal, right-going, left-going, and hexagram:

The number four immediately brings to mind the lowest rank of the Tetractys, the realm of the four elements: Earth, Water, Air, and Fire.  It might be possible that each of the paths in each set given above shares something about one of the elements in common, but how might we discern what those connections and relationships might be?  Let’s take a closer look at what the paths are actually connecting, again going back to our meditations on ΙΑΩ.

  • The paths that go right increase in activity; they are an expression of the masculine or active principle between levels of manifestation.  The Monad, as it differentiates itself into a Dyad, becomes the active force of Light; as Light differentiates itself, it becomes the active force of Sulfur; as Sulfur differentiates itself, it becomes the active force of Fire.  Fire is the lower-rightmost sphere on the Tetractys, indicating that the active principle as represented by an element is Fire.  The paths that go right are thus best associated with the element of Fire.
  • The paths that go left increase in passivity; they are an expression of the feminine or passive principle between levels of manifestation.  Thus, as the Monad descends into the elemental world, it becomes first Darkness, then Salt, then Earth, which is the lower-leftmost sphere on the Tetractys.  The paths that go left are associated with Earth.
  • The paths that are horizontal change in activity or passivity depending on which direction you’re going, but do not change in a level of manifestation.  The Monad, being undifferentiated, cannot change from itself except into itself; Darkness becomes Light, and vice versa; Salt becomes Mercury, and Mercury becomes Sulfur, and vice versa; Earth becomes Water, Water becomes Air, and so forth.  These horizontal paths demonstrate fluidity in energy while maintaining manifestation, which I understand to be the primary quality of Water, which flows from place to place.  The horizontal paths are associated with Water.
  • The hexagram paths change in diverse ways, some only in manifestation level while preserving the active/passive balance, some in drastic active/passive ways while changing manifestation only slightly.  The ability to change in such dramatic ways that should normally take several paths speaks of the quality of Air to me, since Air allows communication over long distances as well as rising and setting among and filling the gaps between the many heavens.  The hexagram paths are associated with Air.

Okay, so now we have four sets of paths that each share an element.  Thus, there should likewise be a way to divide up the 24 letters of the Greek alphabet into four groups of six by respecting their elemental associations.  We know that there are four letters for the four elements of Earth, Water, Air, and Fire; we also know that there are 12 letters for the signs of the Zodiac, which can be divided up by triplicity (elemental quality) into four groups of three.  Thus, we already have four groups of four letters for a total of 16:

Earth Water Air Fire
Capricorn Cancer Libra Aries
Taurus Scorpio Aquarius Leo
Virgo Pisces Gemini Sagittarius

This leaves seven planets and the leftover element of Spirit for a total of eight more letters.  Spirit, for the purposes of this analysis, can be considered a planet, since Spirit is not truly an element, nor is it truly a planet or zodiac sign, but a type of meta-force that can fit anywhere and accomplish anything as a foundation for other forces to combine and work with it.  Since Spirit is kinda-sorta higher than an element and kinda-sorta lower than a planet, yet can fit amongst either, we can think of these as a group of eight forces, which can be divided up into four groups of two based on their element.  Happily, by our association of the planets with the elements in our alchemical Tetractys of Life, we already know that Saturn is of Earth, Venus of Water, Jupiter of Air, and Mars is of Fire.  This leaves the Moon, Sun, Mercury, and Spirit:

  • The Moon, being on the direct descent from the Monad along the Earth paths to Saturn is given to the element of Earth.
  • Similarly, the Sun is given to Fire, since it’s on the direct descent from the Monad along the Fire paths to Mars.
  • Mercury is present in the center of the Tetractys, able to change in many ways to many other forces but never in the same ways that the Air paths do, leaving Mercury assigned to Water.
  • Spirit, being leftover, is given to Air.  However, Spirit as a raw force can transform anything into drastically different forces, performing miracles and works that no other element can, so this attribution is also fitting.

So now we have four groups of six forces, zodiacal and planetary and elemental, divided up along elemental lines:

Earth Water Air Fire
Saturn Venus Jupiter Mars
Moon Mercury Spirit Sun
Capricorn Cancer Libra Aries
Taurus Scorpio Aquarius Leo
Virgo Pisces Gemini Sagittarius

Alright, so now we need to find a way to assign the forces to the paths.  Of the four groups of paths, the Air sign is the odd one out (since it doesn’t fit the pattern of the other three), so let’s leave that aside for now and focus on the Fire, Water, and Earth paths.  We know that we can divide up these groups of six paths into a kind of partial-tetractys of their own consisting of three ranks (a trictys?): the first row has one path, the second row has two, and the third row has three.  We know that, among each division of our forces, we have one element, two planets, and three signs:

Element Earth Water Air Fire
Planet Saturn Venus Jupiter Mars
Moon Mercury Spirit Sun
Sign Capricorn Cancer Libra Aries
Taurus Scorpio Aquarius Leo
Virgo Pisces Gemini Sagittarius

So, based on this 1/2/3 division of both paths and forces, we can assign the single element to the single path of each group, the two planets to the row of two paths in each group, and the signs to the row of three paths in each group.  Assigning the element to the single path is trivial: give Water to the topmost horizontal path, Fire to the leftmost right-descending path, and Earth to the rightmost left-descending path: Tetractys_paths_elements_AWE We know that we have three sets of two planets, and one set is attributed to the elemental spheres directly on the lowest rank of the Tetractys of Life.  The other three appear higher up, indicating a more unmanifest or rarefied nature.  The Fire and Earth planetary paths have an upper path that link the Dyad and Triad and a lower component that link the Triad and Tetrad.  The lower path is given to the “lower” planet, lower as in the sense of manifestation according to the Tetractys, while the upper path is given to the “higher” planet in the same sense.  Thus, the upper path of Fire is given to the Sun, and the lower path to Mars, and the upper path of Earth is given to the Moon and the lower path to Saturn.  The Water path only has two horizontal components within the same rank, though one connects to a passive reagent and the other to an active reagent.  The path that connects to the passive reagent is considered “lower” in the same sense as above, as the path that connects to the active reagent is considered “higher”; thus, the leftward path of Water is given to Venus, and the rightward one to Mercury.

So far, so good.  This only leaves the three paths of each set to be given to the three signs of the Zodiac for each element.  Each of the three Zodiac sign belonging to the same triplicity (element) is assigned a different quadruplicity, also known as a modality: cardinal, fixed, and mutable.  Cardinal signs initiate and begin; fixed signs maintain and hold; mutable signs degrade and prepare for transformation.

Element Earth Water Air Fire
Planet Saturn Venus Jupiter Mars
Moon Mercury Spirit Sun
Sign Cardinal Capricorn Cancer Libra Aries
Fixed Taurus Scorpio Aquarius Leo
Mutable Virgo Pisces Gemini Sagittarius

It’s a staple of astrology that the fixed signs best represent their element, and we know from our meditations before on the name ΙΑΩ that the central path in the row of three paths “maintains” or holds the same essence as the single path on the far side of the tetractys.  Thus, since that single path represents an element, the middle path on the other side of the tetractys should be the Zodiac sign that best represents that element, i.e. the fixed sign.  Thus, the middle path on each side of the Tetractys should be given to Taurus for the Earth paths, Scorpio for the Water paths, and Leo for the Fire paths: Tetractys_paths_elements_FWE_fixed From this, it remains to assign the cardinal and mutable signs.  Much as how we assigned the “active” planet to the upper or leftward-horizontal path and “passive” planets to the lower or rightward-horizontal paths based on whether they were more manifest or unmanifest in the Tetractys, we can apply a similar method here based on whether a zodiac sign is cardinal (more active) or mutable (more passive).  Thus, as we read the Earth zodiac sign paths from the Monad down to the bottom, we read Capricorn, Taurus, Virgo; as we read the Fire zodiac sign paths from the Monad down to the bottom, we read Aries, Leo, Sagittarius.  The Water paths are more active on the right and more passive on the left, so if we read the Water zodiac sign paths from left to right, we read Pisces, Scorpio, Cancer: Tetractys_paths_signs_FWE Alright!  That covers it for the Fire, Water, and Earth paths of the Tetractys.  That only leaves the confusing hexagram paths of Air, where we can’t use the above system as cleanly anymore.  For one, instead of having three groups of 1, 2, and 3 paths, we have two cyclical sets of 3 paths each.  Both of these cycles have one vertical path, one right-going path, and one left-going path, so neither of them have an imbalance of passivity or activity.  We know that there are three signs of the Zodiac, though, so we can say that the Zodiac signs should all belong on one triangle and the element and two planets (really, the one planet Jupiter and the one meta-element of Spirit) go on the other.  So which should be which?  And, moreover, how do we figure out which line of the zodiac triangle paths is cardinal, fixed, or mutable?

Remember that, in our meditations on the name ΙΑΩ, we linked the long hexagram paths to the different sides of the Tetractys based on how the middle path of the side of the Tetractys linked to the single apex path on the far side.  These long paths then shared the same letter of ΙΑΩ as their shorter rectangular-end paths.  We can apply something similar here, too.  Also remember that 24 is divisible by many numbers, and we’ve so far been thinking about it as 4 × 6.  However, if we link the long paths of the hexagram with the Fire, Water, and Earth sets of lines as we did before with the name ΙΑΩ, we end up with 3 × 8, or three groups of eight paths:

Now, instead of thinking about the groups of paths in terms of four elements, let’s think about them in terms of the three modalities: cardinal, fixed, and mutable.  Cardinal signs are the most active; fixed signs are between active and passive; mutable signs are the most passive.  Thus, if we link these notions of activity and passivity to the three non-Air elements, we get cardinal signs associated with Fire (since they increase in activity), fixed signs with Water (since they hold the level of activity or passivity just as Water maintains manifestation across a rank of the Tetractys), and mutable signs with Earth (since they increase passivity).  Thus, on the triangle that gets the zodiac signs of Air, the paths linked to (at right angles with) the paths of a particular element receive that element’s modality.  So which triangle is the zodiac triangle, and which is the element/planet triangle?

Looking at the triangles, we notice that the one that “points” to the left has a “base” (connecting Light and Air) on the right side of the Tetractys, giving it a foundation of activity tending towards passivity.  Similarly, the triangle that points to the right has a base (connecting Darkness and Water) on the left side, giving it a foundation of passivity tending towards activity.  The type of forces that we’re looking at is the key here: the fixed stars do little on their own besides radiate power, while the planets and elements actively manifest and create far down below.  The fixed stars, then, emit power but do not control it, letting their power and presence be used rather than actively using themselves; the planets and elements emit and radiate their power in the ways they find best for them, acting more than being acted upon.  Thus, the zodiac signs are best given to the triangle pointing to the right, since they’re mostly passive with tendencies towards action, while the planets/elements are best given to the triangle pointing to the left, since they’re mostly active with tendencies towards being acted upon.

So, if the Air signs of the Zodiac are given to the right-pointing triangle, and we know that the vertical line is fixed, the right-going line is mutable, and the left-going line is cardinal, we end up with this arrangement: Tetractys_center_triangle_right_signs Therefore, the left-pointing triangle is given to the forces of Air, Jupiter, and Spirit.  These don’t really fall into the scheme of cardinal/fixed/mutable, but we do know that for the Fire, Water, and Earth sets of paths, the path for the element is always on a “higher register” directly above the fixed sign on the far side of the Tetractys.  If we apply that same logic here, we see that the fixed Air sign Aquarius is on the vertical path of the right-pointing triangle, so the element of Air itself should go on the vertical path of the left-pointing triangle.  Between the planet Jupiter and the quasi-element Spirit, we can argue that Spirit is the more malleable, pervasive, and changeable than the firm and lofty power of Jupiter, which would make Jupiter more active than Spirit.  Since the only two choices we have left here are for a cardinal-active path and mutable-passive path, that would set Jupiter on the path opposite Libra and Spirit on the path opposite Gemini, with the result like this: Tetractys_center_triangle_left_forces And that’s it!  All told, now we have all 24 paths assigned to the 12 signs of the Zodiac, the seven planets, the metaelement Spirit, and the four classical elements in a logical and coherent manner.  This means that we can finally associate each path of the Tetractys of Life with a letter, and with it a number and stoicheic force, in a manner like the following:

 

alchemical_planetary_tetractys_paths

You’ll note that there’s some criss-cross of the paths in the center where the hexagram paths overlap with the others.  In cases like this, the path on top is going to have its associated letter’s numerical value odd (if the one on the bottom is even) or greater than the one on the bottom (if they’re both odd or both even).  To determine an odd number or even number, I ignore the magnitude of the number and reduce it to a number 1 through 9; thus, Kappa, given the value of 20, is reduced to 2, so Kappa is even.  Likewise, Tau, given the value of 300, is reduced to 3, which makes Tau odd.

For the more tabularly inclined, here’s a helpful table plotting out each of the 10 spheres and the 24 paths of the Tetractys of Life, along with a bit about the Pythagorean virtues associated with each sphere on the Tetractys:

Sphere Lambdoma Alchemy Cosmological Virtue
1 1 Monad Infinite Light Henosis
2 2 Darkness Mundus Intuition
3 3 Light Fixed Stars Love
4 4 Salt Moon Satiety
5 6 Mercury Mercury Detachment
6 9 Sulfur Sun Submission
7 8 Earth Saturn Fortitude
8 12 Water Venus Prudence
9 18 Air Jupiter Temperance
10 27 Fire Mars Justice
Path Letter Number Stoicheia Spheres
1 Α 1 Moon 3 5
2 Β 2 Aries 1 3
3 Γ 3 Taurus 2 4
4 Δ 4 Gemini 2 6
5 Ε 5 Mercury 5 6
6 Ζ 7 Cancer 9 10
7 Η 8 Venus 4 5
8 Θ 9 Earth 6 9
9 Ι 10 Sun 2 5
10 Κ 20 Leo 3 6
11 Λ 30 Virgo 4 7
12 Μ 40 Libra 6 8
13 Ν 50 Scorpio 8 9
14 Ξ 60 Water 2 3
15 Ο 70 Mars 5 9
16 Π 80 Sagittarius 6 10
17 Ρ 100 Capricorn 1 2
18 Σ 200 Aquarius 2 8
19 Τ 300 Pisces 7 8
20 Υ 400 Jupiter 3 4
21 Φ 500 Air 3 9
22 Χ 600 Fire 4 8
23 Ψ 700 Spirit 4 9
24 Ω 800 Saturn 5 8

As it turns out (and this was entirely unplanned), this is the tenth post in the series on developing a Greek kabbalah, kampala, Pythagorean framework, tetractean theurgy, or whatever.  In Pythagorean mysticism, the number ten itself is holy, being the number of completion and the number of points in the tetractys, as well as being a unity of a higher order (tens instead of ones).  This post then completes the first cycle of this study, where we now have the basic framework, tools, and understanding needed to progress further in working this system and seeing where it can take us.  At the beginning of this project, I wanted a kabbalah-like system of theurgy and mysticism that would replace the use of Jewish kabbalah or Hermetic qabbalah in place of something that felt closer to what I actually study and practice, and outlined a series of goals to that end:

  1. Provide a cosmological framework that allows for the ten spheres of the cosmos (Earth, Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, Fixed Stars, Divinity)
  2. Provide a cosmological map that allows for traversing the spheres of the cosmos with paths that connect them together
  3. Provide a mapping between the paths of the map with the 24 letters of the Greek alphabet
  4. Provide a means of starting from awareness on the Earth sphere (where the majority of us live and operate on a day-to-day basis) and reaching any other sphere by means of the paths, especially that of Divinity
  5. Provide a description of the creation of the cosmos by means of the cosmological framework and mapping
  6. Provide a means of correspondence to link other forces, concepts, objects, etc. to the paths and spheres on the framework and map
  7. Be rooted primarily in Neoplatonic and Pythagorean thought, referencing Hermeticism as necessary without relying on explicitly Jewish principles that are not also present in Hermeticism

How did we do?  For the most part, we hit nearly all of these targets, and most of them dead center in our targets.  The only things that really need to be explored now are, well, the Tetractys itself.  Sure, we’ve analyzed it and meditated on it and written a lot about it, but all this has been an intellectual exercise.  Now that we have a map of the cosmos, we need to start exploring the cosmos with the help of our map.  All this is theoretical, based on relationships between alchemical and astrological principles, and now we need to put the theory to the test.  How is it that we can use the Tetractys of Life to rise through the spheres, both of the heavens as well as of reality itself, and refine ourselves to reach the One?  For that, we now get to apply our meditations and go deeper into new worlds.  In the future, as I discover more about this system and apply any necessary tweaks or refinements, or perhaps come up with a better name than kampala or Greek kabbalah (though I like the ring of “tetractyeon” more and more) I’ll discuss more about it, but I’m going to bring this series to a close for now.  As one of my favorite games has said, perhaps the ending has not yet been written.

Also, I want to give a shoutout to my good friends Rev. Michael Strojan and Kalagni for helping me out with this.  Without them, I’d still be fighting over some of the petty details and quibbling about path arrangement and such, but their vast knowledge and sharp ingenuity really guided me along the way.  Guys, thank you.