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: 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:

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:

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:

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: 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.

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: 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: 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: 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: 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:

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:

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.