Clarifications on Terms for Symbols

It’s a bit of a pet peeve of mine when people badly use terms in an occult context.  To be fair, different traditions may use certain terms in particular ways that are specific to that particular tradition, which may or may not differ from normal use.  Other groups treat some terms completely interchangeably when, strictly speaking, the terms signify different things.  Generally, however, there’s not much rigor in how people use specific terms, and end up misusing them (through their own ignorance and confusion) or abusing them (to intentionally mislead or annoy others).  I’d like to clear up a few things and offer some of my definitions for particular terms used in an occult context, this time focusing specifically on terms used for different types of symbols.

For any of these terms, “symbol” is the highest-level term I can think of for any of these following terms.   If you’re not sure what kind of symbol a particular thing is, just say “symbol”.  Everyone understands that.  Not everyone understands what a particular person means by “sigil” or “rune”, however.  Granted, these words are given with my personal definitions, and again, may not be those used by other traditions.  However, for the sake of having a regular inventory of words with specific, unambiguous meanings, here’s how I use these particular things.

Glyphs are symbols used to indicate a basic thought or sound.  In other words, a glyph is much like a written-down word.  Individual letters communicate sounds; individual numerals communicate numbers; individual Chinese characters communicate sounds or concepts or words; the glyphs for the planets, zodiac signs, elements, and alchemical concepts communicate those things and only those things.  Glyphs are essentially a generalized notion of a letter in an alphabet; they are characters in a writing system that includes letters, numbers, punctuation,  labels, and so forth.  Glyphs may or may not be used in an occult context; for instance, these words you’re reading right now are composed of glyphs (letters and punctuation of the English alphabet), but so is an astrological chart (the symbols used to denote the planets and Zodiac signs) or a computer science textbook (punctuation and numerals and diagrams to indicate logical connections or mathematical operations).  Glyphs may be used one at a time (using the symbol for the Sun) or in combination with other glyphs (multiple letters to spell out a name).

Seals are symbols that are invented as a complete unit or are received from a spirit.  Seals cannot be decomposed into more basic things, but are a whole unto themselves.  They are symbols that are not generated according to a particular rule or composed according to sacred geometry.  They are simply abstract symbols that refer to something.  Importantly, especially in my own work, seals are “revealed” or given unto someone by a spirit or person to refer to themselves; seals are an abstract “body” to give an idea a graphical or visual form.  Consider the symbols used to refer to spirits in the Lemegeton Goetia; these are not composed of more base units or other symbols, but are whole things unto themselves.  These are seals, and often have no origin besides “this is what I was shown to use and has no rhyme or reason beyond that”.  Seals are to constructed diagrams what barbarous words of power are to words in the dictionary; they may not have any communicable meaning that us humans can understand, but they work.

Sigils are symbols that are constructed according to a particular algorithm.  Think of the standard way of creating a letter-based sigil according to Agrippa (book III, chapter 30) or as used in modern chaos magic, or like with my own shorthand system.  Alternatively, consider the sigils used for the planets with their planetary intelligences and spirits from Agrippa (book II, chapter 22), which are lines drawn over the qameas of particular planets and playing connect-the-dots with the gematria values of individual letters of a name or word.  Sigils are symbols created according to a defined set of rules (combine these letters, connect these numbers on this qamea, etc.).  They are not always artistically made, although the algorithms used to generate a sigil may have some leeway for style and innovation.  A painting may incorporate sigils, but a sigil is not made of pictures; a sigil is a geometric, abstract form composed or generated from glyphs.

Runes are letters of the writing systems used for Germanic languages prior to the introduction of the Roman script.  In other words, runes are no more than letters of a particularly old style of European alphabet.  These can be classified, generally speaking, into two families: the Scandinavian futhark (both Elder and Younger, together used between the 2nd and 11th centuries) and the Anglo-Saxon futhorc.  There were medieval runes used in some astrological contexts, but generally runes stayed out of Hermetic and Western ceremonial stuff.  However, a particular alphabet known as Darlecarlian runes was in use until the 20th century in a small province in Sweden, but this was certainly the exception to the historical abandonment of runic writing.  There are other systems of writing and symbols that are runiform, such as Old Turkic and Old Hungarian, but these bear only a superficial resemblance to Germanic runes, and are not technically runes on their own as they belong to a different writing system, culture, and geographic area.

Pentagrams are five-pointed stars.  That’s it.  Nothing more than that.  You can only really draw a pentagram one way, regardless of orientation.

Hexagrams are six-pointed stars . Again, nothing special here, but there’s a bit more complexity.  The Star of David is nothing more than a hexagram composed of two overlapping equilateral triangles, which is what’s usually meant by “hexagram”.  The unicursal hexagram is another type, though it’s not original to Crowley by any means; the mathematician Blaise Pascal depicts it in one of his works from 1639.  The “elemental hexagrams” shown in the Key of Solomon (book I, chapter 3) are not, strictly speaking, hexagrams (with the exception of one); they are configurations of two triangles each that do not, necessary, combine to form a proper hexagon.

Pentacles are not stars.  They are not necessarily pentagrams, nor are they necessarily hexagrams.  Pentacles are more of a system of symbols that work together in unison for a particular goal; they are something usually, but not always, more elaborate than a sigil and are not necessarily combined in an algorithmic way.  Consider the pentacles from the Key of Solomon (book I, chapter 18), or the Elemental Weapon of the Earth as used in the Golden Dawn, or the protective lamen with the pentagram and extra symbols used in the Lemegeton Goetia, or that used in the Heptameron of Pietro d’Abano.  Pentacles are, essentially, the physical version of a graphic design composed of one or more symbols, often including letters and names, and arranged in a method more akin to sacred geometry than algorithmic combining or tracing.  Pentacles are tangible objects, things you can hold and touch and wear.  All pentacles are talismans, although not all talismans are pentacles.  For instance, a talisman engraved in a circular stone may have the design of a fish surrounded by Hebrew words can be considered a pentacle, but a talisman of a stone fish with words engraved on it is not a pentacle.  Pentacles are generally round, flat objects such as a circular piece of paper or a metal disc that have a design engraved, painted, drawn, or otherwise inscribed upon it as a graphic design of a system of symbols.  Pentacles are not oddly-shaped things like carved statues or rings or wands, despite its talismanic properties or designs on them.  Although the words “pentacle” and “pentagram” are related and were originally used interchangeably, the word “pentacle” started to be used for any magical talisman in the form of a pentagram or hexagram starting in medieval French.  An alternate etymology combines this with an older French word for pendant, pentacol or pendacol, or something worn around the neck.  Indeed, most pentacles are typically worn around the neck as lamens, which is probably the most correct use of this word in my opinion, but can easily be expanded to other (typically circular and flat) objects with a system of magical symbols inscribed upon it.

Tetragrammaton (more properly the Tetragrammaton) is another word for the four-letter name of God, Yod-Heh-Vav-Heh or Yahweh or Jehovah or whatnot.  The word is Greek and literally means “the thing of four letters”.  It is a title to refer to the sacred name of God, akin to the Hebrew haShem “the Name”, but is often used in Hermetic and Solomonic work as itself as a sacred name of God.  However, this is nothing more than a word composed of individual letters; the word “Tetragrammaton” does not refer to any pentacle or other occult design.

Mathetic Exercise: Light-bringing Breath

Today, while making an offering to Apollo, he (if you’ll forgive the pun) shed some light on a bit of mathetic practice.  I’m still dusting off some of the tools and prayers I was working on, but he’s given me some ideas to work with.  While he’s still pretty stoic and detached in his approach to me, he’s generously helped me begin the process of refining and applying some of the things in mathesis I’ve been wanting to develop.  Of this, in addition to the usual daily mathetic stuff I would be doing, he’s given me a breathing exercise to do.  I don’t know if you’ve seen this one particular GIF around the Internet recently, but it suddenly popped in my mind when I asked him what should be done.


So, I took that idea, hashed it out a bit with Apollo, and applied it.  It fills a need I wasn’t aware I needed, but it makes complete sense in retrospect, especially with some ideas I’ve gotten from the late Neoplatonic philosopher and theurgist Iamblichus as of late.

Before we get into the exercise, though, let’s go over a bit of geometry.  We all know the Tetractys, right?  We all know the Tetractys.


One of the many mathematical interpretations of the Tetractys is that it can represent the first four dimensions of geometry, starting with with the zeroth dimension:

  1. A single point, with neither length nor breadth nor depth.  No measure, only location.
  2. Two points, forming a straight line segment with length.  With a line segment, we can identify an infinite line extending in two directions: forward and backward.
  3. Three points, defining a triangle with length and breadth, together known as area.  With a triangle, we can identify an infinite area (a plane) extending in four directions: forward and backward, left and right.
  4. Four points, defining a tetrahedron with length and breadth and depth, together known as volume.  With a tetrahedron, we can identify an infinite volume (a space) extending in six directions: forward and backward, left and right, up and down.

Dion Fortune in her Mystical Qabalah (chap. 28, para. 25) says as much, in more sephirotic terms:

The point is assigned to Kether;
the line to Chokmah;
the two-dimensional plane to Binah;
consequently the three-dimensional solid naturally falls to Chesed.

We can see this using the ten sephiroth of the Tree of Life by dividing it up into four groups of points: one (Kether), two (Chokmah and Binah), three (Chesed, Geburah, Tiphareth), and four (Netzach, Hod, Yesod, Malkuth).  Such a diagram illustrates this idea of emanation in both a geometric way as well as a qabbalistic way.


In a Hermetic, Neoplatonic, Iamblichian, Pythagorean, or whatever sense, the Monad (a.k.a. Kether, the Source, whatever) is the fundamental principle that defines and underlies everything that exists.  (Whether it’s a distinct entity/non-entity/process is something of a debate in the blogosphere and I don’t presume to get into it here.)  Looking at the Tetractys, the Monad is the first step in the process of manifestation: from the Monad comes the Dyad, from the Dyad the Triad, and from the Triad the Tetrad.  The Tetrad is what gives us body and form, but it comes from a higher principle, and that principle comes from a higher one, and so forth.  If we really want to bring change from above down to here, we have to give it form in some sense, or we have to align some part of our being with the process of bringing power from the Source to us.

However, although four points identifies the minimal solid there can exist, we are far more than just four points.  Yes, we are a combination of fire and air and water and earth, but not in equal measures, nor in a regular fashion.  Our bodies are animal, but our spirit partakes in something of the Divine; in order to better make our lives and bodies more appropriate to interacting with the divine, we should try to induce a slightly different body in ourselves that makes ourselves more divine.  For the Neoplatonic Iamblichus, this is the form of the sphere, the most ideal solid there can be, and the body of the heavenly entities.  A sphere is not a tetrahedron, but they are both bodies.  We don’t want to be content with a tetrahedron, as we’re already far too complex to abide in it, but we want to get to a sphere.  In one sense, going from a tetrahedron to a sphere is nothing, after having gone and passed through the point, line, and shape in order to get a form; in another, going from a tetrahedron to a sphere is the most daunting thing of all, as we go from one point to two to three to four is one thing, but to go from four to an infinite number of points is daunting, to say the least.

In addition to all this, it’s known that part of the theurgic practices of Iamblichus involved a process of “light” and filling oneself up with it, which we can also see in other theurgic rituals, like that of the Mithras Liturgy from PGM IV.475-834.  In that, we find the following:

Draw in breath from the rays [of the Sun], drawing up 3 times as much as you can, and you will see yourself being lifted up and ascending to the height, so that you seem to be in midair.  You will hear nothing either of man or of any other living thing, nor in that hour will you see anything of mortal affairs on earth, but rather you will see all immortal things.  For in that day and hour you will see the divine order of the skies…

…So stand still and at once draw breath from the divine into yourself, while you look intently…

The whole Mithras Liturgy is a spiritual astral travel-type of initiation, where one ascends into the heavens and deals directly with the gods and guards of heaven.  However, important to this ritual is an act of ritualized breathing, where one breathes in rays of light or the breath of the divine, and in doing so changes or alters one’s nature or consciousness.  This is also similar to the Howl of Orpheus rite I found a bit ago, with its own special type of breathing and bellowing.  Breathing in divine light is not just the light of a particular planet or a star or fire, but to breathe in the light of the Divine itself, that of the Monad, the fundamental essence that undergirds all things that exist.

So, let’s put this all together into a coherent ritual, shall we?

  1. While sitting or standing, breathe out completely, from the head to the toes, completely exhaling all breath from the lungs.  Make a popping sound to expel all breath once the normal exhale is done.
  2. Breathe in deeply from the toes to the head, picturing a point of Light in your heart.  Hold the breath for four counts, then exhale completely, this time with a hissing sound towards the end.  Maintain the point of Light in your heart as you keep your lungs empty for a few counts.
  3. Breathe in deeply, picturing the point of Light in your heart splitting into two points, one at the crown of your head and one at the soles of your feet, connected by a line of Light rising from the feet, through the spine, to the head.  Hold the breath for four counts, then exhale completely with a hissing sound.  Maintain the line of Light in your body as you keep your lungs empty for a few counts.
  4. Breathe in deeply, picturing the line of Light extending by another point from its middle into a triangle that envelops your body, aligned side-to-side through your body, with its base at your feet and its apex at your head.  Hold the breath for four counts, then exhale completely with a hissing sound.  Maintain the triangle of Light through your body as you keep your lungs empty for a few counts.
  5. Breathe in deeply, picturing the triangle of Light extending by another point from its center into a tetrahedron, with its base at your feet and its apex at your head, completely enveloping you inside.  Hold the breath for four counts, then exhale completely with a hissing sound.  Maintain the tetrahedron of Light through your body as you keep your lungs empty for a few counts.
  6. Breathe in deeply, maintaining the pyramid of Light around you, as you hold the breath, exhale completely, and hold your lungs empty several times.  Silently call out to the Divine Source until you can form some sort of connection, until you can sense the Source of the Light that has been forming within and around you this whole time.  Repeat this step until you have sensed it and formed a connection with it, then continue.
  7. With the lungs completely empty, breathe in deeply, but this time, breathe in the Light from the Source.  As you do so, picture the pyramid around you swelling up slowly, bulging at its sides, until it becomes the shape of a perfect sphere that completely surrounds you.  Repeat this step until you can form a stable, perfect sphere of Light.
  8. Once you’ve formed a stable sphere of Light that surrounds you completely, let your image of yourself dissolve and merge into the sphere, becoming one with it, letting the sphere become your entire body.  Maintain this mental state as a form of meditation as long as desired.
  9. When finished with the meditative sphere of Light, let the image of your body form from the Light within the sphere, maintaining the boundary of the sphere around you as a shield or shell.  Exhale slowly with another popping sound to finish.

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:



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.

Towards a Greek Kabbalah: Plotting Paths on the Tetractys

So now we have a basic map of creation based on the tetractys, using a combination of Pythagorean numerology, Neoplatonic cosmology, and Renaissance alchemy to describe how things come to be.  In the beginning, there is the undifferentiated, divinely simple Monad, from which all things ultimately come.  From this Monad comes a Dyad, the Differentiation between Light and Dark, or Heaven and Mundus.  From these two principles comes a Triad, the three Alchemical Reagents of Sulfur, Mercury, and Salt.  From these three reagents come the four Elements of Fire, Air, Water, and Earth.  Collectively, they form the basic building blocks, processes, and guiding principles of all creation, starting from a simple and complete One to a myriad of forms through differentiation, change, and substance.  It’s through the unification of these substances by means of alchemical processes and knowledge, or better, gnosis of principles that we reverse the process of creation to reattain Union, to ascend back to the Monad and Source.  However, these units on the tetractys tell only half the story; they’re centers and ideas unto themselves, but on their own they can’t do much.  They’re cut off from each other and don’t describe how things actually become, just that they do.

This is where the other half of the Tetractys of Life comes from: we have the stages themselves, now we just need the processes that allow things to progress or regress from stage to stage.  These paths, much as the paths on the Tree of Life in Jewish kabbalah or Hermetic qabbalah, describe how power and essence flows from one stage to the next in order to produce creation or guide henosis, and this is where we combine our meditations on the Greek alphabet with those on the tetractys of emanations.  However, in order to make use of them, we first need to actually figure out what the paths themselves should be and what spheres they should connect on the tetractys.  Also, as a side note, let’s start calling the individual units of the tetractys, when using them as alchemical/planetary concepts, as spheres.  Just to make that clear.

So, we have our unconnected Tetractys of Life.  For simplicity, I’ll use the alchemical version:

Alchemical Tetractys

We know that all things are ultimately connected to and come from the Monad.  However, we run into a problem that’s similar to one on the Tree of Life in kabbalah; we can’t reach many of the spheres directly from the Monad since they’re blocked by other spheres.  For instance, although we might want to connect the sphere of Light with that of Fire, we must first travel through the sphere of Sulfur.  Thus, without trying to “skip” the spheres that block its way, the Monad can only connect to the two spheres immediately below it (Light and Darkness) as well as Mercury in the third row (since that way isn’t blocked by another sphere.

In fact, if we simply take an abstract tetractys and plot all possible paths on it, we end up with a set of paths like this:

Possible Paths on the Tetractys

While it looks nice and is as fully connected as we can get, it contains 33 paths, which is nine paths too many for our needs.  Remember, we need to aim for a set of 24, one for each of the 24 letters of the Greek alphabet, which themselves encompass all number.  Honestly, I dwelled on this for a good few days, trying to figure out how to best create a set of paths with a coherent logic; some made sense in some ways but felt jarringly off, and others just couldn’t add up to 24 even though the logic was nice.  Eventually, I settled on a way that made sense and had the right number of paths, as well as feeling “right”.

So, let’s start with something simpler than a fully connected set of paths and trying to delete off the tetractys.  First, consider the tetractys itself:


We know that, in the process of generation, the Monad (the single dot in the first row) first produces a Dyad; from a divinely simple and undifferentiated Source comes a distinction, an observer and observed, a Mind and a Word, a Creator and Creature, an active and a passive, a positive and a negative.  This gives us our first two paths on the tetractys:

Tetractys_paths1Since all things contain the Monad within themselves and emulate the actions of the Monad in their own limited way, every point on the tetractys that has a lower level can be given the same two paths.  This is the same as in the generation of Plato’s Lambda (based on geometric series of 2 and 3 and their intermingled products), or Pascal’s Triangle (which is based on the addition of units).  This, then, gives us a set of 12 paths.  We’re halfway done!


Next, we assign horizontal paths between the units within the same row.  This connects the diversity into a whole order, a cosmos, within each row, reflecting the indivisibility of the Monad when differentiation and division are present in the world.  This gives us another six paths for a total of 18:


At this point, it’s hard to say what next needs to be connected.  Do we add in paths from the outermost points of the tetractys to the center?  Do we fully connect the points of the fourth row to the third?  Do we connect the second row to the fourth with vertical lines?  This is where we need to start thinking about the relationships between the things that the tetractys represents.  So, let’s take a look at what our alchemical tetractys looks like at this partially-connected stage:


One option for adding on a set of three paths would be to connect the spheres of the Monad, of Earth, and of Fire to the center sphere of Mercury.  After all, Mercury is common to all things and is present in all substance, right?  While it’s a convenient reason, it doesn’t actually hold up.  First, the Monad doesn’t actually have to connect to anything except the two spheres right below it; as an undifferentiated One, the only thing it can possibly do to become anything more complex is to become Two, after which Two can become Three.  So, the Monad shouldn’t connect to Mercury, although we might consider Mercury to be a “lower register” of the Monad in a more manifest way, being a hermaphroditic Reagent between the polarities of Salt and Sulfur.  For a similar reason, Earth and Fire shouldn’t connect to Mercury, either, since Mercury isn’t actually in them; Earth is the most passive of all the elements, being something like the caput mortuum, or the worthless remains or “dead head” without any Spirit left in them; likewise, Fire is already too hot for Mercury, and is what takes spirit out; there’s no volatile Mercury in Fire because Fire is the action of Spirit.

Another option to add a set of six paths, which would bring us up to 24, would be to connect the Monad to the fourth row to Water and Air, Earth to Light and Sulfur, and Fire to Darkness and Salt.  However, if anything, this is worse than the previous attempt, since all these forces are even more distantly connected and different from each other.  So it’d seem like the outermost points of the tetractys are too “extreme” to be connected any further than the two paths they each already have.  These nine possible paths, connecting each extreme point to the center point as well as to the two center points on far side of the tetractys, aren’t going to work for our purposes.

So, what do we know?  We know of 18 paths we should definitely have, and of nine we shouldn’t.  We have 18 + 9 = 27 paths we’ve considered so far, and 33 – 27 = 6 paths we haven’t yet.  What are those leftover six paths?


Six paths revolving around the center from the median two points on each side of the tetractys, altogether forming a hexagram.  Cute, isn’t it?  These last six paths are going to serve us well, but they’re also going to take a much different role in future analyses of the Tetractys of Life.  So, if we fully connect our alchemical Tetractys of Life with these extra six paths, we get the following:


Here, we have the median two spheres of every side of the tetractys connected to six other spheres, making these spheres all fully connected while leaving the extreme spheres connected only to their most closely associated concepts, both on their own row as well as to their neighbors.  This allows anything “middling” and not extreme (pure unmanifest, base passivity, base activity) to become anything else, including on a different level of manifestation.  For instance, Darkness is able to descend into the purely dark reagent Salt or the hermaphroditic reagent Mercury, but can also be involved in the creation of the dark (feminine) element Water as well as the active reagent Sulfur.  Darkness becoming Water makes sense, as does its corresponding opposite of Light becoming Air, since based on the structure of the tetractys we can claim that Water and Air are “lower registers” of Darkness and Light, much as Mercury is of the Monad itself.  Darkness becoming Sulfur, though?  It seems a little odd, but I claim that this works because the Three Reagents come from both the Two Principles, as a balance needs to be struck within each instead of solely by means of Mercury.  Similar reasons apply for Light being connected to Salt, Salt to Air, and Sulfur to Water.

So, with all of this done, we now have 24 paths on our Tetractys of Life.  Each path represents an ability to shift or change, a process between the stages or ingredients that the individual spheres on the Tetractys represents.  Some spheres cannot be connected to each other because of the need for intermediate stages (a path is interrupted by another sphere between the ultimate origin and destination spheres), or because a sphere is too extreme to be connected to another (a path cannot connect the outermost points of the Tetractys except to its two closest neighbors).  Now that we know of the possible means of transitioning between spheres on the Tetractys, we now have an even stronger tool at our disposal for meditation: the ability to meditatively or contemplatively explore the transitions themselves as processes of change between the stages indicated by the spheres.  While we haven’t gotten into the assignment of letters to the paths just yet, there’s still more analysis to be done on the different ways to divide the paths based on geometry and position, which will help to inform us on how to assign the letters to the paths as well as to guide us in meditation of divine concepts and divine names.

Oh, and if you’d like a more complete Tetractys of Life map that combines both alchemical and astrological symbols, here you go: