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:


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.


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.

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