Geomantic Revelations of the Tetractys

The last post on the arithmetic subtleties of the Tetractys got me to thinking.  If I have four rows of things I can select or not select for a collection, I end up with so many results.  The overall number of distinct results, of course, is 10 (Monad through the Decad), but I thought a bit deeper about it.  I mean, I disregarded multiple ways of adding up to a given number before, and what if I took all those into account?  After I did the math, I realized there are 16 ways to add different selections of the ranks of the Tetractys together to get a certain sum.  Four rows, 16 results.  Sound familiar?  Yup.  I accidentally found a way to link the Tetractys to the 16 figures of geomancy.  Before reading, I suggest you brush up on the terms of geomantic operation, specifically for what inversion and reversion is.  Besides, it’s been a while since I mentioned anything substantial about geomancy, so this is an interesting confluence of studies for me.

Whether geomancy has ever been thought about in terms of the Tetractys, I can’t say, though I personally doubt it, but consider the following analysis.  First, let’s assign the four elements of Fire, Air, Water and Earth to the four ranks of the Tetractys:

  • Monad: Fire
  • Dyad: Air
  • Triad: Water
  • Tetrad: Earth

This isn’t that much a stretch.  Yes, the elements properly belong to the Tetrad as a whole, but we also can think of the four elements as numbers in their own right.  We know that Fire is the most subtle and Earth the least, and that Fire is the least dense and Earth the most.  Similarly, the Monad is the most subtle and least concrete number, while the Tetrad is the most concrete and least subtle.  We can assign the four elements accordingly to the four numbers of the Tetractys with agreeable ease.

If we allow for all possible combinations of these four numbers to be either present or absent in a sum, then we get sixteen different results, just how we get sixteen different geomantic figures by allowing for all four elements to be either present or absent.  The list of all the possible ways to add the ranks of the Tetractys are:

  1. None (0): Populus (None)
  2. Monad alone (1): Laetitia (Fire alone)
  3. Dyad alone (2): Rubeus (Air alone)
  4. Monad + Dyad (3): Fortuna Minor (Fire + Air)
  5. Triad alone (3): Albus (Water alone)
  6. Monad + Triad (4): Amissio (Fire + Water)
  7. Dyad + Triad (5): Coniunctio (Air + Water)
  8. Monad + Dyad + Triad (6): Cauda Draconis (Fire + Air + Water)
  9. Tetrad alone (4): Tristitia (Earth alone)
  10. Monad + Tetrad (5): Carcer (Fire + Earth)
  11. Dyad + Tetrad (6): Acquisitio (Air + Earth)
  12. Monad + Dyad + Tetrad (7): Puer (Fire + Air + Earth)
  13. Triad + Tetrad (7): Fortuna Maior (Water + Earth)
  14. Monad + Triad + Tetrad (8): Puella (Fire + Water + Earth)
  15. Dyad + Triad + Tetrad (9): Caput Draconis (Air + Water + Earth)
  16. Monad + Dyad + Triad + Tetrad (10): Via (Fire + Air + Water + Earth)

Note that the numbers 3, 4, 5, 6, and 7 have two ways each to add up to them.  In the last post, we only discussed one each, the formulas that use the basic Monad/Dyad/Triad/Tetrad set, but it’s possible and equivalent to say that 6 is both a combination of Dyad and Tetrad as it is with Monad and Pentad.  The numbers 0, 1, 2, 8, 9, and 10, however, each only have one way to add up to them.  Thus, the numbers that have two ways have two possible figures, and the numbers with only one have one figure.  In this way, we can assign geomantic figures to different collections of the ranks of the Tetractys, but what might this mean?  For numbers that can be added to in two ways (3, 4, 5, 6), we have two figures each.  We’ll call those figures “manifesting” that have more rarefied numbers (such as Puer, which is Monad + Dyad + Tetrad), and “manifested” those that have more concrete numbers (such as Fortuna Maior, which is Triad + Tetrad).  As it turns out, we end up with mobile figures becoming manifesting and stable figures becoming manifested.  Thus, we end up with a chart like the following:

 Sum Manifesting Manifested
0 Populus
1 Laetitia
2 Rubeus
3 Fortuna Minor Albus
4 Amissio Tristitia
5 Coniunctio Carcer
6 Cauda Draconis Acquisitio
7 Puer Fortuna Maior
8 Puella
9 Caput Draconis
10 Via

Going from top to bottom, we see that there are important patterns present in the chart.  Figures for 0 and 10 (Populus and Via) are inverses of each other, as are 1/9 and 2/8.  The manifesting 3 and manifested 7 figures are also inverses, as are manifested 3 and manifested 7, and so forth.  Coniunctio and Carcer are both italicized, since they’re both equally manifesting and manifested and it’s hard to tell which is which, especially since they’re both equally added to by 5 and are in the middle of the list.  We see that the greater the sum, the more “dense” and active the figure becomes, and we get more stable the further down we go (with one exception we’ll get to later).  As might be expected from Iamblichus, the number 5 is the pivot and balance for all the other numbers, and accordingly the manifested and manifesting properties of this number are in agreeable and balanced growth.  We can also note that the “extreme” (0, 10) and median figures (5) are what we’d also call “liminal”; figures that are the same when they’re reversed.  We have this constant shifting balance throughout the structure of this Tetractyan geomancy that keeps popping up, so that’s cool.

If we use our keywords from our prior discussion of the nature of the numbers from 1 through 10, we can attribute them to the geomantic figures:

  1. Individuation: Laetitia
  2. Relation: Rubeus
  3. Harmony: Fortuna Minor (manifesting), Albus (manifested)
  4. Form: Amissio (manifesting), Tristitia (manifested)
  5. Growth: Coniunctio and Carcer (both manifesting and manifested)
  6. Order: Cauda Draconis (manifesting), Acquisitio (manifested)
  7. Essence: Puer (manifesting), Fortuna Maior (manifested)
  8. Mixture: Puella
  9. Realization: Caput Draconis
  10. Wholeness: Via

In this sense, the terms “manifesting” and “manifested” become a little clearer.  Figures that are manifesting bring that quality into existence, while figures that are manifested represent that quality already in existence.  It’s the difference between “becoming/causing” and “existing/evidencing”.  Thus, Fortuna Minor is manifesting harmony, since it requires one to work with others, indicating that one’s own power is not enough to carry the day; other interaction is required.  On the other hand, Albus is manifested harmony, maintaining equanimity and reflection unto itself, self-sufficient and uninvolved with anything else that might disturb it.  Similar cases can be drawn up for the other sums, so it’s interesting to see how geomancy can reflect these numerological concepts in its own logic.

What about the numbers for which there’s only one figure?  The figures of 0, 1, and 2 are the inverses of the figures of 10, 9, and 8, respectively, and if we keep our mobile/manifesting and stable/manifested idea, then 0, 8, and 9 are manifested qualities while 1, 2, and 10 are manifesting.  It seems odd that Populus should be among the mobile/manifesting figures and Via among the stable/manifested, but the swap here makes sense in a cyclical way; after all, with either absolutely nothing or absolutely everything present, we end up able to repeat the whole process, since if everything is all one Thing, one can no longer draw a difference since there’s nothing different (hooray, paradoxes).  So, Individuation and Realization are manifesting and manifested qualities of a metaquality “Becoming”; Relation and Mixture of “Variation”; and…hm.  We have Wholeness as the quality for 10, but what about 0?

What’s probably most bizarre about this interpretation, at least in a strictly Pythagorean sense, is the “sum” of Populus being 0.  Zero was not considered to be a true number by the ancient Greeks, or really by anyone in the Western world, up through the medieval age when Arabic and Indian mathematics started becoming popular to study.  After all, they might ask, “how can nothing be something?”  Besides, with the Tetractys itself, all things are based on the Monad.  The Monad defines and begins all things on the Tetractys and existence itself, yet it itself cannot come from nothing, for it never came or became at all.  We haven’t encountered the notion of “nothingness” before in our mathetic studies, so what might it represent?  Honestly, I’d consider it to represent Emptiness in the Buddhist sense where all things are interconnected and rely upon each other.  It’s not quite Relation or Harmony or any of the other things, but it would be closest to Wholeness; after all, Matter must exist within Space, and all of Matter exists within all other Matter, always influencing and influenced by itself.  It’s weird, though, but think of it like this.  In all things, Populus must exist as the template for all other things, the ideal form that even the Monad itself represents as itself.  Without Populus, we’d have no geomantic figure, just as the Good itself cannot exist apart from Goodness.  Even Wholeness must reside within the form of Emptiness, just like how Populus must be present (even if “hidden” or implied) in every geomantic chart.  So, if Wholeness is the Decad, then Emptiness is the Mēden (Μηδεν), or “Nothing”.  But both, in an obscure sense, are the same.

Focusing more on the qualities of the numbers themselves, we can further pair them up into different groups based on how the geomantic figures there are inverses of each other.  In other words, if two numbers add up to 10 (0 + 10, 1 + 9, etc.), they form a pair:

  • Individuation/Realization (1 + 9 = 10)
  • Relation/Mixture (2 + 8 = 10)
  • Harmony/Essence (3 + 7 = 10)
  • Form/Order (4 + 6 = 10)
  • Emptiness/Wholeness (0 + 10 = 10)
  • Growth (5 + 5 = 10)

These qualities, though paired up to indicate something like an opposition or dichotomy, doesn’t seem to indicate anything of the sort, but rather two interconnected concepts that cannot be separated from each other.  After all, in order for one to become One, something whole and complete in and of itself, it must go through a process of becoming and enforming to become real (Individuation and Realization, 1/9).  In order for different things to relate, oppose, agree, or move with each other, they must be put together and combined (Relation and Mixture, 2/8).  In order for different things to agree, combine, and merge together, they must share certain qualities and be germane to each other (Harmony and Essence, 3/7).  In order for things to possess form, body, and dimension, they must have a structure and consistency that allows them to maintain it (Form and Order, 4/6).  In order for something to exist, it must exist because of something else, or it must allow for itself to be filled with creation (Emptiness and Wholeness, 0/10).  Growth…well, growth expands in all ways, in all dimensions, and itself provides a balance that nurtures and metes out all other qualities (Growth and Growth, 5/5).

So, we have five pairs of qualities of the numbers, and one single quality that forms its own pair.  What might we call these metaqualities?

  • Becoming: Individuation/Realization
  • Variation: Relation/Mixture
  • Accordance: Harmony/Essence
  • Structure: Form/Order
  • Being: Emptiness/Wholeness
  • Growth

These are terms I just pulled off the top of my head, so I don’t expect them to stay permanent terms, but they do tend to fit.  Individuation and Realization are both qualities that are required for anything to become One Thing or one thing.  Relation and Mixture are both required for anything to be different or have difference among others, to either vary or be a variation.  Harmony and Essence are both required for anything to agree with or find similarities with in an accordance.  Form and Order are both required for anything to have a body or to form a body in a coherent structure.  Emptiness and Wholeness are both required for anything to exist, either on its own as a Whole or as part of a Whole filled by it.  Growth can apply to any and all of these things, and mediate between any two qualities that form part of a metaquality pair.  In a way, the metaqualities form their own Tetractys, with Becoming related to the Monad, Variation to the Dyad, Accordance to the Triad, and Structure to the Tetrad.  Growth, as a balance, forms part of the “hidden” Pentad underlying the Tetractys, and the four metaqualities again form another “inverted Tetractys” under it.  Thus, the “upper Tetractys” is composed of Individuation, Relation, Harmony, and Form; the “lower Tetractys” is composed of Realization, Mixture, Essence, and Order.  Growth mediates between the two as the “hidden Pentad”; Emptiness and Wholeness are at once present at all points throughout this dual Tetractys figure.

tetractys_decad

While my Tetractys research is still new to me, geomancy is not, and being able to understand more of the Tetractys with symbols and terms I’m already familiar with is a huge help to me.  Like I said, I don’t know whether this type of analysis has ever been attempted before, but it’s certainly something that I plan on continuing.  Geomancy, after all, is a binary system based on the number four, and within four is 10 and thus all other numbers.  Perhaps the two were meant to be wedded all along.

Internumeric Relationships by Addition on the Tetractys

It’d be rude and vulgar of me to leave the Tetractys as some simple geometric diagram used for plotting paths or meditations.  I mean, the Tetractys is a meditation tool, yes, but to use it merely for working with the Greek alphabet with in a mathetic framework is to ignore the deeper meaning of the Tetractys.  For the Pythagoreans, especially, the Tetractys was more than a set of ten dots; it was the key to all creation and all cosmos.  There’s no evidence that anybody’s used it to plot paths on like I did, which is probably because this is an innovative use for an already heavily used tool based purely on number.  As we’re all aware by now, the Tetractys is a representation of the Monad, Dyad, Triad, and Tetrad to yield the Decad: 1 + 2 + 3 + 4 = 10.  All these numbers are holy to the Pythagoreans and to Western occultists generally, but there’s so much more to the Tetractys than this.

One of the traditional ways of understanding the mysteries of the Tetractys was to take the different ranks of numbers present and add them together to yield a particular number.  For instance, the Monad plus Tetrad yields the Pentad (1 + 4 = 5), while the Monad, Dyad, and Triad together yield the Hexad (1 + 2 + 3 = 6).  All these numbers have their own meaning, all of which are based ultimately on the Monad and, in succession, the meanings given to the other numbers built upon the Monad.  I’d thought I’d investigate what some of these properties are and see what the Tetractys represents in building the numbers of the Decad together based on these relationships between the ranks of the Tetractys.  Specifically, these relationships are based on the arithmetical operation of addition, the straightforward aggregation of two numbers by combining their distinct magnitudes into a single one.  Other operations exist, but those are for another time.

So, to start off with, we have four basic numbers, starting with the Monad and ending with the Tetrad.  We can say that, with the exception of the Monad, all numbers are just collections of Monads in a particular relationship:

  1. Monad = individuation, undifferentiated, undifferentiatable
  2. Dyad = two Monads in relation
  3. Triad = three Monads in harmony
  4. Tetrad = four Monads in form

Note that some of these can be broken down further into simpler groups.  Without repeating any particular number (such as saying that the Dyad is two Monads or the Tetrad is two Dyads), we end up with two extra identities:

  1. Triad = Monad + Dyad
  2. Tetrad = Monad + Triad

It’s crucially important to note that the Dyad, Triad, and Tetrad are more than just a collection of monads.  Number in the esoteric sense is more than just a magnitude or amount, but also a relationship formed between the individuals in the collection.  The only number in this set that has no relationship is the Monad itself, since it exists as a unity unto itself without anything to relate to.  The Dyad is the first number that has a relationship, but can be said to be relationship itself; without the Dyad, relationship cannot exist.  In a more arithmetic sense that the Pythagoreans preferred, all numbers can be divided into two partially overlapping groups of odd (able to be divided into unequal parts only) and even (able to be divided into two equal and unequal parts).  Four, for instance, is even because it can be split up into groups of 1/3 and 2/2.  Five, however, is odd, because it can be split into 1/4 or 2/3, and neither of those are equal splits.  However, the Monad cannot be split at all into anything, and the Dyad can not be split into unequal parts, so neither the Monad nor Dyad are even nor odd, and are thus not true number, though they are sources of number.

Thus, based on the individuation of the Monad and relation of the Dyad, all other numbers can be made, such as the Triad.  It is because of this that the Triad is considered by the Pythagoreans to be the first true number, since the Monad and Dyad are something rarer and rawer.  All amounts can be formed from the Monad, but it’s the relationship (Dyad) between individual Monads that produce a number.  Thus, as the Triad is the first true number, it is also the first odd number, and the Tetrad is the first even number.

So, based on the six above identities, we can form the rest of the numbers from the Pentad (5) to the Decad (10).  If we omit the identities from above and reduce all things to a collection of Monads, Dyads, Triads, and Tetrads, we end up with two ways to form the Pentad, and one way each to form the Hexad, Heptad, Octad, Ennead, and Decad:

  1. Pentad = (Monad + Tetrad) or (Dyad + Triad)
  2. Hexad = Dyad + Tetrad
  3. Heptad = Triad + Tetrad
  4. Octad = Monad + Triad + Tetrad
  5. Ennead = Dyad + Triad + Tetrad
  6. Decad = Monad + Dyad + Triad + Tetrad

Yes, this is all basic arithmetic that we’ve been able to do since kindergarten.  Of course, it’s always the simplest things that hide some of the more profound secrets.  I won’t go over all the associations and theologies behind the numbers for that; you can get a copy of the Theology of Arithmetic by Iamblichus for cheap (or even, dare I say it, for free), and you can read about what the Pythagoreans thought about the numbers of the Decad way back when.  What I want to point out is, at a high level, what these additions of the numbers mean based on the four concepts of monadic individuation, dyadic relation, triadic harmony, and tetradic form.

Monad
The Monad is an individual, unchanging, static, and stable.  It is the only thing that exists, and thus cannot be differentiated from anything (since there’s nothing to differentiate it from).  While we can say that it contains all opposites and extremities within itself, it’d be more proper to say that no concept of opposition or extremity exists within the Monad.  While the Monad exists, nothing exists within the Monad; it can become all and any qualities, but it itself has no qualities.  It is the source of all nature, but is itself beyond nature.  It cannot be divided since it is a unit, an atom, the core of existence itself.  The Monad cannot move, as there is nothing within which it can move (which would imply something that is Monad and something that is not-Monad).  The Monad has no shape, consisting only of a single point that indicates both all sizes and all angles but without anything else to connect to.

Dyad
The Dyad is relation and difference.  Between two Monads, we now know of two things that can be compared as equals, but as different equals.  The Dyad is representative of differentiation, distinction, opposition, and motion, all of which can be thought of as different types of relation.  The Dyad represents a line defined by two points, but is still without shape; it can possess direction and magnitude, but is as yet without definition.  The Dyad allows for things to exist within, around, and outside of other things, since it creates space between and among other things.  While the Monad is pure potential for creation (and all other things), the Dyad is the act of creation itself, since it distinguishes a Creator from the Creature, or the Acted from the Actor.  The Dyad is space, change, action, and relativity.

Triad
The Triad is harmony and proportion, formed from a combination of individuation and relation.  It is the first odd number, and the first number that can be added from other distinct numbers.  The Triad gives the first shape of something, as three points can define an enclosed space.  The Triad indicates actuality, the Creature made through Creation (Dyad) from the Creator (Monad).  However, it is also indicates harmony, since two distinct and different things are linked to and joined by a third.  With the Triad, there is real existence as opposed to potential existence or becoming existence.  Quoth Iamblichus, “‘this’ belongs to the Monad, ‘either’ to the Dyad, and ‘each’/’every’ to the Triad”.  With Triad, there is time: beginning, middle, end; there is communication: speaker, listener, message; there is work: actor, action, acted upon. However, like the Monad, the Triad is static, since it provides for space and size but not change, since it is construction and creation that brought a static shape to being.

Tetrad
The Tetrad is the root of form, formed from a combination of individuation and harmony.  With three points we can define a two-dimensional shape, but with four we can define a solid three-dimensional object.  Moreover, the Tetrad is dynamic, since it is even; while the Triad measures static quantity, the Tetrad measures dynamic quantity, since it provides for motion and change while the Tetrad does not.  Further, the Tetrad allows for forms present in relationship to each other; while the Triad offers a two-dimensional form, the Tetrad allows for two-dimensional forms next to each other as the Dyad allows for Monads to be next to each other.  With both individuation and harmony, one can choose to be part of a harmony or break away from it, acting either inside or outside a given group, and allows for distinct existence apart from, aggregated with, or in conjunction with others.

Pentad
Alone among the numbers, the Pentad is the only one that can be formed in two distinct ways: from the Monad and Tetrad (a combination of individuation and form) and from the Dyad and Triad (a combination of relation and harmony).  In a way, it’s fitting; between all the numbers of the Decad, the Pentad is the middle of them.  Consider that any two numbers that add up to 10 have 5 as the mean (9 + 1, 8 + 2, 7 + 3, etc.); the Pentad is halfway to the Decad, and itself is vital to life.  It is the combination of pure potential and discrete aggregation (Monad and Tetrad), as well as of relation and harmony (Dyad and Triad); it is the combination of an even and odd number in either case, and considered to unify opposites in a dynamic way that allows for growth and change as opposed to the static way of the Triad.  If we consider the Pentad as the sum of Monad and Tetrad, we obtain a view of eternality and potentiality combined with and suspended among temporality and discretion (the four changeable elements acting under unchanging Spirit); if we consider the Pentad as the sum of Dyad and Triad, we obtain a view of motion and action mixed with and changing stasis and relationship.  In either case, the Pentad is where life and concrete reality itself begins, since in the Pentad there is balance, reciprocity, distribution, and especially of growth.

Hexad
The Hexad is the combination of relation and form, producing a dynamic harmony.  Unlike the Pentad, which is dynamic growth, the Hexad is a balance between things in motion.  The presence of distinct qualities bestowed by the Tetrad in relation of the Dyad allows for various dynamic forces to exist dynamically, moving with and acting, co-acting, or reacting together without destruction.  As the Tetrad represents a body and the Dyad represents motion, the Hexad represents a body in motion and can move in six ways, or three sets of two ways: up/down, left/right, forward/backward.  Seen the other way, as the Tetrad represents qualities and the Dyad represents opposition, the Hexad represents an ordering and balance of opposites.  Further, as two Tetrads, the Hexad represents what we commonly see as “Merkava stones”, two interlocked tetrahedrons that represent a combination of bodies and opposites that together unite to form a whole.  While the Pentad is the number of life, the Hexad is the number of order.

Heptad
The Heptad is the combination of harmony and form, producing foundation.  This is hard to describe in a single word, but within the Heptad there are all things finally present to create everything, yet is short of actively creating everything; all manifest sources are present in the Heptad (seven planets of astrology, seven vowels of Greek speech, etc.), though they are as yet too unmanifest on their own.  As a combination of Triad and Tetrad, the Heptad represents the four elements and three reagents, or the three processes that transform the four elements so as to create all things.  As an odd number that cannot be divided, the Heptad is similar to the Monad in that it provides for potential creation, but unlike the Monad, the Heptad is a collection of seven entities that provide the foundation of all manifest things, while the Monad is an undifferentiatable source from which all manifest and unmanifest things come.  If the Hexad represents order, then the Heptad are the things that are ordered within the cosmos provided for by the Hexad, the meat to fill out the Hexad’s bones.  The Heptad is that which essentially exists; the Heptad is essence.

Octad
The Octad is the first addition that involves three numbers: the Monad, Triad, and Tetrad.  Thus, the Octad combines individuation, harmony, and form.  As the Heptad is the combination of the Triad and Tetrad, we can say that the Octad is that which results from the essences of creation into which they flow.  However, as we saw with the Pentad, we can also say that the Monad and Heptad combine such that the Heptad is mixed in within the Monad, as the seven planets are within the eighth sphere of the fixed stars, as the four elements are within the Quintessence.  However, we can also say that the Octad is the combination of two Tetrads, allowing for mixtures and combinations of that which otherwise could only relate to each other by processes; although Sulfur combines and transforms Air into Fire and vice versa if we use the Tetrad + Triad view, we end up with dry air or cool fire between Air and Fire if we use the Tetrad + Tetrad view.  The Octad represents solution and combination of qualities, a single entity produced from essences or qualities and their interquality transformations.  The Octad is mixture.

Ennead
The Ennead is the combination of relation, harmony, and form.  Based on how we might conceive of this, we can say that the Ennead combines the Tetrad and Pentad, the Triad and Hexad, the Dyad and Heptad, or the Monad and Octad, but at its root it combines the Dyad, Triad, and Tetrad.  At its core, it lacks the Monad and possesses the Dyad, indicating that the Ennead is an active number related to creating but not as creator or creature.  In the Ennead is all creating of manifest things, combining tetradic body, triadic intermediation, and dyadic motion.  In the number nine are all the other numbers brought together, the final single-digit whole number.  As there were nine Muses who lead to all Art and nine Curetes who watched over the infant Zeus, the Ennead brings things to completion and perfection without itself being perfect.  The Ennead is realization.

Decad
At long last, we finally reach the Decad, the combination of the Monad, Dyad, Triad, and Tetrad; of individuation, relation, harmony, and form.  In the Decad are all the basic numbers of the Tetractys, and there are many ways to add to the Decad using the lesser numbers, but at its core it is the number formed from 1, 2, 3, and 4 summed together.  Just as in the Ennead there is the process of realization and completion but without something to realize or complete, the Decad augments this with the Monad, allowing for something to be filled with the Ennead.  The Decad represents a discrete entity (Monad) that is distinct from other things (Dyad) that is stable unto itself (Triad) given physical a body (Tetrad).  Moreover, it is also something that can grow (Pentad) while maintaining itself in an order (Hexad) that combines all ethereal essences (Heptad) and concrete mixtures (Octad) being brought together (Ennead).  Without any other number preceding it, the entity represented by the Decad would be lacking and could not be fully realized.  Whether it is the universe we live in or the individual people we live as, we are all representative of the Decad and the journey it has taken to get here.  The Decad is the Whole.

I think it goes without saying that this Pythagorean analysis of the ten numbers of the Decad can easily be mapped onto the Tree of Life in Jewish kabbalah or Hermetic qabbalah, and indeed, I recall seeing many of these things present in the explanations given in works like Alan Moore’s Promethea series.  It makes sense, too, since Pythagoreanism is one of the fundamental philosophies underlying Western occult thought, deep enough to not clearly be distinguished as Pythagorean but also profound enough to affect everything that’s built upon it.  While numerology has never quite been my strong suit, this little exploration of the basic numbers has considerably helped.

Crucible Convention 2014!

Of course, October’s second-biggest event in my life (the first being that noble and highest holiday of my own birth) is still happening: Crucible Convention, as always held by the generous and amazing Omnimancers, this year on October 4, 2014 at the Crowne Plaza Princeton in Princeton, NJ.  Tickets are $40, or $45 if you go to the convention banquet, and the hotel has a discounted rate until September 19th if you want to get a room.  Getting a room is heavily suggested (the hotel discount code is CRU), since occult talks, socializing, and antics go on well until the night, and the Friday night mixer is fantastic to hit up.  If you plan to get the dinner, do so early, since spaces are limited.  The convention schedule can be found here, and you can log in to register here.

Last year was my second year going, and it was a fantastic blast with good knowledge spread and good stories made; my first year was no small amount of fun and education, too.  This year promises to be even better, especially because yours truly is giving his first talk!  Yes, polyphanes will make his conference talk debut at Crucible Convention 2014 on (predictably, given the recent string of posts on it) “Mathesis: Towards a Greek Kabbalah”.  The class blurb from the Crucible Convention class schedule:

Although the traditions of ancient Greece provide the foundation for most Western occulture, the use of Greek techniques and tools is underrepresented in modern Western magic, especially that which falls under the banner of Hermeticism.  Most Hermetic magic practiced today is based on the studies of those who focus on the Jewish mysteries of kabbalah.  While the spiritual technology and philosophy of Jewish, Christian, and Hermetic kabbalah has been invaluable to the development of Hermeticism, Hermetic occulture does not make the best use of kabbalah as Jewish kabbalists do, and even then, kabbalah may not be the best fit for the modern non-Jewish Hermeticist.  As a non-kabbalistic alternative to the practice of the Great Work, polyphanes will discuss a new approach to Hermetic magic using an innovative theurgical and cosmological framework based on Pythagorean and Neoplatonic philosophies called “mathesis”, meaning “teaching of the mysteries”.

If you’ve been keeping up with the posts here, then you’re already ahead of the game (and there’s much to do and explore before I give the talk), but I also want to disseminate this topic as much as I can, since it’s kinda sorta my crowning project at the moment.  I don’t want to pontificate too much and start a schismatic group intent on divorcing Hermeticism from kabbalah, but I do want to give people something to think about, that “hey, there might be other ways to do Hermetic stuff besides kabbalah”.  Not only will it get a much-needed conversation going, it’ll also help in getting feedback from others and improve the system even more.

Save the date, preregister, and come to support me (and a bevy of other fantastic speakers, including my own personal colleagues) at Crucible this year!

Tetractys and Magic

Alright, alright, I can hear some of my readers mutter in the distance.  “Yes, polyphanes, we know you like the Tetractys.  We get it.  You’re on a huge Pythagorean kick lately.  You’ve been on this kick for over a month and a half now.  Yes, it’s awesome.  But what about magic?  What about conjurations and talismans and shit?  When are you going to talk about those things again?”  Don’t worry, I haven’t forgotten.  Yes, I admit I’ve been taken with the Tetractys and this new field of occult mathesis as of late, but to be fair, it’s a huge new thing for me that I didn’t expect to develop.  I honestly feel like I should be spending more time on it, more meditation, more scrying, since it’s all so new and, thus, unexplored.  And, to make proper use of it, I feel like more exploration is definitely needed.  Otherwise I’d just be stumbling around with a wand in the dark, and I like to do my research before jumping into anything.

Though, I also have to wonder: what substantially changes if I use the Tetractys of Life instead of the Tree of Life as my core magical framework?  The best answer I have for that is, well, not terribly much.  I mean, the only real kabbalistic thing I use in my work is the use of particular godnames to conjure the planetary and elemental angels under; maybe I rap several times on the altar to open up a ritual, the number corresponding to the spirit’s sephirah; I might occasionally use a number square to charge something upon.  But, really, that’s about it.  The planets, stars, and elements would exist regardless whether I used the Tree, the Tetractys, or neither, as they have for countless other cultures and magicians before me.

celestial_spheres

The heavens still remain in their usual order, which is probably one thing that neither the Tetractys nor the Tree of Life really affect.  I mean, Saturn is still the next heaven in line under that of the stars, and Jupiter is the next one under Saturn.  In this scheme, there are still ten heavens, with the first one being that of God (Monad) and the last one being that of the Earth (Decad).  Thus, the sphere of the fixed stars is still recognized as the Dyad (2), that of Saturn as the Triad (3), that of Jupiter as the Tetrad (4), and so forth until that of the Moon as the Ennead (9).  The sephiroth are not the planets, and the planets are not the sephiroth; the Tree of Life assimilated the planets into its structure as a later development of the Tree itself, corresponding to the planets without identifying with them.  The planets are still a representation of number, and numeric representations of the planets are still important tools independent of whether they’re placed on the Tetractys or the Tree.  In that light, the magic number squares of the planets can still be used as important tools, and the use of numbers to associate with the planets as well.

In this view, perhaps my idea-in-passing from a ways ago about using a Greek version of the magic number squares could still be used.  After all, the planets are a different realization of number and are associated with the sephiroth, but are not themselves the sephiroth; the number squares are also representations of number in the same way as the planets are.  The magic squares are not kabbalistic in and of themselves in the same way we’d reckon kabbalah; they’re a tool used to understand the kabbalah, but they are not themselves kabbalah.  The only real change to be made here would be to create a set of Greek number squares and find a new set of spirit names to make sigils with; that idea is one I’ll have to pursue for sure.  The hangup I had with that, to be honest, was the fact that I couldn’t easily assign a simple 1-to-10 numbering to each of the dots in the Tetractys.  It’s easier to see the planets or other forces as distinct groups working in tandem with each other on different levels in a conceptual way apart from the nested-spheres view.  The planets are number, too, and with a bit of clever rearrangement can be put into a tetractys of their own.  While I like my arrangement of the planets onto the Tetractys, it’s surely not the only way to do so, though I have good reasons for going with the model I have.

Say some reader says “well, I think the number squares should stick to kabbalah, so we should use another model of numerical mediation”.  Okay, good!  I like making new models and tools.  However, what could be used in their stead?  The regular polygons of a particular number, say?  Well, if you exclude the Monad (which is a simple point) and the Dyad (which is an infinite line or a circle, neither of which are polygons), we run into an issue.  The “true” Greek way of developing a polygon is to use a compass and straightedge, neither of which are marked for degree or length.  While the triangle, square, pentagon, hexagon, octagon, and decagon can be constructed by a compass and straightedge, the heptagon and enneagon cannot.  They can be approximated, sure, but these numbers cannot be made into regular polygons by compass and straightedge alone, similar to the ancient Greek geometrical problems of squaring the circle or doubling the cube.  It’d be like trying to make a magic number square of rank 2, which cannot be done.  While their ideal forms might be good for meditation, it’d be hard to apply those forms in reality or construction of forms.  This itself can be considered a mystery worthy of meditation, but in terms of applying or constructing numbers, I’d prefer number squares myself if the rank of the square is going to be the same as the number of sides of the polygon.

Beyond numbers, what else might have to change?  Colors?  I’ve gotten good enough results with the colors as used in the Golden Dawn Queen and King scales, so I may as well stick to those (though seeing what else the spheres themselves can show me is useful).  Names of spirits?  Obviously, since Greek names and spelling follow radically different rules than Hebrew, but again, those would just have to be obtained through scrying and numerological research.  The associations of other tools, symbols, and the like with the planets is pretty firmly established and I see no reason to change all those.  So, if by and large the major tools of my work aren’t going to change by switching over to the Tetractys from the Tree, what really changes?

alchemical_planetary_tetractys_paths

The set of paths I have on the Tetractys really don’t work for the Tree of Life; if you try to take the standard ten sephiroth and apply the same paths I have on here, you end up with something resembling metaphysical spaghetti.  While the paths on the Tetractys make sense to me, they cannot be separated from the Tetractys.  The Tetractys offers a radically new meditation and theurgic model of manifestation and understanding how the Divine interacts with all that exists.  That’s the big thing that the mathetic Tetractys provides: a modern Neoplatonic/Neopythagorean model of emanation and divine flow from high to low and back up again.  Unlike the Tree of Life with its neatly-defined start and end points that are so diametrically opposed to each other (due to the Jewish conception of the mortal world being so far removed from the divine), the Tetractys shows how everything is involved in a balanced way in the evolution of everything.  The Monad exists as much as it does down here as it does up there, after all; there’s no need of a God to “recede” from itself to allow for creation within-yet-apart from the rest of its own infinity.  There’s no clean start point for us to use the Tetractys, because not only are we composed of all the forces in the Tetractys, but all of the Tetractys is within us equally and directly.  It might make good sense for us to start with the four elements that compose our bodies and senses of self, but we could easily start with ourselves as a unified whole, or a Monad unto ourselves, and see how we quickly devolve/evolve into a Dyad between ourselves and the rest of the cosmos.

What does the Tetractys really represent?  If the Tetractys is fully present within each of ourselves, then that means we can start anywhere and go anywhere on our personal Tetractyes; we can start at Earth and work our way up through the elements, then the reagents, then the principles, all the way up to the Monad and back down to Earth; we can start at Fire and sublimate ourselves to Nothingness and back down to pure matter once more.  The Tetractys of Life is less about state than it is about process, less about what we are and more about how we come to be in every passing moment.  It’s the connections that we should study, I claim, since that’s where the real beauty and action happens.  Once we understand how we work internally, then we can start expanding outwards and relating ourselves to the rest of the cosmos.  I mean, if each of us is an individual Tetractys in the world, then we’re each our own monads, each taking part in an even larger Tetractys that connects and binds us all together.  Once we can understand the grander connections, we can scale back down and back up in a neverending Tetractys fractal, understanding how the cosmos as a whole is based on the same principles we are, and how we can use the same processes with different materia at different levels.  After all, ten monads does not a decad make; it’s the connections and processes between them that link them together into an ordering, a kosmos of its own.

While the Tree of Life in Jewish kabbalah was originally intended to be used as a mediation model to indicate the interaction of the Creator with Creation, and eventually picked up associations and correspondences to further those meditations, Hermeticists and occultists generally took qabbalah into their own hands as a model of magic and system of correspondences as a cosmological framework.  I don’t consider this an abuse of kabbalah, but I do consider it (at worst) a misuse of the system generally, especially when many people don’t have the required background to fully explore kabbalah as it’s meant to be studied and used.  In the same way, I don’t intend for this Tetractys of Life to be used as a system of correspondences but, again, as a meditative and theurgic blueprint for understanding how things come to be.  Tables of correspondence exist aplenty; good meditative models are harder to come by.

Magically, the use of the letters on the Tetractys’ paths deserves exploration.  For instance, the path between Venus/Water and Jupiter/Air is connected by Nu/Scorpio.  And, while the exact correspondences between the signs of the Zodiac and alchemy differ from tradition to tradition, the most common association I’ve seen with Scorpio is the process of Separation, where a mixture of two or more substances into distinct groups, usually with one of the components of the original mixture enriched in one of its resulting groups.  Air and Water are closely related, both being moist and easily blended with other substances, but it’s by their separation that we can see warm air rising and cool water falling, as in the Poemander’s description of the creation of the world.  Alchemically, we can understand separation in this sense of refining a particular lump of mass within a mixture, but we can also see it in other occult ways, too, such as whittling down extraneous forces to get to the heart of a particular matter or spirit.  We know that the path of Nu is a “lower register” in the Tetrad as the single path is directly above it in the Dyad is, or the path of Nu compared with the path of Xi, which we know is associated with Water, that which permits change and flow.  While Air connects and diffuses itself, Water flows and changes things, cutting certain areas off from others or whisking things away from one place to another.  Water is a form of separation, as separation is a representation of Water.

So now that I’ve thought about the place of the Tetractys of Life in magic a bit more, it doesn’t really have as big an effect on my magical practice as I thought it might have (or worried it might have).  Kabbalah was famous for crossing religions and traditions and incorporating more and more tools into its own toolbox; why not let mathesis do the same a bit, especially from those parts that themselves came from Neoplatonism or Pythagoreanism?  My day to day magical practice and religious offerings are going to be maintained, and the colors and materials of my talismans won’t change much if at all.  I will need to make versions of the magic squares using Greek letters and go through the planets and start getting new spirit names (as well as to figure out why there’s a “spirit of spirits” and “intelligence of intelligences” for the Moon and the like from the spirits themselves), but that’s something that we could all make do with, after all.

Oh, and names of God?  I haven’t forgotten about those, either.  Making use of my names of God from my first foray into making a Greek kabbalah, let’s see what we have.  First, recall that the Tetractys is composed of four ranks: a Monad, Dyad, Triad, and Tetrad.  I temporarily propose these names of God for these ranks, all based on Revelation 1:8, which contains all these names of God (attributes, really, but eh):

  1. ho Kyrios, “the Lord”
  2. hē Arkhē kai to Telos, “the First and the Last”
  3. ho Ēn kai ho Ōn kai ho Erkhomenos, “He who Was and Is and Is to Come”.
  4. ho Pantokratōr, “the All-Ruler”

All are God, of course, and the overall monadic name could easily be God (ho Theos), the Aeon (ho Aiōn), the Whole (to Holon), and so forth.  Personally, I’m getting into the habit of using Aiōn or Iaō as my primary go-to names of God, though my old Stoic inclinations always keeps the Whole nearby in my mind.  So, in conjurations, I’ll test how the use of these specific names work, though I’ll also shoot for other names to see whether other appellations or descriptors of God work better, or whether there are more secret names of God to be used.  Who knows?  As this Tetractys model of magic develops, maybe these names’ll be obsoleted in favor of others, or another method can be used entirely.