Elemental Transformations and the Geomantic Figures

It’s interesting what you can pick up from talking with spirits.  The other day, I was enjoying my weekly chat with my ancestors, making the usual offerings and just chewing the fat with them.  I don’t just include the ancestors of my blood and kin, though; the ancestors include everyone whose work or lives led to my own, so it’s a pretty wide field.  Generally speaking, as a magician, I have two large fields for my ancestors: one for ancestors of my blood and kin, and another for those of my faith and practice.  Magicians, priests, pagans, Christians, Jews, Hermeticists, anyone who’s already crossed and yet led to my spiritual life is considered an ancestor, and I have a special place for the ancestors of my Work in my heart.  There are other ancestors thrown into the mix of those two groups, of course, but those are the big ones.

When I told them that I was writing a book on geomancy, some in the ghostly crowd perked their ears up and started chatting more with me.  Geomancy being one of the most popular forms of divination in Europe historically over the past millennium, this isn’t too surprising, though I was caught a little off-guard by how on-board they were with that.  Since I like tapping into the ancestral font of knowledge those who have gone before me provide, I asked them for some advice with geomancy.  Besides some techniques I plan to do some more research on, one of the things they mentioned was performing another elemental analysis of the geomantic figures.  I got an image of Fortuna Maior transforming into Carcer, then again into Fortuna Minor, then again into Coniunctio, and then again into Fortuna Maior in a cycle.  I got the hint, and after a few inspired flashes of insight, I got the gist for a new(?) kind of elemental analysis for the figures.  I’ve already delved into one such analysis before, but this is a different kind focusing on the structure of the figures.

As you might have guessed, this post is gonna get into some geomantic theory.  Run away now if that’s not your thing or get some wine.

When considering the geomantic figures as mathematical objects, I normally ascribe four operations that can be done on them: addition, inversion, reversion, and conversion.  Readers of my De Geomanteia posts may recall this in my descriptions of the figures, but put briefly:

  • Addition: adding two figures to get a third (e.g. Puer added to Puella to obtain Coniunctio).  The interaction, harmony, and force between a pair of figures or forces in the cosmos.
  • Inversion: replacing all the single dots with double dots and vice versa (e.g. Puer inverted becomes Albus).  Everything this figure is not on an external level.
  • Reversion: rotating a figure upside down (e.g. Puer reverted becomes Puella).  The same qualities of this figure taken to its opposite, internal extreme.
  • Conversion: inversion with reversion (e.g. Puer converted becomes Rubeus).  The same qualities of this figure expressed in a similar, contraparallel manner.

The ancestors showed me yet another method to alter a geomantic figure, which I’m tentatively terming descending.  Descending a figure takes the bottommost row of a figure and stacks it on top of the figure, pushing the other rows downward.  Thus, Puer descended once becomes Cauda Draconis; this descends again into Caput Draconis, and again into Puella; and  again into Puer.  In doing this, we get several groups of figures that descend in a particular order: two monadic cycles, one binadic cycle, and three tetradic cycles of descent.

  • Populus descends into Populus
  • Via descends into Via
  • Acquisitio and Amissio descend into each other
  • Laetitia descends into Rubeus, which descends into Albus, which descends into Tristitia, which descends into Laetitia
  • Fortuna Maior descends into Carcer, which descends into Fortuna Minor, which descends into Coniunctio, which descends into Fortuna Maior
  • Caput Draconis descends into Puella, which descends into Puer, which descends into Cauda Draconis, which descends into Caput Draconis

Taken from an elemental viewpoint, this is the process by which the elements of a figure transform into their next most available state.  I forget where I read it from (something from Plato, probably), but the elements have two qualities, only one of which is primary.  The qualities are broken into two pairs of opposing natures: hot and cold, and wet and dry.  For instance, while the element fire is both hot and dry, it is primarily hot and secondarily dry.  The list of the elements then becomes:

  1. Fire: primarily hot, secondarily dry
  2. Air: primarily wet, secondarily hot
  3. Water: primarily cold, secondarily wet
  4. Earth: primarily dry, secondarily cold

Moreover, the elements are capable of changing into each other by replacing one of the qualities with its opposite.  Water, for instance, can turn into earth by making its moisture dry, and air can turn into water by cooling its heat; air can likewise turn into fire by drying its moisture, and fire can turn into earth by removing its heat.  The transformation of the elements can go in either direction, with the process from fire to earth signifying a process of settling or stability and the process from earth to fire signifying entropy or activity.  However, the elements also form a cycle, such that earth can also directly become fire without going through water or air, and likewise fire into earth.

Descending, then, is essentially the “settling” process of the elements applied to the structure of the geomantic figures.  The number of dots within a figure is preserved (note how Laetitia, Rubeus, Albus, and Tristitia descend into each other and all contain the same seven dots in different arrangements).  The reverse process of ascending is the “entropy” process of the elements, where the top line becomes the bottom and the rest of the elemental rows are pushed up.  Since the geomantic figures can be seen as abstract combinations of the elements, what the elements can do, so too can the geomantic figures.

Via and Populus are interesting in that they’re the only figures that descend (or ascend) into themselves.  Since they have the same activity or passivity in every line of their figures, they can only ever descend into what was already present.  I take this to mean that Populus and Via are at extremes of the elements: either there is absolutely nothing or there is absolutely everything, a void or a singularity.  Where there is nothing, nothing can be done since there is nothing to be acted upon; where there is totality, nothing can be meaningfully changed since it already includes everything.

Acquisitio and Amissio, similarly, are unusual in that they only descend into each other, without another two figures filling in the cycle.  Acquisitio is a combination of air and earth; Amissio is a combination of fire and water.  These elemental pairs are opposites, so by preserving their structural relationships, the descent of one figure composed from opposite elements is another figure composed from opposite elements.  No other figure in geomancy are like these two because of this.  Further, while the combination of air and earth produces gain, the combination of fire and air produces loss; moisture/dryness is a separate beast from heat/cold, so while one relies on the material bases of things (Acquisitio) which relies on the energetic and spiritual, the other relies on the energetic means of things (Amissio) which consumes the material and physical.  In order to gain things, one must expend effort or resources for it; in order to lose something, one must get meaning and direction for it.

The real show of descent comes into play with the other twelve figures of geomancy.  The simplest case is that with figures that contain a single active element: Laetitia, Rubeus, Albus, and Tristitia.  Laetitia is pure fire, and is a figure of joy, elation, optimism, and planning, all due to its hot and dry nature.  It has nothing else to go for it, though, so when that energy becomes less goal-oriented (fire) and settles down into a more material state (air), Laetitia becomes Rubeus, which is a figure of violence, chaos, confusion, and destruction.  That same energy is there, but it’s pure and untempered by anything else, so without direction the energy from Laetitia becomes scattered and dispersed.  Over time, the dispersion of energy in Rubeus settles further into Albus, with it starting to collect back into itself in a more contemplative, reflective manner.  The energy becomes less capable of causing change and is now more capable of being changed, becoming passive (not in elemental terms, here) instead of active.  Further, once the detached reflection of Albus settles further into Tristitia, the energy becomes locked down and completely crystallized into matter, unable to do anything on its own and only capable of being acted upon as a basis for other work.  Tristitia is a figure of fixidity and rigidness, without ability to move or act; it is only when the material of Tristitia is consumed and rejuvenated can it become active again, burning the dry fuel of Tristitia into Laetitia once more.

The next tetrad of figures in descent is Fortuna Maior, Carcer, Fortuna Minor, and Coniunctio.  Here, Fortuna Maior is a figure of slow and independent development, like a river carving out a canyon by its own nature and movement.  However, over time that energy becomes less and less, with all its potential used up; this devolves the nurturing force of Fortuna Maior into Carcer, which is no longer nourishing but only vacant.  Nothing can be done with this energy as it is, since it has lost all means of interacting with the world around itself; it is only when an outside force picks it up can it be sustained or made use of again, as indicated by the descent of Carcer into Fortuna Minor.  This mingling of forces leads to further mingling, focusing less on action and more on interaction, leading from Fortuna Minor to Coniunctio.  Communicationa and interaction becomes the theme, at least for a short while, until the interaction of forces settles further into self-action, separation of ways into one’s own path, which leads once again to the force of Fortuna Maior.

The last tetrad of figures in descent is Caput Draconis, Puella, Puer, and Cauda Draconis.  Caput Draconis is the figure of beginnings, with everything but fire being present; unlike its inverse of optimistic Laetitia which is all plan and no potential, Caput Draconis has all the material and interactive potential but nowhere and no impetus to use it; it is a pure seed.  The force of Caput Draconis, once it settles into Puella, becomes patient and harmonizing, aware of one’s physical means and of the need of others to make use of it.  In this phase, there is still little means to use something, but at least the desire for use is present.  Puella awaits the arrival and energy of Puer, which is the force that uses what Puella has to offer while having little of its own to use.  Puer is active and direct, countering Puella’s passivity and indirectness, and seeks to find and join with.  However, once Puer attains this and uses up everything obtained, this all settles down into an ending with Cauda Draconis; either the hero accomplishes his journey successfully or falls short and fails having exhausted his means prematurely.  Cauda Draconis is everything but earth, all energy and interaction but no means or substance, and quickly falls apart.  However, the residue from the collapse of Cauda Draconis plants the germ for the next iteration, starting with Caput Draconis again.

Bear in mind that each figure is a representation of the four elements that compose everything in our world; it’s not a stretch to consider the geomantic elements like alchemical formulae or states of the cosmos, and if we consider the figures to represent closed systems (as opposed to open systems that the operation of addition affords us), then we can analyze how a situation can evolve based on a single figure.  This enables us to make better use of single-figure readings: if we draw Coniunctio as a single answering figure for a query about a relationship, we can certainly say that things are going well and will continue to do so, but the relationship will also allow for self-discovery by means of the relationship and eventual self-growth (Fortuna Maior), with periods of being alone to process it or with difficulty (Carcer), and recovery with the help of the partner to come back to more connection (Fortuna Minor).  Likewise, if we add two figures in a house chart to understand the interaction between them, we can use the descent of the figures to see how that interaction will progress over time independent of the other factors in the chart.

Similar explanations of the tetrads of the figures can be given for the ascent transformation, as well, but I leave that as an exercise for the interested geomancy-minded reader.  Consider what we’re doing when we descend a figure: we take the elements within that figure, and turn the secondary quality into its opposite and make it the primary quality.  So, fire, which is primarily hot and secondarily dry, turns into air by our taking the secondary quality (dry) and turning it into its opposite (wet) and making it primary; the element that is primarily wet and secondarily hot is air.  The ascent of the figure is the opposite case: we take the primary quality of the elements, turn that into its opposite, and make it secondary.  Thus, fire (primarily hot and secondarily dry) becomes earth by taking its primarily quality (hot), turning it into its opposite (cold) and making it secondary; the element that is primarily dry and secondarily cold is earth.  I would say that it’s more natural for an element to descend than ascend, since it’s easier to change an element’s secondarily quality than it is to change its primary quality, so while the descent of the elements indicates a natural evolution without interference, the ascent of the elements can indicate a forced evolution from within the situation itself.  A situation might go either way, depending on the actions of those involved in the situation, but until outside forces are brought in to break the transformation by ascent or descent through addition, things are going to keep cycling in a particular pattern metaphorically and realistically.

Not a bad idea from sharing some rum with dead folk.

Geomantic Mathematics

Generating a complete geomantic chart can be a little daunting for people new to the art of geomancy.  I think it’s simple enough to learn, but there’s a fair bit of calculation involved.  It’s definitely more difficult than Tarot, where you just shuffle some cards and lay them out wherever you damn well please, but not as difficult as doing an astrological chart by hand (but then, who does that anymore?).

Still, there are fewer possible geomantic charts one might get than there are Tarot spreads ((78-10)! or (156-10)!, depending on whether you use reversed cards, and that’s just for the Celtic Cross) or astrological configurations (big big big big number, even if you limit yourself to just the seven traditional planets and whole degrees).  Since the four Mothers essentially define the rest of the chart, and since each Mother can be one of the 16 geomantic figures, there are only 16×16×16×16 = 65536 possible geomantic charts.  Any chart not in this set of charts are invalid and impossible to properly calculate.  How might you determine whether a given geomantic chart is valid?  There are three rules to validate a chart:

The Judge must be an even figure.  It is impossible for a well-formed geomantic chart to have an odd Judge; evenness is often called “impartiality”, and Judges as well as judges must be impartial in deciding a case.  Judge figures must be even due to the formation of the Daughters from the Mothers.  The Daughters make use of the same points from the Mothers, transposed so that they’re arranged in a different direction; thus, the number of points in the Mothers are the same as those in the Daughters.  Any number duplicated yields an even number, and the process of adding figures (or distilling them from the Mothers/Daughters to the Nieces to the Witnesses) preserves this kind of parity.  Thus, the Witnesses must be either both odd or both even, and in either case must add to an even figure.  The Judge is the only figure in the chart where this rule must apply.

At least one figure must be repeated in the chart.  As it turns out, no complete Shield chart with 16 geomantic figures can have all 16 distinct figures; there must be at least one repeated figure in the chart somewhere.  It may be possible that the first 15 figures (Mothers, Daughters, Nieces, Witnesses, and Judge) are distinct, but then the Sentence must of necessity repeat one of the other figures.  Consider that the Judge is formed from the two Witnesses, which themselves are formed from the four Nieces, which are formed from the eight Mothers and Daughters combined.  The Judge has eight separate roots, which may very well be distinct.  However, the Sentence is formed from adding the Judge to the First Mother.  Because the Judge also relies on the First Mother (via the Right Witness and First Niece), you’re essentially adding the First Mother to itself, which yields Populus; Populus, when combined with any other figure, repeats that figure.  Because of this “hidden repetition” in the chart, there’s bound to be at least one figure repeated in the chart somewhere, even if it’s just the Sentence.  That said, there are only 16 charts that have the first 15 figures unique, but that’s a topic for another day.

The inseparable pairs must add to the same figure.  This is an idea picked up from the Madagascan tradition of geomancy of sikidy, and shows the validity of the internal structure of the chart.  The idea here is that certain pairs of figures in the chart must add to the same figure: adding the First Niece to the Judge, the Second Mother to the Sentence, and the Second Niece to the Left Witness all yield the same result.  Similarly, the Left Witness added to the Sentence, the Right Witness to the First Mother, and the Second Niece to the Second Mother also yield the same result.  This is because the “units” that add up to any child figure (First and Second Mothers for the First Niece, or all the Mothers and Daughters for the Judge, or all the Mothers and Daughters for the Sentence with the First Mother duplicated) are the same within these groups of inseperables.  Any set of addition of “units” where two figures are repeated cancel each other out, forming Populus; the remaining figures add up to a particular figure that the other inseperables must also add to.

So, as an example, say that we have the following chart, where we have Via, Acquisitio, Coniunctio, and Laetitia as the Mothers.  Carcer, Cauda Draconis, Amissio, and Fortuna Minor are the Daughters; Amissio, Cauda Draconis, Caput Draconis, and Coniunctio are the Nieces; Rubeus and Tristitia are the Witnesses, Acquisitio is the Judge, and Amissio is the Sentence.

Example Geomantic Tableau

The Judge is Acquisitio, which is an even figure, formed from two odd figures; this is good.  There is multiple repetition in the chart (Acquisitio, Coniunctio, Cauda Draconis, and Amissio are all repeated somewhere in the chart), which is also good.  The two sets of inseparables add up the figures as below:

  1. First Set (sum of Third and Fourth Mothers with all the Daughters)
    1. First Niece + Judge = Amissio + Acqusitio = Via
    2. Second Mother + Sentence = Acquisitio + Amissio = Via
    3. Second Niece + Left Witness = Cauda Draconis + Tristitia = Via
  2. Second Set (sum of the Second, Third, and Fourth Mothers)
    1. Left Witness + Sentence = Tristitia + Amissio = Puella
    2. Right Witness + First Mother = Rubeus + Via = Puella
    3. Second Niece + Second Mother = Cauda Draconis + Acquisitio = Puella

Since the two sets of inseparable pairs add up to the same figures, respectively Via and Puella, this also checks out.  We can now rest assured that our geomantic chart is valid and proper for reading.

Do I do all these checks every time I calculate a geomancy chart?  Lol nope.  When I calculate a geomancy chart by hand (I sometimes use a program I wrote for this to automatically give me all the information I want from a chart), I’ll often just check the parity of the Judge and leave it at that.  Still, learning these rules and how the internal structure of the shield chart works is important to geomancy, since it underlies not only the mechanics of getting the divination system to work but also indicates important spiritual and oracular connections between the otherwise disparate symbols used.

The Geomantic Emblems and their Rulerships

Last time I brought up the geomantic emblems (previously called geomantic superfigures, 256 16-line “figures” that each contain all 16 geomantic figures within themselves), I described a few bits about the elemental representation and force within each figure.  In the process, I described a method where each geomantic emblem can be elementally analyzed and given an “elemental essential” rulership, by taking the “pure elemental” lines, and also how to split up the emblems into four figures to give them an entire geomantic chart as background.  However, I also mentioned that all 256 emblems could be reduced to a set of 16 by rotating them around; in other words, there are 16 sets of 16 topologically equivalent geomantic emblems.  16 is a significant number in geomancy, as my astute readers may have noticed, and I brought up how tempting and tantalizing it would be to assign a set of rulerships that correspond these 16 sets of geomantic emblems to the 16 figures of geomancy.  I didn’t have the method done just then, but I’ve finally come up with a way to link the two sets of symbols.  The correspondences are, using the list from last time:

  1. Laetitia: 1000010011010111
  2. Carcer: 1000010011110101
  3. Fortuna Minor: 1000010100110111
  4. Puer: 1000010100111101
  5. Acquisitio: 1000010110011110
  6. Populus: 1000010110100111
  7. Coniunctio: 1000010111100110
  8. Albus: 1000010111101001
  9. Tristitia: 1000011001011110
  10. Rubeus: 1000011010010111
  11. Amissio: 1000011010111100
  12. Puella: 1000011011110010
  13. Fortuna Maior: 1000011110010110
  14. Caput Draconis: 1000011110100101
  15. Cauda Draconis: 1000011110101100
  16. Via: 1000011110110010

How did I go about finding these correspondences?  A lot of math, hand-wringing, and sangria, that’s for sure.  If, dear reader, you’re interested in finding out how I corresponded the figures to the emblems, please continue after the break, but I’m going to warn you.  This post is long and at times tedious, and is full of binary mathematics and lots of 1s and 0s.  This post is only for the hardcore geomancy geeks like me out there, and it helps to have a solid footing in computer science, basic/low-level programming exercises, and binary/discrete mathematics.  Even I’m kinda shocked by how lengthy and pointlessly in-depth this post is, if that’s any indication of what you’re in for.  If you want to stop reading now, I forgive you and completely understand.  If you want to find out why I allocated the above emblems and their rotated variants to the figures like I did above, read on.  Either way, expect another post in the near future on how to use these emblems, their geomantic rulership, and elemental analyses in magic and divination!

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