# Sum of their Parts: The Planetary Syntheses of the Geomantic Figures

I don’t make as much of a practice of meditating on the geomantic figures as I sometimes feel I should.  It’s an important practice, I think, that really opens up some truly amazing doors in the understanding of the geomancer to not just get an intellectual feel for these sixteen symbols of elemental presence or absence, of elemental action, reaction, and interaction, but also to get a truly profound, soul-touching understanding of them.  This is crucially important, I claim, for any new geomancer: perhaps even before studying the techniques of geomancy (which are pretty straightforward, really), they should make an effort to truly learn what the figures are, not just what they mean or stand for through rote memorization of correspondence lists or the like.  In doing so, we learn more about the figures and how they play out in the world around us.

Back during January, during some of my usual daily prayers, the thought arose to me that maybe I shouldn’t just be meditating on the figures more often than once a year or so, but also to simply consider newer and other ways to understand them. After all, we have all these mathematical ways of understanding the figures, the various operations that can be applied to a figure to transform it into another, but one of the most important for us is addition: the process of taking two figures and combining them mathematically to form a third.  This is the fundamental technique that allows us to come up with the Nieces from the Mothers or Daughters, the Witnesses from the Nieces, the Judge from the Witnesses, and the Sentence from the Judge and First Mother.  The process of addition can be interpreted in one of three ways:

• Us + Them = Interaction
• Start + End = Transition
• Factor + Context = Conclusion

In all cases, what addition shows us is what happens when you add the symbolism of one figure to the symbolism of another.  For instance, consider the two figures Puer + Laetitia = Acquisitio.  What could this mean?  Well, let’s consider it according to the three models of addition above:

• (Us + Them = Interaction) Our youthful energy, drive, and brazenness is faced with a happy time and people more than happy to uplift us and support us.  The combination of like minds, with the enthusiasm of Puer on our side combined with the optimism of Laetitia on the other, yields great gain for us all.  However, that gain is only incidental; what matters more is finding people willing to help us as we need to, so that we’re not the only ones striving for something.
• (Start + End = Transition) A stoked start to matters, full of energy and gumption and not a small amount of willingness to step on toes to get our way, is going to indeed get our way and find everything that we seek.  It’s this very nature of winning, when all we want to do is win, that will get us to a state of true happiness and bliss.  Money isn’t what matters, but it certainly helps us in our overall goals to celebrate the goodness that life has in store for us.
• (Factor + Context = Conclusion) Put a bull in a china shop, and you can expect things to get broken.  However, put a bull in a lush field full of other happy cows, and you can expect the bull to be in a happy place, indeed, doing what bulls naturally want to do: eat, sleep, and procreate.  When a huge bundle of energy like yourself is put in a situation where it’s own heat and drive is redirected and put to useful ways, all that energy you have goes to natural, proper ends that just works well for everyone in the end, so long as that energy is allowed to do what it naturally needs and wants to do.

With addition, we can expand our notions of 16 geomantic figures to 256 geomantic processes, each of which can be interpreted along the three models above, all of which touch on the same core idea but which can be phrased in different ways appropriate to different models of understanding or different situations in which they appear.  This is where the complexity of geomancy truly lies, I feel, and the only way to really navigate these complexities is through having a profound, intuitive understanding of the figures, which only comes about through study, contemplation, and meditation.

To be fair, not all such study, contemplation, and meditation needs to be done sitting on a mat and pathworking or scrying the figures.  Sometimes we can take a more logical or synthetic approach as opposed to a mystical one which itself can yield a fertile ground for further meditation, and today, I want to take a new twist on that.  We know that addition is an important operation in geomancy that can yield not just new figures but also new understandings of the figures, but we also know that there are 16 figures, which can be reasonably broken down into eight pairs of figures, each pair relating to one of the planets (Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, and the Nodes).  If there’s a pair, then there can be addition:

Planet First Figure Second Figure Synthesis Figure
Moon Populus Via Via
Mercury Albus Coniunctio Rubeus
Venus Puella Amissio Tristitia
Sun Fortuna Maior Fortuna Minor Via
Mars Puer Rubeus Carcer
Jupiter Acquisitio Laetitia Puer
Saturn Tristitia Carcer Laetitia
Nodes Caput Draconis Cauda Dracions Carcer

What we have here is a table of what happens, what figures result when you add the two figures belonging to the same planet together.  Thus, consider the two figures of Mercury, Albus and Coniunctio.  If you add them together, you get the figure Rubeus.  What might this mean symbolically, not just for the figures of Mercury but for a geomantic understanding of Mercury itself?  Remember that the addition of figures shows us what the core themes of interaction, transition, and conclusion are between two forces, but in this case, we’re taking the two sides of each planet and seeing what happens when we synthesize them together.

There are a few observations we can make right off the bat:

• In all cases except for the figures of the Moon, the synthesis figure is both a different figure than either the original figures and also belongs to a different planet than the planet that the original figures belonged to (Jupiter in the case of the figures of Saturn, Mars in the case of Jupiter, etc.).
• Two figures are repeated among the synthesis figures: Carcer (formed from both the figures of the Nodes as well as the figures of Mars) and Via (figures of the Sun and figures of the Moon).  Mathematically, this is because these are the only planets whose two figures are inverses of each other, and Via can only result when you add inverses.  This suggests that only the figures of the Moon and the Sun are truly opposites of each other and reflect two totally distinct sides of each planet; all the other planets share something in common and show different themes without being complete opposites.
• The synthesis figures are always going to belong to the Moon (Via), Mars (Puer or Rubeus), Jupiter (Laetitia), or Saturn (Carcer or Tristitia).  Mercury, Venus, and the Sun do not appear at all in this mix.  This is an interesting contrast to the Judges that can result from a geomantic chart, where only Mars is unrepresented as a Judge.
• Saturn has a plurality of synthesis figures with three out of eight, Mars has two, the Moon has two, and Jupiter has one.  This is another interesting contrast to the number of figures belonging to the planets for the possible Judges that can form in a chart: the Moon has two possible Judges, the Sun has two, Mercury has one, Venus has one, Jupiter has one, and Saturn has one, with Mars having none at all.
• Three of the four pure-elemental figures (Laetitia, Rubeus, and Tristitia) are present among the synthesis figures, but Albus is left out, the figure of pure Water.  Coincidentally, we have the inverse of Albus, Puer, as the synthesis of Jupiter, the figure that has everything but water.  In fact, with the exception of Via, all the planetary synthesis figures lack Water entirely as an element.

What we’re building up to is an understanding of a geomantic understanding of the planets (including the pair of Nodes together as a “planet” in its own right, at least for the sake of the model here) by seeing what happens when we add—synthesize—the two figures of a planet.  As opposed to simply looking at the different way a planet can express its energy, what we’re arriving at is a geomantic symbol of the core nature or tension of that planet, and how that nature relates to other planets as well.

With that in mind, let’s take a deeper dive into this and see how this plays out for each pair.  While I’m sure there’s more to be said than just a simple paragraph about each synthesis pair, this should be enough to get started for the sake of contemplation and meditation on the figures.  Note that the focus here is on the synthesis figure, irrespective of the order in which the synthesis takes place (e.g. Albus + Coniunctio and Coniunctio + Albus both add up to Rubeus equally).

Moon: Populus + Via = Via

This one is almost too easy, given that this is the only synthesis of planetary figures that yields a figure of the same planet as its components.  However, we should consider why that synthesis figure is Via and not Populus.  Via is the figure of change, and that is fundamentally the nature of the Moon: the Moon is in a constant state of flux, never appearing the same from one night to the next in its raw appearance.  As the fastest of the seven planets, the Moon constantly shifts between signs and lunar mansions on a scale completely beyond all the other planets, which is why the Moon symbolically has her planetary joy in House III.  However, more than that, Via is the one figure that has all four elements present and active; in astrology and astrological magic, the Moon is the planet that gathers up the light of all the other planets and can act as a stand-in for any other planet as necessary.  As the lowest of the planets, the Moon is also the closest planet to Earth, the realm of totally manifested reality, and thus the Moon is closest to the realm of the elements themselves.  In this light, Via is almost boringly obvious as the figure that relates to the essence of the Moon.

Mercury: Albus + Coniunctio = Rubeus

I suppose it’s super fitting, given that Mercury is generally considered a mutable planet harmonious with the element of Air, that the two Mercurial figures of Albus and Coniunctio add to form the figure whose sole active element is Air: Rubeus.  However, Rubeus is generally a hot and dangerous figure, one of deceit, treachery, lies, theft, and confusion—but are these not also things that trickster Mercury is known for?  We praise Mercury as being the planet of communication and commerce, travel and trade, language and science, and all this is true, but if a planet can bestow something, it can just as easily corrupt or deny those things, too: if Mercury grants a strong mind, it can also grant a weak or debilitated mind, or one that’s so strong that it becomes a deadly weapon in its own right (cf. “the pen is mightier than the sword”, and spilled ink can lead to spilled blood).  Further, we should never ignore the mythological aspects here of Hermēs being the slayer of Argos, in some myths by beheading with a golden sword, in others by bludgeoning with a rock, through with a scheme of trickery and plotting involved in such a thing, and ultimately to rescue (steal) Iō from Hēra.  If Albus is the mind at its most refined and noble, then Rubeus is the mind at its most raw and corrupt; it’s perhaps a good thing that Hermēs is the messenger of the gods acting on their behest rather than his own, since if Hermēs were to take his power into his own hands rather than using it on behalf of Zeus and the other gods, as the Homeric Hymn to Hermēs suggests, his greatest inclination is to lie, cheat, steal, deceive, and hoodwink all others endlessly for his own selfish gain.  We should remember that the mind is not just a tool but a power unto itself, and without harnessing that power and refining it through wisdom and morality, that power will serve itself more than anything else in ways that are cruel, crude, despicable, and destructive.

Venus: Puella + Amissio = Tristitia

Now this is an odd one: the figures of Venus add up to the figure of Saturn, Sorrow.  Off the bat, my first thought is that Saturn has its exaltation in Libra, a sign of Venus, but that’s not saying much about why Tristitia would be the synthesis figure for Venus.  There is also the notion that, to me at least, I associate Venus most strongly with the element of Water, and each of the elements has a particular motion associated with it: Air expands and Earth contracts, Fire goes upward and Water goes downward—and Tristitia is a figure of downwards motion, yet that too doesn’t seem to hit on the connection here all that well.  There’s something about the raw, simple power of pure Earth that turns the volatile passion of Amissio into the stabilized harmony of Puella: the feeling of having enough, the knowledge that everything is going to be alright, the blessing of experience and memory, the ability to dull or blunt emotional pain (whether one’s own or that of another).  All of these things are Earthy, sure, but none of these things strike me as Sorrowful.  But there is something here: all these things come about as the result of labor.  The fields and the forest may be abundant and fruitful, sure, but what good is all of that if you do not toil in the fields to ensure a harvest, or wander in the fields risking cuts and bites to pluck berries and mushrooms?  Venus, in all its splendor, is not a planet known for its labor, but there is a deeper, more profound labor going on behind the pretty face, whether done up for a night out or marred by tears from a bad night: there’s a profound emotional labor going on, either in the process of it that causes emotional volatility or as a result of it that produces emotional stability.  Venus, as a primary symbol of femininity, is also a symbol of childbirth, and how arduous and painful can that be, filled with tears and groans and moaning?  Tristitia is a profound figure that makes things alright in the end, but the process of that can be hard and long—but always results in pleasure, once the clouds clear from the skies.

Sun: Fortuna Maior + Fortuna Minor = Via

The other synthesis pair of figures that yield Via, it’s somewhat surprising to find that the figures of the Sun synthesize into a figure of the Moon.  After all, if Via is all about change, what do we make of this since we know the Sun to be a symbol of perfection and eternity itself?  We should still remember that even if the Sun itself is perfect and timeless, how the Sun relates to the Earth is not: the Sun rises and sets and itself marks the most fundamental change in the world, that of the day-night cycle, as well as that of the seasonal cycle as the Sun gradually moves above and below the celestial equator along the ecliptic.  Heck, think of the neopagan concept of the Wheel of the Year that discusses the various solar events of solstices, equinoxes, and zodiacal midpoints and how this tells an agricultural story of the birth, growth, triumph, fall, death, and rebirth of the Sun.  We should also note the reference in PGM XII.201ff (the Royal Ring of Abrasax ritual) to “yours is the processional way of Heaven”, referring most likely to the starry road of the ecliptic—and what is Via if not literally a road?  Rather than Via indicating change itself as it does for the Moon, for the Sun, Via instead indicates the process of change rather than the thing that undergoes change: while the roads we take in life take their toll, the roads themselves remain themselves and do not themselves go anywhere.  So too does the Sun show the road that we take, season in and season out, year in and year out, and even though the Sun will always remain the Sun, we constantly change as we follow the Sun throughout the times of life.

Mars: Puer + Rubeus = Carcer

The first of two synthesis pairs that yield Carcer, this pair of the figures of Mars shows a bold hero facing the endlessly tumultuous battle, the stoic soldier fighting against a raving berserker.  The notion of Carcer here is that of being locked into battle, a constant and neverending struggle of violence from which one cannot escape.  This is the figure that demonstrates the endless drive to break through and break free despite the utter impossibility of doing so (cf. the prisoner unfairly imprisoned who constantly plots and works their way out of prison) as well as the endless anger and frustration of trying to break free from that which binds oneself: we shouldn’t forget that Fire is present in Carcer, too, after all!  On top of this, Carcer is the figure of separation, which is the crucial action of Mars: the fundamental purpose of a blade is to cut, which divides one thing from another (whether a rope bridge spanning a chasm or the blood from its body).  In struggle, Mars separates one person/side/thing from another, yet the person/side/thing that is separated from the other will always be locked into a struggle with it, whether the struggle of imprisonment, of war, or of life and death itself.  While we might consider Puer to be a sword and Rubeus a battleaxe, Carcer would then be a sort of shield, another thing that cuts off one from another without doing much to resolve that separation.

Jupiter: Acquisitio + Laetitia = Puer

Now this is a fun one: the two Jovial figures adding up to a Martial one.  Why should two otherwise beneficial figures that lead to happiness—material and financial on the one hand, emotional and spiritual on the other—lead to something that so easily ruins happiness?  Crucially, there’s always too much of a good thing, and if any planet exemplifies the idea of “too much”, it’s Jupiter.  Jupiter is the planet of expansion, but to expand requires force, and Zeus, as king of Olympos, has all the force in the world to wield, whether for weal or for woe: there is nothing that can withstand the might of Zeus.  More than that, when we have good things, we want more good things, and that want, if not tempered by wisdom, can become a corruption of them, as acid (a Martian thing!) dissolves lesser metals.  Acquisitio’s desire for wealth can become insatiable greed, and Laetitia’s desire for hope and success can become reckless daring.  Jupiter is pure power, and that power is to make things more Jupiter through force, one way or another.  After all, how often do kings and rulers in our own world resort to the application of force, oftentimes brutal, whether against their own people or others, in order to satisfy their needs for resources, space, or the fulfillment of their state’s ambitions?  If the nature of a king is to rule, then the underlying ability that allows that king to rule is the application of force.

Saturn: Tristitia + Carcer = Laetitia

Just as it’s somewhat surprising to find that the figures of the Sun yield a figure of the Moon, it’s also weird to see the figures of Saturn synthesizing into a figure of Jupiter, doubly so since Laetitia is the reverse of Tristitia.  Structurally speaking, this synthesis is a lot like what’s going on with the Mercurial figures (an axial figure plus a pure elemental figure), and in that light, seeing how we took a heavily mythological twist to that analysis, perhaps it’s fitting to bring up that Kronos was once a benevolent, almost Jovial king during the Golden Age when humanity “lived like gods without sorrow of heart, remote and free from toil and grief: miserable age rested not on them…”.  It is true that Saturn is the planet is melancholy, depression, toil, labor, old age, decrepitude, and the like, but that’s just its effects from our side: consider that once you strip away everything else that is unessential baggage (a la one’s Saturn return), that which remains is the pure essence of the thing, and this itself is freedom and a kind of joy unto itself, a revealing of truth from the deception of incarnation.  Plus, Saturn is the highest of the planets in the heavens, and Laetitia is the figure of upwards motion, indicating Saturn’s top position above all, closest to Divinity and showing the way to true joy where old age and death no longer have any power or presence.  The way to such a destination is fraught with endless problems and terrible toil, just as the course of the afterlife in Egyptian thought through the Duat, but so long as you hold true to the course and can survive everything thrown at you, your ultimate destination is a place of eternal joy, not of emotion but beyond all emotion.

Nodes: Caput Draconis + Cauda Draconis = Carcer

The second of two synthesis pairs that yield Carcer, the two figures of the lunar nodes here don’t show the struggle and separation side of Carcer, but rather show the other aspect of this figure as a cycle.  Consider the ouroboros, the symbol of eternity of the snake swallowing its tail, an apt symbol for the combination of the Head and Tail of the Dragon: the cycle of beginning and ending is an eternal one, for when one thing ends, another must begin, and where one thing begins, another must have ended.  This is the eternal cycle of creation and destruction, the cycle of life and death itself, the cycle of saṃsāra into which we are constantly born time and time again whether as reincarnation or as rebirth.  The only way to break out of the prison of the world is to break the world itself; the only way to escape creation is to cease being created and to cease participating in creation entirely.  After all, in many religions and cosmologies, the world has a fundamental start point and a fundamental end point, but these are often outside time itself.  In this, Carcer represents not just the cyclical creation/destruction of the cosmos, but also the walls that separate that which is inside creation from that which outside it entirely; this is the dragon in the ninth heaven, above the fixed stars themselves within creation but still below the domain of God outside creation.

# Another System of Elemental Affinities for the Geomantic Figures

There’s not a lot of modern geomantic literature out there, it’s true.  Most geomantic stuff written is decisively pre-modern (a good deal of which is already digitized and free to access by anyone!), and the rest of it that is modern is…well, sometimes it’s hit or miss, though there are more winners among the lot than not.  Still, compared to the endless books put out on Tarot or astrology or runes or playing cards, there’s just not a lot out there as far as geomancy books are concerned.  But, interestingly enough, it turns out that the French have been quite busy with geomancy in the 20th century.

Unlike modern Anglophone publications on geomancy, of which there really haven’t been all that any, I’ve got at least a dozen books stacked on my desk, all published in the 20th century in French, some more scholastic or academic than others, some more pop-divination or pop-occult than others.  It’s honestly refreshing in many ways, though not nearly so surprising in others; after all, the French are well-known for having colonized much of Africa and large parts of the Middle East, and I’m positive that their colonialism and imperialism fed into their anthropological and cultural studies of many of the places that they situated themselves and took over.  Without putting a silver-lining spin on it, this research does help Western understanding of African and Arabic styles of geomancy, and has led to plenty of texts being written in French on geomancy, deriving information from both the Western European tradition as well as the African and Arabic traditions of the art.

Much of the French geomantic literature is pretty standard stuff that you’d find in any other geomantic text, but there are a lot of surprising finds, too.  Some of the more outré topics I’ve invented or delved into (e.g. geomantic emblems or geomantic magic squares) were already known to and explored by French geomancers, which is an incredible relief to me—it means that I’m not the only crazy one in the room, and I don’t have to completely reinvent the wheel when I can see what else has already been written about it—or some of the really obscure finds I’ve had to piece together were already well-described and known to the French (e.g. the traditional assigning of the geomantic figures being based on an older system of associations to the lunar mansions) but perhaps the one most startling thing about many (but not all) French geomantic texts is the system of elements they use to describe the elemental rulerships and affinities of the figures.  As we all know, the geomantic figures are composed of different combinations of the four classical elements, but each figure is also generally aligned with one particular element as a whole.  Which element that would be is based on one of two systems, an older and more pervasive one that appears based on which elements are active or passive in a figure (e.g. Albus given to Water) and a slightly more recent one based on the planetary-based zodiacal rulerships of the figure (e.g. Albus given to Gemini because it’s a Mercury-ruled figure).  Heck, I’ve even come up with a theoretical association of my own, also based on the elemental structure of a figure but less symbolic and more based on what cancels out and what’s left after that (though I don’t myself use this one).

But this particular system so common in so many French geomancy texts is different.  Like the traditional elemental system and my own innovative theoretical one, this French system is also structural, but it’s not really based on which individual elements are active or passive in a figure.  Rather, it’s based on the dot patterns of the upper two lines of a figure.  Consider the qura`ah (or qirrah), the spindle-dice so commonly used in and associated with Arabic and Persian geomancy:

As I’ve mentioned before, a pair of these spindle-dice are used together to generate four Mother figures all at once: you take both, spin the blocks on each spindle, and slap them down together on the table, and you read pairs of blocks, one from each spindle.  So, in the image above, the four Mothers that would result from that particular arrangement of spindle-dice are Caput Draconis, Acquisitio, Caput Draconis, and Albus.

Geomantic figures are essentially binary numbers (base-2): you have four rows, each row having one or two dots, giving you a choice of sixteen figures (2⁴ = 16).  However, you could also consider the geomantic figures as quarternary numbers (base-4), too: rather than considering individual rows, you look at the upper two rows and bottom two rows together.  In this way, rather than a single row being one of two options (single point or dual point), you get a pair of rows that has one of four options (4² = 16: single-single, single-dual, dual-single, dual-dual).  If we break down a geomantic figure into two pairs of rows rather than four individual rows, we can consider what the symbolism of a pair of rows means.

What these French geomancies do is give a different elemental association to the points found in pair of rows:

• Single-single (shaped like a vertical line, :, e.g. the upper part of Fortuna Minor): Fire, a single flame burning upwards.
• Single-dual (shaped like an upwards-pointing triangle, , e.g. the upper part of Puella): Water, something that pours out and expands downwards.
• Dual-single (shaped like a downwards-pointing triangle, , e.g. the upper part of Caput Draconis): Air, something that rises and expands upwards.
• Dual-dual (shaped like a square, , e.g. the upper part of Albus): Earth, the stability of the level plane.

EDIT:  Okay, I don’t know what’s going on, but apparently the dot patterns don’t show up in text right on all computers.  On some computers it displays as described, but on other computers it displays where the Earth four-point square is set to Air, the Water upwards-triangle is set to Earth, and the Air downwards-triangle is set to Water.  I don’t know how to resolve that or why that happens.  The content of the post is right, but the dot characters here may not be depending on your platform, browser, etc.

Some texts go further and try to relate these point-arrangements to the I Ching—which I don’t agree with due to a lack of any significant connection historical or otherwise—saying that single-single Fire is given to old Yang, dual-single Air to young Yin, single-sual Water to young Yang, and dual-dual Earth to old Yin.  Whatever.  I don’t agree with a Chinese or I Ching-based origin of geomancy, as there’s already plenty of evidence suggesting that geomancy originates in Arabia, and even if not, I’d still favor a north African origin anyway.  What connections there are between geomancy and I Ching, I find, are entirely superficial, and it didn’t help that European missionaries didn’t know what else to call fēng shuǐ besides “geomancy”, leading to centuries of misnaming and misunderstanding.  Just like with the pips of dominoes and the points of geomancy (as I brought up a bit ago), just because things look kinda similar doesn’t mean that they share a common origin.

Back to the topic at hand.  This is an interesting way to adapt the four-element symbolism to the simple shapes produced from two, three, or four points put together.  Admittedly, I find it a little weird, since I’d normally be inclined to give the single-dual upwards-pointing triangle to Air and dual-single downwards-pointing triangle to Water, but I get where this symbolism is going from; after all, Water is associated with downwards motion and Air with upwards (or at least sideways) motion, and I’d want to look at the shapes these points make from the perspective of direction rather than expansion, but I get it.

That’s the whole basis for this elemental symbolism.  To find the elemental association of a particular figure, simply look at the upper two lines of a figure, and that point arrangement gets you the ruling element of that figure.  That’s all there is to it.  Thus:

• Fire figures (upper two lines single-single): Via, Cauda Draconis, Puer, Fortuna Minor
• Air figures (upper two lines dual-single): Caput Draconis, Coniunctio, Acquisitio, Rubeus
• Water figures (upper two lines single-dual): Puella, Amissio, Carcer, Laetitia
• Earth figures (upper two lines dual-dual): Fortuna Maior, Albus, Tristitia, Populus

Far less common than this, though, some texts will also look at the bottom two rows of a figure in the same way to get a sub-element, such that Via is Fire-on-Fire, Albus is Earth-on-Water, and so forth, but that’s super uncommon—but, then, so is the notion of sub-element or secondary elemental rulers in general (even if I make heavy use of such symbolism).  Most texts simply leave the association at one element based on the upper two rows, and that’s about it.  Still, because I’m fond of tables and charts, we can come up with a simple such table that plots out which figure belongs to which primary (upper) and secondary (lower) elemental structures:

Upper
Fire
(:)
Upper
Air
(⸪)
Upper
Water
(⸫)
Upper
Earth
(⸬)
Lower
Fire
(:)
Via Caput
Draconis
Puella Fortuna
Maior
Lower
Air
(⸪)
Cauda
Draconis
Acquisitio Carcer Tristitia
Lower
Water
(⸫)
Puer Coniunctio Amissio Albus
Lower
Earth
(⸬)
Fortuna
Minor
Rubeus Laetitia Populus

I suppose the symmetry of the figures would be better preserved if I swapped around the Air and Water rows and columns, but I rebel at that, personally, so whatever.

As far as how to use such a system of elemental affinities and rulerships, I mean, it’s the same as any other: they can be used as a basis for meditating upon and contemplating the figures, understood in relationship to other figures, compared in terms of elemental strengths or weaknesses based on what’s around it or where it’s placed in a chart, and the other usual uses; in that, it’s just another system of elemental rulerships available for the figures, just like any other.  What I can’t really figure out, however, is where this system came from.  It doesn’t appear in any older European or Western text I’m aware of, and only seems to appear in most (but not all) French texts, suggesting a common language-bound origin—and, given the French history of colonialism and imperialism in areas where African and Arabic traditions of geomancy were practiced, might have just such an origin.  Plus, the use of pairs of rows in a figure does neatly echo the use of spindle-dice, which were historically only found in the Middle East and South Asia, further suggesting an Arabic practice—though maybe not an utterly ancient one, since the spindle-dice were not there from the beginning of the practice and I don’t recall seeing any row-pairwise analysis of figures brought up in any of the texts I’ve glanced over.

Now, back in the days from the old Geomantic Campus Yahoo! Group days, I swear I saw some image of some North African instance of geomancy that gave these same row-pairwise associations of the elements (like there was a tarp up in the background of a reading being done with some diagrams, including linking the four elements to the Tetragrammaton), but looking back through the group (before the old archives of all Yahoo! groups vanish in a few days), I can’t seem to find anything along those lines, so maybe I saw such a thing somewhere else.  I know I’ve come across such a thing a long time ago, but at the time I didn’t think much of it, so I don’t have any notes or references to such a system.  (If anyone knows the picture, direct me to it, as I’d be greatly appreciative.)  And, as I’ve said, most—but not all—of these modern French geomancy texts seem to share this system, and it really only seems to be French geomancy texts that do this.  To me, this indicates a single, common origin that spread outwards from there within the Francophone geomanticulture (hey, we have “occulture”, why not “geomanticulture” too?).  Happily, many French geomantic texts include a bibliography, so it’s not terribly hard to track down such texts.

From what I can see, this system of elements likely happened at some point between 1940 and 1986.  I give these two dates because these are the years of publication for the famous French occultist, Mason, and Martinist Robert Ambelain, who published La Géomancie Magique in 1940 and La Géomancie Arabe in 1986; in the former, he gives the usual older European (pre-Agrippa) form of elemental assignments to the figures, but in the latter, this row-pairwise one.  However, earlier texts than La Géomancie Arabe use this system, too, like in the 1978 La géomancie: un art divinatoire by Alain le Kern.  So, probably somewhere around the 1950s, this new method of assigning elements came into the French geomanticulture (the word’s sticking with me now), and may well have an Arabic origin or, more likely, a North or Northwest African origin.  Beyond that, I can’t currently tell.

Still, it’s a nifty system.  Another method to think about, for those who find a logic in it.

# Revisiting the Sixteen Realms of the Figures

Happy solar new year!  Today’s the first full day of spring according to the usual zodiacal reckoning, with the spring equinox having happened yesterday afternoon in my area; if I timed it right, this post should be coming out exactly at my area’s solar noon.  I hope the coming year is bright and full of blessing for all of you.

I’m taking the day to celebrate, as well, and not just for the freshness of the new year.  Since the start of the calendar year, when I made that post about a sort of feast calendar for geomantic holy days, I’ve been busy coming up with an entirely new devotional practice.  It’s not really my doing, but it’s a matter of inspiration, and…well, it’s an impressive effort, even by my own standards.  As part of it, around the start of the month (fittingly, the start of this current Mercury retrograde period!), I undertook my first celebration of the Feast of the Blessed Dead, my own recognition, honoring, and feasting with the blessed ancestors of my kin, faith, work, and practices.

And, of course, far be it from me to pass up a half-decent photo op.

According to the scheme I made for a geomantic calendar, after the Feast of the Blessed Dead at sunrise begins the Days of Cultivation, 16 days of prayer, meditation, study, fasting, purification, and the like.  In a way, it’s kinda like a kind of Lent or Ramaḍān, but at least for only 16 days instead of a lunar month or 40 days.  After those are done, it’s the Feast of Gabriel the Holy Archangel, Teacher of the Mysteries.  Which happens to coincide (either on the day of or day after, depending on the exact time) with the spring equinox.  Yanno, today.  So I’m quite thrilled to bring this ordeal to an end and take things easier again—especially after a good two hours of prayers, rituals, and offerings this morning—but I can’t take it too easy; one of the many benefits I’ve been seeing from doing this practice is that it’s forcing me to get back to a daily practice again, something I’ve been meaning to do now that I have the time again in the way I want to but just haven’t.

(As a side note: one of the things I’ve been doing is a kind of fast, not a whole or total fast, but something more like a Ramadan or orthodox Lent with extra dietary restrictions: no eating or drinking anything except water between sunrise and sunset, one large meal after sunset, no meat nor dairy nor eggs nor honey nor any other animal product.  It wasn’t my intention to go vegan; instead, I had this elaborate progressive fasting scheme that took inspiration from kosher dietary restrictions and the Fast of Daniel from the Book of Daniel, but that proved way too complicated for such a short-term thing, so I just decided to omit meat and dairy, but that then extended to all animal products, so.  I have to say, it’s been a good exercise, all the same, and the intermittent fasting regimen is something I may well keep up, as I’m seeing other benefits besides spiritual focus, even if I do find myself being cold a lot more often than before; more reason to cultivate inner-heat practices.  All that being said, I am excited to indulge in a whole-ass pizza or tub of orange chicken tonight.)

One of the practices I was doing every day during these Days of Cultivation was a contemplation on one of the sixteen figures of geomancy.  In a way, I was returning to one of the oldest and first major things I ever did in my geomantic studies.  John Michael Greer in his Art and Practice of Geomancy, as part of the section on geomantic magic, instructs the reader to “scry” the figures.  Rather than scrying into a crystal ball or anything like that, what he means is an active contemplation and visualization of the figures, or in more Golden Dawn-ish terms, engage in a kind of pathworking of the figures: visualize the figure clearly, then see it emblazoned on a door of some kind, then go through the door and see what you see, hear what you hear, and experience what you experience as part of the realm or world of that figure.  This is a deeply profound and intimate way to learn about the figures, once you have a basic understanding of their usual meanings and correspondences, because you’re actually entering the worlds of the figures themselves.  Those who recall my De Geomanteia posts from way back will remember that I gave an elaborate visualization or scene that helped to impart some of the meaning of that figure; those are the direct results of my contemplations of the figures from years ago.  (If you never read those posts, check them out!  I talk about the figures in depth and at length, and talk a bit about some really useful geomantic techniques, too.)

So, I decided to try contemplating the figures again, except this time, I brought a lot more of my art to bear (I wasn’t really a magician back in those days!) and fit it within the framework of this burgeoning devotional practice, calling on my guardian angel as well as the archangel Gabriel, that famous celestial being who taught the founders of geomancy their art, to help me understand the figure through its mysteries.  The process was, fundamentally, the same, except with some preliminary and concluding prayers (which helped in ways I would never have conceived of even a few months ago, much several years ago): visualize the figure, see it form a door, mentally go up to the door and knock, open the door, and go on through.  I augmented this process by using the geomantic salutes as well as by intoning the epodes for a figure and reciting the orison for a figure (16 short hymns of the figures, available in my Secreti Geomantici ebook!) for an all-around way to get as much of me engaged in the process as I could without breaking out into a fuller ritual involving incenses or candles or the like.  For the order, I used my trusty elemental ordering of the figures according to their primary and secondary elemental rulerships, based on the structure of the figures rather than their planetary or zodiacal correspondences.  So, I started with Laetitia on the first day, Fortuna Minor on the second, Amissio on the third, and so forth, up until Tristitia on the last and final day.

I was looking forward to seeing what new knowledge I could get, getting reacquainted with these figures I see and use so often in my work, maybe even revisiting the same scenes I saw so long ago.  Interestingly enough, that wasn’t the case.  Instead, what I was shown was a city, a vast metropolitan city filled with skyscrapers and towers that came to an abrupt end at a single, long road that ran from an infinite East to an infinite West, on the opposite side of which was an equally-vast forest, filled with every kind of tree and bush and plant imaginable.  Every figure-contemplation took place along that road, dividing that vast city and that vast forest, but every figure-contemplation was drastically different: time of day, weather, what was happening, the condition of the city; heck, there even seemed to be a notion that sometimes years or even decades would pass along that road between visualizations.  In a way that caught me off-guard, the elemental ordering of the figures I used told a deep, intricate, and coherent story of the flow of time of that place, between the metropolitan inhabitants of the city and the autochthonous inhabitants of the forest, ranging from celebration to war to cataclysm to peace and all the things between.

In a way, I guess I was revisiting the realm of Via itself.  After all, the fact that all these visualizations took place along a Road was not lost on me, and seeing how this figure is often considered to be the first figure of geomancy in the historiolas that we have as well as having all elements present, and that I was using an elemental ordering of the figures to arrange and schedule my contemplations of them…well, I guess it makes sense, in retrospect.

I didn’t want to give a whole new set of intricate visualizations, much less share some of the intimate things I witnessed in each contemplation, but I did want to share a few things with you from what I saw: primarily, the form of the door that formed for each figure, and a brief lesson to learn from each figure.  The doors you might see in your own contemplations may well be different, but I figure that giving some sort of description for what to expect could help.  The lessons were, for those who follow me on Twitter, shared day by day in a short-enough form to encapsulate some of the high-level important messages that I could deliver from each realm of the figure.  Perhaps they, too, can be helpful for those who are learning about the figures, or want something to start with that they can expand on in their own meditations.

Laetitia
A large arched banded wooden door situated in a fluted pillar-supported stone arch, opening towards
There are always reasons to celebrate, but celebration need not mean partying. While some take time off, others still serve, and they too have cause to celebrate. To truly celebrate is to rejoice in work, channeling hope into power; true praise of God is praise through Work.

Fortuna Minor
A square, wide, wooden door banded with iron and surrounded by cut stone, opening towards
Don’t chase after sunsets. Diminishing returns will waste you time, and time is something you can’t waste anymore. All we have is all we have; prepare when you can, make do when you must. It’s all we can do to look after ourselves and our own; find independence through community.

Amissio
A normal cheap white bedroom door with plain threshold, opening outwards
Better to be homeless in loss than to build a home on it, lest your foundation sink into quicksand. Refugees, divorcees, ex-employees, we all suffer loss time and again; it hurts, and it hurts to stay and it hurts to go, but in accepting loss, we leave loss behind.

Cauda Draconis
A weak, filthy, dusty, shaky door that smells, opening outwards
This world is meant to end, and yet we are meant to make it last. We must do what we can when we can—but at the proper time, and no sooner? Collapse early, avoid the rush. Loss is nothing compared to perdition; how simple we are to focus only on the now when all else is at stake.

Puer
Enthusiasm can wash over any disaster like an opportunistic wave, but when faced with actual problems, it can end in dashing oneself against rocks in order to break them, or fleeing to fight another battle and another day. Waves will break and scatter but overwhelm all the same.

Rubeus
A black door, almost invisible, opening outwards
Unbridled desire is like air, stale though thinking it’s fresh, trapped in a cyclone that wrecks damage it cannot see. Over and over it runs roughshod over all, consuming and hurting all. Only true fresh thought clears the air, bringing helpful change instead of harmful calamity.

Coniunctio
A rustic door with a fine, elaborate lintel, opening outwards
In war, all else looks like peace; in peace, all else looks like war. It’s in the liminal space between them, a blue hour of life, that everything and everyone can come together as equals. Not as allies, but as equals in crisis, equals in opportunity, equals in assessment.

Acquisitio
A marble door with engraved inlays of lapis and gold, flanked by fluted columns, opening towards in half
After reckoning comes work; after assessment, business. All come as equals, sharing to increase, increasing their share, carrying our past forever with us. True wealth is practical knowledge, an endless font to always build, augment, and—soon—to rejoice. “Go forth and multiply.”

Puella
An opalescent glass door with a shiny chrome frame, opening outwards
Beauty is an emergent property out of assessment, union, and work. We don’t find beauty; it finds us, when we’re in the embrace of equals whom we don’t just acknowledge but truly know are our equals. Beauty is a property of truth, and truth comes from acceptance of the world.

Via
A color-changing veil suspended from an arch, sliding to the left
Every infinitesimal moment has infinite potential, every one a knife-blade, a parer of possibilities. In each moment lies every potential of every kind of action; it’s up to us to take it, transforming the world and ourselves. Geomancy isn’t called “cutting the sand” for nothing.

Albus
A white wooden door in a white, rough-cut stone threshold, opening towards
After we (re)build, the dust settles, and we can see clearly; purity of the heart leads to purity of the mind. We hollow the church, and fill the world as a monastery, living in peace to remember and re-member. But don’t forget: believing we have peace doesn’t mean we really do.

Populus
A thin, white, translucent veil divided in half, suspended from a thin smooth metal frame, parting to open from the middle
Love leads to peace, but without further direction, leads to inertia and languor. Utter clarity of vision leads us to live utterly in the here and now, and makes us forget our lessons, even as we return to how things always were. We take too much for granted; we lose our way.
*Note: this one feels like it should be first or last, a complete return to how things always were.

Carcer
A double door, the inner one of thick wrought iron bars opening towards, the outer one of heavy steel bulkhead opening outwards
Inertia stops to become hollow convention, which becomes enforced restriction. The word of God is replaced by the word of law, and we become isolated and ignorant of the larger world, and keeps us bound to the same old same old, always for the best, and if you’re not convinced…

Caput Draconis
A pair of elegant-yet-subdued baroque French doors, ivory with bright gold leaf accents, opening outward from the middle
With enough rules, even rulers become slaves, and all the old guard wander in lost memories. It’s the too-young, those too fresh to have known anything else, that begin the coup, but all they know is how to prepare and destroy. Chaos? Yes! The climactic Big Bang, a fecund reset.

Fortuna Maior
A gate of warm gold set with bars of iron with iron gateposts on either side, opening outward from the middle
Forced dominion toils to keep order, but true royalty has no need for force. Rulers naturally assume their role, and all rule their own proper domain; as planets in their orbits, all take care of their own work, honest and pure. Independent success, all for the sake of the All.

Tristitia
The heavy, metal-covered stone door of a tomb with a ring for a handle, opening towards
The Work is easy to start, but hard to continue; hope flees and dread finds us instead. The plague of “what if?” seeps into us like polluted air into sod, turning fertile grass into barren dust. The Sun has set, but will rise again; keep going until dawn, for then there is hope.

# On Geomantic Figure Magic Squares

We all know and love magic squares, don’t we?  Those grids of numbers, sometimes called “qamea” (literally just meaning “amulet” or “talisman” generally in Hebrew, קמיע or qamia`), are famous in Western magic for being numerological stand-ins or conceptions of the seven planets, sure, such as the 3×3 square for Saturn, the 5×5 square for Mars, and so forth, but they’re also huge in Arabic magic, too, from which Western magicians almost certainly got the idea.  Sure, magic letter squares are ancient in the West, such as the famous Sator Square from Roman times until today, and have more modern parallels in texts like the Sacred Magic of Abramelin, but magic number squares are fun, because they combine numerical and numerological principles together in an elegant form.

Which is why I was caught off-guard when I saw these two squares online, the first from this French blog post on Arabic geomancy and the other shared in the Geomantic Study-Group on Facebook:

Well…would you take a look at that?  Geomantic magic squares!  It took me a bit to realize what I was seeing, but once it hit me, I was gobsmacked.  It might not be immediately apparent how to make a geomantic magic square, but it becomes straightforward if you consider the figures as numbers of points, such that Laetitia stands in for 7, Puer for 5, Carcer for 6, and so forth.  Sure, it’s not a traditional kind of n × n number square that goes from 1 to n², but there are plenty of other magic squares that don’t do that either in occult practice, so seeing a kind of geomantic figure magic square actually makes a lot of sense when they’re viewed as numbers of points.  In this case, the magic sum of the square—the sum of the columns or rows—is 24.

Consider that first magic square, elegant as it is.  When it’s oriented on a tilt, such that one of its diagonals is vertical, we have the four axial figures (Coniunctio, Carcer, Via, and Populus) right down the middle, and all the other figures are arranged in reverse pairs in their corresponding positions on either side of the square.  For instance, Amissio and Acquisitio are on either side of the central axis “mirroring” each other, as are Tristitia and Laetitia, Fortuna Maior and Fortuna Minor, and so forth.  This is a wonderful geometric arrangement that shows a deep and profound structure that underlies the figures, and which I find particularly beautiful.

Of course, knowing that there are at least two such geomantic figure magic squares, and seeing possibilities for variation (what if you rearranged the figures of that first magic square above such that all the entering figures were on one side and all the exiting figures on the other?), that led me to wonder, how many geomantic magic squares are there?  Are there any structural keys to them that might be useful, or any other numerical properties that could be discovered?  So, late one evening, I decided to start unraveling this little mystery.  I sat down and wrote a quick program that started with the following list of numbers:

`[ 4 , 5 , 5 , 5 , 5 , 6 , 6 , 6 , 6 , 6 , 6 , 7 , 7 , 7 , 7 , 8 ]`
• Why this list?  Note that the figure magic squares rely on counting the points of the figures.  From that point of view, Puer (with five points) can be swapped by Puella, Caput Draconis, or Cauda Draconis in any given figure magic square and it would still be another valid magic square that would have the same underlying numerical structure.  There’s only one figure with four points (Via), four figures with five points (Puer, Puella, Caput Draconis, Cauda Draconis), six figures with six points (Carcer, Coniunctio, Fortuna Maior, Fortuna Minor, Amissio, Acquisitio), four figures with seven points (Albus, Rubeus, Laetitia, Tristitia), and only one figure with eight points (Populus).  If we simply focus on the point counts of the figures themselves and not the figures, we can simplify the problem statement significantly and work from there, rather than trying to figure out every possible combination of figures that would yield a magic square from the get-go.
• How does such a list get interpreted as a 4 × 4 square?  There are 16 positions in the list, so we can consider the first four positions (indices 0 through 3) to be the top row of the square, the second four positions (indices 4 through 7) to be the second row, the third four positions (indices 8 through 11) to be the third row, and the fourth four positions (indices 12 through 15) as the fourth row, all interpreted from left to right.  Thus, the first position is the upper left corner, the second position the uppermost inside-left cell, the third position the uppermost inside-right cell, the fourth position the upper right corner, the fifth position the leftmost inside-upper cell, the sixth position the inside-upper inside-left cell, and so forth.  This kind of representation also makes things a little easier for us instead of having to recursively deal with a list of lists.
• How do we know whether any permutation of such a list, interpreted as a 4 × 4 square, satisfies our constraints?  We need to add up the values of each row, column, and diagonal and make sure they add up to our target number (in our case, 24).

Starting from this list, I set out to get all the unique permutations.  Originally, I just got all 16! = 20,922,789,888,000 possible permutations, thinking that would be fine, and testing them each for fitting the target number of 24, but after running for twelve hours, and coming up with over 170,000 results with more being produced every few minutes, I realized that I’d probably be waiting for a while.  So, I rewrote the permutation code and decided to get only unique permutations (such that all the 5s in the base list of numbers are interchangeable and therefore equal, rather than treating each 5 as a unique entity).  With that change, the next run of the program took only a short while, and gave me a list of 368 templates.  We’re getting somewhere!

So, for instance, take the last template square that my program gave me, which was the list of numbers [6, 6, 5, 7, 8, 5, 6, 5, 6, 7, 6, 5, 4, 6, 7, 7].  Given that list, we can interpret it as the following template magic square:

 6 6 5 7 8 5 6 5 6 7 6 5 4 6 7 7

And we can populate it with any set of figures that match the point counts accordingly, such as the one below:

 Fortuna Minor Fortuna Maior Puer Laetitia Populus Puella Carcer Cauda Draconis Amissio Albus Acquisitio Caput Draconis Via Coniunctio Rubeus Tristitia

Excellent; this is a totally valid geomantic figure magic square, where the point counts of each row, column, and diagonal add to 24.  To further demonstrate the templates, consider the two images of the figure magic squares I shared at the top of the post.  However, although I was able to find the first magic square given at the start of the post (the green-on-sepia one), the second one (blue with text around it) didn’t appear in the list.  After taking a close look at my code to make sure it was operating correctly, I took another look at the square itself.  It turns out that, because although all the rows and columns add to 24, one of the diagonals adds up to 20, which means it’s not a true geomantic figure magic square.  Welp!  At least now we know.

But there’s still more to find out, because we don’t have all the information yet that we set out to get.  We know that there are 368 different template squares, but that number hides an important fact: some template squares are identical in structure but are rotated or flipped around, so it’s the “same square” in a sense, just with a transformation applied.  It’s like taking the usual magic number square of Saturn and flipping it around.  So, let’s define three basic transformations:

1. Rotating a square clockwise once.
2. Flipping a square horizontally.
3. Flipping a square vertically.

We know that we can rotate a square up to three times, which gets us a total of four different squares (unrotated, rotated once, rotated twice, rotated thrice).  We know that we can leave a square unflipped, flipped horizontally, flipped vertically, and flipped both horizontally and vertically.  We know that a square can be rotated but not flipped, flipped but not rotated, or both rotated and flipped.  However, it turns out that trying out all combinations of rotating and flipping gets duplicate results: for instance, flipping vertically without rotating is the same as rotating twice and flipping horizontally.  So, instead of there being 16 total transformations, there are actually only eight other templates that are identical in structure but just transformed somehow, which means that our template count of 368 is eight times too large.  If we divide 368 by 8, we get a manageable number of just 46 root templates, which isn’t bad at all.

What about total possible figure squares?  Given any template, there are four slots for figures with five points, four slots for figures with seven points, and six slots for figures with six points.  The figures of any given point count can appear in any combination amongst the positions with those points.  This means that, for any given template square, there are 4! × 4! × 6! = 414,720 different possible figure squares.  Which means that, since there are 368 templates, there are a total of 152,616,960 figure squares, each a unique 4 × 4 grid of geomantic figures that satisfy the condition that every column, row, and diagonal must have 24 points.  (At least we’ve got options.)

What about if we ignore diagonals?  The blue magic square above is almost a magic square, except that one of its diagonals adds up to 20 and not 24.  If we only focus on the rows and columns adding up to 24 and ignore diagonals, then we get a larger possible set of template squares, root template squares, and figure squares:

• 5,904 template squares
• 738 root template squares
• 2,448,506,880 possible figure squares

So much for less-magic squares.  What about more-magic squares?  What if we take other subgroups of these squares besides the rows, columns, and diagonals—say, the individual quadrants of four figures at each corner of the square as well as the central quadrant, or the just the corner figures themselves, or the bows and hollows?  That’s where we might get even more interesting, more “perfect” geomantic figure magic squares, so let’s start whittling down from least magic to most magic.  Just to make sure we’re all on the same page, here are examples of the different patterns I’m considering (four columns, four rows, two diagonals, five quadrants, four bows, four hollows, one set of corners):

To keep the numbers manageable, let’s focus on root template square counts:

• Rows and columns only: 738 root templates
• Rows, columns, and diagonals: 46 root templates
• Rows, columns, diagonals, and all five quadrants: 18 root templates
• Rows, columns, diagonals, all five quadrants, bows, and hollows: 2 root templates
• Rows, columns, diagonals, all five quadrants, bows, hollows, and the four corners: 2 root templates

With each new condition, we whittle down the total number of more-magical root templates from a larger set of less-magical root templates.  I’m sure there are other patterns that can be developed—after all, for some numeric magic squares of rank 4, there are up to 52 different patterns that add up to the magic sum—but these should be enough to prove the point that there are really two root templates that are basically as magical as we’re gonna get.  Those root templates, along with their transformations, are:

1. [6, 4, 7, 7, 8, 6, 5, 5, 5, 7, 6, 6, 5, 7, 6, 6]
1. Unflipped, unrotated: [6, 4, 7, 7, 8, 6, 5, 5, 5, 7, 6, 6, 5, 7, 6, 6]
2. Unflipped, rotated once clockwise: [5, 5, 8, 6, 7, 7, 6, 4, 6, 6, 5, 7, 6, 6, 5, 7]
3. Unflipped, rotated twice clockwise: [6, 6, 7, 5, 6, 6, 7, 5, 5, 5, 6, 8, 7, 7, 4, 6]
4. Unflipped, rotated thrice clockwise: [7, 5, 6, 6, 7, 5, 6, 6, 4, 6, 7, 7, 6, 8, 5, 5]
5. Flipped, unrotated: [7, 7, 4, 6, 5, 5, 6, 8, 6, 6, 7, 5, 6, 6, 7, 5]
6. Flipped, rotated once clockwise: [6, 8, 5, 5, 4, 6, 7, 7, 7, 5, 6, 6, 7, 5, 6, 6]
7. Flipped, rotated twice clockwise: [5, 7, 6, 6, 5, 7, 6, 6, 8, 6, 5, 5, 6, 4, 7, 7]
8. Flipped, rotated thrice clockwise: [6, 6, 5, 7, 6, 6, 5, 7, 7, 7, 6, 4, 5, 5, 8, 6]
2. [8, 6, 5, 5, 6, 4, 7, 7, 5, 7, 6, 6, 5, 7, 6, 6]
1. Unflipped, unrotated: [8, 6, 5, 5, 6, 4, 7, 7, 5, 7, 6, 6, 5, 7, 6, 6]
2. Unflipped, rotated once clockwise: [5, 5, 6, 8, 7, 7, 4, 6, 6, 6, 7, 5, 6, 6, 7, 5]
3. Unflipped, rotated twice clockwise: [6, 6, 7, 5, 6, 6, 7, 5, 7, 7, 4, 6, 5, 5, 6, 8]
4. Unflipped, rotated thrice clockwise: [5, 7, 6, 6, 5, 7, 6, 6, 6, 4, 7, 7, 8, 6, 5, 5]
5. Flipped, unrotated: [5, 5, 6, 8, 7, 7, 4, 6, 6, 6, 7, 5, 6, 6, 7, 5]
6. Flipped, rotated once clockwise: [8, 6, 5, 5, 6, 4, 7, 7, 5, 7, 6, 6, 5, 7, 6, 6]
7. Flipped, rotated twice clockwise: [5, 7, 6, 6, 5, 7, 6, 6, 6, 4, 7, 7, 8, 6, 5, 5]
8. Flipped, rotated thrice clockwise: [6, 6, 7, 5, 6, 6, 7, 5, 7, 7, 4, 6, 5, 5, 6, 8]

That second one, for instance, is the root template of that first figure magic square given above (green-on-sepia), unflipped and rotated clockwise twice.  So, with these, we end up with these two root template squares, from which can be developed eight others for each through rotation and reflection, meaning that there are 16 template squares that are super magical, which means that there are a total of 6,635,520 possible figure squares—414,720 per each template—once you account for all variations and combinations of figures in the slots.

That there are 16 templates based on two root templates is suggestive that, maybe, just maybe, there could be a way to assign each template to a geomantic figure.  I mean, I was hoping that there was some way we’d end up with just 16 templates, and though I was ideally hoping for 16 root templates, two root templates is pretty fine, too.  With 16 figures, there are at least two ways we can lump figures together into two groups of eight: the planetary notion of advancing or receding (advancing Populus vs. receding Via for the Moon, advancing Albus vs. receding Coniuncto for Mercury, advancing Fortuna Maior and receding Fortuna Minor for the Sun, etc.), or the notion of entering or exiting figures.  Personally, given the more equal balance of figures and the inherently structural nature of all this, I’m more inclined to give all the entering figures to one root template and all the exiting figures to the other.  As for how we might assign these templates to the figures, or which set of templates get assigned to the entering figures or exiting figures, is not something I’ve got up my sleeve at this moment, but who knows?  Maybe in the future, after doing some sort of structural analysis of the templates, some system might come up for that.

More than that, how could these squares be used?  It’s clear that they’ve got some sort of presence in geomantic magic, but as for specifically what, I’m not sure.  Unlike a geomantic chart, which reveals some process at play in the cosmos, these geomantic squares are more like my geomantic emblems project (and its subsequent posts), in that they seem to tell some sort of cosmic story based on the specific arrangement of figures present within the square or emblem.  However, like those geomantic emblems, this is largely a hammer without a nail, a mathematical and structural curiosity that definitely seems and feels important and useful, just I’m not sure how.  Still, unlike the emblems, figure squares actually have a presence in some traditions of geomancy, so at least there’s more starting off there.  Perhaps with time and more concentrated translation and studying efforts, such purposes and uses of figure squares can come to light, as well as how a potential figure rulership of the sixteen most-magical templates can play with the 414,720 different arrangements of figures on each template and how they feel or work differently, and whether different arrangements do different things.  Heck, there might be a way to assign each of the different combinations of figures on the templates to the figures themselves; after all, 414,720 is divisible by 16, yielding 25,920, which itself is divisible by 16, yielding 1620, so there might be 1620 different figure squares for each of the 256 (16 × 16) combinations of figures.  Daunting, but hey, at least we’d have options.

Also, there’s the weird bit about the target sum of the magic squares being 24.  This is a number that’s not really immediately useful in geomancy—we like to stick to 4 or 16, or some multiple thereof—but 24 is equal to 16 + 8, so I guess there’s something there.  More immediately, though, I’m reminded of the fact that 24 is the number of permutations of vowels in my system of geomantic epodes for most figures.  For instance, by giving the vowel string ΟΙΕΑ (omikron iōta epsilon alpha) to Laetitia, if we were to permute this string of vowels, we’d end up with 24 different such strings, which could be used as a chant specifically for this figure:

ΟΙΕΑ ΟΙΑΕ ΟΕΙΑ ΟΕΑΙ ΟΑΙΕ ΟΑΕΙ
ΙΟΕΑ ΙΟΑΕ ΙΕΟΑ ΙΕΑΟ ΙΑΟΕ ΙΑΕΟ
ΕΟΙΑ ΕΟΑΙ ΕΙΟΑ ΕΙΑΟ ΕΑΟΙ ΕΑΙΟ
ΑΟΙΕ ΑΟΕΙ ΑΙΟΕ ΑΙΕΟ ΑΕΟΙ ΑΕΙΟ

From that post, though, Populus only has a three-vowel string, which can be permuted only six times, but if we repeat that chant four times total, then we’d still end up with 24 strings to chant, so that still works out nicely:

ΙΕΑ ΕΑΙ ΑΙΕ ΕΙΑ ΙΑΕ ΑΕΙ
ΙΕΑ ΕΑΙ ΑΙΕ ΕΙΑ ΙΑΕ ΑΕΙ
ΙΕΑ ΕΑΙ ΑΙΕ ΕΙΑ ΙΑΕ ΑΕΙ
ΙΕΑ ΕΑΙ ΑΙΕ ΕΙΑ ΙΑΕ ΑΕΙ

So maybe 24 is one of those emergent properties of some applications of geomantic magic that could be useful for us.  Perhaps.  It’s worth exploring and experimenting with, I claim.

In the meantime, I’ll work on getting a proper list drawn up of all the templates for the various types of geomantic magic squares—ranging from less magic to more magic—at least just to have for reference for when further studies are or can be done on this.  This is more of a curiosity of mine and not a prioritized topic of research, but at least I know it exists and there’s the potential for further research to be done on it for future times.

# More on Geomantic Epodes and Intonations

One of my colleagues on Facebook, Nic Raven Run of Ravens Hall Press, asked me an interesting question to follow up on my post on epodes for the elements and geomantic figures from the other day.  In that post, I offered a set of single syllables that could be chanted or intoned like a bīja, or “seed syllable” mantra, for each of the four elements based on an obscure geomantic method of interpretation (the BZDḤ technique), which I also extrapolated into a system of single syllable intonations for each of the sixteen geomantic figures.  To that end, here are the two systems I would most likely use in my own practice, one based on the BZDḤ system and one based on strict stoicheia for the elements:

• Hybrid Greek system
• Fire: bi (ΒΙ)
• Air: zu (ΖΥ)
• Water: (ΔΗ)
• Earth: ha (Ἁ)
• Exact Mathēsis system
• Fire: kho (ΧΟ)
• Air: phu (ΦΥ)
• Water: ksē (ΞΗ)
• Earth: thō (ΘΩ)

And their corresponding expansions into the two systems of geomantic epodes using the two systems I would recommend (with the pure elemental epodes in bold text showing their location in the geomantic systems):

Hybrid Greek System (ΒΖΔΗ)
Primary Element
Fire Air Water Earth
Secondary
Element
Fire ΒΙ
BI
Laetitia
ΖΙ
ZI
Puer
ΔΙ
DI
Puella

HI
Carcer
Air ΒΥ
BU
Fortuna Minor
ΖΥ
ZU
Rubeus
ΔΥ
DU
Via

HU
Caput Draconis
Water ΒΗ

Amissio
ΖΗ

Coniunctio
ΔΗ

Albus

Fortuna Maior
Earth ΒΑ
BA
Cauda Draconis
ΖΑ
ZA
Acquisitio
ΔΑ
DA
Populus

HA
Tristitia
Exact Mathēsis System (ΧΦΞΘ)
Primary Element
Fire Air Water Earth
Secondary
Element
Fire ΧΟ
KHO
Laetitia
ΦΟ
PHO
Puer
ΞΟ
KSO
Puella
ΘΟ
THO
Carcer
Air ΧΥ
KHU
Fortuna Minor
ΦΥ
PHU
Rubeus
ΞΥ
KSU
Via
ΘΥ
THU
Caput Draconis
Water ΧΗ
KHĒ
Amissio
ΦΗ
PHĒ
Coniunctio
ΞΗ
KSĒ
Albus
ΘΗ
THĒ
Fortuna Maior
Earth ΧΩ
KHŌ
Cauda Draconis
ΦΩ
PHŌ
Acquisitio
ΞΩ
KSŌ
Populus
ΘΩ
THŌ
Tristitia

What this gets us is a system of single-syllable units that can represent not only the four elements but all sixteen figures.  In addition to being useful for energy work exercises among other magical practices, it also gives us an interesting method of encoding geomantic figures phonetically.  For instance, we could encapsulate an entire geomantic chart based on the four Mother figures, such that e.g. BIZAZIDĒ would be interpreted as Laetitia (BI), Acquisitio (ZA), Puer (ZI), and Albus (DĒ).  Another way we could use these is to encapsulate one of the 256 combinations of figures in two or three syllables: for instance, the combination of Coniunctio (ZĒ) and Acquisitio (ZA) to form Fortuna Maior (HĒ) could be written succinctly as ZĒZA or more fully as ZĒZAHĒ.  There are plenty of ways to extend such a system, ranging from Abulafia-like meditating on the 256 permutations of syllables to using them in geomantic candle magic a la Balthazar Black’s technique.

However, note that each such epode is basically considered a unit; yes, it’s composed of an elemental consonant and a vowel that, although they are inherently based on the Greek notion of planetary associations, can be reckoned as elemental symbols as well, and the combination of them composes a single syllable based on the primary (consonant) and secondary (vowel) elements of the geomantic figures.  What Nic was asking about was an alternative system of epodes: how could we use the elemental epodes to “compose” a geomantic figure in the sense of describing which elements were active and passive?  For instance, we could simply describe Via as BIZUDĒHA since it has all four elements, but how might one represent a figure with one or more passive elements?  Nic suggested a phonetic approach using a system of using two sets of vowels, using open vowels for active elements and close vowels for passive elements.  The system Nic was suggesting would be to effectively use a series of diphthongs to approximate such vowels.

I didn’t like this approach, to be honest.  For one, the reason why I’m using the vowels I’m using (which themselves are a mix of open and close in the systems I suggest) are (a) because the Greek system is particularly amenable to occult works and (b) because I’m relying not so much on phonetics as I am the occult symbolism and correspondences of the letters to the planets and, by those same correspondences, to the elements.  In that framework, diphthongs really mess with the system, because a diphthong involves several vowels which “muddle” the planetary/elemental symbolism that I’m trying to accomplish.  Plus, such a system would necessitate eight distinct but more-or-less balanced vowel sounds, and the Greek alphabet or phonetics isn’t really geared for that.  Now, that said, the idea isn’t a bad one!  However, because I’m not operating from purely phonetic principles, it’s not for me to go along that route.  I encouraged Nic (and I encourage others as well, if there are others to whom this idea is appealing) to explore such a phonetic approach to representing elements and their compositions to form geomantic figure representations.

There are other approaches to creating composed epodes for the geomantic figures, though, which I also discussed with Nic.  The first hunch I had was to simply include or omit the basic letters needed; for instance, if the consonants BZDḤ represent Fire, Air, Water, and Earth respectively, then combinations of those letters would represent the active elements in a figure, and we could fill in the vowels according to the rules of instinctual Arabic methods or the methods of pronouncing Greek generated words from before.  So, Via (with all four elements) would simply be BZDḤ or “bahz-dach”, Amissio (with just Fire and Water) would be BD or “bahd”, Fortuna Maior would be DḤ or “dach”, and so forth.  Populus, however, having no elements active, could be represented through silence, soft breathing, or something else entirely like “hmmmm” (using the notion that the Semitic letter for M, Arabic mīm or Hebrew mem, has its origins in the hieroglyph and word for “water”, which is the dominant element of Populus).  It’s an idea, but one I don’t particularly like, either, as it seems clunky and inelegant to use without regularity or much appeal, especially since the use of Ḥ only really works in Arabic, as we’d just end with a vowel in the Greek system which could be unclear.  We could use the mathētic approach of using ΧΦΞΘ instead, but we can do better than that.

Instead of using consonants, let’s think about a system that just uses the seven pure Greek vowels.  Recall in the systems above from the earlier post that there’s a way to use the Greek vowels, which normally represent the planets, to represent the four elements as well:

In the last row of my mathētic Tetractys, note how we have the four non-luminary and non-Mercury planets each associated to one of the four elements: Mars with Fire, Jupiter with Air, Venus with Water, and Saturn with Earth.  Though this system doesn’t quite match Cornelius Agrippa’s Scale of Four (book II, chapter 7), it does with his broader and more fuller explanations and detailing of the planets earlier in his Three Books of Occult Philosophy (book I, chapters 23 through 29).  Thus, as applied in my exact mathētic system of epodes, we can use Omicron (Mars) for Fire, Upsilon (Jupiter) for Air, Ēta (Venus) for Water, and Ōmega (Saturn) for Earth.  The letters Iōta (Sun), Alpha (Moon), and Epsilon (Mercury) are not used in the exact mathētic system of epodes, but are in the vague hybrid system from before, being a little easier to use and distinguish.

The connection I made for using these vowels was based on another notion I had of arranging the seven planets into the geomantic figures.  In that topic, one could envision taking seven planetary objects (talismans, coins, stones, etc.) and arranging them on an altar in a regular way to represent the graphical forms of the geomantic figures.  The method I gave for doing this was described like this:

Since we want to map the seven planets onto the points of the figures, let’s start with the easiest ones that give us a one-to-one ratio of planets to points: the odd seven-pointed figures Laetitia, Rubeus, Albus, and Tristitia.  Let us first establish that the four ouranic planets Mars, Jupiter, Venus, and Saturn are the most elementally-representative of the seven planets, and thus must be present in every figure; said another way, these four planets are the ones that most manifest the elements themselves, and should be reflected in their mandatory presence in the figures that represent the different manifestations of the cosmos in terms of the sixteen geomantic figures.  The Sun, the Moon, and Mercury are the three empyrean planets, and may or may not be present so as to mitigate the other elements accordingly.  A row with only one point must therefore have only one planet in that row, and should be the ouranic planet to fully realize that element’s presence and power; a row with two points will have the ouranic planet of that row’s element as well as one of the empyrean planets, where the empyrean planet mitigates the pure elemental expression of the ouranic planet through its more unmanifest, luminary presence.  While the ouranic planets will always appear in the row of its associated element, the empyrean planets will move and shift in a harmonious way wherever needed; thus, since the Sun (as the planetary expression of Sulfur) “descends” into both Mars/Fire and Jupiter/Air, the Sun can appear in either the Fire or Air rows when needed.  Similarly, Mercury can appear in either the Air or Water rows, and the Moon in either the Water or Earth rows (but more on the exceptions to this below).

This led us to having the following arrangements:

Note that Via is the only figure that uses only the so-called “ouranic” planets Mars, Jupiter, Venus, and Saturn, because Via is the only figure with all elements active.  All the other figures, having at least one element passive, will involve one or more of the planets Mercury, Sun, or Moon, because those “empyrean” planets mitigate and lessen the elemental presence of the row that they’re found in.  The only major exception to this arrangement is—you guessed it—Populus, which uses a different arrangement entirely.  For more information about how and why these figures are arranged with the planets in the way they are and how they might otherwise be used, see the relevant post on my blog, linked just above.  The terms ouranic and empyrean are a distinction I make in my Mathēsis work to distinguish the twelve non-zodiacal forces into three groups, as demonstrated in this post.

Now, remember that each planet has its own vowel, and note where the planets appear in the arrangements above for each figure.  We can come up with a rule that transforms the figures into sequences of vowels to represent the figures like this:

1. For all figures except Populus:
1. Every row will have either a single ouranic planet (Mars, Jupiter, Venus, Saturn) or both an ouranic and empyrean planet (Moon, Sun, Mercury).
2. If a given elemental row has an empyrean planet present as well as an ouranic planet, use the vowel of the empyrean planet there.
3. Otherwise, if a given elemental row has only an ouranic planet present, use the vowel of the ouranic planet.
2. For the figure Populus:
1. All planets are present in their own arrangement to represent the voids of Populus.
2. Use all the vowels, some mutually-exclusive set, or just keep silent.

Thus, consider the figure Via.  In each row, it only has an ouranic planet, so we simply use their corresponding vowels: ΟΥΗΩ.  For Coniunctio, note how we have two empyrean planets in the figure, the Sun alongside Mars and the Moon alongside Saturn; we would use their corresponding vowels instead of their ouranic equivalents, getting us the vowel string ΙΥΗΑ (Iōta instead of Omicron and Alpha instead of Ōmega).  Likewise, Puer has the empyrean planet Mercury present alongside Venus, so its vowel string would be ΟΥΕΩ (Epsilon instead of Ēta).  The only exception to this would be Populus, as noted above, which could be represented either as the entire vowel string ΑΕΗΙΟΥΩ or as simple, holy silence, but we can talk more about that later.

This gets us the following vowel epodes for the figures:

• Laetitia: ΟΙΕΑ
• Fortuna Minor: ΟΥΙΑ
• Amissio: ΟΙΗΑ
• Cauda Draconis: ΟΥΗΕ
• Puer: ΟΥΕΩ
• Rubeus: ΙΥΕΑ
• Coniunctio: ΙΥΗΑ
• Acquisitio: ΙΥΑΩ
• Puella: ΟΕΗΑ
• Via: ΟΥΗΩ
• Albus: ΙΕΗΑ
• Populus: More on that in a bit.
• Carcer: ΟΙΑΩ
• Caput Draconis: ΕΥΗΩ
• Fortuna Maior: ΙΑΗΩ
• Tristitia: ΙΕΑΩ

What’s nice about this system is that, at least for all the non-Populus figures, we have four vowels that we can intone.  Anyone familiar with the classical Hermetic and Neoplatonic texts and techniques is familiar with how vowel-intoning was considered a pure and sacred practice, and now we can apply it to the figures as well as the planets!  Even better, since each geomantic figure uses a distinct set of vowels, we can permute them in any which way.  Thus, if we wanted to engross ourselves in the world of, say, Laetitia, we could intone all possible variations of its vowel string:

ΟΙΕΑ ΟΙΑΕ ΟΕΙΑ ΟΕΑΙ ΟΑΙΕ ΟΑΕΙ
ΙΟΕΑ ΙΟΑΕ ΙΕΟΑ ΙΕΑΟ ΙΑΟΕ ΙΑΕΟ
ΕΟΙΑ ΕΟΑΙ ΕΙΟΑ ΕΙΑΟ ΕΑΟΙ ΕΑΙΟ
ΑΟΙΕ ΑΟΕΙ ΑΙΟΕ ΑΙΕΟ ΑΕΟΙ ΑΕΙΟ

For each of the non-Populus figures which have four distinct vowels, there are 24 possible permutations of its vowel string, with six permutations that begin with each one of the vowels.  Going through and intoning each permutation could be a powerful meditative practice for each of the figures, and probably especially effective for magical practices, too.

What about Populus?  For that, we have all seven vowels ΑΕΗΙΟΥΩ, and to permute all seven of those would…take a considerably longer time than the other figures (there are 5040 possible permutations).  Though going through all such permutations would also be a powerful practice, there are better ways we can use our time.  For one, what about the sequence ΑΕΗΙΟΥΩ itself?  It’s simple and straightforward, but it doesn’t really reflect the arrangement of planets we use for Populus: note how we have the empyrean planets (Sun, Mercury, and Moon) down the middle with the ouranic planets (Mars, Jupiter, Venus, Saturn) around the sides in a distinctly mathētic pattern.  For this arrangement, we could use the vowel string ΙΟΥΕΗΩΑ: we have Iōta at the beginning, Epsilon in the middle, and Alpha at the end, with the other four vowels in their elemental order interspersed between them, the hot elements Fire and Air in the first half and the cold elements Water and Earth in the second half.  Using this pattern, we could imagine a kind of lightning-bolt descending from the Sun down to the Moon through Mars, Jupiter, Mercury, Venus, and Saturn, a pattern that would take us from the hottest, brightest, most active powers down to the coldest, darkest, most passive powers.

Another way is to use a condensed vowel string: rather than using the ouranic planets’ vowels at all, why not limit ourselves to the empyrean planets, which are only ever used for passive elements anyway in this scheme?  In this reckoning, we could reduce ΙΟΥΕΗΩΑ to ΙΕΑ (reflecting the center empty “gap” of the dots in the figure Populus), just as we commonly figure that the divine name ΙΑΩ is a reduction of the full string ΑΕΗΙΟΥΩ.  Plus, we only ever see the string ΙΕΑ in the (permutations of) the string for the figures that are mostly passive anyway: Laetitia (ΟΙΕΑ), Rubeus (ΙΥΕΑ), Albus (ΙΕΗΑ), and Tristitia (ΙΕΑΩ).  If there were any vowel string that could be considered the inverse of that of Via (ΟΥΗΩ), the mutually-exclusive remaining set of vowels ΙΕΑ would be it!  We could then permute this string in a simple set of six permutations, too:

ΙΕΑ ΕΑΙ ΑΙΕ
ΕΙΑ ΙΑΕ ΑΕΙ

Instead of doing either ΙΟΥΕΗΩΑ or permutations of ΙΕΑ, though, there’s another approach to us: if Populus is devoid of elements, then it has nothing at all, and thus has nothing to intone, so Populus could simply be represented by a pure, holy silence devoid of intonations.  This is also entirely appropriate, and would symbolically make Populus a vacuum of empty space, a blank template upon which the other elements could be applied.  Entirely fitting to represent Populus on its own.

Of course, using that logic, then why would we bother using the empyrean planets’ vowels at all to represent the passive elements in a figure?  We could just stick with the ouranic planets that are active, which would get us the following “short” set of vowel intonations, such as Ο for Laetitia, ΟΥ for Fortuna Minor, ΟΥΗ for Cauda Draconis, and so forth.  Not nearly as elegant, perhaps, but could also work.  I’m not a fan, personally, as it then begins to conflate the elemental presences of the figures with purely planetary ones.  For instance, Laetitia being simply represented by Omicron would then conflate Laetitia with the planet Mars, even though Laetitia is solidly linked to Jupiter, and likewise Rubeus with Upsilon to Jupiter and not Mars.  I wouldn’t recommend this system, personally.

So, where does that leave us?  At this point, there are three systems of epodes I would recommend for working with the geomantic figures, two of which are single-syllable epodes (one based on the BZDḤ system with Greek vowels, and one derived from that same system using a purer stoicheic/mathētic approach), and one of which is based on mathētic principles to come up with intonable, permutable vowel strings.

Figure Single Syllable Vowel String
Hybrid Mathēsis
Laetitia ΒΙ
BI
ΧΟ
KHO
ΟΙΕΑ
Fortuna Minor ΒΥ
BU
ΧΥ
KHU
ΟΥΙΑ
Amissio ΒΗ
ΧΗ
KHĒ
ΟΙΗΑ
Cauda Draconis ΒΑ
BA
ΧΩ
KHŌ
ΟΥΗΕ
Puer ΖΙ
ZI
ΦΟ
PHO
ΟΥΕΩ
Rubeus ΖΥ
ZU
ΦΥ
PHU
ΙΥΕΑ
Coniunctio ΖΗ
ΦΗ
PHĒ
ΙΥΗΑ
Acquisitio ΖΑ
ZA
ΦΩ
PHŌ
ΙΥΑΩ
Puella ΔΙ
DI
ΞΟ
KSO
ΟΕΗΑ
Via ΔΥ
DU
ΞΥ
KSU
ΟΥΗΩ
Albus ΔΗ
ΞΗ
KSĒ
ΙΕΗΑ
Populus ΔΑ
DA
ΞΩ
KSŌ
ΙΟΥΕΗΩΑ or ΙΕΑ
or just keep silent
Carcer
HI
ΘΟ
THO
ΟΙΑΩ
Caput Draconis
HU
ΘΥ
THU
ΕΥΗΩ
Fortuna Maior
ΘΗ
THĒ
ΙΑΗΩ
Tristitia
HA
ΘΩ
THŌ
ΙΕΑΩ

This is all well and good, but where does this actually leave us?  What the past few posts on these tangentially-geomantic topics are accomplishing is taking the sixteen geomantic figures and coming up with new ways to apply them in ways outside of strict divinatory purposes, giving them new media such as sound to be “played” or transmitted through, and using those media to accomplish other tasks.  If the planets can be used for astrology as well as magic, there’s no reason why the figures can’t be used for geomancy as well as magic, either.  The ability to form meditative or magical epodes for concentrating, contemplating, and connecting with the figures on deeper levels plays into the same systems that geomantic gestures or energy centers or altar arrangements do: using these figures for a magical, world-changing purpose instead of a merely predictive one.

By the same token, however, so much of this is highly experimental.  All magic is at some point, but given the novelty and how mix-and-match I’m being between Greek letter magic and geomantic systems, this is all deserving of some deep practice and reflection and refinement.  I’m sharing this on my blog because…well, it’s my blog, and it’s interesting to share my theories here, and to spread some of my ideas out there to get feedback on by those who are interested.  At the same time, so much of all this is just theoretical and musings on how to apply certain ideas in certain ways.  I’m confident I can get them to work, but that’s not a guarantee that they will.  Experimentation and practice is absolutely needed, not only to get my own aims and goals accomplished, but even just to see whether certain methods work at all for anything.

Still, while we’re at it, let’s make up a new practice, shall we?  Let’s say we want to have a formalized way of conjuring up the power of a given figure, such as for some intense contemplation or pathworking.  In my Secreti Geomantici ebook, wherein I talk about lots of different magical practices involving geomancy and geomantic figures, I provide a set of sixteen prayers for each of the figures.  We can use those in combination with the geomantic epodes above to come up with a more thorough invocation of a figure.  The process I have in mind would be to recite the hybrid single-syllable epode as few as four or as many as sixteen times (or as many times as there are points in the figure), recite the given orison of the figure, then permute through its vowel string.  Thus, for Laetitia, we could do the following, while sitting before an image of Laetitia (or an altar of planetary talismans arranged in the form of the figure Laetitia) while holding the geomantic hand gesture of Laetitia:

ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ

Jovian Laetitia, standing tall
Granting hope in the hearts of all
Blazing spirit, o fulgent flame
Flashing brightest, of rousing fame
In our dark minds you spark pure Fire
Calcining spite to high desire
Grand arch of joy, embrace us here
And bring us tidings glad and clear

ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ

ΟΙΕΑ ΟΙΑΕ ΟΕΙΑ ΟΕΑΙ ΟΑΙΕ ΟΑΕΙ
ΙΟΕΑ ΙΟΑΕ ΙΕΟΑ ΙΕΑΟ ΙΑΟΕ ΙΑΕΟ
ΕΟΙΑ ΕΟΑΙ ΕΙΟΑ ΕΙΑΟ ΕΑΟΙ ΕΑΙΟ
ΑΟΙΕ ΑΟΕΙ ΑΙΟΕ ΑΙΕΟ ΑΕΟΙ ΑΕΙΟ

ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ

See?  By coming up with small, individual innovations and extrapolations and translations of one set of symbols from one medium into another, we can start using each on their own effectively, or we can start plugging them in to come up with bigger, better, and more profound practices that can really pack a punch.  Geomancy has every potential and every capability to become a full magical and spiritual practice in its own right that can fit right in with any other Western or Hermetic practice based on their own symbol sets; just because extant literature is lacking on the subject doesn’t mean it can’t be done, after all, and with a bit of thought and ingenuity, there are so many avenues that open themselves up for ready exploration.

One final thought about the use of these vowel epodes: we know that for any non-Populus figure, there are 24 permutations of the vowel string epodes.  So, that makes 15 × 24 = 360.  Which is a…stupidly pleasing number, to be honest.  As we all know, Using this little tidbit, we could conceive of a sort of year-long geomantic practice, focusing on one of the permutations of vowel epodes for the figures per day.  This gives us 15  24-day “months” of figures, with five or six days leftover at the end of the year.  In leap years that have six epagomenal days, we could use the permutations of the short epode ΙΕΑ for Populus; in non-leap years, we could just focus on the whole epode ΙΟΥΕΗΩΑ, or we could just keep silent (perhaps more fitting for epagomenal days).  It’s not entirely balanced in that regard, but it does have its own logic and cleanliness that could make it a viable yearly-daily practice for meditating on the epodes of the figures.  I might expand on this idea at a later point, or perhaps rework my geomantic Wheel of the Year to match it in some sense, but it’s something to mull over for now.  The next leap year isn’t for another year and a half, after all.

# On the Elemental and Geomantic Epodes

Ever since I wrote that post about how the physical body can be represented by geomantic figures, I’ve been trying to puzzle something out for myself.  At the end of the post, I introduce the concept of a system of geomantically-derived energy centers in the body based on four centers and four elements: the Fire center in the head, the Air center in the throat, the Water center in the upper belly, and the Earth center at the perineum.  This is based on the Geomantic Adam diagram given in MS Arabe 2631, which divvies up the geomantic figures to the parts of the body in a way that’s untied to any astrological method (which is the usual method used in European and Western geomancies):

In addition to proposing four such energy centers, I also propose three possible sets of intonations based on the obscure BZDH technique from some forms of geomancy, and also suggest that the sixteen geomantic gestures or “mudras” can be used in addition with these to form the basis of a kind of geomantic energy practice.  However, I didn’t really describe any implementation beyond laying these individual parts of such a hypothetical practice down, because I hadn’t yet come up with a way to put the parts together into a whole.  I’ve been puzzling over how to do just that since the post went up earlier this summer.  I mean, it’s not hard to just slap some energy into parts of the body and call it a day, but let’s be honest: I want to do this right and be able to incorporate it into my own practice in a way that’s not harmful, and as we all know by now, it’s just as easy to use energy to make a body awful as much as it can be made awesome.

Now, I was originally going to just write a post about a more-or-less solid energy practice that uses four energy centers in the body, one for each of the four elements.  I’m still going to write that post, because I already started it, but I realized that there’s a significant chunk of it that needs to be clarified in its own post, because there’s a number of options one might choose for it with different bits of logic and arguments for and against each choice.  This section kept growing and growing, and it eventually dwarfed the actual point of the post itself, so I decided to get this bit out of the way first, especially since I’ve already introduced the topic when I brought up the notion of a geomantic energy practice to begin with.

For me in my magical practice, the spoken word is important, especially when it comes to things that are intoned, such as barbarous words or particular chants.  For instance, the seven Greek vowels are absolutely vital to my work, because each vowel is associated with one of the seven planets.  In fact, each of the letters of the Greek alphabet has its own spiritual associations to the planets, signs of the Zodiac, and elements.  It’s the elemental letters that are the focus here now: if I wanted to intone a special word to attune myself to the power of an element just like how I’d intone a vowel to attune myself to the power of a planet, what would I use?  I can’t really intone a consonant, so I invented special “power words” for the four elements by taking the corresponding consonant for the element, intoning ΙΑΩ, and ending with the consonant again, as below:

• Fire: ΧΙΑΩΧ (KHIAŌKH)
• Air: ΦΙΑΩΦ (PHIAŌPH)
• Water: ΞΙΑΩΞ (KSIAŌKS)
• Earth: ΘΙΑΩΘ (THIAŌTH)

This method works, but to be honest, I’ve never really liked it.  It’s always felt kind of imbalanced and inelegant, especially compared to some of the more refined barbarous words of power or the simplicity and clearness of the vowels for the planets.  When I first started thinking of what I could intone for a geomantic energy practice, my routine use of these words first came up, but I quickly remembered that there are other options available to me besides just this.  All I need to find is some appropriate, elegant system of four words for intoning for the sake of attuning to the four elements.

Also, what am I calling this particular type of power word, anyway?  These are small, usually single-syllabled things to intone or chant to attune with a particular force.  I suppose that these are barbarous names of a sort, but the fact that they’re so easily constructed doesn’t seem quite appropriate to call them “barbarous”.  The closest thing I can think of are bīja, which is a Sanskrit term meaning “seed”, but referring to single syllable mantras that can be intoned and thought of as encapsulating or emanating particular elements or powers.  Think of the syllables oṃ, dhīḥ, hūṃ, or other single-syllable such mantras found in tantric Buddhism or Hinduism.  These are powerful syllables and contain some aspect of the cosmos or dharma in their own right, and many deities, bodhisattvas, buddhas, and other entities or powers have their own bījas.  That’s a good concept and term for this, but I can’t think of any Western or non-Sanskrit term to call them, like how we might have “chant” or “orison” for the word mantra, “gesture” for mudra, or “energy center” for chakra.  Since I like having Greek-based terms, here are a few I would think are appropriate:

• Odologue, which could come either from ᾠδόλογος ōidólogos meaning “song-word” or, alternatively, ὁδόλογος hodólogos meaning “road-word”, and either Greek word could be used here.  Odology, after all, can refer to “the study of the singing voice” or “the study of roads and paths”, and considering the purpose and use of these bīja-like words,
• Rhizophone, from Greek ῥιζόφωνη rhizóphōnē, literally meaning “root sound”.  This is about as close a calque to bīja as I could think, helpfully suggested by Kalagni of Blue Flame Magick (who has a new website now, go update your RSS readers and links!).
• Epode, which is simply the Greek word ἐπῳδή epōidé, meaning “song sung to something”, and more figuratively an enchantment, charm, or spell.  Unlike odologue or rhizophone, epode is actually a known word, both in Greek and in English, and though it can be used more broadly for spells or charms in general, the notion of something being sung here is important, which is basically intonation.  Though I like the above two words, let’s be honest: epode here is probably the best to go with.
• There are other words used in Greek to refer to magic spells or charms, like kḗlēma or thélktron or other words, so we can reserve “epode” for what are basically mantras.
• “Epode” could be used to give a useful Greek translation of “mantra” generally, as opposed to just bīja syllables, which are themselves considered single-syllable mantras.  For this, “root epode” or “small epode” could be used to clarify single-syllable epodes.
• Likewise, “epode” wouldn’t necessarily be of the same type of word as “names”, ὀνόματα onómata, referring to the barbarous words of power that may simply be spoken, shouted, or intoned depending on the situation.  Plus, the barbarous names themselves aren’t usually constructed, patterned after anything, or even understood as having distinct or intelligible meanings.

So, what we’re doing here is coming up with elemental epodes, simple words that can be intoned or sung to attune or call down the forces of the elements, just how the intonation of the seven Greek vowels can do the same for the planets.  In fact, those vowels, when sung in a magical way, would become epodes in their own right.

Anyway, back to the topic at hand.  One straightforward option is to just use the Arabic or Greek words for the four elements themselves as things to intone:

• Arabic:
• Fire: nar (نار, pronounced “nahr”)
• Air: hawa’ (هواء, pronounced “HAH-wa” with a sharp stop in the throat)
• Water: ma’ (ماء, pronounced “ma” with a sharp stop in the throat)
• Earth: turab (تراب, pronounced “tuh-RAHB”)
• Greek:
• Fire: pũr (πῦρ, pronounced “pür” like with the German ü or French u, or as “peer”)
• Air: aḗr (ἀήρ, pronounced “ah-AYR”, smoothly without a stop in the sound)
• Water: húdōr (ὕδωρ, pronounced “HEE-dohr” or “HÜ-dohr”, again with that German/French sound)
• Earth: gē̃ (γῆ, pronounced “gay”)

However, I’m not a fan of doing this.  For one, the words themselves aren’t necessarily important if the resonance and link between what’s uttered/intoned and what’s being connected with is strong.  Here, all I really have to go is the semantic meaning of the words.  Plus, I don’t like how some of them are two syllables and others only one, and they all feel inelegant in some of the same ways as my *ΙΑΩ* words from above.  So, while the words for the elements could be used, it’s not one I’d like to use.

And no, I won’t use Latin or English for such things, either.  I don’t hold either to be a very magical language like how I’d hold Greek or Hebrew or Arabic, largely due to the lack of meaningful isopsephy/gematria or stoicheia of the letters for the Roman script common to both Latin and English.  I also didn’t list Hebrew here because, for the sake of my energy work, I largely focus on Greek stuff (for the Mathēsis side of things) or Arabic (for the geomantic side), and Hebrew doesn’t fit into either category.

However, there is another option for coming up with an intonation that is rooted in geomantic practice: the BZDH (or BZDA) technique.  This is a little-known technique in Western geomancy that seems to have had more use in Arabic geomancy.  As I said in the earlier post about the geomantic figures and the human body:

From my translation of the 15th century work Lectura Geomantiae:

By the Greek word “b z d a” we can find the house of the figures, which is to say in which house the figures are strongest, wherefore when the first point starting from the upper part of the beginning figure is odd, the second house is strong; when the second point is odd, the seventh house is strong; when the third point is odd, the fourth house is strong; when the fourth and last point is odd, the eighth house is strong. Thus we will find by this number the proper houses of the figures; by “b” we understand 2, by “z” 7, by “d” 4, by “a” 8, as in this example: “b z d a”.

This may not make a lot of sense on its own, but compare what Felix Klein-Franke says in his article “The Geomancy of Aḥmad b. `Alī Zunbul: A Study of the Arabic Corpus Hermeticum” (AMBIX, March 1973, vol. XX):

The best taskīn is that of az-Zanātī; it bears the key-word bzdḥ: according to the principle of Gematria, the transposition of letters of a word into numbers, in place of bzdḥ there result the numbers 2748. Thus the Mansions of the taskīn are indicated; each spot denotes one of the four elements; in the 2nd Mansion there is only the element Fire (Laetitia, ḥayyān), in the 7th Mansion only Air (Rubeus, ḥumra), in the 4th Mansion only Water (Albus, bayāḍ), and in the 8th Mansion only Earth (Cauda Draconis, rakīza ẖāriǧa).

Stephen Skinner clarifies this even further in his works on geomancy.  From his 1980 book “Terrestrial Astrology: Divination by Geomancy”:

Further specialized configurations or taskins are outlined together with mnemonics for remembering their order. Gematria, or the art of interpreting words in terms of the total of’ the numerical equivalents of each of their letters, is introduced at this point. Using the mnemonic of a particular taskin such as Bzdh, Zunbul explains that the letters represent the four Elements, in descending order of grossness. Each letter also represents a number in Arabic, thus:

b – 2 – Fire
z – 7 – Air
d – 4 – Water
h – 8 – Earth

This mnemonic therefore indicates House number 2 for Fire, House number 7 (Air), House number 4 (Water), and House number 8 (Earth). For each of the Houses indicated in this taskin, we see that the second is most compatible with Fire, the seventh with Air, and so on. Therefore, if the geomantic figure Laetitia (or in Arabic Hayyan), which is solely Fire, occurs in the second House, this would be. an extremely favourable omen. Likewise, the occurrence of Rubeus (or Humra), which is solely Air, in the seventh House would also be extremely auspicious. Further chapters are devoted to even more complicated combinations of the basic figures, and to labyrinthine rules for everything from marriage to medicine. Diagnosis by raml even became a lay rival of the latter, and tables were educed of the relationship between specific parts of the body and the geomantic figures.

In other words, based on these letters, we could intone a particular sound that starts with the letter “b” for Fire, “z” for Air, “d” for Earth, and “ḥ” (think of the guttural “ch” of German, but further back in the throat).

So, in this technique, we have four consonants that correspond to four elements.  We could use this BZDH technique to use these four consonants, each associated with one of the four elements according to an obscure technique in Arabic and early Western geomancy, to create a simple, clear syllable for each element when paired with a simple long vowel:

• Arabic method:
• Fire:  (با)
• Air:  (زا)
• Water:  (دا)
• Earth: ḥā (حا)
• Greek method:
• Fire:  (ΒΗ)
• Air:  (ΖΗ)
• Water:  (ΔΗ)
• Earth:  (Ἡ)
• Latin method:
• Fire: ba
• Air: za
• Water: da
• Earth: a

Note that I’m largely using the “ah” sound a lot for these.  For one, in Greek, this is the vowel Alpha, which is associated with the Moon, which is one of the planets closest to the sphere of the Earth and which is one of the planets most aligned with the element of Earth.  Additionally, this would be represented in Arabic with the letter ‘Alif, which has the form of a straight vertical line, much like the geomantic figure Via (or Tarīq using its Arabic name), which is also a figure associated with the Moon and which is important as it contains all four elements; in this case, the “ah” sound would be most aligned to that of the powers of geomancy as a whole, I would claim.  Note, also, how the Latin transcription of ḥ (to represent the element Earth) turned into “a”; if you wanted to think of geomancy as primarily being an oracle of Earth (which is a claim I take some issue with), then the “ah” sound would indeed be closest for phonologically working with the elements from a geomantic perspective and from our worldly, manifest basis.  Yet, we’re using Ēta for the Greek method given above; for one, this is because there’s no distinct vowel for “long a”, but “long e” is a close-enough approximation.  Using ΒΑ, ΖΑ, ΔΑ, and Ἁ for them would work as well, but using Ēta is also acceptable in this case.

Now, remember that these four consonants are used because they have their origins in being specifically labeled as elemental in the original geomantic technique from whence they come due to their numerological (gematria or isopsephic) significance. The mnemonic BZDḤ was used based on the numerological values of those letters in Arabic: bāʾ for 2, zāy for 7, dāl for 4, and ḥāʾ for 8.  Interestingly, these same consonants were used in the European version of the technique as BZDA (with A replacing Ḥāʾ, though it makes more sense to consider it H) even though it’s not technically the letters that were important, but their numerical equivalents.  If we were to simply go by their numerological (or numeric order) basis, then we should use ΒΔΗΘ for Greek or BDGH for Latin.  I suppose that one could use these letters instead for the BZDH technique-based intonation syllables, but I feel like using the original BZDH (or BZDḤ) is truer to the elements themselves, though the true Greek system could also work given their stoicheic meanings: Bēta associated with the Fire sign Aries, Delta associated with the Air sign Gemini, Ēta (used consonantally as an aspiration/aitch letter) representing the planet Venus which can be associated with the element of Water, and Thēta associated with the element of Earth itself.  So, one could also use a Greek ΒΔΗΘ system like this (using Ēta below, but again, Alpha would also work):

• Fire:  (ΒΗ)
• Air: (ΔΗ)
• Water: (Ἡ)
• Earth: thē (ΘH)

Or a Latin BDGH system as:

• Fire: ba
• Air: da
• Water: ga
• Earth: ha

Again, I’m not a fan of using Latin generally, but I can see an argument for using a BDGH system here because it’s not really words, isopsephy, or stoicheia here that are necessarily important.  However, if we were to use Greek isopsephy for determining which letters to use to represent the four elements for a Greek ΒΔΗΘ system, why not use the Greek stoicheia for them, instead?  It breaks with why we were using numbers to begin with, but we already know the letters Khi, Phi, Ksi, and Thēta work quite well for the four elements themselves, so if we were taking a purely elemental approach, it seems more proper to just use the elemental letters instead of the numerologically-appropriate letters and their natural vowels (specifically their long versions to keep with the theme of using long vowels for the epodes):

• Fire: khei (ΧΕI)
• Air: phei (ΦΕI)
• Water: ksei (ΞΕI)
• Earth: thē (ΘH)

There are definitely arguments for the use of the stoicheically-appropriate letters (ΧΦΞΘ) over the others, or the isopsephically-appropriate ones (ΒΔΗΘ), or the transliterated Arabic ones (ΒΖΔΗ).  In a more Mathēsis-pure approach, I’d probably go with the stoicheic letters, but in this particular case, I’d recommend most the transliterated Arabic ones, because that set of letters ties this energy practice closest to the original geomantic technique.  I suppose experimentation would show which is best, but I’m most comfortable sticking with the BZDH technique.

However, even using the BZDH technique as a foundation for this, an interestingly extensible system of syllables can also be devised where the BZDH technique of using different consonants is mixed with using Greek vowels that were similar enough in element to those four consonants.  For this mashup, I used my Mathēsis understanding of the planets and their positions on the mathētic Tetractys or the planetary arrangement for the geomantic figures to get vowels for the elements, and settled on using Iōta (Sun) for Fire, Upsilon (Jupiter) for Air, Ēta (Venus) for Water, and Alpha (Moon) for Earth.  Though Mars would be more appropriate for Fire and Saturn for Earth, their corresponding vowels are Omicron and Ōmega, which may not be distinct enough for this purpose, as I feel like it should be, so I made a sufficiently-acceptable substitution to use the Sun for Fire instead of Mars, and the Moon for Earth instead of Saturn.

What’s nice about combining the BZDH technique with the planetary vowels is that we can mix and match both systems and, using our system of primary and secondary elements of the figures, get a distinct epode not only for the four elements but also for each of the sixteen geomantic figures, which can be extraordinarily useful in its own right for other magical and meditative purposes.  (And here I thought that little innovation of mine was no more than “a few sprinkles on the icing of the cake of Western geomancy” when it’s come in use time and time again!)  So, let’s see about making such a full system for all sixteen figures using the three competing Greek systems (Transliterated ΒΖΔΗ, Isopsephic ΒΔΗΘ, Stoicheic ΧΦΞΘ):

Transliterated ΒΖΔΗ System
Primary Element
Fire Air Water Earth
Secondary
Element
Fire ΒΙ
BI
Laetitia
ΖΙ
ZI
Puer
ΔΙ
DI
Puella

HI
Carcer
Air ΒΥ
BU
Fortuna Minor
ΖΥ
ZU
Rubeus
ΔΥ
DU
Via

HU
Caput Draconis
Water ΒΗ

Amissio
ΖΗ

Coniunctio
ΔΗ

Albus

Fortuna Maior
Earth ΒΑ
BA
Cauda Draconis
ΖΑ
ZA
Acquisitio
ΔΑ
DA
Populus

HA
Tristitia
Isopsephic ΒΔΗΘ System
Primary Element
Fire Air Water Earth
Secondary
Element
Fire ΒΙ
BI
Laetitia
ΔΙ
DI
Puer

HI
Puella
ΘΙ
THI
Carcer
Air ΒΥ
BU
Fortuna Minor
ΔΥ
DU
Rubeus

HU
Via
ΘΥ
THU
Caput Draconis
Water ΒΗ

Amissio
ΔΗ

Coniunctio

Albus
ΘΗ
THĒ
Fortuna Maior
Earth ΒΑ
BA
Cauda Draconis
ΔΑ
DA
Acquisitio

HA
Populus
ΘΑ
THA
Tristitia
Stoicheic ΧΦΞΘ System using Vague Elemental Vowels
Primary Element
Fire Air Water Earth
Secondary
Element
Fire ΧΙ
KHI
Laetitia
ΦΙ
PHI
Puer
ΞΙ
KSI
Puella
ΘΙ
THI
Carcer
Air ΧΥ
KHU
Fortuna Minor
ΦΥ
PHU
Rubeus
ΞΥ
KSU
Via
ΘΥ
THU
Caput Draconis
Water ΧΗ
KHĒ
Amissio
ΦΗ
PHĒ
Coniunctio
ΞΗ
KSĒ
Albus
ΘΗ
THĒ
Fortuna Maior
Earth ΧΑ
KHA
Cauda Draconis
ΦΑ
PHA
Acquisitio
ΞΑ
KSA
Populus
ΘΑ
THA
Tristitia

Note that in the ΧΦΞΘ system below, instead of using Iōta for Fire and Alpha for Earth (as given in the “vague elemental vowels” table immediately above), I went with Omicron for Fire and Ōmega for Earth because, well, if we’re going to go all the way and stick solely to using stoicheically-appropriate consonants, it makes sense to follow through and stick to using the most precisely, stoicheically-appropriate vowels. However, it breaks with the other systems here, so while this is perhaps the most suited to a pure Mathēsis or purely-Western approach, it doesn’t fit with any of the others and it makes a total break with any BZDH system we have.  Additionally, the similarity between Omicron and Ōmega here can cause some confusion and difficulty for those who aren’t precise with their pronunciations, even if the system is precisely correct as far as stoicheia goes.

Stoicheic ΧΦΞΘ System using Exact Elemental Vowels
Primary Element
Fire Air Water Earth
Secondary
Element
Fire ΧΟ
KHO
Laetitia
ΦΟ
PHO
Puer
ΞΟ
KSO
Puella
ΘΟ
THO
Carcer
Air ΧΥ
KHU
Fortuna Minor
ΦΥ
PHU
Rubeus
ΞΥ
KSU
Via
ΘΥ
THU
Caput Draconis
Water ΧΗ
KHĒ
Amissio
ΦΗ
PHĒ
Coniunctio
ΞΗ
KSĒ
Albus
ΘΗ
THĒ
Fortuna Maior
Earth ΧΩ
KHŌ
Cauda Draconis
ΦΩ
PHŌ
Acquisitio
ΞΩ
KSŌ
Populus
ΘΩ
THŌ
Tristitia

deep breath

Okay.  So, that’s all a lot of tables and lists and examples and options to pick from, all of which are nice and all, but where does that leave us?

What we wanted to come up with was a set of four simple intonable syllables—our “epodes”—to work with the four classical elements of Fire, Air, Water, and Earth, much as how we have the seven Greek vowels to work with the seven traditional planets.  While a straightforward option would be to simply intone the words for the elements themselves, we can use an obscure geomantic technique that gives us four consonants to reflect the four elements, which we can then intone by adding a vowel to it.  However, we can make variants of this system based on how far we want to take the logic of why we have those four consonants to begin with, even going so far as to come up with a set of sixteen epodes for each of the geomantic figures.  These geomantic epodes work within the same overall system because the geomantic figures are compositions of the four elements, and the figures Laetitia, Rubeus, Albus, and Tristitia are the geomantic figures that represent single elements unmixed with any other, which is a fact I’ve been able to use before for coming up with gestures for the four elements using the same logic.

Now, because of all the possibilities of what script to use (Arabic, Greek, Roman), what consonants to use (BZDH or the script-appropriate variants based on numerical order within that script’s alphabet), and what vowels to use (the “ah” sound, Ēta for Greek variants, or using stoicheically-appropriate vowels based on the planetary affinities towards the elements), we end up with quite a few different options for our elemental epodes:

Fire Air Water Earth
Words Arabic نار
nar
هواء
hawa’
ماء
ma’
تراب
turab
Greek πῦρ
pũr
ἀήρ
aḗr
ὕδωρ
húdōr
γῆ
gē̃
Latin ignis aer aqua terra
ΙΑΩ Names ΧΙΑΩΧ
khiaōkh
ΦΙΑΩΦ
phiaōph
ΞΙΑΩΞ
ksiaōks
ΘΙΑΩΘ
thiaōth
Transliterated Arabic با
زا
دا
حا
ḥā
Greek
Ēta
ΒΗ
ΖΗ
ΔΗ

Greek
Alpha
ΒΑ
ba
ΖΑ
za
ΔΑ
da

ha
Roman BA ZA DA A
Isopsephic Greek
Ēta
ΒΗ
ΔΗ

ΘH
thē
Greek
Alpha
ΒΑ
ba
ΔΑ
da

ha
ΘΑ
tha
Roman BA DA GA HA
Hybrid Transliterated ΒΙ
bi
ΖΥ
zu
ΔΗ

ha
Isopsephic ΒΙ
bi
ΔΥ
du

ΘΑ
tha
Mathēsis Natural
Vowels
ΧΕΙ
khei
ΦΕΙ
phei
ΞΕΙ
ksei
ΘΗ
thē
Vague
Vowels
ΧΙ
khi
ΦΥ
phu
ΞΗ
ksē
ΘΑ
tha
Exact
Vowels
ΧΟ
kho
ΦΥ
phu
ΞΗ
ksē
ΘΩ
thō

See now why I had to break all this out into its own separate post?

Originally, I was using the ΙΑΩ-based epodes, but I never really liked them, especially compared to all the other elegant options we have now based on the BZDH technique or its variants.  Of course, we have quite a few options now, and there are plenty of arguments for and against each one.  Here’s what I recommend based on your specific approach:

• If you’re using a strict Arabic or classically “pure” geomantic system apart from planetary or other concerns and want to stick to the root of geomancy as much as possible, despite any other advantages out there from the other systems, use the Transliterated BZDH system, most preferably the Arabic system (bā/zā/dā/ḥā) or the Greek-Alpha system (ΒΑ/ΖΑ/ΔΑ/Ἁ), depending on how good your pronunciation skills at pharyngeal consonants are.
• If you’re using a purely Greek system that wants to use the advantages of the stoicheia of the Greek alphabet as much as possible, use the Mathēsis system with exact vowels (ΧΟ/ΦΥ/ΞΗ/ΘΩ).
• If you’re a general Western geomancer with no particular leanings towards or against any particular niche, use the Hybrid system with transliterated consonants (ΒΙ/ΖΥ/ΔΗ/Ἁ).  This would be considered the middle approach between the two extremes of “original root source” and “Mathēsis-only stoicheia please”, and is probably appropriate for the largest number of people given its ease of use and pronunciation.

Likewise, for the use of the geomantic epodes:

• If you want a more general use, go with the Transliterated ΒΖΔΗ System.
• If you want a specialized mathētic use, go with the Stoicheic ΧΦΞΘ System with exact vowels.

Of course, given all the options above, there’s plenty of room for experimentation, and I’m sure one could extend the logic of the BZDH system (whether through transliteration, isopsephy, or stoicheia) even further and combining it with other vowel systems to come up with more options, or there would be still other ways to come up with elemental epodes (and maybe even geomantic epodes, as well) that aren’t based on the BZDH or ΧΦΞΘ systems!  As with so much else with geomantic magic, there’s so much to experiment and toy with, because it’s such a fertile and unexplored field of occult practice, so if you want to experiment with these or if you have other systems you use, I’d love to hear about them in the comments!

# On the Structure and Operations of the Geomantic Figures

When I did my recent site redesign and added all those new pages on prayers, rituals, and whatnot, I also consolidated a few pages into ones that fit neatly together, and got rid of a few entirely that didn’t need to be on here anymore.  There weren’t many of those, to be fair, but the main casualties of that effort were my handful of pages on geomancy.  While it may seem odd that I, of all people, would take down pages on the art I love so much, it was partially because I’m continuing to prepare for my book and wanted to rewrite and incorporate the information of those pages in a better way than what was presented there, and partially because the idea for those pages has long since turned stale; I was going to have an entire online “book” of sorts, but I figure that I’ve written enough about geomancy on my blog that it’s probably easier to just browse through the geomancy category and read.  So, if you end up finding a broken link (which I do my utmost to keep from happening), chances are you’re seeing a relic of an earlier age on this blog that connected to those pages.  After all, even though I’d like to keep my blog in perfect running order, I’m also not gonna scroll through 600-odd posts and comb through each and every link.

One of the things that those lost geomancy pages discussed was the mathematical operations of the figures.  I’ve talked about the mathematics behind the Judge and the Shield Chart before, as well as the Parts of Fortune and Spirit, and I’ve discussed a sort of “rotary function” that rotates the elemental rows up and down through the figures before, but there are three big mathematical operations one can do on the figures themselves that reveal certain relationships between them.  I mention them on my De Geomanteia posts of the figures themselves, though now that the original page that describes them is down, I suppose a new post on what they are is in order, if only to keep the information active, especially since every now and then someone will come asking about them.  This is important, after all, because this information is definitely out there, but it’s also largely a result of my own categorization; I haven’t seen anyone in the Western literature, modern or ancient, online or offline, talk about the mathematical relationships or “operations” between the figures in the way I have, nor have I seen anyone talk about one of the operations entirely, so this post is to clear up those terms and what they signify.

First, let me talk about something tangentially related that will help with some of the operation discussion below.  As many students of geomancy are already aware, a common way to understand the figures is in terms of their motion, which is to say, whether a figure is stable or mobile.  Structurally speaking, stable figures are those that have more points in the Fire and Air rows than in the Water and Earth rows (e.g. Albus), and mobile figures are those that have more points in the Water and Earth rows than in the Fire and Air rows (e.g. Puer).  In the cases where the top two rows have the same number of points as the bottom two rows (e.g. Amissio or Populus), the figures are “assigned” a motion based on their general effects.

• Stable figures: Populus, Carcer, Albus, Puella, Fortuna Maior, Acquisitio, Tristitia, Caput Draconis
• Mobile figures: Via, Coniunctio, Rubeus, Puer, Fortuna Minor, Amissio, Laetitia, Cauda Draconis

Stable figures are generally seen as graphically looking like they’re “sitting upright” when viewed from the perspective of the reader, while mobile figures are considered “upside down” or “unbalanced” when read the same way.  In a similar sense, stable figures generally have effects that are slow to arise and long to last, while mobile figures are just the opposite, where they’re quick to happen and quick to dissipate.  Consider mobile Laetitia: a figure of optimism, elevation, hope, and bright-burning joy, but it’s easy to lose and hard to maintain.  This can be contrasted with, for instance, stable Tristitia: a figure of slow-moving depression, getting stuck in a rut, languishing, and losing hope.

The idea of motion, I believe, is a simplification of an older system of directionality, where instead of there being two categories of figures, there are three: entering, exiting, and liminal.  All entering figures are stable, all exiting figures are mobile, and the liminal figures are considered in-between:

• Entering figures: Albus, Puella, Fortuna Maior, Acquisitio, Tristitia, Caput Draconis
• Exiting figures: Rubeus, Puer, Fortuna Minor, Amissio, Laetitia, Cauda Draconis
• Liminal figures: Populus, Via, Carcer, Coniunctio

In this system, entering figures are seen as “bringing things to” the reader or reading, and exiting figures “take things away from” the reader or reading, while liminal figures could go either way or do nothing at all, depending on the situation and context in which they appear.  For instance, consider Acquisitio, the quintessential entering figure, which brings things for the gain of the querent, while exiting Amissio is the opposite figure of loss, taking things away, and all the while liminal Populus is just…there, neither bringing nor taking, gaining nor losing.

The liminal figures also serve another purpose: they are also sometimes called “axial” figures, because by taking the upper or lower halves of two axial figures, you can form any other figure.  For instance, the upper half of Populus combined with the lower half of Via gets you Fortuna Maior, the upper half of Coniunctio with the lower half of Carcer gets you Acquisitio, and so forth.  This way of understanding the figures as being composed of half-figures is the fundamental organization of Arabic-style geomantic dice:

Entering figures, like stable figures, look like they’re “coming towards” the reader, while exiting figures look like they’re “going away” from the reader, much like mobile figures.  The reason why the liminal figures (“liminal” meaning “at the threshold”) are considered in-between is that they look the same from either direction, and are either going both ways at once or going in no direction at all.  Populus and Carcer went from liminal to stable due to their long-lasting effects of stagnation or being locked into something, while Via and Coniunctio went from liminal to mobile for their indications of change, movement, and freedom.

Alright!  With the basic structural talk out of the way, let’s talk about operations.  In essence, I claim that there are three primary operations one can do on a figure to obtain another figure, which may or may not be the same as the original figure.  These are:

• Inversion: replace the odd points with even points, and even points with odd points.  For instance, inverting Puer gets you Albus.
• Reversion: flip the figure vertically.  For instance, inverting Puer gets you Puella.
• Conversion: invert then revert the figure, or revert and invert the figure.  For instance, converting Puer gets you Rubeus (Puer →Albus → Rubeus to go the invert-then-revert route, or Puer → Puella → Rubeus to go the revert-then-invert route).

In my De Geomanteia posts, I briefly described what the operations do:

• Inversion: everything a figure is not on an external level
• Reversion: the same qualities of a figure taken to its opposite, internal extreme
• Conversion: the same qualities of a figure expressed in a similar manner

And in this post on a proposed new form of Shield Cart company based on these operations, I described these relationships in a slightly more expanded way:

• Inversion: The two figures fulfill each other’s deficit of power or means, yet mesh together to form one complete and total force that will conquer and achieve everything that alone they could not.
• Reversion: The two figures are approaching the same matter from different directions and have different results in mind, looking for their own ends, but find a common thing to strive for and will each benefit from the whole.
• Conversion: The two figures are similar enough to act along the same lines of power and types of action, but express it in completely different ways from the outside.  Internally, the action and thoughts are the same, but externally, they are distinct.  Think bizarro-world reflections of each other.

These trite descriptions are a little unclear and, now that several years have passed, I realize that they’re probably badly phrased, so it’s worth it to review what these relationships are and how they tie into other conceptions of figure relationships.  After all, inversion and reversion both deal with the notion of something being a figure’s opposite, but we often end up with two separate “opposites”, which can be confusing; and, further, if you take the opposite of an opposite, you get something similar but not quite the same (inversion followed by reversion, or vice versa, gets you conversion).

To my mind, inversion is the most outstanding of the operations, not because it’s any more important than the others, but because it’s so radical and fundamental a change from one figure to the other.  To invert a figure, simply swap the points with their opposites: turn the odd points even and the even points odd.  You could say that you’re turning a figure into its negative, I suppose, like flipping the signs, levels of activity, or polarity of each individual element.  Most notably, the process of inversion is the only one that we can perform through simple geomantic addition of one figure with another; to invert a figure, simply add Via to it, and the result will be that figure’s inversion.  Because inversion is simply “just add Via”, this is probably the easiest to understand: inverting a figure results in a new figure that is everything the original figure isn’t.  We turn active elements passive and passive elements active, male into female and female into male, light into dark and dark into light.  What one has, the other lacks; what one forgets, the other remembers.

So much for inversion.  Reversion is as simple as inversion, but there’s no “just add this figure” to result in it; it’s a strictly structural transformation of one figure based on that figure’s rows.  To be specific and clear about it, to revert a figure, you swap the Fire and Earth lines, as well as the Air and Water lines; in effect, you’re turning the figure upside down, so that e.g. Albus becomes Rubeus or Caput Draconis becomes Cauda Draconis.  Note that unlike inversion where the invert of one figure is always going to be another distinct figure, there are some figures where the reversion is the same as the original figure; this is the case only for the liminal figures (Populus, Via, Carcer, Coniunctio), since rotating them around gets you the same figure.  By swapping the points in the lines of the elements that agree with each other in heat (dry Fire with dry Earth, and moist Air with moist Water), you get another type of opposite, but rather than it playing in terms of a strict swap of polarity like from positive to negative, you literally turn everything on its head.

Both inversion and reversion get you an “opposite” figure, but there are different axes or scales by which you can measure what an “opposite” is.  As an example, consider Puer.  If you invert Puer, you get Albus; this is an opposite in the sense that the youthful brash boy with all the energy in the world is the “opposite” of the wise old man without energy.  What Puer has (energy), Albus lacks; what Albus has (experience), Puer lacks.  On the other hand, if you revert Puer, you get Puella; this is another kind of opposite in the sense that the masculine is the opposite of the feminine.  What Puer is (masculine, active, emitting), Puella isn’t (feminine, passive, accepting).  This type of analysis, where inversion talks about “has or has not” and reversion talks about “is or is not” is the general rule by which I understand the figures, and holds up decently well for the odd figures.  It’s when you get to the even figures that this type of distinction between the operations by means of their descriptions collapses or falls apart:

• For non-liminal even figures, the inversion of a figure is the same as its reversion.  Thus, “is” is the same thing as “has”.  For instance, Acquisitio is the total opposite of Amissio, since they are both reversions and inversions of each other; gain both is not loss and loss does not have gain.
• For liminal even figures, the reversion of a figure is the same figure as itself.  Thus, “has” makes no sense, because the figure isn’t speaking to anything one “has” or “lacks” to begin with.  For instance, Carcer’s reversion is Carcer; Carcer is imprisonment and obligation, it doesn’t “have” a quality of its own apart from what it already is.  On the other hand, Carcer’s inversion, what Carcer is not, is Coniunctio, which is freedom and self-determination.  Again, Coniunctio describes a state of being rather than any quality one has or lacks.

Between inversion and reversion, we can begin to understand the pattern of how the babalawos of Ifá, the West African development and adaption of geomancy to Yoruba principles and cosmology, organize their sixteen figures, or odu:

Rank Latin Name Yoruba Name Relationship
1 Via Ogbe inversion
2 Populus Oyẹku
3 Coniunctio Iwori inversion
4 Carcer Odi
5 Fortuna Minor Irosun inversion-
reversion
6 Fortuna Maior Iwọnrin
7 Laetitia Ọbara reversion
8 Tristitia Ọkanran
9 Cauda Draconis Ogunda reversion
10 Caput Draconis Ọsa
11 Rubeus Ika reversion
12 Albus Oturupọn
13 Puella Otura reversion
14 Puer Irẹtẹ
15 Amissio Ọsẹ inversion-
reversion
16 Acquisitio Ofun

With the exception of the even liminal figures, which are grouped in inversion pairs at the beginning of the order, it can be seen that the other figures are arranged in reversion pairs, with the even non-liminal figures grouped in what is technically either inversion or reversion, but which are most likely considered to just be reversions of each other.  Note how the non-liminal even figure pairs are placed in the order: they separate the strict-inversion pairs from the strict-reversion pairs, one at the start of the strict-reversion pairs and one at the end.  While it’s difficult to draw specific conclusions from this alone (the corpus of knowledge of odu is truly vast and huge and requires years, if not decades of study), the placement of the figures in this arrangement cannot be but based on the structure of the figures in their inversion/reversion pairs.

In another system entirely, Stephen Skinner describes some of the relationships of figures in Arabic geomancy in his book “Geomancy in Theory and Practice”, at least as used in some places in northern Africa, where the relationships are described in familial terms and which are all seemingly based on inversion:

• Man and wife
• Tristitia and Cauda Draconis
• Laetitia and Caput Draconis
• Albus and Puer
• Puella and Rubeus
• Coniunctio and Carcer
• Brothers
• Fortuna Minor and Fortuna Maior
• Acquisitio and Amissio
• No relation
• Via and Populus

Stephen Skinner doesn’t elaborate on what “man and wife” or “brothers” means for interpreting the figures, but if I were to guess and extrapolate on that small bit of information alone (which shouldn’t be trusted, especially if someone else knowledgeable in these forms of geomancy can correct me or offer better insight):

• For figures in “man and wife” pairings, the first figure is the “husband” and the second figure is the “wife”.  Though I personally dislike such an arrangement, it could be said that the husband figure of the pair dominates the wife figure, and though they may share certain similarities that allow for them to be married in a more-or-less natural arrangement, the husband figure is more powerful, domineering, overcoming, or conquering than the wife figure.  The central idea here is that of domination and submission under a common theme.
• For figures in “brothers” pairings, the figures are of equal power to each other, but are more opposed to each other than in harmony with each other, though they form a different kind of complete whole.  Thus, they’re like two brothers that fight with each other (in the sense of one brother against the other) as well as with each other (in the sense of both brothers fighting against a third enemy).  The central idea here is that of oppositions and polarity that form a complete whole.
• For the two figures that have no relation to each other, Via and Populus, this could be said that they are so completely different that they operate in truly different worlds; they’re not just diametrically opposed to each other to form a whole, nor is one more dominant over or submissive to the other in the same theme, but they’re just so totally and completely different that there is no comparison and, thus, no relationship.

Of course, all that is strictly hypothetical; I have nothing else to go on besides these guesses, and as such, I don’t use these familial relationships in my own understanding of the figures.  However, these are all indicative ways of how to view “opposites”, and is enlightening on its own.  However, note the specific figures in each set of relationships.  With the exception of Coniunctio and Carcer, all the husband-wife pairs are odd figures, so the only possible relationship each figure could have in their pair is inversion.  For the brother pairs, however, these are the even non-liminal figures, where the figures could be seen as either inversions or reversions of each other.  This could well be a hint at a difference between the meanings of inversion and reversion in an African or Arabic system of understanding the figures.

Alright, so that all deals with inversion and reversion, which leaves us with one final operation.  Conversion, as you might have gathered by now, is just the act of performing inversion and reversion on a figure at the same time: you both swap the parity of each row, and rotate the order of the row upside down (or vice versa, it’s the same thing and doesn’t matter).  In a sense, you’re basically taking the opposite of an opposite, but you’re not necessarily going from point A to point B back to point A; that’d just be inverting an inversion or reverting a reversion.  Rather, by applying both operations, you end up in a totally new state that is at once familiar while still being different.  For instance, consider Puella.  Puella’s conversion is Albus, and at first blush, it doesn’t seem like there’s much in similarity between these two figures except, perhaps, their ruling element (Water, in this case).  But bear in mind that both Puella and Albus don’t like to act, emit, or disturb things; Puella is the kind, welcoming hostess who accepts and nurtures, while Albus is the kind, wizened old man who accepts and guides.  Neither of them are chaotic, violent, energetic, or brash like Puer or Rubeus, and while they don’t do things for the same reason or in the same way, they end up doing things that are highly similar, like the same leitmotif played in a different key.

However, this is a little weird for the liminal figures, because a liminal figure’s reversion is the same as itself; this means that a liminal figure’s conversion is the same as its inversion (because the reversion “cancels out”).  Thus, converting Populus gets you Via, and converting Carcer gets you Coniunctio.  While these are clearly opposites of each other, it speaks to the idea that there’s a sort of “yin in the yang, yang in the yin” quality to these figure pairs.  This is best shown by Populus, which is pure potential with all activity latent and waiting to be sprung, and Via, which is pure activity but taken as a whole which doesn’t, on the whole, change.  Likewise, you can consider Carcer to be restriction of boundaries, but freedom to act within those set parameters, and Coniunctio, which is freedom of choice, but being constrained by the choices you make and the paths you take.

It’s also a little weird for the non-liminal even figures, because the reversion of these figures is the same as its inversion, which means that the conversion of an non-liminal even figure gets you that same figure itself.  While the “opposite of an opposite” of odd figures takes you from point A to B to C to D, the nature of the non-liminal even figures takes you from point A to B right back to A.  This reflects the truly is-or-is-not nature of these figures where there’s only so many ways you can view or enact the energies of what they represent: either you win or you lose, either you gain or you lose.  You might not win using the same strategy as you expected to use, but winning is winning; you may not get exactly what you thought you were after, but you’re still getting something you needed.

With these three operations said, I suppose it’s appropriate to have a table illustrating the three results of these operations for each of the sixteen figures:

Figure Inversion Reversion Conversion
Populus Via Populus Via
Via Populus Via Populus
Albus Puer Rubeus Puella
Coniunctio Carcer Coniunctio Carcer
Puella Rubeus Puer Albus
Amissio Acquisitio Acquisitio Amissio
Fortuna Maior Fortuna Minor Fortuna Minor Fortuna Maior
Fortuna Minor Fortuna Maior Fortuna Maior Fortuna Minor
Puer Albus Puella Rubeus
Rubeus Puella Albus Puer
Acquisitio Amissio Amissio Acquisitio
Laetitia Caput Draconis Tristitia Cauda Draconis
Tristitia Cauda Draconis Laetitia Caput Draconis
Carcer Coniunctio Carcer Coniunctio
Caput Draconis Laetitia Cauda Draconis Tristitia
Cauda Draconis Tristitia Caput Draconis Laetitia

Looking at the table above, we can start to pick out certain patterns and “cycles” of operations that group certain figures together:

• A figure maintains its parity no matter the operation applied to it.  Thus, an odd figure will always result in another odd figure through any of the operations, and an even figure will always yield another even figure.
• A figure added to its inverse will always yield Via.
• A figure added to its reverse will always yield one of the liminal figures.
• A figure added to its converse will always yield another of the liminal figures, which will be the inverse of the sum of the original figure and its reverse.
• If the figure is odd, then its inversion, reversion, and conversion will all be unique figures, but each figure can become any of the others within a group of four odd figures through another operation.
• If the figure is even and liminal, then its reversion will be the same as the original figure, while its inversion and conversion will be the same figure and distinct from the original.
• If the figure is even and not liminal, then its inversion and reversion will be the same figure and distinct from the original, while its conversion will be the same as the original figure.

The odd figures are perhaps most interesting to analyze in their operation groups.  Note that the four figures that result from the operations of a single odd figure (identity, inversion, reversion, and conversion) all, at some point, transform into each other in a neverending cycle, and never transform in any way into an odd figure of the other cycle.  More than that, we can break down the eight odd figures into two groups which have these operational cycles, or “squadrons”, one consisting of Puer-Albus-Puella-Rubeus and the other of Laetitia-Caput Draconis-Cauda Draconis-Tristitia:

Note that the Puer squadron has only figures of Air (Puer and Rubeus) and Water (Puella and Albus), while the Laetitia squadron has only Fire (Laetitia and Cauda Draconis) and Earth (Tristitia and Caput Draconis), and that the converse of one odd figure yields another odd figure of the same element.  Coincidentally, it was this element-preserving property of conversion that led me to the Laetitia-Fire/Rubeus-Air correspondence, matching with the elemental system of JMG and breaking with older literature in these two figures.  More numerologically, also note how each squadron has two figures with seven points and two figures with five points; this was marked as somewhat important in how I allotted the figures to planetary arrangements before, but it could also be viewed under an elemental light here, too.  If each squadron has two figures of the pure elements (Albus and Rubeus in the Puer squadron, Laetitia and Tristitia in the Laetitia squadron), then the converse of each would be the harmonic opposite of the pure element according to their subelemental ruler::

• Laetitia (pure Fire) converts to/harmonizes with Cauda Draconis (primarily Fire, secondarily Earth)
• Rubeus (pure Air) converts to/harmonizes with Puer (primarily Air, secondarily Fire)
• Albus (pure Water) converts to/harmonizes with Puella (primarily Water, secondarily Fire)
• Tristitia (pure Earth) converts to/harmonizes with Caput Draconis (primarily Earth, secondarily Air)

On the other hand, now consider the even figures.  Unlike the odd figures, where the same “squadron scheme” applies for two groups, there are actually two such schemes for even figures, each scheme having one pair of figures.  For the liminal even figures, a figure’s inverse is the same as its converse, and its reverse is the original figure.  On the other hand, for the even entering/exiting even figures, a figure’s inverse is the same as it’s reverse, and its converse is the original figure:

Due to how the squadrons “collapse” from groups of four into groups of two for the even figures, the same elemental analysis of harmonization can’t be done for the even figures as we did above for the odd figures.  However, it’s also important to note that each element has four figures assigned to it, two of which are odd (as noted above) and two of which are even:

• Fire: Fortuna Minor (primarily Fire, secondarily Air), Amissio (primarily Fire, secondarily Water)
• Air: Coniunctio (primarily Air, secondarily Water), Acquisitio (primarily Air, secondarily Earth)
• Water: Via (primarily Water, secondarily Air), Populus (primarily Water, secondarily Earth)
• Earth: Carcer (primarily Earth, secondarily Fire), Fortuna Maior (primarily Earth, secondarily Water)

By looking at the inverse relationships of the even figures (which is also converse for liminal figures and reverse for non-liminal figures), we can also inspect their elemental relationships:

• Carcer (primarily Earth, secondarily Fire) inverts to Coniunctio (primarily Air, secondarily Water).  Both the primary and secondary elements of each figure are the opposite of the other, making these two figures a perfect dichotomy in every way.
• Via (primarily Water, secondarily Air) inverts to Populus (primarily Water, secondarily Earth).  Though both these figures share the same primary element, the secondary elements oppose each other.  In a sense, this is a more bland kind of opposition that Carcer and Coniunctio show.
• Acquisitio (primarily Air, secondarily Earth) inverts to Amissio (primarily Fire, secondarily Water).  Unlike Carcer and Coniunctio, and despite that these figures are reversions-inversions of each other, their elemental natures complement each other in both their primary and secondary rulers by heat, as Air and Fire (primary rulers) are both hot elements, and Earth and Water (secondary rulers) are both cold elements.
• Fortuna Maior (primarily Earth, secondarily Water) inverts to Fortuna Minor (primarily Fire, secondarily Air).  Similar to Acquisitio and Amissio, these two figures are reversions-inversions of each other, but their elemental natures complement each other in moisture, as Earth and Fire (primary rulers) are both dry elements, and Water and Air (secondary elements) are both moist elements).

Note that Carcer and Coniunctio along with Via and Populus (the liminal figures) show a more rigid opposition between them based on their inversion pairs than do Acquisitio and Amissio along with Fortuna Maior and Fortuna Minor (the non-liminal even figures).  Liminality, in this case, shows a forceful dichotomy in inversion, while actually possessing motion suggests completion of each other in some small way.  In this post I wrote on how the natures of the elements complement or “agree” each other based on the element of figure and field in the Shield Chart, these could be understood to say something like the following:

• Disagree (Carcer and Coniunctio, Via and Populus): Undoing and harm to the point of weakness and powerlessness, force and constriction from one into the other unwillingly.  This is more pronounced with Carcer and Coniunctio than it is Via and Populus, since Via and Populus still agree in the more important primary element, in which case this is more a complete undoing for strength rather than weakness, an expression of transformation into an unknown opposite rather than a forced march into a known but undesired state.
• Agree in heat (Acquisitio and Amissio): Completion and aid to both, but transformation in the process for complete change in goals and intent.
• Agree in moisture (Fortuna Maior and Fortuna Minor): Balance and stabilization that lead to stagnation and cessation of action, but with potential that must be unlocked or initiated.

Admittedly, this post took a lot longer to write than I anticipated, largely because although the mathematics behind the operations is pretty easy to understand, the actual meaning behind them is harder to nail down, and is largely a result of introspection and reflection on the figures involved in these operations.  For my own part, I don’t claim that my views are the be-all-end-all of these mathematical or structural relationships between the figures, and I would find this a topic positively begging for more research and meditation by the geomantic community as a whole, not just to flesh out more of the meanings and the relationships of the figures themselves, but also how they might be applied in divination as part of divinatory technique rather than just symbolism, like how I suggested using them for a mathematical/structural form of Shield Chart company.

So, what about you?  Do you think anything of these operation-based relationships of the figures?  Are there any insights you’d be willing to share regarding these operations and relationships?  Is there anything you can thread together from the observations I’ve made above that makes things flow better or fit together more nicely?  Feel free to share in the comments!