# 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.