Mathētic Order of Offerings to the Theoi

One of the longest spiritual practices I’ve maintained more-or-less continually, or at least kept around in one form or another, is that to the Greek gods.  I have a shrine to a few of them in my temple, and though the form and shape of it has waxed and waned over the years, I’ve kept venerating and offering to them since I got started, pretty much.  From my apartment after college where I had Hermēs in one corner of my bedroom and Asklepios against the wall, and after with Dionysos joining Asklepios; then moving into a house with my boyfriend and having an entire room for my spiritual stuff, with an elaborate set of glass shelves for the theoi, with separate spaces for Zeus and Aphroditē and Apollo and Hephaistos and even Hadēs at one point; now into the house I moved in with my now-husband and having another room set up with different qualities and things got downsized a bit.  Hestia, of course, has been around in every house in one form or another, and Dionysos has gone from having an entire shrine dedicated and decorated to him to being…reduced in size but not in presence to a special contraption I set up just for him.  All the same, throughout all these changes, I’ve still kept up my worship of the theoi.

My practices have changed somewhat between moves from house to house and temple to temple; for instance, in the last place where I lived, my temple room was across from the hallway bathroom and had a window outside, so it was trivial to dump offerings out or get water anytime I needed.  Now, however, my temple is in a basement room with no easy access to either external ventilation or a sink or drain of any sort.  This makes disposing of old offerings and libations a little different, and given the lack of ventilation and general light, it’s easy for libations set out to evaporate really quickly or get mold faster than I would’ve thought otherwise.  That makes, for instance, the use of many small libation vessels for each theos I have enshrined a pain, because they all have to be hauled up the stairs to the kitchen to be emptied and washed then all hauled back downstairs, and so forth.  Besides that, I used to open the window during ritual as a symbolic act as a means to “let the god in” and for incense offerings to reach the heavens, but I can’t do that at this point, so I have to adjust my processes for that.

As I’m getting back to my daily practice (and struggling to find out how to make things more efficient and effective while still making things count), I’ve also been digging through my notes to see what insights I had before, what my proposed methodologies or practices were, and how I managed to get by before and how I did things.  I suppose that’s one benefit of blogging so much, because I found two such posts on my method of offering to the theoi, specifically within the context of Mathēsis, one post on general daily mathētic practices, the other on a specifically mathētic procedure to make offerings to the gods.  The former is good for me to review anyway, because it’s something I need to get back on as well, either by reworking it to be less-than-daily or by incorporating it into my general daily practices, and because it recommends a regular, daily offering or invocation of the god of the day according to my Grammatēmerologion calendar.  The latter is actually useful, because it documents one such way that an invocation and offering to a god might be done, whether associated with a particular day or otherwise, and whether it’s a grand offering or just a small quick invocation.

However, as I look back on this procedure, there are things that I really would feel more comfortable changing than keeping the same.  (That’s one good benefit of writing my own blog; I get to make the claim that anything I write can be improved on later!)  Between my own experiences and interactions with the theoi on their own terms and by bringing in other ideas that I’m comfortable with applying across the board, there are some things I’m getting into the habit of that I wouldn’t’ve considered before.  For instance, while in the past I would often (but not always) make a perfunctory and preliminary offering to Hestia while also saying that it’s not strictly necessary, nowadays I’m definitely on the side of always making an offering to her to start with before any others, though I’m not entirely convinced that every offering must also conclude with another one to her, as well.  Rather, I’m now in the habit of honoring Zeus in every offering, regardless whether he’s the focus of my prayers or not, due to his role as divine cosmic king who rules over the three realms; at first I had his name praised and made a perfunctory offering to him before any other god (besides Hestia), but after some conversation, I make him last.  Or second-to-last, if Hestia gets a final offering as well.

So, let me draw out my process and my thinking.  It is true that many of the theoi operate independently in some respects, but it is also true that they are all part of the same pantheon and part of the same cosmic schema.  Just as you can’t remove a single number from the Decad and have it still remain the Decad, you can’t really remove a single theos from the theoi and have it remain the pantheon.  However, not every individual theos needs to be worshipped at all times, but a few key ones that allow for worship to happen at all makes more sense.  For that, the general order of invocation and offering that I use nowadays goes like this:

  1. Perfunctory initial offering to Hestia.  Hestia should always get the first offering, because she’s the goddess of the hearth and home itself.  Without her, we would have nowhere to live, build, or establish shrines; it is only by her support that we can make such offerings in our own homes, dwellings, and temples.  If one is living in the wild and makes offerings in a pristine place untouched by civilization with offerings that are not the products of agriculture or animal husbandry, then I would make an argument that an offering to Hestia is not needed, but it would still be appreciated as she is still rightly the eldest of the first generation of the Olympian Theoi.
  2. Perfunctory offering of wine to Dionysos.  This step is sometimes skipped depending on what I’m offering.  If I’m offering wine in this ceremony, and I’m either going to run out of an existing bottle or if I’m opening a new bottle of wine for any reason, I open it up here and pour a small amount for Dionysos, giving him thanks for his own sacrifices and allowing us to partake in his sacrifice of flesh and the grape which allows us to perform our own sacrifices.  In many ways, Dionysos is the god of wine as well as the god in wine; by opening a new bottle and giving him the first pour, we recognize his presence and dedicate our sacrifices to his own.
  3. Perfunctory offering to Hermes.  Hermēs is important to always recognize, and by calling on him, we ensure that our prayers can be heard by any and all the gods.  Hermēs is the messenger of the gods, to be sure, but he’s also the messenger between gods and mankind; it’s by him that we come to know the will and desires of the gods, but it’s also by him that they come to know our prayers and supplications.  Hermēs is, indeed, the god of prayer and ritual in general, just as Hestia can be said to be the goddess of shrines in general and Dionysos the god of sacrificing wine in general.  Plus, this helps with the notion of “bringing the god in” for when I call upon the presence of a particular deity; before, I’d open the window as a formal “opening of the gate”, but since I don’t have a window anymore, this seems to suffice as well.  It’d still be great to have a window or some other aperture, but I simply don’t have that option available to me.
  4. Main offering.  This is where the actual invocation to the god begins.  All their prayers and invocations and offerings and whatnot take place after all the initial offerings are made.
  5. Perfunctory concluding offering to Zeus.  At the end of the ceremony, once the other offerings are made, Zeus should also always be honored, as the divine ruler of the cosmos, the father of gods and men, and the supreme king of all.  In honoring Zeus who rules over the three domains of sky, sea, and land, we also honor all those who live within them, both mortal and immortal.  This suffices not only to render tribute to the god of gods, but also to recognize the divinity of all the other gods who fall under Zeus’ domain.
  6. Other perfunctory concluding offerings.  As Hestia is the first-born of Rhea and Kronos, she is also their last-born; she was born first from Rhea’s womb, and torn out last from Kronos’ belly.  The Homeric Hymn to Hestia (#24) says that “without you mortals hold no banquet, where one does not duly pour sweet wine in offering to Hestia both first and last”.  However, I don’t think that this sort of concluding offering is strictly needed after that of Zeus, but it can certainly be done; if it were, I think it would also be appropriate to honor both Hermēs and Hestia both for both their roles as divinities of prayer-speaking as well as that of shrine-keeping.  In other words, after the main offering and offering to Zeus, we work backwards: if we start with Hestia and Hermēs, we end with Hermēs and Hestia.  It’s something I’m still working out, admittedly.

This idea of a ritual process, going through multiple divinities in order to sacrifice to one, may seem needlessly complicated; I know I thought that at one point, and before, I’d just go to my Apollo shrine and do my thing and be done with it.  That said, I think of my other traditions where there is absolutely an order to worship, where certain divinities must be honored before others; this idea works for the Greek gods, too.  Plus, there are other examples of having such an order; consider the Hellenist reconstruction group Elaion and their ritual templates shared by Elani Temperance over at Baring the Aegis, where every ritual begins with a libation to Hestia, to Gaia, and to Themis before proceeding with the main event, and all of which conclude with a final offering to Hestia.  This also makes sense: just as we honor Hestia for being the goddess of hearth and home and shrine, so too do we honor the Earth for supporting all that happens and to divine Law and Order for that which is proper that all might continue to be proper.  Sure, it might seem easier to just make offerings to one god (and a lot less use of wine and oil and incense), but the more I think about it and the more I practice it, the more sense it makes to really go in for the process and proper sequencing of things in a formal offering.

Of course, all that above is just the general template, and templates change in certain circumstances.  For instance, if I were to just make an offering to Hestia for Hestia’s own sake, I wouldn’t really bother with Hermēs or the other gods, because Hestia is already right there present in my home, so Hestia is one of the very few (perhaps the only) divinity I could just sacrifice directly to and not get the rest of the gang involved and not feel bad about it.  In general, however, there’s always going to be a process, and there are certain rules to how that process might change in certain examples.  Let’s consider a few examples, with the main event in bold text and anything unexpected in italics:

  1. Hestia
    1. Dionysos (if new bottle of wine), Hestia, Zeus
    2. Because Hestia is always first no matter what, she still comes first.  However, as she’s immediately present and we’re already making an offering to her, we don’t need the messenger/interpreter presence of Hermēs.  If a new bottle of wine is to be opened, a perfunctory offering to Dionysos should come first before Hestia, though this is really more a respect gesture than anything else.  Likewise, Zeus can still be honored afterwards, but beyond Hestia and honoring the hearth itself that even the gods honor, there’s not too much that needs to be done.
  2. Dionysos
    1. Hestia, Hermēs, Dionysos, Zeus, other conclusions
    2. Normally, we’d have a perfunctory offering to Dionysos before Hermēs if we’re opening a new bottle of wine.  However, if I’m offering to Dionysos himself, I’d skip that stage and celebrate him entirely in his own part of the ceremony.  Instead of being given just a token, perfunctory offering, he gets his own full thing going on.  After Dionysos is honored, then we’d give a perfunctory offering to Zeus, and if desired, any other concluding offerings to e.g. Hermēs and Hestia.
  3. Hermēs
    1. Hestia, Dionysos (if new bottle of wine), Hermēs, Zeus, other conclusions
    2. Pretty straightforward here; Hermēs takes his usual place after Dionysos (if needed) and before Zeus, but as there are no other gods to be worshiped, Hermēs himself becomes the focus.  Instead of giving Hermēs a perfunctory offering, he gets a full offering here.
  4. Zeus
    1. Hestia, Dionysos (if new bottle of wine), Hermēs, Zeus, libation to all the gods, other conclusions
    2. Like with Hermēs, instead of just getting a perfunctory offering, Zeus himself is celebrated in full.
    3. However, remember that Zeus is normally celebrated in every ceremony to remind ourselves of his divine and cosmic importance, and by him, we can honor all the other gods and goddesses of the cosmos.  However, if we’re worshiping and offering to Zeus as Zeus alone, then we’d need something to step in to formally recognize all the other entities of the cosmos, hence a separate step for the “libation to all the gods” after Zeus.  This would be perfunctory, as the offering to Zeus any other time would be.
  5. Apollo
    1. Hestia, Dionysos (if new bottle of wine), Hermēs, Apollo, Zeus, other conclusions
    2. This is the basic template, using Apollo as the main offering.  Nothing unexpected here.
  6. Asklepios
    1. Hestia, Dionysos (if new bottle of wine), Hermēs, Apollo, Asklepios, Zeus, other conclusions
    2. This is essentially the basic template, with Asklepios as the main offering, but note how we’re also honoring Apollo immediately before him.  This is because, as I reckon it, Asklepios is not sufficiently independent or major of a god in his own right.  Sure, he can be offered to independently and on his own, but I find it more proper to recognize his father Apollo first.  In other words, to use a royal metaphor, Asklepios is a noble in the royal court ruled by Apollo; as Apollo is the ruler of that court, he gets first honors, and then any
    3. A similar case would go for any other minor god that is clearly part of another god’s “court”, such as Hēbē under Hēra, Eros under Aphroditē, Tykhē under Zeus, Nikē under Athena, and so forth.   Recognize the primary god of that court first with a perfunctory offering, then the minor god as the main offering.

Although the Greeks may not have conceived of their gods as belonging to “courts” per se, I think it’s still a useful classification of the minor gods and goddesses around central rulers who were more well-known.  For instance, I would consider all the thalassic deities Triton, Nereus, and the Nereides and Naiadēs including Thetis to all belong to the court of Poseidon, who either is the father, husband, brother, or conquering usurper of the other gods.  In sacrifice and myth, this may not really be true, but it’s a really useful way to organize “groups” of the theoi for the purposes of my Grammatēmerologion calendar, which assigns the letters of the Greek alphabet to the days of the lunar month, and by the letters, to individual signs of the Zodiac or other powers, which are associated the major gods of the Hellenic pantheon.  For instance, in the Grammatēmerologion, the twenty-third day of the lunar month is given to the letter Tau.  Tau is given to the zodiacal sign of Pisces, which is associated with the theos Poseidon; thus, it makes sense to cluster the worship of all the oceanic deities onto the day of Tau, just as all the deities associated with Hēra like Hēbē and Eileithyia are given to Hēra’s day of Sigma and so forth.  If nothing else, honoring the “court ruler” of a minor god also counts as honoring the primary god of the same day that minor god would be worshiped on, which fulfills part of my daily mathētic practices.

So, when I say “perfunctory offering”, what exactly do I mean?  Basically, a token offering, a nod, something I give just enough to recognize the divinity I’m making such an offering to.  It’s really little more than a very quick pour of wine or clean water, no more than an ounce or a few drops, accompanied by a few words of honor and veneration, calling upon their aid.  If I feel like it, I’ll recite the entire Orphic Hymn or one of the shorter Homeric Hymns to them, but in general, what I’ll say is something short, like:

Hestia, as you were first born of Rhea and last born of Kronos, so too do you receive the first offering and the last!  Queen goddess of the hearth, without you we could not live nor could we offer to the gods.  Right and proper it is to honor you first in all such rites.

Dionysos, roaring lord of reborn life, yours is the blood of the vine which we cut and rend that we might live and live well.  As you spilled your blood that we might partake in it, I give you the first offering of this bottle that you might always be honored in every pour and spill.

Hermēs, you are the messenger of gods and men, to whom we all turn in all our rites.  Hear my prayers, take these sacrifices, and carry them aloft to divine ears and immortal hands!  May all the righteous ways of worship be opened for me and for the gods!

With that, I’ll pour out a bit of wine and olive oil out—not a lot, because it’s better to give a little so that we always have something to give, and if we’re going through the process, then we’ve already got a lot to give.  From what I’ve been doing, it seems that a standard set of offerings will take around half a normal 750ml bottle of wine and maybe an ounce or two of olive oil.  While before I was pouring straight from the wine bottle into individual vessels for each individual divinity, which was fine when I could more easily wash them or empty them without having to schlep them up and down stairs, I’m now in the habit of using a large white bowl I set before my entire Greek shrine, and pouring in libations into that from a smaller white bowl.  That way, I can partake of the libation and give a toast to each of the gods as I offer, and I replicate the old practice of pouring a libation out on the ground itself.  The bowl, of course, keeps it all contained instead of splashing everywhere, and is easier to carry up instead of four or six silver or glass chalices full of wine and oil.

Of course, all of the above—the process, the order, the perfunctory offerings versus the main offerings, the courts, etc.—only really count if I’m making an actual offering to the theoi.  On days when I don’t, either because I don’t want to or don’t need to, there’s no need to go through all of that.  Instead, a simple invocation will suffice.  For instance, say that it’s the day of Gamma; Gamma is associated with Taurus, and thus with Aphroditē.  If I’m going to make a full offering to Aphroditē that day, then yes, I’ll go through the process of Hestia, Dionysos, Hermēs, Aphroditē, Zeus, &c.  However, if I’m not, whether because I’m too tired or don’t plan on doing an offering to Aphroditē that day, then I’d just call on her and give her a simple prayer; rather than giving her a main offering in the midst of a bunch of perfunctory offerings, I’d just give her a perfunctory (or bigger) invocation with no other process involved.  In other words, if all I’m doing is verbally honoring and recognizing the god of the day, then there’s no sacrifice or offering, so the whole process of offering doesn’t apply.  Easy, indeed, and if it’s all I need to get by for a daily practice, then all the better.

I’m sure, given enough time, this proposed method will continue to change.  What is becoming clear to me is that it’s easier for me to bundle my already-existing Hellenic/Greek practices into my overall Mathēsis work, which is fine by me; the less I have to arrange as separate “practices”, especially when one directly comes from the other and is going to subsume it anyway, the better.  By refocusing my Hellenic work into my Mathēsis work, I can better focus both together and synthesize them in a way that reduces stress and conflict while still being able to expand and expound on both.  Plus, if this Mathēsis stuff is actually going to head in the direction I want it, having processes for this sort of thing are definitely a needed and beneficial organizing principle.

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!

Random silliness to entertain yourselves with.

A number of my friends on Twitter make use of this website called Shindanmaker, a kind of random fortune-telling site:

Shindanmaker is a joke web service which diagnoses you by your inputting your name.  Although “Shindan” originally means “diagnosis”, sometimes the meaning of “fortune-telling” is also used.  You can enjoy Shindan made by other users and you can also make them.

Often, they’re kinda silly, though they can be fun.  You just put in your name (any name will do), and it randomly selects for you a particular result for any given shindan.  Look through the site and see what appeals to you; they’re all free and simple to use.  They’re meant to be posted to Twitter in some ways, so if you have a Twitter account (and you totally should and follow me), you can post your results for any of them.

Last night, I got bored and decided to try my hand at making a few shindans.  A simple one I made (available here) generates four geomancy figures based on your name.  This changes from day to day, so it can help in getting a “chart for the day” based on your name.  It can be useful, I assume, so why not give it a whirl the next time you’re interested in doing a daily divination?  Another one was based off some banter between me and the boyfriend, and determines how presh (precious) you are.  Just a silly little thing.

Another one I made, though, is entirely a joke.  You know how a lot of magical or religious organizations have really obscure, long, complex, or convoluted names, right?  I decided to make a random magical order generator, complete with assigning you a rank or grade within the organization.  So, for instance, as of this writing, if I put in “polyphanes”, I get “polyphanes is a Bellator Jovis in the Qabbalistic Skete of the Earthy Death”.  Not bad for a random generator, eh?  It’s just a cute little thing, but it could be helpful for people wanting to start a magical order of their own or something, even if only in tabletop RPGs for the sake of making a dungeon master’s life easier.  I’m still expanding it with whatever adjectives and nouns I can find that are appropriate, so it’ll probably get more varied as time goes on.

And, yes, while it’s possible to get “X is a Magister Templi in the Hermetic Order of the Golden Dawn”, you have about a 1 in 24,224,311,440 chance of doing so (as of this writing).  Good luck!  Feel free to share or post your results in the comments.

Ordering the Geomantic Figures

Occult systems of knowledge, at least those in European traditions, have a huge affinity for symbols.  For instance, astrology has the stars, the zodiac, the planets, and the aspects; Tarot has its 78-card deck; qabbalah has its sephiroth and paths and names of God and gematria.  Sometimes these symbols in different systems can be corresponded neatly (or not-so-neatly) with each other, much as different metric units can be converted into each other by reducing them down to a particular set of units.  Geomancy, with its sixteen geomantic figures, is no exception, and has connections to the planets, the elements, and so forth.  Nifty figures, them.  You might be interested in reading up about them if you’re so inclined.

Unlike other occult systems of knowledge, however, geomancy doesn’t have a fixed or canonical order for the figures.  Tarot has the Major Arcana and Minor Arcana with their numbered cards and ranks and suits, which can afford some structured ordering, and astrology has the order of the zodiac signs plus the planets in geocentric order from or to the Earth.  Geomancy hasn’t held a specific or meaningful ordering of its own for the figures, which is a little confusing at first.  Sure, there are ways to order the figures, but there is no ordering of them of geomancy’s own design for its own benefit.  Every author seems to prefer their own order in every single text, though it usually borrows at least in part from astrology (either the order of the zodiac signs or the planets associated with the figures).

First, let’s make two terms clear from computer science: sets and lists.  A set is a collection of things with no implication of order, while a list is an ordered collection of things.  There is no notion of “first” or “last” or “next” within a set; something is either a member/included with the set, or excluded from the set.  On the other hand, lists impose an ordering on the things within itself, with there being a first thing, a next thing, and so on until we get to the last thing; every think in a list has an index, its position within the list.  While astrology, Tarot, and the like have lists for their symbols (the numbering of the cards in the deck, the planets from geocentrically furthest to closest to the Earth), geomancy has never really had a fixed list.  It’s more accurate to talk of sets instead of lists for geomancy, at least in its historical development.

Several common methods of ordering the geomantic figures that I’ve seen include:

  • Binary ordering, where each geomantic figure is read as a number in binary.  As with the geomantic emblem notation, a line with two dots is represented as 0 and a line with one dot as 1.  Thus, Populus becomes 0000, which in binary is zero; Tristitia becomes 0001, which is 1; Via becomes 1111, which is 16; and so forth.
  • Planetary ordering, where each geomantic figure is ordered by its corresponding planet.  This relies on the use of a particular order of the planets; I prefer the traditional Chaldaean order, moon-first (Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn).  I set the figures Caput Draconis and Cauda Draconis, ruled by the nodes of the Moon, at the end; for each pair of figures, I put the masculine/active/direct/waxing/rising figure first and the feminine/passive/retrograde/waning/setting figure second (e.g. Populus followed by Via followed by Albus followed by Coniunctio…).
  • Zodiacal order, where each geomantic figure is ordered by its corresponding zodiac sign.  This is complicated by there being different zodiacal attributions to the figures, but I tend to stick with Gerard of Cremona’s system (as presented in his “On Astronomical Geomancy”), but I know other geomancers use Agrippa’s system (such as John Michael Greer).  This is further complicated when several figures are assigned to the same sign; some authors (like Gerard of Cremona) simply set them next to each other without care for order, while others (like JMG) place them at the end.
  • Emblematic order, where each figure is ordered by its placement in a particular geomantic emblem.  Which of the 256 emblems you pick, however, depends on a particular purpose and other factors.

Personally speaking, I use either the binary ordering or Chaldaean planetary ordering, when I care to order them at all.  Do you guys care about imposing an order on the geomantic figures, or do you care?  Does the notion of a list versus a set of geomantic figures matter in your work?