On an English Alphabet Grammatomancy

The other night, I got an email from a reader with a question.  This sort of thing happens often; in general, I enjoy taking the honest questions from my readers about practice, theory, and everything in between when it comes to the occult, as it often helps them as much as it does me by putting my thoughts in readable order and making me think.  It’s not that common I have to put some questions off, and generally that’s because they involve so much investigation and life-work that it becomes better to take the road to take a proper consultation with me for a really in-depth approach to answering such questions.  However, more often than not, simple one-off questions get prompt answers.  (If you’re interested, dear reader, check out the Contact page.)

Regrettably, this email I got didn’t have a good email address attached to it.  When I tried sending my reply, the email was immediately returned as undeliverable due to a non-existent email address.  It’s unfortunate, especially since this is the first time this has happened.  I have no other way of trying to get in contact with this person besides putting out a call on my Twitter and Facebook pages, so unless this particular reader of mine stalks me on either of those media, I don’t have a way to get back in contact with them.  (Let that be a lesson to everyone, to double-check all your entries when you try to contact someone!)  In that case, perhaps it’s best I just answer the email by making a new post specifically on this topic.  Turning a reader question by email into a post isn’t my usual approach, but between a lack of a means of communication and because the question in question is actually a thought-provoking topic, it’d be good to get the word out all the same.

What this particular reader was asking was about grammatomancy, the divination system I like that uses the letters of the Greek alphabet in a way not unlike Nordic rune divination.  In grammatomancy, each letter of the Greek alphabet is associated with a different oracular statement, and each statement begins with a different Greek letter.  For instance, the letter Gamma (Γ) has the oracle “Γῆ σοι τέλειον καρπὸν ἀποδώσει πόνων”, which translates to “The Earth will give you the ripe fruit of your labors”.  Traditionally, grammatomancy was performed by taking a bowl and filling it with 24 different pebbles or potsherds or other similar type of token, and each token had a different letter engraved on it.  Ask your question, draw out a random token, and look up the associated oracle; bam, there’s your answer.  Personally, I prefer a different approach of using dice, specifically two throws of a 12-sided die; I wrote about my method to use dice in this older post of mine.

What the reader asked was this:

I’m looking for simple instructions on how to set up dice with letters from the English alphabet, not Greek letters or symbols, including how many dice, how the letters are assigned to them, and any other info you may have.  The word “grammatomancy” goes right back to some site that gives the Greek info.

First, if I understand the situation correctly, the word “grammatomancy” started with this website.  The original source of the information I used by Apollonius Sophistes (John Opsopaus) simply calls it the Greek alphabet oracle, even in his more recent book The Oracles of Apollo: Practical Ancient Greek Divination for Today, and I honestly don’t recall the word “grammatomancy” or its Greek form “γραμματομαντεια” being used before its appearance in this 2013 post.  If it was, I apologize for my hubris, and would love to be corrected, but to my knowledge, searching online for the word grammatomancy will likely end you up at something I wrote.  Because of that, and because I’ve only discussed grammatomancy in terms of the Greek alphabet, all the resources available under that word are going to focus on the Greek alphabet.

Now, what about the actual question the reader asked?  Is there a way to use dice to randomly generate English letters?  The short answer is “no”, because of how many letters there are in the English alphabet.

The Greek alphabet as used since ancient times has 24 letters; there were a few extra letters at the start, like digamma and qoppa, but those were disused from an early period and kept around only for numeric and accounting purposes by specialists.  24 is a rather pleasing number, because it can be factored into several different sets of numbers, specifically 2 × 12, 3 × 8, and 4 × 6.  These are all fairly manageable numbers, and can be translated into dice throws quite easily.  For instance, you could use two throws of a 12-sided die (my preferred method), where the first throw determines the first half or second half of the alphabet (odd number = first 12 letters, even number = second 12 letters), and the second throw determines which letter in that set to pick; if I throw a 5 and a 9, for instance, I’ll look at the ninth letter of the first half of the Greek alphabet, which in this case is Iota.  Instead of rolling twice, you could flip a coin to determine heads for the first half of the alphabet and tails for the second half; in effect, you’re using a 2-sided die and a 12-sided die simultaneously.  Alternatively, you could throw a 4-sided die to determine which set of six letters to look at, and the 6-sided die to determine which letter in that set to pick; a 3 on the 4-sided die followed by a 3 on the 6-sided die would get you the third letter of the third set of six, which would be the fifteenth letter, which would be Omikron.  Heck, you could just use a 24-sided die (they exist!) and just associate each letter of the Greek alphabet with each number in order.

The problem with the English alphabet is that it has 26 letters.  Unlike the number 24, 26 cannot be broken down so neatly into smaller pairs of factors; you could only really break it down into 2 × 13.  While there are 13-sided dice and 26-sided dice out there, these are very uncommon specialty items, and probably not what the reader was asking about given how rare they are.  So, what could an English-minded grammatomancer do in this case?  There are several options that present themselves:

  • Don’t bother with dice at all and just use a bag of tokens or a bowl of pebbles.  This is the trivial non-answer, of course, and is not necessarily as convenient as just using plain old poker dice or tabletop RPG dice.
  • Use specially-made English alphabet dice.  They exist, sure, but again, this is a specialist option, and not very useful.
  • Increase the number of options to use from 26 to another number that can be easily factored into smaller numbers.  For instance, if you were to include a “space” letter (comparable to the modern Nordic “wyrd rune”), you get 27 options, which can be broken down into 3 × 9; if you were to include two extra letters (like the Spanish Ll and Ñ), you get 28 = 4 × 7.  However, both of these options aren’t really useful either, because 9-sided and 7-sided dice are only slightly easier to come by than 13-sided dice, which is to say “not very”.  The next greatest number that could be used for a standard set of tabletop roleplaying dice would be 32 = 4 × 8, so a roll of a 4-sided die and an 8-sided die, but this means having to use six extra letters or reinterpreting them as “wild” options that make you throw the dice again until you get a valid letter.  (This is basically what the alphabet dice in the above option does.)
  • Decrease the number of options to use from 26 down to 24.  This may seem like blasphemy (how dare I suggest deleting letters!), but consider that the English alphabet is a modern repurposing of the older Roman alphabet, which originally only had 21 letters and was later increased to 23 during the classical period.  In English use, the letters J and U are essentially “duplications” of the original letters I and V, and it was only up until recently that you’d often find things spelled as “Ierusalem” or “Vnder the sea”.  If you were to fold J into I and V into U, you’d go back down to 24 letters, and then you could use the same options that the Greek alphabet uses.

Personally, if I were pressed to make a choice that forced me to use dice, I’d go with the last option and get rid of J and U at the expense of considering them their own letters, because it seems most convenient that way.  I’d still consider using tokens a better choice than dice for the English alphabet, though.

However, this is only half the answer to what the reader asked about.  Once a method is found for using dice, what about the letters themselves for divination?  When we look at the Greek alphabet, we find historical evidence across the eastern Mediterranean that uses the Greek alphabet as a form of divination, with multiple sets of oracles associated with them, sometimes overlapping and sometimes distinct based on the region.  For the Roman alphabet, however, I don’t know of any such sources.  We have nursery rhymes and mnemonics that associate the letters of the English alphabet to different things, sure, but nothing of the same scale and focus as the Greek alphabet oracles that dot the ancient world.  To that end, I have no resources at my disposal and know of none that exist otherwise that discuss the letters of the English or Latin alphabets as an oracle in a grammatomantic way.

Should someone want to develop a set of oracular statements for each letter of the English alphabet, I would think it a good development, especially if the user of such a system wanted to find a more mystical way of applying the English alphabet in spiritual practices, or reinterpreting it as a “Theban oracle” by using the Theban alphabet cipher for English (which, as an aside, note how it already collapses I/J and U/V, and how W is just a duplication of U/V, technically reducing it down to 23 letters as used since classical Rome).  However, I would find using the Greek alphabet to be more useful from the get-go, not least because there are already sets of oracles ready to go for the Greek letters, but because the Greek alphabet already has associations to numbers, planets, signs, and elements via stoicheia and isopsephia as well as to hundreds of other classical concepts, animals, birds, stones, and procedures according to texts like the Kyranides.  In other words, the Greek alphabet already has information, lore, history, and power in it that the English alphabet basically lacks.  I won’t knock an English system of grammatomancy, but it’d need quite a bit of work, innovation, and invention to get it to a similar usable state that the Greek system presents immediately.

I hope that helps!  May the reader who sent me this question find this answer useful, and may everyone ensure to check their email addresses for correctness and validity before using them in contact forms.

Two new translations from Latin on medieval astrology!

While browsing through my computer for old files for something I was trying to look up, I came across some old translations that had been sitting there, untouched and unloved.  I meant to compile a few more and publish it as another ebook, but I don’t have the original book to translate from anymore (it’s a hard-to-find critical edition from a university library), so so much for that idea.  Instead of just letting them languish and gather electronic bit dust on my hard drive, I decided to polish them up a bit and let them shine on some distant server’s hard drive instead for the whole world to see.

These two translations are from the text Hermes Trismegistus, Astrologia et divinatoria (Corpus Christianorum, Continuatio Medievalis 144C, Brepols: Turnhout, 2001), which is also the very same collection of manuscripts, texts, and other critical editions that gave me the Lectura Geomantiae and the Liber Runarum, medieval texts on geomantic divination and runic magical practice, respectively.  Now joining those two translations, I now present to you the following two:

  • Liber De Accidentibus (“The Book of Accidents”).  This translation consists of a collection of astrological aphorisms and rules about particular astrological arrangements or phenomena and how they may be used in forecasting, as in mundane or horary astrology.
  • De Amicitia vel Inimicitia Planetarum (“On the Amity and Enmity of the Planets”).  This translation describes a simple form of mundane astrology based on the planetary rulers of particular parts of the world and how their motions through the signs ruled by other planets impact or affect those areas of the world.

You can find these pages up under the site menu: Occult→ Liber Divinationis → (pagename), where I’ve also bundled the Liber Runarum page with them under the overall heading Liber Divinationis, or “The Book of Divination”.

I hope you enjoy, and maybe even find them useful in some small way!

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-
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-
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!


Selected entries from the Enchiridion of the Stoic philosopher Epictetus which are on my mind as of late:

7.  Consider when, on a voyage, your ship is anchored; if you go on shore to get water you may along the way amuse yourself with picking up a shellish, or an onion. However, your thoughts and continual attention ought to be bent towards the ship, waiting for the captain to call on board; you must then immediately leave all these things, otherwise you will be thrown into the ship, bound neck and feet like a sheep. So it is with life. If, instead of an onion or a shellfish, you are given a wife or child, that is fine. But if the captain calls, you must run to the ship, leaving them, and regarding none of them. But if you are old, never go far from the ship: lest, when you are called, you should be unable to come in time.

11.  Never say of anything, “I have lost it”; but, “I have returned it.” Is your child dead? It is returned. Is your wife dead? She is returned. Is your estate taken away? Well, and is not that likewise returned? “But he who took it away is a bad man.” What difference is it to you who the giver assigns to take it back? While he gives it to you to possess, take care of it; but don’t view it as your own, just as travelers view a hotel.

14.  If you wish your children, and your wife, and your friends to live for ever, you are stupid; for you wish to be in control of things which you cannot, you wish for things that belong to others to be your own. So likewise, if you wish your servant to be without fault, you are a fool; for you wish vice not to be vice, but something else. But, if you wish to have your desires undisappointed, this is in your own control. Exercise, therefore, what is in your control. He is the master of every other person who is able to confer or remove whatever that person wishes either to have or to avoid. Whoever, then, would be free, let him wish nothing, let him decline nothing, which depends on others else he must necessarily be a slave.

16.  When you see anyone weeping in grief because his son has gone abroad, or is dead, or because he has suffered in his affairs, be careful that the appearance may not misdirect you. Instead, distinguish within your own mind, and be prepared to say, “It’s not the accident that distresses this person., because it doesn’t distress another person; it is the judgment which he makes about it.” As far as words go, however, don’t reduce yourself to his level, and certainly do not moan with him. Do not moan inwardly either.

And a Stoic…well, not quite a prayer, but I use it as one, compiled and rewritten from several sources including Cleanthes and Euripides:

Lead me, o Zeus, and holy Destiny,
T’wherever my post in life’s battle be.
Willing I follow; were it not my will,
Wicked and wretched would I follow still.
Fate guides the willing but drags the unwilling.

Futile though it might be, I bring this up as an exercise to myself and as a reminder to my readers, because I’m going through a bit of a tough time.  I’m not writing this to ply sympathies or condolences, but rather as just an exploration of my own thoughts and feelings, recorded more for myself than anyone else.  Recently, my husband’s and my cat died.  Her name is Isis, and she has always been, and always will be, a Very Good Cat.

My husband grew up at his grandparents’ house, and about…twelve? thirteen? years ago, there was a particular cat that was hunting and haunting the backyard and forest of their house.  They would entice this cat with food, and she’d come up and eat from them, and would even hop into my husband’s lap for pets and brushing.  She must have been a stray, since she obviously knew the touch of humans and had been spayed, but she seemed to adapt quite well to being taken care of, such as it was.  Eventually, after a year or so, on his way home from a party, my husband saw the cat at the back door with a giant bloody gash on her face; apparently she got in a nasty fight and wanted some help.  He asked her if she was ready to be indoors again.  She looked at him, huffed, and strutted right inside, and didn’t go back outside again.  He named her Isis, a large black Maine coon mix with a white tuft of fur on the front of her lower neck; he didn’t know exactly how old she was, but definitely around four years old at that point.  She gave my husband many years of support and emotional connection in the times when he had nobody else but her.

She lived in his grandmother’s house for a good long while, and while I was dating my husband before we married, I would occasionally catch glimpses of her, but she was always so skittish and not at all sociable.  She’d occasionally stare out the front window or prowl around the house, but she was far from a sociable animal.  When my husband and I moved into our current house, we decided to bring her over to live with us; by this point, she was already like 14 years old, and she had feline leukemia virus all her life, though it never bothered her any.  We did this because he wanted her to live with us, sure, but knowing she was getting on in years, we wanted to make sure the last part of her life was comfortable, easy, and peaceful, away from the stress of being at his grandparents’ house.  After the initial acclimation period, Isis changed dramatically towards both him and me; she was an adorable little attention whore, chirped and chatted, started playing with catnip and feather toys for the first time, and couldn’t get enough of sleeping with us in bed.  Even my husband was caught off-guard by how much she had changed, as if she finally got to be a pampered little kitten again, and hand to God did she enjoy it for all it was worth, as did we.  She was adorable in every way, even if she did piss on some of the rugs now and again or drank from our offering glasses on some of the shrines around the house.

Over the past few weeks, I noticed I haven’t had to refill her food bowl with kibble up as much as I thought I should.  I didn’t pay it any mind, but towards the end of the month, my husband and I realized that we haven’t had to replenish it at all.  She really cut back on eating to eating nothing, and we weren’t able to entice her to eat much of fresh tuna or turkey.  She had been lying around the house in places we didn’t often see her.  She didn’t come up to bed with us when it was bedtime.  She was even more lethargic and less playful and chatty than we were accustomed to her being.  It dawned on us; she was getting to the last stages of her life.  That realization was not easy; on a weekend when everything else was going sideways, this was the last thing we wanted to have to face.  Neither my husband nor I got much sleep.  We mostly stayed awake evaluating her condition, trying to get her to eat or drink at least a little, and just pet and brushed her as much as we could in between having our bouts of tears.  She was getting bonier, and her breath was getting to have a new and unpleasant odor.  We took her to the emergency vet (by the time we were able to get anywhere with her, most vets had already closed for the weekend), and they ran some tests on her; we couldn’t get a clear diagnosis, but we did get a prescription for an appetite stimulant.

She still wouldn’t eat more than a nibble of tuna.

Against every fiber in his body, my husband made the decision that it was time.  I made the arrangements to take her back to the emergency vet on my way back home from working ceremony, and…I needed some time in the car alone before I could get face going inside my house.  I wasn’t aware I could even make some of those sounds.

I won’t recount the whole process of her passing.  Suffice it to say that she went quietly and peacefully, bundled in her tortilla blanket, being pet and loved and hugged and brushed.  She went out with a soft purr, knowing and feeling that she was loved.

We found out afterwards that it was the cancer catching up to her in force, and there wouldn’t’ve been much we could’ve done anyway besides just making her passing as easy as possible.  We did what we had to.

I bundled up her dishes, toys, and blankets and put them in a box, placed under the table in our office where she liked to lie down.

I haven’t been around much death in my life.  Bones, rot, mold, and the effects of death, sure; I mean, it’s a natural part of life, if not the most expected, inevitable, and boring part about the entire thing.  We may not know what happens afterward with complete certainty, but we know that it happens to everything that lives.  But as for actual living creatures dying that I’m aware of, that I care for?  It’s different.  Last year, my grandmother passed away, but it was hard to feel too sad about it.  Sure, there was a touch of grief, but I was far happier than anything for her.  Passing away at the age of 96, becoming a great-great-grandmother in her own life, having outlived three of her husbands, having inherited a small fortune from one of them, having traveled the world, having gotten a college education for a woman in a time when that was difficult, living wherever she wanted, enjoying being as sharp and quick as Olenna Tyrell herself, being surrounded by family and comfort all her life, having passed away quietly and peacefully and painlessly…in short?  My Nana Jane won at life.  It’s hard to not celebrate a life and death such as hers.

Isis basically had that same equivalent status for cats when she went, but…it’s so much harder.  I suppose that’s just the nature of it when she’s effectively your baby that you watch out for, care for, nurture, and nourish.  It’s not as difficult now as in the days and hours leading up to her passing, but it’s still not easy, especially when you keep seeing motions out of the corner of your eye you expect to be her, hearing creaks in the floorboards you expect to be her, a pair of black boots sitting in a sunbeam you expect to be her, a ruffle in the blankets on the bed you expect to be her.

I’ve been trying to revisit some of my earlier Stoic learning and practices, before I really committed myself to Neoplatonism and Hermetic philosophies.  Stoicism isn’t a perfect philosophy, but for dealing with much of the bullshit of life, it affords a fantastic worldview and helps to cool the heart and head from the heat of passion and drama.  For myself, I admit that I had Isis in my life a lot less than my husband had her in his, but her death still hurts.  We brought her into our home with the understanding and expectation that she wouldn’t have much longer to live no matter what, and we made the choice to give her an easy, good death with the understanding and expectation that there’s nothing else that could be done no matter what, but…it’s so hard to make the leap from an intellectual understanding of something and the emotional acceptance of it.  Like SMBC’s The Falling Problem, I could go on for hours about the nature of the situation, the diagnosis and prognosis, what the expected social, emotional, and physical effects would be upon me and my husband, and all the rest…but it doesn’t impact the actual experience of the same thing.  Worse, if not outright embarrassingly, all that mental preparation does exceedingly little to absolutely nothing for emotional preparation.

At that point, I suppose it’s less a job for rationalization and more of one for faith.  I can’t even really say “trust”, because trust in…what?  Isis, for all her love and adorability, is still a cat, and as Wittgenstein once wrote, if a lion could speak, we could not understand him.  There’s only so much I can figure out or know about cats and their behavior, so I have to have faith that she knew she was loved and taken care of to the best of our ability until and through her very last heartbeat and breath.  I have to have faith in my spirits that they heard my pleas to watch over her, guide her, accompany her, entertain her, and protect her as she uses up the last of her nine lives to go…wherever it is cats go, and that once she gets her spiritual bearings, that maybe she’ll choose to stick around for us.  I have to have faith in my gods that they can and do support me to point out to me the strength I have and to give me the help I need to get through this as best as I’m able.  I have to have faith that everything really will be alright, even if it doesn’t yet feel like it is.  I have to have faith in myself that I’ll be alright, even if I don’t yet feel like I am.

And even then, faith feels like a bandage over a gushing wound; triage is no substitute for actual healing, and there’s no real regimen to heal this sort of pain besides taking my time.  I suppose that’s inevitable, too.

I could waste words on how to live your own lives better, spending more time with the ones you love, being more forgiving and compassionate, not taking things for granted, blah blah blah.  There’s no point to that here; I’m not in a great state to give advice, and there are more than enough others who have given that same advice in better ways and in more appropriate venues.  This is just…a reflection, I suppose, a processing of grief over loss.  I suppose I could rewrite that in geomantic terms, by saying Tristitia plus Amissio yields…well, Puella: the compassionate Maiden who takes all in under her roof, the pleasant Hostess who heals and nurtures, the all-accepting Lady of Fortune who shares her love for all until it’s time to move on.  Fitting, I suppose.  Puella is often described as fickle, but I find that an uncharitable description; it’s only because that fortune must pass over everyone equally, that all things must have balance, and that everyone gets their fair share of time and love before that time and love passes away.  It may never feel fair, especially in the heat of the moment or in the cold of the withdrawal, but Puella is the fairest and the Fairest force there is.

It’ll take time, but it won’t take too long.  It may be bad, but it’s not the worst thing.  It may hurt, but I’ve had worse.  Even through the tears and the wailing and the jaw-clenching-so-hard-I-might-shatter-my-teeth, there’s still that glimmer of love and appreciation in the muck and the rot and the ash.  I still have, at least a little bit, that happiness we were able to have Isis in our lives for at least a little bit, to love her and be loved by her, and to see things through to the end for her.

Her name is Isis, and she has always been, and always will be, a Very Good Cat.