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!

On the Geomantic Parts of Fortune and Spirit

Whether it’s Tarot, geomancy, runes, or any other kind of art, I consider divination in general to be a process of three basic steps:

  1. Hash out, refine, and formally ask the query.
  2. Perform the divination to manipulate the symbols into a readable format.
  3. Interpret the reading.

In geomancy, that second step is the whole process of developing the four Mothers and the rest of the chart from them.  After the querent and I refine the query sufficiently and settle on the final form of the question to be asked, and once I manipulate my tools (cards, dice, or whatever) to come up with the four Mother figures, I then proceed to draw out the entire geomantic chart with all the relevant information I’d need to start with.  Once that’s done, this is what my scribbling and scratching typically ends up like:

The exact process I follow to arrive at this mess of lines and symbols from which I divine the fates and facts of the world is this:

  1. Draw out the four Mothers, then the Daughters, Nieces, and Court.
  2. Label the terminals for the Via Puncti with the elemental glyphs above the Mothers and Daughters, where possible.
  3. Draw out a simple square house chart, and populate it with the first twelve figures of the Shield Chart.
  4. Count the number of odd points in the House Chart to find the Part of Spirit, and label it (I use a circle with two diagonal lines coming out of the bottom like legs, for which I can’t find a compatible Unicode glyph that looks similar enough, but Chris Brennan suggests using an uppercase Greek letter phi Φ, for which I like using the specific glyph U+233D “APL Functional Symbol Circle Style” ⌽).
  5. Based on the Part of Spirit, label the coordinating house for the Part of Fortune (⊕).
  6. Based on the sum of odd points from calculating the Part of Spirit, add the odd points of the Court to find the odd point sum of the Shield Chart.
  7. Find the difference between the odd point sum of the Shield Chart and 64, double it, and add that to the odd point sum to find the Sum of the Chart.

You can see the different steps I took broken down by the above list fairly clearly as I did them (orange, red, green, yellow, pink, blue, cyan):

Making the Shield and House Charts is nothing special for us at this point, and I’ve discussed the Via Puncti before on my blog.  The Sum of the Chart is also fairly common knowledge, whereby you sum up all the points of the sixteen figures in the Shield Chart and compare it to 96 to determine how fast or slow the situation will resolve; again, it’s something I’ve discussed before.  Still, it might surprise you that I don’t actually calculate it directly, but base it on my calculations of the Part of Spirit (due to the mathematics of geomancy, the method works out to the same result).  Likewise, I don’t calculate the Part of Fortune directly, but also base it on the Part of Spirit.  So what gives?  What are these Parts, how are they calculated, and how are they used in geomancy?

First, let’s go with the more well-known of the two Parts, the Part of Fortune.  How do we find this indication?  From Christopher Cattan’s book The Geomancie (book III, chapter 21):

The question being made, after that we have judged by the houses, figures, angles, companions, aspects, the way of point, and by all the other sorts and manners before said, now resteth it to judge by the Part of Fortune.  The Part of Fortune figures, which afterwards ye must divide into twelve parts, and that which remaineth give unto the figures.  As if there rest two ye must give into unto the second figure, if there do remain four to the fourth figure, if there be six to the sixth figure, if there be eight to the eighth figure, if there be ten to the tenth figure, if there be twelve to the twelfth figure.  As by example, if the figure be of 72 points, or 84 or 96 or 108 points, then the part of fortune shall go into the twelfth.  But if the said points of the figure made, being divided by twelve, there do remain but two, as if there remain seventy and four where there remaineth but two, then (as before we have said) ye must give that unto the second house, and there shall be the Part of Fortune.  The which if the figure and house be good (for both the one and the other must be looked upon) you shall judge good, and if it be evil ye shall also judge evil; and so likewise shall ye do of all the other figures.  But if the figure be good, and the house ill, or contrary, the house good and the figure ill, you shall judge the said Part of Fortune to be mean.  And, to end ye may the more easier know the place where the figure falleth, which is called the Part of Fortune, ye shall mark it with this mark, 🌞, and thereafter ye shall judge all the question by the example that followeth. …

Many do use another manner to find Part of Fortune, in taking all the points as well of the twelve houses as the two Witnesses, and the Judge, which they do part by twelve (as is aforesaid) but because I have found no truth therein I will speak no more thereof.

If the mark Cattan proposes shows up as an embarrassingly incongruous sun emoji (like it does for me), then that’s just how it appears on your browser.  I’m using the Unicode character U+1F31E “Sun with Face” glyph as the closest approximation without overlapping with the usual glyph for the Sun (☉) for the symbol from the original text (fourth line, first character):

From Robert Fludd’s Fasciculus Geomanticus (book II, chapter 2):

Of the discovery of the part of fortune, and its placement in schemata.

Now the part of fortune ⊕ is to be discussed.  The part of fortune is of great importance in the view of the Geomancers just as in the view of the Astrologers, and is of great consideration: for in their view the sign of ⊕ and the steps to discover the Hyleg are chiefly considered, and through them the house, into which [the part of fortune] falls into as a result of the projection, truly seizes great life and energy by itself.  …

This part of fortune is to be considered with the utmost exactness, for if it falls into a good house and figure, it is of no small weight for bringing about judgment; if truly in an evil [house and figure], it brings about no meager impediment to judging [the schema].

Fludd then goes on to give other methods of calculating similar things “if the above method is seen to be obscure”, but the phrase “Part of Fortune” doesn’t appear, and he mostly focuses on ways of constructing entirely new charts for the purpose of a clearer judgment.

Lastly, the description of the Part of Fortune from John Michael Greer in his Art and Practice of Geomancy (chapter 6) on the Part of Fortune:

… The Part of Fortune, as the name implies, indicates a house from which the querent can expect good fortune to come in the situation.  In financial divinations it usually refers to a source of ready cash.

What about the Part of Spirit?  To start with, calling it that is my own innovation.  In the extant geomantic literature, it’s more commonly called the Index.  JMG discusses it since it appears in Fludd and Cattan, and though I’m unsure if it appears any earlier, Cattan is the one who (as far as I’m aware) introduced it (book III, chapter 18) by calling it one of the ways to find “the point of instruction”:

Another rule [to know for what intent a chart was made for] is to take all the uneven points of all the twelve figures, and give one to the first, one to the second, one to the third, and so consequently unto all the others, until that all the points be bestowed, and then if the last point remain on the first house, it signifieth thereby that the person hath desired to have that figured be made upon some of the demands which be of the first house; if it rest upon the second, it signifieth that the question or demand of the movable goods, or other things contained in the second house; and so shall you judge of the other houses where the point doth stay.  And if it do happen that the point of the intent do stay in the house of the thing demanded, or in the fifth, ye must judge according to the significations that the Judge doth show unto you; and when ye will judge by the same Judge, you must also take the uneven points of the Witness and the Judge, and bestow them amongst them; but that rule which is only by the 12 houses, is the better, more sure and certain. …

Fludd basically says the same thing (book II, chapter 3) and even with the same name in the chapter header (“De punctis instructionis…”), so I won’t translate it here.  As for JMG, he calls it the method the “projection of points”  and the resulting figure the “Index” (chapter 6):

… This can ferret out hidden factors in the chart.  Projection of points is done by counting up the number of single points in the first twelve figures of the chart, leaving the double points uncounted.  Take the total number of single points and subtract 12; if the result is more than 12, subtract 12 again, and repeat until you have a number less than 12.  If the final number is 0, this stands for the twelfth house.

The house identified by the projection of points is called the Index, and represents the hidden factor at work in the situation. …

Okay, enough reciting from resources.  Based on all the above, the methodology for finding the Part of Fortune goes like this:

  1. Add up the number of all points in the twelve houses of the House Chart.
  2. Divide by twelve.
  3. The remainder points to the house of the Part of Fortune.  If the remainder is 0, then it points to the twelfth house.

The Part of Spirit’s method is nearly identical, except instead of counting all the points, we count just the single points.  For example, given the figure Acquisitio, if we’re counting all the points in it, we have six points, but if we’re just counting single points, then we only have two.  Thus, if (for either sum) we get 88, we divide that by 12.  That gets us 7.333…, so our remainder is 4 because 12 × (7.333… – 7) = 4; phrased another way, 88 ÷ 12 = 7 + 4/12.  Thus, we look at the fourth house for the given Part for which we’re doing a calculation.

Before continuing on with how we use these indications in geomancy, it’s probably best to talk about what a Part even is.  The Parts (also sometimes called Arabic Parts or Lots) are an old doctrine in astrology, dating back to at least the time of Ptolemy’s Tetrabiblos and seen in both Arabic and European astrological treatises since.  At least 97 were in use in the ninth century according to the Arabic astrologer Albumassar, over a hundred listed by the Italian astrologer Bonatti in his works, and more were developed since then, even in our modern era incorporating the outer planets past Saturn.   The Parts are constructed points in a horoscope based on the sums and differences of other observable points (e.g. Ascendant or Midheaven) or physical objects (e.g. planets or luminaries).  In essence, a Part is a mathematical harmonic between different astrological notes that describes certain in-depth areas in a querent’s life or situation that could, in theory, be sussed out by looking at the planets and their aspects alone, but are more explicitly specified by their corresponding Part.

For instance, if we’re looking at indications of someone’s mother, we could look at the ruler of the fourth house in a chart, or we could look at the Part of the Mother, which is calculated as follows:

Mother = Asc + Moon – Saturn

In other words, we start from the Ascendant, add the ecliptic longitude (the position in the Zodiac) of the Moon, then subtract the ecliptic longitude of Saturn.  Thus, in a horoscope where we have the Ascendant at 25° Scorpio, the Moon at 19° Gemini, and Saturn at 3° Taurus, then our calculation would look like this:

(25° Sco) + (19° Gem) – (3° Tau)
205° + 79° – 33°
251°
(11° Cap)

With those points as above, we end up with 251° on the ecliptic, which in zodiacal notation is 11° Capricorn, which is the degree of the Part of the Mother.  This is strictly a mathematical point, much like midpoints are in modern astrology, but used specifically to determine the presence, state, and effects of one’s mother (or all mothers) in a horoscope, and can then be interpreted like any other planet in the horoscope, except that they only receive aspects instead of making them.

While the technique isn’t as popular as it once was, even today many modern astrologers take note of the Part of Fortune.  From Bonatti’s Liber astronomiae (translated by Robert Zoller in The Arabic Parts in Astrology):

This part signifies the life, the body, and also its soul, its strength, fortune, substance, and profit, i.e. wealth and poverty, gold and silver, heaviness or lightness of things bought in the marketplace, praise and good reputation, and honors and recognition, good and evil, present and future, hidden and manifest, and it has signification over everything.  It serves more for rich men and magnates than for others.  Nevertheless, it signifies for every man according to the condition of each of those things.  And if this part and the luminaries are well disposed in nativities or revolutions, it will be notably good.  This part is called the part of the Moon or the ascendant of the Moon, and it signifies good fortune.

The Part of Fortune is a weird part, because it actually has two formulas to calculate it, only one of which is used depending on whether the horoscope is that of a day chart (Sun above the horizon) or a night chart (Sun below the horizon):

Day Fortune: Ascendant + Moon – Sun
Night Fortune: Ascendant + Sun – Moon

Later in Liber astronomiae, Bonatti describes the Part of Spirit, which he also calls the Part of the Sun or the Part of Things to Come, as follows:

The pars futurorum signifies the soul and the body after the pars fortunae and the quality of these, and faith, prophecy, religion, and the culture of God and secrets, cogitations, intentions, hidden things and everything which is absent, and courtesy and liberality, praise, good reputation, heat, and cold. …

In other words, if the Part of Fortune describes the material well-being (or lack thereof) of a horoscope, then the Part of Spirit describes the spiritual well-being; just as the Part of Fortune describes our connections to the world outside us, the Part of Spirit describes the connections of the world inside us.  Fittingly enough, the calculation for the Part of Spirit is the reverse of the Part of Fortune: while the Part of Spirit also uses two formulas, one for day and one for night, the formulas themselves are switched from the Part of Fortune:

Day Spirit: Ascendant + Sun – Moon
Night Spirit: Ascendant + Moon – Sun

Thus, the Part of Fortune and Part of Spirit are intimately connected by how they’re calculated; if you know the location of one, you know the location of the other.

Bringing the notion of the Part of Fortune into geomancy from astrology necessitated an obvious conceptual change in how it’s calculated; without degrees or the ability for certain things to fall among them, it would normally have been impossible to calculate any Part.  However, Cattan either invented or learned a way to find an equally-significant sign in geomancy by adapting the methods available to us in geomancy by counting the points and divvying the sum of the House Chart among the houses.  What none of the older geomancers seem to have noticed is that there’s an intimate relationship between the Part of Fortune and the Index in geomancy: if you know the location of one, you know the location of the other.

First, note that the Part of Fortune and the Index can only fall in even-numbered houses (e.g. house II, house IV, house VI, etc.) due to the mathematical intricacies of geomancy; this is true for similar reasons and with similar logic for why the Judge of a geomantic chart must always be an even figure.  (Why Cattan makes this explicit for the Part of Fortune but suggests wrongly that the Index can be in odd houses is a mystery to me; perhaps he simply didn’t anticipate that a calculation based on odd points could result in only even numbers.)  Thus, by performing the calculations of the Part of Fortune and Index, we can get only one of six numerical results: 2, 4, 6, 8, 10, and 0 (with 0 signifying that the sum in the calculation was evenly divisible by 12, and thus indicates the twelfth house).

After many charts of calculating the Part of Fortune and Index separately, I noticed a pattern emerging: the sums of the two separate calculations for the Part of Fortune and Index always add up to 12 (2 + 10, 4 + 8, 6 + 6, 8 + 4, or 10 + 2) or 24 (12 + 12).  Thus, if the Part of Fortune were in the eighth house, then because 12 – 8 = 4, I knew immediately that the Index would be in the fourth house; if the Index were in the sixth house, then the Part of Fortune would also need to be in the sixth house; if either indication was in the twelfth house, so would the other indication.  Again, if you know the location of one, you know the location of the other.

The mathematics behind this relationship can be described like this: if there are four rows in each figure and we’re looking at a collection of twelve figures, then there are 4 × 12 = 48 total rows.  Each row must be odd or even, and the number of odd rows plus the number of even rows must equal 48.  Plus, we know that since the houses of the Part of Fortune and Part of Spirit must both add up to 12 or 24, both of which are evenly divisible by 12, then we know that the sum of all the odd points plus all the points total must also be evenly divisible by 12.  We can check this mathematically as follows.  First, in mathematical notation, let us use the % sign to represent the modulo function, which is “the remainder after dividing by a number”.  Thus,

x = number of odd rows in the House Chart
x = number of points in the odd rows of the House Chart
x % 12 = remainder of x divided by 12 = Part of Spirit

y = number of even rows in the House Chart
y + x = 48
y = 48 – x

2y = number of points in the even rows of the House Chart
2y + x = number of all points in the House Chart
2 × (48 – x) + x
96 – 2x + x
96 – x
(96 – x) % 12 = Part of Fortune

((2y + x) + x) % 12
(96 – 2x + x + x) % 12
96 % 12
0
Q.E.D.

It was this interesting relationship between these two indications that reminded me of the relationship between the astrological Parts of Fortune and Spirit, and thus what led me to start calling the Index the Part of Spirit and reanalyzing it in that light.  Even though there’s a huge difference between how the astrologers calculate these two Parts in astrology versus how we would in geomancy and where they might be found in their separate House Charts, I find that the relationship between them is identical and, for that purpose, hugely useful in geomantic interpretation.

To briefly describe my own personal view of these Parts based on all the foregoing, the geomantic Part of Fortune indicates the source, manner, and condition of the material life of the querent: bodily health, material wealth, worldly means, and so forth.  Likewise, the geomantic Part of Spirit indicates the same but for the spiritual life of the querent: mental and spiritual well-being, divine gifts, aid from spirits or gods, and so on.  I also read notions of resources and capabilities for the querent (to answer “what can I count on to accomplish it?”) in the Part of Fortune and notions of fate and destiny of the querent (“what should I be focusing on or having faith in?”) into the Part of Spirit.

Going beyond the basic interpretation of the Parts themselves, I’ve also found a trend in charts when the two Parts are both in the sixth house or both in the twelfth house:

  • If the Part of Fortune and Part of Spirit are both in house VI, then the matter is completely in the hands of the querent.  The querent has the ultimate say and ability to determine how the situation will proceed, and can change the reality of it as they need to depending on the course of action they take.  Their actions or lack thereof will be the crucial determiner in whether and how the situation will proceed.
  • If the Part of Fortune and Part of Spirit are both in house XII, then the matter is completely out of the querent’s hands.  All the querent can do in the situation is react accordingly and adjust their conceptions and perceptions of the situation, because the reality of the situation will proceed without their input regardless of their attempts.  No matter what the querent might attempt, the situation will continue unfolding as it will.

Also, as one other use, I often use the Part of Spirit in readings about magical, occult, or divine ritual for the sake of figuring out what particular courses of action might be best, or determining what path one ought to take, whether in a specific ritual or in a general direction.  It’s a small extra thing, but for a practicing magician like myself who consults with and is consulted by other magicians, it’s a useful thing to know.  I touched on this very briefly in my old post on geomancy and magic, but now the reasoning behind it all becomes clear.

All that said, remember that the Parts can only fall in even-numbered houses.  In a sense, this is similar to the idea that figures that are even can be considered objective because only even figures can be Judges (as I wrote at length before).  In this case, the even-numbered houses deal with, in order: material goods, land and family, health and servants, death and spirits, work and office, mystery and restriction.  We exclude the odd-numbered houses, which deal with: the querent themselves, communication, creation/procreation/recreation, relationships and rivalries, religion and faith, friendships and patronage.  There’s a similar “inherent to my personal life and relationships” versus “external to my personal life and relationships” difference between the even and odd houses as there is between the objective versus subjective qualities between the even and odd figures.  It is because these things are more external to us that they can be things pointed to help us or focus on, because they’re things that we’re not necessarily in full control or knowledge of.

As a side note, I only read the Parts in a radical (unrotated) chart.  When the chart is rotated for a third-party reading, I don’t bother looking at or interpreting the Parts of Fortune and Spirit, because they’re house-based calculations and not figure-based, so they don’t get rotated with the chart and (to my mind) have no importance or meaning in such a rotated chart.  I find that the Parts work best (if at all) when applied to the querent themselves in a situation, and I haven’t found it useful to rotate the Parts with the rest of the chart for a third party.

Similarly, I don’t swap my calculations of the Parts of Fortune and Spirit around based on whether it’s daytime or nighttime, because the notion of a diurnal or nocturnal geomantic chart doesn’t make sense; after all, a solar figure might never even appear in a given chart, or it might appear both above and below the horizon in a geomantic House Chart.  Instead, it makes more sense for the Part of Spirit to only rely on odd points (the points that represent active elements, excised and above the world of passive matter) and the Part of Fortune to rely on both odd and even points (the co-mingling of active Spirit and passive Matter that results in the world around us).

Further, although there are over a hundred possible Arabic Parts (depending on tradition, era, and author you’re looking at), I’m disinclined to say that there are more than these two Parts in geomancy.  After all, the logic for the Parts in astrology is easily extensible, but in geomancy we’re far more limited based on the techniques and tools that we use, but at the same time, we have other techniques that can fill in just as easily (such as adding the figures of two houses together, the triads in the Shield Chart, and so forth).  That we call them “Parts” in geomancy is more due to conceptual parallel in what they mean more than how they’re calculated than anything else.

The only other way I can think of to extend the technique of geomantic Parts would be to calculate a new Part based on tallying only the even points in a House Chart and taking the remainder after dividing by 12, which could be worth exploring, but I’m unsure what it might indicate; perhaps using my own tripartite view of the world, if the Part of Spirit (odd points only) indicates the influence of the spiritual Cosmos and the Part of Fortune (odd and even points) indicates the influence of the humane World, then this third unnamed Part (even points only) might indicate the influence of the material Universe.  Who knows?  It might show something of good use in divination, if a pattern can be detected.

Ah, and one final thing, just to finish off the intro to the post regarding the Sum of the Chart.  Instead of tallying up all the individual points of the 16 figures in the Shield Chart, I take a shortcut method: find the odd sum of the chart (odd sum of the House Chart, already calculated for the Part of Spirit, plus the number of odd rows in the four Court figures), find the difference between that and 64, double it, and add it to the odd sum to come up with the total Sum of the Chart.  The reason why this works is much like some of the logic in why the Parts of Fortune and Spirit have to add up to 12 or 24: because each figure has four rows and there are 16 figures, then there are 4 × 16 = 64 total rows of points in the Shield Chart.  Since every row must be even or odd, the number of odd rows added to the number of even rows must add to 64.  Since it’s easiest to find the number of odd rows in the chart after we calculate the Part of Spirit (we just need to take into account four more figures), once we have that number we just subtract it from 64 to get the number of even rows.  Remembering that an even row has two points in it, we double that to get the number of points in the even rows, add to it the number of odd rows (which have only one point in each), and voilà, the Sum of the Chart is yours.

More Thoughts on Shield Chart Company

Last time, I posted my collected thoughts on the rule of company in interpreting geomantic charts.  The rule, as taught nowadays, seems to have originated with the French geomancer Christopher Cattan, but after a bit of discussion with a student, seems to have pointed more towards something like the rule of triads like what Robert Fludd used in his interpretation of the Shield Chart rather than an extra way to get more significators out of the House Chart in case the significators themselves don’t perfect, like what John Michael Greer proposes in his Art and Practice of Geomancy.  I offered my thoughts there on how we might apply those same rules of company (company simple, company demi-simple, company compound, and company capitular) to the parents in a given triad, but I think we could offer more variations based on what we know of the figures, as well.

First, let’s talk about company capitular.  This rule has bugged me in the past, where we say that two figures are in company if they share the same Fire line (so Albus and Populus would be in company, but not Albus and Puer).  Why don’t we care about the other lines?  When it comes to company capitular, much like the case with the Via Puncti being limited in the literature to just the Fire line, we can also expand this rule a bit to focus on the similarity of the figures based on which of their lines are in agreement.  Using the above framework, I would normally say that c.  However, if we were to go to a more elemental way of looking at the figures, we can then rename and refine “company capitular” into “elemental company” and offer a new set of analytical rules:

  • Elemental company can be made multiple ways at once, and can be seen as a separate system beyond the methods of company simple, demi-simple, and compound.
  • A shared active line indicates an overwhelming desire or power in the method indicated by the elemental line.
  • A shared passive line indicates a complete apathy or powerlessness in the method indicated by the elemental line.
  • Company by Fire (same Fire line) shows that both parents want the same thing out of the situation.
  • Company by Air (same Air line) shows that both parents are thinking and saying the same things about the situation.
  • Company by Water (same Water line) shows that both parents feel the same way about the situation.
  • Company by Earth (same Earth line) shows that both parents have the same material means and physical basis to attain the outcome.

So, let’s say we have a First Triad (describing the nature and condition of the querent) where we have Coniunctio and Rubeus as the parents; the resulting child is Albus.  Thus, we can see that the parents of this triad are in passive company by Fire and Earth, in active company by Air, and not in company by Water.  While we know that the overall condition of the querent is placid and calm and not very active (Albus), we can also say that this is because they’re only constantly thinking about something intently (active company by Air) without having much to act (passive company by Fire) nor having much to act upon (passive company by Earth).  Through the querent’s reflection and mulling things over, they lose their intense and active feelings on the matter and let it go (not in company by Water).

That said, I suppose that this particular example isn’t particularly helpful, as it’s more a description of how the figures are interacting based on their elemental composition rather than an interaction between people or whether there’s support involved for the querent or other people involved in a given matter.  We know that we have passive company by Fire and Earth and active company by Air, so if we were interpreting this as a normal rule of company, we could say that there’s lots of concerted talk with others and lots of talking to people, but not much else going on, and that talk isn’t helpful when it comes to communicating feelings or helping sympathize or empathize with others, leading to solitude and loneliness on the parts of individual people.

Maybe elemental company isn’t the best approach.  However, there’s another way we could expand on the rule of company when implemented in the triads, and that’s based on the rule of company compound, where two figures are in company if they’re reverses of each other (e.g. Albus and Rubeus, or Caput Draconis and Cauda Draconis).  With company compound, the parent and their allies 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 help each other out where they themselves lack the power they get from the other.  The thing is, however, that the reversion of a figure is essentially a mathematical transformation of a figure, not elemental or otherwise occult, and there are other mathematical transformations we could use instead to obtain other forms of company.

Although I haven’t discussed it explicitly on my blog much, I have briefly gone over the mathematical transformations of the figures in an earlier post, and I’ve also explicitly stated what the given transformation is of each figure in the relevant posts in my De Geomanteia series.  For our purposes here, there are three types of mathematical transformations of the figures:

  • Inversion: replacing all the single dots with double dots and vice versa (e.g. Puer inverted becomes Albus).  Everything a figure is not, but on an external level.
  • Reversion: rotating a figure upside down (e.g. Puer reverted becomes Puella).  The same qualities of a figure taken to its opposite, internal extreme.
  • Conversion: inversion with reversion (e.g. Puer converted becomes Rubeus).  The same qualities of a figure expressed in a similar, contraparallel manner.

So, if we were to make separate rules of company for these transformations, we might end up with four types of company, were we to keep company simple around as well.  Company compound would be renamed company reverse, and we’d add in “company inverse” and “company converse” into the mix as well, for a total of four “mathematical company” methods:

  • Company simple: both parents are the same figure (e.g. Albus and Albus).  The significator and their allies are completely in line with each other, from approach to energy, and are identical in all regards.  Complete harmony and support.
  • Company inverse: the parents are inverses of each other (e.g. Albus and Puer).  The significator and their allies 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.
  • Company reverse: the parents are reverses of each other (e.g. Albus and Rubeus).  The significator and their allies 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.
  • Company converse: the parents are converses of each other (e.g. Albus and Puella).  The significator and their allies 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.

Interestingly, because these are mathematical operations performed on the figures, if we know what the operation is, we nearly always already know what the child will be if we know the parents and type of company they’re in.  For instance, we know that when two figures are added to each other, if those figures are inversions, the result will always be Via (e.g. Populus and Via, Albus and Puer, Laetitia and Caput Draconis).  Likewise, if two figures are in company simple, we’re adding the same figure to itself, so the result will always be Populus.  However, the other types of company give us a bit more interesting stuff to chew on:

  • Company reverse
    • Cannot be formed if parents are both Via, both Populus, both Coniunctio, or both Carcer.  These figures are reversions of themselves, the so-called “axial” figures.  In these cases, we have company simple.
    • Cannot be formed if parents are Fortuna Major and Fortuna Minor (or vice versa), or Acquisitio and Amissio.  These figures are inversions of themselves, and so we have company inverse.
    • Child will be Carcer if parents are Laetitia and Tristitia, or Caput Draconis or Cauda Draconis.
    • Child will be Coniunctio if parents are Albus and Rubeus, or Puer and Puella.
  • Company converse
    • Cannot be formed if parents are Populus and Via, or Carcer and Coniunctio.  The axial figures have a converse that is their inverse, and so we have company inverse.
    • Cannot be formed if parents are both Fortuna Maior, both Fortuna Minor, both Acquisitio, or both Amissio.  These figures are converses of themselves, and so we have company simple.
    • Child will be Carcer if parents are Laetitia and Cauda Draconis, or Tristitia and Caput Draconis.
    • Child will be Coniunctio if parents are both Albus and Puella, or Rubeus and Puer.

Note that, in all cases where we use these company rules for parents in a triad, we always have a child that will be an axial figure: always Populus if company simple, always Via if company inverse, and either Carcer or Coniunctio if company reverse or company converse.  Thus, if we see any child figure in the Shield Chart as an axial figure, we know immediately that its parents will be in company.  Further, based on this child figure, we could see at a glance whether a triad is referring to a single person developing over time with the help or assistance of others (if Via or Carcer), or whether the triad is referring to multiple people interacting and dealing amongst themselves (if Populus or Coniunctio); additionally, we can see whether there is progress and change involved (if Via or Coniunctio) or whether things stagnate and become fixed (if Populus or Carcer).  However, this is a very naïve way of reading a triad, and may not always hold up depending on the specific triad being interpreted as well as the query and intuition of the diviner.

As an example, let’s consider a First Triad where the First Mother is Albus.  Again, we’re considering what the condition and overall state of the querent is, so let’s see what the four possibilities of company would be and their resulting triads:

  • Company simple (Second Mother Albus, First Niece Populus):  Not much to speak of, really.  As in all cases where the child is Populus, what has been is what will be.  However, the querent is likely not alone and has at least one other friend who shares their same state of mind and condition, and are coming together in harmony and unison to help each other out or facilitate their actions together.
  • Company inverse (Second Mother Puer, First Niece Via):  On its own, we could say that the state of the querent will be turned completely on its head, with all this passive contemplation turning into daring, heedless action.  If the chart or intuition of the diviner suggests that the querent is with someone else, this is someone who’s constantly playing devil’s advocate and goading the querent onto radical change, and together they complete and fulfill each other in many ways.
  • Company reverse (Second Mother Rubeus, First Niece Coniunctio):  Fun times, except ew.  This is a weird combination of people, and I’d hardly call them “allies” in any sense; they’re both arguing with each other to the point of talking past each other, yet in their harsh and loud words, they eventually come to a concordance and progress together.  Strange bedfellows, indeed.
  • Company converse (Second Mother Puella, First Niece Carcer): This is probably the most pleasing of all companies possible, as it provides the querent with someone sufficiently different yet operating on the same principles to reinforce the condition and state of the querent.  In this case, this would be good to solidify the nature of the querent and give them some stability, but with the risk of codependency and a potential for getting locked into their current state without trying to actively change things.

All these rules of company so far discussed are based on something structural about the figures, either the elemental structure in the first set (originally based on an expansion of company capitular) or the mathematical structure in the second set (expanding off company compound).  What about company demi-simple?  In that rule, both figures in company are ruled by the same planet, and indicates that the significator and their allies are different, but share enough characteristics for them to complement each other and understand each other enough to accomplish the same thing.  If we use a more occult basis for establishing company, I can think of two more ways to find these out, forming a set of four “magical company” rules:

  • Company simple: both parents are the same figure (e.g. Albus and Albus).  The significator and their allies are completely in line with each other, from approach to energy, and are identical in all regards.  Complete harmony and support.
  • Company zodiacal: both figures are ruled by the same zodiacal sign (e.g. Caput Draconis and Coniunctio).  The significator and their allies are put together by fate and must contend with the same matter together, though not perhaps in the same way.  The zodiacal rulership of the figures can be found in this post.  Not all signs have two figures, so company zodiacal can only be formed when both figures are ruled by the signs Taurus, Gemini, Virgo, and Scorpio, the only signs using Gerard of Cremona’s method that have two figures assigned to them.  Otherwise, using Agrippa’s method, company zodiacal can only be formed when both figures are ruled by the signs Cancer, Leo, and Virgo.
  • Company planetary: both figures are ruled by the same planet (e.g. Albus and Coniunctio).  This would have been company demi-simple in the original rules of company given by Cattan, but here, we can say that the inner drive of the significator and their allies are the same, though their external expression is different but aimed at the same overall goal.
  • Company elementary:  both figures are ruled by the same element (e.g. Albus and Populus).  The outer expression and actions of the figures are similar and get along well enough for the time being, although their inner drives and ultimate goals differ.  The elemental rulership of the figures can be found in this post.

These methods of company do not rely on anything structural in the figures (with the exception of company simple), but rely on the higher meanings of element, planet, and sign attributed to the figures to see how close the figures are to each other and whether they can form enough of a relationship to work together.  Additionally, unlike the other sets of company rules, I think it’s best that two figures can be in company multiple ways at the same time (like Carcer and Tristitia, which would be in company both planetary and elemental) rather than having one form of company “overwrite” the others.  Still, if an overwriting rule were put in place, I think it would go company simple (sameness), then company zodiacal (fated), company planetary (inner drive the same), and company elementary (outer expression the same).  It is a little frustrating that so few figures can enter into company zodiacal with each other, however, but I think that might also be for the best.

So, to recap, we have four sets of rules of company:

  1. Canonical company (given by Cattan): company simple, company demi-simple, company compound, company capitular
  2. Elemental company (based on the elemental structure of the figures): company by Fire, company by Air, company by Water, company by Earth
  3. Mathematical company (based on the mathematical relationships of the figures): company simple, company inverse, company reverse, company converse
  4. Magical company (based on the occult associations of the figures): company simple, company zodiacal, company planetary, company elementary

Of these, I think elemental company can be thrown out as a viable technique, as it doesn’t really tell us anything we didn’t already know, but instead is another way to look at the simple addition of figures, which isn’t a great way of telling whether someone has allies or external support, and strongly differs from the other methods entirely.  Mathematical company and magical company, however, bear much more possibility because they explore actual relationships among the figures, one by means of their structure and one by means of their correspondences.  When applied to the parents in a triad, I think we can definitely use these in addition to or instead of Cattan’s canonical company rules to understand whether a person in a reading has allies and, if so, of what type and means.

All this hasn’t really touched on the role of the child in a triad, however, when it comes to rules of company.  That said, these rules are all about pairs of figures, and with the exception of the Sentence, all figures are parents and can enter into company with at least one other figure.  I think it might be best to leave it at Cattan’s barely-explained way of seeing which parent the child agrees with most, whether it be by ruling planet or element or whatever, and judge a triad much as we might judge the Court with the added clarity of seeing who helps who attain what in a given triad.

Internumeric Relationships by Addition on the Tetractys

It’d be rude and vulgar of me to leave the Tetractys as some simple geometric diagram used for plotting paths or meditations.  I mean, the Tetractys is a meditation tool, yes, but to use it merely for working with the Greek alphabet with in a mathetic framework is to ignore the deeper meaning of the Tetractys.  For the Pythagoreans, especially, the Tetractys was more than a set of ten dots; it was the key to all creation and all cosmos.  There’s no evidence that anybody’s used it to plot paths on like I did, which is probably because this is an innovative use for an already heavily used tool based purely on number.  As we’re all aware by now, the Tetractys is a representation of the Monad, Dyad, Triad, and Tetrad to yield the Decad: 1 + 2 + 3 + 4 = 10.  All these numbers are holy to the Pythagoreans and to Western occultists generally, but there’s so much more to the Tetractys than this.

One of the traditional ways of understanding the mysteries of the Tetractys was to take the different ranks of numbers present and add them together to yield a particular number.  For instance, the Monad plus Tetrad yields the Pentad (1 + 4 = 5), while the Monad, Dyad, and Triad together yield the Hexad (1 + 2 + 3 = 6).  All these numbers have their own meaning, all of which are based ultimately on the Monad and, in succession, the meanings given to the other numbers built upon the Monad.  I’d thought I’d investigate what some of these properties are and see what the Tetractys represents in building the numbers of the Decad together based on these relationships between the ranks of the Tetractys.  Specifically, these relationships are based on the arithmetical operation of addition, the straightforward aggregation of two numbers by combining their distinct magnitudes into a single one.  Other operations exist, but those are for another time.

So, to start off with, we have four basic numbers, starting with the Monad and ending with the Tetrad.  We can say that, with the exception of the Monad, all numbers are just collections of Monads in a particular relationship:

  1. Monad = individuation, undifferentiated, undifferentiatable
  2. Dyad = two Monads in relation
  3. Triad = three Monads in harmony
  4. Tetrad = four Monads in form

Note that some of these can be broken down further into simpler groups.  Without repeating any particular number (such as saying that the Dyad is two Monads or the Tetrad is two Dyads), we end up with two extra identities:

  1. Triad = Monad + Dyad
  2. Tetrad = Monad + Triad

It’s crucially important to note that the Dyad, Triad, and Tetrad are more than just a collection of monads.  Number in the esoteric sense is more than just a magnitude or amount, but also a relationship formed between the individuals in the collection.  The only number in this set that has no relationship is the Monad itself, since it exists as a unity unto itself without anything to relate to.  The Dyad is the first number that has a relationship, but can be said to be relationship itself; without the Dyad, relationship cannot exist.  In a more arithmetic sense that the Pythagoreans preferred, all numbers can be divided into two partially overlapping groups of odd (able to be divided into unequal parts only) and even (able to be divided into two equal and unequal parts).  Four, for instance, is even because it can be split up into groups of 1/3 and 2/2.  Five, however, is odd, because it can be split into 1/4 or 2/3, and neither of those are equal splits.  However, the Monad cannot be split at all into anything, and the Dyad can not be split into unequal parts, so neither the Monad nor Dyad are even nor odd, and are thus not true number, though they are sources of number.

Thus, based on the individuation of the Monad and relation of the Dyad, all other numbers can be made, such as the Triad.  It is because of this that the Triad is considered by the Pythagoreans to be the first true number, since the Monad and Dyad are something rarer and rawer.  All amounts can be formed from the Monad, but it’s the relationship (Dyad) between individual Monads that produce a number.  Thus, as the Triad is the first true number, it is also the first odd number, and the Tetrad is the first even number.

So, based on the six above identities, we can form the rest of the numbers from the Pentad (5) to the Decad (10).  If we omit the identities from above and reduce all things to a collection of Monads, Dyads, Triads, and Tetrads, we end up with two ways to form the Pentad, and one way each to form the Hexad, Heptad, Octad, Ennead, and Decad:

  1. Pentad = (Monad + Tetrad) or (Dyad + Triad)
  2. Hexad = Dyad + Tetrad
  3. Heptad = Triad + Tetrad
  4. Octad = Monad + Triad + Tetrad
  5. Ennead = Dyad + Triad + Tetrad
  6. Decad = Monad + Dyad + Triad + Tetrad

Yes, this is all basic arithmetic that we’ve been able to do since kindergarten.  Of course, it’s always the simplest things that hide some of the more profound secrets.  I won’t go over all the associations and theologies behind the numbers for that; you can get a copy of the Theology of Arithmetic by Iamblichus for cheap (or even, dare I say it, for free), and you can read about what the Pythagoreans thought about the numbers of the Decad way back when.  What I want to point out is, at a high level, what these additions of the numbers mean based on the four concepts of monadic individuation, dyadic relation, triadic harmony, and tetradic form.

Monad
The Monad is an individual, unchanging, static, and stable.  It is the only thing that exists, and thus cannot be differentiated from anything (since there’s nothing to differentiate it from).  While we can say that it contains all opposites and extremities within itself, it’d be more proper to say that no concept of opposition or extremity exists within the Monad.  While the Monad exists, nothing exists within the Monad; it can become all and any qualities, but it itself has no qualities.  It is the source of all nature, but is itself beyond nature.  It cannot be divided since it is a unit, an atom, the core of existence itself.  The Monad cannot move, as there is nothing within which it can move (which would imply something that is Monad and something that is not-Monad).  The Monad has no shape, consisting only of a single point that indicates both all sizes and all angles but without anything else to connect to.

Dyad
The Dyad is relation and difference.  Between two Monads, we now know of two things that can be compared as equals, but as different equals.  The Dyad is representative of differentiation, distinction, opposition, and motion, all of which can be thought of as different types of relation.  The Dyad represents a line defined by two points, but is still without shape; it can possess direction and magnitude, but is as yet without definition.  The Dyad allows for things to exist within, around, and outside of other things, since it creates space between and among other things.  While the Monad is pure potential for creation (and all other things), the Dyad is the act of creation itself, since it distinguishes a Creator from the Creature, or the Acted from the Actor.  The Dyad is space, change, action, and relativity.

Triad
The Triad is harmony and proportion, formed from a combination of individuation and relation.  It is the first odd number, and the first number that can be added from other distinct numbers.  The Triad gives the first shape of something, as three points can define an enclosed space.  The Triad indicates actuality, the Creature made through Creation (Dyad) from the Creator (Monad).  However, it is also indicates harmony, since two distinct and different things are linked to and joined by a third.  With the Triad, there is real existence as opposed to potential existence or becoming existence.  Quoth Iamblichus, “‘this’ belongs to the Monad, ‘either’ to the Dyad, and ‘each’/’every’ to the Triad”.  With Triad, there is time: beginning, middle, end; there is communication: speaker, listener, message; there is work: actor, action, acted upon. However, like the Monad, the Triad is static, since it provides for space and size but not change, since it is construction and creation that brought a static shape to being.

Tetrad
The Tetrad is the root of form, formed from a combination of individuation and harmony.  With three points we can define a two-dimensional shape, but with four we can define a solid three-dimensional object.  Moreover, the Tetrad is dynamic, since it is even; while the Triad measures static quantity, the Tetrad measures dynamic quantity, since it provides for motion and change while the Tetrad does not.  Further, the Tetrad allows for forms present in relationship to each other; while the Triad offers a two-dimensional form, the Tetrad allows for two-dimensional forms next to each other as the Dyad allows for Monads to be next to each other.  With both individuation and harmony, one can choose to be part of a harmony or break away from it, acting either inside or outside a given group, and allows for distinct existence apart from, aggregated with, or in conjunction with others.

Pentad
Alone among the numbers, the Pentad is the only one that can be formed in two distinct ways: from the Monad and Tetrad (a combination of individuation and form) and from the Dyad and Triad (a combination of relation and harmony).  In a way, it’s fitting; between all the numbers of the Decad, the Pentad is the middle of them.  Consider that any two numbers that add up to 10 have 5 as the mean (9 + 1, 8 + 2, 7 + 3, etc.); the Pentad is halfway to the Decad, and itself is vital to life.  It is the combination of pure potential and discrete aggregation (Monad and Tetrad), as well as of relation and harmony (Dyad and Triad); it is the combination of an even and odd number in either case, and considered to unify opposites in a dynamic way that allows for growth and change as opposed to the static way of the Triad.  If we consider the Pentad as the sum of Monad and Tetrad, we obtain a view of eternality and potentiality combined with and suspended among temporality and discretion (the four changeable elements acting under unchanging Spirit); if we consider the Pentad as the sum of Dyad and Triad, we obtain a view of motion and action mixed with and changing stasis and relationship.  In either case, the Pentad is where life and concrete reality itself begins, since in the Pentad there is balance, reciprocity, distribution, and especially of growth.

Hexad
The Hexad is the combination of relation and form, producing a dynamic harmony.  Unlike the Pentad, which is dynamic growth, the Hexad is a balance between things in motion.  The presence of distinct qualities bestowed by the Tetrad in relation of the Dyad allows for various dynamic forces to exist dynamically, moving with and acting, co-acting, or reacting together without destruction.  As the Tetrad represents a body and the Dyad represents motion, the Hexad represents a body in motion and can move in six ways, or three sets of two ways: up/down, left/right, forward/backward.  Seen the other way, as the Tetrad represents qualities and the Dyad represents opposition, the Hexad represents an ordering and balance of opposites.  Further, as two Tetrads, the Hexad represents what we commonly see as “Merkava stones”, two interlocked tetrahedrons that represent a combination of bodies and opposites that together unite to form a whole.  While the Pentad is the number of life, the Hexad is the number of order.

Heptad
The Heptad is the combination of harmony and form, producing foundation.  This is hard to describe in a single word, but within the Heptad there are all things finally present to create everything, yet is short of actively creating everything; all manifest sources are present in the Heptad (seven planets of astrology, seven vowels of Greek speech, etc.), though they are as yet too unmanifest on their own.  As a combination of Triad and Tetrad, the Heptad represents the four elements and three reagents, or the three processes that transform the four elements so as to create all things.  As an odd number that cannot be divided, the Heptad is similar to the Monad in that it provides for potential creation, but unlike the Monad, the Heptad is a collection of seven entities that provide the foundation of all manifest things, while the Monad is an undifferentiatable source from which all manifest and unmanifest things come.  If the Hexad represents order, then the Heptad are the things that are ordered within the cosmos provided for by the Hexad, the meat to fill out the Hexad’s bones.  The Heptad is that which essentially exists; the Heptad is essence.

Octad
The Octad is the first addition that involves three numbers: the Monad, Triad, and Tetrad.  Thus, the Octad combines individuation, harmony, and form.  As the Heptad is the combination of the Triad and Tetrad, we can say that the Octad is that which results from the essences of creation into which they flow.  However, as we saw with the Pentad, we can also say that the Monad and Heptad combine such that the Heptad is mixed in within the Monad, as the seven planets are within the eighth sphere of the fixed stars, as the four elements are within the Quintessence.  However, we can also say that the Octad is the combination of two Tetrads, allowing for mixtures and combinations of that which otherwise could only relate to each other by processes; although Sulfur combines and transforms Air into Fire and vice versa if we use the Tetrad + Triad view, we end up with dry air or cool fire between Air and Fire if we use the Tetrad + Tetrad view.  The Octad represents solution and combination of qualities, a single entity produced from essences or qualities and their interquality transformations.  The Octad is mixture.

Ennead
The Ennead is the combination of relation, harmony, and form.  Based on how we might conceive of this, we can say that the Ennead combines the Tetrad and Pentad, the Triad and Hexad, the Dyad and Heptad, or the Monad and Octad, but at its root it combines the Dyad, Triad, and Tetrad.  At its core, it lacks the Monad and possesses the Dyad, indicating that the Ennead is an active number related to creating but not as creator or creature.  In the Ennead is all creating of manifest things, combining tetradic body, triadic intermediation, and dyadic motion.  In the number nine are all the other numbers brought together, the final single-digit whole number.  As there were nine Muses who lead to all Art and nine Curetes who watched over the infant Zeus, the Ennead brings things to completion and perfection without itself being perfect.  The Ennead is realization.

Decad
At long last, we finally reach the Decad, the combination of the Monad, Dyad, Triad, and Tetrad; of individuation, relation, harmony, and form.  In the Decad are all the basic numbers of the Tetractys, and there are many ways to add to the Decad using the lesser numbers, but at its core it is the number formed from 1, 2, 3, and 4 summed together.  Just as in the Ennead there is the process of realization and completion but without something to realize or complete, the Decad augments this with the Monad, allowing for something to be filled with the Ennead.  The Decad represents a discrete entity (Monad) that is distinct from other things (Dyad) that is stable unto itself (Triad) given physical a body (Tetrad).  Moreover, it is also something that can grow (Pentad) while maintaining itself in an order (Hexad) that combines all ethereal essences (Heptad) and concrete mixtures (Octad) being brought together (Ennead).  Without any other number preceding it, the entity represented by the Decad would be lacking and could not be fully realized.  Whether it is the universe we live in or the individual people we live as, we are all representative of the Decad and the journey it has taken to get here.  The Decad is the Whole.

I think it goes without saying that this Pythagorean analysis of the ten numbers of the Decad can easily be mapped onto the Tree of Life in Jewish kabbalah or Hermetic qabbalah, and indeed, I recall seeing many of these things present in the explanations given in works like Alan Moore’s Promethea series.  It makes sense, too, since Pythagoreanism is one of the fundamental philosophies underlying Western occult thought, deep enough to not clearly be distinguished as Pythagorean but also profound enough to affect everything that’s built upon it.  While numerology has never quite been my strong suit, this little exploration of the basic numbers has considerably helped.

Pythagorean Correspondences to the Tetractys

As many of my readers know, as well as those in Western occulture generally, correspondences are a big thing for us.  Based on our shared philosophical and educational lineages, we like to say that “A is like B”; we understand that the light of the Sun is much like the heat of fire, which itself is like the luster of gold based on certain shared properties.  In recognizing these shared properties, we immediately come to a system of symbols, where one thing can stand in for another, as well as to a system of harmonic relationships, where two things can be used compatibly with each other because they share the same ideas.  On a large scale, we call this system of symbolism one of correspondence, where something corresponds to something else.  This is often used in emanationist frameworks, where these correspondences cross levels of manifestation.  For instance, the Sun being an astrological planet is on a higher level than the element of Fire, which is itself on a higher element than actual fire or gold.  However, we can use any of these things to represent or produce a harmony with the other since they’re all corresponded to each other.

Probably one of the most valuable resources for this comes from the Second Book of Occult Philosophy by Cornelius Agrippa, where Agrippa presents a set of correspondences that link various names of God, planets, choirs of angels, ranks of the blessed, elements, prophets, and the like to each other based on certain shared properties.  Crucially, however, Agrippa organizes this by number.  Thus, he has a Scale of Four (book II, chapter 7) to correspond things that are easily divisible into one of four groups, a Scale of Seven (chapter 10) for things grouped into sevens, a Scale of Ten (chapter 13), and so forth.  Each of these are immensely useful for magicians, since they provide us with symbols and ritual ideas at a glance.  Aleister Crowley’s famous Liber 777 and, more recently, Stephen Skinner’s Complete Magician’s Tables offer these but on a much grander scale, corresponding far more things together on a qabbalistic basis than Agrippa does in his Scale of Ten.

Of course, finding systems of correspondence is an old thing, and even back in classical and antique times do we see the foundations of these systems of correspondence set up and used.  And, well, you can see where I’m taking this, aren’t you?  The Tetractys, that venerable Pythagorean symbol, was seen to contain within itself the foundations of all life and existence in every conceivable form, and not just in a strictly emanationist way.  Each rank of the tetractys, based on whether it related to the Monad, Dyad, Triad, or Tetrad, was associated to something else that formed part of the cosmos.

One good source for this comes from Iamblichus’ Life of Pythagoras, where he gives a good overview of the life of Pythagoras (duh) as well as a number of his teachings (though nowhere in depth as I’d like).  The Taylor translation linked above, however, also contains an extensive collection of other Pythagoreans who followed Pythagoras and wrote down what the Teacher (ostensibly) said, as well as a set of notes where Taylor inspects the things Iamblichus says and expands on them where the original author was annoyingly terse to our modern readers.  Part of this expansion is where Taylor talks about how the Tetractys wasn’t just a number but a graphical mnemonic, if you will, of various things

Monad Dyad Triad Tetrad
Number 1 2 3 4
Doubling Progression 1 2 4 8
Tripling Progression 1 3 9 27
Even Geometry Point Line Polygon Solid
Odd Geometry Point Open curve Closed curve (circle) Cylinder
Element Fire Air Water Earth
Platonic Solid Tetrahedron Octahedron Icosahedron Cube
Growth of Vegetation Seed Length Breadth Depth
Communities Individual Family Town State
Power of Judgment Intellect Science Opinion Sense
Parts of an Animal Rational Irascible Epithymetic Body
Seasons Spring Summer Autumn Winter
Ages of Man Infancy Youth Adulthood Old Age

Well, would you look at that, it’s a table of correspondence along the same path as Agrippa’s Scale of Four.  It’s not quite the same (Agrippa gives Summer, Spring, Winter, and Autumn instead of Pythagoras’ Spring, Summer, Autumn, Winter, and I’m personally in favor of using Agrippa’s associations or a variation thereof, especially considering how Athenians started their year at the summer solstice), and there are a few hard-to-understand terms and progressions, but for the most part it’s definitely something useful in seeing how emanation works in everything.

I mean, sure, the can of Monster energy drink next to me is something that emanated from the Source just as I did, but it has a different body and different contents than I do.  Consider the body of the can, the metallic mostly-cylindrical shape the drink comes in.  The can wasn’t born, so it can’t age in the way a human ages, but consider how soft drink cans are made for a bit.  The cylindrical can was stretched out from a circular cut from a flat sheet of aluminum; from this, we got the tetrad-corresponded cylinder from the triad-corresponded circle.  Of course, this circle itself has depth, since it’s a cutout from an aluminum sheet which is a body; all bodies have three dimensions (length, breadth, and depth), without any one of which it’d only be a two-dimensional shape.  So, whence the circle itself?  The circle itself is a form, not a body, an idea that can interact with others.  Whence the form of a circle?  The form of a circle is made from a curved line traveling around a point.  After all, all circles only need two points for a definition: a center and a boundary.  The curved line demonstrates motion and direction, both of which are relative concepts (in order to move, you need something to move from both in terms of location, speed, orientation, etc.).  The curved line, then, comes from the single point, the Monad of all shapes and forms and bodies.

So why is the tetradic form of a circle a cylinder and not a sphere?  After all, isn’t the sphere the thing most like a circle in the third dimension?  Sorta, yeah, but a sphere is (according to Pythagoras and other Pythagoreans) a perfect body, and there is nothing we can make in the cosmos that is perfect due to the constant actions of Difference, Existence, and Sameness as well as the upheaval and drama in the four elements.  Rather, the tetradic form of a circle is a circle with depth, the most straightforward of which is a stack of circles, forming a cylinder.  It makes sense, though a little counterintuitive.

Between Agrippa and Taylor’s exposition of the correspondences of fourfold things to the Tetractys, a lot of intellectual work has already been cut out for us in studying how the Tetractys can relate to individual things.  Then again, that’s just it; this kind of analysis is good for understanding individual things, and it’s the relationships of those things that are just as important, if not moreso.  In fact, one of the more famous divisions of things is the Quadrivium, literally “four ways”: four types of mathematics used throughout the classical, medieval, and Renaissance worlds.  In this, arithmetic is an understanding of bare number (Monad), followed by music (in the broad sense) as an understanding of relationship and modulation (Dyad), followed by geometry as an understanding of static form (Triad), followed by astronomy which is an understanding of moving bodies (Tetrad).  Just as one can’t study astronomy without a knowledge of geometry, and geometry of music (for the study of proportions and ratios is a type of music in the classical, ideal sense!), and music of arithmetic, the Tetractys itself indicates that the relationships between things are where the real action lies in the cosmos.

After all, wasn’t that the whole point of my developing mathesis, anyway?  To discover relationships more than units?  To understand the changes between the different methods of manifestation rather than the methods themselves?  Something is still missing, and that’s where mathesis becomes mathematic, in our modern sense of numbers and relationships.  After all, if we’re still trying to analyze stuff as individual units, then we’re dealing with things as individual monads.  A Dyad is more than just two monads put next to each other; it is a relationship between the two that makes two monads into a Dyad.  That relationship is often called “music” in Pythagorean literature, but it’s not necessarily the music of instruments or sounds.  Music, in this case, is the means of progression, movement, and patterns.  It is not enough to study sheer quantity in the arithmetic sense, and it is yet too much to study harmony in the geometric sense.  Another type of analysis-and-synthesis is needed for the Dyad.

Elemental Transformations and the Geomantic Figures

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Geomantic Mathematics

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

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

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

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

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

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

Example Geomantic Tableau

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

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

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

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