# The Chaplet of Eight Dragons, or, the Rosary of the Geomancers of Allahabad

More surprises from 20th century French geomancy texts, but this one caught me really by surprise.

As I mentioned the last time I brought up these modern French geomancy texts, there’s an interesting mix of elements that are both plainly familiar and starkly unfamiliar in terms of the usual tradition of Western geomancy.  Obviously, the bulk and foundation of these works are from the usual Western sources from the medieval and Renaissance periods, including Robert Fludd, Henri de Pisis, Christopher Cattan, and others; that much isn’t surprising.  What is surprising is that there’s so much different in them that we don’t see in the modern English geomantic literature, which I assume is due to the introductions of African and Middle Eastern geomantic techniques and concepts that resulted from French imperialist and colonialist activity.  There’s no other European examples of some of the techniques and associations these French texts make, even if it’s not explicit—but sometimes it is, as in this interesting little thing, Le Rosaire des Géomanciens d’Allahabad or “The Rosary of the Geomancers of Allahabad”:

It’s a kind of beaded necklace, in an interesting pattern broken down into eight sections, each of which is composed of one segment of white beads and another of black beads, sometimes of one bead per “slot”, sometimes of two.  For reasons that we’ll discuss soon, another term for this device is Le Chapelet des Huit Dragons, “The Chaplet (or Wreath) of Eight Dragons”.

The moment I laid my eyes upon it, I knew immediately what this was based on.  Years ago, I had come up with the notion of geomantic “superfigures” (which I later called “emblems”), combinations of 16 rows of single or double points that, for every consecutive set of four rows (plus three “hidden” rows at the end duplicating the first three), contain all sixteen geomantic figures.  As a mini-example, consider a series of seven rows: single, double, double, double, double, single, single (·::::··); rows 1 through 4 gives the figure Laetitia, rows 2 through 5 Populus, rows 3 through 6 Tristitia, and rows 4 through 7 Fortuna Maior.  If we extend that, we can come up with a series of single/dual point sequences that contain all sixteen geomantic figures exactly once, which was what I intended to do with my superfigure/emblem idea.  Unfortunately, even after coming up with a (really stupidly complex) way of assigning rulerships and correspondences of the 256 emblems to the base 16 figures, as well as thinking of ways to actually use the damn things, I never really got all that far with them.  (If you’re not familiar with this notion, at least read the first two posts linked above in this paragraph, which explain about the structure and what “hidden” means for those final three lines.)

I had no idea nor any means at the time to find out whether such a concept had ever before arisen in the minds of other geomancers, but given that geomancy is a thousand years old and spread across so much of the world, I would have been surprised if I were truly the first to come up with this idea.  Still, I hadn’t encountered anything of the like in any geomantic text I had come across, nor had I yet—until I came across these French geomantic texts, which finally gave me something to work with.  The two texts I’ve found this in (there may well be more that I just haven’t come across yet) is Francis Warrain’s Physique, métaphysique, mathématique, et symbolique cosmologique de la Géomancie (1968), along with the highly eclectic Joël Jacques’ Les signes secrets de la Terre Géomancie (1991).  Interestingly, however, it does not appear in Robert Ambelain’s La Géomancie arabe (1984), which takes a good chunk of its information from his earlier La Géomancie magique (1940), which suggests a different origin entirely (which isn’t to say that Ambelain’s later text was an accurate or precise representation of Arabic geomancy, because it’s not, but it does have a few other different interesting things in it related to jinn lore).

Warrain’s book includes a lengthy chapter, Cycles des seize figures Géomantiques Emboitées (“Cycles of the Sixteen Nested Geomantic Figures”), which talks about these sorts of things; I’m going through it slowly with the generous help of Google Translate, because my French isn’t exactly up-to-par for casual reading.  However, the following chapter (my translation) talks directly about this interesting rosary, albeit only briefly, as it seems to be more of a note in a later edition of Warrain’s manuscript.  (The edition of his book I have is from 1986, while the esotericist and metaphysician Warrain himself died in 1940, making this a posthumous release of an earlier work.)

Editor’s note: We found in one of the last manuscripts of “La Géomancie”, revised and reworked rather late by Francis Warrain himself, the following additional text, concerning this present problem of “The Nesting of Figures” to which he provides additional documentation. We give below this complete amending text:

Oswald Wirth succeeded in representing the complete sequence of the sixteen Figures on a circle divided into sixteen equal parts, each carrying a single point (“monopoint”) or a double point (“bipoint”), these points being distributed so that starting from any radius and traversing the circumference always in the same direction (“dextrogyre” or “sinistrogyre”) the points located on four consecutive rows give, when one reads them successively four to four, and progressing each time from a point (monopoint or bipoint), the sixteen different Figures of Geomancy, without any of them being repeated.

It is possible, by doing so, and by modifying each time certain successions of points, to obtain 8 different combinations in the grouping of the Figures and to produce materially, using wood beads or glass beads or vegetable seeds, eight different “geomantic rosaries” of 24 grains each, which can close by butting on themselves, or which, abutted to each other and closed in a closed cycle, constitute a long “rosary” made of 128 successive rows of monopoints and bipoints, 64 rows from one and 64 rows from the other, or 192 beads in total.

Other researchers than Oswald Wirth (I learned only late) had also realized this problem in a very complete way, in all its generality.

Mr. Marcel Nicaud, renowned painter, xylographer, and famous fresco artist, attached to the Musées Nationaux Français, and had fully achieved this by a simple and precise mathematical process which was personal and invented by a special technique. (1)

I will present this problem of “Sixteen nested geomantic figures” in general, and as I have personally conceived and solved it. Are there other solutions to discover? I don’t think I can say!

The singular designation of “Rosary of the Eight Dragons” is given to this “Rosary” because, arranged in a circle on a plane, it comprises, placed in the 8 directions of space, the unchanging representation of the Figures of Caput Draconis and of Cauda Draconis separated from each other by the Figure of Via, that is to say the symbolic representation of 8 “Amphisbenes” or mythological tantric two-headed dragons.

(1) It is to Marcel Nicaud, skillful engraver and subtle esotericist, that the illustration of this astonishing masterpiece of arithmology and symbolic esotericism is due, due to the prodigious traditional knowledge of one of our last “Authentic Masters” which is entitled From Natural Architecture, or Report by Petrus Talemarianus on the establishment, according to the principles of Tantrism, Taoism, Pythagorism and Cabal, of a “Golden Rule” used for the Realization of the Laws of Universal Harmony and contributing to the accomplishment of the “Grant Work”. Les Editions Véga, Paris, 1950.  It is from this “summa” that we extracted the “Geomantic Rosary” illustrating the text opposite.

(2) These “rosaries” are commonly used, it seems, in certain and highly secret tantric sects as supports for very complex metaphysical meditations, as well as for geomantic divinatory uses, and also for subtle purposes of “recognition initiation”.

It’s a short section, admittedly, and doesn’t say a lot, but it does give some names of other Western esotericists (especially the famous Oswald Wirth, contemporaneous with Warrain) to look up for future research regarding the geomantic emblems (however they phrased or worded the concept).  The Nicaud book is extant, both in French and in English, but it’s difficult and expensive to find, so it may be some time before I can get my hands on it.  I don’t know which Wirth book Warrain refers to, but I’ll see if I can dig it up.

In Jacques’ book, on the other hand…well, Les signes secrets de la Terre Géomancie is, like I said, a rather eclectic text.  It places a good amount of emphasis on the transnational, transcultural role of geomancy, by which I mean equating Western geomancy with Ifá and I Ching, which isn’t a great approach in my opinion, and it makes a lot of the usual New Age jumps between Hinduism and Buddhism and this and that and the other into one confused mess with questionable numerological and etymological leaps of logic.  Still, eclectic and spastic as it can be, it also has a few good points on this particular topic (capitalization preserved from the original text, my translation):

To return to a more particularly cosmogonic research: to this desire to inscribe the Geomantic Figures in the astral cycles, at least to give them a representation which could represent the Sky, to this desire to unite the mantic arts around the divine Revelation of the origin of things, we will dwell for a moment on what appeared to us as an African contribution to Geomancy, an external contribution to the Mediterranean basin which can be considered as a bridge between the worlds, from one culture to another: the Rosary!

There is a form of representation of the distributing Figures of traditional Geomancy that it is possible to compare the lunar cycles which we spoke above: it is the geomantic Rosary which is said to serve as a sign of recognition to some magicians of the East. This geomantic rosary also bears the names of “Rosary of Allahabad”, “Rosary of the Geomancers of Allahabad” or “Rosary of the Eight Dragons”.  With regard to this designation, it is quite difficult to formulate an exact explanation because no ancient rosary has been found in this city in the north of India.  However, in Arabic, Allahabad means “the City of God” or, in other words, “the Heavenly City”.  It therefore seems somewhat random to us to want to link this name to a current geographic reality; the Agharta concept would be more acceptable…

The total number of beads composing the rosary is 192, making it therefore possible to link the reduction to the name of JERUSALEM (Yod-Resh-Vav-Shin-Lamed-Mim = 93, which is 99 less than 192) which leads us to think that the name “Rosary of the Geomancers of Allahhabad “, since Jerusalem is also a holy city of Islam, is a rather recent name indeed for the rosary.   The rosary is in the form shown in the figure above.  Each DRAGON is red, the color of fire, and made up of three elements: AIR-FIRE-WATER, in this order, i.e of a coupling and an opposition.  The total number of points in each DRAGON is eight.  Eight is the first female cubic number, and eight represents the EARTH (the element absent from the composition of the DRAGON), the element in which has the deepest mysteries. It is a conventional chthonic symbol called number of Pluto (the One who lives under the Earth).  It is a sacred sign among the Japanese, representing multiplicity, shown in the form of an eight-petaled flower, a representation of the Lotus also found in many Western representations of Romanesque art.  Eight is the letter Ḥeth of the Hebrews, the first letter of the word Ḥai (Ḥeth-Yod-Heh) which means LIFE (8 + 1 + 5 = 14 = 5⁷), and is also the first letter of the name of the eighth Sephirah, HOD, or Glory.  Eight is the symbol of infinity, but let us also remember: the eight arms of Vishnu, the eight spokes of the Wheel of the way of Buddhism, the eight paths of the Tao, the eight forms of SHIVA.  “The one whom Christ brings to life is placed under the figure EIGHT”, wrote Clement of Alexandria in the 2nd century; this is not surprising because, if 8 is turned onto its side, it represents infinity, but it also takes the form of a stylized fish, a primitive symbol of Christianity, the religion which by epiphany connects man to eternity.

These eight deployments represent ALL the composition possibilities of the 16 Distributing Figures of Geomancy preceded or followed by the DRAGON. Symbolically, they connect the first two male and female couples (1 + 0) by the 10 lines of each of the cycles to the essence of the Zodiac, the Ouroboros.  10 is Malkuth, the Kingdom.  The dragon bites its tail, which in no way means that the theme at rest, i.e. that in which each Figure is in its place, is among these cycles.  Each now has the keys that will allow him to discover the riches of the rosary and especially why it is also called “rosary”.  Six rows of the DRAGON among eight red points, ten rows for the cycle among sixteen black points: note, however, that in the sacred language of Christians, Hebrews, and Arabs, red has always been associated with FIRE and divine love, but black symbolizes the night and everything that is more malicious than death.

Interestingly, Jacques uses that possibly Arabic but definitely French system of elements and elemental associations to pairs of rows of figures, both in the passage above and throughout his book, but Warrain doesn’t appear to use the system at all.  Warrain, likewise, didn’t mention anything about colors for the beads; although Jacques may have found another text that talks about it, he doesn’t list Wirth or Nicaud in his bibliography, so his use of colors might well be an innovation or extrapolation from the image on his part.

So, with those introductions out of the way, let’s talk about the structure of this device.

• The “Chaplet of Eight Dragons” (hereafter “the Rosary”) is broken down into eight sections, each section an emblem of itself, all starting with the binary structure 011110 (:····:), itself consisting of the figures Caput Draconis, Via, and Cauda Draconis.  The other rows of a given section provide the rest of the emblem.
• The draconic points/beads (for the 011110 segments) are always in another color (e.g. red) compared to the non-draconic beads that provide the rest of one complete emblem (e.g. black).  The draconic segment 011110 of each section is important, as it grounds and anchors the Rosary to eight directions, with the gaps between them consisting of the same number of beads/points but in an irregular way.
• Each section consists of 24 points/beads, eight from the draconic segment and 16 from the non-draconic segment.
• There are sixteen total emblems that start with 011110, but there are only eight sections on the Rosary.  In the depiction above, those eight sections are the following emblems (with their corresponding geomantic figure breakouts), starting with the 011110 segment at the top and proceeding clockwise around the Rosary, with the “hidden” final three lines (which are the first three of the following 011110 segment, which fully completes the emblem) in parentheses:
1. 0111101100101000(011): Caput Draconis, Via, Cauda Draconis, Puer, Puella, Coniunctio, Fortuna Minor, Carcer, Albus, Acquisitio, Amissio, Rubeus, Laetitia (, Populus, Tristitia, Fortuna Maior)
2. 0111101000010110(011): Caput Draconis, Via, Cauda Draconis, Puer, Amissio, Rubeus, Laetitia, Populus, Tristitia, Albus, Acquisitio, Puella, Coniunctio (, Fortuna Minor, Carcer, Fortuna Maior)
3. 0111100001101001(011): Caput Draconis, Via, Cauda Draconis, Fortuna Minor, Laetitia, Populus, Tristitia, Fortuna Maior, Coniunctio, Puer, Amissio, Rubeus, Carcer (, Albus, Acquisitio, Puella)
4. 0111100101101000(011): Caput Draconis, Via, Cauda Draconis, Fortuna Minor, Carcer, Albus, Acquisitio, Puella, Coniunctio, Puer, Amissio, Rubeus, Laetitia (, Populus, Tristitia, Fortuna Maior)
5. 0111101100001010(011): Caput Draconis, Via, Cauda Draconis, Puer, Puella, Coniunctio, Fortuna Minor, Laetitia, Populus, Tristitia, Albus, Acquisitio, Amissio (, Rubeus, Carcer, Fortuna Maior)
6. 0111101000011001(011): Caput Draconis, Via, Cauda Draconis, Puer, Amissio, Rubeus, Laetitia, Populus, Tristitia, Fortuna Maior, Coniunctio, Fortuna Minor, Carcer (, Albus, Acquisitio, Puella)
7. 0111100001001101(011): Caput Draconis, Via, Cauda Draconis, Fortuna Minor, Laetitia, Populus, Tristitia, Albus, Rubeus, Carcer, Fortuna Maior, Coniunctio, Puer (, Amissio, Acquisitio, Puella)
8. 0111100100001101(011): Caput Draconis, Via, Cauda Draconis, Fortuna Minor, Carcer, Albus, Rubeus, Laetitia, Populus, Tristitia, Fortuna Maior, Coniunctio, Puer (, Amissio, Acquisitio, Puella)
• The other eight emblems that start with 011110 are also present on the Rosary; they simply need to be read counterclockwise around the Rosary.  Starting from the 011110 segment at the top and proceeding counterclockwise from there in the depiction above, these get us the following emblems (with their corresponding geomantic figure breakouts), with the “hidden” final three lines in parentheses:
1. 0111101011000010(011): Caput Draconis, Via, Cauda Draconis, Puer, Amissio, Acquisitio, Puella, Coniunctio, Fortuna Minor, Laetitia, Populus, Tristitia, Albus (, Rubeus, Carcer, Fortuna Maior)
2. 0111101011001000(011): Caput Draconis, Via, Cauda Draconis, Puer, Amissio, Acquisitio, Puella, Coniunctio, Fortuna Minor, Carcer, Albus, Rubeus, Laetitia (, Populus, Tristitia, Fortuna Maior)
3. 0111101001100001(011): Caput Draconis, Via, Cauda Draconis, Puer, Amissio, Rubeus, Carcer, Fortuna Maior, Coniunctio, Fortuna Minor, Laetitia, Populus, Tristitia (, Albus, Acquisitio, Puella)
4. 0111100101000011(011): Caput Draconis, Via, Cauda Draconis, Fortuna Minor, Carcer, Albus, Acquisitio, Amissio, Rubeus, Laetitia, Populus, Tristitia, Fortuna Maior (, Coniunctio, Puer, Puella)
5. 0111100001011010(011): Caput Draconis, Via, Cauda Draconis, Fortuna Minor, Laetitia, Populus, Tristitia, Albus, Acquisitio, Puella, Coniunctio, Puer, Amissio (, Rubeus, Carcer, Fortuna Maior)
6. 0111101001011000(011): Caput Draconis, Via, Cauda Draconis, Puer, Amissio, Rubeus, Carcer, Albus, Acquisitio, Puella, Coniunctio, Fortuna Minor, Laetitia (, Populus, Tristitia, Fortuna Maior)
7. 0111100110100001(011): Caput Draconis, Via, Cauda Draconis, Fortuna Minor, Carcer, Fortuna Maior, Coniunctio, Puer, Amissio, Rubeus, Laetitia, Populus, Tristitia (, Albus, Acquisitio, Puella)
8. 0111100001010011(011): Caput Draconis, Via, Cauda Draconis, Fortuna Minor, Laetitia, Populus, Tristitia, Albus, Acquisitio, Amissio, Rubeus, Carcer, Fortuna Maior (, Coniunctio, Puer, Puella)

That’s what we know from looking at this thing at a glance.  The next big thing to figure out would be why this specific order of emblems is used on the Rosary, and for that, we need to pick up on a few other details looking at the general structure of the Rosary:

• Proceeding clockwise around the Rosary from the topmost draconic segment, the emblems used follow 011110 using an odd-odd-even-even-odd-odd-even-even pattern for the first non-draconic row, i.e. the first non-draconic row in the first two segments have a single point each, the next two double, the penultimate two single, and the last two double.
• However, the final non-draconic row of each section has double, double, single, double, double, single, single, single points.  This leads to an interesting asymmetry where if we go clockwise around the Rosary, we have a regular pattern, but no such pattern if we go counterclockwise.
• There’s almost a perfect symmetry with the first full figure from the non-draconic segment clockwise around the Rosary: the first and fifth non-draconic segments start with 1100 (Fortuna Minor), the second and sixth 1000 (Laetitia), the third and seventh 0001 (Tristitia), but the fourth starts with 0101 (Acquisitio) and eighth with 0100 (Rubeus).  However, at least for the first three non-draconic rows, the symmetry is perfect.  Following the initial Caput Draconis-Via-Cauda Draconis breakout of every section, this gives the first and fourth sections (which start with the non-draconic 110) an initial figure breakout of Puer-Puella-Coniunctio; the second and fifth sections (100) Puer-Amissio-Rubeus; the third and sixth sections (000) Fortuna Minor-Laetitia-Populus; and the fourth and eighth sections (010) Fortuna Minor-Carcer-Albus.
• This also means that the first, second, fifth, and sixth sections, because the first non-draconic row has a single point/bead, have Puer as the first breakout figure following the initial Caput Draconis-Via-Cauda Draconis breakout of every section, and that the third, fourth, seventh, and eighth sections all have Fortuna Minor as the first breakout figure.
• There’s much less symmetry counterclockwise, however: the first and fifth non-draconic segments counterclockwise have 1011 and 0001 (Puella and Tristitia), the second and sixth 1011 and 1001 (Puella and Carcer), the third and seventh 1001 and 0110 (Carcer and Coniunctio), and the fourth and eighth have 0101 and 0001 (Acquisitio and Tristitia).  The only symmetry I can find here is that the first non-draconic row of the first and fifth segments are opposed (1 and 0, yielding the figures Puer and Fortuna Minor), the second and sixth aligned (1 and 1, both yielding Puer), the third and seventh opposed (1 and 0, again yielding Puer and Fortuna Minor), and the fourth and eighth aligned (0 and 0, both yielding Fortuna Minor).
• Looking at the two rows on either side of the draconic segments clockwise as “bounds” for each “dragon”, then going clockwise, then the first dragon is bound double-double, the second double-single, the third double-double, the fourth single-double, the fifth double-single, the sixth double-single, the seventh single-double, and the eighth single-single.  This means that there are two double-double bound dragons, one single-single bound dragon, two single-double bound dragons, and three double-single bound dragons.  No real symmetry here to speak of.

All sixteen 011110-starting emblems are represented, eight clockwise and eight counterclockwise; this is why this is a “Chaplet of the Eight Dragons” and not “Chaplet of the Sixteen Dragons”.  However, based on the lack of symmetry going counterclockwise around the Rosary, or at least given how little symmetry there is going counterclockwise compared to there is going clockwise, it seems that there really is directionality involved in the Rosary, and that it seems stronger going clockwise.  This means that the eight emblems read clockwise around the Rosary are probably more important than those going counterclockwise, or that the eight counterclockwise emblems arise as an effect from the positioning of the eight clockwise ones.

What doesn’t rely on directionality, however, is something I hadn’t noticed before when it came to the geomantic emblems: starting from any point of any emblem and taking the first four figures drawn from the seven rows starting from the one chosen, if you take those seven rows as representing four overlapped geomantic figures and then take them as four Mother figures for a geomantic chart, the four Mother figures will be the same as the four Daughter figures.  More concretely, say you randomly choose a point on the Rosary, and you end up at the first row of the segment 1000010.  Breaking that out, you get the four figures Laetitia (1000), Populus (0000), Tristitia (0001), and Albus (0010).  If you use those as Mother figures for a geomantic chart, then the four Daughters that result will also be Laetitia, Populus, Tristitia, and Albus, in that same order.

This is a fascinating property that I hadn’t picked up on before, and yields a special class of geomantic chart I call “repetitive charts”: charts where the four Mothers are the same as the four Daughters and in the same order, and thus the first two Nieces are the same and in the same order as the last two Nieces, the two Witnesses are the same, the Judge is Populus, and the Sentence is always the same figure as the First Mother.  There are 1024 (2¹⁰) such repetitive charts, and there’s a particular way you can construct one based on the sixteen rows of points of the four Mother figures.  First, remember that the sixteen rows that collectively comprise the Mother figures are the same as those that comprise the Daughter figures, just read horizontally across from top to bottom instead of vertically down from right to left:

 Daughter 1 ← Row 13 Row 9 Row 5 Row 1 Daughter 2 ← Row 14 Row 10 Row 6 Row 2 Daughter 3 ← Row 15 Row 11 Row 7 Row 3 Daughter 4 ← Row 16 Row 12 Row 8 Row 4 ↓ ↓ ↓ ↓ Mother 4 Mother 3 Mother 2 Mother 1

In order to create a repetitive chart, certain rows have to be the same, reflected across the top right-bottom left diagonal:

 C B A ∗ E D ∗ A F ∗ D B ∗ F E C

Thus, Row 2 must be the same as Row 5 (A), Row 3 must be the same as Row 9 (B), Row 4 must be the same as Row 13 (C), and so forth.  Thus, if the third row of the First Mother has a single point, then the first row of the Third Mother must also have a single point.  Rows 1, 6, 11, and 16 are marked by asterisks (∗) and can be anything, single or double, and won’t affect the repetitiveness of the chart.  Thus, there are ten distinct choices to make here: the six mandated-repeated rows A, B, C, D, E, and F, and the four wildcard rows (∗).  Because there are ten choices to make between two options, this means that we have 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 2¹⁰ = 1024 repetitive charts.

Turning back to the Rosary, we know that there are 128 rows on the Rosary, which means that there are 128 options for picking out such charts if we use it clockwise, and another 128 options counterclockwise, which means we have 256 possibilities total for picking out charts using this method.  However, not all these charts are distinct, because the same sequences of seven rows (e.g. 0111100) appear multiple times in the Rosary.  If we focus on just all possible combinations of single or double points among seven rows, then this means that there are only 2⁷ = 128 possible distinct charts, but not all combinations of points among seven rows are present on the Rosary, either (e.g. the case of 1111111, where all four Mothers are Via).  In fact, based on the figure breakouts given above, we know there are only 74 possible distinct charts using the Rosary, formed from the following Mothers:

1. Acquisitio, Amissio, Rubeus, Carcer (2 repetitions)
2. Acquisitio, Amissio, Rubeus, Laetitia (2 repetitions)
3. Acquisitio, Puella, Caput Draconis, Via (6 repetitions)
4. Acquisitio, Puella, Coniunctio, Fortuna Minor (4 repetitions)
5. Acquisitio, Puella, Coniunctio, Puer (2 repetitions)
6. Albus, Acquisitio, Amissio, Rubeus (4 repetitions)
7. Albus, Acquisitio, Puella, Caput Draconis (4 repetitions)
8. Albus, Acquisitio, Puella, Coniunctio (4 repetitions)
9. Albus, Rubeus, Carcer, Fortuna Maior (2 repetitions)
10. Albus, Rubeus, Laetitia, Populus (2 repetitions)
11. Amissio, Acquisitio, Puella, Caput Draconis (2 repetitions)
12. Amissio, Acquisitio, Puella, Coniunctio (2 repetitions)
13. Amissio, Rubeus, Carcer, Albus (2 repetitions)
14. Amissio, Rubeus, Carcer, Fortuna Maior (4 repetitions)
15. Amissio, Rubeus, Laetitia, Populus (6 repetitions)
16. Caput Draconis, Via, Cauda Draconis, Fortuna Minor (8 repetitions)
17. Caput Draconis, Via, Cauda Draconis, Puer (8 repetitions)
18. Carcer, Albus, Acquisitio, Amissio (2 repetitions)
19. Carcer, Albus, Acquisitio, Puella (4 repetitions)
20. Carcer, Albus, Rubeus, Laetitia (2 repetitions)
21. Carcer, Fortuna Maior, Caput Draconis, Via (4 repetitions)
22. Carcer, Fortuna Maior, Coniunctio, Fortuna Minor (1 repetition)
23. Carcer, Fortuna Maior, Coniunctio, Puer (3 repetitions)
24. Cauda Draconis, Fortuna Minor, Carcer, Albus (3 repetitions)
25. Cauda Draconis, Fortuna Minor, Carcer, Fortuna Maior (1 repetition)
26. Cauda Draconis, Fortuna Minor, Laetitia, Populus (4 repetitions)
27. Cauda Draconis, Puer, Amissio, Acquisitio (2 repetitions)
28. Cauda Draconis, Puer, Amissio, Rubeus (4 repetitions)
29. Cauda Draconis, Puer, Puella, Coniunctio (2 repetitions)
30. Coniunctio, Fortuna Minor, Carcer, Albus (3 repetitions)
31. Coniunctio, Fortuna Minor, Carcer, Fortuna Maior (1 repetitions)
32. Coniunctio, Fortuna Minor, Laetitia, Populus (4 repetitions)
33. Coniunctio, Puer, Amissio, Acquisitio (2 repetitions)
34. Coniunctio, Puer, Amissio, Rubeus (4 repetitions)
35. Coniunctio, Puer, Puella, Caput Draconis (2 repetitions)
36. Fortuna Maior, Caput Draconis, Via, Cauda Draconis (8 repetitions)
37. Fortuna Maior, Coniunctio, Fortuna Minor, Carcer (1 repetition)
38. Fortuna Maior, Coniunctio, Fortuna Minor, Laetitia (1 repetition)
39. Fortuna Maior, Coniunctio, Puer, Amissio (4 repetitions)
40. Fortuna Maior, Coniunctio, Puer, Puella (2 repetitions)
41. Fortuna Minor, Carcer, Albus, Acquisitio (4 repetitions)
42. Fortuna Minor, Carcer, Albus, Rubeus (2 repetitions)
43. Fortuna Minor, Carcer, Fortuna Maior, Caput Draconis (1 repetition)
44. Fortuna Minor, Carcer, Fortuna Maior, Coniunctio (1 repetition)
45. Fortuna Minor, Laetitia, Populus, Tristitia (8 repetitions)
46. Laetitia, Populus, Tristitia, Albus (8 repetitions)
47. Laetitia, Populus, Tristitia, Fortuna Maior (8 repetitions)
48. Populus, Tristitia, Albus, Acquisitio (6 repetitions)
49. Populus, Tristitia, Albus, Rubeus (2 repetitions)
50. Populus, Tristitia, Fortuna Maior, Caput Draconis (4 repetitions)
51. Populus, Tristitia, Fortuna Maior, Coniunctio (4 repetitions)
52. Puella, Caput Draconis, Via, Cauda Draconis (8 repetitions)
53. Puella, Coniunctio, Fortuna Minor, Carcer (3 repetitions)
54. Puella, Coniunctio, Fortuna Minor, Laetitia (3 repetitions)
55. Puella, Coniunctio, Puer, Amissio (2 repetitions)
56. Puer, Amissio, Acquisitio, Puella (4 repetitions)
57. Puer, Amissio, Rubeus, Carcer (4 repetitions)
58. Puer, Amissio, Rubeus, Laetitia (4 repetitions)
59. Puer, Puella, Caput Draconis, Via (2 repetitions)
60. Puer, Puella, Coniunctio, Fortuna Minor (2 repetitions)
61. Rubeus, Carcer, Albus, Acquisitio (2 repetitions)
62. Rubeus, Carcer, Fortuna Maior, Caput Draconis (3 repetitions)
63. Rubeus, Carcer, Fortuna Maior, Coniunctio (3 repetitions)
64. Rubeus, Laetitia, Populus, Tristitia (8 repetitions)
65. Tristitia, Albus, Acquisitio, Amissio (2 repetitions)
66. Tristitia, Albus, Acquisitio, Puella (3 repetitions)
67. Tristitia, Albus, Rubeus, Carcer (2 repetitions)
68. Tristitia, Fortuna Maior, Caput Draconis, Via (4 repetitions)
69. Tristitia, Fortuna Maior, Coniunctio, Fortuna Minor (1 repetition)
70. Tristitia, Fortuna Maior, Coniunctio, Puer (3 repetitions)
71. Via, Cauda Draconis, Fortuna Minor, Carcer (4 repetitions)
72. Via, Cauda Draconis, Fortuna Minor, Laetitia (4 repetitions)
73. Via, Cauda Draconis, Puer, Amissio (6 repetitions)
74. Via, Cauda Draconis, Puer, Puella (2 repetitions)

Organized by how many repetitions there are for each set of Mothers:

1. One repetition (8 sequences)
1. Carcer, Fortuna Maior, Coniunctio, Fortuna Minor
2. Cauda Draconis, Fortuna Minor, Carcer, Fortuna Maior
3. Coniunctio, Fortuna Minor, Carcer, Fortuna Maior
4. Fortuna Maior, Coniunctio, Fortuna Minor, Carcer
5. Fortuna Maior, Coniunctio, Fortuna Minor, Laetitia
6. Fortuna Minor, Carcer, Fortuna Maior, Caput Draconis
7. Fortuna Minor, Carcer, Fortuna Maior, Coniunctio
8. Tristitia, Fortuna Maior, Coniunctio, Fortuna Minor
2. Two repetitions (24 sequences)
1. Acquisitio, Amissio, Rubeus, Carcer
2. Acquisitio, Amissio, Rubeus, Laetitia
3. Acquisitio, Puella, Coniunctio, Puer
4. Albus, Rubeus, Carcer, Fortuna Maior
5. Albus, Rubeus, Laetitia, Populus
6. Amissio, Acquisitio, Puella, Caput Draconis
7. Amissio, Acquisitio, Puella, Coniunctio
8. Amissio, Rubeus, Carcer, Albus
9. Carcer, Albus, Acquisitio, Amissio
10. Carcer, Albus, Rubeus, Laetitia
11. Cauda Draconis, Puer, Amissio, Acquisitio
12. Cauda Draconis, Puer, Puella, Coniunctio
13. Coniunctio, Puer, Amissio, Acquisitio
14. Coniunctio, Puer, Puella, Caput Draconis
15. Fortuna Maior, Coniunctio, Puer, Puella
16. Fortuna Minor, Carcer, Albus, Rubeus
17. Populus, Tristitia, Albus, Rubeus
18. Puella, Coniunctio, Puer, Amissio
19. Puer, Puella, Caput Draconis, Via
20. Puer, Puella, Coniunctio, Fortuna Minor
21. Rubeus, Carcer, Albus, Acquisitio
22. Tristitia, Albus, Acquisitio, Amissio
23. Tristitia, Albus, Rubeus, Carcer
24. Via, Cauda Draconis, Puer, Puella
3. Three repetitions (9 sequences)
1. Carcer, Fortuna Maior, Coniunctio, Puer
2. Cauda Draconis, Fortuna Minor, Carcer, Albus
3. Coniunctio, Fortuna Minor, Carcer, Albus
4. Puella, Coniunctio, Fortuna Minor, Carcer
5. Puella, Coniunctio, Fortuna Minor, Laetitia
6. Rubeus, Carcer, Fortuna Maior, Caput Draconis
7. Rubeus, Carcer, Fortuna Maior, Coniunctio
8. Tristitia, Albus, Acquisitio, Puella
9. Tristitia, Fortuna Maior, Coniunctio, Puer
4. Four repetitions (21 sequences)
1. Acquisitio, Puella, Coniunctio, Fortuna Minor
2. Albus, Acquisitio, Amissio, Rubeus
3. Albus, Acquisitio, Puella, Caput Draconis
4. Albus, Acquisitio, Puella, Coniunctio
5. Amissio, Rubeus, Carcer, Fortuna Maior
6. Carcer, Albus, Acquisitio, Puella
7. Carcer, Fortuna Maior, Caput Draconis, Via
8. Cauda Draconis, Fortuna Minor, Laetitia, Populus
9. Cauda Draconis, Puer, Amissio, Rubeus
10. Coniunctio, Fortuna Minor, Laetitia, Populus
11. Coniunctio, Puer, Amissio, Rubeus
12. Fortuna Maior, Coniunctio, Puer, Amissio
13. Fortuna Minor, Carcer, Albus, Acquisitio
14. Populus, Tristitia, Fortuna Maior, Caput Draconis
15. Populus, Tristitia, Fortuna Maior, Coniunctio
16. Puer, Amissio, Acquisitio, Puella
17. Puer, Amissio, Rubeus, Carcer
18. Puer, Amissio, Rubeus, Laetitia
19. Tristitia, Fortuna Maior, Caput Draconis, Via
20. Via, Cauda Draconis, Fortuna Minor, Carcer
21. Via, Cauda Draconis, Fortuna Minor, Laetitia
5. Six repetitions (4 sequences)
1. Acquisitio, Puella, Caput Draconis, Via
2. Amissio, Rubeus, Laetitia, Populus
3. Populus, Tristitia, Albus, Acquisitio
4. Via, Cauda Draconis, Puer, Amissio
6. Eight repetitions (8 sequences)
1. Caput Draconis, Via, Cauda Draconis, Fortuna Minor
2. Caput Draconis, Via, Cauda Draconis, Puer
3. Fortuna Maior, Caput Draconis, Via, Cauda Draconis
4. Fortuna Minor, Laetitia, Populus, Tristitia
5. Laetitia, Populus, Tristitia, Albus
6. Laetitia, Populus, Tristitia, Fortuna Maior
7. Puella, Caput Draconis, Via, Cauda Draconis
8. Rubeus, Laetitia, Populus, Tristitia

Now, 74 is a really strange number that doesn’t really appear otherwise in geomancy, and the distributions here are a little unusual, so maybe there’s something to investigate along those lines more.  Perhaps there’s significance to these 74 charts in some way, but I’m not so sure.  For that matter, there could be other significance or meaning attributed to the whole emblematic order of the Rosary, but it’s not clear to me.  Still, even if this post raises more questions than it answers regarding this intriguing little device, at least all this is something to note, whether for my or future geomancers’ research, so maybe someone can do something with this information.

# On Mistakes in Divination

A few days ago, I was chatting with one of my good Twitter friends in private messages.  He’s a pretty cool guy, and though I met him through a few mutual furry contacts we have online, I also found out he was an occultist, so we have fun things to talk about now and again.  He’s been learning geomancy lately (a highly worthwhile endeavor!), and he posed to me a question:

Consider a reading, where the seer fucks up and their dyslexic ass misreads Albus as Fortuna Maior, or got turned around with the meanings of say, Capricorn and Sagittarius.  Would the reading be wrong, or would it be adequate to take that slip as part of the system that produces the interpretation?  And, if the seer realizes their fuckup, should they make a full redaction and correction, or should they make a “transformation” in the reading like old Yin and old Yang in I Ching readings?

He had already guessed what my answer would be, and he was right, but he still wanted to know what my thoughts were.  It was a pretty fruitful discussion for us both, and I want to share some of the insights from that conversation more publicly.  And no, I’m not upset with him!  It just turns out that I have some Thoughts and Opinions in where we differ, and I think these are good things to talk about here.

I know that there are some diviners who everything that happens in a reading, whether in geomancy or in another system entirely, as omens of significance.  Like, say you’re shuffling a deck of Tarot cards for your usual spread, and a card slips out of the deck and falls face-up.  Some people say that that card is important and should be interpreted like any card in the spread itself; I hope he can correct me if I’m wrong, but I think it was Gordon White from Rune Soup who said something along the lines of “the only thing that card means is that you’re bad at shuffling”—and that’s a viewpoint I agree with (and if he didn’t say that or doesn’t agree with it, then I guess we disagree).  I don’t take all omens in a divination reading that relies on a divination system (i.e. a process with rules and standards and checks and skill) as significant, but only those that are produced according to the system within the boundaries of the system.  There’s a place and a role for intuition to play in divination, to be sure, but when it comes to mistakes, well…mistakes are just that: mistakes.

Without any exaggeration, I can claim that geomancy is a mathematical form of divination: geomancy relies on binary processes of addition and recursion using the binary structure of the 16 geomantic figures to produce a chart.  And there aren’t an infinite number of charts, nor are there 16! (2.092279 × 1013) different charts, or even more than that.  In fact, there are far fewer charts: only 65,536 (164) possible charts are permitted within the mathematical rules of geomancy.  By definition, any chart that does not fall into one of those 65,536 charts is not a valid chart, and there are multiple ways of checking to make sure a chart is valid.  So, you can’t have a chart where all four Mother figures are all Populus and have any other figure in the chart that isn’t Populus; such a chart just isn’t possible, any more than there could be a Tarot spread with three Empresses in a row or a horoscope where Venus opposes the Sun.  Such impossible charts are inherently invalid, and indicate that there was a mistake in your mathematics when calculating the chart; the proper approach isn’t to inspect the chart as it was drawn, but to go back and fix your error so you have a correct chart to look at.  Heck, although it wasn’t said so bluntly, there are some texts that say that “if the Judge is an odd figure, the chart is cursed and must be thrown out”; in a mathematically valid chart, the Judge must always be an even figure (containing an even number of points, e.g. Fortuna Maior with 6 points), so if you have one with an odd Judge (e.g. Puer with 5 points), that means you made a mistake.

But here’s the thing: you can make a mistake in multiple places in the chart, and a mistake anywhere in the chart means that the whole chart gets messed up.  The only four truly independently-generated figures there are in a geomantic chart, where the four figures have no inherent relationship to each other, are the four Mothers.  The Daughters rely on the Mothers, the Nieces rely on the Mothers and the Daughters, the Witnesses rely on the Nieces (and thus the Mothers and Daughters), the Judge relies on the Witnesses (and thus the Nieces, and thus the Mothers and Daughters), and the Sentence relies on the First Mother as well as the Judge (and thus, ultimately, the Four Mothers).  A mistake in the chart in the Daughters, Nieces, Witnesses, or Court indicates that there’s a break in the calculation that causes the whole chart to become invalid.  In other words, any of the figures from the fifth figure (First Daughter) to the sixteenth (Sentence) relies on all the other figures to be correct; if one figure is calculated wrong, even if it doesn’t impact the rest of the figures in the chart, it still means that the whole chart is off.

Now, on the rare occasion, I have seen some people in the geomancy Facebook group I admin post a chart that has a mistake in it, and generally one of the community will be sharp and fast enough to point out that mistake.  However, there is the rare time now and again that someone will still want to interpret the invalid, erroneous chart, because “well, that’s what they made in the moment”.  Like…I get it, but that’s not how geomancy works.  Geomancy is a system, a body of (more or less) well-defined and well-understood rules that must be applied for it to be considered “geomancy”.  To break those rules is to break the system, and you end up in the realm of “undefined behavior”, which doesn’t give you a lot to stand on besides pure intuition.  And geomancy, while making use of intuition, cannot simply rely on it in favor of the actual rules that keep things grounded in the actual art and practice of geomancy.

Now, to be sure and to be fair, there is absolutely a role for intuition in geomancy!  This is where we can explore our connection to the Divine and plumb its depths in order to come up with true and truly artful interpretations that pull every ounce and gram of nuance and detail out of a chart, even a single figure or a single passation of a figure from one house to another.  But that connection must be solid in order for it to be of use, and you still have to be sure you’re looking at the right things.  I’ve seen people in a variety of settings whose intuitions are strong, but not strong enough to not be swayed by what they’re looking at; it’s often what they’re looking at that kickstarts or unlocks their intuition, so if what they’re looking at is wrong, then while they might be getting messages, it’ll end up being a case of garbage-in garbage-out.  And that gets nobody anywhere good.  Sure, there are times where your intuition or spirit guides or what-have-you will kick in strong and give you ultimately-right answers with a fundamentally wrong chart, essentially covering for your mistakes, but it’s not guaranteed, it’s not trustworthy, it’s not reliable, and it’s still a problem because you made a mistake and didn’t spot or correct it.

Basically, what it comes down to is this: if there’s an error in the calculation of the chart or in the generation of the Mothers, then that’s on you to notice and to fix, then start interpreting the correct chart.  Consider a library, where each book is a particular destiny or fate for individual queries put to divination, and you want to find the book for the specific query the querent in front of you is asking; the geomantic chart is the call number for that book.  If you have the right call number, then you have the right book, and all you need to do is read from it; easy enough!  But if you have the wrong call number, then you’ll get the wrong book which won’t speak to the query put to divination by the querent—heck, you may end up with a call number for a book that doesn’t even exist.  This is why it’s crucial to make sure that we calculate the chart correctly, because if we don’t, we’re not going to get a chart that properly responds to the query put to divination: any mistake that occurs in the calculation of the chart will mess with the interpretation of the chart.

And that’s a whole other level to worry about, too!  Even if you have the chart mathematically correct, you can still mess up in the interpretation of the chart, like if you misread Fortuna Maior for Fortuna Minor or if you thought that Amissio was a figure of Mercury instead of Venus.  As a geomancer, you need to make sure that you know your symbols well enough to at least avoid major blunders in their interpretation.  These symbols are a thousand years old and are known across the Old World from Morocco to Mumbai, from Madagascar to Murmansk, and though there are definitely variations in how some geomancers or how some traditions of geomancy interpret them, the core meanings are the same no matter where you turn.  To make an egregious error in thinking that Caput Draconis talks about death or that Amissio talks about great gains in wealth is to show that you’re not getting the right information, and that will mess up the interpretation accordingly.  Just because you say things that are wrong doesn’t mean they become right because you’re “in the zone” and getting lost in the moment of talking; it just means you’re wrong and getting carried away with yourself.

My friend countered that the interpretation of a geomantic chart should embrace our imperfections and slips of reading or memory, but I countered with the metaphor of a doctor measuring someone’s blood pressure.  If their blood pressure meter is broken, the wrong numbers will result; if the blood pressure meter uses the wrong-sized armband, the wrong numbers will result; if the doctor mentally flips the numbers so that the systolic pressure is read on the bottom and the diastolic pressure on the top, the wrong numbers will result.  And wrong numbers means that the doctor is going to get a bad understanding and could gauge the person to be healthy when they’re not, or that they’re in danger when they’re fine.  Let’s not kid ourselves here: this kind of mistake can kill someone, and such a mistake cannot be tolerated or allowed by the doctor, so the doctor must make sure that the blood pressure meter is working and calibrated properly, that they’re using the right equipment for their patient, and that they’re reading and properly understanding the numbers that result.  The doctor cannot afford mistakes in tending to their patient, and neither can we, as diviners, afford mistakes in tending to our querents.  When people come to us for divination, they sometimes come to us to save their lives.  Divination can often be a matter of literal life and death for some people who know it, and more’s the pity, those who aren’t even aware of it yet.  There should be absolutely no expense spared in effort, skill, practice, study, or tools to make sure that everything in our divination readings is absolutely correct as possible, including making our calculations and double-, triple, even quadruple-checking them according to the rules within our system.  The rules of geomancy, when aided (but not replaced) by intuition, are what ensures that it work, so we need to make sure we understand the system at work.

To use another medical metaphor, consider someone coming to you for herbal medicine.  Ideally and hopefully, you can get a good read on the person and their symptoms and you know your herbs well enough to give them a particular kind of herbal concoction to help them improve themselves.  Sometimes, we can rely on intuition or spiritual guidance to pick the herbs for us, passing our hands over our jars and bundles and going “mmm…yes, this one feels right for you”.  But let’s be honest: if you don’t have a good grasp of your patient’s symptoms, or if they’re not telling you all their symptoms, or if you misremember certain properties of herbs or don’t know them to begin with, you can make a mistake in the medicine you give them that could poison them, incapacitate them, or otherwise make their situation worse.  I don’t care how strong someone’s intuition is: if my goal is to help someone, then the least I can do is to do no harm, so I’m going to do whatever I can to make sure I can at least hit that bare minimum threshold, which requires me to make sure I don’t make mistakes in what I do.  People come to us diviners for help, and it’s our job as diviners to help them and not hurt them; thus, it’s of paramount importance that everything in my divination work be done as properly and correctly as possible.  Heck, I’ll still pull out my notes and reference books when doing divinations; even if I think I know the figures and rules after ten years of constant use and study, I’ll still double-check and cross-check myself to make sure I’m on a good path with what I’m doing.  Making mistakes, honest or careless or with good intentions or otherwise, is still making mistakes, and that’s not something we can tolerate, nor is it anything I would take a chance with.

Now, sure, if geomancy were a more free-form kind of divination that relies far more on intuition, like bone-throwing or fire-scrying or trance states of remote viewing or possession, then this would all be a moot point, because pure intuition (so long as that connection is strong and clear) doesn’t have rules that can be broken.  Likewise, forms of divination that are developed on-the-spot or that have rules that can be bent or tossed aside in the moment, like some kinds of bone-throwing or nonce Tarot spreads, don’t have this issue, again because there are no rules that keep things correct, because it’s going to be correct by default.  And, of course, there are forms of divination that are strictly omen-based, like Roman augury, where you must inspect everything that happens or everything that is said as being of potential significance!  But geomancy isn’t like those forms of divination; geomancy has rules, and we use those rules and systems to enhance and ground our intuition, not the other way around.

Now, I don’t want to be misunderstood here: I’m not trying to say that geomancy is just about the rules, because it’s not, nor that there is no role that intuition plays, because there absolutely is.  Technique and intuition go hand-in-hand with geomancy, as I once said long ago with a beautiful metaphor based on Bernadette Brady’s Predictive Astrology: The Eagle and the Lark, and the dumbing-down of geomancy that reduced it only to a rule-based system ended up in the cultural forgetting and setting-aside of geomancy in favor of more intuitive methods of divination like Tarot that we saw in the West.  Intuition helps reach where rules cannot, but let’s be clear here: it really is the rules that do the bulk of the work in geomantic divination, and if you falter in the understanding or application of the rules, your intuition may not be enough to cover the distance that you’re falling short of.  Yes, there are times where intuition can do just that, and I’m not saying that it can’t or doesn’t; there are times when we’re so plugged in to the querent and tuned in to the query that we can clearly see without the use of geomancy, or that we can get at obscure meanings of the figures that don’t normally apply because of the peculiarities of a given situation.  However, if you’re using a system composed of rules like geomancy, and unless you’re a professional medium or clairvoyant or honest-to-gods psychic, you can’t always rely on that helping you out when you make a mistake, nor can you always be certain that your connection is 100% clear and strong enough to do so—and if you do have such a strong intuitive connection, then chances are you don’t need geomancy anyway.  Even so, geomancy is still more technique-based than intuition-based, and although intuition plays a role in refining and aiming the rules of geomancy, it’s still the rules of geomancy themselves that point us in the right direction to begin with, so we need to make sure that we’re facing the right way to see in that way.

Remember: an honest mistake is still a mistake, and mistakes can be costly.

# Geomantic Shields versus Geomantic Tetractyes

A bit ago on Curious Cat, I got asked a particularly delightful and perceptive question about some of the mathematical mechanics behind how we develop the Shield Chart in geomancy.

Generating the Nieces, Witnesses, and Judge make perfect sense, as the convergence of (XORing) two trends/situations/events create another trend/situation/event. But what, philosophically, is happening when the Daughters are generated? What does transposing a square matrix actually mean here?

This person is asking a really cool question that boils down to this: why do we do the Shield Chart the way we do?  It makes sense to add up figures to get new figures, which mathematically and symbolically shows us the interaction between those two figures and “distills” the both of them into a single new figure, but why do we bother with transposing the Mother figures into four Daughter figures?  We’re all taught in the beginning of pretty much any geomantic text how to develop the Shield Chart, but while the most important mathematical and symbolic mechanism for generating new figures is by adding them together, it’s that transposition from Mothers into Daughters that I don’t think I’ve ever touched on symbolically, nor have I seen anyone else touch on them before.  I wanted to answer the question just on Curious Cat when I got it, but there was no way for me to fully flesh out that topic in just 3000 characters, so…well, here we are!

When you think about it, why would the original geomancers have come up with such a complicated method to begin with that we use?  If you have four elements to start with, and a method to reduce two figures into one, then it would seem like the more straightforward and apparent method to use just that would be to apply it to all consecutive pairs of figures: figure one plus figure two, figure two plus figure three, figure three plus figure four, and so forth.  This would, in effect, take four figures down into three, three down into two, and two figures down into one, yielding a sort of geomantic tetractys (just with the row of four at the top going down to one instead of the reverse).  This also makes a lot of sense when you look at it; it gets rid of the whole need for transposition of Daughters at all, and seems to be something that just makes more sense to someone (or to a group of people) who may not be as mathematically inclined.  Yet, despite the simplicity of it, why don’t we see this method being used at all for such a geomantic tetractys in any of the literature?

Well…the thing about a “geomantic tetractys chart” is that I have indeed come across it before, but only once, and that only in a modern French text, that of Robert Ambelain’s 1940 work La Géomancie Magique.  Towards the end of the text, pages 200 to 202, Ambelain describes based on reports just such a tetractys-based approach to geomancy as apparently used by some Tuareg diviners (my translation):

The Tuareg Figure of Darb ar-Raml.  One of our correspondents and friends, an officer of the Moroccan Goumier (the same one who procured the members of «G.E.O.M», their sumptuous finely-cut red copper almadels), transmits to us this curious process of geomantic interrogation, still used by some nomads of the desert.

The geomancer (usually a woman) waits to perform this rite on Friday. After drawing a pentagram over a crescent moon on the sand, the diviner utters an invocation to the Evening Star, then marks a single point in the center of the star.  Then, under the sand, the diviner draws an equilateral triangle, and divides it into sixteen small triangles with four oblique lines and three horizontal lines. ([This shape appears to be a] memory of the feminine-yonic cult of Ishtar or of Astarte).

This done, the diviner marks the sixteen lines of ordinary dots and forms the four Mothers, which they then place in the upper row of the triangle.  Then the diviner copulates each of the Mothers with the next (first and second, second and third, third and fourth), and places these three new figures that he places in the second row.  After this, they copulate these three new figures together, thus forming two new ones, which are placed in the third row.  Finally, they copulate finally these last two figures together, then gets the one that constitutes the Judgment, considered simply as a pure answer (yes or no, good or bad).  By copulating the Judgment with the Mother, the diviner can further detail the answer.

Note the analogy of this graph with some geometric ornaments found on the cushions, fabrics and leathers of these regions, and also with tassels or pompoms during pyramids on both sides of the episcopal coat of arms.  All these motifs comprising ten pieces (4-3-2-1), are mere reminders of the mysterious Pythagorean tetractys:

and the Hebrew Tetragrammaton:

Both of these are esoteric reminders of the great Hermetic Secret showing us the four elements (Fire-Air-Water-Earth) that generate the three higher principles (the Salt, Mercury, and Sulfur of the Philosophers) which give rise to the Mercurial Principle and the Sulfuric Principle, i.e. the “Father” and “Mother”, [which then give rise to the] mysterious Philosopher’s Stone, the famous ferment red phosphorescent…*

Further, this same method of the nomads of the desert also has a strange resemblance to the secret emblem of the Knights Templar, who, from these same regions, may have brought it back…

The symbolism of the sons of Hermes are universal…

* The Tuareg-style geomantic chart is bastardized from the Hermetic point of view.  The alchemists will know how to restore the secret order of the four Mothers and thus generate Dry, Hot, and Wet…

The thing is, this is the only such instance of a tetractys-based approach to geomancy that I’ve ever seen, and I don’t know how much we can trust Ambelain or his reporter.  Plus, I’ve noticed quite a lot of stuff in modern French geomantic literature that seems to take some pretty wide divergences from medieval and Renaissance Western geomantic literature generally; besides potentially having a more active body of occultists who engage in geomantic research and development of techniques and study, I also think that it’s because of how French imperialism expanded so strongly across Africa and the Middle East over the past few centuries, and their anthropologists and occultists picked up quite a lot from their old colonial holdings.  That said, there’s generally a lack of any sort of citation, so sifting through the modern French geomantic literature can be confusing when picking out what was from Western practice versus what was from Arabic practice.

Anyway, the fundamental idea here with this “geomantic tetractys chart” is basically what we’re used to, but instead of transposing the Mothers to get the Daughters, we only focus on the four Mothers we get originally, and more than that, we throw in a third “Niece” into the mix, which then gets us two “Witnesses” just for the Mothers, yielding a “Judge” for the Mothers.  Okay, sure, I guess.  But what’s mathematically going with such a geomantic tectracys?  If we take any Shield Chart that we’re already familiar with and use the Four Mothers and the right side of the chart (Mothers, first two Nieces, and Right Witness), and compare the overall results with a geomantic tetractys formed from those same four Mothers, then the geomantic tetractys “judge” is the same as our Right Witness, but the figures above are almost always different than our First and Second Nieces.  What gives?  Let’s do a bit of math.  First, let’s set up our symbols for the geomantic tetractys:

F1 = First Mother
F2 = Second Mother
F3 = Third Mother
F4 = Fourth Mother

C1 = First Child
C2 = Second Child
C3 = Third Child

W1 = First Witness
W2 = Second Witness
J = Judge

Next, let’s define the Children, Witnesses, and Judge according to what figures add up for them:

C1 = F1 + F2
C2 = F2 + F3
C3 = F3 + F4
W1 = C1 + C2
W2 = C2 + C3
J = W1 + W2

While the Children figures in a geomantic tetractys are produced from adding together pairs of Mothers, the Witnesses are produced by adding together the pairs of Children.  But, because the Children are just sums of Mothers, we can reduce the terms by replacing a Child figure with its parent terms:

W1 = C1 + C2
= (F1 + F2) + (F2 + F3)
= F1 + F2 + F2 + F3

W2 = C2 + C3
= (F2 + F3) + (F3 + F4)
= F2 + F3 + F3 + F4

But note how each Witness has two of the same figure inherent in its calculation, with the Second Mother appearing twice in the First Witness and the Third Mother appearing twice in the Second Witness.  Any figure added to itself yields Populus, and so drops out of the equation.

W1= F1 + (F2 + F2) + F3
= F1 + Populus + F3
= F1 + F3

W2 = F2 + (F3 + F3) + F4
= F2 + Populus + F4
= F2 + F4

While in a Shield Chart, the First Niece is the sum of the First and Second Mothers, but in our tetractean First Witness, the First Witness is the sum of the First and Third Mothers.  Likewise, the tetractean Second Witness is the sum of the Second and Fourth Mothers.  Knowing this, we can proceed onto expanding the tetractean Judge, which, as expected, is just the sum of the four Mothers:

J = W1 + W2
= (F1 + F3) + (F2 + F4)
= F1 + F2 + F3 + F4

So, in effect, the tetractean Judge will always be the same as the Right Witness of the Shield Chart, and the First Child and Third Child the same as the First Niece and Second Niece.  It’s the presence of the Second Child, however, that makes the First and Second Witnesses of the geomantic tectratys different, which then causes a mismatch between what we’d otherwise expect in the tetractean Witnesses.  Still, the overall idea is the same: we’re distilling four figures down into one.

But this doesn’t explain why we ended up with the Shield Chart method of doing that instead of a tetractys-based method; after all, the Tetractys is a well-known symbol across many cultures for thousands of years now, so why didn’t we end up with the a geomantic tetractys method?  I think I touched on this idea a bit earlier in my post about the potential bird-based origins of geomancy when we discussed the Arabian nature of even numbers being more positive than odd numbers:

However, even with what little we have, we kinda start to see a potential explanation for why a geomantic chart is created in such a way that the Judge must be an even figure, and why we use such a recursive structure that takes in four figures and then manipulates them to always get an even figure as a distillation of the whole chart, whether or not it’s favorable to the specific query.  Related entries to `Iyān in Lane’s Lexicon, specifically عِينَةُ `iynah (pg. 2269), refer to “an inclining in the balance” or set of scales, “the case in which one of two scales thereof outweighs the other”, as in “in the balance is an unevenness”.  In this light, even numbers would indicate that things are in balance, and odd numbers out of balance; this idea strikes me as similar to some results used in Yòrubá obi divination or Congolese chamalongo divination or other African systems of divination that make use of a four-piece set of kola nuts, coconut meat, coconut shells, cowries, or some other flippable objects, where the best possible answer is where two pieces face-up and two fall face-down, while there being three of side and one of the other either indicates “no” or a generally weak answer.  For the sake of the Judge, then, we need it to be impartial (literally from Latin for “not odd”) in order for it to speak strongly enough to answer the question put to the chart.  Heck, in Arabic terms, the word that I’ve seen used for the Judge is میزان mīzān, literally “balance” or “scales” (the same word, I might add, that’s used to refer to the zodiac sign Libra).

And, to look at it another way, how is an even figure formed? An even geomantic figure is formed from the addition of either two odd parents or two even parents; in either case, the parity of one figure must be the same as the other figure in order for their child figure to be even.  Thus, for the Judge, the Witnesses must either both be even or they must both be odd.  “Brothers”, indeed; as that old Bedouin saying goes, “I against my brothers; I and my brothers against my cousins; I and my brothers and my cousins against the world”.  Brothers implies a similarity, a kinship, and even if they fight against each other, they must still be similar enough to come to terms with each other.  And consider the mathematical and arithmetic implications of what “coming to terms” can suggest!  Thus, the two Witnesses must be alike in parity in order for the scale of the Judge to work itself out, and perhaps, the figure with more points would “outweigh” the other and thus be of more value.  For example, if we have a Right Witness of Laetitia and a Left Witness of Puella, both odd figures, then the Judge would be Fortuna Maior, but Laetitia, having more points, would “outweigh” Puella, favoring the Right Witness representing the querent.  Thus, perhaps the Judge might be taking on the role of `Iyān and the Witnesses its two “sons”?  After all, you need both the Witnesses in order to arrive at the Judge, so telling them to hurry up would naturally speed up the calculation of the Judge.

And a little more again, once we got more of the bird symbolism in the mix:

We’re starting to tap into some of the symbolism behind even and odd here, and we can see that we were on the right track from before, but this time it’s made a bit more explicit; we might have considered that, perhaps, birds seen in pairs was considered a good omen in general, while a lone bird was considered bad, and that could still be the case especially for birds like the golden oriole that forms long-term pair-bonds, but now we’re tapping into deeper cultural lore about separation and number.  When the result of divination is even, then things are in pairs, considered fortunate because it suggests coming together or staying together (remember that the origin of the Arabic word for “even” ultimately comes from Greek for “yoked together”, as in marriage); when the result is odd, then it implies separation and being left alone (literally “wholly one”).  For a migratory, nomadic people living in a harsh environment, survival often depended on your tribe and not being left alone or being cast out, for which separation could truly mean an ill fate up to and including death by dehydration, starving, heat, or exposure; the same would go for humans from their tribes as it would for animals from their herds.  To consider it another way, if the marks being made in the sand are “eyes”, then in order to see clearly, we need to have two of them, since eyes naturally come in pairs (at least for us humans and many other animals).  If we end up with an odd number, then we’ve lost an eye, and cannot see clearly.

While I can’t point to this as saying “this is why”, I think this gives a good base for my conjecture here: we use the Shield Chart method that involves distilling the Mothers into the Right Witness, transposing the Mothers into the Daughters and distilling those figures into the Left Witness, and then distilling those two figures into the Judge because this method guarantees that the Judge will always be an even figure.  Just distilling the Mothers into a single figure can yield either an odd or an even figure, but if we use the Daughters as well as the Mothers, we always end up with an even figure.  Why do we care about this?  Because even numbers, in the original Arabian system, were considered more fortunate, comparable, approachable, and beneficial for all involved rather than odd numbers; indeed, the very word “impartial” to this day means “even”.  I’ve noted before that even figures tend to relate to objective things while odd figures relate to subjective things:

Because the Judge must be even, this narrows down the number of figures that can occur in this position from sixteen down to eight: Populus, Via, Carcer, Coniunctio, Fortuna Maior, Fortuna Minor, Aquisitio, and Amissio. It is for this reason that I call these figures “objective”, and the odd figures (Puer, Puella, Laetitia, Tristitia, Albus, Rubeus, Cauda Draconis, and Caput Draconis) “subjective”; this is a distinction I don’t think exists extant in the literature outside my own writings (which also includes contributions to the articles on geomancy on Wikipedia). I call the even figures “objective” because they are the only ones that can be Judges; just as in real life, where the judge presiding over a court case must objectively take into account evidence to issue a judgment and sentence, the Judge in a geomantic chart must likewise reflect the nature of the situation and answer the query in an impartial (a Latin word literally meaning “not biased” or “not odd”), fair, balanced, and objective way. It’s not that these figures are Judges because they inherently possess an astrological or magical quality called objectivity, but I call them objective because they’re mathematically able to be Judges.

I’ll let you read that post further, dear reader, as it gets more into the mathematics behind the evenness of the Judge and what it means for a figure to be odd or even and how that relates to its meaning and interpretation.  But, suffice it here to say that I think we use the Daughters as well as the Mothers so that mathematically we always deal in terms of evenness, for an even judgment, an even heart, an even mind, an even road.

So that explains (at least potentially) the mathematical reason behind why we have to have the Daughters.  But what about the other part of the original Curious Cat question?  What is philosophically or symbolically happening when we generate the Daughters from the Mothers?  It’s literally just the same points from the Mothers that we look at horizontally instead of vertically.  Don’t believe me?  Consider: say that you’re using the original stick-and-surface method of generating Mother figures, and you take up all those leftover points and put them into a 4×4 grid, starting in the upper right corner and going first vertically downwards and from right to left:

 Row 13 Row 9 Row 5 Row 1 Row 14 Row 10 Row 6 Row 2 Row 15 Row 11 Row 7 Row 3 Row 16 Row 12 Row 8 Row 4

If we read the leftover points allocated in this way in vertical columns, from top to bottom and from right to left, we get the four Mother figures.  If, instead, we read the leftover points allocated in this table in horizontal roads, from right to left and top to bottom, we get the four Daughter figures:

 First Daughter ← Row 13 Row 9 Row 5 Row 1 Second Daughter ← Row 14 Row 10 Row 6 Row 2 Third Daughter ← Row 15 Row 11 Row 7 Row 3 Fourth Daughter ← Row 16 Row 12 Row 8 Row 4 ↓ ↓ ↓ ↓ Fourth Mother Third Mother Second Mother First Mother

This is what I and the Curious Cat poster mean by “transposing”; we change (transpose) how we read the square matrix of points from primarily vertical to primarily horizontal.  This is simply a mathematical formalization of the usual phrasing of the method we use to get the Daughters from the Mothers: take the Fire lines of each of the four Mothers (rows 1, 5, 9, 13) and rearrange them vertically to get the first Daughter, the Air lines of the four Mothers (rows 2, 6, 10, 14) to get the second Daughter, and so forth.

When you consider what transposition does, all we’re doing is looking at the same exact points from a new perspective; instead of reading the 4×4 matrix above from the bottom, we’re reading it from the side.  If the points we get from generating the four Mothers are the “raw data”, the actual symbolic point-based representation of our situation, then by reading them “from the side” as the Daughters means we’re looking at the situation from literally a point of view that is not our own.  In other words, if the Mothers represent our view of the situation we’re facing, the Daughters represent the view of everyone else who isn’t us or affiliated with us.  We can see this in the meaning of the Witnesses, which are themselves the distillations of their corresponding Mothers or Daughters; the Right Witness (the distillation of the four Mothers) represents the querent’s side of things, and the Left Witness (the distillation of the four Daughters) represents the quesited’s side of things.  To use a courtroom analogy, the Right Witness represents the defense of the person being tried, and the Left Witness is the prosecution.  It’s the Judge that hears out both sides and favors one side, the other, both, or neither depending on the arguments and evidence that the defense and prosecution present.

Moreover, it’s this method of using two Witnesses that necessarily produce an even Judge that won out as the dominant form of geomancy (or was the original one even in the oldest of times) over a tetractean form of geomantic chart because the geomantic tetractys method doesn’t produce a complete answer (given what we said above); all it does is it illustrates the complexity of the querent’s situation but only as far as the querent themselves is concerned and what they’re aware of or what they can see.  The tetractys method does not touch on how the rest of the world might perceive their situation, how the querent fits into the broader world, or how their situation could be seen from an outside point of view.  We can’t just coddle our querents, after all, and make them the center of the world when they’re just one part of it; yes, the querent is an integral and major point of any situation of their own, to be sure, but geomancy talks about the world as a whole, in which the querent only plays one part.  The shield chart method resolves this by not only ensuring an even Judge figure that allows us to more clearly see the answer in a situation unclouded by emotion or subjectivity, but also by factoring in how other people necessarily perceive and interact with the same situation the querent is, which the querent themselves might not be able to see from their own point of view.

Geomancy is, fundamentally, a spiritual science of mathematics that analyzes the raw data that the cosmos gives us through the points obtained in divination.  Understanding the symbolic meaning of the figures is just one part of the science of geomancy; it’s the mathematics behind adding figures together to distill them and transposing four Mothers into four Daughters that gives us more symbols—and, thus, more information—to work with.  In this light, the mathematics itself becomes a technique for us to understand what a geomantic chart is telling us.

Also, just a small note: last month, April 2019, was the most-viewed month of the Digital Ambler in its history of over nine years, with 21630 views and 6667 visitors.  Thank you, everyone, for all the hits, attention, and love for the Digital Ambler!  I couldn’t do it without you, and you guys make blogging and writing so much fun for me and for everyone.  Thank you!

# 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.

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.

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

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:

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.

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.

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.