Geomantic Shields versus Geomantic Tetractyes

May 1, 2019 By polyphanes in geomancy, occult Tags: curious cat, mathematics, robert ambelain, shield chart, tetractys 1 Comment

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!

More on Geomantic Epodes and Intonations

September 3, 2018 By polyphanes in geomancy, mathesis, occult Tags: contemplation, epode, geomantic figures, geomantic magic, incantation, intonation, meditation, orison, planetary hexagram, secreti geomantici, tetractys, vowel 4 Comments

One of my colleagues on Facebook, Nic Raven Run of Ravens Hall Press, asked me an interesting question to follow up on my post on epodes for the elements and geomantic figures from the other day. In that post, I offered a set of single syllables that could be chanted or intoned like a bīja, or “seed syllable” mantra, for each of the four elements based on an obscure geomantic method of interpretation (the BZDḤ technique), which I also extrapolated into a system of single syllable intonations for each of the sixteen geomantic figures. To that end, here are the two systems I would most likely use in my own practice, one based on the BZDḤ system and one based on strict stoicheia for the elements:

Hybrid Greek system
- Fire: bi (ΒΙ)
- Air: zu (ΖΥ)
- Water: dē (ΔΗ)
- Earth: ha (Ἁ)
Exact Mathēsis system
- Fire: kho (ΧΟ)
- Air: phu (ΦΥ)
- Water: ksē (ΞΗ)
- Earth: thō (ΘΩ)

And their corresponding expansions into the two systems of geomantic epodes using the two systems I would recommend (with the pure elemental epodes in bold text showing their location in the geomantic systems):

Hybrid Greek System (ΒΖΔΗ)
		Primary Element
		Fire	Air	Water	Earth
Secondary Element	Fire	ΒΙ BI Laetitia	ΖΙ ZI Puer	ΔΙ DI Puella	Ἱ HI Carcer
	Air	ΒΥ BU Fortuna Minor	ΖΥ ZU Rubeus	ΔΥ DU Via	Ὑ HU Caput Draconis
	Water	ΒΗ BĒ Amissio	ΖΗ ZĒ Coniunctio	ΔΗ DĒ Albus	Ἡ HĒ Fortuna Maior
	Earth	ΒΑ BA Cauda Draconis	ΖΑ ZA Acquisitio	ΔΑ DA Populus	Ἁ HA Tristitia

Exact Mathēsis System (ΧΦΞΘ)
		Primary Element
		Fire	Air	Water	Earth
Secondary Element	Fire	ΧΟ KHO Laetitia	ΦΟ PHO Puer	ΞΟ KSO Puella	ΘΟ THO Carcer
	Air	ΧΥ KHU Fortuna Minor	ΦΥ PHU Rubeus	ΞΥ KSU Via	ΘΥ THU Caput Draconis
	Water	ΧΗ KHĒ Amissio	ΦΗ PHĒ Coniunctio	ΞΗ KSĒ Albus	ΘΗ THĒ Fortuna Maior
	Earth	ΧΩ KHŌ Cauda Draconis	ΦΩ PHŌ Acquisitio	ΞΩ KSŌ Populus	ΘΩ THŌ Tristitia

What this gets us is a system of single-syllable units that can represent not only the four elements but all sixteen figures. In addition to being useful for energy work exercises among other magical practices, it also gives us an interesting method of encoding geomantic figures phonetically. For instance, we could encapsulate an entire geomantic chart based on the four Mother figures, such that e.g. BIZAZIDĒ would be interpreted as Laetitia (BI), Acquisitio (ZA), Puer (ZI), and Albus (DĒ). Another way we could use these is to encapsulate one of the 256 combinations of figures in two or three syllables: for instance, the combination of Coniunctio (ZĒ) and Acquisitio (ZA) to form Fortuna Maior (HĒ) could be written succinctly as ZĒZA or more fully as ZĒZAHĒ. There are plenty of ways to extend such a system, ranging from Abulafia-like meditating on the 256 permutations of syllables to using them in geomantic candle magic a la Balthazar Black’s technique.

However, note that each such epode is basically considered a unit; yes, it’s composed of an elemental consonant and a vowel that, although they are inherently based on the Greek notion of planetary associations, can be reckoned as elemental symbols as well, and the combination of them composes a single syllable based on the primary (consonant) and secondary (vowel) elements of the geomantic figures. What Nic was asking about was an alternative system of epodes: how could we use the elemental epodes to “compose” a geomantic figure in the sense of describing which elements were active and passive? For instance, we could simply describe Via as BIZUDĒHA since it has all four elements, but how might one represent a figure with one or more passive elements? Nic suggested a phonetic approach using a system of using two sets of vowels, using open vowels for active elements and close vowels for passive elements. The system Nic was suggesting would be to effectively use a series of diphthongs to approximate such vowels.

I didn’t like this approach, to be honest. For one, the reason why I’m using the vowels I’m using (which themselves are a mix of open and close in the systems I suggest) are (a) because the Greek system is particularly amenable to occult works and (b) because I’m relying not so much on phonetics as I am the occult symbolism and correspondences of the letters to the planets and, by those same correspondences, to the elements. In that framework, diphthongs really mess with the system, because a diphthong involves several vowels which “muddle” the planetary/elemental symbolism that I’m trying to accomplish. Plus, such a system would necessitate eight distinct but more-or-less balanced vowel sounds, and the Greek alphabet or phonetics isn’t really geared for that. Now, that said, the idea isn’t a bad one! However, because I’m not operating from purely phonetic principles, it’s not for me to go along that route. I encouraged Nic (and I encourage others as well, if there are others to whom this idea is appealing) to explore such a phonetic approach to representing elements and their compositions to form geomantic figure representations.

There are other approaches to creating composed epodes for the geomantic figures, though, which I also discussed with Nic. The first hunch I had was to simply include or omit the basic letters needed; for instance, if the consonants BZDḤ represent Fire, Air, Water, and Earth respectively, then combinations of those letters would represent the active elements in a figure, and we could fill in the vowels according to the rules of instinctual Arabic methods or the methods of pronouncing Greek generated words from before. So, Via (with all four elements) would simply be BZDḤ or “bahz-dach”, Amissio (with just Fire and Water) would be BD or “bahd”, Fortuna Maior would be DḤ or “dach”, and so forth. Populus, however, having no elements active, could be represented through silence, soft breathing, or something else entirely like “hmmmm” (using the notion that the Semitic letter for M, Arabic mīm or Hebrew mem, has its origins in the hieroglyph and word for “water”, which is the dominant element of Populus). It’s an idea, but one I don’t particularly like, either, as it seems clunky and inelegant to use without regularity or much appeal, especially since the use of Ḥ only really works in Arabic, as we’d just end with a vowel in the Greek system which could be unclear. We could use the mathētic approach of using ΧΦΞΘ instead, but we can do better than that.

Instead of using consonants, let’s think about a system that just uses the seven pure Greek vowels. Recall in the systems above from the earlier post that there’s a way to use the Greek vowels, which normally represent the planets, to represent the four elements as well:

In the last row of my mathētic Tetractys, note how we have the four non-luminary and non-Mercury planets each associated to one of the four elements: Mars with Fire, Jupiter with Air, Venus with Water, and Saturn with Earth. Though this system doesn’t quite match Cornelius Agrippa’s Scale of Four (book II, chapter 7), it does with his broader and more fuller explanations and detailing of the planets earlier in his Three Books of Occult Philosophy (book I, chapters 23 through 29). Thus, as applied in my exact mathētic system of epodes, we can use Omicron (Mars) for Fire, Upsilon (Jupiter) for Air, Ēta (Venus) for Water, and Ōmega (Saturn) for Earth. The letters Iōta (Sun), Alpha (Moon), and Epsilon (Mercury) are not used in the exact mathētic system of epodes, but are in the vague hybrid system from before, being a little easier to use and distinguish.

The connection I made for using these vowels was based on another notion I had of arranging the seven planets into the geomantic figures. In that topic, one could envision taking seven planetary objects (talismans, coins, stones, etc.) and arranging them on an altar in a regular way to represent the graphical forms of the geomantic figures. The method I gave for doing this was described like this:

Since we want to map the seven planets onto the points of the figures, let’s start with the easiest ones that give us a one-to-one ratio of planets to points: the odd seven-pointed figures Laetitia, Rubeus, Albus, and Tristitia. Let us first establish that the four ouranic planets Mars, Jupiter, Venus, and Saturn are the most elementally-representative of the seven planets, and thus must be present in every figure; said another way, these four planets are the ones that most manifest the elements themselves, and should be reflected in their mandatory presence in the figures that represent the different manifestations of the cosmos in terms of the sixteen geomantic figures. The Sun, the Moon, and Mercury are the three empyrean planets, and may or may not be present so as to mitigate the other elements accordingly. A row with only one point must therefore have only one planet in that row, and should be the ouranic planet to fully realize that element’s presence and power; a row with two points will have the ouranic planet of that row’s element as well as one of the empyrean planets, where the empyrean planet mitigates the pure elemental expression of the ouranic planet through its more unmanifest, luminary presence. While the ouranic planets will always appear in the row of its associated element, the empyrean planets will move and shift in a harmonious way wherever needed; thus, since the Sun (as the planetary expression of Sulfur) “descends” into both Mars/Fire and Jupiter/Air, the Sun can appear in either the Fire or Air rows when needed. Similarly, Mercury can appear in either the Air or Water rows, and the Moon in either the Water or Earth rows (but more on the exceptions to this below).

This led us to having the following arrangements:

Note that Via is the only figure that uses only the so-called “ouranic” planets Mars, Jupiter, Venus, and Saturn, because Via is the only figure with all elements active. All the other figures, having at least one element passive, will involve one or more of the planets Mercury, Sun, or Moon, because those “empyrean” planets mitigate and lessen the elemental presence of the row that they’re found in. The only major exception to this arrangement is—you guessed it—Populus, which uses a different arrangement entirely. For more information about how and why these figures are arranged with the planets in the way they are and how they might otherwise be used, see the relevant post on my blog, linked just above. The terms ouranic and empyrean are a distinction I make in my Mathēsis work to distinguish the twelve non-zodiacal forces into three groups, as demonstrated in this post.

Now, remember that each planet has its own vowel, and note where the planets appear in the arrangements above for each figure. We can come up with a rule that transforms the figures into sequences of vowels to represent the figures like this:

For all figures except Populus:
1. Every row will have either a single ouranic planet (Mars, Jupiter, Venus, Saturn) or both an ouranic and empyrean planet (Moon, Sun, Mercury).
2. If a given elemental row has an empyrean planet present as well as an ouranic planet, use the vowel of the empyrean planet there.
3. Otherwise, if a given elemental row has only an ouranic planet present, use the vowel of the ouranic planet.
For the figure Populus:
1. All planets are present in their own arrangement to represent the voids of Populus.
2. Use all the vowels, some mutually-exclusive set, or just keep silent.

Thus, consider the figure Via. In each row, it only has an ouranic planet, so we simply use their corresponding vowels: ΟΥΗΩ. For Coniunctio, note how we have two empyrean planets in the figure, the Sun alongside Mars and the Moon alongside Saturn; we would use their corresponding vowels instead of their ouranic equivalents, getting us the vowel string ΙΥΗΑ (Iōta instead of Omicron and Alpha instead of Ōmega). Likewise, Puer has the empyrean planet Mercury present alongside Venus, so its vowel string would be ΟΥΕΩ (Epsilon instead of Ēta). The only exception to this would be Populus, as noted above, which could be represented either as the entire vowel string ΑΕΗΙΟΥΩ or as simple, holy silence, but we can talk more about that later.

This gets us the following vowel epodes for the figures:

Laetitia: ΟΙΕΑ
Fortuna Minor: ΟΥΙΑ
Amissio: ΟΙΗΑ
Cauda Draconis: ΟΥΗΕ
Puer: ΟΥΕΩ
Rubeus: ΙΥΕΑ
Coniunctio: ΙΥΗΑ
Acquisitio: ΙΥΑΩ
Puella: ΟΕΗΑ
Via: ΟΥΗΩ
Albus: ΙΕΗΑ
Populus: More on that in a bit.
Carcer: ΟΙΑΩ
Caput Draconis: ΕΥΗΩ
Fortuna Maior: ΙΑΗΩ
Tristitia: ΙΕΑΩ

What’s nice about this system is that, at least for all the non-Populus figures, we have four vowels that we can intone. Anyone familiar with the classical Hermetic and Neoplatonic texts and techniques is familiar with how vowel-intoning was considered a pure and sacred practice, and now we can apply it to the figures as well as the planets! Even better, since each geomantic figure uses a distinct set of vowels, we can permute them in any which way. Thus, if we wanted to engross ourselves in the world of, say, Laetitia, we could intone all possible variations of its vowel string:

ΟΙΕΑ ΟΙΑΕ ΟΕΙΑ ΟΕΑΙ ΟΑΙΕ ΟΑΕΙ
ΙΟΕΑ ΙΟΑΕ ΙΕΟΑ ΙΕΑΟ ΙΑΟΕ ΙΑΕΟ
ΕΟΙΑ ΕΟΑΙ ΕΙΟΑ ΕΙΑΟ ΕΑΟΙ ΕΑΙΟ
ΑΟΙΕ ΑΟΕΙ ΑΙΟΕ ΑΙΕΟ ΑΕΟΙ ΑΕΙΟ

For each of the non-Populus figures which have four distinct vowels, there are 24 possible permutations of its vowel string, with six permutations that begin with each one of the vowels. Going through and intoning each permutation could be a powerful meditative practice for each of the figures, and probably especially effective for magical practices, too.

What about Populus? For that, we have all seven vowels ΑΕΗΙΟΥΩ, and to permute all seven of those would…take a considerably longer time than the other figures (there are 5040 possible permutations). Though going through all such permutations would also be a powerful practice, there are better ways we can use our time. For one, what about the sequence ΑΕΗΙΟΥΩ itself? It’s simple and straightforward, but it doesn’t really reflect the arrangement of planets we use for Populus: note how we have the empyrean planets (Sun, Mercury, and Moon) down the middle with the ouranic planets (Mars, Jupiter, Venus, Saturn) around the sides in a distinctly mathētic pattern. For this arrangement, we could use the vowel string ΙΟΥΕΗΩΑ: we have Iōta at the beginning, Epsilon in the middle, and Alpha at the end, with the other four vowels in their elemental order interspersed between them, the hot elements Fire and Air in the first half and the cold elements Water and Earth in the second half. Using this pattern, we could imagine a kind of lightning-bolt descending from the Sun down to the Moon through Mars, Jupiter, Mercury, Venus, and Saturn, a pattern that would take us from the hottest, brightest, most active powers down to the coldest, darkest, most passive powers.

Another way is to use a condensed vowel string: rather than using the ouranic planets’ vowels at all, why not limit ourselves to the empyrean planets, which are only ever used for passive elements anyway in this scheme? In this reckoning, we could reduce ΙΟΥΕΗΩΑ to ΙΕΑ (reflecting the center empty “gap” of the dots in the figure Populus), just as we commonly figure that the divine name ΙΑΩ is a reduction of the full string ΑΕΗΙΟΥΩ. Plus, we only ever see the string ΙΕΑ in the (permutations of) the string for the figures that are mostly passive anyway: Laetitia (ΟΙΕΑ), Rubeus (ΙΥΕΑ), Albus (ΙΕΗΑ), and Tristitia (ΙΕΑΩ). If there were any vowel string that could be considered the inverse of that of Via (ΟΥΗΩ), the mutually-exclusive remaining set of vowels ΙΕΑ would be it! We could then permute this string in a simple set of six permutations, too:

ΙΕΑ ΕΑΙ ΑΙΕ
ΕΙΑ ΙΑΕ ΑΕΙ

Instead of doing either ΙΟΥΕΗΩΑ or permutations of ΙΕΑ, though, there’s another approach to us: if Populus is devoid of elements, then it has nothing at all, and thus has nothing to intone, so Populus could simply be represented by a pure, holy silence devoid of intonations. This is also entirely appropriate, and would symbolically make Populus a vacuum of empty space, a blank template upon which the other elements could be applied. Entirely fitting to represent Populus on its own.

Of course, using that logic, then why would we bother using the empyrean planets’ vowels at all to represent the passive elements in a figure? We could just stick with the ouranic planets that are active, which would get us the following “short” set of vowel intonations, such as Ο for Laetitia, ΟΥ for Fortuna Minor, ΟΥΗ for Cauda Draconis, and so forth. Not nearly as elegant, perhaps, but could also work. I’m not a fan, personally, as it then begins to conflate the elemental presences of the figures with purely planetary ones. For instance, Laetitia being simply represented by Omicron would then conflate Laetitia with the planet Mars, even though Laetitia is solidly linked to Jupiter, and likewise Rubeus with Upsilon to Jupiter and not Mars. I wouldn’t recommend this system, personally.

So, where does that leave us? At this point, there are three systems of epodes I would recommend for working with the geomantic figures, two of which are single-syllable epodes (one based on the BZDḤ system with Greek vowels, and one derived from that same system using a purer stoicheic/mathētic approach), and one of which is based on mathētic principles to come up with intonable, permutable vowel strings.

Figure	Single Syllable		Vowel String
Figure	Hybrid	Mathēsis	Vowel String
Laetitia	ΒΙ BI	ΧΟ KHO	ΟΙΕΑ
Fortuna Minor	ΒΥ BU	ΧΥ KHU	ΟΥΙΑ
Amissio	ΒΗ BĒ	ΧΗ KHĒ	ΟΙΗΑ
Cauda Draconis	ΒΑ BA	ΧΩ KHŌ	ΟΥΗΕ
Puer	ΖΙ ZI	ΦΟ PHO	ΟΥΕΩ
Rubeus	ΖΥ ZU	ΦΥ PHU	ΙΥΕΑ
Coniunctio	ΖΗ ZĒ	ΦΗ PHĒ	ΙΥΗΑ
Acquisitio	ΖΑ ZA	ΦΩ PHŌ	ΙΥΑΩ
Puella	ΔΙ DI	ΞΟ KSO	ΟΕΗΑ
Via	ΔΥ DU	ΞΥ KSU	ΟΥΗΩ
Albus	ΔΗ DĒ	ΞΗ KSĒ	ΙΕΗΑ
Populus	ΔΑ DA	ΞΩ KSŌ	ΙΟΥΕΗΩΑ or ΙΕΑ or just keep silent
Carcer	Ἱ HI	ΘΟ THO	ΟΙΑΩ
Caput Draconis	Ὑ HU	ΘΥ THU	ΕΥΗΩ
Fortuna Maior	Ἡ HĒ	ΘΗ THĒ	ΙΑΗΩ
Tristitia	Ἁ HA	ΘΩ THŌ	ΙΕΑΩ

This is all well and good, but where does this actually leave us? What the past few posts on these tangentially-geomantic topics are accomplishing is taking the sixteen geomantic figures and coming up with new ways to apply them in ways outside of strict divinatory purposes, giving them new media such as sound to be “played” or transmitted through, and using those media to accomplish other tasks. If the planets can be used for astrology as well as magic, there’s no reason why the figures can’t be used for geomancy as well as magic, either. The ability to form meditative or magical epodes for concentrating, contemplating, and connecting with the figures on deeper levels plays into the same systems that geomantic gestures or energy centers or altar arrangements do: using these figures for a magical, world-changing purpose instead of a merely predictive one.

By the same token, however, so much of this is highly experimental. All magic is at some point, but given the novelty and how mix-and-match I’m being between Greek letter magic and geomantic systems, this is all deserving of some deep practice and reflection and refinement. I’m sharing this on my blog because…well, it’s my blog, and it’s interesting to share my theories here, and to spread some of my ideas out there to get feedback on by those who are interested. At the same time, so much of all this is just theoretical and musings on how to apply certain ideas in certain ways. I’m confident I can get them to work, but that’s not a guarantee that they will. Experimentation and practice is absolutely needed, not only to get my own aims and goals accomplished, but even just to see whether certain methods work at all for anything.

Still, while we’re at it, let’s make up a new practice, shall we? Let’s say we want to have a formalized way of conjuring up the power of a given figure, such as for some intense contemplation or pathworking. In my Secreti Geomantici ebook, wherein I talk about lots of different magical practices involving geomancy and geomantic figures, I provide a set of sixteen prayers for each of the figures. We can use those in combination with the geomantic epodes above to come up with a more thorough invocation of a figure. The process I have in mind would be to recite the hybrid single-syllable epode as few as four or as many as sixteen times (or as many times as there are points in the figure), recite the given orison of the figure, then permute through its vowel string. Thus, for Laetitia, we could do the following, while sitting before an image of Laetitia (or an altar of planetary talismans arranged in the form of the figure Laetitia) while holding the geomantic hand gesture of Laetitia:

ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ

Jovian Laetitia, standing tall
Granting hope in the hearts of all
Blazing spirit, o fulgent flame
Flashing brightest, of rousing fame
In our dark minds you spark pure Fire
Calcining spite to high desire
Grand arch of joy, embrace us here
And bring us tidings glad and clear

ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ

ΟΙΕΑ ΟΙΑΕ ΟΕΙΑ ΟΕΑΙ ΟΑΙΕ ΟΑΕΙ
ΙΟΕΑ ΙΟΑΕ ΙΕΟΑ ΙΕΑΟ ΙΑΟΕ ΙΑΕΟ
ΕΟΙΑ ΕΟΑΙ ΕΙΟΑ ΕΙΑΟ ΕΑΟΙ ΕΑΙΟ
ΑΟΙΕ ΑΟΕΙ ΑΙΟΕ ΑΙΕΟ ΑΕΟΙ ΑΕΙΟ

ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ ΒΙ

See? By coming up with small, individual innovations and extrapolations and translations of one set of symbols from one medium into another, we can start using each on their own effectively, or we can start plugging them in to come up with bigger, better, and more profound practices that can really pack a punch. Geomancy has every potential and every capability to become a full magical and spiritual practice in its own right that can fit right in with any other Western or Hermetic practice based on their own symbol sets; just because extant literature is lacking on the subject doesn’t mean it can’t be done, after all, and with a bit of thought and ingenuity, there are so many avenues that open themselves up for ready exploration.

One final thought about the use of these vowel epodes: we know that for any non-Populus figure, there are 24 permutations of the vowel string epodes. So, that makes 15 × 24 = 360. Which is a…stupidly pleasing number, to be honest. As we all know, Using this little tidbit, we could conceive of a sort of year-long geomantic practice, focusing on one of the permutations of vowel epodes for the figures per day. This gives us 15 24-day “months” of figures, with five or six days leftover at the end of the year. In leap years that have six epagomenal days, we could use the permutations of the short epode ΙΕΑ for Populus; in non-leap years, we could just focus on the whole epode ΙΟΥΕΗΩΑ, or we could just keep silent (perhaps more fitting for epagomenal days). It’s not entirely balanced in that regard, but it does have its own logic and cleanliness that could make it a viable yearly-daily practice for meditating on the epodes of the figures. I might expand on this idea at a later point, or perhaps rework my geomantic Wheel of the Year to match it in some sense, but it’s something to mull over for now. The next leap year isn’t for another year and a half, after all.

Mathetic Year Beginning Mismatch, and a Revised Grammatēmerologion

May 9, 2018 By polyphanes in mathesis, occult, whining Tags: astronomy, epoch, equinox, new year, new years, protokhronia, solstice, tetractys, zodiac 15 Comments

Much like how I recently encountered one devil of an author having put something out for public use (though it turned out to be a complete non-issue), now I’m facing another one, this time a lot more serious for me.

So, here’s the issue I face. I have this thing called the Grammatēmerologion, a lunisolar calendar system that allots the letters of the Greek alphabet to the days, months, and years in a regular, systematized way. I developed this system of keeping track of lunar months and days for my Mathesis work, a system of theurgy based on Neoplatonic and Neopythagorean philosophy and practices in a Hermetic and loosely Hellenic framework largely centered on the use of the Greek alphabet as its main vehicle for understanding and exploring spirituality. Not only can the Grammatēmerologion be used as a system of calendrical divination a la Mayan day sign astrology (or tzolk’in), but also for arranging for rituals, festivals, and worship dates in a regular way according to the ruling letter of the day, month, and (rarely) year. Sounds pretty solid, right? I even put out a free ebook for people to use and reference, should they so choose, just for their convenience in case they were curious about the Grammatēmerologion for their own needs.

However, this isn’t the only system of time and timing that I need to reference. In reality, I’m dealing with two cycles: one is the calendrical cycle of the Grammatēmerologion, which starts a new year roughly at the first New Moon after the summer solstice, and the zodiacal cycle that starts at the spring equinox. The fact that they don’t line up is something that I noted rather early on, yet, passed off easily as “well, whatever, not a big deal”. However, the more I think about it and how I want to arrange my own system of rituals and ritual timing, the more I realize that this is actually a big deal.

Let’s dig into this a bit more. Why does the Grammatēmerologion start at the first New Moon after the summer solstice? This is because the Grammatēmerologion is loosely based on the old Attic calendar, which had the same practice; for the Attics and Athenians, the new year started with summer. Why did I bother with that? Honestly, because the system seemed easy enough to apply more-or-less out of the box, and there is a rather convenient solar eclipse on the summer solstice in 576 BCE that would serve as a useful epoch date, this also being the first time the Noumenia coincided with the summer solstice since the stateman Solon reformed Athenian government and laws in 594 BCE. I figured that this was a pleasant way to tie the Grammatēmerologion into a culturally Greek current as well as tying it to an astronomical event to give it extra spiritual weight.

However, by linking it to the summer solstice, I end up with two notions of “new cycles”, one based on this lunisolar system and one based on the passage of the Sun through the signs of the Zodiac. The zodiacal stuff is huge for me, and only stands to become even bigger. While there can truly be no full, exact match between a lunisolar calendar (Grammatēmerologic months) and a strictly solar one (Zodiacal ingresses), having them synced at least every once in a while is still a benefit, because I can better link the Noumēnia (the first day of the lunar month) to an actual zodiac sign. This would give the months themselves extra magical weight, because now they can officially overlap. Technically, this could still be done with the Grammatēmerologion as it is, except “the beginning of a cycle” ends up having two separate meanings: one that is strictly zodiacal based, and one that is lunisolar and slapped-on starting a full season later.

The issue arises in how I plan to explore the Tetractys with the letter-paths according to my previous development:

The plan was to traverse the 10 realms described by the Tetractys according to the letters of the Greek alphabet, using twelve paths associated with the signs of the Zodiac, starting with Bēta (for Aries). This would be “the first step”, and would indicate a new cycle, just as Aries is the first sign of the Zodiac and, thus, the astrological solar year. Pretty solid, if you ask me, and the cosmological implications line up nicely. Except, of course, with the notion of when to start the year. If I really want my Grammatēmerologion system to match well as a lunisolar calendar for my needs, then I’d really need to make it sync up more with the Zodiac more than it does, at least in terms of when to start the year. So long as the Grammatēmerologion calendar has its Prōtokhronia (New Years) within the sign Aries, this would be perfect, because then I could give, at minimum, the first day of the first month of the year to the first sign of the Zodiac.

So, there are several solutions that I can see for this:

Set the Prōtokhronia (New Year) of the Grammatēmerologion to be the first New Moon after the spring equinox, using the first occurrence of this time after the original epoch date of June 29, 576 BCE. This would put the first Noumenia of the most recent cycle 69 on April 15, 2010, though the epoch date would remain the same; we’d simply shift what letters would be given to what months. This would be the least change-intensive option, but it causes all significance to the epoch year to vanish and seems like a giant kluge to me.
Set the Prōtokhronia of the Grammatēmerologion to be the first New Moon after the spring equinox, using a new epoch date where a solar eclipse occurred up to two days before the spring equinox so that the Noumenia coincides with the equinox, hopefully in a year wherein something meaningful happened or which fell within a 19-year period (one Metonic cycle) after a moment where something meaningful happened. There are very few such dates that satisfy the astronomical side of things.
Reconfigure my own understanding of the flow of the Zodiac to start with Cancer (starting at the summer solstice) instead of with Aries (spring equinox). This…yikes. It would leave the Grammatēmerologion system intact as it is—even if at the expense of my own understanding of the nature of the Zodiac (which bothers me terribly and would go against much of well-established education and understanding on the subject) as well as the letter-to-path assignment on the mathetic Tetractys (which doesn’t bother me terribly much, since I still admit that it’s still liable to change, even if it does have a neat and clean assignment to it all). This is the least labor-intensive, but probably the worst option there is.
Leave both the Grammatēmerologion and zodiacal cycles as they are: leave the Grammatēmerologion to continue starting at summer and the zodiac to start in spring, and just deal with the mismatch of cycles. This just screams “no” to me; after all, why would I tolerate something that causes me anguish as it is without any good reason or explanation for it, especially in a system that I’m designing of my own free will and for my own needs? That would be ridiculous.

Based on my options above, I’m tempted to go with establishing a new epoch for the Grammatēmerologion to be set at a solar eclipse just before the spring equinox, with the Prōtokhronia set to coincide with the spring equinox itself. If I want a reasonable epoch date that goes back to classical times or before…well, it’s not like I have many options, and comparing ephemerides for spring equinoxes and solar eclipses (especially when having to deal with Julian/Gregorian calendar conversions) is difficult at the best of times. Here are such a few dates between 1000 BCE and 1 BCE, all of which use the Julian calendar, so conversion would be needed for the proleptic Gregorian calendar:

March 30, 1000 BCE
March 30, 935 BCE
March 28, 647 BCE
March 27, 628 BCE
March 27, 609 BCE
March 27, 563 BCE
March 27, 544 BCE
March 25, 294 BCE
March 25, 275 BCE
March 24, 256 BCE
March 24, 237 BCE

As said before, the Attic-style summer-starting Grammatēmerologion has its epoch in 576 BCE, the first time that the Noumenia coincided with the summer solstice (and immediately after a solar eclipse), and the first such time either happened following Solon’s reforms in Athens. The date that would most closely resemble this for a Mathetic spring-starting Grammatēmerologion would have its epoch in 563 BCE, only a handful of years later. In the proleptic Gregorian calendar, this would mean that we’d start the epoch on March 21, 563 BCE, with the Noumēnia falling on the day after, the first day the New Moon can be seen and the first full day of spring.

On its face, this would seem to be an easy change to make; just change the epoch date and recalculate everything from there, right? After all, I have all the programs and scripts ready to go to calculate everything I need, and since we know that a full grammatēmerologic cycle is 38 years which would get us to basically the next time the New Moon happens just after the spring equinox, we know that we’d currently be in cycle 68 (starts in 1984 CE). Except…the spring equinox in 1984 occurs on March 20, and the New Moon occurs on…April 1. That’s quite a large drift, much larger than I’d expect. So I investigated that out and…yeah, as it turns out, there’s an increasing number of days’ difference between the spring equinox and the following New Moon over successive cycles. I forgot that the Metonic cycle isn’t exact; there is a small amount of error where the lunar cycle shifts forward one day every 219 years, and between 1984 CE and 563 BCE, there’re 2550 years, which means a difference of just over 11 days…which is the number of days between March 20 and April 1, 1984.

And on top of that, I had originally calculated my original epoch date for the Attic-style summer-starting calendar incorrectly: the New Moon should have been on June 17, 576 BCE, not June 29; as it turns out, I had misconverted 576 BCE for year -576, when it should have been -575 (because 1 BCE is reckoned as year 0, 2 BCE as year -1, and so forth). I majorly screwed myself over there; not only is my epoch system not working for how the revised Grammatēmerologion should work, but the epoch for the original Grammatēmerologion was wrong, anyway. Splendid.

So much for having a long-term classically-timed epoch, then. Without periodically fixing the calendar alignment or using a more precise cycle, such as the Callipic or Hipparchic cycle which still have their own inaccuracies, there’s still going to be some drift that won’t allow for establishing long-term cycles how I originally envisioned. I still want to use the 38-year dual Metonic cycle, but since there’s no real need to tie it to any historical period except for my own wistfulness, I suppose I could use a much more recent epoch. The most recent time that a solar eclipse happened just before the spring equinox, then, would have been March 20, 1643 CE, putting us in cycle 10 that starts in 1985 CE (which would start on March 22, since the New Moon is on March 21, just after the spring equinox on March 20, which is acceptable), making 2018 CE year 33 in the cycle. The next cycle would start on March 22, just after the New Moon on March 21, just after the spring equinox (again) on March 20. Again, this would be acceptable. The issue of drift would be more evident later on, say, in year 3277 CE, which would start on March 27, which is definitely several days too late. We start seeing a stable drift of more than two days starting in 2213 CE, but looking ahead a few years, we can see that 2216 CE would have a Prōtokhronia start perfectly on March 20, the day of that year’s spring equinox.

So, here’s my method for applying corrections to the Grammatēmerologion:

Establish an epoch where the Prōtokhronia starts on the day of or the day after the spring equinox.
Grammatēmerologic cycles are to be grouped in sets of seven, which would last 266 years, after which the drift between the dual Metonic cycle and the solar year becomes intolerable. (We could use six cycles, getting us to 228 years, but seven is a nicer number and the error isn’t always completely stable at that point just yet due to the mismatch between lunations and equinoxes.)
After the end of the seventh grammatēmerologic cycle, start up a “false” cycle to keep track of full and hollow months, until such a year arrives such that the Prōtokhronia of that year starts on the day of or the day after the spring equinox.
That year is to mark the new epoch, and a new set of cycles is established on that day. (This leads to a “false” cycle of only a few years, none of which should be lettered as usual.)

Let’s just make this simple, then: forget about aligning the beginning cycles with a spring equinox tied to a solar eclispe, and just settle for when the Noumēnia is either on or the day after the spring equinox. The most recent time a New Moon coincided with the spring equinox was in 2015 CE. Knowing that the New Moon coincided with the spring equinox on March 20 that year, this makes the epoch date for this cycle March 21, 2015. This means that we’re currently in year four of the first cycle. While I’m not entirely thrilled about losing the whole equinox eclipse significance thing, setting 2015 as a cycle start epoch makes sense; after all, the whole system of Mathesis really could be considered to start around then.

However, there’s one extra wrench thrown into the works for this; I want to make sure that the Prōtokhronia always falls while the Sun is in the sign of Aries, so the Noumēnia of the first month of the year must fall when the Sun has already crossed the spring equinox point. Because twelve lunar months isn’t long enough to ensure that, we’d need to ensure that certain years are full (13 lunar months) and other years are hollow (12 lunar months), and it turns out that the regular Metonic scheme that the old Attic-style Grammatēmerologion doesn’t ensure that. For instance, the first year of a cycle, according to the Metonic scheme, is supposed to be hollow; if we start the first year off immediately after the spring equinox, then the second year will start off about two weeks before the spring equinox, so we’d need to change how the years are allocated to be full or hollow. And, to follow up with that, tweaks also need to be made to the scheme of figuring out which months are full (30 days) or hollow (29 days) to make sure they stay properly aligned with the dates of the New Moon, while also not going over the Metonic count of 235 lunar months consisting of 6940 days.

So. After a day or so of hastily plotting out lunar phases, equinox dates, and eclipse times, I reconfigured my scripts and programs to calculate everything for me to account for all the changes to the Grammatēmerologion, rewrote my ebook to document said changes, and now have a revised Grammatēmerologion for the period between March 2015 and March 2053. In addition, I took the opportunity to explore a useful extension of the Grammatēmerologion system and the seven-day week to account for days of planetary strength or weakness, as well, and documented them in the ebook, too. (Normally, there would be no interaction, but this is one that actually makes sense in how the powers of the letters of the day are channeled.)

Download the revised Grammatēmerologion (March 2015 — March 2053) here!

I apologize for the confusion, guys. Even though I know few people are ever going to take this little pet project of mine seriously, I regret having put something out that was so broken without realizing it. I’m taking down the old version from my site, and only keeping the new revised version up; if anyone is interested in the old copy (even with its flaws), I can send it to them upon request, but I’d rather it not be so freely available as it was.

Arranging the Planets as the Geomantic Figures

October 22, 2017 By polyphanes in geomancy, mathesis, occult Tags: al cummins, element, geomantic figures, geomantic magic, planetary hexagram, planetary talisman, tetractys 6 Comments

A few weeks ago, the good Dr Al Cummins and I were talking about geomantic magic. It’s a sorely understood and understudied aspect of the whole art of geomancy, and though we know geomantic sigils exist, they’re never really used much besides in addition to the usual planetary or talismanic methods of Western magic. While I’ve been focusing much on the techniques of divination, exploring the use of geomancy and geomantic figures in magical workings is something of a long-term, slow-burn, back-burner thing for me. Al, on the other hand, has been jumping headlong into experimenting with using geomancy magically (geomagy?), which fascinates me, and which gives us nigh-endless stuff to conjecture and experiment with. After all, there’s technically nothing stopping us from seeing the geomantic figures as “units” in and of themselves, not just as extensions of planets projected downward or as combinations of elements projected upwards, so seeing how we could incorporate geomancy into a more fuller body of magic in its own right is something we’re both excited to do.

One of these talks involved my use of the geomantic gestures (mudras, or as I prefer to call them, “seals”). I brought up one such example of using a geomantic seal from a few years ago: I was at the tattoo parlor with a magic-sensitive friend of mine in the winter, and it had just started to snow. I had to run across the street to get cash, and I decided that it wasn’t that cold (or that I could bear the weather better) to put on my coat. I was, as it turns out, incorrect, and by the time I got back, I was rather chilled to the bone. So, in an attempt to kickstart the process of warming back up, I threw the seal for Laetitia and intoned my mathetic word for Fire (ΧΙΑΩΧ). My sensitive friend immediately turned and picked up on what I was doing without knowing how. I hadn’t really tried that before, but since I associate Laetitia with being pure fire (according to the elemental rulers/subrulers of the figures), I decided to tap into the element of Fire to warm myself up. Since that point, I use the seals for Laetitia, Rubeus, Albus, and Tristitia as mudras for the elements of Fire, Air, Water, and Earth, respectively, like in my augmentation of the Calling the Sevenths ritual (e.g. in my Q.D.Sh. Ritual to precede other workings or as general energetic/spiritual maintenance).

Talking with Al about this, I came to the realization that I instinctively used the figures to access the elements; in other words, although we consider the figures being “constructed” out of the presence or absence of the elements, from a practical standpoint, it’s the opposite way around, where I use the figures as bases from which I reach the power of the elements. That was interesting on its own, and something for another post and stream of thought, but Al also pointed out something cute: I use the figures of seven points as my seals for the elements. This is mostly just coincidence, or rather a result of using the figures with one active point for representing one of the four elements in a pure expression, but it did trigger a conversation where we talked about arranging the seven planets among the points of the geomantic figures. For instance, having a set of seven planetary talismans, I can use each individually on their own for a single planet, or I can arrange them on an altar for a combined effect. If the seven-pointed figures can be used for the four elements, then it’d be possible to have elemental arrangements of the planets for use in blending planetary and elemental magic.

So, that got me thinking: if we were to see the geomantic figures not composed of the presence or absence of elements, but as compositions of the planets where each planet is one of the points within a figure, how might that be accomplished? Obviously, we’d use fiery planets for the points in a figure’s Fire row, airy planets for the Air row, etc., but that’s too broad and vague a direction to follow. How could such a method be constructed?

I thought about it a bit, and I recalled how I associated the planets (and other cosmic forces) with the elements according to the Tetractys of my mathesis work:

Note how the seven planets occupy the bottom two rungs on the Tetractys. On the bottom rung, we have Mars in the sphaira of Fire, Jupiter in Air, Venus in Water, and Saturn in Earth; these are the four essentially elemental (ouranic) planets. The other three planets (the Sun, the Moon, and Mercury) are on the third rung, with the Sun in the sphaira of Sulfur, the Moon in the sphaira of Salt, and the planet Mercury in the sphaira of the alchemical agent of Mercury. Although we lack one force (Spirit) for a full empyrean set of mathetic forces for a neat one-to-one association between the empyrean forces and the four elements, note how these three planets are linked to the sphairai of the elements: the Sun is connected to both Fire and Air, Mercury to both Air and Water, and the Moon to both Water and Earth.

Since we want to map the seven planets onto the points of the figures, let’s start with the easiest ones that give us a one-to-one ratio of planets to points: the odd seven-pointed figures Laetitia, Rubeus, Albus, and Tristitia. Let us first establish that the four ouranic planets Mars, Jupiter, Venus, and Saturn are the most elementally-representative of the seven planets, and thus must be present in every figure; said another way, these four planets are the ones that most manifest the elements themselves, and should be reflected in their mandatory presence in the figures that represent the different manifestations of the cosmos in terms of the sixteen geomantic figures. The Sun, the Moon, and Mercury are the three empyrean planets, and may or may not be present so as to mitigate the other elements accordingly. A row with only one point must therefore have only one planet in that row, and should be the ouranic planet to fully realize that element’s presence and power; a row with two points will have the ouranic planet of that row’s element as well as one of the empyrean planets, where the empyrean planet mitigates the pure elemental expression of the ouranic planet through its more unmanifest, luminary presence. While the ouranic planets will always appear in the row of its associated element, the empyrean planets will move and shift in a harmonious way wherever needed; thus, since the Sun (as the planetary expression of Sulfur) “descends” into both Mars/Fire and Jupiter/Air, the Sun can appear in either the Fire or Air rows when needed. Similarly, Mercury can appear in either the Air or Water rows, and the Moon in either the Water or Earth rows (but more on the exceptions to this below).

As an example, consider the figure Laetitia: a single point in the Fire row, and double points in the Air, Water, and Earth rows, as below:

First, we put in the ouranic planets by default in their respective elemental rows:

Note how Mars takes the single point in the Fire row, while Jupiter, Venus, and Saturn occupy only one of the points in the other rows; these three empty points will be filled by the three empyrean planets according to the most harmonious element. The Moon can appear in either the Earth or Water rows, and Mercury can appear in either the Water or Air rows, but in the case of the figure Laetitia, the Sun can only appear in the Air row, since the Fire row has only one point and is already associated with Mars; thus, in Laetitia, the Sun goes to Air, Mercury to Water, and the Moon to Earth.

Following this rule, we get Rubeus with Jupiter occupying the sole Air point and the Sun moving to the Fire row as the second point, Albus with Venus in the sole Water point and Mercury moving to the Air row, and Tristitia with Saturn in the sole Earth point and the Moon moving to the Water row.

With those done, it would then be easy to see what Via would look like as a collection of planets: just the four ouranic planets Mars, Jupiter, Venus, and Saturn in a straight vertical line, the four purely-elemental ouranic planets without any of the mitigating empyrean ones, since the empyrean planets don’t need to be present to mitigate any of the ouranic ones.

Leaving aside Populus for the moment, what about the five-pointed and six-pointed figures? In the case of five-pointed figures (e.g. Puer), we have to leave out two of the empyrean planets, and only one in the case of the six-pointed figures (e.g. Fortuna Maior). For these figures, we decided to break with the foregoing empyrean-to-element rule and institute two new ones for these figures.

For five-pointed figures, use Mercury as the sole empyrean planet for the row with two dots, regardless where it may appear:

For six-pointed figures, use the Sun and Moon as the empyrean planets for the two rows with two dots, regardless where they may appear, with the Sun on the upper double-pointed row and the Moon on the lower double-pointed row:

Note how these two rules give us four figures where the empyrean planets do not appear where we would otherwise have expected them:

Fortuna Maior (Sun in Water)
Fortuna Minor (Moon in Air)
Caput Draconis (Mercury in Fire)
Cauda Draconis (Mercury in Earth)

I figured that this departure from the original empyrean-to-elemental-row idea was useful here, since it allows us to emphasize the structure of the figures and respect the natural affinities of the empyrean planets to each other. The Sun and Moon have always been considered a pair unto themselves as the two luminaries; without one, the other shouldn’t necessarily be present in such a planetary arrangement. Thus, for the five-pointed figures that omit the Sun and Moon, we would then use only Mercury, as it’s the only empyrean planet available. Likewise, if either the Sun or Moon is present, the other should also be present; for the six-pointed figures, this means that Mercury is the only empyrean planet omitted. An alternative arrangement could be used where you keep following the prior rules, such that Fortuna Maior uses the Sun and Mercury, Fortuna Minor uses Mercury and the Moon, etc., but I rather like keeping the Sun and Moon both in or out together. It suggests a certain…fixity, as it were, in the six-pointed figures and mutability in the five-pointed figures that fits well with their even/objective/external or odd/subjective/internal meanings.

For all the foregoing, I’m torn between seeing whether the order of planets within a row (if there are two) matters or not. In one sense, it shouldn’t matter; I only assigned the ouranic planets to the right point and the empyreal planets to the left because of the right-to-left nature of geomancy, and coming from a set theory point of view, the order of things in a set doesn’t really matter since sets don’t have orders, just magnitude. On the other hand, we typically consider the left-hand side of things to be weaker, more receptive, more distant, or more manifested from the right-hand stronger, emitting, near, or manifesting (due, of course, to handedness in humans with the usual connotations of “dexter” and “sinister”), but relying on that notion, I do feel comfortable putting the empyrean planets (if any) on the left-hand points of a figure, with the ouranic planets on the right-hand side, if not the middle. It’s mostly a matter of arbitrary convention, but it does…I dunno, feel better that way.

So that takes care of the figures of four, five, six, and seven points. We only have one figure left, the eight-pointed figure Populus. As usual with this figure, things get weird. We can’t simply slap the planets onto the points of Populus because we only have seven planets; we’d either need to bring in an extra force (Spirit? Fixed stars? the Earth?) which would necessitate an eighth force which simply isn’t available planetarily, or we’d have to duplicate one of the existing seven planets which isn’t a great idea (though, if that were to be the case, I’d probably volunteer Mercury for that). However, consider what the figure of Populus represents: emptiness, inertia, void. What if, instead of filling in the points of the figure Populus, we fill in the spaces left behind by those points? After all, if Populus is empty of elements, then why bother trying to put planets where there’ll be nothing, anyway? If it’s void, then put the planets in the voids. I found it easiest to conceive of seven voids around and among the points of Populus in a hexagram pattern:

Rather than filling in the points of Populus, which would necessitate an eighth planet or the duplication of one of the seven planets, we can envision the seven planets being used to fill the gaps between the points of Populus; seen another way, the planets would be arranged in a harmonic way, and Populus would take “form”, so to speak, in the gaps between the planets themselves. The above arrangement of suggested points to fill naturally suggests the planetary hexagram used elsewhere in Western magic (note that the greyed-out circles above and below aren’t actually “there” for anything, but represent the voids that truly represent Populus around which the planets are arranged):

Simple enough, but I would instead recommend a different arrangement of planets to represent Populus based on all the rules we have above. Note how the center column has three “voids” to fill by planets, and there are four “voids” on either side of the figure proper. Rather than using the standard planetary hexagram, I’d recommend putting the three empyrean planets in the middle, with the Sun on top, Mercury in the middle, and the Moon on the bottom; then, putting Mars and Jupiter on the upper two “voids” with Venus and Saturn on the bottom two “voids”:

Note the symmetry here of the planets in the voids of Populus. Above Mercury are the three hot planets (the right-hand side of the Tetractys), and below are the three cold planets (the left-hand side of the Tetractys). On the right side are Mars and Venus together, representing the masculine and feminine principles through Fire and Water; on the left, Jupiter and Saturn, representing the expansive and contracting principles through Air and Earth; above is the Sun, the purely hot unmanifest force among the planets; below is the Moon, the coldest unmanifest force but closest to manifestation and density; in the middle is Mercury, the mean between them all. Around the planet Mercury in the middle can be formed three axes: the vertical axis for the luminaries, the Jupiter-Venus axis for the benefics, and the Saturn-Mars axis for the malefics. Note how Mercury plays the role of mean as much as on the Tetractys as it does here, played out in two of the three axes (Sun-Moon on the third rung, and Venus-Jupiter by being the one of the third-rung “parents” of the two elemental sphairai on the fourth rung). The Saturn-Mars axis represents a connection that isn’t explicitly present on the Tetractys, but just as the transformation between Air and Water (hot/moist to cold/moist) is mediated by Mercury, so too would Mercury have to mediate the transformation between Fire and Earth (hot/dry to cold/dry); this can be visualized by the Tetractys “looping back” onto itself, as if it were wrapped around a cylinder, where the sphairai of Mars/Fire and Saturn/Earth neighbored each other on opposite sides, linked together by an implicit “negative” Mercury. Further, read counterclockwise, the hexagram here is also related to the notion of astrological sect: the Sun, Jupiter, and Saturn belong to the diurnal sect, while the Moon, Venus, and Mars belong to the nocturnal sect; Saturn, though cold, is given to the diurnal sect of the Sun to mitigate its cold, and Mars, though hot, is given to the nocturnal sect of the Moon to mitigate its heat, with Mercury being adaptable, possesses no inherent sect of its own, but changes whether it rises before or after the Sun.

That done, I present the complete set of planetary arrangements for the sixteen geomantic figures, organized according to reverse binary order from Via down to Populus:

So, the real question then becomes, how might these be used? It goes without saying that these can be used for scrying into, meditating upon, or generally pondering to more deeply explore the connections between the planets and the figures besides the mere correspondence of rulership. Magically, you might consider creating and consecrating a set of seven planetary talismans. Once made, they can be arranged into one of the sixteen geomantic figures according to the patterns above for specific workings; for instance, using the planetary arrangement of Acquisitio using the planetary talismans in a wealth working. If you want to take the view that the figures are “constructed” from the planets much how we construct them from the elements, then this opens up new doors to, say, crafting invocations for the figures or combining the planets into an overall geomantic force.

However, there’s a snag we hit when we realize that most of the figures omit some of the planets; it’s only the case for five of the 16 figures that all seven planets are present, and of those five, one of them (Populus) is sufficiently weird to not fit any sort of pattern for the rest. Thus, special handling would be needed for the leftover planetary talismans. Consider:

The five-pointed figures omit the Sun and the Moon. These are the two visible principles of activity/positivity and passivity/negativity, taking form in the luminaries of the day and night. These could be set to the right and left, respectively, of the figure to confer the celestial blessing of light onto the figure and guide its power through and between the “posts” of the two luminaries.
The six-pointed figures omit the planet Mercury. Magically, Mercury is the arbiter, messenger, and go-between of all things; though the planetary talisman of Mercury would not be needed for the six-pointed figures, his talisman should be set in a place of prominence at the top of the altar away from the figure-arrangement of the rest of the talismans to encourage and direct the flow of power as desired.
The only four-pointed figure, Via, omits all three of the empyrean planets. As this figure is already about directed motion, we could arrange these three talismans around the four ouranic planetary talismans in the form of a triangle that contains Via, with the Sun beneath the figure to the right, the Moon beneath the figure to the left, and Mercury above the figure in the middle; alternatively, the figure could be transformed into an arrow, with the talisman of Mercury forming the “tip” and the Sun and Moon forming the “arms” of the arrowpoint, placed either on top of or beneath the figure of Via to direct the power either away or towards the magician.

The eight-pointed figure Populus, although containing all seven planets in its arrangement, does so in a “negative” way by having the planets fill the voids between the points proper. Rather than using the planets directly, it’s the silent voids between them that should be the focus of the works using this arrangement. As an example, if we would normally set candles on top of the planetary talismans for the other arrangements, here we would arrange the planetary talismans according to the arrangement for Populus, but set up the candles in the empty voids where the points of Populus would be rather than on top of the talismans themselves.

All told, this is definitely something I want to experiment with as I conduct my own experiments with geomantic magic. Even if it’s strictly theoretical without any substantial ritual gains, it still affords some interesting insights that tie back into mathesis for me. Though it probably doesn’t need to be said, I’ll say it here explicitly: this is all very theoretical and hypothetical, with (for now) everything here untested and nothing here used. If you do choose to experiment with it, caveat magus, and YMMV.

The Digital Ambler

Always Forward Between Heaven and Earth

Tag Archives: tetractys

Geomantic Shields versus Geomantic Tetractyes

More on Geomantic Epodes and Intonations

Mathetic Year Beginning Mismatch, and a Revised Grammatēmerologion

Arranging the Planets as the Geomantic Figures