In the process of geomantic divination, one of the first things we do as geomancers is actually construct the whole chart from the first four Mothers that we derive by a random means.  Through this, we calculate the four Daughters, the four Nieces, and the four figures of the Court.  The Court, as my geomantically-inclined readers are already aware, is composed of the Right Witness, the Left Witness, the Judge, and the Sentence.  Throughout the history of geomancy, the Judge has nigh-universally been seen as the most important figure of the entire chart, and every interpretation must rely on the Judge in at least some way to understand what the chart proclaims for the query asked of it.  However, the Judge isn’t just some random figure; there are intricate mathematical relationships between the Judge and the rest of the chart, one of the effects of which is that the Judge must be an even figure.  However, the reason why this is on a higher, more philosophical level aren’t usually stated clearly.  Between a recent email about the Judges of geomancy and a discussion on the Facebook geomancy group, there’s a bit about the Judge that I feel might need a little unpacking from a higher, theoretical level to understand why it is what it is and how it relates to the process of interpreting the geomantic chart.

The email sent to me asked several questions, but they can be broken down and rephrased into the following.

• Why are the Judges even?
• What does it mean for a Judge to be an even figure?
• Do the mathematical limitations of what can and can’t be a Judge make us lose out in geomantic divination?
• Does the Judge miss anything as far as the whole answer to the query goes, and if so, where can we find it?

I answered the dude in the email, but I’d like to flesh out my answers a bit more fully here.

First, the Judge must be even due to the mathematics in the geomancy chart.  A paper by Marcia Ascher, “Malagasy Sikidy: A Case in Ethnomathematics” (Historia Mathematica 24, 1997, pp376—395) fully describes the reasoning as it is in Madgascar’s form of geomancy, but the exact same logic works in Western geomancy, as well.  For the mathematically disinclined among us, the idea is that the Judge is ultimately the sum of the four Mothers and four Daughters:

Judge = Right Witness + Left Witness
Judge = (First Niece + Second Niece) + (Third Niece + Fourth Niece)
Judge = ((First Mother + Second Mother) + (Third Mother + Fourth Mother)) + ((First Daughter + Second Daughter) + (Third Daughter + Fourth Daughter))

When we add two figures together in geomancy, we’re not really coming up with a numeric sum of points between the two added figures, but coming up with the parity (even or odd) of the number of points between them.  Further, recall that there must be an equal number of points in the four Mothers as there are in the four Daughters, because they’re all formed from different arrangements of the same points.  Because geomantic addition (a variant on the logical/mathematical function called the “exclusive or” or XOR function) only preserves parity, what the Mothers and Daughters add together to numerically doesn’t matter, because their parity will still match.  Thus, because the four Mothers are together summed to find the Right Witness and the four Daughters together to find the Left Witness, both the Right and Left Witnesses must share the same parity.  Two figures that are both odd or both even, i.e. share the same parity, will add together to form an even figure.  Thus, because both Witnesses share the same parity, the Judge must therefore be an even figure.  It can be shown, further, that the Judge is the only figure produced in the process of geomantic divination that this is necessarily true; any other figure in the chart may be odd or even, but only the Judge must be even.  Because of this, we use this mathematic property to help us figure out whether a chart is mathematically valid and well-constructed; if we find that the Judge is an odd figure, then there’s something not right in how the chart is calculated, and we need to find out where the error lies so we can correct it before we continue with interpreting the chart.

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.

What does it actually mean in real-world terms, then, for these Judge-eligible figures to be “objective”?  It means that they represent certain states of the cosmos that can be seen from both sides of a situation, something that plays out externally, concretely, and factually in a way that can be colored, but not tampered, by emotional, mental, or otherwise subjective states of perception that only apply in a one-sided way (note the “both sides” and “one-sided” phrasing here and how it applies to even versus odd).  This can be seen by how the different inverse pairs of figures play out in their significations, apart and away from any correspondence to sign or planet or element:

• Aquisitio and Amissio relate to notions of obtaining, losing, acquiring, or missing some object.  You can dress it up however you want or arrive at it by different means (inventing, destroying, getting something on your own, getting someone to get rid of something for you, etc.), but at the end of the day, you either have something or you don’t.
• Carcer and Coniunctio relate to notions of being isolated, conjoined, restricted, freed, cut off, or brought into some process.  You either have freedom and choices, or you don’t.
• Fortuna Maior and Fortuna Minor relate to notions of independence or dependence.  You either can do something on your own, or you can’t; you either need outside help or resources not normally available to you, or you don’t.
• Populus and Via relate to notions of passivity, activity, inertia, liveliness, stagnation, passion, multitude, or solitude.  There is either nothing going on, or there is something going on; things either change or they don’t.

If it sounds like a very black-and-white, cut-and-clear, binary way to view the universe, it’s because it is.  While I’m all about seeing the fine gradations of how things play out on large scales, understand that the cosmos provides a truly limitless spectrum of experiences, and often look for third, fourth, and other choices when presented with a dilemma, it doesn’t change the fact that the cosmos itself doesn’t always operate in a fuzzy, shade-of-grey manner; after all, you can’t have something halfway, either you have it or you don’t, just like how a light switch cannot be both “off” or “on” or halfway between them.  There is no third option, no halfway point, no spectrum involved in these dichotomies.  Geomancy itself is based upon binary mathematics, the numerical science of what is and what is not, what is true and what is false, what is odd and what is even, without allowing for anything in the middle of two choices.  However, when you have a whole situation and cosmos presented before you, we start to find shades of grey developing when we have a number of such binary choices or qualities in the same place, conflicting and meeting with each other; those subjective states are emergent properties of an otherwise objective system, where we have a multitude of reactions based on a single action.

What are those reactions, those shades of grey, those subjective states?  That’s where the odd figures come into play:

• Puer and Puella reflect the old-school gender dichotomy of male and female, emitting or receptive, extroverted or introverted, visiting or hosting.
• Laetitia and Tristitia reflect the two emotional states of joy or sorrow, jubilation or grief, uplifting or depression, optimistic or apprehensive.
• Albus and Rubeus reflect the two states of the mind which can be calm or turbulent, reflective or chaotic, wise or foolish, impotent or violent.
• Caput Draconis and Cauda Draconis reflect the two perspectives to a situation of beginning or ending, constructive or destructive, fortunate or unfortunate, opening or closing.

Note that these are all things that cannot really be shared, and are unique to each and every person, each and every “side” in a situation.  One person’s trash is another person’s treasure, after all; what I perceive as good, you might perceive as bad, and what I may be fearful of, you may be eagerly anticipating with relish.  Plus, these figures are much more liable to be considered ends of a spectrum rather than a strict dichotomy; ask any genderfluid person how male or female they feel on a given day, if either at all, and consider how truly complex the mind is in a troubling situation where some parts of it might be chaotic and other parts tranquil or focused, and how much each set of parts might be of either state.  Moreover, even within a single person, some of these internal subjective states can change from moment to moment, but it doesn’t change necessarily what actually happens externally to them unless they make an external action.  For instance, upon realizing that I’ve completed a long-running task, I might go through a series of emotions about it ranging from wistful nostalgia to exuberant gratitude that it’s over to regret that I could have done more while I was in the process of it; none of these actually change the fact that the task is complete, hence the subjective/objective distinction.  Further, while we might be able to witness these states of gender, emotion, mind, or perspective in another person, they are nothing actually realized in the real world without a concrete action being taken.

Because of all this, when the dude who emailed me asked whether it’s a loss for us as geomancers that the Judge is limited to one of only eight figures from the total of sixteen, I emphatically replied to the contrary: that the Judge must be even is simply part of how geomancy works, which cannot be compared as it is to other forms of divination like Tarot or runes where each symbol is obtained independently of the others, and that the Judge’s even parity gives us both a practical guide to checking the chart in addition to an insight into what the figures themselves are.  If this limits us at all, it does so that we cannot make a faulty, subjective, misguided judgment that would cause more harm than good by relying overmuch on subjective, internal feelings that do not have a concrete place to play in the actual world; in such a case, it’s not a limitation of us being unfairly cut off from a world of possibilities that we should have a right to explore, but a limitation protecting us from a world where things make even less sense than they already do, and thus where we have no business being.  Remember that we come to geomancy (and divination generally) for advice, guidance, and answers; it would do us no good to simply validate our feelings or be told that we should feel some other type of way when what we need is concrete information about what happens and what to do about it.

Now that we understand the full import of why the Judges must be even from both a mathematical and philosophical standpoint, let’s move on to that final question: does the Judge lack anything with respect to the answer for the chart?  I would say that no, it doesn’t, because the Judge is the full, whole, and complete distillation of the entire geomantic chart into a single figure, and as such represents the entire answer by itself.  This is the reason why it is the single most important figure in the chart, because it encapsulates the entire thing from start to end, and as I’ve suggested before, in a well-constructed reading, the Judge will always answer the query as best as one of those eight even figures can.  The thing is, however, that situations and queries presented to geomancy can often be complex, and the Judge being just one figure still must answer in a way that a single figure can, which is necessarily high-level and possibly vague.  It’s not that the Judge “omits” anything, but that some of the finer details that play into the high-level answer cannot be answered with a single figure alone.  Thus, we have the rest of the figures in the chart and all the other techniques available to us: the Witnesses, Via Puncti, perfection, company, elemental analyses, etc.  If the Judge, even at its high-level station, can answer the query on its own, great!  If not, then the Judge’s word sets the context and frames the information that is delivered to us by the rest of the chart and the rest of the art of geomancy.  In some ways, this is the opposite to the methods of judgment used in other divination systems, such as Tarot or runes, where you’re given a bunch of details that together must build up to a final judgment, but in geomancy, the judgment is given to you right off the bat via the Judge, and it’s up to the geomancer to dig deeper according to their level of ability, curiosity, and need for such details.

This all leads to something that was asked about on the Facebook geomantic group.  As some of my readers may recall, Dr Al Cummins recently hosted his set of geomancy classes, which were a resounding success (and he looks forward to having more in the future).  Someone in the Facebook group was in them, and noted something that Dr Al said about a chart “avowing or disavowing” the query, but wasn’t clear on what Dr Al meant by that, and how it relates to notions of perfection, aspect, and so forth.  I chimed in with my understanding of what Dr Al meant, which he validated in the same thread.  The notion of avowing or disavowing is a little-known distinction of some Judges taken from some Renaissance geomancers, where the Judge either clearly answers the query as phrased or not.  In other words, a Judge avows or owns the query if the nature and significations of the Judge clearly and explicitly relates to the nature of the query to give a straightfoward answer all on its own; a Judge disavows or disowns the query if its nature and significations have no apparent relation to what it asked.  Thus, an avowing Judge resonates with what’s being asked, and a disavowing Judge does not.  If the Judge avows the query, then little else needs to be said beyond the significations of the Judge itself in order to give an answer to the querent, though it might be minimal and further exploration can be useful to be more detailed and exact with the answer; if the Judge disavows the query, then further inspection, interpretation, or investigation are needed to figure out why the Judge is what is is, why it says what it says, and how it relates to the query at hand.

Consider a case where the querent asks “will I get my lost wallet back?”.  This query falls under the general field of questions of dealing with possession.  The two figures that avow this type of query are, naturally, Aquisitio (will possess) and Amissio (will not possess).  If we get Amissio as the Judge for such a query, then we can say that the Judge avows the query, the answer is “no, you will not get your lost wallet back”, and we’re technically done at that point; investigating the rest of the chart may tell us where it is, what happened to it, what can be done to recoup any losses, who might have found it if anyone, and so forth, but none of that is technically needed to give the core answer of “no”.  However, if we get another figure like Coniunctio as the Judge for such a query, which relates more to connections rather than possessions, then we’d say that the Judge disavows the query because there is no natural relationship between the semantic field of the Judge and that of the query; Coniunctio does not clearly say “yes” or “no” to such a query.  In this case, we’d have to start looking deeper into the chart to figure out what Coniunctio actually means: does it mean that you’ll have to be in the market to get a new one because the old one was lost, or that you’ll have to meet with someone to get it back, or that you losing it was part of a toll or sacrifice you had to make to get further along, or that you’ll find it again through happenstance and the goodwill of spirits?  It’s unclear from the Judge itself; though the Judge still gives an answer to the query, it’s too high-level and encapsulates too many things to give a clear “yes” or “no” answer.

Going back to the binary dichotomy of the objective figures, if you consider the semantic field of a query that has one of two end results (e.g. “I will get my wallet back” or “I will not get my wallet back”), then although the end result must be one of two choices, the power of geomancy is that it plays out the whole scheme of the cosmos before us in all its shades and variations before it gets to one result or the other.  Judges that avow the query simply reflect the dichotomy of a situation, no ifs, ands, or buts allowed.  Judges that disavow the query give a “shade of grey” answer that must be analyzed until it can be judged on what side of the threshold it actually falls on, like finding out whether a given electrical current will actually trip a circuit breaker only by playing things out and tracing out the circuit and voltage; at the end, the breaker will be tripped or it won’t, but it remains to be seen whether it will or not until it actually happens.  That investigation is what a disavowing Judge mandates.

I should mention, however, that a disavowing Judge doesn’t mean that the Judge doesn’t answer the query.  After all, the Judge is still the encapsulation of the whole situation, and still contains the answer as much as one that avows the query; an insightful and experienced geomancer can probably get a good feel for what the Judge says regardless of whether it avows or disavows the query.  The distinction here is that an avowing Judge readily answers the query asked of the chart since it naturally falls into the binary dichotomy of the query, and a disavowing Judge is focused elsewhere in the situation than that is asked, but still contains the answer within itself.  It might be theorized that disavowing Judges, because they demand a deeper investigation into the chart, indicate that the situation is deeper than what is asked and that there’s more behind the scenes of the querent’s life than what they say, but that’d be a bold claim even coming from me.  More realistically and conventionally, it’s better to say that a disavowing Judge will still answer the query, but it’s focused on an answer that’s not “yes” or “no”, indicating that there’s more to say than just that.