Four Coin Divination of Hermes

So, between geomancy, grammatomancy, and astragalomancy, as well as a working knowledge of astrology both horary and otherwise, my divination needs are pretty much set.  I can determine what’s going on with a few throws of bones or letters or geomantic figures, and all these methods have served me well.  The problem is that, often, these oracles give me too much information when I don’t need anything more than a yes or no answer.  Geomancy is definitely geared for that with its inherent binary structure, but drawing up a full geomantic chart can sometimes be a little too much for something that needs a quick answer or confirmation from the spirits.  Although simpler than geomancy, grammatomancy and astragalomancy provide too much to interpret.  For instance, if I want to know whether a bottle of wine is sufficient payment for asking Hermes to help me out with something, getting “The one on the left bodes well for everything” is a little too vague and unclear for me.

Yes/no divination is one of the simplest forms of divination that can be done with tools.  You don’t need much more than a coin to flip, after all, but that seems a little too basic, and I do appreciate a bit of nuance.  I mean, imagine how body language, intonation, and subtle gestures can change a “yes” or “no” from your parents.  I suppose I could use whether the isopsephy of the letter or the sum of the astragaloi is odd or even for yes or no, but that seems like reaching a bit.  That said, I actually do have a divination system perfect for this, that of nkobos, a set of four cowrie shells I use in my ancestor and ATR work.  In it, you take four cowrie shells that have the “lump” shaved or cracked off so that it can fall on one of two sides; you ask your question to the spirits, throw the shells, inspect how many fall with the natural mouth up or down, and get your answer based on that.  This is identical to the use of chamalongos, or coconut shells, as used in Santeria and Palo and several other ATRs.  While I have a set of fed and prepared cowrie shells I use when working with my ancestors and spirits in those traditions, it always seemed weird to me to use them with other spirits, even though they provided a very useful tool in answering yes/no divination questions.  After all, cowries weren’t especially used in Greece or Europe generally, nor were coconut shells.  Add to it, I always kept getting hints that the methods of reading shells with ATR spirits was a little different from the theoi and other spirits I work with, like a different manner of interpretation was needed.

Thus, I decided to give up my cowrie shells and use them only with ATR spirits and ancestors, and make a new form of divination with the gods and spirits I normally work with generally and Hermes specifically.  I took the nkobo style of divination, modified it according to the hints I’ve been getting, and ended up with a four-coin divination method in honor of Hermes.  With no further ado, I present to you Οι Χρησμοι των Τεσσερων Νουμισματων, the Oracles of the Four Coins!  Though it is named after him, I’m making a deal with Hermes so that I can use this divination system not just with him but with any spirit with Hermes as ερμηνευτης and αγγελος, interpreter and messenger, between me and the other spirits I work with.

For this method of divination, you will need four coins, small enough so that they can all easily be held in the hand.  Four pennies are perfect for this, for those who live in the US.  Since I work near the Postal Museum in Washington, DC, the museum has one of those penny stretcher-impresser machines with four designs (Ben Franklin, Inverted Jenny, Inverted Train, and Pneumatic Tube stamp designs), so I went there during a recent monthly feast day for Hermes and got them, etched a Mercury symbol on the back, then consecrated them later that night.  You might also get four small gambling tokens, four Mercury dimes, four foreign coins, four ancient Greek coins, four flat stones with each side colored white or black, or other similar objects.  So long as you can establish which side is heads and which is tails, you’ll be set.

The process of divination is simple: ask your question, shake the coins up, cast them down onto a surface, and inspect how many are heads and how many are tails.  The order doesn’t matter; just count how many fall on which side.  In this manner, there are five possible results, and if we assume an ideal coin, they each have a 20% chance of falling (but, of course, the result is decided by the gods).  The meanings of each throw are generally as follows:

  1. All heads (Αγαθα, Blessing): Absolute yes.  The blessing of the gods.  Ease, swiftness, and success.  The gods are pleased with you and you have their aid.  You are acting on the blessed path in line with the will of the gods.  A yes from the heart.  The most positive of results.
  2. Three heads, one tails (Αναβασις, Ascent): Tentative yes.  Rephrase the question to be more specific.  The gods have already spoken.  Don’t ask what you already know.  Propitiating the gods may be helpful.  You may be missing something.  You may need further action to ensure success.
  3. Two heads, two tails (Τετροδος, Four-Way Crossroads): Simple yes but becoming “meh”.  All ways open.  Anything is possible.  You can do it if you so choose, or not if you don’t want to.  It doesn’t matter.  Freedom in any and all directions.  Keep asking more questions.  The gods don’t particularly care whichever way you choose.
  4. One heads, three tails (Καταβασις, Descent): No, perhaps reluctantly.  The situation is not going in that direction.  You’re barking up the wrong tree.  Nothing’s working against you, but it’s just not going to happen.  The gods have judged the matter against you.
  5. All tails (Ατηρια, Evil): Absolute no, a spiteful or angry no.  Don’t ask and stop asking.  Major problems impeding you from your situation.  The gods are angry at you.  You may be cursed, crossed, or stuck in too much miasma.  You need purification, fasting, and propitiation.  You plan or ask about unlawful and amoral things.  Don’t get yourself involved.  The most negative of results.

In a way, this is a lot similar to how I had originally planned the use of my two ten-sided dice divination.  Instead of it being heads or tails on four coins, I rolled 2d10 using a standard tabletop gaming set of dice.  In that system, 99-80 would be associated with Agatha, 79 through 60 with Anabasis, 59 through 40 with Tetrodos, 39 through 20 with Katabasis, and 19 through 00 with Atēria.  That, too, was also based on shell divination, but it was mostly a means by which I could use all seven of my RPG dice in addition to the grammatomancy d12 and geomancy d4, d8, d20, and d6.  Ah well, live and learn.

In addition to getting quick yes/no answers from Hermes on a variety of topics, one of the reasons why I developed this system of divination is so that I can interact with all of the Greek gods and goddesses and heroes and demigods in order to ascertain their wishes and will.  Yes, the coin divination method belongs to Hermes proper, but remember that Hermes is the messenger god who goes between gods and men and is a friend to them both.  The coins can be thrown to ask any spirit and any god what their will is through the intercession and messages of Hermes, who communicates between us and them.  I find this a very valuable thing in my work, although I may resort to other forms of divination such as reading omens or, should I ever develop a proper hand at animal sacrifice, haruspicy.

Theoretically, this is similar to making a geomancy figure: all we need is a way to get a binary result four times, then compare how many of each binary result we get.  You could draw four lines of random dots each (odd or even), pluck up four potatoes and count how many eyes are on each (odd or even), roll a die four times (odd or even), pull four playing cards (red or black), or the like.  That said, I prefer using coins for Hermes since, after all, he is a god of commerce and coins are one of his symbols.  Plus, keeping four coins in your pocket is rather convenient and easily disguised.

Since this is a coin-based divination method, a variant of sortilege, I suppose the proper term for it would be numismatomancy, literally “divination by coins”.  And, since we’re able to make a well-formed word ending in “-mancy”, why not make some ritual numismatomancy?  Honestly, I could write up new rituals for all this, but after describing ritual astragalomancy and the consecration rituals and how to ask a query of the gods, you may as well just review that and adapt it accordingly for the coins from the knucklebones.  Similar rules for how the coins bounce and fall and their relative positions of how they fall can be devised, as well, to get even more nuance out of a single throw of the coins.

As I mentioned, the order the coins are thrown in don’t matter, just how many fall heads or tails.  However, if you draw a distinction between the coins or note the order in which they fall, you could also do geomancy using these.  If you have coins A, B, C, and D, then coin A would relate to the Fire line, coin B to the Air line, coin C to the Water line, and coin D to the Earth line; a throw of heads would mean that line is active, and a throw of tails means that line is passive.  However, the idea came to me that, well, if there are 16 possible combinations of these throws, and if the divination system is assigned to Hermes, then why not take a clue from astragalomancy and assign each combination to a different aspect of Hermes?  It’s not unreasonable to do this; astragalomancy has certain throws relate to Hermes Tetragonos (Hermes Four-Sided, i.e. Herm), Hermes Diaktoros (Hermes the Leader), Hermes Paignios (Hermes the Playful), and Hermes Kerdemporos (Hermes who Brings Gain in Trade).  Besides, I’ve seen Sannion do something similar with his Net of Orpheus, where he links different throws of coins to the different members of the pantheon of the Thiasos of the Starry Bull (though he also has his own Coins of Hermes divination method that I know nothing about, the jerk!).  I may approach Hermes and see how he feels about such a method, and if he likes the idea, which epithets he’d like to ascribe to which throw.  For instance, the throw of tails-heads-tails-heads, which in geomancy would be given to the figure Acquisitio, could be given to Hermes Kerdemporos based on the similarity between the geomantic figure and the epithet of Hermes.  It’s an idea for me to explore.

Speaking of Sannion’s divination system, he mentions the following when describing his Net of Orpheus, which he made as an Orphic variant of the Chain of Saint Michael, a Sicilian/Italian derivative form of geomancy using a series of four Saint Michael medallions in a chain, not unlike the opele chain of a babalawo (diviner priest) of Ifá.  Sannion says:

That said, I do feel a little culturally appropriative since it comes from a living and lineaged tradition (Italian folk Catholicism) which I am not a part of (despite my heredity: my mom was as thoroughly Americanized as they come) but on the other hand I’m not claiming any such thing or the cachet associated with doing so – I’m being perfectly upfront that I found this system and modified it for my own uses, so I kind of hope that cancels that out. (On the other hand Orpheus had a reputation for traveling around and stealing people’s religious tech, as does Melampos the other founder of Bacchic Orphism, so I guess that just means I’m keeping the tradition alive!) Plus, while I think it entirely within the realm of possibility that this technology developed independently in the Mezzogiorno and nevertheless respect the lineage of those who are working with it now – there are some striking similarities between it and Ifá and Mẹrindínlógún, to the point that I’m a little suspicious of its antiquity.

To be honest, I don’t think it’s that big a deal.  Yes, I am deriving a similar form of divination as he was from a similar-ish source.  That said, the Sicilian Chain of Saint Michael is a variant of geomancy, as I see it, just with the association of particular saints to the figures (which is a helpful correspondence for Catholic or conjure-minded geomancers to know).  Every form of geomancy as well as Ifá, Mẹrindínlógún, Nkobo, and Chamalongos all come from Africa and all share a binary system of attaining occult knowledge.  Then again, the system itself is so simple and direct that it’s not inconceivable that other cultures in other eras and areas could have devised similar systems on their own, like the Chinese system of jiaobei.  I see no harm in appropriating and modifying a system to “make” a new one of my own, especially if it can help ascertain the will of the gods better and more clearly.  If I can’t tell whether Hermes wants one bottle of wine or two, or whether he wants me to drop off a particular offering at a crossroads or just throw it in the trash, nobody is going to be particularly happy with the results.

Since getting four pennies is easy for me to obtain, as is getting those stretched pennies from the Postal Museum (which is as much a temple to Hermes Angelos as I’ll ever seen one), I’m considering getting a bunch of these together, consecrating them, and selling them on my Etsy, or just taking custom commissions for them.  What do you think?  Would you be interested in such a set?  Lemme know in the comments if you do, and if the response is strong enough, I might make a permanent listing on my Etsy page for consecrated coins for the purpose.

Search Term Shoot Back, September 2013

I get a lot of hits on my blog from across the realm of the Internet, many of which are from links on Facebook, Twitter, or RSS readers.  To you guys who follow me: thank you!  You give me many happies.  However, I also get a huge number of new visitors daily to my blog from people who search around the Internet for various search terms.  As part of a monthly project, here are some short replies to some of the search terms people have used to arrive here at the Digital Ambler.  This focuses on some search terms that caught my eye during the month of September 2013.

“visualize offerings water light incense flowers”  — Visualized offerings are good for some spirits, or for complex astral rituals.  However, for most purposes, why not actually get the physical offerings themselves, and offer actual water, candles, incense, and flowers?  They’re more concrete and, if the spirit is “low” (i.e. an elemental spirit, genius loci, shade, etc.), they’ll be able to benefit more directly since they’re closer to the physical realm.

“munich manual english” — As far as I’m aware, there is no full translation of the Munich Manual into English, though I have translated some excerpts from it (which you can find under the Rituals menu above).  That said, it’s been suggested I take that on as my next big translation project, and I think I’ll oblige.  No idea when it might be ready, but it wouldn’t be unwelcome, as far as I can tell. 

“blessing the sator square” — It’s unclear how the SATOR Square was actually used, only that it came up time and again since the early Roman empire as a kind of memetic charm.  One theory is that it acted as a sign for hidden Christians, since reorganizing the SATOR Square can yield a different arrangement of two PATERNOSTERs intersecting at the N, with two As and two Os leftover (alpha and omega).  As a charm, I believe that the mere construction of the SATOR Square suffices to “bless” or charge it, though other consecrations can be added on top of it (cf. the second pentacle of Saturn from the Key of Solomon).  Depending on the purpose used, you’d consecrate it as you would any other talisman, charm, or tool.

“eskimo fucking” — I assume that’s how eskimos happened in the first place.  (Also, what…?)

“geomantic designs for capricorn” — You’d want to go with the geomantic figures for Carcer or Populus and their associated geomantic sigils.  Carcer is linked to Capricorn through its association with Saturn retrograde; Populus is directly associated to Capricorn in Gerard of Cremona’s system of astrological correspondences (which I use personally in my geomantic work).

“if i write de name of ma boyfriend n put it in de annoiting oil n pray over it can it makes him love like crazy?” — First, I’m honestly impressed people write unironically in an eye-dialect like this; after all, written communication is meant to help spoken communication cross time and space in a way that sound vibrations can’t, and writing as one speaks is certainly not a wrong way to do it.  As for the question itself, the answer is (as it often is in magic) that it depends.  Writing his name on a hoodoo-style name paper, and using something like “Come Here Boy” or another love-drawing/love-forcing oil on it with a prayer or repetition of a psalm over it, it can certainly induce love or love-craziness.  Caveat mage, though; Jason Miller has a story about someone who did this on a particular girl, and not only did the girl fall head-over-heels in love with him, but she ended up becoming an overzealously jealous, codependent, clingy stalker that the dude only wanted to get rid of after, like, two weeks.  Be careful what you wish for, my readers.

“how to kssss hole body” — I hope you wash that hole first.  I also hope you can tell me what exactly you were looking for.

“what to ask during geomancy” — Anything you want, really; geomancy is another system of divination, and divination exists to answer questions.  That said, it helps to ask questions that are clear, concise, and concrete: vague, open-ended, undefined questions tend to work badly with geomancy.  A good question in geomancy often takes the form of “will X happen with conditions Y?”, with X and Y clearly defined and stated.

“how to convert geomantic figures into binary” — Pretty simple, actually.  The method I use is to use a four-bit number, interpreting a single point (active element) as 1 (logic high) and a double point (passive element) as 0 (logic low).  The first bit in the number is the fire line, the second bit the air line, the third bit the water line, and the fourth bit the earth line; in other words, if you read a four-bit number from right to left, it’d be the same as reading a geomantic figure from top to bottom.  Thus, 0101 is Acquisitio, 1000 is Laetitia, 1101 is Puer, 1111 is Via, 0000 is Populus, and so forth.

“how long can you keep holy water in a bottle” — It depends on the type of holy water, and for what.  From a religious standpoint, the blessing may “wear off” over time, or may be depleted if anything unclean contaminates the whole bottle.  Any liquid can get physically contaminated over time without proper preparation, so it helps to make sure the bottle you’re using is thoroughly sanitized and that the water is used in a short time, often no longer than five days.  Using holy water that uses herbs like basil or hyssop can also easily get contaminated, and you’ll see a wispy web-like growth in the bottle over time.  For this reason, I make my holy water with just purified water and salt that I boil for twenty minutes and pour it into only sanitized bottles I’ve washed out with boiling water and soap.

“house blessing preparation” — Get a few white candles, incense that stings the eyes and nose, incense that sweetens the air, holy water, some clean white clothes, and a book of religious texts or prayers of your choice.  Wash yourself thoroughly and ablute in the holy water, meditate and focus yourself, dress in the clothes while praying for protection and light for yourself, light a candle in each room of the house, pray in each room of the house for protection and guidance in the house, waft the sharp incense in each room of the house, pray that all evil and defilement be removed from the house, sprinkle holy water in each room of the house, pray that all impurity and filth be washed from the house, waft the sweet incense in each room of the house, pray for happiness and joy to fill the house, pray to offer your thanks and for the assistance received, relax. 

“howtoinvokeadonai” — Youusehisnameinaprayer,begginghimforhispresenceandaidtohelpyouinyourlife.Youdon’thavetobeJewishorChristiantocallonADNI,butyoudoneedtohavefaithinhispowerandbeabletoanswertotheresponsibilityofcallinguponhim.AnynumberofprayersintheSolomonicandHermetictraditions,goingasfarbackasthePGMatleast,usethenameADNI,sohaveatandexplorewhatusesyoumightcomeupwith.  Also, please never type like this ever, even if you’re on a lot of DMT.

“hermetics most feared adversary” — I think it’s sloths, for some reason, but I’m unsure why.  Alkaloid herbs may have been involved, or so I’m told.

Geomantic Mathematics

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

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

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

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

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

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

Example Geomantic Tableau

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

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

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

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

The Geomantic Emblems and their Rulerships

Last time I brought up the geomantic emblems (previously called geomantic superfigures, 256 16-line “figures” that each contain all 16 geomantic figures within themselves), I described a few bits about the elemental representation and force within each figure.  In the process, I described a method where each geomantic emblem can be elementally analyzed and given an “elemental essential” rulership, by taking the “pure elemental” lines, and also how to split up the emblems into four figures to give them an entire geomantic chart as background.  However, I also mentioned that all 256 emblems could be reduced to a set of 16 by rotating them around; in other words, there are 16 sets of 16 topologically equivalent geomantic emblems.  16 is a significant number in geomancy, as my astute readers may have noticed, and I brought up how tempting and tantalizing it would be to assign a set of rulerships that correspond these 16 sets of geomantic emblems to the 16 figures of geomancy.  I didn’t have the method done just then, but I’ve finally come up with a way to link the two sets of symbols.  The correspondences are, using the list from last time:

  1. Laetitia: 1000010011010111
  2. Carcer: 1000010011110101
  3. Fortuna Minor: 1000010100110111
  4. Puer: 1000010100111101
  5. Acquisitio: 1000010110011110
  6. Populus: 1000010110100111
  7. Coniunctio: 1000010111100110
  8. Albus: 1000010111101001
  9. Tristitia: 1000011001011110
  10. Rubeus: 1000011010010111
  11. Amissio: 1000011010111100
  12. Puella: 1000011011110010
  13. Fortuna Maior: 1000011110010110
  14. Caput Draconis: 1000011110100101
  15. Cauda Draconis: 1000011110101100
  16. Via: 1000011110110010

How did I go about finding these correspondences?  A lot of math, hand-wringing, and sangria, that’s for sure.  If, dear reader, you’re interested in finding out how I corresponded the figures to the emblems, please continue after the break, but I’m going to warn you.  This post is long and at times tedious, and is full of binary mathematics and lots of 1s and 0s.  This post is only for the hardcore geomancy geeks like me out there, and it helps to have a solid footing in computer science, basic/low-level programming exercises, and binary/discrete mathematics.  Even I’m kinda shocked by how lengthy and pointlessly in-depth this post is, if that’s any indication of what you’re in for.  If you want to stop reading now, I forgive you and completely understand.  If you want to find out why I allocated the above emblems and their rotated variants to the figures like I did above, read on.  Either way, expect another post in the near future on how to use these emblems, their geomantic rulership, and elemental analyses in magic and divination!

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Geomantic Superfigures

Back in my college days (all those many years ago, all two of them), I studied computer science, as did many of my friends.  Sometimes we’d solve theoretical or coding problems for fun over dinner in the dining hall, or make references to them in jokes or details about our lives.  It made sense, after all, especially when that’s all you’re studying for weeks on end most of the year.  One time, while walking back from class to our apartments, some of my friends and I were talking about strings.  Not strings as in balls of yarn, but ordered sequences of symbols.  For instance, my name, “polyphanes”, is a string composed of several letters in the Roman alphabet.  Other strings are “euphony”, “polygraph”, “cat”, and “polyandrous”; some could be things like “123456”, where the symbols are Arabic numerals; “10001010011”, binary numerals; or “TCAGAGAGCT”, DNA nucleotides.  I think you get the idea.  Strings can have many symbols (“polyphanes”), one symbol (like “p”), or even no symbols (the so-called empty string, or “”).

Strings are very useful in computer science, and are a very robust tool in the hands of someone who knows how to use them.  For instance, you can take a snippet out of a string to make another string, specifically substring: “p” and “poly” are substrings of “polyphanes”.  They both are strings in and of themselves, but appear within the larger string “polyphanes”.  Substrings are strings that are composed of part or all of another string that is at least as large as the substring.  The empty string, “”, is by definition a substring of any string, including itself.  Now, say you have several strings “polyphanes”, “polygraph”, and “polyandrous”.  Say you want to know whether there exists a substring common to all of them.  From above, we know that the empty string is part of all of them, but that’s trivial to find out and doesn’t help us any.  We know that “p” is part of all of them, as is “a”, but “g” only appears in “polygraph”.  Again, this is mostly easy to figure out, but say you want to know what the longest common substring is between them.  In this example, the longest common substring (LCSubS) is “poly”, with a length of four symbols.  Finding the LCSubS is nontrivial, and can be a pretty complex problem in its own right.  The LCSubS problem comes into heavy employ when dealing with DNA sequencing, when you have several strands of DNA and want to find the longest common sequence of nucleotides that they may have in common.  If there aren’t any, we return the empty string, “”, meaning that there is nothing common at all between them.

Let’s flip the idea on its head, now: say you have several strings “rec”, “cyc”, “l” and “ab”.  Is there a word (a string of Roman letters that makes sense in the English language) that makes use of all of these strings?  Sure: “recyclable”: it can be formed by combining the above strings in a particular way.  Viewed from the point of view of substrings, “recyclable” has “rec”, “cyc”, “l”, and “ab” as substrings.  In this case, “recyclable” is a string and the shorter ones are substrings; alternatively, “rec” and the rest are strings and “recyclable” is a superstring.  A superstring is a string that contains several other strings.  Makes sense, right?  Just as, above, we wanted to find the LCSubS, we can also try to find the shortest common superstring (SCSupS).  “Recyclability” is one possible superstring, but it’s not the shortest.

It was this SCSupS problem that my friends were talking about in particular, and I mostly took a backseat to this conversation (I wasn’t in their class that was discussing this problem).  However, it got me to think about one of my hobbies: geomancy.  In geomancy, the geomantic figures like Puer or Albus can be seen as strings of one or two dots, or as I prefer, binary numerals.  If we let single dots (active elements) be represented by the binary numeral 1 and double dots (passive elements) by the binary numeral 0, and order the symbols from left to right as we would a geomantic figure from top to bottom, we get the following strings to represent the geomantic figures:

Figure Binary Representation
Populus 0000
Via 1111
Puer 1101
Albus 0010
Puella 1011
Rubeus 0100
Laetitia 1000
Caput Draconis 0111
Tristitia 0001
Cauda Draconis 1110
Amissio 1010
Acquisitio 0101
Carcer 1001
Coniunctio 0110
Fortuna Maior 0011
Fortuna Minor 1100

I prefer these binary representations, myself, when I need to illustrate the structure of geomantic figures in a text-only medium.

Anyway, you have these four-bit strings of binary numbers that correspond to the sixteen geomantic figures.  They’re each strings.  Now, normally in geomancy we’re concerned with adding figures together (such that Puer and Albus make Via, or 1101 + 0010 = 1111).  But in the context of strings, why not try applying this idea of SCSupS to the geomantic figures?  For instance, there are works of geomancy that use five-lined figures, or even six-lined ones.  Heck, the I Ching, a kind of Chinese geomancy, with its 64 hexagrams can be considered in a way similar to this.  Let’s take Hexagram 22, 賁 (Adorning), which looks like the following:

We can consider it to have the binary structure of 100101 (using a 1 to represent a solid Yang line and a 0 to represent a broken Yin line).  If we want to take a substring of length 4 from this string, we have four choices: 1001 (characters 1 through 4), 0010 (characters 2 through 5), or 0101 (characters 3 through 6).  In this case, we could say that the strings of length 4 are substrings of the string of length 6, or we could say that the strings of length 4 have the string of length 6 as their superstring.  The overlap provided by the figures helps 100101 to be the SCSupS for these strings; we could put them end to end, like 100100100101 (read: 1001-0010-0101), but that’s really long with a length of 12; we could overlap a few of them to make 00101001 (read: 0010-0101-1001, with overlap between the 010 of the first two figures and the 1 of the last two figures), but that has length 8.  100101 is the shortest common superstring with a length of 4, because the overlap between the substrings is at their max (three symbols between the first two and the last two figures).  It’s kinda nifty.

So, if you can overlap some of the figures to form a superstring, why not try to make a superstring that contains all 16 geomantic figures to make a geomantic superfigure?  This took some doing, and I eventually wrote a program to cycle through and figure out the minimum length of the superstrings that do this, but it turns out that there are 256 possible geomantic superfigures of length 19: a “geomantic figure” of a sort that has 19 rows of dots, with each substring of 4 rows being one of the sixteen geomantic figures.  Why is 19 the minimum length for a geomantic superfigure?  The math is easy: from the example above using Hexagram 22 which has a length of 6 and has three substrings of length 4, where each figure overlaps with the next using three of its rows, we can say that “for a geomantic superfigure, the shortest possible length is the number of figures contained in it n + 3″.  Since there are 16 figures, a geomantic superfigure must be that plus three, or 19.

Consider an example:

0000100110101111000
0000 0001 0010 0100 1001 0011 0110 1101 1010 0101 1011 0111 1111 1110 1100 1000
Populus, Tristitia, Albus, Rubeus, Carcer, Fortuna Maior, Coniunctio, Puer, Amissio, Acquisitio, Puella, Caput Draconis, Via, Cauda Draconis, Fortuna Minor, Laetitia

In this case, we overlap Populus with Tristitia with Populus’ lower three lines and Tristitia’s upper three lines (0000 : 0001 = 00001), then we repeat the process with the next figure (00001 : 0010 = 000010), and so on.  We end up with the string 0000100110101111000 of length 19 which, for every possible substring of length 4, contains all 16 geomantic figures.  In other forms of representation, such as dot or line notation, we can get the following visual forms:

 

The third style, the intersecting lines, is interesting, and brings to mind bindrunes (special “master” runes that are composed of other runes) or supersigils that combine other sigils.  The central idea is the same: combine several shapes, strings, or figures to form a more cohesive larger one.  Here, with this geomantic superfigure, it composes the essence of all the geomantic figures in a particular order (Populus to Tristitia to Albus to Rubeus…).  That order of the figures, how different states flow from one to another, is encapsulated in a single glyph.  Further, if you connect the ends of the Laetitia on the bottom to the top of the Populus, you have a neverending loop, a cycle of manifestation or transformation in the figures.

As I mentioned before, there are 256 of these geomantic superfigures, or 16² superfigures.  Some can be looped back onto itself, and some can’t, but each has the same 16 figures as its components in different orders.  Each order and superfigure has meaning, like a kind of geomantic universe of its own, and can be employed in some kinds of geomantic sigil magic.  This isn’t something I’ve actively used or dealt with in my own work yet, but it’s interesting to note, and if nothing else, is an interesting academic and mystical exercise.  However, I feel like this is too interesting to not put up for aspiring geomantically-minded mages to never have heard about.  If you want the complete list of 256 geomantic superfigures, let me know and I’ll send you a file listing them.