Understanding and Employing the Geomantic Emblems

Alright, so now that we’ve gone over what the geomantic emblems are, how we can analyze them elementally, and how we can assign cycles of the emblems to the sixteen figures of geomancy, I wanted to give a bit more analysis and start getting into how we can use these emblems.

First, we know we can take a 16-line emblem and break it down into four 4-line geomantic figures.  We can assign each of these figures to the four elements, and take lines 1, 6, 11, and 16 to form an essential figure that represents the geomantic emblem elementally.  For instance, the Fire Subelemental Figure of a given geomantic emblem can be constructed by taking the fire lines in order: fire of fire (line 1), fire of air (5), fire of water (9), and fire of earth (13).  The Air, Water, and Earth lines can be constructed similarly by taking those respective subelemental lines.  By adding the subelemental figures together, we can obtain an “elemental sum” figure that represents how the elements interact in the emblem as a whole, as opposed to the overarching essential elementa figure that defines the emblem elementally.

We can also use these four figures as four Mothers in a geomantic chart, and use the chart as a whole to understand the emblem.  Just by adding the four figures together, though, we can obtain a “sequential sum” figure, which is the same as the Right Witness from the geomantic chart generated by the emblem.  As it happens, only even figures can ever be the sequential sum of an emblem, with Populus happening twice as many times (64) as any other sequential sum (32) except Via, which never happens.  Although the Judge of the geomantic chart generated from the emblem (we’ll call it the “Judge sum”) indicates how the emblem effects itself in the world (qualified by its elemental essence), the sequential sum indicates from what perspective or what cause it wants to act (Right Witness vs. Judge).  Coincidentally, the elemental sum figure of the emblem represents the Left Witness, just as the subelemental figures represent the four Daughters of the geomantic chart (fire subelemental figure is First Daughter, etc.).

When we go to cycles, there are several operations we can perform on a geomantic emblem just like how we can perform on a geomantic figure: inversion (flipping the bits from 1 to 0 and from 0 to 1), reversion (reading the emblem from the 16th line to the 1st), and conversion (inversion + reversion).  Unlike geomantic figures, which may have themselves as conversions or repeat the same figure between their inversion and reversion, the geomantic emblems have unique inversions, reversions, and conversions that don’t repeat.  Just as the emblems fall into specific emblematic cycles, so too do their inversions, reversions, and conversions.  The cycles have a specific pattern of this:

  • Populus: inversion Caput Draconis, reversion Fortuna Major, conversion Rubeus
  • Via: inversion Laetitia, reversion Fortuna Minor, conversion Cauda Draconis
  • Albus: inversion Acquisitio, reversion Tristitia, conversion Conjunctio
  • Conjunctio: inversion Tristitia, reversion Acquisitio, conversion Albus
  • Puella: inversion Amissio, reversion Puer, conversion Carcer
  • Amissio: inversion Puella, reversion Carcer, conversion Puer
  • Fortuna Major: inversion Rubeus, reversion Populus, conversion Caput Draconis
  • Fortuna Minor: inversion Cauda Draconis, reversion Via, conversion Laetitia
  • Puer: inversion Carcer, reversion Puella, conversion Amissio
  • Rubeus: inversion Fortuna Major, reversion Caput Draconis, conversion Populus
  • Acquisitio: inversion Albus, reversion Conjunctio, conversion Tristitia
  • Laetitia: inversion Via, reversion Cauda Draconis, conversion Fortuna Minor
  • Tristitia: inversion Conjunctio, reversion Albus, conversion Acquisitio
  • Carcer: inversion Puer, reversion Amissio, conversion Puella
  • Caput Draconis: inversion Populus, reversion Rubeus, conversion Fortuna Major
  • Cauda Draconis: inversion Fortuna Minor, reversion Laetitia, conversion Via

Now we have a number of ways to understand the emblems:

  1. figure sequence from expanding the emblem: the order of the figures as they appear within the emblem
  2. essential elemental figure: the condensation of the pure elements taken from the subelemental lines of the emblems in their proper places, representing the elemental force of the figure as a while
  3. subelemental figures: the condensation of specific elements taken from the subelemental lines of the emblems in their places, representing how each of the four elements within each emblem presents itself geomantically
  4. geomantic chart: the geomantic chart that is generated by taking the emblem as four Mothers in sequence
  5. Right Witness/sequential sum figure: the figure that appears as Right Witness in the geomantic chart generated by the emblem, or the combination of the four figures presented in the geomantic emblem in sequence, indicating from what perspective or what cause it wants to act
  6. Left Witness/elemental sum figure: the figure that results from adding the four subelemental figures of the emblem, or the Left Witness in the geomantic chart generated by the emblem, indicating how the elements interact in the emblem as a whole as well as how the emblem is affected by external situations
  7. Judge sum figure: the figure that appears as Judge in the geomantic chart generated by the emblem, indicating how the emblem effects itself in the world
  8. emblematic cycle: the structural basis underlying the
  9. inverse emblem: everything this emblem is not on an external level
  10. reverse emblem: the same qualities of this emblem taken to its opposite, internal extreme
  11. converse emblem: the same qualities of this emblem expressed in a similar manner

For example, for the geomantic emblem 1000010110100111, we have the following information:

  • figure sequence: 1000 (Laetitia), 0000 (Populus), 0001 (Tristita), 0010 (Albus), 0101 (Aquisitio), 1011 (Puella), 0110 (Coniunctio), 1101 (Puer), 1010 (Amissio), 0100 (Rubeus), 1001 (Carcer), 0011 (Fortuna Maior), 0111 (Caput Draconis), 1111 (Via), 1110 (Cauda Draconis), 1100 (Fortuna Minor)
  • essential elemental figure: Via (water)
  • fire subelemental figure: Amissio (fire)
  • air subelemental figure: Acquisitio (air)
  • water subelemental figure: Fortuna Maior (earth)
  • earth subelemental figure: Acquisitio (air)
  • elemental sum figure: Carcer(earth)
  • Judge sum figure: Carcer (earth)
  • sequential sum figure: Populus (water)
  • emblematic cycle: Populus
  • inverse emblem: 0111101001011000 (Caput Draconis cycle)
  • reverse emblem: 1110010110100001 (Fortuna Major cycle)
  • converse emblem: 0001101001011110 (Rubeus cycle)

This gives us a huge amount of information for each of the 256 emblems, and this is all still fairly preliminary research, too.  Now that we have all these tools and methods of interpreting and understanding the emblems, the big question is how?  And for what purpose?  What do the emblems represent, and how do they fit into the larger idea of the cosmos, divination, and magic?

Each of the geomantic figures is composed from the four elements, and whether those elements are active or passive.  In a way, the figures represent 16 states of the cosmos at any given time, little snapshots of how any situation is evolving and resolving into a new state.  The geomantic emblems combine all 16 geomantic figures into a cycle, representing whole cosmoses on their own, complete situations and how they can be represented through a process of continuously evolving geomantic figures.  Read one way, the force within an element becomes more and more subtle, first appearing as earth then as water, then air, then fire, eventually being left entirely above what it was, while other forces come into play to take the place of the ascended element.  Read another way, the forces within an emblem begin a process of descent from the highest and most subtle realms to the most dense and material, describing a process of materialization and concretization instead of reification and deification.

Each situation has a beginning, a process that leads from the beginning to the end, and the end itself which must reflect the beginning.  We know that, although our emblem analysis uses 16 lines, emblems as a whole were first discovered as 19-line superfigures.  However, the final three lines must be the same in each emblem as the first three lines, which provides the repetition that allows the emblem to overlap onto itself as a cycle and allows for the complete expansion of the emblem into 16 figures, which are both ways the emblem reflects the beginning in the end. Certain patterns always appear in each cosmic process, and some parts of each process have the same flow.  Consider the geomantic emblems: all the geomantic emblems have the same constituent parts (the 16 geomantic figures), but these don’t appear randomly within the emblem.  We know that Laetitia must always be followed by Populus which must always be followed by Tristitia, which can be followed by either Albus or Fortuna Maior.  Similarly, we know that Caput Draconis must be followed by Via which must always be followed by Cauda Draconis, which can be followed by either Puer or Fortuna Minor.

All this boils down to a simple(?) choice.  When one wants to influence a situation to go a certain way or to inspect a particular state of a situation/the world, look to the geomantic figures.  When one wants to create a whole system or investigate how cosmic processes work as a while, look to the geomantic emblems.  Whether it’s for divination, magic, planning, meditation, theurgy, or other occult work, emblems are systems, while figures are states within a system.  Knowledge of systems requires a wider view than any specific view alone; one needs to step back or have foreknowledge of what’s going on in order to correctly assess what process one finds themselves in, and then what can be done to proceed along the process in a desired manner (if the process is changeable) or in a manner that can at least be known in advance (if the process is unchangeable).

In a way, it’s like the difference between knowing the astrological forecast for a given event at a given time, and seeing how the interaction of the natal/electional horoscope for an event and its progression or transits affects a situation, process, or life across its duration.  The difference is state versus system, or single snapshot versus whole process.

So, how can the geomantic emblems be used?  Though this is still really new stuff that needs exploration and experimentation, I’ve got a few ideas:

  • Jewelry and talismans: incorporate the emblems into magical items, either graphically (drawing or writing the emblem onto the item) or structurally (knotting, braiding, or shaping the item to resemble the emblem).  The emblem can be used to bring about a prescribed process and flow of a situation.  Likewise, they can be engraved on wands or staves to represent a middle pillar of the world, kind of like a world-tree or similar central supporting force underlying a conduit of power.
  • Representations of the cosmos: by enlarging the definition of “system” to reflect the entire cosmos, entire cosmological processes can be understood on a grand scale as an interplay of the elements.  Alternatively, they can be seen as processes that define or mark a whole sequence of events, much as a person’s natal chart or a talisman’s electional chart, that indicates where strengths, weaknesses, and dignities lie.
  • Decoration and resonance: I’ve done some experimenting with using graphical presentation of the geomantic emblems as sigils or decorative motifs, including a set of armband tattoos that look like a cross between an arabesque lattice and a scifi data printout.  Generating infinite arabesques from the emblems or incorporating them in an area or on art by necessity also incorporates the energy of the geomantic figures, as well as their flow and elemental associations, that can subtly affect the nature or energies in a given place.

Your thoughts?  Hopefully the geomantic emblems aren’t too far above your head, dear reader, and maybe you might even be willing to share some of your thoughts and possible applications of them in divination and magic.

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 (Emblems) Revisited

A while back, I mentioned something about geomantic superfigures, which has recently become another focus of mine.  The De Geomanteia posts I’m doing are awesome for getting me to revisit old topics in geomancy, and I feel like the superfigures (I should a devise better name than that, perhaps “geomantic emblems”?) are something to be worked on a little more.  In a nutshell, geomantic superfigures are 19-row figures that, if you take any four consecutive rows, yields one of the 16 geomantic figures, and all 16 selections of four consecutive rows yield all sixteen geomantic figures exactly once.  They’re basically microcosms of the universe represented geomantically.  I suggest reading the old post above on the geomantic superfigures to get an idea of what they are.  There are 256 different geomantic superfigures, which is significant since 256 = 16².

I developed the idea for geomantic superfigures emblems a while ago as an exercise in combining a particular problem from computer science algorithms and DNA sequencing with geomancy, and though it seems useful, I never really developed a use for it, and so the idea and the list of 256 emblems just sat there gathering dust.  Recently on the Geomantic Campus mailing list, the geomancer prunesquallori picked up the idea and did some more analysis on it, and came up with a few awesome observations:

  1. Each geomantic emblem has 19 lines, but the last three lines must always be the same as the first three lines, i.e. line 1 = line 17, line 2 = line 18, line 3 = line 19).
  2. Because of the repetition of lines, we can reduce the size of the geomantic emblem to 16 lines without losing any information.  This is a far more appealing number than 19, geomantically speaking.
  3. One can rotate the 16-line emblems line by line, i.e. old line 1 becomes new line 16, old line 2 becoming new line 1, … old line 16 becoming new line 15.  This, when combined with the above, will yield another valid geomantic emblem.
  4. Each emblem can be rotated a total of 16 times, which produces a cycle.  Because there are 256 emblems, each of which can be rotated into or is rotated from another 16 emblems, we can reduce the 256 emblems to 16 if we ignore what position we begin at.

Consider the geomantic emblem from the last post, which we described as the binary string 0000100110101111000.  This figure contains, taking successive groups of four consecutive bits (0 represents a passive line and 1 an active line), the geomantic figures Populus, Tristitia, Albus, Rubeus, Carcer, Fortuna Maior, Coniunctio, Puer, Amissio, Acquisitio, Puella, Caput Draconis, Via, Cauda Draconis, Fortuna Minor, and Laetitia.  However, notice that the last three binary digits and the first three are the same; we can reduce the figure in size to the emblem 0000100110101111.  We can take for granted that the last three bits are going to be 000 since the first three are 000, so we leave them unwritten.  If we rotate the emblem by two bits to the right, we get 1100001001101011 in 16-bit form, or 1100001001101011110 in 19-bit form, which is another valid geomantic emblem.  This geomantic emblem contains, in order, the geomantic figures Fortuna Minor, Laetitia, Populus, Tristitia, Albus, Rubeus, Carcer, Fortuna Major, Conjunctio, Puer, Amissio, Acquisitio, Puella, Caput Draconis, Via, and Cauda Draconis.

Knowing that we can break down the emblems into 16-bit strings, or 16-line emblems, makes interpreting and using them a good bit easier.  For a simple elemental interpretation of the emblems, consider that a normal 4-row geomantic figure has one row for each of the four elements fire, air, water, and earth from top to bottom.  If we magnify the geomantic emblems into four groups of four rows, the first set of four rows can be assigned to fire as a whole, the second set to air, the third set to water, and the fourth set to earth.  Within these sets, we assign each individual row to an element as we would normally, so the first row of a set is assigned to fire, the second to air, and so forth.  By using this scheme, we can interpret the geomantic emblem as having whole geomantic figures representing how a particular element manifests.

Moreover, in using this scheme, we then can have lines that represent a particular element within a particular element.  The fire row of the fire quartet of lines would be “fire of fire”, or pure fire; the air row of the fire quartet would be “air of fire”, the interactive or mobile force of fire.  The system would continue so there’d be sixteen combinations: fire of fire, air of fire, water of fire, earth of fire, fire of air, air of air, and all the way down to earth of earth at the bottom.  By seeing how the interplay of elements works within the elements themselves, we can get a deeper understanding of the emblem they appear in.  Conversely, if we take the pure elemental lines out of the emblem and combine them, we can get a geomantic figure that can capture the essence of the emblem.  In this manner, there would be 16 emblems per geomantic figure.

As an example, consider the emblem 0000100110101111 from above.  Breaking it down into four groups of four lines, we have Populus (0000), Carcer (1001), Amissio (1010), and Via (1111).  Populus represents the force of fire in the emblem, Carcer the force of air, Amissio the force of water, and Via the force of earth.  If we took the pure elemental lines (fire of fire, line 1; air of air, line 6; water of water, line 11; earth of earth, line 16), we get the figure Tristitia (0001).   If we look at the emblem 1100001001101011, we have Fortuna Minor (1100) for the force of fire, Albus for the force of air (0010), Coniunctio for the force of water (0110), and Puella for the force of earth (1011).  Taking the pure elemental lines, we get the figure Puella (1011).  Fortuna Minor in this emblem would be especially powerful, since it’s a figure ruled by fire appearing as the force of fire in the emblem.

Also, consider that in having a 16-row emblem, we have the same number of rows required to develop a full geomantic chart, which can also help elaborate or expand on the nature of the sequence of figures that combine to form a geomantic emblem.  Given the emblem 1100001001101011, using Fortuna Minor, Albus, Coniunctio, and Puella for the four Mother figures, we find that the Judge is Coniunctio, the Sentence is Amissio, the Via Puncti doesn’t lead anywhere, the sum of the chart is 94, the Part of Fortune is in house 10, and the Part of Spirit is in house 2.  The rest of the chart I leave for the reader to derive, but interpreting this chart could yield even more information on a particular geomantic emblem that would help in unfolding its meaning or core.

Going back a bit, I mentioned above that there are 16 cycles of emblems, where if you rotate a particular emblem 15 times in succession you get another valid emblem.  Repeating this for all 16 emblems yields 256 total emblems.  Starting from an arbitrary point, the 16 16-bit cycles are:

  1. 1000010011010111
  2. 1000010011110101
  3. 1000010100110111
  4. 1000010100111101
  5. 1000010110011110
  6. 1000010110100111
  7. 1000010111100110
  8. 1000010111101001
  9. 1000011001011110
  10. 1000011010010111
  11. 1000011010111100
  12. 1000011011110010
  13. 1000011110010110
  14. 1000011110100101
  15. 1000011110101100
  16. 1000011110110010

Keep in mind that, because emblems can be cycled, you could all start these so that they start with the part of the emblem that goes 1111 and still have valid emblems.  It’s probably better to picture them as rings or bands instead of strings to emphasize their cyclic nature.  They’re presented above so that they start with 10001 for convenience.

Since there are 16 cycles, each of which can produce 16 emblems, I figured that there would be a way to link each cycle to one of the 16 geomantic figures, affording yet another way to classify the emblems but in a helpful non-elemental manner.  This would help in picking out specific emblems from the set of 256, such as by saying “the emblem in the Albus cycle beginning with Puella”.   However, doing this is tricky, since the cycles are independent of starting point, and so using arbitrary lines in the emblem is about as good as labeling two otherwise identical spheres A and B based on where you happened to touch them first.  A lot of the methods I first tried  made use of assigning a “start point” somehow, which defeated the whole purpose.  Other methods I tried allocated multiple emblems to a given figure but skipped over others entirely, which was also unhelpful.

However, in the end, a method of allocating the sixteen emblematic cycles to the sixteen figures of geomancy was found!  How, might you ask?  With a lot of work and structural analysis, that’s for damn sure.  Stay tuned to see what that method is and what the sixteen emblematic cycles are corresponded with.