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.

A Little Light

I’ve been working a lot with the forces of light recently, in terms of the ring consecration and other ongoing works which are having a significant effect on me, my Work, and my life in general.  I received a short prayer today that’s supposed to help me focus on and help me in working with light.

Blessed is he that walks in the light.
Blessed is he that follows the path of the light.
Blessed is he that is guided by the light.
Blessed is he that walks in the light.

Holy Light, guide me.
Holy Light, surround me.
Holy Light, support me.
Holy Light, fill me.

It turns out that working with the force of light is something for me to work on for a good while more, if not a lifetime project, which is something for me to enjoy as well as focus on.  How fortuitous, then, that my magical motto reflects just this same notion: Lautitia Laborum Lucis Laetor, “I Rejoice in the Splendor of the Works of the Light”.  Even though I’ve kept my motto pretty much a secret and unused, I figured it was a good choice to announce it to the world today, especially what with my recent work and results with the light.  I didn’t choose the motto recently by any means; in fact, I chose it back about a year or so ago.  The motto’s been hovering on the blog this whole time, too: the letters LLLL forms the four corners of the sigil up at the top of the blog, my personal emblem.  It’s unclear whether I’ll choose to go with the grandiose appellation “Frater LLLL” anytime soon over the simpler “polyphanes”, but now it’s official.

UPDATE (6/29/2012): Since I’m bored, I decided to make a translation of the prayer in Latin.  Enjoy!

Benedictus qui venit in luce.
Benedictus qui sequitur luce.
Benedictus qui dicetur luce.
Benedictus qui vadit in luce.

Lux Sanctum, duce me.
Lux Sanctum, saepi me.
Lux Sanctum, sustine me.
Lux Sanctum, comple me.