Another Look at the Heptagram Rite

So, in going over my notes and prayers lately, I’ve been thinking of shaking up my regular practices and trying out new formats for prayers, devotions, rituals, and the like.  Rituals that are whole unto themselves, like the Trithemian conjuration ritual, don’t need any further framing or whatever done before or after them except for, say, meditation and purification, but other things could certainly benefit from restructuring or being placed into a structure.  One of the things that could benefit from that is my Invocation of the Solar Guardians, specifically the fuller version of them; I mean, as a simple homage unto itself to the guardian gods of the four stations of the Sun, it works fine unto itself, but it can also be used as part of a grander ritual, such as part of warding or cosmos-building.  One application I’d like to experiment with it is to use the Invocations as a form of sun-worship to recognize the seasonal changes of the equinoxes and solstices, but for a proper and full ritual to mark the turning of the Sun, I’d personally want more than just a few words to say.  Hence, framing rituals.

I didn’t expect to start with much, honestly, but after even a brief look through my notes and collected rituals, I found plenty of things to combine that include lustration, temple/circle warding, consecration of a candle, dismissal of spirits, thanksgiving offering of incense, and so forth, mostly pulled from or based on sources across the PGM.  I want to give it a few tries and refinements before sharing it publicly, but one of the things I wanted to include was, of course, the Heptagram Rite or, as is sometimes known, Calling the Sevenths to Induce Equilibrium which is a much more modern appellation.  Essentially, this is a method of attuning to the forces of the cosmos (specifically the planetary or celestial forces) by means of intoning the seven vowels of the Greek alphabet while facing certain directions and making certain motions.  In short:

  1. Face east.  Extend both hands to the left.  Intone Α.
  2. Face north.  Extend only the right fist forward.  Intone Ε.
  3. Face west.  Extend both hands outward as if in embrace.  Intone Η.
  4. Face south.  Place both hands on the belly.  Intone Ι.
  5. Face down.  Bend over and touch the ends of the toes.  Intone Ο.
  6. Face forward.  Place the right hand on the heart.  Intone Υ.
  7. Face up.  Place both hands on top of the head.  Intone Ω.

Simple enough!  I’ve used this as a quick act of attuning myself or of energy work in preparation for a larger ritual as well as part of a daily practice of energy work.  It’s nothing special, but it is highly effective.

Well, perhaps unsurprisingly, this ritual comes from the PGM, as part of a much larger text, PGM XIII.734—1077, a large, mostly well-preserved section in the Greek Magical Papyri entitled “Tenth Hidden Book of Moses” (which is mostly, but not entirely, complete).  The ritual, named “the spell to which God gives attention”, is an invocation of God by means of the seven planets and their seven letters to obtain a vision or achieve some request.  It is intended to be done at dawn, though no specific day or other circumstance is given.  Unlike the common Heptagram Rite, which is a modern adaptation of part of this ritual taken from lines 824—841, the larger invocation which I call the Grand Heptagram Rite is not intended to be used as a framing ritual to prepare or attune oneself before another working, but rather on its own as its own complete ritual.  I’ve written about it before on my blog, and have a whole page up for it under Rituals, which I direct you to look at for more information.

Well, I took a look at my notes again, and then went back to the PGM to do some more research, and I came up with a few more observations.  To my horror, it seems that I left off the final lines of the final invocation from the text, either to my oversight or confusion.  I had it mostly complete, up through line 886.  I’ve added the “seven auspicious names” to the final invocation to the page on my blog, and I apologize for the confusion and error on my part.  However, the text does not end at this point, either; in fact, it goes on quite a bit longer, though I’m unsure how much to actually include as part of what I’d call the Grand Heptagram Rite proper.  Starting on line 889 of the text:

This initiation is performed to the suns of the thirteenth day of the month, when the gold lamella is locked off and one says over it: ΙΑΙΑ ΙΥ ΟΗ ΙΕΥΟΩ ΗΩΙ ΕΟ Η ΩΥ ΕΗ ΥΩΗ ΩΩΟ ΩΩΙ ΩΑΩ ΕΩ ΟΗ ΥΩ.  Then more completely, ΑΩΕΥΗ ΟΑΙ ΙΟ ΗΥΕΩΑ ΟΥΩ ΩΟ ΕΙ ΟΥ ΗΟ ΟΙΥΥ ΩΥΥ ΩΙ Α ΕΕ ΗΗΗ ΙΙΙΙ ΟΟΟΟΟ ΥΥΥΥΥΥ ΩΩΩΩΩΩΩ ΑΩ ΕΟΗ ΕΩΗ ΙΑΑ ΗΩΙ ΗΙΩ.  In [the] initiation these things are said six times with all [the rest?], and the seven vowels are written on the gold lamella to be licked off, and on the silver lamella the seven vowels for the phylactery ΟΗΩ ΑΩ ΟΟΟ ΥΟΙΗ ΟΥ ΥΗΙ ΣΟΡΡΑ ΘΩΩΜ ΧΡΑΛΑΜΠΗΑΨ ΑΤΟΥΗΓΙ.  The following series of vowels [are written as] “wings”; and on the gold lamella write ΑΩΕΥΗΟΙ and on the silver ΙΟΗΥΕΩΑ…

Betz has a footnote here that says that “something, probably directions from another rite, seems to have fallen out of the text.  It resumes near the end of another spell”; indeed, several diagrams of vowels written in slanting rows follows, with another footnote: “this has no clear connection to the proceeding words, so Preisendanz conjectures a lacuna.  However, this may be the continuation of the lost spell in which the vowels stood.”  Based on the text that continues from this point, though there are a series of barbarous words with a start that bears high similarity to the last string in the above section, I’m inclined to agree; the final part of this “initiation” involving the lamellas and phylacteries seems to be incomplete.  Additionally, there’s no mention of any use of lamellas before this point.  The rest of the Tenth Book of Moses has mostly different sets of barbarous words attributed to various sources and a handful of charms.

So, on its own, what does the Grand Heptagram Rite (more originally “the instruction for the recitation of the heptagram and the spell to which the god gives attention”) do?  The introduction to this section of the PGM says that this text is “for this personal vision”, and that it is to work with and call upon Ogdoas, “the god who commands and directs all things” (though the Ogdoad is, more properly, a combination of eight Egyptian gods considered as a whole unit who created the universe and who represent the masculine and feminine aspects of the primeval world, and which were heavily worshiped in Hermopolis).  The rest of the text after the initial explanation is simply the ritual to be spoken, followed by the incomplete initiation above (which also doesn’t seem to match well with the rest of the text as it is, suggesting that it really is a separate ritual).  In context within the broader PGM, the Tenth Book of Moses takes place before the Eighth Hidden Book of Moses (PGM XIII.343—646 and 646—734), which itself is before another Eighth Book of Moses (PGM XIII.1—343).  This is an interesting batch of texts, and Betz has quite a bit to say about how this is essentially a compilation of several versions of the same text along with other information from other texts, especially “Mosaic” ones.  These books being called the “Eighth” and “Tenth” Books of Moses, when nothing is said of a ninth, seventh, sixth, or so on can be attributed to the prestige given to the numbers 8 (for the Ogdoad of Egyptian belief) and 10 (for the Decad of Pythagorean belief).  PGM XIII in its entirety can be considered, in many ways, a grimoire compiled out of several sub-grimoires in the same tradition, much as one might find several versions of the Key of Solomon bound together as a complete text.  It’s a fascinating section of the PGM, and I’m sure much more can be said about it than what is appropriate here.

Back to the Grand Heptagram Rite in the Tenth Book of Moses.  Unlike an exorcism ritual like that of the Headless Rite (which can be bent to a sort of empowerment ritual according to the tweaks of Crowley and Mathers), this seems to be more of a ritual to call upon and bring forth the presence of the Divine, either for a divinatory vision or for initiation into that god’s power (especially since the Grand Heptagram Rite is followed by what seems to be an introduction to an initiation), though part of the prayer establishes a connection then and there in the ritual:

Your name and your spirit rest upon the good.  Come into my mind and my understanding for all the time of my life and accomplish for me the desires of my soul.  For you are I, and I you.  Whatever I say must happen, for I have your name as a unique phylactery in my heart, and no flesh, although moved, will overpower me; no spirit will stand against me, neither daimon nor visitation nor any other of the evil beings of Hades because of your name, which I have in my soul and which I invoke.

However, if we were to include the beginning part of the subsequent initiation (PGM XIII.889ff) as part of the text, then we’d adopt the following procedure:

  1. Remain pure from the start of the lunar month through the thirteenth day of the lunar month, upon which the ritual is to be performed.
  2. Between the first and twelfth days of the lunar month counting from the first visibility of the new Moon, prepare two small tablets, one of gold and one of silver, the silver tablet able to be worn around the neck as a pendant.
    On the silver tablet, engrave or write in permanent ink the following:


  3. Before sunrise on the thirteenth day of the lunar month, just as the Moon approaches fullness but has not yet become full, prepare yourself in white clothing, wear the silver tablet around your neck, saying the following:


  4. Οn the gold tablet, write in water-soluble ink the following:


  5. At sunrise, go outside and face the Sun, say the following over the gold tablet:


  6. Lick the writing off the gold tablet, then say over the gold tablet:


  7. Recite the Grand Heptagram Rite in its entirety.
  8. Perform the preceding four steps (writing on the gold tablet, facing the Sun, praying over the gold tablet, licking the gold tablet, praying over the gold tablet a second time, and performing the Grand Heptagram Rite) again at midday and a third time at sunset.

In my estimation, I don’t think that whole procedure involving performing the ritual three times on the thirteenth day of the lunar month with the gold and silver tablets is called for, since I don’t think the initiation described starting on line 889 is necessarily about the Grand Heptagram Rite (though I don’t think it would hurt, either).  Though the barbarous words here can get messy, especially the strings of vowels, I find that the Grand Heptagram Rite is a wonderful ritual on its own accord for inducing cosmic visions and approaching the sense of divinity, when done on its own for its own sake.  That the Heptagram Rite itself, the simple seven-vowels-seven-gestures-seven-directions that became known more recently as the Calling the Sevenths is so powerful is a testament to the overarching power of the Grand Heptagram Rite.

Which brings me back, rather circuitously, to the use of it in a general sense as part of a daily practice or framing ritual.  The Grand Heptagram Rite is, in my view, far too large and unwieldy to include as part of a ritual process or framing ritual, especially given its strings of barbarous names that can be hard to rattle off or memorize.  On the other hand, the Heptagram Rite can often be too short and quick to allow things to settle in; it’s great as part of broader work, but it may not be suitable when dealing with heavier forces, nor would it be good if someone’s out of shape and needs something stronger to bend them back into shape.  There’s a wide gap between the entirety of the Grand Heptagram Rite and the Heptagram Rite, and I wanted something of a halfway point between the two in length, something that could be a little more empowering than the shorter of the two and a little more generic than the longer of the two.  What follows is my attempt to bridge that gap

  1. Recite the first invocation to Aiōn (PGM XIII.843—848):

    I call on you, eternal and unbegotten Aiōn, who are One, who alone hold together the whole creation of all things, whom none understands, whom the gods worship, whose name not even the gods can utter.  Inspire from your breath, ruler of the Pole, him who is under you!  I call on you as the gods call you!  I call on you as the goddesses call you!  I call on you as the winds call you!

  2. Salute each direction with the vowels (PGM XIII.849—870)
    1. Face east, extend both hands to the left, and say:

      I call on you as the east: Α ΕΕ ΗΗΗ ΙΙΙΙ ΟΟΟΟΟ ΥΥΥΥΥΥ ΩΩΩΩΩΩΩ

    2. Face north, extend only the right fist forward, and say.

      I call on you as the north: Ε ΗΗ ΙΙΙ ΟΟΟΟ ΥΥΥΥΥ ΩΩΩΩΩΩ ΑΑΑΑΑΑΑ

    3. Face west, extend both hands outward as if in embrace, and say:

      I call on you as the west: Η ΙΙ ΟΟΟ ΥΥΥΥ ΩΩΩΩΩ ΑΑΑΑΑΑ ΕΕΕΕΕΕΕ

    4. Face south, place both hands on the belly, and say:

      I call on you as the south: Ι ΟΟ ΥΥΥ ΩΩΩΩ ΑΑΑΑΑ ΕΕΕΕΕΕ ΗΗΗΗΗΗΗ

    5. Face down, bend over and touch the ends of the toes, and say:

      I call on you as the earth: Ο ΥΥ ΩΩΩ ΑΑΑΑ ΕΕΕΕΕ ΗΗΗΗΗΗ ΙΙΙΙΙΙΙ

    6. Face forward, place the right hand on the heart, and say:

      I call on you as the sky: Υ ΩΩ ΑΑΑ ΕΕΕΕ ΗΗΗΗΗ ΙΙΙΙΙΙ ΟΟΟΟΟΟΟ

    7. Face up, place both hands on top of the head, and say:

      I call on you as the cosmos: Ω ΑΑ ΕΕΕ ΗΗΗΗ ΙΙΙΙΙ ΟΟΟΟΟΟ ΥΥΥΥΥΥΥ

  3. Recite the second invocation to Aiōn, based on the first version of the Eighth Book of Moses (PGM XIII.64—71ff) and the Headless Rite (PGM V.140 and 141):

    I call on you, who are greater than all, the creator of all, the self-begotten who see all and are not seen, who hear all and are not heard!  For you gave to Hēlios glory and all power, and to Selēnē the privilege to wax and wane and have fixed courses, yet you took nothing from the earlier-born darkness, but apportioned all things so that they should be equal!  For when you appeared, both Order and Light arose!  All things are subject to you, whose true form none of the gods can see, who change into all forms!  You are invisible, o Aiōn of Aiōns, and through you arose the celestial pole from the earth!  Hear me and help me, o lord, faultless and unflawed, who pollute no place, for I bear witness to your glory! Lord, King, Master, Helper, empower my soul!

(Note: I talk about why I changed the original order of the invocations here, going counterclockwise in agreement with the vowels, on the main ritual page.)

Essentially, what this shortened form of the ritual does is call upon the same attunement and cosmos-building that the Heptagram Rite does, itself framed by invocations to Aiōn, while allowing things to settle in more comprehensively and from all ways.  The main thing I wanted to accomplish here, however, was to avoid using barbarous names or vowel permutations where possible, hence why I’ve avoided including them in the “I call on you as by the voice of the [male] gods” and “…as the voice of the [female] goddesses”.  However, instead of continuing with the invocation to Aiōn from the Tenth Book of Moses (lines 871ff., starting “I call on your name, the greatest among gods…”), I opted for another invocation to Aiōn pulled from the Eighth Book of Moses, also because it doesn’t involve barbarous words, but also because the focus shifts here from a specific request for the divine apparition of Aiōn (as in the Tenth Book) to a general invocation (as in the Eighth Book), augmented by a single line from the Headless Rite (line 140 and 141, “Lord, King, Master, Helper, save the soul”).

(I’d also like to note that the first invocation to Aiōn from PGM XIII.843—848 is the origin of Jason Miller’s prayer to Aeon that he gives in his Advanced Planetary Magic ebook.  In that text, he describes the “Heptasphere” ritual, which is the Calling of the Sevenths followed by the prayer to Aeon, though without the usual motions from the PGM.  It is effectively the same thing as I’m trying to do, just not as long or as involved as I’m describing here.)

Though I’m comfortable with this middle-path ritual as it is, one of the things I don’t yet know about is any visualizations to be performed.  Normally, when doing the usual Heptagram rite, I just visualize the pure color of the planet coming from the direction I’m facing: purple from the East, orange from the North, and so forth.  For this, however, a visualization would need to take into account something more complex…probably?  I’d still want to keep the seven colors visualization as a base, but augment it with…not sure.  Visualizing seven sets of the seven vowels in each direction, or a seven-pointed star with each ray in a different planetary color for each direction?  Perhaps I could repurpose a line from further in the Tenth Book, line 880:

…Become for me lynx, eagle, snake, phoenix, life, power, necessity, images of God!…

I could feasibly read this as here are four animals and three ideas, all of which are images of God.  And, since there are four cardinal directions, plus below, center, and above, each of these images could be given to each direction we face in the ritual.  This could further be augmented by the final “seven of the auspicious names” at the very end of the Grand Heptagram Rite:

Direction Vowel Planet Image Name
East Α Moon Lynx ΧΕΧΑΜΨΙΜΜ
North Ε Mercury Eagle ΧΑΓΓΑΛΑΣ
West Η Venus Snake ΕΗΙΟΥ
South Ι Sun Phoenix ΙΗΕΑ
Down Ο Mars Life ΩΟΗΟΕ
Center Υ Jupiter Power ΖΩΙΩΙΗΡ
Up Ω Saturn Necessity ΩΜΥΡΥΡΟΜΡΟΜΟΣ

Of course, all of this is incredibly hypothetical at this point, and it doesn’t seem to match up entirely nicely; after all, why should the Eagle be given to the North for Mercury, or Lynx to the East for the Moon?  If there’s any merit to linking up the directions/vowels/planets to the images in this way, and the images aren’t just given in a random order, then the answer might lie in Egyptian mythology and cosmology; after all, the Eighth Books and Tenth Book of Moses definitely have distinct Egyptian influences, and in Egyptian cosmology, the Lynx was said to be the enemy of the Serpent (Mafdet vs. Apep), while the Phoenix…well, doesn’t really have much of a connection with Eagles, though its solar nature cannot be denied, especially as it was considered the animal avatar of the Sun god Re.  Eagle, on the other hand, is more confusing; it wasn’t a traditional animal in Egyptian cosmology, though it could be equated with the falcon, the animal of Horus, and thus an equivalent to Jupiter or Zeus or to Helios.  Which, again, doesn’t necessarily match; we’d expect Thoth, an ibis or baboon, as an equivalent for Mercury/Hermes.  It could be argued either way, I suppose; it’s something for me to experiment with, all the same.

All that leaves me with one last thing: what to call this?  I don’t want to have to rename the Heptagram and Grand Heptagram Rites to different names to accommodate this middle-path version, though to be honest, that might be best.  For my own reference from this point on, I’ll use these terms:

  • Calling the Sevenths: the simple seven-directions, seven-vowels, seven-motions attunement ritual (previously “Heptagram Rite” or “Heptasphere Rite”)
  • Minor Heptagram Rite: the shortened ritual procedure as described above in this post
  • Major Heptagram Rite: the full ritual procedure from PGM XIII 763—887 (previously “Grand Heptagram Rite”)

So, fine.  The page on the Heptagram Rite has been updated with corrections and additions, and these are the terms I’ll use from now on to refer to these rituals.  And, better than that, I have a new attunement ritual and invocation to use, try out, and tweak for improvements.  In addition to offering a slightly fuller form of Calling the Sevenths, it also adds in useful invocations for power, assistance, and divine aid, which (in my own routines) can simplify my ritual process and make other things obsolete or redundant, which makes things even more efficient for me, whether in daily practices or in framing rituals.

What about you, dear reader?  Do you have any experience with the Heptagram Rite in any of its forms, whether the shorter Calling the Sevenths or the whole process of PGM XIII.734ff?  Do you have your own PGM-style framing rituals that make use of the directions or vowels?  Feel free to share your experiences in the comments!

De Regnis: Visualization, Meditation, Contemplation

Although most of my writing is visible and accessible through my blog and my ebooks, there are a bunch of writing projects that I don’t necessarily intend for public release.  When I was recently going through my old documents folder on my computer, I found a writing project I had intended to be a compendium of Hermetic and Neoplatonic knowledge, guidance, and advice that would serve to document my understandings and work as a textbook unto itself, both for my benefit and any who might come after me.  This project, De Regnis or “On Kingdoms”, got pretty far along before it got abandoned, though parts of it serve as seeds or are outright cannibalized for some of my other works.  Though I have no plans to continue writing this text, I want to share some of the sections I wrote that can act as a useful introduction to some of the practices of Hermetic magic in a modern context.  My views and practices and experiences have grown considerably since then, but perhaps it can help those who are just getting started or are curious about how to fortify their own practices and views.  If you have any views, comments, suggestions, or ideas on the topics shared in this post, please feel free to share in the comments!

Today’s selection will be on the topics of visualization, meditation, and contemplation.

On Visualization

Visualization is the act of using the imagination to form in-depth images in the mind. While this may sound like mere daydreaming, visualization is far more powerful and capable of creating whole immersive worlds. Using the imagination to create images, then, implies a greater sense of“image” than simply a mental picture, and visualizations should indeed be more than just a fleeting thought in the mind. Visualization makes use of the mind’s full range of senses and perception to create an image, both from the physical senses and the ethereal senses. Visualization is essential in picturing or working with spirits, traveling mentally to other spiritual realms, and understanding and directing the flow of cosmic forces, just as the physical senses are necessary in helping one walk around a city or engaging in conversation with a friend.

Humans interact with the world with five primary physical senses: sight, sound, touch, taste,and smell. As humans have evolved to have refined and delicate organs of sight, the sense of sight tobe the strongest and first developed imaginative faculty of the mind. The relative ease of picturing the face of a friend, guessing how something might look now based on past experiences, or recalling a vivid visual memory can attest to this. However, the most intense and immersive of memories,dreams, and visualizations generally make use of all the senses. It is by all the senses working together that people interact with the world, and when one sense is hindered, the other senses compensate by bringing more information to the mind so as to comprehend physical reality.

The mind can be thought of as a machine that processes data. It can be argued well that humans do not experience the world directly, but only through the filter of their senses. For instance, though many people might perceive an icy lake as cold, someone with nerve damage in the hands might not perceive any change from that to a blazing bonfire. Similarly, though people might perceive one apple as red and another as green, someone with colorblindness might not perceive any difference at all between the two. The senses deliver sensory data from the physical world to the brain, which processes and unites them into a more-or-less coherent perception for the mind to understand and work with. However, the mind is more capable of creating and understanding the world than the brain itself is; while the brain can only process the information that the sensory organs give it, the mind can process all that and more all simultaneously.

A simple visualization exercise begins with physically picking up a small everyday object, say, a pencil. Observe the pencil: looking at it with the eyes is not enough. See every detail of the pencil,every groove and edge, every dent and scratch, the color differentiation on the eraser, the smooth sheen on the graphite, the angle the graphite has been worn down by writing. Feel the weight of the pencil, the temperature of it when picked up and how slowly its temperature changes when held, the smoothness or roughness of its parts. Smell and taste the pencil, the thick odor of its graphite, the rubbery tang of the eraser, the skin and sweat rubbed onto it with use. Hear the pencil and listen closely as the graphite squeaks and rubs onto paper or wood, the dull quiet brush of the eraser rubbing off the marks. Completely witness the pencil using every physical sense.

Afterwards, put the pencil down and close the eyes. Recall every memory, every perceived sensation of the pencil that was obtained from witnessing it, hear how it sounded, smell how it tasted, feel how it felt, see how it seemed. Recreate the pencil in the mind from the perception of weight to the perception of smell to the perception of how light reflected off it. Hold the complete image in the mind for a minute without letting it dissipate, then let it go. Half an hour later, try it again without picking up or observing the pencil in the meanwhile. Try it the next day. If details are lost, go back to the pencil and find those details and bring them back into memory. Over the course of several days, slowly increase the time spent visualizing the pencil from one minute to five minutes.

Once the pencil can be recalled in its entirety at any moment, repeat the same process with something a little larger or a little more complex, then again with something even larger or more complex. Proceed from the pencil to a fruit, a chair, a bed, a door, an empty room, a sparsely decorated room, a fully furnished room, a house, a building, a forest. Over time, the process of visualizing increasingly complex things, places, and people will become easier and the images more in-depth, more lifelike, and more real to the mind. Experiment with more complex things, such as an instrument playing a song or a meal being eaten. Learn how to recreate or newly create whole things in the mind, and the mind will be strengthened and capable of working with the immaterial realms of spirit.

On Meditation

Meditation is the act of reflecting or measuring oneself mentally, permitting one’s own mind to come to terms with itself by itself independent of external stimuli. In a sense, it allows the mind to settle down into stability unperturbed by thoughts that arise. The mind has been described,in one sense, as a mirror: it reflects anything put in front of it, though its true nature is clear and reflective. By letting the mind be reflective instead of reflecting something, the true nature of the mind can become known instead of the constantly buzzing, chattering, thinking mind that humanity has grown accustomed to.

The breathing exercises in the previous section lay the groundwork for meditation, and indeed form a style of meditation on their own. By focusing one’s awareness on a single, repetitive, cyclical act, one begins to shake the mind free from the thoughts that cloud it. When such thoughts arise in meditation, let them arise and let them pass without clinging onto them, following them, or becoming angry at their arising. All one needs to do is return to the original act of being aware.

While the breathing exercises focus on being aware of one’s own breath, meditation begins by being aware of one’s own thoughts instead of thinking them. Sit as before, comfortably and relaxed, and begin the fourfold breath exercise for a short while. When ready, having focused the awareness on the breath and permitting thoughts to arise and pass, begin becoming aware of the arising of thoughts themselves. Note where they appear to arise in the brain and in the mind, what other string of thoughts or stimuli caused a thought to arise from simply being aware of thoughts,and let them go. If a particular thought cannot be let go, say “I will think of this and deal with it later, but now it is time to let it go” and do so; if the thought persists as in a repetitive song, permit it to continue and direct the awareness away from it. Whenever the awareness attaches itself to a thought instead of being focused on the arising of thoughts, and whenever this is realized, bring the awareness back to the arising of thoughts without anger or shame. This should be practiced for five minutes a day after breathing exercises every day, working up to ten, then twenty, then indefinitely.

After this has been established with some level of repeatable skill, turn the awareness onto the act of being aware itself. Though perhaps recursively confusing, this focuses the mind on its own reflective nature without being reflective of anything; in this state, the mind is free of thoughts and can enter into deeper levels of trance or spiritual states suitable for magical working. Begin as before with the fourfold breath, then being aware of the arising of thoughts. After being aware of how thoughts arise in the mind, become aware of the mind and the act of awareness, of awareness itself. Hold that awareness, not letting other thoughts intrude as usual. Maintain this for as long as one can, and repeat the process every day. This may sound and seem difficult, but once attained can be repeated with ease.

On Contemplation

While meditation allows the mind to focus and explore itself on its own terms, letting other thoughts arise on their own as they will until they arise no more, this same focus and single-mindedness can be applied towards a thought to greatly expand its ability to be understood. As opposed to merely thinking a thought, focusing one’s awareness on a thought, topic, or concept allows the mind to fully enter into and explore it. This style of meditation is called contemplation, and in contemplation one comes to understand and support something from its fundamental axioms to its furthest implications.

Before beginning contemplation of an idea or thought, it helps to be intimately familiar with that idea or thought. Precede the contemplation with extensive reading, note-taking, discussion,and even idle banter involving the concept. Learn about its history, its development, its uses, its origins, its risks, its benefits, its correspondences, its associations, its causes, and its conditions.Whatever can be learned about it ahead of time will help in contemplation.

As before, begin by sitting comfortably, beginning breathing exercises, and enter into a meditative state. Consciously call up the idea or thought to be contemplated, then focus all awareness on that, exploring every thought that arises based on that original thought. If other completely unrelated thoughts arise, let them arise on and out on their own as before; if a thought can be made to fit or be associated with the contemplation, explore why.

As opposed to meditation before, where one wants to abstain from thinking consciously with a part of a distracted mind, contemplation seeks to completely absorb the mind in consciously thinking with its entire force.As opposed to meditation, where the mind is kept from wandering to focus on itself, contemplation allows the mind to wander down paths and avenues of thought related to the topic. Images,smells, sounds, memories, colors, and related thoughts that arise during contemplation, unless the mind is truly wandering off the path into distraction, help illumine or offer details or nuances or meanings to the topic being contemplated. Thoughts that seem to come from “outside” the mind,especially when contemplating the seal of a spirit, may also be indicative of the topic.Contemplation is not simply thinking about a thing.

Contemplation is completely absorbing the mind into a thing, deconstructing it, inspecting every aspect of it from every angle, discovering new angles and new aspects, using different techniques of thought to understand and comprehend it, and relating the meaning of it to one’s own experience: physically, mentally, spiritually, emotionally, and eternally.

Compilation Paralysis

I’ve been on a compilation kick lately.  I mentioned in a recent post of mine about the Orphic Hymns that I’m compiling a personal temple text from a variety of sources because I don’t like having books in my temple room if I can avoid it; for instance, I have a copy of Dervenis’ Oracle Bones Divination that, up until quite recently, I’ve been using as my reference for astragalomancy, and have kept it with my shrines for the Greek gods.  This…makes me uncomfortable, so I transcribed all the necessary information from that into a personal ebook for me to keep a printout of instead.  Not only do I get to finally put the damn book back on the bookshelf after way too long, but I also get to reformat it, reorganize it, and include other information I want to reference, as well as tweak some of the translations for my own tastes.

Of course, one thing led to another.  I also included a few pages for grammatomancy, which also references a good chunk of my Mathesis correspondences to the letter, and because Opsopaus included the Delphic Maxims in his Oracles of Apollo book, I decided to include those, too.  Again, nothing too elaborate or in-depth; I have enough experience with these systems and the backgrounds and contexts in which they were written to not have to have all the extra information in a temple reference.  The final result is something I could be content with…except, of course, I wasn’t.  Given all the references to the other gods between grammatomantic correspondences to the zodiac signs and, by those, to the Greek gods (cf. Agrippa’s Orphic Scale of Twelve, book II chapter 14), I wanted to also have a section for the Orphic Hymns.  This is reasonable; after all, my personal vademecum-enchiridion-prayerbook has a number of them already transcribed, and while I won’t use all the Orphic Hymns in my practice, why not have a complete set for reference, just in case?  It wasn’t hard to find a copy of the Greek texts as well as the Taylor translations that I could simply copy, paste, and format for LaTeX’s customary needs.

But, of course, why stop there?  I also ended up adding Gemisthus Plethon’s hymns as well as those of Proclus, which I find useful for my Neoplatonic uses as well as my devotional ones.  And, if we’re going with devotions, I decided to also include a few prayers attributed to Hermes Trismegistus from the Corpus Hermeticum, the Asclepius, and so on, and because of those, I also wanted to bring in a few things from the PGM, which then became more than a few things from the PGM, and then I added in the planetary invocations from the Picatrix because those would be useful, too…

The ebook I was preparing ballooned from a simple reference for divination to a compendium of devotional and oracular texts.  Whoops.

But, yanno, I was hooked!  I wanted to bring in what I could, because it might be useful, whether in a devotion to the theoi or in divination or needing something to reference for meditation.  And, so, my penchant for completionism and perfectionism kicked in—hard—and I’ve been looking through my other references and books, trying to pick out useful prayers, invocations, rituals, and the like for my temple.  In effect, I was essentially making a typed-up version of my vademecum, with a different focus and with plenty more texts that I’m not accustomed to using.

This is all well and good, of course, assuming I could actually use the thing.  And in the form it was in, even in the form it had been in, it was quite plenty useful, and definitely satisfied my original needs of having a handy divination reference in my temple.  But since I brought in all these other things, I knew I wanted more, and because I wanted more, I also knew that it was incomplete.  And how would I tolerate having something be incomplete?  The idea is as distasteful as unnecessarily having books in my temple room.  Because it was incomplete, I didn’t want to print it out prematurely, especially with having to deal with page numbers or section enumeration, because if I wanted to add or fix something, I’d have to go back and reprint the damn thing for consistency, and even though I can get by by using the office printers once in a while for personal ends, I didn’t want to waste that much paper and ink.  Editing a text is one thing—I’m not opposed to using interim texts with scratched-in notes—but putting something on paper, especially printing something out, gives me a hard-to-achieve and yet so-satisfactory feeling of something being “fixed”, even if it is for my eyes only.  So, in order to make printing this thing meaningful, I wanted to make sure it was worthy and proper for printing.

It’s been over a month since I had the original problem of “I need a quick reference for divination”.  It’s also been over a month since I’ve had a workable, totally satisfactory solution for this problem, too, and yet I still haven’t fulfilled my needs.  Instead, I got caught up in a problem I call “compilation paralysis”: not wanting to proceed in some matter due to a fear of not having enough resources, options, or sources.

Some authors, especially those in academia or in teaching-types of writing, might know the feeling well, of not feeling like you have adequate source material to publish.  I have that same sensation, too, for my geomancy book-in-progress, knowing that there’s still so much more that might be included but…well, the benefits diminish after a certain point, and well before that, it’s probably better to cut out stuff that’s truly extraneous and unnecessary before adding anything more.  It does, in fact, help to start off with too much and cut down rather than having the opposite problem, and this is a habit I picked up in college for my research papers (getting down to the ten-page mark was a lot easier than trying to BSing and subtle-formatting my way up to it).  But, at the same time, consider the context: what these authors are dealing with is a single book on a single topic that is published for a single need.  Once that need is met, the book is (in theory, at least) publishable; further books can be written or new editions made with further appendices, but those aren’t strictly needed.  My problem, in this case, is dealing with something for me and me alone that needs to satisfy my sometimes-nebulous needs.

One of the reasons why I support people having a notebook or, perhaps even better from a utilitarian standpoint, a binder with written pages for their vademecum-enchiridion-prayerbooks or records of their prayers and rituals is because these are essentially living documents; as we grow in practice, they grow, too.  As we find new prayers, rituals, and correspondences, we add them in, organization be damned.  We can reevaluate the real use of these things we add, and reorganize what makes the cut, when we fill the first notebook and move onto the second one, as I did not too long ago.  These aren’t things that need to be polished, edited, or fixed in any way except what serves our needs in prayer and ritual, and as such, don’t need to be fancy, embellished, typeset, illumined, or otherwise made particularly fancy.  In fact, I have a personal fear of using those beautifully handcrafted, leatherbound, embossed, etc. journals I see floating across the internet and bookstores because I tremble at the thought of messing up such a beautiful work with errors or wasted paper; not only is my calligraphy not up to par to match the beauty of these books, but I find these things to be more appropriate to true works of devotion and love that are complete and refined unto themselves.  (I only speak for myself, of course.)

So, like, with my personal enchiridion, I don’t particularly care about making errors; there are scratchmarks, crossouts, and addenda all over the damn thing.  The important thing for me is not to waste space, so I try to be as efficient as possible cramming in as much information and references as possible into as few pages and lines as possible.  This is fine; after all, it’s my own personal thing, and nobody else needs to see or use it; besides, Moleskines can be expensive for such a notebook, even if they’re the perfect size to carry around (and fit in a Hyundai car manual leather case, I might add, which gives it extra padding and some extra utility, in case you wanted to try that out as a Moleskine bookcover).  The things I add to my enchiridion are a testimony to my growth and directions and shifts in focus I take in my practice, which I find is informative on its own.  The only important criterion I have for adding stuff to it, truly the only one, is whether something is going to be useful to me; if not, I’m not gonna waste the time writing it in or the ink to write it.

That’s what reminded me to get out of my compilation paralysis.  There’s no need to be scared or anxious about not having enough sources; if I need something later, I can just add it it.  It’s not like I didn’t already have these sources and there’s a threat of losing them; I’ve never needed a copy of the Homeric Hymns or the Nabataean prayers to the Sun or Saturn on hand when I didn’t already have my enchiridion or my copy of the Picatrix at hand, after all, so why should I be so worried about not having them in this temple reference?  I can always add new things into the overall document, print out the necessary pages, and just add them into the binder where appropriate.  It’s not that big a deal.  I know for a fact that I can always get this information should I need it, and if I haven’t needed it yet, there’s no harm to start off with that which I know I need right now and add stuff later.  I’ve got more than enough source material for what I need, anyway, and it’s more manageable to deal with two small binders than one massive one.

It’s a bitter pill for me to swallow, but even I have to admit it: none of us needs to know everything about our practices right out of the gate.  It might be nice, to be sure, but that’s also kind of the beauty of it, to let growth happen organically, especially if you’re in a practice that you’re developing on your own, as so many magicians and pagans are.  You don’t need full copies of the Homeric Hymns or Orphic Hymns in both Greek and English the moment you decide to build a shrine to one of the gods; you don’t need to know all the specific proportions of all the ingredients for the obscure incenses needed for all the planets from the Picatrix when you’re not even going to bother with a planet you’re going to interact with tonight once and probably not again for a few years more.  Part of the practice is just that: practice.  We do things, and then we do both more things and we do those same things more.  We learn, we accumulate, and we incorporate what we do into what eventually becomes our whole practice.  Part of that is necessarily finding more things to add and adding them at the proper time, as well as changing the things we do as we need to change them so as to keep doing them better or, at least, keep doing things better for our own sakes.  If we need to make emendations, do so at the proper time; you don’t know what would need them until you do or until they’re pointed out to you, and so much of that is based upon trial and error, experimentation and evaluation.  It’s not that big a deal.

There’s no need to worry, and there’s no cause for paralysis.  All you need to do is, simply, do.  Amend, fix, and add when you need to.  Don’t worry about trying to have everything ready for everything, especially when you don’t know what “everything” consists of.  Relax, then Work.

Mathetic Year Beginning Mismatch, and a Revised Grammatēmerologion

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

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

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

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

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

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

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

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

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

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

  1. March 30, 1000 BCE
  2. March 30, 935 BCE
  3. March 28, 647 BCE
  4. March 27, 628 BCE
  5. March 27, 609 BCE
  6. March 27, 563 BCE
  7. March 27, 544 BCE
  8. March 25, 294 BCE
  9. March 25, 275 BCE
  10. March 24, 256 BCE
  11. March 24, 237 BCE

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

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

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

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

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

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

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

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

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

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

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