A Little Discourse On Apianus’ Cosmological Diagram

Okay, so, this thing:

A lot of people who’ve been around in Western occulture or astrology have probably encountered this image before in one context or another (it’s even appeared before on my own blog in a discussion about Ashen Chassan’s implementation of the Trithemian conjuration ritual and again when I discussed the Hermetic tormentors in CH XIII), and so many of us are familiar with this image to one degree or another.  True, it’s a really neat depiction of a Renaissance version of the geocentric Ptolemaic model of the solar system and cosmos, but there’s other stuff going on in it that I really want to explore and explain.

To start with, where does this image come from, and what specifically does it depict?  This illustration of the celestial spheres was originally made by the German humanist, mathematician, astronomer, and cartographer Petrus Apianus (anglicized as Peter Apian) in his 1524 work Cosmographia.  Apianus depicts this “scheme of the divisions of the spheres” for his second chapter, “on the motion of the spheres and the division of the heavens”.  At the center of the image we have the Earth, depicted as a circle of seas and land (corresponding to the elements of Water and Earth), surrounded by a sphere of clouds (Air) and that by flames (Fire). Outside the Earth, in successively larger concentric circles, we have the seven celestial spheres for the seven planets following the usual Chaldaean ascending order: Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn.  Skipping to the outermost edge of the whole thing (the eleventh “sphere”, as it were, though it’s really more like the infinitude beyond the spheres as a whole), we have “the Empyrean Heaven, Dwelling-place of God and of all the Chosen”. This is divine infinity beyond all the spheres, unlimited and unbounded and unmoving, under/within which all creation exists.  All straightforward stuff for most people, I suppose.

But it’s the stuff between the heaven of Saturn and the empyrean heaven that trip up a lot of people: the eighth, ninth, and tenth spheres.  To head off such speculation at the pass: no, it’s nothing qabbalistic or sephirothic in any meaningful sense (Apianus doesn’t appear to have been interested in such stuff).  Each of these circles in Apianus’ diagram all have the twelve signs of the Zodiac in them, but they’re respectively described as “the eighth heaven of the firmament”, “the ninth crystalline heaven”, and “the tenth heaven, the first cause”.  While all being zodiacal, they’re all somehow…different?  On top of that, they’re not all aligned with each other, only the eighth heaven has little stars in it, and the ninth heaven has this weird quartered-circle symbol at the ends of the sectors for Virgo and Pisces.  So what’s going on here, exactly?

Welcome, dear reader, to the funtime of medieval astronomy and cosmology!

Let’s start with the tenth sphere, the Primum Mobile (“First Mover”).  Ironically, despite being the most distant finite sphere of all (finite at least in comparison to the truly infinite empyrean heaven surrounding it), this is probably the easiest for us to approach.  The Primum Mobile is the outermost sphere and rotates endlessly, setting all things underneath/within it into motion as well, much like if you spin a pitcher of water, the water inside the pitcher itself won’t spin immediately but is set into motion by the spinning of its container.  In the old geocentric model of the cosmos, the Primum Mobile rotates constantly, performing one complete rotation every 24 hours, moving clockwise from the East to the South to the West to the North all the way back to the East.  According to Apianus, there exists precisely one and only one star in this tenth heaven.  Which star?  He doesn’t say and it’s not wholly clear to me, though if I were to leap to an assumption, I’d say that it’d be the northern pole star α Ursae Minoris (aka Polaris), given how this star was historically and culturally reckoned to be the axis (literally the “pole”) of rotation of all the heavens.

Let’s skip over the ninth heaven for a moment and take a look at the eighth heaven called the “firmament” in Apianus’ diagram.  This heaven is what contains the background stars of the nighttime sky that don’t wander around from night to night, month to month, or year to year.  This is why we call such stars “fixed stars”, as opposed to the “wandering stars” (ἀστέρες πλανῆται asteres planētai) of the planets (whose motion is defined according to their own heavens).  It’s because the eighth heaven of the firmament contains the fixed stars that Apianus’ diagram has all these stellated figures in this circle.  As for the motion of the eighth sphere, Apianus describes it as being subject to the motion of the tenth sphere such that they move all at once as the tenth sphere does, which is why the night sky as a whole rotates around the Earth once per 24-hour period.  Easy enough, I guess.

Between the eighth and tenth spheres is the ninth, described as “crystalline or aqueous” by Apianus (though just labelled as “crystalline” in the diagram).  First, what we can pick out is those two quartered circles.  Although they occur at the ends of the sectors for Virgo and Pisces, they’re really intended to be between these signs and the ones that follow to mark the equinoxes: the September equinox (occurring at the end of Virgo and the start of Libra) and the March equinox (occurring at the start of Aries and end of Pisces) respectively.  As for the motion of this heaven, Apianus says that the ninth heaven “vibrates” (trepidat), which causes the fixed stars in the eighth heaven to move forward and backward.  This would make no sense to modern folk today, but what Apianus is describing was a feature of older forms of astronomy: trepidation, a sort of oscillation in the precession of the equinoxes.  While an obsolete theory nowadays, trepidation has its origins as far back as the 4th century CE and was popular generally from the 9th to 16th centuries (putting Apianus roughly at the end of that period).

First, let’s back up a bit and talk about precession of the equinoxes (and yes, the ancients knew about axial precession all the way back in the 2nd century BCE).  Imagine a top, like the child’s toy: you pick it up, you give it a twist, and it spins around on its point upon a flat surface until it loses enough momentum to keep itself balanced.  At first, when the momentum is fast, the top stands upright, but as it continues, it eventually develops a kind of “wobble”, such that the axis of rotation is no longer precisely upright but ends up rotating on its own in a circle.  As the axis itself wobbles and rotates around, it causes the whole top to rotate in a different way on top of its already ongoing rotation around the axis, including the relative position of where such rotation around its axis “starts”.  This is what is meant by “axial precession”, and when it’s applied to the Earth as a whole, we call it “precession of the equinoxes” because it’s what causes the whole of the background sky to appear to “rotate backwards” relative to its daily regular motion—which includes the equinox points where the ecliptic (the Sun’s path around the sky) crosses the celestial equator.  The axis of the Earth precedes in a complete loop roughly once every 26000 years (currently 25772 years given our current observed rate of precession).

The theory of trepidation, on the other hand, suggested that the rate of the precession of the equinoxes was not a constant rate, but varied and could go either forward or backward.  In the original theory from the classical era, reversing its direction every 640 years or so.  Thus, given a rate of precession of 1° every 80 years, after 8° (thus 640 years), the precession would reverse into procession, such that the equinoxes would move forward eight degrees for the next 640 years, then reverse again, and so forth.  In later and more popular models from the medieval period (especially in Islamic astronomy), trepidation was more of a smaller, less-rigid variation that added to the motion of precession, where the oscillation provided by trepidation occurred over 7000 years, causing the precession of the equinoxes to take place over 49000 years rather than 26000.  It’s this later model that Apianus was describing and subscribed to when he says that the ninth heaven “trepidates”.

Interestingly, the ninth heaven (at least in Apianus’ model) was starless.  While the eighth sphere was full of fixed stars (all conceived of as being roughly the same distance away from the Earth in this geocentric model) and the tenth having just its one sole star (Polaris?), the ninth is a void having nothing in it—except, perhaps, the “waters which were above the firmament” (Genesis 1:7).  Apianus using this biblical model to describe the distant heavens would explain his description of the ninth heaven as being “aqueous”, and would moreover suggest that the wobbling of trepidation could be accounted for by the ripples and waves occurring in such celestial waters.

So there we have it!  We’ve finally knocked out what those intermediate heavens are in Apianus’ famous cosmological diagram, situated between the planetary heavens and the ultimate divine one.  While some of this might be a new thing for some, when placed in its own historical context, all of this is the natural development and expected evolution of a Renaissance take on the geocentric Ptolemaic cosmic model, depicted in a beautifully concise diagram.

But there’s still one issue left: why do the zodiacal sectors not line up in those eighth, ninth, and tenth heavens?  If you look at the eighth and ninth spheres, they line up exactly at Aries and Libra (the equinox points), but they seem to diverge slightly (starting at the east-north-east part of the diagram) before converging again (at the opposite, west-south-west part).  I have honestly no explanation for this beyond it being an artistic whoopsie; after all, sometimes considerations of space and communicability (in the form of the stellated figures and the circle labels) make accuracy and precision a secondary concern.  I feel like there should be a better reason than that, but I haven’t honestly found one beyond it just being something handmade in a constrained space.

But then there’s the dramatic mismatch between the zodiacal sectors of the eighth and ninth heavens with that of the tenth heaven, which can’t possibly be just a slip.  The tenth heaven has Aries starting at the due east point of the diagram, while the eighth and ninth heavens have it starting to the northeast.  What gives?

Well, using my handy-dandy free-to-use planetary observer software Stellarium for the year 1524, we can see exactly what’s going on:

The bright slightly-slanted orange line is the ecliptic, with the faint orange grid of lines being the ecliptical coordinate grid based off it to look at points in the night sky.  The bright more-slanted blue line is the celestial equator (which divides the sky into a “north” part and “south” part).  The ecliptic intersects with the equator at two points, which is where we call the equinox points.  In this case, the image above is centered on the March equinox point, where the ecliptic goes from being below the celestial equator (on the right) to above it (on the left).  The small squiggly faint blue lines in the background indicate constellations, and as you can see, the March equinox point is hanging out somewhere in Pisces, with Aries to the left and Aquarius to the right.

It should be remembered at this point that Western astrology (and historical astronomy, for that matter) has been founded on the notion of a “tropical zodiac”, which is to say a zodiacal system comprising twelve equal 30° segments of the night sky (according to the ecliptic) where the starting point of it (0° Aries) aligns with the March equinox point (where the ecliptic crosses to rise above the celestial equator).  Thus, we consider the segment from 0° to 30° of the ecliptic to be the sign Aries, from 30° to 60° Taurus, from 60° to 90° Gemini, and so on through from 330° to 360° (o°) to be Pisces.  The issue here—as many of my astrologer friends on Twitter are tired of hearing—is that this notion of “sign” doesn’t match up cleanly with the actual physical constellations of the night sky.  Although the constellations were more-or-less aligned with the signs once upon a time, due to precession of the equinoxes, the constellations began drifting “forward” from the signs while the signs drifted “backwards” from the constellations.  Again, precession here was something known to older astrologers from a very early date, so this came as no surprise to any of them—and it’s precisely this mismatch that Apianus is documenting between the eighth/ninth heavens and the tenth heaven.

Thus, in Apianus’ diagram, the tenth heaven’s zodiacal sectors represent the tropical zodiac (aligned to the seasons and the ecliptical crossing of the celestial equator), while the eighth and ninth heavens represent the actual constellations and stars of the sky (which would be a sidereal zodiac, literally “according to the stars” as opposed to according to ecliptical intersections).  This is why the equinox markers (those quartered circles) are placed in Pisces and Virgo in Apianus’ diagram (because technically we have those equinoxes occur while the Sun is in one sign according to the tenth heaven but in another constellation according to the eighth/ninth), and why the Aries sector of the eighth/ninth heavens in Apianus’ diagram start in the northeast rather than th eeast, just as it does celestially if you consider the March equinox point to be due (celestial) east.

Also, one more note: yes, it’s true that while the tropical zodiac doesn’t align with the constellations, neither does the sidereal zodiac.  In both of these zodiacal systems, we’re working with signs, not constellations, and a sign is defined as being a 30° segment of the ecliptic.  The tropical and sidereal zodiacs are identical in every regard except for one: at what point along the ecliptic it should start as being o° Aries.  The tropical zodiac defines this to always be the intersection between the ecliptic and the celestial equator, but the sidereal zodiac…well, it’s a little more complicated.  The sidereal zodiac aims to be closer to the constellations by using what’s called an ayanāṃśa to account for the precession of the equinoxes, and there are a number of different ones in use with some more popular than others (resulting in what’s technically a number of sidereal zodiacs rather than just one).  The issue with even this sidereal approach, however, is that the actual constellations themselves that lend their names and symbolism to the signs don’t neatly align with this equal-segments-of-30° approach.  Some signs are much shorter than 30° (as short as Scorpio’s 6°), some signs much larger (as large as Virgo’s 44°), and there’s even that dumb stupid notion of there being a “thirteenth sign” (Ophiuchus) because its constellation is considered close enough to the ecliptic to make it count (it doesn’t).

Courtesy of this article from Kosmic Mind, here’s a depiction and comparison of the tropical zodiac (inner circle), rough sidereal zodiac (middle circle), and the constellations (outer circle):

Apianus’ diagram makes use of a sidereal zodiac for the eighth and ninth heavens but a tropical zodiac for the tenth heaven, but does not bother with trying to use the constellations themselves (because they weren’t ever really used except perhaps in classical Babylonian or otherwise ancient Mesopotamian times).

Anyway, I thought this was all pretty neat to consider and learn about.  While we today all understand, given the advances of astronomy and physics we’ve had over the past five centuries since Apianus’ time, that a heliocentric model of our solar system is a more accurate descriptor of what’s going on, the geocentric model is still what we intuitively “see” and “feel” from our perspective down here on Earth.  It’s for that reason, coupled with the various and varied religious and cultural traditions that we inherit, that the geocentric model likewise helps us for innumerable spiritual endeavors and systems, too.  I mean, as a comparison, consider the following diagram, produced by Walter Scott in volume 3 of his Hermetica, page 374 in his discussion of the sixth Stobaean Fragment (SH 6):

SH 6 talks about the decans and their relationship to the signs and how their energies affect us down here, and in the course of such a discussion, we end up with a cosmological model again consisting of ten spheres: with the Earth in the center, there’s the seven planetary heavens around that, the eighth heaven of the Zodiac, the ninth heaven of the decans, and then the outermost heaven that wraps around everything.  In this fragment, Hermēs describes the heaven of the decans to be “in between the circle of the universe and that of the zodiac, dividing both circles”, and that the decans “buoy up, as it were, the circle of the universe and define the shape of the zodiac”.  Hermēs describes here also the motion of these heavens with each other, with the tenth heaven whirling constantly, the ninth heaven slowing it down and throttling it, and the planets being whirled around and accelerated by the motion of the decans; in this, the decans move both the planets as well as the outermost sphere of the cosmos itself.  It’s certainly not the same model as what Apianus was describing over a thousand years later, but there are certainly commonalities as both share in a common geocentric Ptolemaic ancestor, and both aim to describe the cosmos according to what we can see and observe down here on Earth.

Notably, we should also remember that what Apianus was getting at wasn’t so much to describe a spiritual reality of the cosmos, but rather a scientific one according to the science of his time.  His Cosmographia is an incredible and well-designed work, and besides the fascinating woodcarved illustrations also included little movable dials and tools that allowed readers to interact with the illustrations to learn about cosmology, geography, cartography, and other sciences.  As a result, it’s been argued that such a work as his not only facilitated better understanding of such topics popularly, but also spurred on the field of amateur astronomy precisely by equipping people with the basic tools they needed, preparing for and facilitating the later scientific revolutions that were to come.  However, even if his aim was more purely “scientific” in the modern sense of the word, we can’t neglect that such sciences are just one part of our lives, with the physical aspects to be integrated with the spiritual, which would also go a ways in explaining why Apianus’ cosmological diagram depicting the various heavens is so popular in occult discussions even today.  (And which also lends itself to some rather beautiful modern pieces of art as well.)

And yes, as the astrologer and geomancer Eric Purdue (yes, the same one who recently translated Cornelius Agrippa’s Three Books of Occult Philosophy afresh and correctly into modern English!) took the opportunity to reiterate on Twitter: the signs lie outside the stars, and we shouldn’t conflate signs with constellations.

The above post was originally a thread on Twitter, which you can read here but which I’ve reformatted and expanded into a proper blog post.  Although I made it earlier this summer and then promptly forgot about it, a conversation on one of the Discord servers I’m on reminded me that I wrote about it, so I figured that I may as well make it a bit more visible and readable.

On Timing Daily Prayers to the Degrees of the Decans

I’ve had this idea in my head for prayer practice that revolves around the notion of cycles.  For instance, as part of my daily prayer practice, I’ve written a set of seven prayers, one for each of the seven days of the week, which I recite on an ongoing cycle.  They’re not necessarily planetary prayers, like you might find in the Hygromanteia or Heptameron, but they do have some planetary allusions and hints thrown into them.  The seven-day week, which is fundamentally a Mesopotamian invention, makes for a simple cycle of prayers, but I’ve been thinking about ways I could incorporate more cycles into my prayers.  For instance, a simple and short invocation for each of the days of a lunar month—with my Grammatēmerologion, my oracular Greek letter lunisolar calendar—based around the powers and potencies of each of the letters of the Greek alphabet, along with their spirits or gods, could be something fun to toy around with.  There’s lots of opportunities for this sort of practice:

  • the four turns of the Sun each day, a la Liber Resh (sunrise, noon, sunset, midnight)
  • the seven days of the week
  • the 24 planetary hours of a given day
  • the four (or eight) phases of the Moon (new, crescent, first quarter, gibbous, full, disseminating, third quarter, balsamic)
  • the 29/30 days of a synodic lunar month
  • the 28 days of a sidereal lunar month (a la the 28 lunar mansions)
  • the 30/31 days of a solar month (a la the 12 signs of the Zodiac)
  • the four seasons (solstices and equinoxes), perhaps also with the four cross-quarter days (midpoints between the solstices and equinoxes)
  • the 10 days of a decan
  • when a planet stations retrograde or direct
  • when eclipses occur
  • when a planet or star is seen at its heliacal rising or setting

There are lots of opportunities to engage in prayers linked to or with the natural cycles of the cosmos, many of which are fundamentally astrological in nature.  The idea of coming up with a large-scale overarching prayer practice that engages in such cycles, to me, would be a fantastic way to recognize these natural cycles, bring oneself into alignment with them, and tap ever more greatly into the power of these cycles, especially when certain cycles interact or sync up with each other.  By aligning ourselves with these cycles, we can not just make use of χρονος khronos “time” generally, but also καιρος kairos “the moment”, the fleeting opening of opportunity itself that allows us to do the best thing possible.  There’s this Hermetic notion—it’s hard to find the note I was referencing for it, but I’m pretty sure it’s in Copenhaver’s Hermetica or Litwa’s Hermetica II—that we rely on kairos in order to fully carry out the process of rebirth in the Hermetic mystical sense, and that would be determined by the processes of Providence, Necessity, and Fate along with the very will of God.

Along these lines, I wanted to come up with a new cycle of prayers for myself, one specifically for the decans.  Some might know these as faces, the 36 10° segments of the ecliptic, three to a sign of the Zodiac.  The decans are old, as in ancient Egyptian old, and play a part in the astrological prognosticatory and magical literature of the Egyptians, Arabs, Brahmins, and Hermeticists the world over.  We see them referenced in magical-medical texts going back to the classical period, and they also appear in such texts as the Picatrix as well as Cornelius Agrippa (book II, chapter 37).  Though they come up time and time again, they also take so many wildly different forms between traditions and texts, which is fascinating on its own merits.  We even see Hermēs Trismegistus himself talk about the decans and their importance in the Sixth Stobaean Fragment.  In that part of the Hermetic cannon, Hermēs explains to Tat that the decans belong to a celestial sphere between the eighth sphere of the fixed stars and the higher sphere of the All, being a backdrop to the very stars themselves, and thus higher than the constellations and signs of the Zodiac.  These decans exert “the greatest energy” on us and the world, and they drive “all general events on the earth: overthrows of kings, uprisings in cities, famines, plagues, tsunamis, and earthquakes”.  In other Hermetic texts, like the Sacred Book of Hermēs to Asclepius, the decans also rule over specific parts of the body and the injuries and illnesses that afflict them (which is a very Egyptian concept indeed that we see in purer forms of Egyptian religion and spiritual practice).

You can probably guess where I’m going with this: more prayers and a ritual practice dedicated to the decans.  This would consist of two parts:

  • An invocation of the powers of the decan itself, according to its specific form and name and virtues, to be done when the Sun enters that decan.
  • One prayer per each day the Sun is in a given decan, a set of ten prayers to be recited over a ten day decanal “week”.  Since the Sun spends about one day per degree, this means that each degree of a decan can be considered a separate day, and each day with its own prayer.

After some thinking, I was able to come up with a relatively straightforward set of prayers for the decans themselves at the moment (or the first sunrise following) the Sun’s ingress into them, but it’s the latter part I’m still struggling with.  I have ideas about what to base them on—the ten Hermetic virtues from the Corpus Hermeticum, the Pythagorean symbolism of the first ten numbers, and so forth—but coming up with those prayers is a slow process, indeed.

In the meantime, I’ve been working on a bit of a programming project, something to plan ahead and help me figure out what such a prayer practice would look like scheduled out.  This is basically what I was doing with my Grammatēmerologion project, coding up a variety of astronomical functions to calculate the various positions and attributes of celestial bodies for any given moment, and courtesy of SUBLUNAR.SPACE (whose online customizable almanac is an invaluable and deeply treasured tool for any magician nowadays), I was tipped off to a much easier and faster way to develop such astronomical programs: the Swiss Ephemeris codebase, of which I found a Python extension for even more flexibility.

And that’s when the problems started.  (Beyond the usual mishaps that come along with any nontrivial programming project.)

See, as it turns out, there are more days in a year than there are degrees in a circle—which means that while the Sun moves roughly one degree per day, it actually moves slightly less than one degree per day.  This is why we have 365 days (or 366 days, in leap years) in a year.  To the ancient Egyptians, they considered the civil solar year to only have 12 months of 30 days each, each month consisting of three decans, with a leftover set of five days at the end of the year, considered to be the birthdays of the gods Osiris, Horus, Set, Isis, and Nephthys.  These intercalary (or epagomenal) days were considered a spiritually dangerous and liminal time, but once those days were over, the calendar was brought back into sync with its proper cycle.  However, what I wanted to do is to come up with a 10-day cycle linked to the degrees of the Sun, which means I would have to deal with these epagomenal days throughout the year instead of bundled up all at the end.  My logic was simple:

  • Start counting decan day assignments (decan day-numbers) starting from the first sunrise after the March equinox (which is when the Sun enters 0° Aries as well as the first decan).
  • Judge the degree of the ecliptical position of the Sun based on sunrise of any given day.
  • Take the whole degree of the Sun (e.g. if 9.459°, then 9), divide by 10, take the remainder, and that’s your day in the cycle.  Thus, if o°, then this is our first day; if 1°, the second day; if 2°, the third day;…if 9°, the tenth day.  Thus, when we hit the next o° day, we start the cycle over.
  • If the whole degree of the Sun is the same as the previous day (e.g. 7.998° for today and 7.014° for yesterday), then this is an epagomenal day, and we say either no prayer at all or an eleventh special prayer not otherwise used except for epagomenal days.

A relatively simple method, all told.  Or so I thought.  When I actually ran the program, I noticed that there were not five epagomenal days (e.g. 1-2-3-4-5-X-6-7-8-9-10, where X is the epagomenal day) in the final count, but seven, which was…weird.  This would mean that there were 367 days, which would be wrong, except that there were 365 outputs.  It turns out that there were two skipped days (e.g. 1-2-3-4-5-6-7-9-10, but no 8), one in early December and one in mid-February.  On top of that, although I expected the epagomenal days to be spaced out more-or-less equally throughout the year, they were all between early April and mid-September.  After looking into this, and making sure my code was correct (it was), what’s going on is this:

  • I made the mistake of assuming that the Sun moves at a constant speed each and every day of the year.  It doesn’t, for a variety of astronomical factors.
  • The Sun spends more time in the northern celestial hemisphere (about 185 days) than in the southern celestial hemisphere (about 180 days).
  • The Sun moves slower in winter around perihelion than in the summer around aphelion.
  • From winter through summer, the sunrise gets earlier and earlier, pushing the judgment-time of each day earlier and earlier, while in summer through winter, the reverse happens.

Talk about vexation: I had here what I thought was a perfectly reasonable method—and to a large extent, it is—yet which results in the cycle just skipping days, which I intensely dislike, since it breaks the cycle.  Without doubling up prayers on the skipped days, which I’d really rather like to avoid, it means that I couldn’t use this otherwise simple method to figure out a decanal 10-prayer schedule that would be in sync with the Sun.

After thinking about it some, I considered five different ways to associate the days to the degrees of the decans:

  1. The “Egyptian” method.  This is the most old-school and traditional, and mimics the behavior of the actual ancient Egyptian calendar: starting from the New Year, assign an unbroken cycle of days from day one to day ten 36 times.  This gradually becomes more and more unsynced as time goes on, but we throw in five or six epagomenal days at the very end to catch up all at once before the next New Year.  Simple, traditional, clean, but it’s really the worst of the bunch with the accumulating degree differences that get resolved all at once at the end of the year instead of periodically throughout the year.
  2. The “plan-ahead” method. Like the Egyptian”method, this is a pretty artificial way to allocate the days, but elegant in its own way, and spreads out the epagomenal days across the year more-or-less regularly.  We know that, at least for the foreseeable future, we’re going to deal with either normal years of 365 days or leap years of 366 days.  For normal years, we need to have five epagomenal days, so we insert an epagomenal day after the 8th, 15th, 22nd, 29th, and 36th decans (or, in other words, every seventh decan not including the first).  For leap years, we need six epagomenal days, which we insert after the 6th, 12th, 18th, 24th, 30th, and 36th decan (i.e. every sixth decan).  Note that we judge a year to be a normal year or a leap year based on the Gregorian calendar year prior to a given March equinox; thus, for this method, we start assigning days from the March 2020 equinxo using the normal method because the prior calendar year, 2019, was not a leap year; we use the leap year method starting from the March 2021 equinox because the prior calendar year, 2020, was a leap year.
  3. The “true degree” method.  This is the method mentioned before: starting with the New Year at the March equinox, when the true degree of the Sun is exactly 0° and using sunrise at one’s location as the reference time, take the degree of the Sun and compare it to the degree at the previous day’s reference time.  If the degree is in the next whole number (e.g. 23.005° and 22.025°), the day proceeds to the next whole number; if the degree is in the same whole number (e.g. 23.985° and 23.005°), then it’s an epagomenal days.  The problem, as stated earlier, is that due to the varying speed of the Sun as the Earth travels between perihelion and aphelion (which also has the effect of the Sun spending more time in the northern celestial hemisphere than in the southern celestial hemisphere), we end up with more epagomenal days than expected around aphelion, and with days that are outright skipped around perihelion.  While the exact match of day to degree is appealing, it’s the skipped days that breaks cycles and which ruins the whole prayer system I was trying to devise.
  4. The “average degree” method.  This is a variation on the true degree method, only instead of using the Sun’s true position at the reference time on each day, we take a theoretical position of the Sun based on its average daily motion of 360.0°/365.2421897 days = 0.98564735989°/day.  Starting with the New Year at the March equinox, when both the true degree and average degree of the Sun is exactly 0°, using sunrise at one’s location as the reference time, take the theoretical average degree of the Sun (advancing it by the Sun’s average daily motion day by day at the reference time) and compare it to the degree at the previous day’s reference time, with the same epagomenal rule as before.  The benefit to this method is that it gets us the expected number of epagomenal days which are evenly distributed throughout the year without skipping any other days; the downside is that, as we get closer to the September equinox, the theoretical average position of the Sun drifts further away from the true position by as much as 3.780°, putting us three or four days out of sync with the true position.
  5. The “rebalanced true degree” method.  This is an extension of the true degree method above.  We start with the assignments of days to degrees as before, extra epagomenal days and skipped days and all, but we “rebalance” the days by removing some epagomenal days and reinserting them where we were earlier skipping days.  For every skipped day, we alternate between choosing the first and last of the epagomenal days.  So, if we have seven epagomenal days on year days 24, 59, 83, 105, 127, 151, and 182, and we have two skipped days on days 274 and 333, then we first remove the first epagomenal day from day 24 and reinsert it on day 274, and then the last epagomenal day from day 181 (was 182 before we removed the other one) and insert it on day 333.

So, five different methods of assigning days a decan day-number, one of which (the Egyptian method) being the most regular and artificial with the worst drift, one of which (the true degree method) being the most accurate and realistic yet which skips days entirely, and three other methods (plan-ahead, average degree, rebalanced true degree) that vary in terms of computational complexity and accuracy.  We know that the true degree method is the most accurate, so we can plot the various other methods against it to visually see how bad the drift is between it and the other methods.  In the following graphs, the true degree method is given in red, with the other method being compared to it in blue.  Epagomenal days are marked as having a decan day-count number of -1, hence the severe dips at times.  Where the blue and red lines are more in sync, the method is better; where the lines depart, the method gets worse.  The true degree method gives an epagomenal day in decans 3, 6, 8, 11, 13, 15, and 18, and if you look close enough, you can see the skip in the days towards the end of decans 27 and 33.

Just visually looking at these methods, we can see that all four methods start off the same for a little more than the first two decans, but after that, most of them begin to diverge.  The Egyptian method is worse in how often and by how much it diverges, with that nasty flatline of epagomenal days at the end, and the plan-ahead method doesn’t fare much better, either; note also how both of these methods end with epagomenal days for at least the final day of the year.  The average degree method doesn’t look too bad, though it does get worse around the September-October area of the year before it gets better again, eventually getting back in sync for the final three decans of the year.  By far the most pleasing and in-sync graph we see is with the rebalanced true degree method, which does vary a little bit but by no means as bad or as irregularly as the other methods; we have about five decans where they’re in sync, 22 where they’re one day off, and nine when they’re off by two days.

But, besides just looking at them with my eyeballs, how should I best compare the accuracy of all these methods?  What I settled on was a ratio between the day’s decan day-number according to a particular method and the true degree expected for the Sun for that day:

  1. If a given day is an epagomenal day, throw out the value entirely, and don’t factor it into calculations.
  2. For a given day reckoned at the reference time (sunrise on the March equinox for a given location), find the Sun’s true ecliptic position.
  3. Take the whole degree of the Sun (e.g. if 9.227°, 9).
  4. Divide the number from the previous step by 10 and take the remainder.
  5. Add one to the previous step.
  6. Divide a given day’s decan day-number by the previous step.

The shortcut to this method would basically be to divide the method’s decan day-number for a given day against the true degree method’s decan day-number, but I wanted to be sure I was getting the Sun’s true position here for mathematical rigor.  This ratio indicates the general percentage difference we expect; if the ratio is 1, then the given method’s decan day-number is what we’d expect; if more than 1, it’s ahead of what we expect; if less than 1, behind what we expect.

Doing some simple math on these ratios for these given methods gets us the following statistics (omitting the epagomenal days entirely), judged against the year from the March 2020 equinox through the March 2021 equinox (considered a normal year).  I calculated these results based on a prototype decanal calendar starting on March 20, 2020 at 11:12 UTC (the first sunrise after the spring equinox for my town’s given longitude) for 365 days.

Method Mean Median Min Max STD Variance
Egyptian 1.71222574 1 0.1 8 1.856253825 3.445678262
Plan-ahead 1.467144864 1.333333333 0.1 6 1.09989769 1.209774928
True degree 1 1 1 1 0 0
Average degree 1.351345416 1.166666667 0.1 5 0.9200161032 0.8464296301
Rebalanced true degree 1.211630551 1.2 0.1 3 0.5348857385 0.2861027532

In the 2020/2021 year, we can see that it’s the rebalanced true degree method that has the lowest standard deviation and variance, with the mean closest to 1.  This means that the rebalanced true degree method gets us the closest decan day-numbers to what the Sun’s actual position is on the whole, being at worst three days ahead (compared to the potential of being five, six, or eight days ahead with the other non-true degree methods).

For another look, we can also consider the leap year (according to our rule above) for the March 2021 equinox through the March 2022 equinox.  I calculated these results based on a prototype decanal calendar starting on March 20, 2021 at 11:13 UTC for 366 days.

Method Mean Median Min Max STD Variance
Egyptian 1.704857316 0.85 0.1 8 1.89868141 3.604991096
Plan-ahead 1.432609127 1.333333333 0.1 6 1.044951208 1.091923027
True degree 1 1 1 1 0 0
Average degree 1.338694885 1.2 0.1 5 0.8991436886 0.8084593728
Rebalanced true degree 1.142828483 1.142857143 1 2 0.3982472329 0.1586008585

We get even better results during leap years, it’d seem, at least based on this example alone; we’re only a max of two days ahead of the Sun’s true position, and we have even less variance and deviation than before.

If I were to go with any system of assigning a 10-day repeating cycle of prayers to the days to keep more-or-less in sync with the position of the Sun as it goes through the decans, I’d go with the rebalanced true degree method.  Still, even if it’s the most in sync, it’s not truly in sync, as there really isn’t such a system possible without skipping days due to the inconvenient misalignment of physical phenomena with discrete human systems of calendrics.  As SUBLUNAR.SPACE commiserated with me about on Facebook, as he found out when he was coding his own almanac program, the decans “do not like to be pushed into human patterns”, and that we really have to choose degrees or days, because we can’t have both.  In his almanac, he settled with marking things by the actual ingress, which was the common practice in the decan calendars of Ptolemaic times.  On top of that, as far as calculation goes, it’s among the more complicated, requiring manual rebalancing after figuring out the true degree day equivalences first for the whole year until the next March equinox; easy enough to do by a computer program, but tedious or outright difficult to do by hand.

For now, I’m going to content myself with marking the Sun’s ingress into the decans, and leave it at that.  For one, though I’d like to engage in a 10-day cycle of prayers aligned with the decans, and even though I have some sort of system in place to explore that, I still don’t have those damn ten (or eleven) prayers written up for them.  But, at least knowing what the schedule looks like is a start.

Genius in the Picatrix: Ritual Prep and Setting the Altar

Last time, we started talking about a particularly interesting bit of the Ġāyat al-Ḥakīm, the “Goal of the Wise”, sometimes just known as the Ġayah, but definitely better known in the West as the Picatrix, most likely written in Arabic sometime in the middle of the 11th century CE.  Everyone knows the Picatrix, everyone loves the Picatrix; it’s a fantastic text of astrological magic, and among the earliest of true grimoires in Europe.  Although focused on what we’d nowadays call stellar image magic, the creation of astrological talismans bearing magical images and scenes made under particular stellar configurations, the text is famous for its wide inventory of bizarre magical concoctions and confections for a variety of purposes, its lengthy invocations to the planetary spirits, and its preservation of older pagan practices from the Hermetists, Sabians, Nabataeans, and various other Mediterranean peoples.  It is not, however, a particularly theurgical text on the whole, even though it contains a wealth of information on philosophy, spiritual and cosmic frameworks, and the like in how and why magic works the way that it does.  Yet, in book III, chapter 6, we encounter an interesting section on the “Perfect Nature”, a sort of guiding spirit or genius, originally encountered by Hermēs Trismegistus himself.  The last post went on at length analyzing the meaning of the vignette of Hermēs Trismegistus encountering Perfect Nature; if you need a refresher on what we talked about last time, go read the last post!

So, after the vignette, or rather as part of it, Perfect Nature introduces itself to Hermēs Trismegistus.  But he doesn’t just stop there (Warnock/Greer translation):

I asked him who he was, and he replied: “I am Perfect Nature; if you wish to speak to me, call me by my proper name, and I will answer you.” I asked him them by what name he was called, and he answered me, saying, “By the four names mentioned above I am named and called.” I asked him next at what times I should call him, and how I should make the invocation.

At this point, Perfect Nature describes a ritual to Hermēs Trismegistus to be done to invoke the Perfect Nature as a form of divine communion.  According to the Picatrix, which itself claims that all this is according to the Kitab al-Isṭamāḵis/Liber Antimaquis, “the ancient sages used to perform this working every year” (the Atallah/Kiesel translation says “once or twice a year”) “for the sake of their spirits, so that they might put in order their Perfect Natures”.  The Picatrix also goes on to say that Aristotle himself claims that this allowed the ancient sages to have “his proper virtue infused into him by exalted spirits, by whose powers their senses were closed, their intellects opened, and sciences revealed to them”, and that “this virtue was conjoined with the virtue of the planet ruling the radix of the nativity” (i.e. one’s ruling planet, the almuten of one’s natal chart) “so that the virtue thus co-created in them strengthened them and gave intelligence to them”, and that in this way the sages “helped themselves in their knowledge and understanding, and the increase of their business and possessions, and guarded themselves from the plots of their enemies, and did many other things”.

Warnock and Greer make an important observation at this point in their translation:

This entire passage is reminiscent of the Poemandres, the first dialogue of the Corpus Hermeticum, in which Hermes has a conversation with a similar spiritual being.  The ritual that follows is of great interest; it seems to bridge the gap between classical rituals for evoking a guardian spirit, of the sort found in the Graeco-Egyptian magical papyri, and early modern rituals for the same purpose such as the famous Abramelin working.

Based on the ritual that follows and everything we already know about the Perfect Nature, I’m absolutely in agreement with them.  Perfect Nature is already being presented through the vignette as an actual spirit one can interact with, and is described as a sort of spirit that neatly fills the role of genius, tutelar, agathodaimōn, or guardian angel.  What’s interesting about the Picatrix, however, is that it also breaks out the single entity of Perfect Nature into its four works of Meegius/Tamāġīs, Betzahuech/Baġdīswād, Vacdez/Waġdās, and Nufeneguediz/Nūfānāġādīs, each corresponding to a particular power—or individual spirit, if you choose to interpret the Picatrix that way.  In either case, Perfect Nature is both one and many: a single entity with distinct powers, or a single entity as a collective of four spirits.  I lean towards the former interpretation, as discussed earlier.

According to the Latin Picatrix and its translations, the ritual to commune with Perfect Nature is to be done when the Moon is in the first degree of Aries (i.e. between 0°0’0″ Aries and 0°59’59.999…” Aries); it does not matter whether the ritual is done during the daytime or nighttime, so long as the Moon is in this degree of Aries.  On average (and this can vary incredibly depending on the specific speed of the Moon at this time, based on where the Moon’s apogee/perigee is relative to the first degree of Aries), this gives you a window about 110 minutes long on average, or a little less than two hours, once every 28-ish days.  This also puts the Moon starting a new sidereal cycle, coinciding with:

  • The first lunar mansion, An-Naṭḥ (Alnath), which is good “to go on a journey, so as to travel safely and return in good health…to place discord and enmity between husband and wife, and between two friends so that they become enemies, and to sow discord between two allies…to cause servants to flee” (book I, chapter 4), as well as “for destruction and depopulation” (book IV, chapter 9).
  • The first face/decan of Aries, “a face of strength, high rank and wealth without shame” (book II, chapter 11), which makes one to be “always victorious in battle, litigation and controversy and gain what they wish, and are never defeated; and…to hinder the milk of beasts and destroy their butter” (book II, chapter 12).

Granted, these observations are really more for making talismans in the vein of stellar image magic than anything connected to the present ritual, although the notions of “going on a journey safely and in good health” along with “strength, high rank, and wealth without shame” and victory without defeat are always nice suggestions, too.  What matters most is that the Moon is in the first degree of Aries; if you wanted to put a nice touch on it, you could aim for this to coincide with a planetary hour and/or day corresponding to the planet that governs you, or have a sign of that planet rising or culminating, but these are secondary concerns at best.  However, in the Atallah/Kiesel translation of the Arabic Picatrix, the phrasing is given somewhat differently: “when the Moon comes down to the level of the Head of Aries at any time in either day or night”.  This might be a poetic or idiomatic way of saying the same thing the Latin Picatrix is saying (“cum Luna in primo gradu Arietis fuerit in die vel in nocte”), but it could be interpreted in other ways.  For instance, knowing that the first lunar mansion is associated with the star β Arietis (Sheratan, the lower/first horn of Aries), we could do away with signs and lunar mansions entirely and link the entire ritual to the conjunction of the Moon with this star, ignoring the effects of precession.  Still, I think the simple explanation here is the easiest and most straightforward: the ritual is to be done in that brief window of time when the Moon is in the first degree of Aries.

Taking a step back, now that we know when to do the ritual, what about preliminary purification or other spiritual preparations to be made ahead of the ritual?  Although the Picatrix doesn’t really say much about this, it does say that the philosopher Tintinz the Greek (طمطم الهندي Ṭumṭum al-Hindī in the Arabic Picatrix, a name known to students of geomancy as a student of Hermēs Trismegistus) claims that “one who desires to perform this work ought to abandon all intention and contemplation concerning other things, because the root and foundation of all these workings consists of contemplations” (see above about the role of contemplation as the main vehicle for empowering images), and that either the philosopher Caraphzebiz (in the Arabic Picatrix, كرفسايس Karafsāyis?) or his student Amenus (in the Latin Picatrix, who is not mentioned in the Arabic Picatrix as far as I can tell), likewise says that (Warnock/Greer translation):

…any sage who wanted to work magic, and preserve himself with the powers of the spirits, ought strictly to give up all cares and all other sciences beside this one, because when all the senses and the mind, and all contemplations about other things, are strictly turned to magic, it may be acquired with ease; and since many assiduous contemplations are appropriate to this science of magic, the magician must wrap himself in these, rather than being wrapped around any other things.

In other words, yeah, works of purification and other preliminary preparations of the mind, spirit, soul, and body should be undertaken before this ritual, even if only to refine the focus and desire of the person who undertakes it.  This is especially backed up by what Ibn Khaldūn says in the Muqaddimah:

A man is said to have done this after he had eaten but little and done dhikr exercises for several nights. A person appeared to him and said, “I am your perfect nature.” A question was put to that person, and he gave the man the information he desired.

So, based on this, I would suggest engaging in a period of fasting accompanied by works of steadfast devotion and sincere prayer, especially the repetition of divine names or chants (perhaps including the Four Names of Perfect Nature as well?), at least for three days leading up to the ritual, but more preferably seven or longer, perhaps even for a full lunar month starting from the previous time the Moon entered the first lunar mansion.

Before or during this preparatory period, gather together the following supplies:

  • Almond oil
    • If one has an allergy to nuts, substitute with a neutral oil not otherwise listed here.
  • Walnut oil
    • Warnock/Greer and Attrell/Porreca both only say “nut oil” based on the Latin “oleum nucum”, but Atallah/Kiesel specify “walnut oil” for دهن الجوز duhn al-jawz.  The word there can mean nut generally, but it is used specifically for walnuts as well.
    • If walnuts are a no-go, use another nut-based oil that is not almond oil that’s sweet and good for baking or in cooking desserts, like hazelnut or macadamia nut.
    • If one has an allergy to nuts, substitute with pine nut oil.
  • Sesame oil
    • Atallah/Kiesel say “vinegar oil”, and I have no idea what they mean by that.  Perhaps a thick, reduced vinegar, like a balsamic vinegar?
    • The Arabic phrase used for this is دهن الخل duhn al-ḵall, which does literally mean “oil of vinegar”, and is called for in another part of the Picatrix (book III, chapter 11, “that you may appear in the form of any animal you wish”), where, again, the Latin Picatrix renders this as “sesame oil”.  There are also other Latin works based on Arabic works that do seem to regularly translate sesame oil for “oil of vinegar”.
    • The confusion here is between دهن الخل duhn al-ḵall (oil of vinegar) and دهن الحل duhn al-ḥall (oil from whole sesame seeds).  In Arabic script, the difference is of the presence or absence of a single dot, which can confuse the two meanings.  In general, it seems that the use of “vinegar” here is a typo in the Arabic, given how common it was across the Mediterranean to translate this phrase as “sesame oil” into a variety of languages by different translators.
    • I suppose, however, that one could make an argument that this is something more alchemical than anything else (a la “oil of egg” or “oil of gold”), but this seems unlikely to me.
    • I would most recommend sesame oil (reading it as duhn al-ḥall), as it makes the most sense in this context, though if the vinegar approach were taken (reading it as duhn al-ḵall), this would probably be implied to be balsamic vinegar.
  • Cow’s milk butter
    • I’d recommend unsalted butter, personally.
    • Although there exist non-dairy butter substitutes, I cannot recommend their use due to the symbolic importance of this having come from a living creature (more on that later).
    • In the case of an extreme allergy to dairy, I might recommend the use of shea butter or cocoa butter, but only as an extremely limited case.
  • Wine
    • Atallah/Kiesel just say “alcohol”, though the word used in the Arabic Picatrix is خمر ḵamr, wine.  However, no specific type of wine is mentioned in the Latin Picatrix or its translations.  My personal preference would be a semi-dry white wine, and barring that a light sweet red wine, but that’s just me.
  • One large glass serving dish
    • A large low glass bowl would be perfect for this, even better if it had a separation in the middle (a la a chips-and-dip serving platter).
  • Eight glass pint-sized pitchers or tumblers
    • Each of these holds the wine, oil, or butter.  Warnock/Greer say that each of these pitchers “should have a capacity of around one pint”, while Attrell/Porreca and Atallah/Kiesel both say that these pitchers should be big enough to hold one pound of the wine, oil, or butter.  Checking WolframAlpha, making these to be pint-sized containers does in fact check out.
    • However, that assumes we know exactly which “pound” is intended for use.  One avoirdupois pound (standard in the modern US) is 453.6 grams which is equivalent to 497mL or 16.8 fl oz, but there are other definitions of pound out there historically, too, and may be closer to what was intended in the original Picatrix (using olive oil as a neutral base for unit conversion and comparison here):
      • Roman pound, equivalent to 328.9 grams (360mL, 12.2 fl oz)
      • Byzantine gold pound, which was originally 327.6 grams (359mL, 12.1 fl oz) but decreased over time to about 319 grams (349mL, 11.8 fl oz)
      • Byzantine silver pound, equivalent to 333 grams (365mL, 12.3 foz)
      • Byzantine oil pound, equivalent to 256 grams (280mL, 9.48 fl oz)
    • Based on these, I’d personally go with the Byzantine oil pound, which means instead of using pint-sized (16oz) pitchers, one needs more like 10oz containers, so a little more than half that size, about the size of a standard disposable styrofoam cup or a little more than halfway of a Solo cup.  I think this is fine, especially as almond oil or walnut oil can be expensive.
    • No material for these pitchers is specified, though I’d recommend glass to match the large serving dish above and the symbolism of the glass lantern in the vignette.
  • Sugar
    • Date palm sugar would be best if you wanted to go for cultural or historical accuracy.
  • Honey
  • Coal
  • Incense blended or compounded from frankincense and mastic
    • Atallah/Kiesel say “kandar, a good-smelling glue”.  From what I can find, this is actually a Persian term that just refers to frankincense, but probably high- or top-grade milky-white frankincense.  However, a gloss in the footnotes says that either a part of this phrase that references what to use (بالكية والكندر) is either just frankincense or is frankincense and mastic.  I’d go with using both.
  • Aloeswood (aka oudh or agarwood)
  • One tall candle
  • Two braziers for burning incense
  • A table

Before the ritual, physically clean and spiritually cleanse the ritual area so that it may be made “clean and splendid”.  Although the Picatrix says “house” here, this should better be understood to mean one’s temple space or ceremonial chamber—though cleaning and purifying the whole house where this would take place certainly wouldn’t be a bad idea.

Once the ritual area has been appropriately cleaned and cleansed, prepare the altar.  On the eastern side of the ritual area, set up a table (a card table, coffee table, etc. would be perfect for this).  The Warnock/Greer translation says “a raised table”, the Attrell/Porreca translation “a table raised from the ground”, and the Atallah/Kiesel translation “a table…on a step higher than the ground”.  What we’re looking at is a table set on a dais or other low platform, with the dais probably no more than a foot in height.  For comfort’s sake, I’d recommend the dais be a little larger than the table itself, but not too much so.  An impromptu platform made from bricks, a piece of plywood supported by some low cinderblocks, or the like would be perfect.

Before setting up the altar, a particular kind of sweet confection must be made with butter, honey, walnut oil , and sugar.  Based on the Latin and Latin-translated Picatrix alone, this may look like a sweet whipped creation, much like a buttercream frosting.  Atallah/Kiesel, however, say that this is “a candy” (later, “candies”, suggesting less a mass of substance and more parceled-out bits of it) made with “lots of sugar” and that “it needs to be very sweet and heavy on oil”.  Rather than buttercream frosting, what this may mean is to aim for something closer to toffee or butterscotch candy.

The altar should have the following things on it:

  • One pint-sized pitcher of almond oil, set towards the east on the altar
  • One pint-sized pitcher of walnut oil, set towards the west on the altar
  • One pint-sized pitcher of cow’s milk-based butter, set towards the south on the altar
    • This could be solid or melted or something else; given the presence of liquid oils for the other three such containers, melted butter or even clarified butter may be meant here.  My preference would be for whipped or otherwise non-compacted butter.
  • One pint-sized pitcher of sesame oil, set towards the north on the altar
  • Four pint-sized pitchers of wine, one placed to each of the four directions on the altar
    • These may be placed immediately to the side of the containers of the oils and butter along the edge of the table, or just beside them closer to the center, or with the pitchers of wine on the outside and the pitchers of oil and butter on the inside.
  • A glass dish filled with the candy/confection made from cow’s butter, walnut oil, honey, and sugar, placed in the center of the altar
    • No description of the containing dish is given beyond “glass”, but to my mind, simple clear glass would be best; the other containers for wine and oil would best be made of the same material, ideally even in a matching style.
    • Clear a space in the center of the dish to hold the candle later, if at all possible.

I suppose, of course, that one could also cover the table with a tablecloth; I’d recommend a white linen cloth that hangs down generously around the table, but that’s just me.  None is mentioned in the original text, so we’d be fine without it.

In addition to preparing the ritual space and the altar, we also need to prepare two braziers or censers, one to burn a mixture of frankincense and mastic (or just frankincense, maybe? per the Arabic Picatrix), the other to burn aloeswood, but the Picatrix does not say where to put these things.  If free-standing braziers are to be used (which seems to be the best practice here), I would put the one with frankincense and mastic to the north of the altar and the one with aloeswood to the south, at least three feet away on either side, depending on how much space one has available.  If smaller censers are to be used, they may be put on platforms of their own (milk crate-sized boxes would be perfect, or taller standing pillars if you wanted to be fancy) in the same positions.  Other options for using smaller censers could be to put them directly on the altar itself (I’d recommend keeping to the north/south positioning halfway between the cups and the dish) or underneath the altar directly on the dais (which I don’t find likely or recommended here at all).  The brazier approach, or otherwise keeping the censers off and away from the altar, seems to be the most reasonable.

Unlike other parts of the Picatrix that specify the metal to be used for the censers (e.g. book IV, chapter 2), no description of the material is given, so it probably doesn’t matter.  Simple braziers, made from a steel or iron bowl or chafing dish to hold the coals and incense and supported on metal or wooden legs as a tripod, or otherwise simple small censers, would really be best, especially given the simplicity of the ritual as a whole.  However, if you wanted to customize this aspect of the ritual setup for yourself based on other Picatrix practices for your own ruling planet, the metals from book III, chapter 7 would be good to observe:

  • Saturn: iron
  • Jupiter: tin
  • Mars: bronze or brass
  • Sun: gold
  • Venus: electrum (gold and silver alloy)
  • Mercury: “fixed mercury” (mercury alloy)
  • Moon: silver

If you wanted to go the extra mile, you could also make a special censer for yourself based on the instructions given in book III, chapter 5.  Such a censer would be best used for works with a particular planet, to be made with that planetary metal in the form of a hollow cross, open at the top to allow smoke to exit, and with the container for the coal/wood/fire and the incense underneath such that all the smoke of the incense would flow up through the cross and out the top.  This also has the beneficial symbolic association of smoke rising up a single channel, in the sense of rising up from a pit or straight up to Heaven in our inverted vignette.  Again, this is almost certainly and entirely unnecessary for the present ritual, but the Picatrix does have quite a lot of tech to share.  For reasons that we’ll get to later, a more general metal or material rather than one specific to any given planet might be better; better to keep it simple.

And yes, of course, for those who are operating on a budget and cannot afford braziers/censers, frankincense/mastic resin, and aloeswood (whether as whole wood chips or as powder), using self-igniting stick or cone incense is also acceptable.  It’s definitely better to go with loose incense on coals, especially as stick and cone incense tends to be compounded with fillers and other scents, but it’ll work for those who need it to work.

All this is a lot to talk about the initial ritual prep, but there’s still more to talk about along these lines, not to mention the ritual itself.  That’ll be in the next post, so stay tuned!

New Translation on Magical Medieval Runes, and an Elemental Cipher

Recently, I got the translating bug again, and managed to get a few texts translated from medieval Latin to English, and since these texts haven’t been translated elsewhere, why not share my productions with the world and help out expanding the knowledge we mighty magi possess?  One such text, taken from the book “Hermes Trismegistus, Astrologia et divinatoria” (Corpus Christianorum, Continuatio Medievalis 144C, Brepols: Turnhout, 2001), is called the Liber Runarum, or “Book of Runes”, a 15th century text found in a few manuscripts describing a method of using runes (yes, actual Nordic runes!) in tandem with Hermetic astrological and angelic magic.  Unlike the runic correspondences offered by, say, Crowley in Liber 777 or Skinner in his “Complete Magician’s Tables”, this offers a simple method of ascribing the runes to the stars, linking them to the rest of the body of Hermetic knowledge.  You can find the whole translation posted here, runes and all, but I wanted to talk about a specific method given in the Liber Runarum to write magical texts for talismans, charms, and the like.

So, the text starts off with listing twelve signs based on the signs of the Zodiac.  These twelve signs, starting with Salmadis and ending with Rynybel, appear to be of equal size and area, just as the signs of the Zodiac are themselves.  However, they start off a little skewed from the Zodiac proper, with the start of Salmadis beginning at the “end” of Aries, or the start of the third decan (20° into Aries).  Since these signs are called “extracted” or “abstracted” in the text, I’ll call them “extracted signs” here.  To list the Zodiac signs beside their corresponding extracted signs:

Zodiac Sign Extracted Sign
Aries First Decan Rynybel
Second Decan
Third Decan Salmadis
Taurus First Decan
Second Decan
Third Decan Lathlim
Gemini First Decan
Second Decan
Third Decan Celecht
Cancer First Decan
Second Decan
Third Decan Rohob
Leo First Decan
Second Decan
Third Decan Ayleyl
Virgo First Decan
Second Decan
Third Decan Alyobe
Libra First Decan
Second Decan
Third Decan Baltarie
Scorpio First Decan
Second Decan
Third Decan Affoguil
Sagittarius First Decan
Second Decan
Third Decan Hanapel
Capricorn First Decan
Second Decan
Third Decan Balyoel
Aquarius First Decan
Second Decan
Third Decan Cariophel
Pisces First Decan
Second Decan
Third Decan Rynybel

Each of the extracted signs is associated with two “runes”, or letters of the medieval runic alphabet still in use in the 15th century in parts of Europe and which have a more-or-less one-to-one correspondence with the Latin script in use at the time, which is the Latin alphabet we’re used to minus the letters J (a variant of I),  and U and W (variants of V) .  Each of the extracted signs is associated with two letters, with the exception of Rynybel, which only has one letter.  These letters are given to the extracted signs in the order of the standard Latin alphabet; thus, Salmadis is given A and B, Lathlym is given C and D, and so forth through Rynybel, which is given only Z.  Interestingly, each of the letters is also given an elemental nature from the four classical elements: fire, earth, air, and water.  However, these letters are given elements based on the Zodiacal sign, not the extracted sign, that they most closely are associated with.  So, for example, the extracted sign Salmadis starts off in Aries, a fire sign, and ends in Taurus, an earth sign; A “is taken from the first part” of Salmadis, and B “from the second”.  So, A, being closer to Aries, is given to the element of fire and B, being closer to Taurus, is given to earth.  This pattern follows all the way through, with Z being given to water due to its placement with Pisces.

Zodiac Sign Zodiac Element Extracted Sign Extracted Rune Runic Element
Aries Fire Rynybel
Salmadis A Fire
Taurus Earth B Earth
Lathlim C Earth
Gemini Air D Air
Celecht E Air
Cancer Water F Water
Rohob G Water
Leo Fire H Fire
Ayleyl I Fire
Virgo Earth K Earth
Alyobe L Earth
Libra Air M Air
Affoguil N Air
Scorpio Water O Water
Baltarie P Water
Sagittarius Fire Q Fire
Hanapel R Fire
Capricorn Earth S Earth
Balyoel T Earth
Aquarius Air V Air
Cariophel X Air
Pisces Water Y Water
Rynybel Z Water

And yes, although I’m using the Latin alphabet, the texts use a version of medieval runes.  Imagine that you’re using the runes, and you’ll be set.  Below are one such version of the runes as given in the Liber Runarum, coupled with their standard medieval runic counterparts and their Latin transcriptions.  For the sake of this post, I’ll just refer to the runes by their Latin letter equivalents.

Runes of the Liber Runarum

So, why does this matter?  For inscribing magical talismans and image magic, of course, as was the fad in medieval and Renaissance Europe.  The Liber Runarum is, like many other texts at the time, a book of angelic magic, and the text gives a list of angels, their associated planets, things they govern or rule, and the like.  All this, plus a specific method for writing the names of angels or other things on talismans for magical purposes, by associated the elements with the letters so that inscribed words may be properly aligned to the forces of the cosmos.

However, the method for writing words on magic items according to the Liber Runarum is…convoluted and obscure.  I had to bust out Google Translate to understand the introduction to the text written in Italian to get a better grasp of the method, and it’s still pretty hard to explain.  Basically, the text proposes a kind of magical cipher to obscure or occlude the written word itself by means of the elements themselves.  The text says this on the manner of working:

Now it is to be said about the changing of the figures abstracted from the stars according to the different parts of the signs, in the way that a figure entering under is put in the place of an opposing figure, and in this manner a change of the figures is made, which is nothing other than the removing of an opposing figure and a placing forth of another figure suitably entering under. So as to understand this change, moreover, the difference of the abstracted figures is to be noted by some standing alone, some obstructing, some entering under. Figures standing by themselves are those which do not need change but are suitably placed in a sculpture according to the need of a good combination.  Opposing figures are those which cannot be placed in the sculpture due to the mixing of the arrangement of figures.  Figures entering under are those which are well-put in the place of opposition.  It is also to be noted that the figures standing by themselves make opposing figures and vice versa, and similarly figures entering under make those standing by themsleves and will oppose.  However, of the figures standing by themselves it is to be known that they are unchanging and always placed in the sculpture without change and make the sculpture to ascend into the circle or the parts of the signs by which it had fallen, which are the figures that from the upper parts of the circle, or rather the Zodiac, [that] are taken with respect to the figures which are those placed in the sculpture.

Believe me, it’s not because I’m a shitty translator of Latin that it’s obscure (though I do credit myself a bit with that).  Even the curator of the text himself called the method hard to understand, but given a few examples presented in the texts themselves, the method does become apparent.  The method of writing in this manner relies on understanding the flow of the elements according to the Zodiac: fire, earth, air, water (just like Aries, Taurus, Gemini, Cancer, and so forth).  The “starting element” of the cycle depends on the first letter found in the word; the other letters must either fit naturally with this order or be changed to another letter of the alphabet to agree with it.  Thus, the meanings of the terms in the passage above become a little clearer:

  • Figure standing by itself: a letter whose elemental nature agrees with the elemental position of the word.
  • Figure opposing: a letter whose elemental nature is different from the elemental position of the word.
  • Figures entering under: a letter replacing an opposing letter to supply the needed element for that elemental position.

Of course, the method still isn’t clear as to which of suitable elemental letters to pick to replace a letter.  There are five or six letters per element, and the examples given in the original manuscripts do seem to follow some sort of pattern.  After looking at the examples myself and trying to figure out which is which (no easy task), the method of writing a cipher using this elemental system can be described (as best as I can understand it) as follows:

  1. Write out the full word.
  2. Inspect the element associated with the first letter of the word.  This letter begins the cycle of elements for the rest of the word.
  3. Inspect the successive letters of the word, noting the elements of the letters and the prescribed element for that position in the word.
  4. If a given letter has the same element as the position itself, leave it be.
  5. If a given letter has a different element as the position itself, change this letter to be replaced to the next letter in the alphabetic cycle with the needed element, the letter itself being taken from the extracted sign closest to the zodiac sign with a triplicity of the same element as the letter to be replaced.

Complex?  Of course it is, it’s from the 15th century.  Let’s walk through a few examples.  Consider a name from the same text as this cipher is pulled from, Acelaceyl:

  • The first letter of this word is A, the element of which is Fire.  Since the word is nine letters long and the first letter of the word is associated with Fire, the cycle of elements that the letters must obey will be Fire-Earth-Air-Water-Fire-Earth-Air-Water-Fire.  The letters themselves in the word are A (fire), C (earth), E (air), L (earth), A (fire), C (earth), E (air), Y (water), L (earth).  Most of the letters in the word follow this pattern, except the first L and the last L, which have different element than the order prescribes; the first L is earthy when a water letter is needed, and the last L is earthy when a fire letter is needed; both of these letters must be replaced to another with a proper elemental nature.
  • The first L needs to be replaced by a water letter; the next water letters in the alphabet after L are O and P.  O is taken from the second part of Affoquil, which starts in the third decan of Libra, and P is taken from the first part of Baltharie, which starts in the third decan of Scorpio.  L itself is earthy, so whichever of the signs Affoquil (holding O) and Baltharie (holding P) is closest to an earth sign will be selected.  Affoquil is closer to Virgo than Baltharie is to Capricorn, so Affoquil is chosen, replacing the first L with O.
  • The second L needs to be replaced by a fire letter; the next fire letters are Q and R.  Q is taken from the second part of Baltharie and R from the first part of Hanapel.  Whichever of these signs is closest to an earth sign will be chosen.  Hanapel is closer to earthy Capricorn than Baltharie is to Virgo (indeed, Baltharie overlaps into Capricorn!), so Hanapel is chosen, replacing the second L with R.
  • By replacing these letters in this way, we get the resulting cipher ACEOACEYR.

Another example: let’s look at the word IAO SABAOTH, the Latinate rendition of a fairly popular godname.  Here, we’ll encipher a whole phrase based on the first letter of the phrase:

  • The first letter is I, which is Fire.  The phrase IAO SABAOTH has ten letters, so the cycle must be Fire-Earth-Air-Water-Fire-Earth-Air-Water-Fire-Earth.  The letters themselves are I (fire), A (fire), O (water), S (earth), A (fire), B (earth), A (fire), O (water), T (earth), H (fire).  Of these, only the I of IAO and the first A, B, and O of SABAOTH fit according to this pattern; all the other letters must be changed.  In other words, to use underlined letters to signify the letters to be changed, IAO SABAOTH.
  • The A of IAO is fiery and needs to be replaced by an earth letter.  The next two earth letters are B and C, from Salmadis and Lathlym, respectively.  Salmadis is closer to a fire sign (Aries) than Lathlym is (Leo), so Salmadis’ letter B replaces A.
  • The O of IAO is watery and needs to be replaced by an air letter.  The next two earth letters are V and X, from Balyoel and Cariopel, respectively.  Cariopel is closer to a water sign (Pisces) than Celecht is (Scorpio), so Cariopel’s letter X replaces O.
  • The S of SABAOTH is earthy and needs to be replaced by a water letter.  The next two water letters are Y and Z, from Cariopel and Rynybel, respectively.  Cariopel is closer to a water sign (Pisces, overlapping it) than Rynybel is (Cancer, though it overlaps Pisces as well), so Cariopel’s letter Y replaces S.
  • The second A of SABAOTH is fiery and needs to be replaced by an air letter.  The next two air letters are D and E, from Lathlym and Celecht, respectively.  Lathlym is closer to a fire sign (Aries) than Celecht is (Leo), so Lathlym’s letter D replaces A.
  • The T of SABAOTH is earthy and needs to be replaced by a fire letter.  The next fire letter is A, from Salmadis.  Because the A from Salmadis is alone without a companion fire letter, A is chosen by default to replace T.
  • The H of SABAOTH is fiery and needs to be replaced by an earth letter.  The next two earth letters are K and L, from Ayleyl and Alyobe, respectively.  Ayleyl is closer to a fire sign (Leo) than Alyobe is (Sagittarius), so Ayleyl’s letter K replaces H.
  • By replacing these letters in this way, we get the resulting cipher IBX YABDOAK.

So, with the rule and examples understood (as surely you have, dear reader), here’s my conversion chart for any letter of the Latin runic alphabet into any element as needed.  Bold letters indicate no change needed, and also the natural element of a given letter.  To read this chart, find the letter to be enciphered in the leftmost column, then read across to find its enciphered equivalent according to the element needed.

Letter Fire Earth Air Water

Because of the many-to-one conversion (the A in a cipher could stand for seven letters including itself), it’d be very, very difficult to decipher a word already enciphered without a lot of ingenuity and knowing probable letter combinations in a given language.  Then again, this same mechanism of obfuscation helps obscure the meaning of the text from human eyes and human minds, just as common methods of sigilization do, and also help to align a given word with the starry forces that govern existence down here.  The obfuscation part is kinda ingenious, not gonna lie, especially for doing stellar magic generally and leaving behind magical items in public without being too blatantly skeevy or sketchy.  After all, why write “DIE IN A FIRE” and get arrested or fired when you can write “DPHKNGHKVF” instead and have nobody (but the spirits) know the better?  Bonus points if you actually use medieval runes, futhark, futhorc, or, hell, even Theban script.

Of course, the method above is what I can say on the matter.  The different versions of the Liber Runarum offer different examples, with one manuscript showing the names of the angels written four times each, each time using a different change.  I honestly don’t know why this might be, or whether some of them are just wrong or are further confused or use a different method, but the above cipher is simple and regular enough to be easily applied in magical inscriptions.  Alternatively, different letters might be used (while still fulfilling that same elemental restriction) based on their exact sign, using more zodiacal and planetary reasons for selecting a particular letter over another for a given purpose.