A Hermetic Musing on Fate, Necessity, and Providence

This post was originally a short tweet thread I shared last September, but I don’t think I ever shared it outside Twitter, and I think I phrased some things in it that even I hadn’t realized were as big as I do now.  I’ve reformatted it and embiggened it slightly for a proper blog post, but the gist is the same.

So, a few definitions first, largely based on SH 12—14:

  1. Providence is the will of God.
  2. Necessity is what comes up with what needs to happen in order for Providence to be fulfilled.
  3. Fate is what arranges things in order for that which Necessity declares to come about.

In software engineering terms, Providence is the requirement that specifies what is to be done, Necessity is the design that specifies how it’s to be done, and Fate is the code that does what the requirement says in the manner the design says. The execution of the code—the carrying-out of Fate—is the actual activity that happens in the cosmos, right down to our own lives.

And what are the agents of Fate, you might ask?  What are the entities that facilitate and serve Fate to bring it about?  It’s the planets and stars themselves, which are not just indicators of Fate but the things that provide all things that exist down here with the energy (in the philosophical sense of activity or being-at-work-ness) to do what they need to do to be born, to grow, to die, and decay—and, in the process, fulfill whatever purpose it was meant to achieve.

That the planets are the agents of Fate is why astrology is the first (and most important) Hermetic art, because the study of the planets and stars allows us to learn about Fate, and thus about Necessity and Providence, and thus God and our relation to it. Our external and bodily lives are commanded by Fate, and Fate is not up to us to change in the Hermetic worldview, no more than we can make Mercury not go retrograde when we find it inconvenient. Fate is going to happen one way or another; we must learn to live with it.  (This is where a good understanding of Stoicism comes into play when studying Hermeticism.)

But, the thing is, your soul—that which you really are—is not your body; rather, our souls come from a place beyond the cosmos, and thus a place beyond Fate.  As such, our souls are not compelled by Fate the way our bodies and external lives are.  Our bodies are creations of the cosmos, and the cosmos is ruled by Fate, and so our bodies are naturally controlled by Fate as well as a production of it (and, by extension, the seven planets).  The soul, which only wears the body like how the body wears a shirt, is only impelled, not compelled, by Fate, in the same way that while the quality of a shirt can make a body comfortable or uncomfortable, the body is not fundamentally bound to the same fate as the shirt.  That saying that we’re spiritual entities having a physical experience, or that we should only be in the world and not of the world?  That notion is critically Hermetic, and we need to take that to heart.  We can’t be in control of everything (or even anything) external on the level of the body, but internally on the level of the soul, we can overcome it all.

It is in rising above the powers of Fate that we conquer it, by learning what it does and how it plays out that we learn the exceptions in the code and the behavior unspecified by the design and the loopholes in the requirements. Only once we rise above Fate can we make it our plaything., but in order to do so, we need to understand how Fate actually plays out on the low level once we see what Fate is trying to accomplish at a high level.  This is why alchemy is the second Hermetic art: alchemy is the study and science of learning how the activities and energies of the cosmos play out specifically at the level of material creation and manifestation, in the world we live in. Astrology looks above to see “why”, alchemy looks below to see “how”. And, well, as the Emerald Tablet (and so many others who love to quote it) says, “as above, so below”.

Learning Fate’s activity/energeia by alchemy and Fate’s power/dynamis by astrology, that’s where the third Hermetic art comes in: theurgy. Theurgy doesn’t change Fate to fight against Necessity or change Providence. Rather, it works by Fate to do what is best—what is Necessary—in accordance with highest Providence.  In working by Fate, we rise up to Fate’s own level and surpass it, able to at last be consciously and intentionally free of Fate.  Theurgy relies on knowing that which is above, that which is below, and the relationship between the two to not just go up or down, but to go beyond both entirely.  (After all, when you’re talking about a sphere, any direction away from the center is technically “up”.)

To borrow a bit of Christianity for a moment: angels are said to have no free will, but consider instead that they have will, just that their will is to fulfill God’s will. In this, the will of an angel is the will of God to be expressed through that angel.  The same goes for us, too. Theurgy is what allows us to make our will God’s will, which also makes God’s will our will. And if God is for you, sharing the one and same will, who can be against you?

When your own will is Providence, what need would you have to fight with Fate, when Fate itself could not fight with you?

Hermeticism FAQ: Part IV, Practice

Continuing our Hermeticism FAQ series (see part I, part II, and part III here), let’s continue today with (the final) Part IV, on the various practices of Hermeticism!

What practices are part of Hermeticism?

Although the “philosophical Hermetica” are great for teaching doctrine, they offer very little in the way of actual practice, whether day-to-day routine practice or things for non-routine ritual.  However, we do know that prayer to God is something Hermēs Trismegistos encourages, especially at sunrise (preferably outdoors facing east) and at sunset (again preferably outdoors facing south), along with at nighttime immediately before going to bed.  Practices of purity and asceticism are also encouraged, both for their training of the body as well for the work of engaging divinity without being polluted by the passions of base matter.  In tandem with study of the discourses and other arts, frequent meditation should be engaged with, both for the purposes of delving deeper into the meanings of the teachings as well as to gain insight regarding one’s own nature and the nature of the cosmos generally.  For those who are building shrines for the gods, calling the gods down into statues for more immediate contact and worship of them is recommended, by the means of filling the statues with sacred substances, burning incense before them, bathing them in sacred liquids, and the singing of hymns to seat them in their terrestrial bodies; rather than just statues or other images, bodily possession by the gods may also be attempted.  When ready, works of spiritual elevation and divine ascent should be undertaken, which can be considered among the crowning acts (though far from a one-time effort) a Hermeticist should endeavor towards.  Besides these, many other practices as described in the “technical Hermetica” or which are borrowed from any number of other magical and spiritual traditions may also be incorporated.

Are there any particular gods I should worship?

The only divinity one is strictly required to worship and venerate in Hermeticism is God, and that in a way that is often distinct from other gods; rather than burning incense or making material sacrifices, the true worship of God consists of a sacrifice of speech and the singing of hymns in sacred silence, adoring the Creator by means of their Creation.  Beyond that, whatever other gods one worships (if one worships other gods at all) is entirely up to the student.  For those who are willing, Hermēs Trismegistos himself is an excellent candidate to receive worship for those who follow the Way of Hermēs, whether as a divinity in his own right or as a deified hero-prophet; the same goes for the students of Hermēs Trismegistos, like Asklēpios (the Egyptian Imhotep), Tat (another instance of Thōth), and Ammōn (the Egyptian Amun).  While Greek and Egyptian religion offers many such deities to worship, to say nothing of the many syncretic religious entities present in texts like the Greek Magical Papyri, there is no limit nor rule as to which gods one should worship, so long as one worships God.

Did the classical Hermeticists practice magic, and should we continue to practice magic today?

Although the “philosophical Hermetica” is silent on the subject, and although Zosimus of Panopolis suggests that Hermēs Trismegistos disavowed magic, it is a fact that Hermeticism has long been associated with magical works of many types, and indeed, ancient Egyptian religion saw little distinction between religious works and magical works, to the point where the very concept of magic itself (Heka) in Egypt was venerated as a deity in its own right in addition to the view that the gods had such supernatural power at their disposal to accomplish all manner of works.  Magic is simply the operational use of subtle forces or spiritual entities in addition to or instead of physical or bodily ones to achieve particular ends, and as such, the study of such forces and entities is part and parcel of the study of the cosmos as much as the study of any material or physical force or entity.  This being the case, classical Hermeticists (along with Egyptian priests themselves, and in company with many other wandering magicians of the day) certainly practiced magic, as this was a valid way to engage with the various powers of the cosmos, and thus we are both enabled and encouraged to today.  Of course, such works should be held to a high moral and ethical standard—but so should any other work, whether or not it can be considered “magical”.

What about astrology or alchemy?

These two arts have long been held to be Hermetic, and there’s good reason for saying so; even in the core classical Hermetic texts themselves, there is much astrological symbolism and even directives to engage in the study and practice of astrology to better understand the nature of the cosmos and of divinity.  Alchemy is somewhat more complicated of a subject, becoming more popular and well-studied in the late classical and post-classical periods, but is also tied to Hermetic practices of the creation of medicine, ink, oils, and talismans.  Different texts from different time periods will focus on these arts to various degrees, but they are certainly important for the practical side of Hermeticism, and those who are interested in Hermeticism are encouraged to study and engage with them.  Remember that the study of astrology is what helps us understand more about the processes of Fate; if astrology is the “as above”, then alchemy provides the “so below”, since it helps us understand the processes of change in the cosmos, learning how the activities and energies of the cosmos play out at a low level.  The power and potentiality of Fate can be learned through astrology, and the activity and actuality of Fate can be learned through alchemy.  Even if neither are strictly required, by learning both, one has a strong footing to engage in the work of theurgy.

What about theurgy?

Theurgy (from Greek theourgia, “divine work” or “god-work”) is the ritual mystical practice of participating in the presence of the divine, whether individual gods or God itself.  On the one hand, this can be considered the work of lifting oneself up to the level of the gods through spiritual elevation and divine ascent; on the other, it can also be considered the work of bringing the gods down to our level, either by having them inhabit sacred statues or other idols or by possessing their devotees for the gods to perform work down in our world.  In either case, the ultimate goal of theurgy is to unite ourselves with the divine, fulfilled through rites of purification of the body and soul along with communion with the gods.  It should be noted that this is not a kind of “coercion of the gods” where the gods are “forced” down (as if such a thing were possible in Hermetic terms), nor is it the case that we “trap” the gods in statues for our own bidding.  This is an act of communion, such as inviting someone to live in your home and share your table, and similar acts can be seen in the tradition of “living statues” of Hinduism and in many other pagan traditions across the world.  In a smaller sense, although not always done with theurgical goals in mind, the work of ensoulment and enlivening images can also be seen in the consecration of talismans, where one “brings to life” a particular object for it to confer some benefit, either by having a “shard” of the power of some force (like a planet) empower an object or by having a spirit come to inhabit the object.

What about thaumaturgy, and how is it different from theurgy?

Thaumaturgy (from Greek thaumatourgia “wonder-working”) is a way to describe magic in general, especially magic that is intended to create change or other paranormal phenomena in our world.  In other words, thaumaturgy is another word for most magic most people do and have done the whole world over since time immemorial.  Although some people consider theurgy to be “high magic” and thaumaturgy to be “low magic”, it should be noted that the difference between theurgy and thaumaturgy consists primarily in ends or goals, not in the means or methods; the same method one might use to raise a shade of the dead to learn where buried treasure lies may well be the same method one calls upon the presence of a god to bask in their glory in unity with them.

Are initiations involved or required in practicing Hermeticism?

“Initiation” in its literal sense indicates the beginning of something new, but in a religious context, it refers to the formal induction into a mystery, something secret that bestows some sacred or mystical power, license, experience, or knowledge, generally one protected as secret by a group dedicated to that mystery.  Importantly, an initiation is conferred upon an initiate by someone who is already initiated; it is something given, not merely taken.  In that light, although individual groups that profess Hermeticism may have their own mysteries may require initiations to access such mysteries, Hermeticism as a whole does not require them, and the very notion seems to be unknown according to the Hermetic texts.  That beings said, there are mysteries in Hermeticism, and are described as such in terms of being acts of spiritual elevation or divine ascent in order to behold divine visions.  Engaging in this work may be considered an initiation of sorts, whether or not there is one there to guide a student in such an endeavor.  It is perhaps better to consider this an initiation only when one who has already undertaken such a feat guides another in undertaking that same feat; beyond that, when one undertakes it on their own without such guidance, it might better be said to not be an initiation in the technical sense, even if it does acquaint one with a mystery of the Divine apart and away from any such group.  It’s a complicated topic to discuss, but suffice it here to say that there are often initiatory experiences involved in the higher works one undertakes in Hermeticism, whether or not one is initiated into a group by other human beings.

Is divination okay in Hermeticism?

Absolutely!  Divination is more than just “telling the future”, although it also does that, too; it is the act of approaching the gods to come to know them and what they have to say.  Not only does this fall in line with ancient practices that span the entire world, upholding old traditions of the oracles of the many gods, but it also is explicitly justified in the Hermetic texts as something legitimate we can do, so that we can know what has been, what is, and what will be.  Plus, so many forms of divination have been assigned to Hermēs Trismegistos, or even just Hermēs in the purely Greek sense, not least of which is astrology, that it’s hard to not separate out the work and study of divination from Hermeticism.

Do I need to be a vegetarian or vegan to be a Hermeticist?

At the end of the Perfect Sermon, there is a direction given by Hermēs Trismegistos to his students where they are to eat a “meal that includes no living thing” or “holy food which has no blood in it” following a prayer of thanksgiving to God.  Some interpet that this is an injunction for students of Hermēs Trismegistos to be vegetarian (or even vegan) in general, while others hold to a more limited opinion that only certain ritual meals need to be vegetarian.  It’s a good question, but there’s no one right answer.  It is known that those initiated into the Orphic and Pythagorean mystery cults were famously vegetarian as a constant ascetic practice (and also excluded certain kinds of beans due to their textural similarity to flesh), and it is also known that Egyptian priestly purity practices involved many abstinences from any number of animal products, both the eating of meat and otherwise (like the wearing of wool).  For our purposes today, while maintaining a vegetarian (or vegan, if one so chooses) diet is an excellent ascetic choice one can make, it can be agreed upon as important to abstain from consuming animal products prior to engaging in ritual and to only consume vegetarian (or vegan) food as part of ritual where ritual meals are called for, regardless whether sacrifices to the gods or spirits require meat or other animal products.

What about qabbala/kabbalah/cabala?

This term (all really the same word, just different transliterations from the Hebrew) refers to the overall mystical tradition of Judaism, which builds upon earlier Jewish traditions of hekaloth literature and merkaba mysticism along with Bablyonian and Hellenistic influence.  Although its origins ultimately lie in much earlier Jewish practices, qabbala as its own discipline only arose in the medieval period around 1200 CE.  Due to the complicated and messy history of Judaism in Europe, qabbala became integrated with non-Jewish systems of magic and mysticism, and earned central importance to magical systems like those of the Golden Dawn and Thelema.  While the study of qabbala, in its various forms and approaches, may be useful to some modern Hermeticists of various styles, it is not in and of itself Hermetic in the same sense that the Corpus Hermeticum is Hermetic, though due to the Neoplatonic and broadly Hellenistic influences upon the development of qabbala, it may be integrated with Hermetic practices.

Can I incorporate modern or non-Hermetic practices into Hermeticism?

By all means, feel free!  Considering the difficulty we have in reconstructing the practices of classical Hermeticists, to say nothing of the variety between their practices as well as the practices of various Hermeticists throughout the past 2000 years, there is plenty that can be done by us today in service to the Way of Hermēs. Just bear in mind that just because you might use a practice within a Hermetic context does not automatically make it “Hermetic”, and it is also worthy to remember the context in which such a practice arose and what its design and purpose is for.  Some things can be adapted or adopted for Hermetic ends quite neatly and nicely, other things less so, and some practices are best kept separate from Hermeticism entirely depending on their nature and purpose.

Will Hermeticism make me powerful, give me spells to get laid, etc.?

Sigh.  Technically yes, and I won’t deny that a fundamental drive for magic is the drive to get laid and get paid, but we’re also here to recognize that there’s more to life than just power, sex, money, and the like.  There’s magic, and then there’s magic for Hermetic ends, and while the same spell can be used for a Hermetic end as well as a non-Hermetic end, there’s a reason greed and lust are outlined as “irrational torments of matter” that we’re meant to purge ourselves from.  Let’s try to be a little more mature in the future, yes?

“The Adocentyn Temple Almanac” Preferences Questionnaire

This is just a quick update for tonight, but for once, I’d like some input from you, my amazing and darling readers.

As some of you might recall or have seen me go on about on Twitter, I’ve been working on a bit of a fun project lately, an automated almanac project that I call “The Adocentyn Temple Almanac” (or TATA for short, because I’m cute like that).  This is a project where, using the well-loved Swiss Ephemeris codebase and typesetting the output with LaTeX into something nice, I can produce a customizable almanac document for (almost) any populated latitude, longitude, and altitude on Earth.  It’s my hope that this becomes a truly useful thing for people: after all, can you imagine having a customized astrological/astronomical almanac for your very own temple room in your house or communal space, specific for where you might actually stand and see the stars?  My plan is, in exchange for a modest fee, to produce this almanac (made custom for each person, with a preliminary check to see what information they’d like) as a high-quality PDF, which you can have on your mobile device or laptop as needed, or which you can send off to a printer to have a hardcopy for on-hand off-line reference in your own temple space.

I’ve been working on TATA on and off for a bit now, and I’ve gotten a lot of features built into it already (all of which can be turned on or off as a user might desire):

  • Sun ingress Zodiac signs and decans
  • Sun transit seasons and season midpoints
  • Moon ingress Zodiac signs and lunar mansions
  • Moon phases
  • First and last sightings of the Moon
  • Solar and lunar eclipse times
  • Lunar month day numbers
  • Decan day numbers (using my “rebalanced true degree method” I mentioned in an earlier post)
  • Rising sign and culminating sign windows
  • Rising, setting, culminating, and settling times for the Sun, Moon, planets, and stars
  • Planetary hours
  • Simple ritual windows

Even so, however, because I have a perfectionist streak and because I want this to be the best, most useful, and most flexible bit of software that I can make it, I need your help to figure out what else I should build into this!  After all, there are some things that I just don’t know whether they’d be popular or some things I just don’t know about in general, and there are other things that I do know about and haven’t yet developed because I don’t know how desirable they’d be.  For that, I need to turn to you—yes, you!—to let me know what you think.

If you’re interested in helping me out with, please fill out this questionnaire on Google Forms.  You’ll need a Google account to take it, but this way you can change your responses afterwards if you have a wit-of-the-stair moment and need to add in something later.  It should only take about ten to thirty minutes, depending on your speed of answering and thinking about possibilities, but do feel free to suggest in the questionnaire whatever you might like!  After you’ve taken it, please also share this post (or my post on Facebook or tweet on Twitter) to your magical, astrological, priestly, occult, or spooky friends to also get their input.  I’ll keep everyone updated, to be sure, as this is a project I hope to bring to light and made accessible for anyone interested before the end of 2020, so please be sure to get your answers in soon to help guide my continuing effort on TATA!

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.