Compilation Paralysis

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

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

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

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

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

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

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

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

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

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

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

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

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

Learning the Astragalomantic Oracular Verses

The way that astragalomancy works is pretty simple; Kostas Dervenis in his Oracle Bones Divination calls it the “Greek I Ching”, noting the similarity of the method.  Basically, what you do is you roll five knucklebones, or astragaloi, and you note the sides that come up.  The astragaloi act like four-sided dice, and each of the 56 different rolls you get (the order doesn’t matter) indicates a different outcome.  Each roll is associated with a particular godname and a matching oracular verse, not unlike grammatomancy (the methods are basically the same).  So, really, there’s little room for interpretation: roll the astragaloi, read the corresponding verse, and that’s your answer.  Expanding and meditating on the verse as it relates to the situation or the query is often necessary, but there’s little other inspiration to be had here, which is just as well.  I’m sure I can fit some more mystical aspects into it later, of course, but that’s later once I learn all the verses.

It’s learning the verses, however, that’s proving something of a struggle for me.  Each verse is four or five lines long, and there are 56 different verses.  Learning the one-line verses associated with the 24 letters of the Greek alphabet took a bit of time on its own, but that’s child’s play in comparison to this.  My memory may be good, but it’s not that good to just up and memorize a book’s worth of divination.  I want to be able, eventually, to pull out my astragaloi whenever needed and on the spot do a reading with them, which may mean that I won’t have a book of verses with me at any given moment, so I want to memorize them and know them by heart.  Getting there is hard, so I’m trying out different ways of learning them and comparing what I’ve done with other methods.

Geomancy, for instance, was easy because each set of meanings could be tied to a graphical form, the geomantic figure composed of four lines of one or two dots in each line.  Grammatomancy was easy because I had the 24 Greek letters as graphical forms to link their meanings and verses to, as well as the fact that the alphabet itself formed an index and acronym for the verses themselves (at least in Greek).  And, while I don’t know Tarot half as well as I probably should as a Hermetic magician, learning the symbolism could easily be done by association with the pretty pictures of the cards themselves (if I even bother to go that route, since the pictures lend themselves well to impromptu interpretation as they already are).    These all use some sort of graphical image as a symbol to which can be linked a referent, the verse or meaning; my mind plays well with these instead of just straight-up words or numbers.

Astragalomancy, however, is different; I’m just getting a set of numbers, a numeric ID, that gives me a particular verse and meaning.  It’s a different beast, and the lack of a distinct symbol bothers me.  The ID doesn’t register to my mind as a graphical image or a symbol in the same way a geomantic figure does, especially given the different forms it can take.  Consider the throw where you get two khion (1) throws, a hyption (3), a pranēs (4), and a kōon (6).  While I might write this down as 11346, there are 60 different permutations of this ID.  Add to it, the original sources don’t tend to list the numbers in a simple manner, so the actual ID of this is 43611 in the book!  While each verse begins with a description of the throw (in this case, “one four, one three, one six, and two ones: …”), that’s not helpful without me just up and memorizing all the verses by heart and running through them one by one until I get to the one I need, or until I get to the point where automatic recital of each verse is possible just from the start of each one (and, moreover, how each first line starts).  That takes time, and I’m trying to get up to speed as fast as possible with this.

Flashcards help, though, and I was able to link the sums of the throws to the Greek letters (one of the ways to do grammatomancy with astragaloi) in a day with this method.  For this, the online service Quizlet is amazing, and if you’re so interested, you can check out the sets of flashcards I’ve made for your own study.  Linking the throws to the letters involves summing up the sides of the astragaloi, however, and just observing the throws themselves isn’t a link I can make directly to the Greek letter just yet.  Over time, perhaps, as I regularly use the astragaloi it can happen, but I need that intermediate step first that detaches the throw to the Greek letter directly.  However, the way Quizlet works, you need to type in the answer to a given prompt more-or-less directly, and while it may be a useful activity for me to go through all the oracles themselves and make a one- or two-word summation of every verse, I haven’t gotten around to doing that just yet.  So, for me, the first step is to learn the throws of the astragaloi and how they associate with the different gods associated with each throw.

Still, that alone is difficult without some sort of pattern or method, and then I realized that I have a method for this.  Every software engineer is taught this method of “divide and conquer” (or, in Greek, διαίρει καὶ βασίλευε, diairei kai basileue), where you take a large problem and divide it up into smaller chunks that can more easily be solved, linking them all together in the end once they’re all good to go.  Looking at the astragalomantic throws, I realized that I can reorder the throws into a pattern that’s more numerically pleasing where there are 18 groups of 3 or 4 throws each, based partially on the Roman game of tali or knucklebones.  I group some of the smaller groups into larger ones based on the abstract number pattern linking them together:

  • Dogs and Vultures (all throws the same number, four possible throws)  e.g. 11111, 33333
  • Iacti Veneris + 1 (all four sides represented, four possible throws) e.g. 11346, 13446
  • 4X 1Y (four throws one side and last throw another, 12 possible throws with four groups of three based on X) e.g. 11113, 46666
  • 3X 2Y (three throws one side and two throws another, 12 possible throws with four groups of three based on X) e.g. 33444, 33666
  • 3X 1Y 1Z (three throws one side and two throws different, 12 possible throws with four groups of three based on X) e.g. 11134, 34446
  • 2X 2Y 1Z (two throws one side and two throws another and last throw another, 12 possible throws with four groups of three based on Z) e.g. 34466, 13344

Sure, it’s not exactly a traditional arrangement of the throws or a traditional way of enumerating them, but it works for me.  Every day I’ll study one or two more groups, learning what the pattern is and the throws of a similar pattern with different numbers, adding in the new rows to a Quizlet flashcard quiz and practicing it every hour or so until I build myself up enough to tackle the whole lot of 56 throws.  All in all, this isn’t a bad way to learn the basic associations of throws with the gods, and given my normal speed of memorization and learning, it’ll take about two or three weeks to learn all the associations of throws and gods comfortably enough that I can identify them at a glance.

Once I get the memorization of throws and gods down, and (if I deem it worthwhile) the memorization of the canonical order of the gods, then it’ll be time to link the association of throws and oracles down.  However, I plan on using the god-associations as a halfway point, so that I’ll actually be linking the oracle to the god and the god to the throw.  Thus, by recalling the god as a symbol, I can recall the oracle to which the symbol refers.  Learning each oracle will take more time than learning the god, since each verse also has to be memorized.  That said, I can speed up the process by learning the gist of each oracle first, then going back to learning the verses themselves, but we’ll see how I feel about that.  Given this, I expect it to take me two months or so of study and practice to memorize the verses, both by Quizlet and by constant use of the oracle to get me used to throwing the bones literally instead of just looking at flashcards.

How about you?  How do you learn a large block of information in a short period of time?  Are there any tips or tricks for memorization or recalling large amounts of information at once?

On Astragalomantic Probabilities

Using the astragaloi, or knucklebones, for divination has really intrigued me lately, as if you couldn’t tell from my last two posts on the subject.  Something about them feels different from other divination tools I’ve used; it could be that they’re actual bones taken from a living creature once, or that they just feel more arcane and ancient than my divination dice or cards I’m known to use.  All the same, they’re quickly becoming my favorite divination tool (besides geomancy generally), and I’m struck by their power and potency in getting answers.  The method is overall simple: take five astragaloi, throw them, and find the oracular verse associated with the combination of the sides that come up.  It’s simple, but elegant and straightforward.

However, they’re also different from my other divination tools in that they have really weird statistical properties.  Consider a die: every side of the die has (approximately) an equal chance of coming up when thrown.  Thus, on a six-sided die, throwing a 1 comes up as often as throwing a 2, 3, 4, 5, or 6.  Knucklebones, however, are different: they’re not ideal Platonic solids, nor are they regularly shaped in any sense.  Their organic and geometrically awkward shape results in there being different probabilities in throwing an astragalos on any given side.  Of course, the probabilities will differ slightly based on the individual knucklebone used and how hard it’s thrown, but based on an analysis by Phil Winkelman, we can approximate throwing an astragalos onto a particular side as follows:

  • Khion (1): 10%
  • Hyption (3): 40%
  • Pranēs (4): 40%
  • Kōon (6): 10%

It struck me that, because of the statistical probabilities associated with each number, not all oracular verses associated with each throw of the astragaloi will come up equally.  Some verses might be relatively common, while others would be extraordinarily uncommon to obtain, whether for good or evil.  Having some free time on my hands, I decided to run a short statistical analysis on how common different throws of the astragaloi would come up and how that would affect divination using astragaloi as compared to my other divination methods or suggested ways to use the astragalomantic oracular verses.

For instance, consider the use of astragaloi for grammatomancy.  Grammatomancy is my expanded version of the Greek alphabet oracle, and traditionally you would use five astragaloi for obtaining a Greek letter by throwing the bones and summing up the sides of the astragaloi.  So, for instance, if you threw (1,1,6,4,3), the sum would be 1 + 1 + 6 + 4 + 3 = 15.  The minimum sum you can get is 5 (1,1,1,1,1) and the maximum is 30 (6,6,6,6,6); based on how the numbers add up, you could not obtain a sum of 6 which requires (1,1,1,1,2) nor a sum of 29 which requires (6,6,6,6,5).  Between the numbers 5 and 30 inclusive, excluding the numbers 6 and 29, there are 24 possible sums.  Thus, we can associate each sum with one of the 24 Greek letters, starting with 5 = Ω and 30 = Α.  However, because the probability of an astragalos rolling on a 1 or 6 is 0.1, and on a 3 or 4 is 0.4, we get different possibilities for rolling different combinations of astragaloi and, further, obtaining different sums.  Below is a table that maps each letter of the Greek alphabet with its corresponding astragaloi sum (presented both in Arabic numerals and Greek numerals) and the probability one will obtain that letter from rolling five astragaloi.  The more extreme (higher or lower) the sum, the more rare the throw.  Thus, it’s extraordinarily unlikely that one will obtain Α or Ω with astragaloi (0.001% of the time), but comparatively common to obtain Μ and Ν (15.48% of the time).

Letter Astragaloi Sum Probability
Numerical Greek
Α 30 Λʹ 0.00001
Β 28 ΚΗʹ 0.0002
Γ 27 ΚΖʹ 0.0002
Δ 26 ΚϜʹ 0.0016
Ε 25 ΚΕʹ 0.00325
Ζ 24 ΚΔʹ 0.008
Η 23 ΚΓʹ 0.02
Θ 22 ΚΒʹ 0.0328
Ι 21 ΚΑʹ 0.0624
Κ 20 Κʹ 0.09674
Λ 19 ΙΘʹ 0.12
Μ 18 ΙΗʹ 0.1548
Ν 17 ΙΖʹ 0.1548
Ξ 16 ΙϜʹ 0.12
Ο 15 ΙΕʹ 0.09674
Π 14 ΙΔʹ 0.0624
Ρ 13 ΙΓʹ 0.0328
Σ 12 ΙΒʹ 0.02
Τ 11 ΙΑʹ 0.008
Υ 10 Ιʹ 0.00325
Φ 9 Θʹ 0.0016
Χ 8 Ηʹ 0.0002
Ψ 7 Ζʹ 0.0002
Ω 5 Ε 0.00001

For me, being used to my divination dice, this is shocking.  I use a dodecahedron die (d12, 12-sided die) for grammatomancy, where I roll the die twice.  The first roll gives me an odd or even number, which refer to the first 12 or last 12 letters in the Greek alphabet, while the second roll gives me the letter within that set according to its rank.  So, if I roll a 5 and an 8, I end up with the Greek letter Theta (eighth letter of the first half of the alphabet).  Using a 12-sided die where every side has an equal chance of turning up (approximately 8.333% of the time), every letter of the Greek alphabet has an equal chance of occurring (4.1667% of the time).  The statistical difference between getting the same Greek letter with a 12-sided die used in this way compared to using five knucklebones is huge; we’d get Α on the die 4.1667% of the time, but on the astragaloi only 0.00001% of the time.  It’s not impossible, just far more unlikely.  Then again, another classical method of grammatomancy was the method of ψηφοι, psēphoi or “pebbles”, where one has a jar of stones each marked with a different letter.  By reaching into the jar and pulling out a random stone, you get approximately an equal chance of obtaining any single Greek letter, which gets us the same results as using a 12-sided die in my fashion of using one.  Whether the use of astragaloi or psēphoi was more common for grammatomancy isn’t clear to me, but both methods work.

So what about the actual throw for proper astragalomancy, where we’re looking at the combination that results instead of the sum that’s formed from the combination?  We know that:

  • There are four sides (1, 3, 4, 6) on each astragalos
  • There are five astragaloi
  • Order of the dice doesn’t matter

Thus, although there are 1024 possible combinations of astragaloi, we only end up with 56 possible throws of the astragaloi when we disregard the order and only consider unique combinations of the bones.  Below is a table that shows the probability for each possible throw of the astragaloi; remember that order doesn’t matter, so (1,1,3,4,6) is equivalent to (1,3,6,4,1) and (6,3,1,4,1).  Generally, the more 3s and 4s there are, the more likely a particular throw is.  Thus, we end up with a probability of 0.0001% for (1,1,1,1,1) and (6,6,6,6,6) as our most unlikely throws, and a probability of 10.24% for (3,3,3,4,4) and (3,3,4,4,4) as our most likely throws.

Throw Sum Probability
1 1 1 1 1 5 0.00001
1 1 1 1 3 7 0.0002
1 1 1 1 4 8 0.0002
1 1 1 1 6 10 0.00005
1 1 1 3 3 9 0.0016
1 1 1 3 4 11 0.0032
1 1 1 3 6 13 0.0008
1 1 1 4 4 11 0.0016
1 1 1 4 6 13 0.0008
1 1 1 6 6 15 0.0001
1 1 3 3 3 11 0.0064
1 1 3 3 4 12 0.0192
1 1 3 3 6 14 0.0048
1 1 3 4 4 13 0.0192
1 1 3 4 6 15 0.0096
1 1 3 6 6 17 0.0012
1 1 4 4 4 14 0.0064
1 1 4 4 6 16 0.0048
1 1 4 6 6 18 0.0012
1 1 6 6 6 20 0.0001
1 3 3 3 3 13 0.0128
1 3 3 3 4 14 0.0512
1 3 3 3 6 16 0.0128
1 3 3 4 4 15 0.0768
1 3 3 4 6 17 0.0384
1 3 3 6 6 19 0.0048
1 3 4 4 4 16 0.0512
1 3 4 4 6 18 0.0384
1 3 4 6 6 20 0.0096
1 3 6 6 6 22 0.0008
1 4 4 4 4 17 0.0128
1 4 4 4 6 19 0.0128
1 4 4 6 6 21 0.0048
1 4 6 6 6 23 0.0008
1 6 6 6 6 25 0.00005
3 3 3 3 3 15 0.01024
3 3 3 3 4 16 0.0512
3 3 3 3 6 18 0.0128
3 3 3 4 4 13 0.1024
3 3 3 4 6 15 0.0512
3 3 3 6 6 17 0.0064
3 3 4 4 4 18 0.1024
3 3 4 4 6 20 0.0768
3 3 4 6 6 22 0.0192
3 3 6 6 6 24 0.0016
3 4 4 4 4 19 0.0512
3 4 4 4 6 21 0.0512
3 4 4 6 6 23 0.0192
3 4 6 6 6 25 0.0032
3 6 6 6 6 27 0.0002
4 4 4 4 4 20 0.01024
4 4 4 4 6 22 0.0128
4 4 4 6 6 24 0.0064
4 4 6 6 6 26 0.0016
4 6 6 6 6 28 0.0002
6 6 6 6 6 30 0.00001

These probabilities are still different from the coin-toss method Kostas Dervenis gives in his Oracle Bones Divination.  Dervenis suggests one uses three coins flipped to obtain one of four results (T = tails, H = heads), each with the following probabilities:

  • Khion: HHH (12.5%)
  • Hyption: THH (37.5%)
  • Pranēs: TTH (37.5%)
  • Kōon: TTT (12.5%)

Thus, using coins as a substitute for astragaloi, we’d have a 0.0000305% chance of obtaining a (1,1,1,1,1) or (6,6,6,6,6) roll and a 7.41577% chance of obtaining a (3,3,4,4,4) or (3,3,3,4,4) roll.  These are pretty big changes in the probabilities of particular rolls, and all the other rolls would be affected similarly.  In either case, however, we have a situation where some results will come up far more regularly than others; then again, the oracle overall seems designed to have common outcomes assigned to the common fates, and extraordinary news to uncommon throws.  After all, it’s not every day you have the help of Zeus, King of the Gods and Men at your side, but far more common that you should wait a bit longer since your right time to act in the cosmos isn’t yet here.

So where does this leave us?  Should we forsake the use of dice and coins in favor of authentic knucklebones for astragalomancy since the probabilities of a given outcome are so different based on the tools used?  I don’t think so.  If we were playing a game of chance, then yes, the tools definitely matter, just as weighting a particular die to come up more on a given side would.  However, we’re not simply gambling with the gods here.  Divination is a sacred art and profession, and it helps the gods communicate with us so that we can ascertain their will as well as understand our own fates and our place in the divine order of creation.  Sure, it may be our hands that throw the bones, but it’s the hands of the gods that determine the outcome and how they land.  We’re not just rolling dice on our own, no more than things in the cosmos happen according to pure chance and nothing else.  This is why it’s important to invoke the gods of divination, like Hermes and Apollo, so that they’re involved in the throw of the astragaloi and can help guide them to fall on the proper sides so that we have a proper understanding of their wills and knowledge based on the result of the throw.  In that sense, using dice or bones or coins wouldn’t really matter, since it’s ultimately up to the gods to determine the outcome, and nothing is impossible for the gods.  Although they may have a preference for the system and tools used (hence the consecration and divination ritual from the previous post), they’re pretty handy when it comes to the myriads of tools used for divination.  So long as you’re letting the gods answer when you ask, the tools and their statistical qualities don’t matter in the long run.

Ritual Astragalomancy

Astragalomancy, as I brought up in the last post, is divination using knucklebones.  Besides the fact that I can legitimately say that I “throw the bones” when I do readings, I’m excited to learn about it because it’s such a classical system of divination, and one tied directly to Hermes.  Thing is, however, that it’s pretty straightforward, pretty simple, and pretty clear.  I’m a ceremonial magician.  Can I make something more complex?  You bet your ass I can, so I did with this.  After all, knucklebones and a guide to divination is well and good, but why not consecrate my new divination tools or set up a ritual divinatory framework with them?

Dervenis in his Oracle Bones Divination happily gives instructions on how astragaloi were cleansed and prepared from the actual sheep by repeatedly boiling them in a fresh dilute solution of vinegar and cleaning off whatever can come off until they’re completely cleaned of blood and flesh.  He admits that this is a bit much to ask of the everyday reader in our culture far removed from home butchery, and my knucklebones are already cleaned off.  Still, I figured I’d incorporate this simple act into a ritual of consecration under Hermes to dedicate the knucklebones for divination; the ritual boils the knucklebones more for effect and going through the motions instead of actually cleaning them, but if you’re actually cleaning off flesh and blood from the knucklebones, the ritual can be adapted for that, too.

At dawn on the day of the month given to worship of Hermes (the fourth day of the lunar month if you go by the Attic calendar, or the seventh day if you go by the mathetic calendar), prepare a large batch of khernips and wash yourself off with it.  Set aside frankincense and cinnamon incense, olive oil, white vinegar, clean water, and red wine, and make an offering to Hermes as you would normally with the usual prayers, incense, wine, candles, and whatever else you do; be sure to offer a good-sized glass of wine to the god during your offering.  Present to Hermes the five astragaloi, either by laying them on his altar before his image (if you have one) or by raising them up to the east facing the sunrise; dedicate the astragaloi to him as a gift and a means by which you can communicate with him and he with you for advice, divination, guidance, and direction:

Hail, Hermēs Khrēsmophoros! By your guidance, I seek messages from the gods.
Hail, Hermēs Euskopos! By your guidance, I seek wisdom from on high.
With these five knucklebones, these five astragaloi, I seek to know my life and the world I live in.
O Hermēs, you who love to be a friend to humanity, I give these astragaloi to you!
Let us throw these together as friends, sharing knowledge and wisdom of action and reaction!
Let us throw these together as mates, giving and hearing words of reality and advice!
Accept these five knucklebones, Hermēs Astragalios, as tools by which we may speak together!

After this, take a small pot and wash it out with the khernips.  Take one measure of vinegar and four measures of water in the pot, enough so that the entire amount is enough to completely cover the knucklebones, and heat the solution until it comes to a rolling boil.  Place the knucklebones into the boiling solution and slowly say the Orphic Hymn to Hermes.  Take the knucklebones out of the solution and place them on a clean white towel to dry and cool off, and throw out the liquid from the pot.  If so desired, repeat all this four more times, from rinsing the pot out with khernips to drying out the knucklebones, so that the knucklebones have been washed off five times in diluted vinegar; once, however, is enough, especially if the knucklebones have already been cleaned.

After this, rinse off each knucklebone in the khernips.  Take a shallow bowl and place the five knucklebones in it, and present the knucklebones to Hermes again as clean instruments for divination.  Light the incense of cinnamon and frankincense.  For each of the five knucklebones, take one from the bowl, hold it aloft, and dedicate it to Hermes in work with divination, submerging it in the wine you offered to him earlier:

With this wine, I nourish these bones that they may be fed to work in my divination.
With this wine, I honor these bones that they may help me in my life.
With this wine, I exalt these bones that they may loosen the tongues of the gods.
With this wine, I dedicate these bones to Hermēs that he may speak with his power.

After all five knucklebones have been fed with wine, empty and clean out the bowl, then place them back in the bowl (you may want to pat them dry first) and drizzle them all with the olive oil.  Rub each with the olive oil, making sure that they’re slick and covered with the stuff.  Waft each of the knucklebones in the incense so that the smoke completely surrounds each bone, having come in contact with all its surfaces.  Present the oiled and suffumigated knuclebones in the bowl (again emptied and cleaned out) to Hermes again, setting them before his image (if you have one), and pray:

Hail, Hermēs Khrēsmophoros! By your guidance, I seek messages from the gods.
Hail, Hermēs Euskopos! By your guidance, I seek wisdom from on high.
Great Hermēs guides all on their paths.
Great Hermēs leads all to their ends.
Great Hermēs knows all in their minds.
I dedicate these five astragaloi, to the words and works of Hermēs Astragalios,
that I may not be misguided, that I may not be mislead, that I may not be left in ignorance.
Cleaned, fed, anointed, suffumigated, dedicated,
may Hermēs speak clear and true through his oracles of his dice!

After this, leave the knucklebones on his altar for some time, at least a full day but, if possible, a full lunar month; set a candle on top of the bones every day that they’re being consecrated.  Once the consecration period is over, make an offering to Hermes in thanks for consecrating and accepting the knucklebones as a tool to be used with him for divination; the dice can now be wiped off from any extra oil that did not take and can be kept in a clean, protective bag.  Afterwards, that same day, also make an offering to Apollo, the best friend of Hermes and the other primary god of divination, and present the dice to him that his words may also come across true and clear through the dice with the guidance and aid of Hermes.

With that, our astragaloi are consecrated and ready for use.  Now, how do we go about using them?  Traditionally, astragalomancy was performed in the agora or forum, the town marketplace, by a herm (four-sided pillar topped with a bust of Hermes) with the 56 different oracles inscribed on the sides.  Next to the herm would be a table or a bowl containing the five astragaloi for divination; you’d ask Hermes the question, take up the astragaloi, roll them on the table or on the ground, and look up the corresponding answer.  Pretty simple and straightforward; ritually speaking, we don’t need to do more than just invoke Hermes and ask him our query.  Then again, that’s boring, so let’s be a little fancier.

Before consulting the astragalomancy, it helps to always figure out what exactly you’re going to ask.  I’ve talked about this plenty before, more in person than otherwise, but the query is the most important part of the whole divination process.  Without a good query, your answer’s going to be shit.  A good query follows the rules of the three “C”s:

  • A good divination query is clear.  There is no obscurity, duplicity, or vagueness in the query; you’re being honest about what it is you want to know, and you’re putting it bluntly, frankly, and openly for both yourself, the diviner, and the gods or spirits who answer.
  • A good divination query is concise.  You aren’t droning on for half an hour telling your life story, nor are you taking the garden path when asking your question.  Instead, you’re able to succinctly phrase your question into a single, short sentence.  This goes hand-in-hand with the clarity of the query.
  • A good divination query is concrete.  You know exactly what you’re asking about and you’re asking it clearly and concisely.  You aren’t talking about abstract concepts or hypothetical theoretical potentialities of what ifs, but something that can actually happen with tangible or viewable results.

So, rather than asking “will I ever be happy in my love life?”, which is clear and concise but not concrete, you might ask “will John Doe propose to me by the end of this year?”; instead of asking “am I in the right place in my life” after droning on for an hour about your college mistakes, you might ask “should I leave my current company to work on my start-up idea?”.  You get the gist.  Given the placement of the oracle and given the major focus of the astragalomantic verses, although astragalomancy can be applied to any query, they’re especially powerful for matters involving business, trade, travel, and other worldly affairs.  It’s quite probable that tradesmen, shopkeepers, and other business-minded people would consult the agora astragalomancy before business deals or other ventures as our modern businesspeople consult the stock market and trade indexes.

Once you have the query fixed in your mind, understanding what it is you’re actually going to ask, prepare yourself and a few supplies for making a formal supplication for divination from Hermes.  Wash off with khernips and sprinkle it around the area you’ll be divining in as well as on the astragaloi.  Set the astragaloi before you.  Make an offering to Hermes by lighting a white candle and, if desired, some frankincense incense, and pour out a small amount of wine, praying:

Hail, Hermēs Khrēsmophoros! By your guidance, I seek messages from the gods.
Hail, Hermēs Euskopos! By your guidance, I seek wisdom from on high.
Great Hermēs guides all on their paths.
Great Hermēs leads all to their ends.
Great Hermēs knows all in their minds.
I make you this offering, Hermēs, and I seek your presence here!
I come with a question seeking answers, a query seeking advice!
Accept this light, this incense, and this wine, blessed god, and be pleased with them.
Open now my paths and see now my plight!

Feed the astragaloi with wine, using the fingers of your left hand to dip into the glass of wine for Hermes and sprinkling them onto the astragaloi.  Pray the same wine-feeding prayer as above:

With this wine, I nourish these bones that they may be fed to work in my divination.
With this wine, I honor these bones that they may help me in my life.
With this wine, I exalt these bones that they may loosen the tongues of the gods.
With this wine, I dedicate these bones to Hermēs that he may speak with his power.

Take up the astragaloi in your left hand and speak your query directly into them; focus on the query, breathing onto the astragaloi, until they become warm.  Once they’ve taken on your heat, cup them in both hands, shake them four times, and toss them onto the ground before you.  Make a note of how each astragalos falls, both in terms of which side it falls on (Khion, Hyption, Pranēs, Kōon) and how it falls in terms of speed, bounce, location, direction, and whether it bumps into another astragalos or into another object.  Announce the god associated with the throw of the astragaloi, and read aloud the corresponding oracle associated with the throw of the astragaloi.  Meditate on the god, the oracle, and the manner in which the astragaloi fell and how it all ties into a single answer for your query; if desired, also consult the Greek alphabet oracle interpretation for the sum of the throw.

If there are any more questions to be asked, wash off the astragaloi with khernips and feed them with wine again, saying the prayer as above, then repeat the process of throwing the astragaloi and meditating on the answer.  Once all questions have been asked, the divination ritual can be brought to a close.  Wash off the astragaloi with the khernips once more and pour a bit more wine into the offering for Hermes, thanking him for his answers and guidance from your heart, and asking that he continue to guide you that his advice may not be wasted or spoken in vain.  The candle can be respectfully put out or left burning as an offering.

Of course, if all the above is too much for you, you might invoke Apollo and Hermes, the gods of divination and prophecy, in a simple prayer that Apollonius Sophistes gives on his page about the Greek alphabet oracle.  This is an invocation at the top of a pillar with a set of oracular verses upon which grammatomancy is based, directly preceding the verses themselves.  The prayer runs thus:

Apollo, Lord, and Hermes, lead the way!
And thou, who wanders, this to thee we say:
Be still; enjoy the oracle’s excellence,
for Phoebus Apollo has given it to us,
this Art of Divination from our ancestors.

As far as ritual timing goes, I’d say that pretty much any time is good for Hermaic astragalomancy.  He’s both ouranic and chthonic, liminal, and everywhere all the time; there’s no bad time to work with him for this.  That said, as a matter of custom, any days the agora or market wouldn’t be open is probably a day to not consult the bones for this; in my lunar grammatomantic calendar, the unlettered days would be an example of this.  The usual astrological phenomena apply, of course: be wary of Mercury retrograde, rethink starting a matter when Mercury is afflicted or Moon is void of cource, yada yada.  Taking observance of the weather, a common warning in geomantic practice, is useful, too; you probably don’t want to do divination with the gods when those same gods in charge of the weather and the world are fighting or upset, causing storms or hurricanes or damaging winds or sharp frosts or whatever.  The process of figuring out the query can be coupled with meditation to clear out your own mind and settle your own passions, too, but you probably already know this.

On Astragalomancy

My birthday was last month, and I was fortunate enough to spend it with my mother and sister, with whom I haven’t spent a birthday in something like eight years.  I was in town to watch over my mother after a hip surgery of hers, and it coincided with my birthday (a few days after Crucible, no less!), and besides coming down with a minor cold for a day or two, it was overall a fantastic trip and a good way to spend my birthday.  My mother is the type to always spoil people on their birthday; she lives for gift-giving, and most of her house is filled with Christmas, Hanukkah, and birthday supplies year-round.  One of the rooms in her house (my old room, no less) is filled with nothing but tchotchkes and trinkets that she’s accumulated over the years of working at Lillian Vernon and shopping at antique stores and QVC that she doles out regularly, always somehow replenishing her wares of knick-knacks and the like.  I tend to dislike her taste of gifts, personally.  It’s only occasionally that I find something I like in her house that I’d like to have for myself, and I’d rather her save her money for herself.  She insists otherwise, however, so I just redirect her to my Amazon wish list and she’s content with that, and I’m more than content with her buying me stuff I actually know I want.  She’s really too kind to indulge me at all at this age.

This year, like many years, she’s gotten me books on magic and divination; of the more-than-200 items on my wish list, a vast majority of them are books, so this isn’t surprising.  However, this year she got me a book I’ve had my eye on for a while: Oracle Bones Divination by Kostas Dervenis. The author calls it a “Greek I Ching”, and although I don’t quite agree with that, I can see where he’s coming from.  The book is short and to-the-point, focusing on a form of divination used in ancient and classical Greece where one uses a set of five dice to obtain a particular oracle.  It’s not unlike the use of Greek letter divination or grammatomancy in that light, but there are some major differences; no letters are required here, and while grammatomancy has only 24 results, this form of divination has 56, and the literature explicitly links each result not only to an oracular answer but also to a particular deity or divinity.  However, there’s no one single body of oracular verses for this; many different sites had their own variations, although they generally coincided for the most part.  Fritz Graf’s article “Rolling the Dice for an Answer”  (published in “Mantikê: Studies in Ancient Divination” as part of the series “Religions in the Graeco-Roman World”, vol. 155, Brill, 2005) contains one such list, based mainly on the inscriptions found at Kremma in Pisidia and Perge in Pamphylia, both in Anatolian colonies of the Greeks, while Dervenis’ work is based on other locations from ancient Anatolia; they’re mostly the same, with about 40% of the divine names different and 25% of the oracular verses different.  No one complete list of names and verses survives, though it’s hypothesized that there’s one specific originating text from which derive all the others.

In a word, this book describes Greek astragalomancy, or divination with astragaloi.  Astragaloi (singular astragalos, or Latinized astragalus) are the knucklebones (actually the anklebones) of sheep, goats, or rams, and were used as a type of die by primitive people and are still used in some cultures, especially nomadic, shepherding, or rural communities like those in mountainous areas of Greece or by Mongolian people in traditional games.  Given the way an astragalos is shaped, a person can throw an astragalos like a die and can come up with one of four results, each with a numeric value associated with it:

  • Khion (χιον, “of the island of Chios”), narrow concave side, with a value of 1
  • Hyption (υπτιον, “lying on the back”), broad concave side, with a value of 3
  • Pranēs (πρανης, “lying on the front”), broad convex side, with a value of 4
  • Kōon (κωον, “of the island of Cos”), narrow convex side, with a value of 6


Just a note: classically, the astragaloi were tallied such that they counted the side that was face down.  Us modern people are used to throwing dice to read the side facing up.  It could be that different regions had or have different ways of traditionally throwing dice and counting things up.  I prefer the modern way, although Dervenis doesn’t specify which method to use.

While the names of the four sides are fixed, and the values associated with each name is well known, I found some confusion in figuring out which of the narrow sides was Khion and which was Kōon.  Dervenis gives Khion (1) to the narrow convex side and Kōon (6) to the narrow concave side, while most other sources I’ve found reverse the two, such that Khion is concave and Kōon convex.  I use the latter method since I find it more plausible.  Like any die, the opposite sides add up to 7 (3 + 4 and 1 + 6), and it makes sense that the convex (bulging) side is given to the larger number of a given pair, while the concave (hollow) side is given to the smaller number.  Thus, I give the narrow convex side to 6 and the narrow concave side to 1, even though Dervenis switches them.  It’s really a matter of style, I suppose, since it only affects how I read the bones; the actual oracles themselves don’t change, though my selection of them differs from Dervenis’ method.

The astragalos has a shape approximating that of a rectangular prism, so there are technically six sides to the thing, but the two short sides are too round and narrow for the astragalos to land on them.  Thus, although it’d make sense for an astragalos to have six sides with a value for each (1, 2, 3, 4, 5, and 6), there are really only four results (1, 3, 4, and 6).  A modern tabletop RPG four-sided die can be used instead of an astragalos, substituting 2 with 3, 3 with 4, and 4 with 6.  Alternatively, Dervenis suggests the use of three coins flipped so that three heads is equal to 1, two heads with 3, two tails with 4, and three tails with 6.  Astragaloi can be a little difficult to obtain, but you can find them in some Mongolian traditional supply stores from time to time.  Dervenis suggests one uses three coins flipped to obtain one of four results (T = tails, H = heads):

  • Khion: HHH
  • Hyption: THH
  • Pranēs: TTH
  • Kōon: TTT

The problem with this is that one gets slightly different probabilities using coins than when one rolls actual knucklebones.  In order to get one of four results with three coins, we ignore the order in which we flip the coins.  However, each combination has a 1/8 chance, or 12.5% chance.  There’s only one combination that has all heads or all tails, so Khion and Kōon come up approximately 12.5% of the time each.  Hyption and Pranēs, however, are split with the rest; thus, if Khion and Kōon have 1/8 each, then we have 6/8 leftover, meaning that obtaining a Hyption or Pranēs with coins has a 3/8 chance each, or a 37.5% chance.  Knucklebones, however, have different probabilities due to their odd shapes; rolling a Hyption or Pranēs has about a 40% chance each, but rolling a Khion or Kōon has about a 10% chance each.   Thus, the likelihood of certain outcomes when using coins or when using astragaloi are going to differ.  It reminds me of a similar debate in i ching divination, where the traditional yarrow stalk method yields a different probability than the coin-based method, leading some people to favor one method over the other or claim that coin-based methods are false and misleading.  Still, the difference in outcome probabilities with coins versus knucklebones is much smaller than it is with coins versus yarrow stalks, so perhaps Dervenis is alright in suggesting the use of coins.

In Greek astragalomancy, five astragaloi are thrown and their combination inspected without regard for order.  Thus, a throw of 1-1-1-3-6 is equivalent to one of 6-1-1-3-1, and both are associated with the same oracular verse.  As mentioned before, there are 56 different combinations of throws, but we can view each throw of the astragaloi as a sum of the value of each astragalos.  Thus, 1-1-1-3-6 yields the sum 12.  This sort of summation was used in the ancient game of pleistobolinda, which is basically Greek dice gambling where the highest throw wins (though there are more complex rules to make scoring more fun).  In pleistobolinda with five astragaloi, we can get 24 different results ranging from 5 to 30, with the values 6 and 29 impossible to obtain given the numeric values available to us.  This means we link astragalomancy with grammatomancy, using give astragaloi to obtain one of 24 numbers and link that number to one of the 24 letters of the Greek alphabet.  Happily, Apollonius Sophistes on his page about the Greek alphabet oracle already gives us such a correspondence between the sums of five astragaloi to the 24 letters of the Greek alphabet.  Following the rule of pleistobolinda where the greatest sum wins the round, we give the highest throw of five astragaloi (30) to Alpha, the best oracle in grammatomancy, and the lowest throw (5) to Omega, the worst oracle.  The rest of the letters get assigned their respective values accordingly from high to low based on their position in the Greek alphabet.

Thus, with five astragaloi, we can pick and choose which set of oracles we want to use: if we’re only going to use the sum of the throw, we’d use the Greek alphabet oracle, but if we inspect the combination of individual astragaloi, then we’d use the astragalomantic oracle.  With the same set of tools we can pick and choose how we can get an answer, but it’s not clear to me how to link the two together, if we should at all.  For instance, consider the throw 1-1-1-1-1.  The sum of this throw is 5, associated with Omega with the oracle “you will have a difficult harvest, not a useful one”, which is the worst oracle you can get in grammatomancy.  However, in astragalomancy, the corresponding oracle for this says “Zeus the Savior will inspire you; he will give you happiness and all that you wish for, but sing the praises of Aphrodite and Hermes”.  This is actually quite a nice oracle to get, so long as you pay your respects to the good gods; plus, Dervenis links this throw of the astragaloi to the god Zeus Olympiou, Zeus of Olympos, while grammatomancy would link its corresponding oracle to the planet Saturn and, thus, the titan Kronos.  I see other issues with other results in trying to link Dervenis’ astragalomancy with grammatomancy, so although I can use the same set of tools for both, it may not be great to link the two together unless I find that grammatomancy and astragalomancy serve different ends.  Like, it’d be cool if grammatomancy could suggest a method of action while astragalomancy what will overall happen, but both seem to answer in terms of both advice on action and what will happen.  It’s unclear, although there is some connection between the two; one of the throws has in its oracular verse the verse associated with the letter Kappa (“fighting with waves is difficult; endure, friend”), though whether astragalomancy came before grammatomancy or vice versa isn’t clear.

Happily, the order in which the astragaloi are thrown don’t matter for astragalomancy; while one can simply throw a single astragalos five times, it’s implied that one throws five astragaloi at once.  However, although it’s never said in any text, it’s never mentioned about whether the manner in which the astragaloi themselves fall is interpreted, not just on which side but how far apart they end up, whether they bounce, the overall shape of the astragaloi placement, and the like.  There’re no rules for this, as far as I can tell, but where the astragaloi fall can often be as important as how they fall.  It’s similar to the cowrie shell divination I use; if they tend to fall in a straight line, it indicates motion to or some involvement with a particular entity, especially if all the shells fall in a line leading to a particular shrine or statue.  One flying off in a bizarre direction can indicate a wild hare up something’s ass.  This is far more free-form and is more ominous than oracular, so it all depends on the circumstances of the query, but it’s something to keep in mind.

All the same, astragalomancy is definitely a divination system I plan to be using and studying in tandem with grammatomancy.  After all, the use of dice has always been important for divination (sorcery and sortilege come from the same word, Latin sors meaning “lots” or selection by chance), and are excellent symbols of Hermes, to whom astragaloi and dice generally have always been linked.  Still, the use of knucklebones for divination has a different feel to it, a different charm and aesthetic that feels…well, older, classier, and more classical, and happily the set of knucklebones I bought on Ebay came in a set of 10, so I can keep one on Hermes’ altar and one in a satchel I keep of divination and magical tools on the go.  I’m getting to the point where I prefer to use them over my divination dice (a standard set of tabletop RPG dice from Chessex), but since I went ahead and consecrated my plastic divination dice, I figured why not undergo a consecration ritual for my astragaloi, too? Or, hell, turn astragalomancy from something casually done into something with a bit more flair?