Another Look at the Circle of Petosiris

Again with the same damn text as before, I suppose.  Lately I’ve been polishing up some of my own notes and personal texts that I don’t publicly share, one of which is my personal binder of divination texts I use for the Greek stuff I do, namely grammatomancy, astragalomancy, and some references to the Delphic Maxims that I like.  In the section I have on grammatomancy—much pared down from my De Grammatomanteia ebook, but refined to have more information and correspondences that I personally find useful—I’ve been trying to reorganize some of the information in a better way that reduces my reliance on external resources.  Of course, it’s mostly a “just in case” thing, and some of the stuff I don’t really use…but it doesn’t hurt to have.

One of the things I’ve been wrestling with is how much numerology stuff I want to include.  After all, numerology was considered pretty useful in classical times, and if nothing else, it’s informative and instructive to consider.  I’ve written about it before, specifically onomatomancy, literally “divination by names” (previously I called it “onomancy”, which isn’t wrong but isn’t as correct a term as I should be using).  I wrote three posts about it: one that overlaps numerology with stoicheia, one about using pythmēnes to determine winners, and one that uses particular numerological devices to determine the outcomes of events.  I’ve been debating whether to include summaries of these methods and their charts or rules in my divination binder for my temple, and it’s not a bad idea to, I suppose, though I’m unconvinced I really need to.  Still, it wouldn’t be bad to have, and having the stoicheia-based rules thrown in could be useful, so I’m leaning towards doing it anyway.  That’s what got me looking, once again, at the Circle of Petosiris, a particularly fun numerological tool to determine whether one will recover and live or succumb and die to an illness based on the numerological interactions between a person’s name and the lunar date on which they fall ill.

Get a drink and buckle up, dear reader.  This post got a bit longer than I had anticipated.

For some background on my resources for this, the first reference I found that discussed this particular device was Hugo Magnus’ Superstition in Medicine (1905).  Magnus touches on the topic briefly giving an outline of the topic, but he refers to two other texts: Marcellin Berthelot’s Introduction a l’étude de la chimie des anciens et du moyen age (1889) and a truly wondrous work, Auguste Bouché-Leclerq’s L’astrologie grecque (1899).  Indeed, it’s from Bouché-Leclercq that I ultimately got my images for the Circle of Petosiris, which he’s modified slightly to fix what he believes is an error in the original diagram.  Both of these Circles, however, ultimately come from MS Grec 2419 from the Bibliothèque nationale de France, which is a beast of a 15th century Greek manuscript that contains all sorts of magical, astrological, Solomonic, and other divinatory texts in Greek that I wish someone would translate at some point into English.

With that, let’s look at Bouché-Leclercq’s versions of the two Circles of Petosiris from MS Grec 2419.  Both of these Circles are found in MS Grec 2419, though I could only find them after looking hard; the way the BnF digitized the damn thing screwed up all the folio numbers.  All the same, let’s go with Bouché-Leclercq’s nicely-redone versions of the Circles, because the originals are rather messier and harder to read:

For comparison, take a look at what the Circles look like from the original text.  The two tables on either side of the Circle are, according to Bouché-Leclercq, computations of the days of the lunar month, though I’m not really sure what that means.  In either case, Bouché-Leclercq omits the tables, while Berthelot includes them in his own (faithfully reproduced) image.

 

If you take a closer look at both of these Circles (at least in Bouché-Leclercq’s versions), they have the same basic structure: a circle divided into four quadrants each filled with numbers, with a central middle column divided into an upper half and lower half also filled with numbers.  Thus, each circle contains six zones, and each of them are labeled with a particular outcome based on numbers; going clockwise from the 9 o’ clock position, these are Great Life (upper left), Average Life (upper central), Small Life (upper right), Small Death (lower right), Average Death (lower central), and Great Death (lower left).  Interestingly, the middle sections of the fancier Circle of Petosiris on the right aren’t labeled, but given the similarities and positioning between the Great and Small outcomes on either side, it can be inferred that the middle refers to Average.  In either case, the upper zones reflect outcomes of Life, and the lower zones the outcomes of Death.

Just to make sure the Circles are fully understood, let’s take a closer look at the Greek script in each.  On the left, simple Circle, the central line says Πετοσίρου κύκλος, literally “circle of Petosiros” (spelling intentional on this one).  Around the edge, starting at the 9 o’ clock position and going clockwise, we get the

  1. ἡ μεγάλη ζωή (“the great life”)
  2. μέση ζωή (“middle life”)
  3. ἡ μικρά ζωή (“the small life”)
  4. μικρός θάνατος (“small death”)
  5. μέσος θάνατος (“middle death”)
  6. ὁ μέγας θάνατος (“the great death”)

The fancier Circle has a lot more going on inside it. Above the diagram, there’s the phrase κύκλος Πετοσίρεως, or “circle of Petosiris”.  On the horizontal, we have ὅροι ζωῆς καὶ θανάτου, literally “the borders of life and death”, a pleasant label for such a device, I suppose.  The “lobes” around the edge of the fancier Circle, starting at the 9 o’ clock position and going clockwise, indicate both the course of the Sun around the Earth in a single day as well as the four elements:

  1. ἀρκτικός μεσόγειος (“Arctic [star] over the earth”, i.e. midnight)
  2. πῦρ (“fire”)
  3. ἀνατολή ὑπέργειος (“rising above the earth”, i.e. sunrise)
  4. ἀήρ (“air”)
  5. μεσημβρία μεσόγειος (“midday over the earth”, i.e. noon)
  6. ὕδωρ (“water”)
  7. δύσις ὑπόγειος (“setting under the earth”, i.e. sunset)
  8. γῆ (“earth”)

In other words, if the fancier Circle of Petosiris were to be considered as a compass, north would be to the left, east at the top, south to the right, and west to the bottom.  The use of the elements here is interesting, as it might be thought to allocate certain elemental qualities to certain times of the day.  Continuing on, going around the outermost circle quadrant by quadrant, there are the following four messages:

  1. οὗτοι ταχέως σώζουσιν (“these save from death quickly”)
  2. οὗτοι ἐντός ἑπτά ἡμερῶν σώζουσιν  (“these save from death within seven days”, i.e. slowly)
  3. οὗτοι ἐντός ἑπτά ἡμερῶν ἀναιροῦσιν (“these kill within seven days”, i.e. slowly)
  4. οὗτοι ταχέως ἀναιροῦσιν (“these kill quickly”)

These line up with the text outside the circle and past the lobes, respectively μεγάλη ζωή (“great life”), μικρά ζωή (“small life”), μικρός θάνατος (“small death”), and μέγας θάνατος (“great death”).  It might be inferred, then, that the Average Life and Average Death zones would take effect in a span of three days or less, to use the same week-based timeframe for the Small Life and Small Death, while the Great Life and Great Death zones would take effect within a day.  It’s an odd timing system to use, I suppose, but it does offer a relative sense of scale.

Each quadrant also has a longer message in the innermost circle, though it’s repeated twice within each quadrant, once within each eighth-part of the circle:

  1. ἀρκτικά ὑπέργεια του βοῥῥᾶ (“Arctic [stars] above the earth [in the region] of Boreas [i.e. the north]”)
  2. μεσημβρία ὑπέργειος του βοῥῥᾶ (“midday [stars] above the earth [in the region] of Boreas [i.e. the north]”)
  3. μεσημβρία ὑπόγειος του νότου (“midday [stars] under the earth [in the region] of Notos [i.e. the south]”)
  4. ἀρκτικά ὑπόγεια του νότου (“Arctic [stars] under the earth of the [in the region] of Notos [i.e. the south]”)

These latter messages are probably supposed to represent the four parts of the day—viz. late night between midnight and sunrise, early day between sunrise and noon, late day between noon and sunset, early night between sunset and midnight—but these are given using kind of unusual astronomical phrases that I’m not fully certain I have right.  However, Berthelot doesn’t describe why these additions of times of day, positions of stars, or elements to the fancier Circle of Petosiris might be here, and they don’t seem to actually be used for numerological or onomatomantic divination; Bouché-Leclercq brings this up, and says that their inclusion is a “strange whim” and unknown how it might have been used.  However, based on some of the text (great life, small death, three zones of numbers per hemisphere, etc.), we have an almost identical setup of the basic arrangement of numbers, though Bouché-Leclercq says that the order is mysterious, i.e. it’s unknown why or how the numbers are arranged the way that they are.

The only real difference in how these two Circles of Petosiris are used is by what number one divides by to obtain a remainder; when using the simple Circle, one divides by 29, while with the fancy Circle, one divides by 30.  This matches how the simple Circle only contains numbers from 1 to 29 (αʹ to κθʹ) while the fancier Circle goes from 1 to 30 (αʹ to λʹ).  We know that lunar months have either 29 days (a hollow month) or 30 days (a full month), so it struck me that the simple Circle should be used when one falls ill during a hollow month, and the fancier Circle during a full month; neither Berthelot nor Bouché-Leclercq suggest this, but this makes so much more sense, in that these two Circles can be used alongside each other, just not at the same time!  After all, both of these Circles appear in the same overall text (though perhaps not by the same actual author), so using one for one kind month and the other for the other kind of month makes some sense so that nothing is missed.  Using this idea, the simple Circle can be called the Hollow Circle of Petosiris for use with hollow months of 29 days, and the fancier one the Full Circle of Petosiris for use with full months of 29 days.

In this light, we can compare how the outcomes match between the two Circles:

Quality Outcome Hollow Month
(29 days)
Full Month
(30 days)
Bright Great Life 2, 3, 7, 9, 11 2, 3, 7, 9, 10, 11
Average Life 13, 14, 16, 17, 19, 20 13, 14, 16, 17, 19, 20
Small Life 22, 23, 26, 28 22, 23, 26, 28
Dark Small Death 1, 25, 27, 29 1, 25, 27, 30
Average Death 4, 10, 15, 18, 21, 24 4, 15, 18, 21, 24, 29
Great Death 5, 6, 8, 12 5, 6, 8, 12

Perhaps unsurprisingly, the outcomes of the hollow Circle and the full Circle are almost exactly the same!  There are only three differences between how the days are arranged between the two circles:

  • Day 30 (which doesn’t exist in hollow months) is given to Small Death in full months
  • Day 29 is given to Average Death in full months and to Small Death in hollow months
  • Day 10 is given to Great Life in full months and to Average Death in hollow months

This further reinforces the notion that one circle really is meant for hollow months and the other for full months, and that the two Circles really belong to the same overall system, using one or the other based on the specific month of the illness.  In that sense, we can rearrange this table slightly to show how similar both systems really are:

Quality Outcome Hollow Month
(29 Days)
Common Full Month
(30 Days)
Bright Great Life 2, 3, 7, 9, 11 10
Average Life 13, 14, 16, 17, 19, 20
Small Life 22, 23, 26, 28
Dark Small Death 29 1, 25, 27 30
Average Death 10 4, 15, 18, 21, 24 29
Great Death 5, 6, 8, 12

Note that the regions above the horizon in the full Circle, marked as above the Earth according to the time of day, are labeled in the table above as “Bright”, while the lower regions marked as below the earth are labeled as “Dark”.  This gives an interesting binary quality to each day of the month, which can also help predict how things overall turn out in addition to simple illnesses:

  1. Take the name of the person, find the isopsephic value of the name, divide by the total number of days in the month, and find out whether the remainder is Bright or Dark according to the proper Circle of Petosiris for the type of month.
  2. Find whether the given day of the lunar month on which one initiates a new project, task, or journey is Bright or Dark, according to the proper Circle of Petosiris for the type of month.
  3. If both numbers are Bright, the whole of the project, task, or journey will be fortunate and good.
  4. If both numbers are Dark, the whole of the project, task, or journey will be unfortunate and bad.
  5. If the number of the person is Bright and the number of the day is Dark, the person will be in danger, but they will escape the danger.  More generally, fortune will occur under the appearance of misfortune.
  6. If the number of the person is Dark and the number of the day is Bright, misfortunes will occur under the appearance of fortune, and although things appear to go well, hidden dangers and traps lie about.

In either case, it should be noted that there are slightly more Bright days than there are Dark days; there are always 14 Dark days every month, with 15 Bright days in hollow months and 16 Bright days in full months.  At least there’s a greater chance of success or survival than not, I suppose.

Yet another way that the Circles can be used is to determine which of two parties in a contest, fight, or battle will win.  Take the isopsehic values of each of their names, divide by 30, and find the remainder using the Full Circle of Petosiris to compare their respective results; the value with the better quality will determine the winner.  For instance, in the ever-popular onomatomantic example, Achilles (Αχιλλευς) has the isopsephic value of 1267, which gives a remainder of 7, landing in “Great Life”, while Hector (Εκτωρ) has a value of 1225, which gives a remainder of 25, landing in “Small Death”.  Though not as much is said about this method, several other

  • Bright outcomes automatically become victorious over Dark outcomes.
  • Especially in fatal conflicts, Dark outcomes indicate actual death, whether immediately or after a long-sustained injury or infection.
  • If both parties end up in Dark outcomes, the one with the least bad result will survive the longest but both will lose.
  • If both parties end up in Bright outcomes, the contest may be brought about to an amicable end, with the party with the better outcome having the upper hand.
  • If both parties end up in the same outcome, the contest may be conceived of as equal and coming to a truce or stalemate, or we can resort to other numerological and onomatomantic methods instead (such as the pythmēnes method), though we could also use a simpler rule of just looking at the outcome numbers themselves and comparing directly with them, unless those two numbers are also the same.

In general, it seems like the Circle of Petosiris is actually a multipurpose numerological and onomatomantic tool of divination that can be used to not just determine the outcome of illnesses but of any general event, battle, or project.  What’s interests me and which can be another useful diagnostic tool, however, is the attribution of Brightness or Darkness to particular days.  After all, I already have a lunar calendar (well, really, lunisolar calendar), the Grammatēmerologion, which gives individual days of the lunar months to the letters of the Greek alphabet for prognostication and ritual planning.  If Bright and Dark days can be thought of as naturally tending to fortune or misfortune, respectively, especially for particular people based on their names, then it wouldn’t be hard to conceive of this as further enhancing the Grammatēmerologion system:

Day
Number
Day
Letter
Quality
Hollow Month
(29 days)
Full Month
(30 days)
1 Α Dark
2 Β Bright
3 Γ Bright
4 Δ Dark
5 Ε Dark
6 Ϝ Dark
7 Ζ Bright
8 Η Dark
9 Θ Bright
10 Dark Bright
11 Ι Bright
12 Κ Dark
13 Λ Bright
14 Μ Bright
15 Ν Dark
16 Ξ Bright
17 Ο Bright
18 Π Dark
19 Ϙ Bright
20 Bright
21 Ρ Dark
22 Σ Bright
23 Τ Bright
24 Υ Dark
25 Φ Dark
26 Χ Bright
27 Ψ Dark
28 Ω Bright
29 ϡ Dark
30 Dark

This is kind of weird, though, when you look at it.  Some days that are given to really beneficial or naturally “bright” letters (like Alpha, “the god says that you will do everything well”, or Ēta, “the bright Sun who watches all watches you”) are given to be Dark, and vice versa (like Ōmega, given to Saturn, also has the comparatively awful oracle “you will have a worthless harvest, not a useful one”).  Additionally, the days that are given to obsolete letters (6, 19, and 29) or to unlettered days (10, 20, and 30) don’t really have much of a pattern as to which are Bright or Dark, even though it’s considered in the base Grammatēmerologion system that unlettered days are naturally considered unlucky or ill-favored for ritual or work.  I mean, I’m not really that surprised, considering how the Circle of Petosiris and the Grammatēmerologion system have no connection or shared logic behind them besides both relying on the use of a lunar month, and the fact that the Greek manuscript dates to the 1400s CE, but still.  Perhaps there is a logic behind how the Circle of Petosiris arranges days as Bright or Dark, or amongst the Great/Average/Small Life and Death categories, and I just don’t see it yet. At least I’m in good company of earlier scholars, I suppose.

It’s trying to figure out that order that reminded me of one of the first reasons why I ever learned about the Circle of Petosiris, namely the Sphere of Dēmokritos from PGM XII.351—364, something I mentioned in the original post about this stuff.  It’s a much simpler system, but the underlying method is the same: take the value of the person who has fallen ill, add to it the number of the day of the lunar month, divide by thirty, and take the remainder.

Unlike the more complex Circle of Petosiris with its threefold division of either life or death, the Sphere of Dēmokritos gives only two outcomes: if the result falls in the upper part of the table from PGM XII.351—364, the person will live, and if in the lower section, they will die.

  • Live: 1, 2, 3, 4, 7, 9, 10, 11, 13, 14, 16, 17, 19, 20, 23, 25, 26, 27
  • Die: 5, 6, 8, 12, 15, 18, 21, 24, 22, 28, 29, 30

On a whim, if we redefine “live” as Bright and “die” as Dark, I decided to compare how the Sphere of Dēmokritos matches up with our Circle of Petosiris scheme:

Day Letter Hollow
Circle
Full
Circle
Sphere of
Dēmokritos
1 Α Dark Dark Bright
2 Β Bright
3 Γ Bright
4 Δ Dark Dark Bright
5 Ε Dark
6 Ϝ Dark
7 Ζ Bright
8 Η Dark
9 Θ Bright
10 Dark Bright Bright
11 Ι Bright
12 Κ Dark
13 Λ Bright
14 Μ Bright
15 Ν Dark
16 Ξ Bright
17 Ο Bright
18 Π Dark
19 Ϙ Bright
20 Bright
21 Ρ Dark
22 Σ Bright Dark Dark
23 Τ Bright
24 Υ Dark
25 Φ Dark Dark Bright
26 Χ Bright
27 Ψ Dark Dark Bright
28 Ω Bright Dark Dark
29 ϡ Dark
30 Dark Dark

The overlap here is, frankly, astounding; in general, of the thirty days of the Sphere of Dēmokritos, eight are different from either the Hollow or Full Circles of Petosiris (days 1, 4, 10, 22, 25, 27, 28, and 30), and if we just limit ourselves to the Full Circle of Petosiris, the overlap is even greater where only four days are different (days 1, 4, 25, and 27).  For one text that dates back to the fourth century and another that’s dated to the fifteenth, that’s incredible.  The striking similarities between these systems shows that either they were developed independently using a similar method that happened upon similar results, or (perhaps and hopefully) more likely, that the Sphere of Dēmokritos is an earlier form of the Circle of Petosiris, or closely-related to one of the Circle’s forebears, with only a few changes/copyist errors slipping in along the way and the Circle developing a finer gradation of results from a simple “live” or “die” outcome.

In fact, if you think about it, consider how the numbers are arranged in the Sphere of Dēmokritos: an upper and a lower half, with the upper half indicating life and a lower half indicating death, with three groups of numbers in each half: one on the left, one on the right, and one in the middle.  Consider where the overlaps apply even in how these numbers are arranged: in the Great Life section in the upper left of the Circle of Petosiris, you have 2, 3, 7, 9, and 11; in the Sphere of Dēmokritos, the upper left column has 1, 2, 3, 4, 7, and 9, with 1 and 4 being known as flipped in brightness and with 11 being found in the middle column of the Sphere.  If you plot not only what the overlaps are but where they occur, you have essentially same system, just represented in a more rectangular format!

It’s at this point that I’m getting really hooked now, because now I want to know what the logic is behind why the numbers of the lunar month are arranged the way they are on the Circle of Petosiris.  After a bit, it seems like one of the few (maybe the only?) text that discusses this topic is Otto Neugebauer and George Saliba’s 1989 paper On Greek Numerology (Centaurus, vol. 31, pp. 189—206).  Neugebauer and Saliba document a number of instances of the Circle of Petosiris that are extant in a variety of texts, including the Sphere of Dēmokritos, and even claim that the list of lucky and unlucky days of the Egyptian calendar given in PGM VII.272—283 is a highly corrupted version of this same system.  Neugebauer and Saliba go over about a dozen manuscripts, but they don’t go into depth on how significantly different the Circles of Petosiris of each might differ.  My idea of using one such Circle for hollow months and another for full months makes sense (though I could just as easily use the Hollow Circle for both and just add on day 30 where we’d expect in the Full Circle and make no other changes), but who’s to say whether such a combined approach might ever have been used, especially if there were so many other variations available?  That Bouché-Leclerq inter alia share two such Circles, one based on the number 29 and another based on the number 30, might just be a coincidence of fate and philology.

What’s interesting from Neugebauer and Salida’s paper is something that I glossed over as unimportant at the beginning of this post.  Recall those tables by the Hollow Circle of Petosiris from MS Grec 2419?  Bouché-Leclercq says that those are “computations of the days of the lunar month”.  Neugebauer and Saliba, based on a hint from some of Paul Tannery’s chapter on fragments of similar numerological devices in from Notices et extraits des manuscrits de la Bibliothèque nationale et autres bibliothèques (1886, vol. 31, part 2, pp.231—260), figured out that the large numbers are the numerological equivalents of the actual names of the dates of the lunar month plus an extra word or phrase.  For instance, in the first row of the left table, there’s the number ͵αφπθ = 1589.  Neugebauer and Salida reckon this to be the equivalent of the words ΠΡΩΤΗ (1288) and ΣΕΛΗΝΗ (301), which together add to be 1589.  Indeed, they find that the numerical values of each row are equivalent to the spelled-out name of the date plus the word for Moon in Greek, as the text itself indicates: “reckon also the name of the Moon if it falls from conjunction to full-moon”.  Likewise, the values in the right table all have the number 138 added as a constant, which is explained as “the number of the waning-moon”, literally the word “hollow” (ΚΟΙΛΗ).   Thus, the top row of the right table, day 16, we would expect then to be “sixteen hollow” or ΕΞ ΚΑΙ ΔΕΚΑΤΗ and ΚΟΙΛΗ: 5 + 60 + 20 + 1 + 10 + 4 + 5 + 20 + 1 + 300 + 5 = 431, then 431 + 138 = 569.  Indeed, we find the number φμθʹ, which is 569.

If we were to develop a complete reproduction of this kind of table, then we’d end up with the following.  Where there is more than one set of values for a given day, this shows that there were different ways to write out the name of the day based on the given source of the specific Circle method, e.g. day 16 could be written as ΔΕΚΑΤΗ ΕΚΤΗ or it could be written as ΕΞ ΚΑΙ ΔΕΚΑΤΗ.  I know some of these aren’t necessarily what’s used in modern Greek, but they are attested in the literature Neugebauer and Saliba reference as well as other classical sources.

Day Name Modifier Sum
Word Value Word Value
1 ΠΡΩΤΗ 1288 ΣΕΛΗΝΗ 301 1589
2 ΔΕΥΤΕΡΗ 822 ΣΕΛΗΝΗ 301 1123
3 ΤΡΙΤΗ 718 ΣΕΛΗΝΗ 301 1019
4 ΤΕΤΑΡΤΗ 1014 ΣΕΛΗΝΗ 301 1315
5 ΠΕΜΠΤΗ 513 ΣΕΛΗΝΗ 301 814
6 ΕΚΤΗ 333 ΣΕΛΗΝΗ 301 634
7 ΕΒΔΟΜΗ 129 ΣΕΛΗΝΗ 301 430
8 ΟΓΔΟΗ 155 ΣΕΛΗΝΗ 301 456
9 ΕΝΑΤΗ 364 ΣΕΛΗΝΗ 301 665
ΕΝΝΑΤΗ 414 715
10 ΔΕΚΑΤΗ 338 ΣΕΛΗΝΗ 301 639
11 ΕΝΔΕΚΑΤΗ 393 ΣΕΛΗΝΗ 301 694
12 ΔΩΔΕΚΑΤΗ 1142 ΣΕΛΗΝΗ 301 1443
13 ΔΕΚΑΤΗ ΤΡΙΤΗ 1056 ΣΕΛΗΝΗ 301 1357
14 ΔΕΚΑΤΗ ΤΕΤΑΡΤΗ 1352 ΣΕΛΗΝΗ 301 1653
15 ΔΕΚΑΤΗ ΠΕΜΠΤΗ 851 ΣΕΛΗΝΗ 301 1152
ΠΕΝΤΕ ΚΑΙ ΔΕΚΑΤΗ 809 1110
16 ΔΕΚΑΤΗ ΕΚΤΗ 671 ΚΟΙΛΗ 138 809
ΕΞ ΚΑΙ ΔΕΚΑΤΗ 434 572
17 ΔΕΚΑΤΗ ΕΒΔΟΜΗ 447 ΚΟΙΛΗ 138 585
ΕΠΤΑ ΚΑΙ ΔΕΚΑΤΗ 755 893
18 ΔΕΚΑΤΗ ΟΓΔΟΗ 453 ΚΟΙΛΗ 138 591
ΟΚΤΩ ΚΑΙ ΔΕΚΑΤΗ 1539 1677
19 ΔΕΚΑΤΗ ΕΝΑΤΗ 702 ΚΟΙΛΗ 138 840
ΕΝΝΕΑ ΚΑΙ ΔΕΚΑΤΗ 480 618
20 ΕΙΚΟΣΤΗ 613 ΚΟΙΛΗ 138 751
21 ΕΙΚΟΣΤΗ ΠΡΩΤΗ 1901 ΚΟΙΛΗ 138 2039
22 ΕΙΚΟΣΤΗ ΔΕΥΤΕΡΗ 1435 ΚΟΙΛΗ 138 1573
23 ΕΙΚΟΣΤΗ ΤΡΙΤΗ 1331 ΚΟΙΛΗ 138 1469
24 ΕΙΚΟΣΤΗ ΤΕΤΑΡΤΗ 1627 ΚΟΙΛΗ 138 1765
25 ΕΙΚΟΣΤΗ ΠΕΜΠΤΗ 1126 ΚΟΙΛΗ 138 1264
26 ΕΙΚΟΣΤΗ ΕΚΤΗ 946 ΚΟΙΛΗ 138 1084
27 ΕΙΚΟΣΤΗ ΕΒΔΟΜΗ 742 ΚΟΙΛΗ 138 880
28 ΕΙΚΟΣΤΗ ΟΓΔΟΗ 768 ΚΟΙΛΗ 138 906
29 ΕΙΚΟΣΤΗ ΕΝΑΤΗ 977 ΚΟΙΛΗ 138 1115
30 ΤΡΙΑΚΟΣΤΗ 1009 ΚΟΙΛΗ 138 1147

The reason why these tables are given in MS Grec 2419 and other texts is due to a particular way of using the Circle of Petosiris that I wasn’t taking into account earlier.  The method I thought would be used—perhaps biased by my first encounter with this sort of technique from the Sphere of Dēmokritos from PGM XII.351—364—would be to take the value of the person’s name and the actual number of the lunar date, sum them together, divide by the number of days in the lunar month, and use the remainder.  Rather, it seems that instead of using the raw number (perhaps as a later development, or as an alternative technique?) one would use the value of the actual name of the lunar date instead, and in most cases (there’s at least one manuscript that doesn’t do this) modified by whether the date was during the waxing or waning moon.  The benefit to using the numbers in the table above, whether of the name itself or the name plus a modifier, has the benefit of making more erratic the results of dividing and taking the remainder in a discontinuous, semi-unpredictable way (1589, 1123, 1019, 1315, …), as compared to the sequential order of the actual numbers of the days of the lunar month (1, 2, 3, 4, …).

That means we have several methods to use now for the Circle of Petosiris, although several of them can be ignored because they confuse adding pure numbers with names of numbers.  In any case, we’d take the same approach: come up with a sum, divide by the number of days in the lunar month, and find the remainder among the zones of the proper Circle of Petosiris:

  1. Add the value of the name of the person to the number of the lunar day.
  2. Add the value of the name of the person to the number of the lunar day plus the number of the day of the week.
  3. Add the value of the name of the person to the number of the lunar day plus the value of the name of the day of the week.
  4. Add the value of the name of the person to the value of the name of the lunar day.
  5. Add the value of the name of the person to the value of the name of the lunar day plus the number of the day of the week.
  6. Add the value of the name of the person to the value of the name of the lunar day plus the value of the name of the day of the week.
  7. Add the value of the name of the person to the value of the name of the lunar day plus a modifier.
  8. Add the value of the name of the person to the value of the name of the lunar day plus a modifier and the number of the day of the week.
  9. Add the value of the name of the person to the value of the name of the lunar day plus a modifier and the value of the name of the day of the week.

The same could likewise be done by comparing the value of the name of the person against the number of the lunar date or the value of the name of the date, after dividing and taking the remainder of each by the number of days in the lunar month, and seeing where each remainder falls to compare them.

This is all well and good, and Neugebauer and Saliba have done some pretty intense work to correlate and investigate all the variations in these weird sums and modifiers found where there are such tables with Circles of Petosiris.  However, in an incredibly disappointing conclusion, they finish their paper by saying that “obviously one should now explain how these numbers were classified into strong, medium, and weak ones…our attempts in this direction did not lead to any convincing result.”  As the mathematician and historian Joel Kalvesmaki says on this specific point, they “solved many important problems but left many more outstanding”.  What we’re likely relying on is a fundamentally old tradition of lucky and unlucky numbers within the context of lunar dates, and it doesn’t seem to be clear to anyone why the Circle of Petosiris or the Sphere of Dēmokritos or other such techniques arrange the numbers the way they do.  Neugebauer and Saliba suggest that “since these numbers represent lunar dates, it is plausible to search for astrological motivations”, although Kalvesmaki makes a good point that such a kind of system of days can have any number of mutually-nonexclusive origins: making observations from experience and experiment, informative myths, zodiacal considerations, and the like.

It seems that, unfortunately, I’m at a dead end with this sort of investigation.  Unless I get access to a wide number of manuscripts dating back some two millennia and somehow pick up classical and medieval Greek, I doubt I can get much further along this line of thinking.  I suppose the only thing left is to experimentation.  One easy way would be to use the comparison method: take the value of my name and compare it to any of the combinations above: the number of the lunar day as reckoned from the Noumēnia in my Grammatēmerologion with or without the number of the day of the week added, or the value of the name of the day according to the table with or without the modifier value with or without the value of the name of the number of the day of the week.  I suppose it wouldn’t be hard to write a simple program to do just that, then keep a running log of how good or bad a given day is.  It’s not as satisfying as discovering some long-lost ancient logic or system, but picking out patterns can be just as sweet once you sift through the salt.

Greek Onomancy: Linking Isopsephy with Stoicheia

For someone who doesn’t much care for numerological and onomantic techniques, I sure have caught some kind of bug on this.  Then again, I suppose it’s helpful to brush up on these methods of exegesis and esoteric analysis of individual words.  I have it on my to-do list to analyze the Ephesian Grammata and other barbarous words within a mathetic framework, and besides pure meditation and contemplation, it helps to have some other guiding principles that can tease out deeper meaning.  Seeing how many of our forebears in philosophy, the occult, and religion used many of these techniques and in many different variations for their worldviews, I suppose there’s something to it.  Still, I can’t help but feel like I’m grasping at something hilariously dumb here, but I could use any tool I can get.

The last two posts have discussed a few methods of Greek numerological divination based on names, isopsephy, pythmenes, and modular division (taking the remainder after division).  With these methods, we know how to determine who will win in a fight, how a conflict may be resolved, and whether one will recover from illness and, if so, how soon.  These methods can be expanded in any number of ways, but I want to take this in a slightly different direction.  For me, although the isopsephy of the letters are important, the stoicheia is even more so (at least at my early stage of study).  It’d be awesome to find a way to tie isopsephy and stoicheia together, and I think I’ve found such a way.  Similar methods exist in the extant literature of Greek numerology from the early first few centuries AD, but I’m combining this with the rest of grammatomancy and a few of my other tricks to expand the system a bit further.

The process is similar to the other onomantic methods we’ve seen before, except instead of using 9 or 30 as our divisor, we use 24, since there are 24 letters in the Greek alphabet:

  1. Find the isopsephic value of a word.
  2. Divide each by 24 and take the remainder.
  3. If the remainder is 0, then we use 24.
  4. The letter corresponding in the Greek alphabet with the value is our letter.

Thus, consider my name, polyphanes (πολυφανης) has an isopsephic value of 1339.  1339 % 24 = 19, and the nineteenth letter of the Greek alphabet is Tau (Τ), associated with Pisces, lending my own name Piscean traits.  If we also include the Greek alphabet oracle into this, we know that Tau is associated with the oracle “You will have a parting from the companions now around you”; this can be an overall message to my life, something I should heed in all matters that can direct me as a fundamental bit of advice.  These two factors combined suggest that I’ll have a bit of a problem holding onto friends for a long period of time, possibly due to constant wandering, possibly due to constant mystery and mysticality surrounding me.

However, we can expand this as well by recalling that there are three groups of stoicheic forces represented by the Greek alphabet: five elements, seven planets, and twelve zodiac signs.  Although taking the remainder by dividing by 24 yields an overall view, an all-encompassing force to which a word or name belongs, we can take the remainder by dividing by 5, 7, and 12 to obtain a specific view for what element, planet, and zodiac sign specifically relates to that word under the overall context of the stoicheion obtained by dividing by 24.  Thus, again, using my own name of polyphanes with its isopsephic value of 1339:

  • Element: 1339 % 5 = 4.  The fourth element is Fire (Χ).
  • Planet: 1339 % 7 = 2.  The second planet is Mercury (Ε).
  • Zodiac: 1339 % 12 = 7.  The seventh zodiac sign is Libra (Μ).

Oddly enough, these are all some of the most important things I value in my work.  What about my actual given name, which is in Greek Σαμουηλ?  The isopsephic value of this word is 749, which yields:

  • Stoicheic: 749 % 24 = 5.  The fifth letter is Epsilon (Ε), whose stoicheia is the planet Mercury and whose oracle is “You desire to see the offspring of righteous marriages”.  Mercury certainly is a dominating force in my life (could you guess?), and one of the recurring messages I keep getting is to stop peering around and start acting on what I can and should be acting upon.
  • Element: 749 % 5 = 4.  The fourth element is Fire (X).  Although I’m more earthy than fiery in my birth chart, I still tend to run hot and dry.
  • Planet: 749 % 7 = 7.  The seventh planet is Saturn (Ω).  A planet that’s oddly and powerfully dignified in my birth chart, and with which I have a fascination and reliance upon after Mercury.
  • Zodiac: 749 % 12 = 5.  The fifth zodiac sign is Leo (Κ).  I have nothing in this sign in my birth chart, and it’s not particularly important, but then, this is all just me throwing things off the top of my head.  Leo is a sign of rulership and renown, and I do tend to end up with that despite my best attempts to avoid it.

Thus, by taking the remainder of a given isopsephic value by dividing by some sacred number, we end up with an association of a given word to an overall stoicheic force as well as specific forces that constitute its parts.  We can analyze a word through these stoicheic connections, determining overall esoteric or expressive meanings to each.

However, we can also use these stoicheic associations to make sacred words that “encode” the forces of a given word.  Combinatorically, it’s no different than just taking the isopsehic value itself; any word that has the same isopsephic value will have the same stoicheic associations.  So, let’s say we have our four letters based on a given isopsephic value of a word: stoicheic, elemental, planetary, and zodiacal.  The stoicheic force is both the end and beginning of the word, since it encapsulates and contains that entire word; we have this letter at the start and end of the word.  The other letters fill in the space between the “bookend” stoicheic letters.  Thus, for πολυφανης, we know that our four letters are Τ, Χ, Ε, and Μ.  If we use our rules for pronouncing generated Greek words from before, we might end up with the word Taukhemyt (Ταυχεμυτ, based on ΤΧΕΜΤ) to represent my name as a mantra or obscuration/occultation that focuses the entire forces of the word together, or that might act as a type of spiritual alias for the name based on its stoicheic forces much as the name of the natal genius functions for one in astrology.  For my given name Σαμουηλ, the corresponding letters are Ε, Χ, Ω, and Κ, and the corresponding word might be Ekhōke (Εχωκε).

This sort of linking between the isopsephy of a word and a given letter of the Greek alphabet, along with its corresponding stoicheia, isn’t too far a stretch of isopsephic and numerological techniques.  Similar techniques have been used in methods of onomancy that derive an astrological birth chart from someone’s name by modular divination by 7 and 12 combined with other numbers, and there are echoes of this in some geomantic techniques I’ve used and seen other use as well.  The written works of Joel Kalvesmaki in the modern day are an incredibly useful resource on how Greek numerology was applied, as well as number symbolism was used and interpreted in the late Roman Republic and early Roman Empire period, and I plan on experimenting with some of these techniques in the future besides straightforward isopsephic comparison.  Who knows?  Maybe my own views on what I’ve perceived as nonsense will change.  It’s happened before with orgone tech, after all.

Greek Onomancy: Determining a Winner with Pythmenes

After the last post on onomancy, I realized that there’s more to Greek letter and number divination involving names than simply determining whether a sick person will live or die.  Plus, there are far more ways to count the letters in a Greek word than straightforward isopsephia, and this time I’ll go over a slightly different method that can be used in a more straightforward fashion than looking things up in a complicated table or circular chart.  This is called the method of pythmenes, or “roots”, and is based more on the numbers 1 through 9 than anything else.  The source text for this is from Hippolytus’ Refutation of All Heresies (book IV, chapter 14), which is a fantastic resource of how everyone did things back in the day that were offensive to early Christian sensibilities, including a good chunk of occult knowledge.

For the system of pythmenes, instead of assigning each letter of the Greek alphabet a number 1 through 9 by ones, 10 through 90 by tens, and 100 through 900 by hundreds, we only assign a single digit value to each letter ignoring magnitude.  Thus, Alpha (1), Iota (10), and Rho (100) all have a pythmenic value of 1, even though their isopsephic values differ.  Here’s a full chart comparing the isopsephic and pythmenic values of the Greek alphabet:

Letter Isopsephy Pythmenes
Α 1 1
Β 2 2
Γ 3 3
Δ 4 4
Ε 5 5
Ζ 7 7
Η 8 8
Θ 9 9
Ι 10 1
Κ 20 2
Λ 30 3
Μ 40 4
Ν 50 5
Ξ 60 6
Ο 70 7
Π 80 8
Ρ 100 1
Σ 200 2
Τ 300 3
Υ 400 4
Φ 500 5
Χ 600 6
Ψ 700 7
Ω 800 8

Or, shown a simpler way based on the pythmenic value:

Pythmenes Letters
1 Α, Ι, Ρ
2 Β, Κ, Σ
3 Γ, Λ, Τ
4 Δ, Μ, Υ
5 Ε, Ν, Φ
6 Ξ, Χ
7 Ζ, Ο, Ψ
8 Η, Π, Ω
9 Θ

Alright, so we have our numbers for our letters.  And yes, note that 6 only has two letters assigned to it and 9 only has one; 6 would also be assigned the letter digamma, and 9 would be assigned qoppa and sampi, but these are all obsolete letters and thus unused in pythmenes.  So, how do we use these values?  Generally, the rule to form a pythmenic value of a name is similar to that of calculating an isopsephic value.  However, there’s a little more complexity involved:

  1. Find the pythmenic value of every letter in the name.
  2. If any letters are duplicated, count the duplicated letter only once.
  3. Add up the pythmenic values of all the remaining letters.
  4. Divide the pythmenic sum by nine and take the remainder.  This is the pythmenic value of the name.
  5. If the remainder is 0, then the pythmenic value of the name is 9.

Now, say you want to compare two people who are, say, in a fight, and you want to know who wins.  Take the pythmenic value of each name and compare them:

  • If one pythmenic value is odd and the other even, the larger number wins.
  • If the pythmenic values are both odd or both even but are different numbers, the smaller number wins.

So, what happens when both numbers are the same?  This is where things get a little hairy, and it all depends, but both can be considered equal in power, yet a winner must result.  Generally speaking, if both pythmenic values are the same and are both odd, then the “lesser” one wins; if both values are the same and are both even, the “greater” one wins.  “Lesser” and “greater” are terms I’m applying to the notion of the challenger (“lesser”) and the challenged (“greater”); the challenger is one who must prove their strength or supremacy, while the challenged is the one who has already proved it.  However, “lesser” and “greater” can also imply other criteria such as age, wealth, standing, or other factors depending on the contest or struggle at hand.  Going by old (and admittedly sexist) number symbolism, odd numbers are perceived as masculine and therefore aggressive (“challenging”), while even numbers are perceived as feminine and therefore passive (“challenged”); thus, if both numbers are the same, they fall in line with whichever side agrees with the value.

So, consider two people fighting each other, and let’s pick the names Hector (Εκτωρ) and Patroclus (Πατροκλος) from Homer’s Iliad to determine who wins the fight.  Hector’s name has the pythmenic value of 5 + 2 + 3 + 8 + 1 = 19 % 9 = 1.  Patroclus has a pythmenic value of 8 + 1 + 3 + 1 + 7 + 2 + 3 + ∅ + 2 (the second Ο is a duplicate, so we don’t count it, thus ∅) = 27 % 9 = 0 → 9 (nine divides evenly into 27, so although the remainder is 0, this is pythmenically equivalent to 9).  Both of these numbers are odd but are not equal to each other; thus, Hector, who has the smaller pythmenic value, wins, and indeed, Hector kills Patroclus in their fight.  However, we know that Achilles (Αχιλλευς) also fights Hector after this; the pythmenic value of Achilles is 1 + 6 + 1 + 3 + ∅ + 5 + 4 + 2 = 22 % 9 = 4.  The pythmenic value of Hector’s name is odd, while that of Achilles is even, and since Achilles’ number is larger, Achilles wins and kills Hector.

Instead of determining the winner of two parties in a fight, this same method can be used to find out whether one will live or die in an illness.  We can see the disease as a struggle between patient and illness, and we can use the pythmenic values of the person’s name as well as of the day letter as we did before with the Sphere of Democritus and the Circle of Petosiris.  In the case of both numbers having the same pythmenic value, we can consider the patient to be the “greater” and the illness the “lesser” or that which challenges the patient.  Of course, sometimes the rules also took into account days of the week or other numbers, which could shed a little more light into the situation.

So, let’s say it’s 200 AD, and my name is actually polyphanes (Πολυφανης), and it’s a few days before the full moon, say the 12th of the lunar month.  I suddenly get a fever and I decide to go to bed, and a healer-magician comes by and runs some tests.  The pythmenic value of my name is 8 + 7 + 3 + 4 + 5 + 1 + 5 + 8 + 2 = 43 % 9 = 7.  The pythmenic value of the day number is 12 % 9 = 3.  Bad news for me; both values are odd but not equal, and the day the disease took hold has the smaller value, so the disease wins and I lose, i.e. die.

What if we take into account the day of the week?  Marking Sunday as day 1 and Saturday as day 7, let’s say that the 12th day of the lunar month happened to fall on a Tuesday, which would have the value of 3.  If we add 3 to the day number 12, we get 3 +12 = 15, and 15 % 9 = 6.  The news isn’t so bad after all; now the date on which I fell ill is an even number, and my name has an odd number which is greater, so I’ll win out in the end after all.

A variant of this technique can be applied to the notion of rematches.  If the conflict between the two sides is the first time they’ve fought, then you use the whole names of both.  If, however, this is their second match, drop the first letter of each name before calculating their pythmenic values; if the third match, drop the first two letters; etc.  This process can be continued as long as there exists at least one letter in one of the names, at which point we might expect that to be the final match between the two parties.

And just to leave you with a bit of fun to toy around with, I should mention that there are plenty of variations to this rule, as there are with many Greek numerological traditions.  Some of them follow:

  • Don’t discount repeated letters.  (It’s possible that an earlier form of pythmenes didn’t discount them, but I prefer doing it.)
  • Discount a letter that is repeated twice and only twice.
  • Discount letters that repeat a pythmenic value, e.g. Ω and Η.
  • Divide the end result by 7 instead of 9 to obtain a remainder.
  • Separate the letters out into three groups (vowels, semivowels, and consonants) and apply the pythmenic winner method above to each group of letters in the two names.  Best of three “rounds” wins overall.

Greek Onomancy: The Sphere of Democritus and the Circle of Petosiris

I don’t consider all systems of divination to be equal.  More specifically, I don’t consider all that is considered to be divination to be actual divination.  Geomancy, Tarot, augury, extispicy, horary astrology, and the like are divination systems to me: the interpretation of omens from physically random, spiritually determined sources by means of inspiration and technique.  This is distinguished from prophecy or clairvoyance, which is sheer revelation of messages or sights from the gods, and it’s likewise distinguished from purely mechanical methods of prediction, such as economic and weather forecasts derived from mathematical formulae alone.  All these things, however, share something in common: revelations about the future.  As a diviner, I find this an extraordinarily useful field of magic and occultism, and one of the things I insist those who are interested in magical practices to investigate first.

However, I don’t rank numerology among useful methods of divination or prediction.  I never have, and I doubt I’ll ever ascribe it the same level of predictive power or flexibility as, say, geomancy, and I put numerological methods of divination in the same category as phrenology, palm reading, and other forms of physiognomy.  Something about the use of fixed factors in divination irks me, especially when it comes to matters of names, number, and the body.  Then again, I consider my natal horoscope in astrology to provide useful information, and I do consider haruspicy to be worthwhile; I suppose some fixed factors can be used in divination, if applied judiciously enough.  Moreover, even if I don’t consider such methods to be the most reliable or trustworthy, I’d appear to be in the minority with that view, considering how much of the old literature dating back to Hellenistic times is devoted to these topics.

One of the most well-known and well-used forms of numerological divination involved the isopsephia, or Greek gematria, of a person’s name in determining their health or lack thereof.  Divination was heavily used as a prognostic tool in medicine up even through the Renaissance and early modern times, sometimes through pre-modern medical means like uromancy, sometimes through astrology, and sometimes through numerology.  One such method of numerological divination using names, sometimes called “onomancy”, involves determining whether a patient will live or die from their illness based on their name and the date on which they fell ill.  Although my resources are scant, mostly coming from some Gutenberg texts and the PGM, let me describe two (or three) ways Greek name divination was used with isopsephy to determine how a given matter would turn out.

A few notes first:

  • When we say “the day on which the person fell ill”, we mean the lunar date starting with the Noumenia.  Thus, if someone fell ill three days after the Noumenia, then the day number of the lunar month would be 4.  If someone fell ill on the last day of the month, i.e. the New Moon, then you’d need to check whether that month had 29 or 30 days.  We note the day that someone fell ill based on when they took to rest; for us modern people, that might be the first morning we just couldn’t get out of bed to go to work or class if we were feeling okay the night before, or the very day we suddenly fell nauseated and went home to rest from the office or school.
  • Obviously, given the advance of modern medicine, people don’t tend to get sick as severely or as fatally as they used to (but who knows, that’ll probably change given the end of useful antibiotics and the rise of superbacteria looming over us).  While it’s possible someone could always die from an illness (gotta love human mortality!), consider the more dire warnings given by these divination methods to be something indicating a chronic, debilitating, or acute disease, while the more mild warnings something comparably mild to endure.
  • In mathematical notation, the percent sign (%) used as an operator indicates the “modulo” operation.  While the division mark (÷) indicates division, the modulo mark indicates the remainder.  So, 28 ÷ 9 = 3.333… or 3 with 1 as a remainder, while 28 % 9 = 1.

The first is the Sphere of Democritus, a prognostic technique from PGM XII.351.  This technique determines whether a sick person will live or die based on their name and the calendar date that they fell sick.  First, calculate the isopsephic value of the person’s name and add to it the day of the lunar month on which they fell sick, took to bed, or called out of work.  Once this sum has been found, divide this sum by 30 and take the remainder.  The text gives a rectangular chart divided into two parts; if the remainder is in the upper part, the person will live, but if in the lower part, the person will die.

fig3-hi

  • They will live if the remainder is 1, 2, 3, 4, 7, 9, 10, 11, 13, 14, 16, 17, 19, 20, 23, 25, 26, or 27.
  • They will die if the remainder is 5, 6, 8, 12, 15, 18, 21, 24, 22, 28, 29, or 30.

So, let’s say it’s 200 AD, and my name is actually polyphanes (Πολυφανης), and it’s a few days before the full moon, say the 12th of the lunar month.  I suddenly get a fever and I decide to go to bed, and a healer-magician comes by and runs some tests.  The isopsephy of my name is 1339, and added to the day number 12, this yields 1351.  1351 % 30 = 1, and we find 1 in the upper portion of the Sphere.  Good news!  I’ll be fine.

The next method is the Circle of Petosiris, which was popular enough back in the day to take several forms.  I found two such methods which are essentially the same to each other and to the Sphere of Democritus, but the level of detail is different.  The idea, however, is the same, at least for the first Circle of Petosiris: take the isopsephic value of the person’s name and add it to the day number of the lunar month on which they fell ill.  However, instead of taking the sum and dividing by 30, here we divide by 29 and find the remainder.  Instead of just determining whether someone will live or die, we get more detail:

fig1-hi

 

  • Great life: 2, 3, 7, 9, 11,
  • Average life: 13, 14, 16, 17, 19, 20
  • Short life: 22, 23, 26, 28,
  • Short death: 1, 25, 27, 29
  • Average death: 4, 10, 15, 18, 21, 24
  • Great death: 5, 6, 8, 12

Let’s say that, once more, I’m sick and instead of calling over the healer-magician from before, I call over a different magician who uses the Circle of Petosiris instead of the Sphere of Democritus. Again, the isopsephy of my name is 1339, and added to the day number 12, this yields 1351.  1351 % 29 = 17, and we find 17 in the “average life” section of the Circle.  Good news!  I’ll live reasonably well once I recover without too much a threat of relapse.

The second Circle of Petosiris is more complicated, however, and involves a slightly different method than the first Circle of Petosiris and the Sphere of Democritus.  Generally speaking, however, the technique used for the first Circle can also be used for the Second, dividing by 30 instead of 29, but with a slightly different arrangement of numbers:

fig2-hi

 

  • Great life (speedy recovery): 11, 10, 9, 7, 3, 2
  • Small life (recovery within seven days): 22, 23, 26, 28
  • Small death (destroyed within seven days): 27, 25, 30, 1
  • Great death (speedy death): 12, 8, 5, 6
  • Brightness (vertical line above horizon): 13, 14, 16, 17, 19, 20
  • Darkness (vertical line below horizon): 4, 15, 18, 21, 24, 29

Another method can be used in this Circle such that one takes the isopsephic remainder of the person’s name divided by 30 and compared against the day number of the lunar month on which they fell ill.  These are then both compared against each other.  If both numbers are in Brightness, the combination promises a good figure; if both in Darkness, an unfortunate one.  If the day number of the lunar month is Bright and the number of the person Dark, then misfortune will occur under the pretense of fortune; if the number of the person is Bright and the day number of the month is Dark, the person will do well eventually though they’ll be in danger.  This method is extended more generally such that if one number or the other or both are above the horizon or below, we can get similar answers, though the Bright and Dark numbers themselves appear to be middling between “great life/death” and “small life/death”.

Once more, I’m sick and instead of calling over the healer-magician from before, I call over a different healer who’s much fancier in his techniques and who uses the this second Circle of Petosiris instead of the other methods. Again, the isopsephy of my name is 1339, and added to the day number 12, this yields 1351.  1351 % 30 = 1, and we find 1 in the “small death” section, where I might die within seven days due to the illness.  However, if we compare the numbers of my name and the number of the lunar date, then we compare 1339 % 30 = 19 against 12; 19 is Bright (above the horizon) and 12 is Dark (below the horizon).  All told, this will be reasonably chancey for me, but I should be able to live and get through this with enough help, though I’ll be in danger of dying all the same.

The “lobes” around the edge of the Circle are, starting at the 9 o’ clock position and going clockwise, indicate both the course of the Sun around the Earth in a single day as well as the four elements:

  1. Midnight (Arctic stars over the earth)
  2. Fire
  3. Sunrise (Rising above the earth)
  4. Air
  5. Noon (Midday over the earth)
  6. Water
  7. Sunset (Setting under the earth)
  8. Earth

The octants on the inner circle say much the same thing, though these are really quadrants, since each pair of octants has the same text.  Much as with the outer lobes, these use astronomical phenomena to describe times of day, though some of them don’t make sense (the Arctic stars only ever stay in the north).  Starting at the upper left quadrant and going clockwise:

  1. Nighttime (Arctic stars over the northern earth)
  2. Daytime (Midday over the northern earth)
  3. Nighttime (Midday under the southern earth)
  4. Daytime (Arctic stars under the southern earth)

Tying the Tetractys to the Qualities of the Numbers

This post is going to be a little winding and wending around several topics we’ve gone over recently about the Tetractys, paths, and the like, so I apologize if it’s not as coherent as the others; this is half-exposition, half-exploration, so I hope you have some caffeine handy.  Not too long ago, I had an idea of analyzing the internumeric/arithmetical relationships of numbers as presented by collections of the Monad, Dyad, Triad, and Tetrad in the Tetractys.  This was combined with a geomancy-influenced approach to analyze specific combinations of these numbers which resulted in a deeper understanding of the principles and qualities of the numbers 0 through 10:

  1. Emptiness
  2. Individuation
  3. Relation
  4. Harmony
  5. Form
  6. Growth
  7. Order
  8. Essence
  9. Mixture
  10. Realization
  11. Wholeness

Each of these has a whole explanation about how they’re arrived at and what they mean on a deeper level, but the one-word name for each works pretty well.  However, we could link pairs of these principles or qualities together, balanced around the number 5.  In a deep sense, both the upper number (less than 5) and lower number (more than 5) reflect the same attribute, with the upper qualities reflecting more of an internal nature and the lower qualities more of an external nature.  Those metaqualities are:

  • 0/10: Being
  • 1/9: Becoming
  • 2/8: Variation
  • 3/7: Accordance
  • 4/6: Structure
  • 5: Growth

The diagram illustrating this from before can serve as a good reminder of how these things are all linked together:

tetractys_decad

In a deep sense, the ten qualities described by the ten numbers of the Monad up through to the Decad can be described in another Tetractys: instead of eleven qualities (Monad through Decad plus Mēden, or Nothing/0), we end up with six metaqualities: Becoming, Variation, Accordance, and Structure, preceded by Being and succeeded by Growth.  However, I personally feel that Being and Growth themselves, as metaqualities, are the same: one cannot be (being) without coming to be (growth), nor can one become (growth) without existing enough to become (being).  So, in reality, we have four qualities assigned, yet again, to the Monad, Dyad, Triad, and Tetrad, with another quality given to the “hidden pentad” which forms the threshold between one iteration of the Tetractys and the next.  In essence, we end up with a fractal of meaning for the Tetractys, with tetractyes within tetractyes, tetractyes all the way down.

Anyway, backing up again to the Decad from the Tetrad, I think I figured out a connection between these qualities and the order of the sphairai established from the Gnosis Schema discussed from before.  In case you’ve already forgotten and don’t like rereading old posts, the Gnosis Schema is a series of 12 paths that lead to every sphaira on the Tetractys, first starting at Mercury, then Air, then Fire, then Sulfur, then down to Earth and back to Mercury, then up to the Monad and back again to Mercury.  It’s like the Lightning Bolt Path on the Tree of Life in qabbalah/kabbalah, although this Gnosis Schema is cyclical instead of linear.  This is in contrast to the Agnosis Schema, the set of twelve paths formed by the hexagon and hexagram in the Tetractys that eternally circle but never connect to Mercury, as well as the extreme sphairai of the Monad, Earth, and Fire.

Looking at the Gnosis Schema, the sphairai can be uniquely numbered in the same order as the paths lead to them, skipping over Mercury as it’s repeated:

  1. Mercury
  2. Air/Jupiter
  3. Fire/Mars
  4. Sulfur/Sun
  5. Salt/Moon
  6. Earth/Saturn
  7. Water/Venus
  8. Light/Fixed Stars
  9. The Monad
  10. Darkness/World

The only annoying thing is that the numbering in this manner isn’t contiguous; you can’t go from 4 to 5 without passing over 1 again.  It’s not ideal, but it’s one possible system all the same, and I make no claim to any of this being ideal or correct right out of the gate of development.

So, here’s a different idea.  Instead of just limiting ourselves to counting the sphairai uniquely, why not count them contiguously?  In other words, on the Gnosis Schema, after we go from Mercury (1) to Air (2) to Fire (3) to Sulfur (4), we go back to Mercury (5) to Salt (6) to Earth (7) to Water (8), then back to Mercury (9) to Light (10) to the Monad (11) to Darkness (12), then return to Mercury (13) to begin another cycle.  Since we like numbers 10 and less, let’s reduce them all by taking the remainder of a number larger than 10 when we divide it by 10.  So, if we have the Monad given the number 11, the remainder of 11 ÷ 10 is 1, the remainder of 13 ÷ 10 is 3, and so forth.  So, when we started out with Mercury at 1 when we began our first pass through the Gnosis Schema, we ended up with Mercury at 13 (3).  If we try it again, we end up with Mercury at 25 (5), and again at 37 (7), again at 49 (9), and the next schema would start it at 61 (1).  It takes five complete passes around the Gnosis Schema for us to return to the same number (or reduced number, which is the same in this line of thinking).

So, if we were to chart out a comparison between the schematic numbering of the spheres compared to the pass number of the spheres, we’d end up with the following chart (ignore the System column for now):

Sphaira Schema Continuous Passes System
Pass 1 Pass 2 Pass 3 Pass 4 Pass 5
Mercury 1 1 13 (3) 25 (5) 37 (7) 49 (9) 1
Air 2 2 14 (4) 26 (6) 38 (8) 50 (10) 2
Fire 3 3 15 (5) 27 (7) 39 (9) 51 (1) 3
Sulfur 4 4 16 (6) 28 (8) 40 (10) 52 (2) 4
Mercury 1 5 17 (7) 29 (9) 41 (1) 53 (3) 1
Salt 5 6 18 (8) 30 (10) 42 (2) 54 (4) 2
Earth 6 7 19 (9) 31 (1) 43 (3) 55 (5) 3
Water 7 8 20 (10) 32 (2) 44 (4) 56 (6) 4
Mercury 1 9 21 (1) 33 (3) 45 (5) 57 (7) 1
Light 8 10 22 (2) 34 (4) 46 (6) 58 (8) 2
The Monad 9 11 (1) 23 (3) 35 (5) 47 (7) 59 (9) 3
Darkness 10 12 (2) 24 (4) 36 (6) 48 (8) 60 (10) 4

Incidentally, as it takes five complete passes around the Tetractys for us to reach the same number we started at, I had suggested earlier that we go through Four Initiations (Hermetic, Hot, Cold, Cosmic) that would collectively focus on each force within its own system, or a tetrad of forces extending from the Mercury sphaira out to one of the outermost sphaira:

  1. Hermetic Initiation
    1. Hot System (Mercury → Air → Fire → Sulfur)
    2. Cold System (Mercury → Salt → Earth → Water)
    3. Cosmic System (Mercury → Light → the Monad → Darkness)
  2. Hot Initiation
    1. Hot System with a focus on Mercury (e.g. a deeper acquaintance of the Hot forces)
    2. Hot System with a focus on Air (e.g. seeing Air and how it relates and acts throughout the Hot forces)
    3. Hot System with a focus on Fire (e.g. same as above but with Fire)
    4. Hot System with a focus on Sulfur (e.g. etc.)
  3. Cold Initiation
    1. Cold System with a focus on Mercury
    2. Cold System with a focus on Salt
    3. Cold System with a focus on Earth
    4. Cold System with a focus on Water
  4. Cosmic Initiation
    1. Cosmic System with a focus on Mercury
    2. Cosmic System with a focus on Light
    3. Cosmic System with a focus on the Monad
    4. Cosmic System with a focus on Darkness

In other words, the Hermetic Initiation would be one whole pass through the Tetractys (12 sphairai).  The Hot Initiation would cycle through the first third of the Gnosis Schema four times (4 sphairai × 4 = 16 sphairai, 12 + 16 = 28); the Cold Initiation would cycle through the second third of the Gnosis Schema four times (another 16, so 28 + 16 = 44); the Cosmic Initiation would cycle through the last third of the Gnosis Schema four times (another 16, so 44 + 16 = 60).  All told, we’d hit sixty sphairai before returning ultimately to the Mercury sphaira at 61, itself reduced to 1.

However, notice that as we’re undergoing the Hot, Cold, and Cosmic Initiations, we’re simply looping around four of the sphairai four times, always starting at and passing through Mercury before going to the next set of initiations.  We can assign the numbers 1 through 4 to each of the spheres within each system, which is what the System column in the table above shows.  And, if we can assign certain groups of sphairai to a certain number, then we can see what comparisons and qualities come out of that analysis:

  1. Mercury
  2. Air, Salt, Light
  3. Fire, Earth, the Monad
  4. Sulfur, Water, Darkness

It’s interesting to note that, although Mercury is central to the Gnosis Schema and the Tetractys generally, it forms its own group, always in the worlds but never of the worlds; this, to me, only reinforces its liminal nature as both abyss/boundary and bridge/transformation even more.  The second and fourth groups should look similar to us: they’re the paths we’ve assigned to the letters associated with Air, based on planetary, elemental, or zodiacal symbolism.  The Dyadic systemic group is connected by Air, Jupiter, and Spirit; the Tetradic systemic group is connected by the zodiacal signs of Libra, Aquarius, and Gemini.  Since the Dyad is more about relation/mixture (which speaks to me more strongly of the fixed stars and the zodiac signs) and the Tetrad more about form/structure (more about discrete forces that constitute bodies and action), I question now whether I should swap these associations so that that the Dyadic system is given to the signs of the Zodiac and the Tetradic systemic group is given the forces.

The Triad systemic group, however, is composed of the three outermost and extreme sphairai of the Monad, Earth, and Fire.  They cannot be connected to each other without going through either Dyadic or Tetradic systemic sphairai, nor can they be connected to central Mercury.  However, the Triad is based on harmony and essence, and if nothing else, these three sphairai represent the ultimate foundations (in their own ways) of the cosmos: pure active manifesting force (Fire), pure passive manifested matter (Earth), and the Source of everything and everything in between (the Monad).

Anyway, all this is getting away from the main point I wanted to make: is there a way to link the ten sphairai of the Tetractys with the qualities of the Decad?  Well, the straightforward way would be to associate the ten qualities with the ten sphairai as we numbered them uniquely based on the Gnosis Schema:

  1. Mercury — Individuation
  2. Air/Jupiter — Relation
  3. Fire/Mars — Harmony (??)
  4. Sulfur/Sun — Form (?)
  5. Salt/Moon — Growth (???)
  6. Earth/Saturn — Order
  7. Water/Venus — Essence
  8. Light/Fixed Stars — Mixture (?)
  9. The Monad — Realization
  10. Darkness/World — Wholeness

Some of these make sense, and some really don’t.  I mean, what really catches my eye that sets me off is the association with the Pentad (Growth) with the sphaira of Salt.  I mean, sure, in its astrological sense of the Moon, this sphaira can reflect the notion of growth as much as it would atrophy, increase as well as decrease.  However, the alchemical notion of Salt is not what I’d consider resonant with growth; on its own, Salt is fixed, stable, and dead.  Without either Sulfur to cause change or Mercury to receive it within the vehicle of Salt, growth is simply a moot point.  Then again, without the body provided by Salt, growth can’t happen, either; growth can only happen after a body is present.  And, as our Tetractyean studies indicate, growth (Pentad) can only arise in things with bodies made from the four elements (Tetrad).  So maybe this does make sense.  Maybe the other sphairai with question marks have similar occult reasons as to why they can correspond to the quality of their numbers, but it requires some thought.

Another way to consider the qualities as related to the sphairai is not the “essential quality” of the sphairai (based on their unique schematic numbering), but based on the number we arrive at a sphaira based on the passes through the Tetractys using the Gnosis Schema.  For instance, on our first pass through, Mercury is sphaira #1 and thus associated with Individuation; on the second pass, it’s #3 and associated with Harmony; on the third, it’s #5 and associated with Growth, and so forth.  After five passes, we start over again.  Note how the sphairai of Mercury, Fire, Earth, and the Monad (the Monadic and Triadic systemic sphairai) only ever receive odd (active) numbers in this method, while the middling sphairai (the Dyadic and Tetradic systemic sphairai) only ever receive even (passive) numbers.  This system is much more complicated than the straightforward one we just discussed, but it also reflects a system of constant evolution and development that requires several passes through the Tetractys in order to fully grasp the entirety of each sphaira, both in terms of its alchemical/planetary force as well as its numerological qualities.  I might contrast this with the preceding method as how a planet in astrology has both essential dignity (determined solely by its degree in the Zodiac) and accidental dignity (what else is going on around the planet relative to itself).

Well, if we were to use the essential qualities of the sphairai, we also know that we can combine pairs of the qualities into metaqualities that subsume them, like how Relation and Mixture are both aspects of Variation.  In that sense, we can combine pairs of the sphairai as below:

  • 1/9: Mercury/The Monad — Becoming
  • 2/8: Air/Light — Variation
  • 3/7: Fire/Water — Accordance
  • 4/6: Sulfur/Earth — Structure
  • 5: Salt — Growth
  • 10: Darkness — Being

Thus we have four pairs of sphairai and two sphairai left over.  Coincidentally, these leftover ones have the qualities of Growth (Pentad) and Being (Decad), and I mentioned above that I feel like these two numbers (with Mēden/Nothing as 0) could be paired together as well as one metaquality, say “Reality”.  Of the other four pairs, only one pair has a path between themselves (Air and Light); as both these sphairai fall under the banner of Variation, it could indicate that it is by means of Air (which gives sense to sound, distance, and sight) and Light (by which we see, are seen, and Work) that such variation can be reckoned and worked with.  The other three pairs (Mercury and the Monad, Fire and Water, Sulfur and Earth) lack such a path.  Moreover, these three pairs lack a path in different ways:

  • There’s a clear space for a connection between Mercury and the Monad, but this connects the central sphaira with one of the outermost, which is not allowed.  However, the geometry of this path would mimic that between Darkness/Water and that between Light/Air.  I interpret this to indicate that although the motion needed is possible to make for this path (geometry exists elsewhere), the “distance” to the Monad from Mercury is too far to make.  They’re both Becoming, but at such different stages; one is conception, the other manifestation.
  • Fire and Water are on the same rank of the Tetractys (within the Tetrad), but are separated from each other by the sphaira of Air between them.  No direct connection can be made; either one goes directly through Air, or rises to and falls from Sulfur to get to the other.  Both these forces represent the metaquality of Accordance, and thus need something else to accord with, since these two forces are diametrically opposed to each other.
  • There’s a clear space for a connection between Sulfur and Earth, but this would connect one of the outermost sphaira with one of the middling ones on the far side of the Tetractys.  No other path like this exists, and the disparity between the two is great enough to be geometrically disallowed.  This indicates that, although they both represent Structure, they represent them in two completely different and unrelated ways, an internal, dynamic, and spiritual way (Sulfur) and an external, static, and material way (Earth).  I’d compare these two things to the cardiovascular system and the skeletal system; both are needed to organize and arrange the human body just so, although the former is fluid and quick while the latter is fixed and solid.

alchemical_planetary_tetractys_paths

While I’m not sure how far to take this analysis of numerological qualities/metaqualities and the sphairai on the Tetractys, it does offer me more food for thought as I explore them and the paths that connect them more.  Besides, these give me interesting ways to think about the sphairai on the Tetractys; it’s not inconceivable that these qualities can be used as names for the sphairai themselves, much as the qualities of God are used as names for the sephiroth on the Tree of Life; instead of Victory, we have Essence (or, in Greek, Ουσια).  Alternatively, they could just be called by their force (Water, Υδωρ) or their systemic number (Heptas, Επτας).  While this post seems, in retrospect, to be more mental exercises in analysis rather than digging out occult secrets, there’s still plenty here to chew on as I contemplate and delve deeper into this system-in-development.

Geomantic Revelations of the Tetractys

The last post on the arithmetic subtleties of the Tetractys got me to thinking.  If I have four rows of things I can select or not select for a collection, I end up with so many results.  The overall number of distinct results, of course, is 10 (Monad through the Decad), but I thought a bit deeper about it.  I mean, I disregarded multiple ways of adding up to a given number before, and what if I took all those into account?  After I did the math, I realized there are 16 ways to add different selections of the ranks of the Tetractys together to get a certain sum.  Four rows, 16 results.  Sound familiar?  Yup.  I accidentally found a way to link the Tetractys to the 16 figures of geomancy.  Before reading, I suggest you brush up on the terms of geomantic operation, specifically for what inversion and reversion is.  Besides, it’s been a while since I mentioned anything substantial about geomancy, so this is an interesting confluence of studies for me.

Whether geomancy has ever been thought about in terms of the Tetractys, I can’t say, though I personally doubt it, but consider the following analysis.  First, let’s assign the four elements of Fire, Air, Water and Earth to the four ranks of the Tetractys:

  • Monad: Fire
  • Dyad: Air
  • Triad: Water
  • Tetrad: Earth

This isn’t that much a stretch.  Yes, the elements properly belong to the Tetrad as a whole, but we also can think of the four elements as numbers in their own right.  We know that Fire is the most subtle and Earth the least, and that Fire is the least dense and Earth the most.  Similarly, the Monad is the most subtle and least concrete number, while the Tetrad is the most concrete and least subtle.  We can assign the four elements accordingly to the four numbers of the Tetractys with agreeable ease.

If we allow for all possible combinations of these four numbers to be either present or absent in a sum, then we get sixteen different results, just how we get sixteen different geomantic figures by allowing for all four elements to be either present or absent.  The list of all the possible ways to add the ranks of the Tetractys are:

  1. None (0): Populus (None)
  2. Monad alone (1): Laetitia (Fire alone)
  3. Dyad alone (2): Rubeus (Air alone)
  4. Monad + Dyad (3): Fortuna Minor (Fire + Air)
  5. Triad alone (3): Albus (Water alone)
  6. Monad + Triad (4): Amissio (Fire + Water)
  7. Dyad + Triad (5): Coniunctio (Air + Water)
  8. Monad + Dyad + Triad (6): Cauda Draconis (Fire + Air + Water)
  9. Tetrad alone (4): Tristitia (Earth alone)
  10. Monad + Tetrad (5): Carcer (Fire + Earth)
  11. Dyad + Tetrad (6): Acquisitio (Air + Earth)
  12. Monad + Dyad + Tetrad (7): Puer (Fire + Air + Earth)
  13. Triad + Tetrad (7): Fortuna Maior (Water + Earth)
  14. Monad + Triad + Tetrad (8): Puella (Fire + Water + Earth)
  15. Dyad + Triad + Tetrad (9): Caput Draconis (Air + Water + Earth)
  16. Monad + Dyad + Triad + Tetrad (10): Via (Fire + Air + Water + Earth)

Note that the numbers 3, 4, 5, 6, and 7 have two ways each to add up to them.  In the last post, we only discussed one each, the formulas that use the basic Monad/Dyad/Triad/Tetrad set, but it’s possible and equivalent to say that 6 is both a combination of Dyad and Tetrad as it is with Monad and Pentad.  The numbers 0, 1, 2, 8, 9, and 10, however, each only have one way to add up to them.  Thus, the numbers that have two ways have two possible figures, and the numbers with only one have one figure.  In this way, we can assign geomantic figures to different collections of the ranks of the Tetractys, but what might this mean?  For numbers that can be added to in two ways (3, 4, 5, 6), we have two figures each.  We’ll call those figures “manifesting” that have more rarefied numbers (such as Puer, which is Monad + Dyad + Tetrad), and “manifested” those that have more concrete numbers (such as Fortuna Maior, which is Triad + Tetrad).  As it turns out, we end up with mobile figures becoming manifesting and stable figures becoming manifested.  Thus, we end up with a chart like the following:

 Sum Manifesting Manifested
0 Populus
1 Laetitia
2 Rubeus
3 Fortuna Minor Albus
4 Amissio Tristitia
5 Coniunctio Carcer
6 Cauda Draconis Acquisitio
7 Puer Fortuna Maior
8 Puella
9 Caput Draconis
10 Via

Going from top to bottom, we see that there are important patterns present in the chart.  Figures for 0 and 10 (Populus and Via) are inverses of each other, as are 1/9 and 2/8.  The manifesting 3 and manifested 7 figures are also inverses, as are manifested 3 and manifested 7, and so forth.  Coniunctio and Carcer are both italicized, since they’re both equally manifesting and manifested and it’s hard to tell which is which, especially since they’re both equally added to by 5 and are in the middle of the list.  We see that the greater the sum, the more “dense” and active the figure becomes, and we get more stable the further down we go (with one exception we’ll get to later).  As might be expected from Iamblichus, the number 5 is the pivot and balance for all the other numbers, and accordingly the manifested and manifesting properties of this number are in agreeable and balanced growth.  We can also note that the “extreme” (0, 10) and median figures (5) are what we’d also call “liminal”; figures that are the same when they’re reversed.  We have this constant shifting balance throughout the structure of this Tetractyan geomancy that keeps popping up, so that’s cool.

If we use our keywords from our prior discussion of the nature of the numbers from 1 through 10, we can attribute them to the geomantic figures:

  1. Individuation: Laetitia
  2. Relation: Rubeus
  3. Harmony: Fortuna Minor (manifesting), Albus (manifested)
  4. Form: Amissio (manifesting), Tristitia (manifested)
  5. Growth: Coniunctio and Carcer (both manifesting and manifested)
  6. Order: Cauda Draconis (manifesting), Acquisitio (manifested)
  7. Essence: Puer (manifesting), Fortuna Maior (manifested)
  8. Mixture: Puella
  9. Realization: Caput Draconis
  10. Wholeness: Via

In this sense, the terms “manifesting” and “manifested” become a little clearer.  Figures that are manifesting bring that quality into existence, while figures that are manifested represent that quality already in existence.  It’s the difference between “becoming/causing” and “existing/evidencing”.  Thus, Fortuna Minor is manifesting harmony, since it requires one to work with others, indicating that one’s own power is not enough to carry the day; other interaction is required.  On the other hand, Albus is manifested harmony, maintaining equanimity and reflection unto itself, self-sufficient and uninvolved with anything else that might disturb it.  Similar cases can be drawn up for the other sums, so it’s interesting to see how geomancy can reflect these numerological concepts in its own logic.

What about the numbers for which there’s only one figure?  The figures of 0, 1, and 2 are the inverses of the figures of 10, 9, and 8, respectively, and if we keep our mobile/manifesting and stable/manifested idea, then 0, 8, and 9 are manifested qualities while 1, 2, and 10 are manifesting.  It seems odd that Populus should be among the mobile/manifesting figures and Via among the stable/manifested, but the swap here makes sense in a cyclical way; after all, with either absolutely nothing or absolutely everything present, we end up able to repeat the whole process, since if everything is all one Thing, one can no longer draw a difference since there’s nothing different (hooray, paradoxes).  So, Individuation and Realization are manifesting and manifested qualities of a metaquality “Becoming”; Relation and Mixture of “Variation”; and…hm.  We have Wholeness as the quality for 10, but what about 0?

What’s probably most bizarre about this interpretation, at least in a strictly Pythagorean sense, is the “sum” of Populus being 0.  Zero was not considered to be a true number by the ancient Greeks, or really by anyone in the Western world, up through the medieval age when Arabic and Indian mathematics started becoming popular to study.  After all, they might ask, “how can nothing be something?”  Besides, with the Tetractys itself, all things are based on the Monad.  The Monad defines and begins all things on the Tetractys and existence itself, yet it itself cannot come from nothing, for it never came or became at all.  We haven’t encountered the notion of “nothingness” before in our mathetic studies, so what might it represent?  Honestly, I’d consider it to represent Emptiness in the Buddhist sense where all things are interconnected and rely upon each other.  It’s not quite Relation or Harmony or any of the other things, but it would be closest to Wholeness; after all, Matter must exist within Space, and all of Matter exists within all other Matter, always influencing and influenced by itself.  It’s weird, though, but think of it like this.  In all things, Populus must exist as the template for all other things, the ideal form that even the Monad itself represents as itself.  Without Populus, we’d have no geomantic figure, just as the Good itself cannot exist apart from Goodness.  Even Wholeness must reside within the form of Emptiness, just like how Populus must be present (even if “hidden” or implied) in every geomantic chart.  So, if Wholeness is the Decad, then Emptiness is the Mēden (Μηδεν), or “Nothing”.  But both, in an obscure sense, are the same.

Focusing more on the qualities of the numbers themselves, we can further pair them up into different groups based on how the geomantic figures there are inverses of each other.  In other words, if two numbers add up to 10 (0 + 10, 1 + 9, etc.), they form a pair:

  • Individuation/Realization (1 + 9 = 10)
  • Relation/Mixture (2 + 8 = 10)
  • Harmony/Essence (3 + 7 = 10)
  • Form/Order (4 + 6 = 10)
  • Emptiness/Wholeness (0 + 10 = 10)
  • Growth (5 + 5 = 10)

These qualities, though paired up to indicate something like an opposition or dichotomy, doesn’t seem to indicate anything of the sort, but rather two interconnected concepts that cannot be separated from each other.  After all, in order for one to become One, something whole and complete in and of itself, it must go through a process of becoming and enforming to become real (Individuation and Realization, 1/9).  In order for different things to relate, oppose, agree, or move with each other, they must be put together and combined (Relation and Mixture, 2/8).  In order for different things to agree, combine, and merge together, they must share certain qualities and be germane to each other (Harmony and Essence, 3/7).  In order for things to possess form, body, and dimension, they must have a structure and consistency that allows them to maintain it (Form and Order, 4/6).  In order for something to exist, it must exist because of something else, or it must allow for itself to be filled with creation (Emptiness and Wholeness, 0/10).  Growth…well, growth expands in all ways, in all dimensions, and itself provides a balance that nurtures and metes out all other qualities (Growth and Growth, 5/5).

So, we have five pairs of qualities of the numbers, and one single quality that forms its own pair.  What might we call these metaqualities?

  • Becoming: Individuation/Realization
  • Variation: Relation/Mixture
  • Accordance: Harmony/Essence
  • Structure: Form/Order
  • Being: Emptiness/Wholeness
  • Growth

These are terms I just pulled off the top of my head, so I don’t expect them to stay permanent terms, but they do tend to fit.  Individuation and Realization are both qualities that are required for anything to become One Thing or one thing.  Relation and Mixture are both required for anything to be different or have difference among others, to either vary or be a variation.  Harmony and Essence are both required for anything to agree with or find similarities with in an accordance.  Form and Order are both required for anything to have a body or to form a body in a coherent structure.  Emptiness and Wholeness are both required for anything to exist, either on its own as a Whole or as part of a Whole filled by it.  Growth can apply to any and all of these things, and mediate between any two qualities that form part of a metaquality pair.  In a way, the metaqualities form their own Tetractys, with Becoming related to the Monad, Variation to the Dyad, Accordance to the Triad, and Structure to the Tetrad.  Growth, as a balance, forms part of the “hidden” Pentad underlying the Tetractys, and the four metaqualities again form another “inverted Tetractys” under it.  Thus, the “upper Tetractys” is composed of Individuation, Relation, Harmony, and Form; the “lower Tetractys” is composed of Realization, Mixture, Essence, and Order.  Growth mediates between the two as the “hidden Pentad”; Emptiness and Wholeness are at once present at all points throughout this dual Tetractys figure.

tetractys_decad

While my Tetractys research is still new to me, geomancy is not, and being able to understand more of the Tetractys with symbols and terms I’m already familiar with is a huge help to me.  Like I said, I don’t know whether this type of analysis has ever been attempted before, but it’s certainly something that I plan on continuing.  Geomancy, after all, is a binary system based on the number four, and within four is 10 and thus all other numbers.  Perhaps the two were meant to be wedded all along.

Internumeric Relationships by Addition on the Tetractys

It’d be rude and vulgar of me to leave the Tetractys as some simple geometric diagram used for plotting paths or meditations.  I mean, the Tetractys is a meditation tool, yes, but to use it merely for working with the Greek alphabet with in a mathetic framework is to ignore the deeper meaning of the Tetractys.  For the Pythagoreans, especially, the Tetractys was more than a set of ten dots; it was the key to all creation and all cosmos.  There’s no evidence that anybody’s used it to plot paths on like I did, which is probably because this is an innovative use for an already heavily used tool based purely on number.  As we’re all aware by now, the Tetractys is a representation of the Monad, Dyad, Triad, and Tetrad to yield the Decad: 1 + 2 + 3 + 4 = 10.  All these numbers are holy to the Pythagoreans and to Western occultists generally, but there’s so much more to the Tetractys than this.

One of the traditional ways of understanding the mysteries of the Tetractys was to take the different ranks of numbers present and add them together to yield a particular number.  For instance, the Monad plus Tetrad yields the Pentad (1 + 4 = 5), while the Monad, Dyad, and Triad together yield the Hexad (1 + 2 + 3 = 6).  All these numbers have their own meaning, all of which are based ultimately on the Monad and, in succession, the meanings given to the other numbers built upon the Monad.  I’d thought I’d investigate what some of these properties are and see what the Tetractys represents in building the numbers of the Decad together based on these relationships between the ranks of the Tetractys.  Specifically, these relationships are based on the arithmetical operation of addition, the straightforward aggregation of two numbers by combining their distinct magnitudes into a single one.  Other operations exist, but those are for another time.

So, to start off with, we have four basic numbers, starting with the Monad and ending with the Tetrad.  We can say that, with the exception of the Monad, all numbers are just collections of Monads in a particular relationship:

  1. Monad = individuation, undifferentiated, undifferentiatable
  2. Dyad = two Monads in relation
  3. Triad = three Monads in harmony
  4. Tetrad = four Monads in form

Note that some of these can be broken down further into simpler groups.  Without repeating any particular number (such as saying that the Dyad is two Monads or the Tetrad is two Dyads), we end up with two extra identities:

  1. Triad = Monad + Dyad
  2. Tetrad = Monad + Triad

It’s crucially important to note that the Dyad, Triad, and Tetrad are more than just a collection of monads.  Number in the esoteric sense is more than just a magnitude or amount, but also a relationship formed between the individuals in the collection.  The only number in this set that has no relationship is the Monad itself, since it exists as a unity unto itself without anything to relate to.  The Dyad is the first number that has a relationship, but can be said to be relationship itself; without the Dyad, relationship cannot exist.  In a more arithmetic sense that the Pythagoreans preferred, all numbers can be divided into two partially overlapping groups of odd (able to be divided into unequal parts only) and even (able to be divided into two equal and unequal parts).  Four, for instance, is even because it can be split up into groups of 1/3 and 2/2.  Five, however, is odd, because it can be split into 1/4 or 2/3, and neither of those are equal splits.  However, the Monad cannot be split at all into anything, and the Dyad can not be split into unequal parts, so neither the Monad nor Dyad are even nor odd, and are thus not true number, though they are sources of number.

Thus, based on the individuation of the Monad and relation of the Dyad, all other numbers can be made, such as the Triad.  It is because of this that the Triad is considered by the Pythagoreans to be the first true number, since the Monad and Dyad are something rarer and rawer.  All amounts can be formed from the Monad, but it’s the relationship (Dyad) between individual Monads that produce a number.  Thus, as the Triad is the first true number, it is also the first odd number, and the Tetrad is the first even number.

So, based on the six above identities, we can form the rest of the numbers from the Pentad (5) to the Decad (10).  If we omit the identities from above and reduce all things to a collection of Monads, Dyads, Triads, and Tetrads, we end up with two ways to form the Pentad, and one way each to form the Hexad, Heptad, Octad, Ennead, and Decad:

  1. Pentad = (Monad + Tetrad) or (Dyad + Triad)
  2. Hexad = Dyad + Tetrad
  3. Heptad = Triad + Tetrad
  4. Octad = Monad + Triad + Tetrad
  5. Ennead = Dyad + Triad + Tetrad
  6. Decad = Monad + Dyad + Triad + Tetrad

Yes, this is all basic arithmetic that we’ve been able to do since kindergarten.  Of course, it’s always the simplest things that hide some of the more profound secrets.  I won’t go over all the associations and theologies behind the numbers for that; you can get a copy of the Theology of Arithmetic by Iamblichus for cheap (or even, dare I say it, for free), and you can read about what the Pythagoreans thought about the numbers of the Decad way back when.  What I want to point out is, at a high level, what these additions of the numbers mean based on the four concepts of monadic individuation, dyadic relation, triadic harmony, and tetradic form.

Monad
The Monad is an individual, unchanging, static, and stable.  It is the only thing that exists, and thus cannot be differentiated from anything (since there’s nothing to differentiate it from).  While we can say that it contains all opposites and extremities within itself, it’d be more proper to say that no concept of opposition or extremity exists within the Monad.  While the Monad exists, nothing exists within the Monad; it can become all and any qualities, but it itself has no qualities.  It is the source of all nature, but is itself beyond nature.  It cannot be divided since it is a unit, an atom, the core of existence itself.  The Monad cannot move, as there is nothing within which it can move (which would imply something that is Monad and something that is not-Monad).  The Monad has no shape, consisting only of a single point that indicates both all sizes and all angles but without anything else to connect to.

Dyad
The Dyad is relation and difference.  Between two Monads, we now know of two things that can be compared as equals, but as different equals.  The Dyad is representative of differentiation, distinction, opposition, and motion, all of which can be thought of as different types of relation.  The Dyad represents a line defined by two points, but is still without shape; it can possess direction and magnitude, but is as yet without definition.  The Dyad allows for things to exist within, around, and outside of other things, since it creates space between and among other things.  While the Monad is pure potential for creation (and all other things), the Dyad is the act of creation itself, since it distinguishes a Creator from the Creature, or the Acted from the Actor.  The Dyad is space, change, action, and relativity.

Triad
The Triad is harmony and proportion, formed from a combination of individuation and relation.  It is the first odd number, and the first number that can be added from other distinct numbers.  The Triad gives the first shape of something, as three points can define an enclosed space.  The Triad indicates actuality, the Creature made through Creation (Dyad) from the Creator (Monad).  However, it is also indicates harmony, since two distinct and different things are linked to and joined by a third.  With the Triad, there is real existence as opposed to potential existence or becoming existence.  Quoth Iamblichus, “‘this’ belongs to the Monad, ‘either’ to the Dyad, and ‘each’/’every’ to the Triad”.  With Triad, there is time: beginning, middle, end; there is communication: speaker, listener, message; there is work: actor, action, acted upon. However, like the Monad, the Triad is static, since it provides for space and size but not change, since it is construction and creation that brought a static shape to being.

Tetrad
The Tetrad is the root of form, formed from a combination of individuation and harmony.  With three points we can define a two-dimensional shape, but with four we can define a solid three-dimensional object.  Moreover, the Tetrad is dynamic, since it is even; while the Triad measures static quantity, the Tetrad measures dynamic quantity, since it provides for motion and change while the Tetrad does not.  Further, the Tetrad allows for forms present in relationship to each other; while the Triad offers a two-dimensional form, the Tetrad allows for two-dimensional forms next to each other as the Dyad allows for Monads to be next to each other.  With both individuation and harmony, one can choose to be part of a harmony or break away from it, acting either inside or outside a given group, and allows for distinct existence apart from, aggregated with, or in conjunction with others.

Pentad
Alone among the numbers, the Pentad is the only one that can be formed in two distinct ways: from the Monad and Tetrad (a combination of individuation and form) and from the Dyad and Triad (a combination of relation and harmony).  In a way, it’s fitting; between all the numbers of the Decad, the Pentad is the middle of them.  Consider that any two numbers that add up to 10 have 5 as the mean (9 + 1, 8 + 2, 7 + 3, etc.); the Pentad is halfway to the Decad, and itself is vital to life.  It is the combination of pure potential and discrete aggregation (Monad and Tetrad), as well as of relation and harmony (Dyad and Triad); it is the combination of an even and odd number in either case, and considered to unify opposites in a dynamic way that allows for growth and change as opposed to the static way of the Triad.  If we consider the Pentad as the sum of Monad and Tetrad, we obtain a view of eternality and potentiality combined with and suspended among temporality and discretion (the four changeable elements acting under unchanging Spirit); if we consider the Pentad as the sum of Dyad and Triad, we obtain a view of motion and action mixed with and changing stasis and relationship.  In either case, the Pentad is where life and concrete reality itself begins, since in the Pentad there is balance, reciprocity, distribution, and especially of growth.

Hexad
The Hexad is the combination of relation and form, producing a dynamic harmony.  Unlike the Pentad, which is dynamic growth, the Hexad is a balance between things in motion.  The presence of distinct qualities bestowed by the Tetrad in relation of the Dyad allows for various dynamic forces to exist dynamically, moving with and acting, co-acting, or reacting together without destruction.  As the Tetrad represents a body and the Dyad represents motion, the Hexad represents a body in motion and can move in six ways, or three sets of two ways: up/down, left/right, forward/backward.  Seen the other way, as the Tetrad represents qualities and the Dyad represents opposition, the Hexad represents an ordering and balance of opposites.  Further, as two Tetrads, the Hexad represents what we commonly see as “Merkava stones”, two interlocked tetrahedrons that represent a combination of bodies and opposites that together unite to form a whole.  While the Pentad is the number of life, the Hexad is the number of order.

Heptad
The Heptad is the combination of harmony and form, producing foundation.  This is hard to describe in a single word, but within the Heptad there are all things finally present to create everything, yet is short of actively creating everything; all manifest sources are present in the Heptad (seven planets of astrology, seven vowels of Greek speech, etc.), though they are as yet too unmanifest on their own.  As a combination of Triad and Tetrad, the Heptad represents the four elements and three reagents, or the three processes that transform the four elements so as to create all things.  As an odd number that cannot be divided, the Heptad is similar to the Monad in that it provides for potential creation, but unlike the Monad, the Heptad is a collection of seven entities that provide the foundation of all manifest things, while the Monad is an undifferentiatable source from which all manifest and unmanifest things come.  If the Hexad represents order, then the Heptad are the things that are ordered within the cosmos provided for by the Hexad, the meat to fill out the Hexad’s bones.  The Heptad is that which essentially exists; the Heptad is essence.

Octad
The Octad is the first addition that involves three numbers: the Monad, Triad, and Tetrad.  Thus, the Octad combines individuation, harmony, and form.  As the Heptad is the combination of the Triad and Tetrad, we can say that the Octad is that which results from the essences of creation into which they flow.  However, as we saw with the Pentad, we can also say that the Monad and Heptad combine such that the Heptad is mixed in within the Monad, as the seven planets are within the eighth sphere of the fixed stars, as the four elements are within the Quintessence.  However, we can also say that the Octad is the combination of two Tetrads, allowing for mixtures and combinations of that which otherwise could only relate to each other by processes; although Sulfur combines and transforms Air into Fire and vice versa if we use the Tetrad + Triad view, we end up with dry air or cool fire between Air and Fire if we use the Tetrad + Tetrad view.  The Octad represents solution and combination of qualities, a single entity produced from essences or qualities and their interquality transformations.  The Octad is mixture.

Ennead
The Ennead is the combination of relation, harmony, and form.  Based on how we might conceive of this, we can say that the Ennead combines the Tetrad and Pentad, the Triad and Hexad, the Dyad and Heptad, or the Monad and Octad, but at its root it combines the Dyad, Triad, and Tetrad.  At its core, it lacks the Monad and possesses the Dyad, indicating that the Ennead is an active number related to creating but not as creator or creature.  In the Ennead is all creating of manifest things, combining tetradic body, triadic intermediation, and dyadic motion.  In the number nine are all the other numbers brought together, the final single-digit whole number.  As there were nine Muses who lead to all Art and nine Curetes who watched over the infant Zeus, the Ennead brings things to completion and perfection without itself being perfect.  The Ennead is realization.

Decad
At long last, we finally reach the Decad, the combination of the Monad, Dyad, Triad, and Tetrad; of individuation, relation, harmony, and form.  In the Decad are all the basic numbers of the Tetractys, and there are many ways to add to the Decad using the lesser numbers, but at its core it is the number formed from 1, 2, 3, and 4 summed together.  Just as in the Ennead there is the process of realization and completion but without something to realize or complete, the Decad augments this with the Monad, allowing for something to be filled with the Ennead.  The Decad represents a discrete entity (Monad) that is distinct from other things (Dyad) that is stable unto itself (Triad) given physical a body (Tetrad).  Moreover, it is also something that can grow (Pentad) while maintaining itself in an order (Hexad) that combines all ethereal essences (Heptad) and concrete mixtures (Octad) being brought together (Ennead).  Without any other number preceding it, the entity represented by the Decad would be lacking and could not be fully realized.  Whether it is the universe we live in or the individual people we live as, we are all representative of the Decad and the journey it has taken to get here.  The Decad is the Whole.

I think it goes without saying that this Pythagorean analysis of the ten numbers of the Decad can easily be mapped onto the Tree of Life in Jewish kabbalah or Hermetic qabbalah, and indeed, I recall seeing many of these things present in the explanations given in works like Alan Moore’s Promethea series.  It makes sense, too, since Pythagoreanism is one of the fundamental philosophies underlying Western occult thought, deep enough to not clearly be distinguished as Pythagorean but also profound enough to affect everything that’s built upon it.  While numerology has never quite been my strong suit, this little exploration of the basic numbers has considerably helped.