Unlocking the Observatory: Planets and Numbers

Where were we? We’re in the middle of discussing the obscure Telescope of Zoroaster (ZT), a manual of divination and spirituality originally published in French in 1796 (FZT) at the close of the French Revolution, which was later translated into German in 1797 (GZT) and then again in an abridged form as part of Johann Scheible’s 1846 Das Kloster (vol. 3, part II, chapter VII) (KZT), with Scheible’s work then translated into English in 2013 as released by Ouroboros Press (OZT).  Although OZT is how most people nowadays tend to encounter this system, I put out my own English translation of FZT out a bit ago as part of my research, and while that translation was just part of the work I’ve been up to, there’s so much more to review, consider, and discover when it comes to this fascinating form of divination.  Last time, we talked about how ZT considers its own notion of the “Great Cabala” and why it’s not what people think at first glance. If you need a refresher on what we talked about last time, go read the last post!

※ For those following along with their own copy of ZT (get yours here!), the relevant chapters from ZT are the “Third Step”, “First Supplement”, and “Third Supplement”.

We’ve covered enough of the preliminary big things in these first few posts that clear up (at least some of) the literary and contextual concerns about ZT.  While there’s certainly plenty more to discuss the overall cosmology and spirituality of ZT, we need to talk technique first to make any sense of it.  We’ll start with the actual method and system of ZT today, beginning with the basic symbol set that we use for our tools.  If you’ll recall from back in the first post of this series, dear reader, I mentioned how I consider a good description of ZT to be “numerological sortilege with an astrological flair”.  This wasn’t an exaggeration: every form of divination that involves sortilege (i.e. some variation on casting lots, obtaining random symbols from some store of such symbols), like Tarot or geomancy, requires some symbol set, and for ZT, the symbols used are the nine planets and the numbers 1 through 99.

And yup, it’s nine planets, at least in a sense.  ZT makes use of a nine-planet model based on the traditional seven from the usual Western esoteric systems we all know and love.  In ZT, there are still the planets Mercury, Venus, Mars, Jupiter, and Saturn (just as we’d expect normally), but the Sun and Moon get treated a little differently: while astronomically there is just one of each luminary, in the Great Cabala of ZT there are two: a material Sun and a spiritual Sun as well as a material Moon and a spiritual Moon.  For this reason, ZT draws a distinction between planets and planetary intelligences, and for the purposes of divination, it’s the planetary intelligences that form part of our symbol set.  (I know, I know, I’m upset that ZT doesn’t make use of the North and South Nodes of the Moon, which would be more traditional for Western astrological practice, but then, ZT is very much dead set against astrology and how Western esotericism does stuff anyway, so whatever.)  It’s important to note that ZT makes use of the term “intelligences”, which those who are familiar with grimoiric or more “high church”-kinds of magic are familiar with for being another term for a spiritual entity.  In some texts, though, “intelligence” is not representative of all kinds of spiritual entities.  In his Three Books of Occult Philosophy, for instance, Cornelius Agrippa draws a distinction between planetary intelligences and planetary spirits, the former being in charge of the direction, throttling, and manifestation of the power of a planet, while the latter is more in charge of the actual flow, presence, and activity of a planet.  In the case of ZT, however, where “intelligence” is a super common term encountered in general, it may be assumed that when ZT talks about “intelligences” it’s talking about celestial or heavenly entities in general.

Also, a small side-point of clarification here about the ZT text in general: the author of ZT likes using the terms “physical” and “moral” to distinguish between different aspects of things.  The former makes sense to us as-is, but the latter doesn’t mean something like “pertaining to matters of correct or acceptable behavior”. Rather, the author of ZT uses “moral” to refer to all things spiritual and ethereal, just as “physical” also refers to all things of matter and corporeality.  Maybe this is just a trend in how people spoke back then, so I might be making a mountain out of a molehill, but I at least find it notable from a translator’s perspective.

So, nine planetary intelligences, alright.  Each of them has one or two names; in all cases, at least one name for the intelligences is based on some sort of Greek-like name (which is the name used throughout ZT).  For seven of these nine intelligences, an alternative name derived from Greco-Latin is also given for some of the intelligences (these latter names being claimed to come from “another work, probably more modern than the one which guides us”, which may well be a literary deceit). As with the ZT text itself, we’ll stick to using the primarily Greek-like names given first (and given below in bold) for our study.

  1. Genhelia (matter-Sun ☉), whose name can be derived from Greek γενηλια genēlia “sun-born”.  Alternate name is “Physia” (variant of Greek φυσις phusis “nature”).
  2. Seleno (matter-Moon ☾), whose name can be derived from Greek σεληνος variant of σεληνη selēnē “moon”.  Alternate name is “Hydrogaeo” (male variant of a combination of Greek words for “Water-Earth”).
  3. Erosia (Venus ♀︎), whose name can be derived from Greek ερωσια erōsia variant of ερως erōs “love”.  No alternate name given.
  4. Panurgio (Mercury ☿), whose name can be derived from Greek πανουργιος panourgios “knave, ruffian”.  Alternate name is “Ruffieno” (“ruffian” or, more literally, “pimp”).
  5. Lethophoro (Saturn ♄), whose name can be derived from Greek ληθηφορος lēthēphoros “Lethe-bringing” or “forgetful-bringing”.  No alternate name given.
  6. Aglaé (Jupiter ♃), whose name can be derived from Greek αγλαια aglaia “splendor, shining”.  Alternate name is “Fulgida” (Latin for “shining, flashing”).
  7. Adamasto (Mars ♂︎), whose name can be derived from Greek αδαμαστος adamastos “unsubdued, unconquerable”.  Alternate name is “Gorgonio” (a play off of the Greek Gorgon and a name used for several Christian martyrs).
  8. Psykomena (spirit-Moon ☽), whose name can be derived from Greek ψυχομηνη psychomēnē “soul-moon”.  Alternate name is “Phosphorina” (variant of Greek φωσφορος phōsphoros “light-bringer”).
  9. Psykelia (spirit-Sun ◎), whose name can be derived from Greek ψυχηλια psychēlia “soul-sun”.  Alternate name is “Celsina” (variant of Latin celsus “tall, high, prominent”).

Before we continue, a note on the symbols used for the planets.  As with usual astrological tradition, the glyphs used to represent the non-luminary planets of Venus, Mercury, Saturn, Jupiter, and Mars are the same as expected in any text.  Genhelia (matter-Sun) is represented by the usual solar glyph of a circle with a dot in the middle, while Psykelia (spirit-Sun) is represented with a circle with another circle inside (which may or may not have a dot in the middle of its inner circle).  Seleno (matter-Moon) and Psykomena (spirit-Moon) are both represented with crescent moon glyphs, but Seleno has the points of its crescent pointed towards the right and Psykomena’s towards the left.

ZT doesn’t just stop at giving the high-level information there, however.  A description of the domain, nature, and activity of each intelligence is also provided:

Genhelia ☉
This Intelligence presides over birth, growth, and the formation of the organs; over health and all good natural affections; and over family ties, from parenthood to the most remote affinity. She is sympathetic, serene, gentle, active, and willingly favorable.

Seleno ☾
This Intelligence presides over all the same things as Genhelia, but is an Intelligence that is filthy, selfish, temperamental, and lazy. He disputes with his rival over all the habits of the body which contract through the concurrence of secondary causes. What Genhelia strives to improve or change through education, Seleno willingly corrupts.

Erosia ♀︎
This Intelligence exclusively governs love, either as a passion of the soul or as a universal mode of reproduction. She knows all the joys and all the sorrows that love involves, all its pleasures and all its pains, and of all its moral and physical excesses. She is a burning Intelligence, but a good, magnetic, and vital one all the same.

Panurgio ☿
This Intelligence presides over the agility of the body, its tricks of skill and strength, and the finesse of the mind and spirit. He governs and protects all kinds of industries, is prodigiously active, and his most commendable qualities are in interpersonal skills and eloquence in language. However, he is selfish, insensitive, cunning, prone to deceit, and humanity is directed through him towards the earning of wealth, illicit or otherwise, than towards success which results from thoughtfulness.

Lethophoro ♄
This is the only essentially evil Intelligence, who presides over all the afflictions of humanity from melancholy to despair and from discomfort to death. He distributes all causes of failure, ruin, disease, and dying; he is weak, unfeeling, jealous, and resentful; he hinders all virtues and serves all the disorganizing passions of the social order.

Aglaé ♃
This Intelligence has essentially the same field as that of Panurgio, but purifies and ennobles everything of which its rival makes ill use. She fertilizes all virtues and all useful or estimable talents, restores what is proper to the arts and sciences, and inspires in humanity a disinterested ambition which directs one towards public esteem and fame than towards opulence. Aglaé is frank, fair, and noble, and she distributes literary success, honors, dignities, and all rewards of true merit.

Adamasto ♂︎
This Intelligence presides over any violence, whether merely intended or actually done. He governs war in general and quarrels in particular, and causes the shedding of blood; however, he is generous, open-minded, and incapable of resentment. Adamasto willingly submits to the influence of Erosia who tempers and tames him, as well as to the influence of Aglaé who constantly shows to Adamasto the danger of disgrace, as well as to the influence of Psykelia who spurs Adamasto on to glory. Adamasto’s faultless work is tireless, and his crimes are of his primary movement, but without any stain of baseness or betrayal. Adamasto is, in short, more tempestuous than dangerous, and is only incidentally destructive.

Psykomena ☽
This Intelligence can be called the “Overseer of the Whirlwind of the Immoral World”, who presides over all errors and follies, and who distributes to all indiscriminately all shortcomings, ridiculous non-issues, and all the innumerable strivings for trivial perfections that result in no real use in the final result of a thing. She inspires false steps, dictates frivolous productions, draws up vain projects, and constantly excites humanity into the chasing of some chimera or other. Though libertine and insensitive, she is without gall, a night without malice, serving as she does without generosity. She is especially influential over very young men, old people, and the female sex in general.

Psykelia ◎
This Intelligence is as transcendent in good as Lethophoro is in evil, and sows happiness on all careers open to humanity. She increases the influence of auspicious Intelligences and corrects the malignity of harmful malicious ones; she prepares all great fortunes and unexpected illustriousness. Opulence, victory, and triumph attach themselves to wherever she looks. She renders sublime all good sentiments; she exalts fidelity, constancy, friendship, love, and courage. She maintains the fire of genius, pulling humans out of their worst steps and purifying them to be able to reach for the highest degree of perfection allowable by human nature.

All in all, the natures of the intelligences are about what one would expect for their respective planets, though with a much dimmer view of the lunar intelligences and of Saturn than I would have expected, and a much more realistic and frank one of Mercury than is often encountered or appreciated.

It is on the basis of these nine planetary intelligences (hereafter just “Intelligences”) that we can then proceed to the Numbers.  In the system of ZT, each of the numbers from 1 to 99 is given a set of significations that build up numerologically from simple principles.  Those principles are themselves the Intelligences, each of which is given to one of the “primitive Numbers”, or the single digits 1 through 9, in the same order as the Intelligences are shown above: 1 to Genhelia, 2 to Seleno, 3 to Erosia, 4 to Panurgio, 5 to Lethophoro, 6 to Aglaé, 7 to Adamasto, 8 to Psykomena, and 9 to Psykelia.  It should be stressed that the Intelligences are not numbers themselves, but receive these numbers as a lord does a vassal; in other words, the Intelligences are on a higher ontological level than the primitive Numbers, and the primitive Numbers act as representatives of the Intelligences.

After the primitive Numbers come the compound Numbers, which are double-digit numbers that are themselves composed of the primitive numbers plus the null digit (0).  Each compound number falls into a group of numbers established by the primitive Number it reduces to: the standard numerological procedure of “adding up all the digits until you get a single digit number” is the process here, such that 45 → 4 + 5 = 9, 66 → 6 + 6 = 12 → 1 + 2 = 3, and so forth (or, more mathematically, take the number modulo 9, i.e. divide the number by 9 and take the remainder, replacing a 0 result with 9).  To keep track of all this, ZT provides a table of numbers which maps the 99 numbers to the planetary intelligences.  What’s neat about this, though is that because there are 99 numbers and we add another 9 to them (the Intelligences), if we plot out each series of 9 on separate rows, we get twelve rows total (because 99 + 9 = 108 and 108 ÷ 9 = 12).  What ZT does with that fact is that it allots each consecutive set of nine symbols to one of the twelve signs of the Zodiac in order, as below:

Aries ♀︎ ♂︎
Taurus 1 2 3 4 5 6 7 8 9
Gemini 10 11 12 13 14 15 16 17 18
Cancer 19 20 21 22 23 24 25 26 27
Leo 28 29 30 31 32 33 34 35 36
Virgo 37 38 39 40 41 42 43 44 45
Libra 46 47 48 49 50 51 52 53 54
Scorpio 55 56 57 58 59 60 61 62 63
Sagittarius 64 65 66 67 68 69 70 71 72
Capricorn 73 74 75 76 77 78 79 80 81
Aquarius 82 83 84 85 86 87 88 89 90
Pisces 91 92 93 94 95 96 97 98 99

This table is originally given (and far more beautifully rendered) in ZT as “Plate 2”.  While there are a bunch of other elements on this illustration which we’ll get around to covering, let’s just take a look at the table of numbers itself:

When we take a step back and look at all the Numbers, we can divide up the Numbers into several groups:

  • Primitive Numbers: numbers composed of single digits (9 total)
  • Compound Numbers: numbers composed of two digits (90 total)
    • Simple Compound Numbers: numbers composed of two digits where both digits are different and nonzero (72 total)
    • Double Compound Numbers: numbers composed of the same digit twice, i.e. a primitive number multiplied by 11 (9 total)
    • Tenfold Compound Numbers: numbers composed of one primitive digit and one zero digit, i.e. a primitive number multiplied by 10 (9 total)

As I said earlier, each of these 9 Intelligences and 99 Numbers has their own set of significations and meanings.  That said, we don’t have to memorize meanings for them all, because there’s a trick to it: you only really need to learn the meanings of the Intelligences and the primitive Numbers, and the rest all fall along in a nice, convenient pattern.

As an example, consider the primitive numbers 3 and 7.  3 is the number of Erosia (Venus), and has the meaning of “object of the heart, fecundity, fertility” (under Erosia’s general signification of “love, the universal magnet”).  7, likewise, is the number of Adamasto (Mars), and has the meaning of “military status, chiefs, sometimes competitors” (under Adamasto’s own general signification of “the strength of soul and body, violence, the element of fire”).  Now, if we take 3 and 7 and combine them into a compound number, we get either 37 or 73.  In both cases, these numbers reduce to 1  (3 + 7 = 10 and 3 + 7 = 10 , but 10 → 1 + 0 = 1), which is the number of Genhelia (matter-Sun).  Because of this, both 37 and 73 have something to do with Genhelia’s general domain.  In the case of 37, the meaning is “burning senses, amorous passion”; in the case of 73, “rapt in love, romantic/novelesque adventures” (with “romantic” used in the older sense of fantastic stories of chivalry and nobility”).  Note how both 37 and 73 retain their basic Venereal and Martian qualities (their single digits), but permuted in different ways within the general contextual scope of matter-Sun (their reductions to a primitive number).

To hammer in the lesson, let’s also consider the numbers 5 and 8.  5 is the number of Lethophoro (Saturn), and has the meaning of “ruin, fatal illness, secret enemy” (under Lethophoros’s general signification of “death, darkness, the element of water”); 8 is the number of Psykomena (spirit-Moon), and has the meaning of “the feminine being, the social whirlwind” (under Psykomena’s general signification of “mistake, vanities, inconstancy, foreign countries”).  The compound numbers 58 and 85 both reduce to 4 (5 + 8 = 13 and 8 + 5 = 13, and 13 → 1 + 3 = 4), putting both these numbers under the domain of Panurgio (Mercury).  58 has the meaning of “deceived wife, sometimes her death”; 85 has the meaning of “treacherous woman, sometimes testament”.  Again, note how the compound numbers retain their basic qualities of Saturn and spirit-Moon (according to their single digits) but play out in different ways according to the context of Mercury (their reduction).

We see these things touched on in the list of advice and considerations given towards the end of ZT:

  1. Let us never tire of reflecting on the attributes assigned to each Intelligence, and what about these attributes are respectively analogous to each other or incompatible with each other.
  2. Let us deeply penetrate into the primitive quality that each simple number has, inasmuch as it is often the representative of its own planet and recalls it everywhere it may be.
  3. Let it be ingrained that whenever a simple number appears joined with another to form a compound number, each of the two digits still preserves something that is primitively proper to them, wherever it may fall in some mirror or in some orbit, even one most foreign to its planet or angel.

In general, if we look at the meanings of the compound Numbers, we see a pattern arising: the basic planetary concept expressed by the tens digit acts upon or makes use of the basic planetary concept of the ones digit (e.g. 85 = spirit-Moon on Saturn = woman making use of ruin, but 58 = Saturn on spirit-Moon = ruin falling upon woman).  We just have to remember that each compound Number is bound by three things: the two separate digits it is composed of and the single digit it reduces to.  Thus, although one could conceivably come up with any number of things that 37 might resolve to being “Venus acting upon/making use of Mars” for weal or for woe, we have to remember that we are bound by the semantic limitations of these things falling in line with the general field of matter-Sun (because 37 reduces to 1).

At least, that’s the general idea for understanding the compound Numbers in general, but that works especially for the “simple compound Numbers” (e.g. 78, 29, 32), where a compound Number has two nonzero digits that are different from each other.  What about the other two kinds of compound numbers?

  • For the double compound numbers (aka “doublets” where both digits are the same, i.e. a primitive number multiplied by 11 like 22, 33, 44, etc.), it’s a similar deal as before: take the single digit, compound it upon itself, and interpret it in the context of the primitive number it reduces to.  For instance, consider 6, the primitive number of Aglaé (Jupiter), which has the meaning of “prudence, wisdom, great magistracy” (under Aglaé’s general signification of “fame, arts and sciences, the element of air”).  If we double the number (or, more accurately, multiply it by 11) to get 66, then this number reduces to 66 → 6 + 6 = 12 → 1 + 2 = 3, the number of Erosia (Venus).  As a result, 66 has the indication of “legal marriage, social concord” (Jupiter acting on Jupiter within the context of Venus).  Likewise, using numbers we’ve already encountered before, if we take the number 7 of Adamasto (Mars) and double it, then we get the number 77 which reduces to 77 → 7 + 7 = 14 → 1 + 4 = 5, the number of Lethophoro (Saturn); 77 has the indication of “severe physical accident, violent death”.  It’s the same process as before.
  • For the tenfold compound numbers (aka “nilled numbers” where the ones digit is 0, i.e. a primitive number multiplied by 10 like 20, 30, 40, etc.), the result is a little different.  In the system of ZT, even though zero is a digit, it is not a primitive Number, and so has no Intelligence associated with it.  In this case, a nilled number will always appear in the same column as the primitive number of its corresponding tens digit (e.g. 70 will always appear in the column of Adamasto/Mars because 70 → 7 + 0 = 7).  Such a compound Number has a general indication of the privation, diminution, or depletion of its primitive Number’s general idea.  Thus, 70 can be read as “weakening of Mars”, and thus has the meaning of “weakness, discouragement, cowardice”; 30 can be read as “weakening of Venus” → “celibacy, chastity, monasteries, insensitivity”; 40 can be read as “weakening of Mercury” → “aborted wealth, empty plans or intrigues”.  This is a slightly different pattern than the rest of the compound numbers.

That’s all there is to it: by understanding what the basic meanings of the digits 1 through 9 are, we can permute them and reduce them to come up with a rather specific set of meanings in a well-defined semantic field.  In this way, ZT has its own sort of “astrological numerology”, and rather than having to memorize a set of indications for every Number from 1 through 99 in addition to the nine Intelligences themselves, one really just needs to learn the nine Intelligences and the nine primitive Numbers and then how they can all fit together.  It’s actually a really neat way to generate meanings—which is why we see warnings throughout the ZT that the tables of indications provided for meanings and significations like this are inherently limited and limiting, given that they’re only a few words long and are only meant to illustrate possible meanings that fit the tens digit/ones digit/reduction digit trifecta of symbols, rather than trying to flesh out all possible meanings.  ZT, after all, “is only a key, not a treatise”.

All the same, to fill out the understanding of how the basic symbols of the numbers come together, here’s the list of indications for each of the Intelligences and the Numbers given in ZT (according to my translation of FZT).  The following list of indications comes from the “First Supplement” in ZT, but note that, due to HTML/blog platform restrictions, I’m not able to put in the Unicode glyph for the list element representing the Intelligence itself; instead, the Intelligence is represented by a negative single-digit number, e.g. “-2” represents the intelligence of Seleno, while 2 is the primitive Number that pertains to Seleno.

Genhelia ☉

  1. Existence. Physical soul. The homeland.
  2. The male being. The people. Birth.
  3. (The male child will live only for a short time.) Short duration.
  4. Noble origin. Ascent of the individual.
  5. (A girl will be born.) Acquaintance with a woman.
  6. Burning senses. Amorous passion.
  7. Great profits. Acquisitions. Tutors. Education.
  8. Natural death. (Sometimes bankruptcy.)
  9. Losses. Trials. Legal practitioners.
  10. Rapt in love. Romantic adventures.
  11. Maternity. The mother. Productive causes.
  12. Great age for a man. Experience. Consideration.

Seleno ☾

  1. Kinship. Common interest. The Earth.
  2. Second causes. Society. Clubs.
  3. Sympathy. Dependencies. Twins.
  4. Breakups. Solutions of interests. Hearths.
  5. Whirlwinds of the Great. Courtiers. Falsehood.
  6. Woman giving in. Seduction. Adultery.
  7. Passive attacks. Debates. Outrage.
  8. Happiness crossed. Aborted success. Widowhood.
  9. The Savior. The Avenger. The Peace.
  10. Advantages by strength or skill.
  11. Woman in love. Hysterical passions.
  12. Powerful help. Protectors.

Erosia ♀︎

  1. Love. The universal magnet.
  2. Object of the heart. Fecundity. Fertility.
  3. Reproduction. Amorous enjoyment. Success.
  4. (A son will be born.) Nascent bond.
  5. Celibacy. Chastity. Monasteries. The insensitive object.
  6. Illustrious gallantries. Fortune through love.
  7. Illicit unions. Theatrical overreactors. Wanderers.
  8. Jealousy. Disasters by love.
  9. Legal marriage. (Sometimes social concord.)
  10. Unlucky passion. Corrosive feelings.
  11. Insidious woman. Perverted young man.
  12. Circle of delights. Fortune of chance.

Panurgio ☿

  1. Wealth. Trade. Travels. The seas.
  2. Discoveries. Intrigues. The opposing party.
  3. Aspirant. Talents to be treasured and cherished.
  4. Happy association. Friendship. Letters.
  5. Good fortune for a clever man. Chickens.
  6. Aborted wealth. Empty plans or null intrigues.
  7. Eloquence. Orators. Ascending.
  8. Deceived wife. (Sometimes her death.)
  9. Great success by talent. Enterprises.
  10. Works for glory. Monuments.
  11. Treacherous woman. (Sometimes testament.)
  12. Sublime talents. Mechanical virtuosos.

Lethophoro ♄

  1. Death. The night.The element water.
  2. Ruin. Fatal illness. Secret enemy.
  3. Bad faith, people thereof. (Sometimes doctors.)
  4. Orphans. Bastards. Those bound to misfortune.
  5. Incestuous passions. Shunned pleasures. Vices.
  6. End of a man. Violent thieves. Lawsuit lost.
  7. End of a loved one. (Sometimes ruin avoided.)
  8. Death of a great person. Public disaster.
  9. Dangerous enemy. Hypocrisy.
  10. Severe physical accident. (Sometimes violent death.)
  11. Hospitals. Women dedicated to the service of the sick.
  12. Perversity. Powerful enemies. Great crimes.

Aglaé ♃

  1. Fame. Arts and sciences. The air.
  2. Prudence. Wisdom. Great magistracy. Embassies.
  3. Skillful chemists. Friends of humanity.
  4. Family of merit. Grand establishments.
  5. Virtuous and constant love. Meeting of lovers.
  6. Social utility. All honest professions.
  7. Death of a sage or a friend. To be condemned.
  8. Desertion of good ways. Dangerous actors.
  9. Illustriousnesses. Titles and orders of merit.
  10. Passion for women. Poetic enthusiasm.
  11. Great virtues of women. Heroines.
  12. Great protectors. Virtuous path.

Adamasto ♂︎

  1. The strength of soul and body. Any violence. The element fire.
  2. Military status. Chiefs. (Sometimes competitors.)
  3. Great courage. Obstinacy. War.
  4. Family in discord. Tasks. Civil unrest.
  5. Careful and firm conduct in love. (Success.)
  6. Ascending through feelings. Beloved superiors.
  7. Loss of a parent or associate. To be gone.
  8. Father. Benefactor. Blessings. Favor.
  9. Weakness. Discouragement. Cowardice.
  10. High ranks. Military honors. Generalship.
  11. Pairs. (Sometimes feminine discord.)
  12. Strength and power. States. Armies. Public wealth.

Psykomena ☽

  1. Mistake. Vanities. Inconstancy. Foreign countries.
  2. The feminine being. The social whirlwind.
  3. Nonsensical passions. Punishable enthusiasm.
  4. Public criticism. Gossip.
  5. Quarrels between lovers. Absence.
  6. Maladministration. Shame. Correction.
  7. Loss of the most cherished being.
  8. Family authority. Prohibition. Poverty.
  9. Disturbed brain. (Sometimes an effeminate man.)
  10. Short life for a female being. (Sometimes murderers.)
  11. Great lady. Sovereign woman. Influential woman.
  12. Remarkable extravagance. Crazy and mad people.

Psykelia ◎

  1. Perfection. Heavenly soul. The light.
  2. Nobility. Elevation. All kinds of success.
  3. Household protected by fortune. Fortunate lineage.
  4. Authority over the nation. Public respect.
  5. Conjugal love. Happiness and virtue.
  6. Legacies. Success on critical occasions.
  7. Death of an enemy. Triumph. Lawsuit won.
  8. Loves favored by public opinion. Religion.
  9. Family strength. Federations.
  10. Extreme old age for a woman. Prejudices.
  11. Abdication. Retreat from the whirlwind. (Sometimes degradation.)
  12. The height of prosperity. Sovereignty. Papacy.

If this all seems like a lot, it’s because it is—but at least we know what’s generally going on.  Rather than having to memorize each of the 108 indications given above as being something fixed and immutable, we just need to recognize the pattern and learn from these indications as being more like illustrative examples.

To wrap up this discussion, there are just two big questions on this topic left that we should consider.  First: if you recall that Table of Numbers from before (given in Plate II), there’s not just the Intelligences and Numbers on the table, but also the signs of the Zodiac.  What role do they play in establishing or fleshing out meanings of the Intelligences or Numbers?  Bluntly speaking, I can’t see that they do; if we read the numbers across the table, there doesn’t seem to be a whole lot that ties in the significations to any given Zodiac sign, and ZT never brings these up at all when discussing their meanings.  While it’s not outside the realm of possibility that one could involve the Zodiac signs as an extra consideration or another semantic boundary to establishing the meaning of a given Number or Intelligence, and while the relatively free approach to generating meanings might well be permitted by ZT, I don’t think ZT actually does this.  In short, based on my understanding of ZT, I don’t think the Zodiac signs matter (or should matter) at all for the purpose of establishing, generating, or understanding their meanings.  The signs of the Zodiac, rather, have a different function which we’ll get to later on in describing periods of life of humans and illustrating some temporal concepts, but don’t have a strong symbolic presence in the system of ZT.  While one could feasibly work in the meanings of the signs of the Zodiac somehow into the overall meanings of the Intelligences or Numbers, I don’t think ZT actually implies that this should be done, rather sticking to a purely numerological approach to develop meanings.

The second (and more historically interesting) question: where is ZT getting its system of numerology from?  That is a great question, frankly, and one which I struggled with for quite some time.  There are many systems of numerology that involve the planets in one form or another, but it’s not as common to find one that doubles the Sun and Moon, and less common still to find any set of numerological meanings like what ZT uses.  Either ZT is literally making its own system of numerology up (in the sense of giving certain numbers to certain planets), or it’s taking inspiration from some other obscure source.  I have my suspicions about where it’s coming from, but it requires more context to justify and explain, and we’re not quite there yet; we’ll cover that in a future post.  On the other hand, if you, dear reader, are familiar at all with similar systems, do say so down in the comments; you might be helping everyone trace the development of the system of ZT here in the process (and helping to make up for my own limited research), or at least spurring people on to research more leads to that end!

Revisiting the Revelations of the Numbers

I didn’t expect to write this post so soon after the last one.  After months of nothing new happening, suddenly I write two posts on mathesis and Iamblichean number theory on the Tetractys?  It’s good to be back, that’s for sure.  I suppose this downtime since last year has done me good and given me time to internally process a lot more than I expected.  Get a drink, dear reader, because I’m gonna go on at length for a bit here.

Okay, so, last time, I started (again) contemplating this mathesis stuff I started developing back in 2014.  Mathesis literally means “teaching”, and is the style of theurgy and ritual I’m developing as an exploration of Neo-Pythagorean, Neoplatonic spirituality based more on Hellenic philosophy than the Jewish philosophy inherent in Kabbala, mangled beyond recognition into Hermetic Qabbalah, and which has unfortunately formed a procrustean bed of occultism to which so much (maybe even too much) has been chained down by.  To be fair, there’s a decent amount of Pythagoras in QBLH (regardless of whether it’s Jewish Kabbala, Christian Cabala, or Hermetic Qabbalah), but nobody really knows what Pythagoras actually taught.  We know he was A Thing, but we don’t know which Things he was.  And…well, I find lots of issues that’ve collectively poisoned the well for me in Hermetic Qabbalah, and I find it hard for me to go back to it anymore.  Yeah, I still use the stuff when it’s called for in Western Hermetic ritual, but I want to find something better, hence my exploration of this system I’m (slowly) developing.  A crucial aspect of it is focusing on the Tetractys, the sacred triangle of ten points that represent the fundamental ideal for all things in the cosmos.  Yes, this path involves a lot of meditation on Pythagorean number theory, handed down to us by the Neoplatonists such as Iamblichus, so let’s go back to the basics and recall what we’ve discussed before about the numbers themselves.

In this sort of Pythagorean Tetractyan math, there are ten numbers plus a special “zero” non-number liminal amount that we should concern ourselves with.  Each of these numbers has a special attribute given to it:

  1. Mēden: Emptiness
  2. Monad: Individuation
  3. Dyad: Relation
  4. Triad: Harmony
  5. Tetrad: Form
  6. Pentad: Growth
  7. Hexad: Order
  8. Heptad: Essence
  9. Octad: Mixture
  10. Ennead: Realization
  11. Decad: Wholeness

Moreover, we noted before that there are special relationships between pairs of these numbers if you take the whole Tetractys and reflect it around a central horizontal axis:

  • Being: Mēden/Decad
  • Becoming: Monad/Ennead
  • Variation: Dyad/Octad
  • Accordance: Triad/Heptad
  • Structure: Tetrad/Hexad
  • Growth: Pentad

tetractys_decad

These relationships are, in a sense, a more “ideal” version of each of their correspondent numbers, and form a sort of meta-Tetractys.  For instance, the Monad has the secret of individuation (a thing in the process of becoming a single thing), while the Ennead has that of realization (a thing in the process of becoming real); both reveal the secret of becoming, but do so in different ways.  The numbers after the Pentad are reflections of the numbers going before, both reflecting off an ideal numerical concept.

As a sort of exercise, let’s now take another look at that picture above.  If you take the lower inverted Tetractys, it implies the existence of two boundary “hidden” tetractyes, such that the Hexad is really just a tetrad plus two monads, the Heptad a triad plus two dyads, and so forth.  If we were to keep this all truly reflective, and if there are two “upright but hidden” tetractyes bounding the lower tetractys, then we should also envision two “inverse but hidden” tetractyes bounding the upper tetractys.  Thus, the Monad is just an ennead minus two tetrads, the Dyad an octad minus two triads, and so forth.

tetractys_decad_full

This can then imply another set of mutual relationships between the numbers:

  • Monad and Tetrad
    • Upper Monad/Lower Tetrad = Monad and Hexad
    • Lower Monad/Upper Tetrad = Ennead and Tetrad
  • Dyad and Triad
    • Upper Dyad/Lower Triad = Dyad and Heptad
    • Lower Dyad/Upper Triad = Octad and Triad
  • Pentad

I list the Pentad here as well, but it has no relationship to anything else, as it is not properly part of the Tetractys (either one, upper or lower, upright or inverse), and also because it is “hidden” as something apart, a balance around which the other two tetractyes stand.  That said, if anything, the Pentad is part of a relationship with the Decad, being exactly half of it, and also thus in a relationship with the Mēden, nothingness and emptiness which is nothing more than the flip side of the same coin as the Decad.

However, this all implies that the Monad is not truly just the Monad that is built with nothing before it, but that it is formed from subtracting from the Ennead.  If we treat all numbers as equally and c0-eternally present, then sure, that would work, but that’s not how the ancients thought about these numbers.  To them, the Monad was first, and underlies all other numbers without relying on them for existence.  Thus, it is the Ennead that relies upon the existence of the Monad and not vice versa, so perhaps we shouldn’t rely on this way of conceiving relationships between the numbers.  Alternatively, we might say that the “ideal” concepts of Becoming, Variation, Accordance, and Structure are identical to those of Individuation, Relation, Harmony, and Form in all ways, simply being another set of terms for the same exact things.  This would mean then that the other four ideas of Realization, Mixture, Essence, and Order are reflections of the “pure” or “true” upright Tetractys, and not that they are on the same level being reflected from the “ideal” concepts.  We might then conceive of Mixture being a higher “register” of Relation, that the Octad is a higher “evolution” of the Dyad, much as people claim Uranus is a higher “octave” of the forces of Mercury, or how 20 is a higher base of the number 2.

Thinking of the numbers in this sense means that, every time we proceed from the concept of Monadic Becoming to Tetradic Structure, we then hit the concept of Pentadic Growth, then proceed back up from the Tetrad to the Monad to…well, the Mēden or Decad, take your pick, depending on how you want to conceive of it.  Then you bounce back down from the Monad through the Tetrad, grow upon the Pentad, then back up, then back down, and so forth.  If we use an expanded version of the Tetractys, going from the Monad to the fifteenth rank, we can see this in action, as below:

tetractys_pendedecad

We first proceed from the Monad to the Dyad to the Triad to the Tetrad, then hit the Pentad.  Then, upon reaching the Hexad (really the first higher register of the Tetrad), we go to the Heptad (higher register of the Triad), then the Octad (higher register of the Dyad), then the Ennead (higher register of the Monad), and then we hit the Decad, which you might consider to be a higher register of the Mēden.  After that, we hit the eleventh rank (the Hendecad if you want to be fancy about it), which as we see is an even higher register of the Monad.  Thus, the Dodecad (rank 12) is an equally-high register of the Dyad, the Tridecad (rank 13) of the Triad, and so on.  Note, though, that just as the lower tetractys has two hidden upright tetractyes supporting it on either side, the tetractys of the ranks higher than twelve has four hidden tetractyes, two on each side of each type.

Every time we finish one Tetractys of evolution (Becoming through Structure), we bring all of that with us each step of the way along the next time.  And, every time we finish the next Tetractys, we also bring that one with us, too; note how the third Tetractys in the picture above, ranks 11 through 14, is nestled between both upright and inverse tetractyes, one of each on each side of the central tetractys that we’re developing.  Each time we progress, we build upon and bring with ourselves all that we have done before, again another way to describe the “everything eternally flows” concept of the Gnosis Schema mentioned last time.

So, consider the Hendecad, rank 11.  This row is composed of the Monad, plus two hidden upright monads and two hidden lower tetrads.  The upper monad (rank 1) is associated with the pure concept of Becoming, i.e. Individualization, and the lower tetrad is really another way to describe the Hexad (rank 6), which is associated with Order.  We know that Order is a higher register of the same concept as Form, i.e. Structure, and since we now have both Structure and Becoming together, we now have joined the Monad and Tetrad again in the same relationship we foresaw with our little mental exercise above.  So the relationship between the Monad and Tetrad still stands, as does that of the Dyad and Triad.  Good to know I didn’t have that little mental exercise or Adobe Illustrator use go to waste after all.

So, let’s revisit the relationship between the Monad/Tetrad and Dyad/Triad and flesh those out a bit more.  If we combine the numbers of these relationships and take the median of the sum, we can tease out some finer points of the relationships these numbers have amongst themselves.

  • Monad and Tetrad.  This pairing overall combines the concepts of Becoming with Structure, the formative beginning and end of all things that allow us to discern why we come into being, and as what we come into being.
    • Upper Monad/Lower Tetrad = Monad and Hexad= 1 + 6 = 7, whose median is 4.  Individuation and Order, with Form as the balance.  As a thing comes into being for the first time, it focuses on its place in the overall order of the cosmos and universe into which it finds itself becoming.  However, being initially without form, it thus requires one; the first thing anything requires in order to begin to achieve its goal is a form conducive to its goal and purpose.
    • Lower Monad/Upper Tetrad = Ennead and Tetrad = 9 + 4 = 13, whose median is 7.  Realization and Form, with Essence as the balance.  As a thing becomes manifested and completed, it focuses on its form and how it will help it achieve its goal.  With a form and a manifestation, what becomes the focus of investigation is now purpose, our essence, our telos within the overall cosmos.  We reflect upon ourselves and our forms, having come into being, to question why and for what we come into being.
  • Dyad and Triad.  This pairing overall combines the concepts of Variation with Accordance, the principles of difference and similarity that relate to all things so as to learn what and how to achieve our desired ends.
    • Upper Dyad/Lower Triad = Dyad and Heptad = 2 + 7 = 9, whose median is 5.  Relation and Essence, with Growth as the balance.  As a thing comes into being and realizes what is around it and, moreover, what things are not itself, it learns to discern the essences of things, including its own, by means of comparison.  This is not for idle sophistry; this very act of “know thyself” is a way of growing into ones own essence.  We cannot escape our essence, but we can learn how to grow into it in a way conducive to its purpose.
    • Lower Dyad/Upper Triad = Octad and Triad = 8 + 3 = 11, whose median is 6.  Mixture and Harmony, with Order as the balance.  As we fall into place and amongst our peers and all the other things in the cosmos, we learn how to get along with them.  The sheer power of being mixed among things is the catalyst for attaining harmony, for the overall sake of creating an overall order so as to help us and all other things achieve all our purposes.

All this leaves the issue of the relationship between the Pentad, Decad, and the Mēden.  We see that, just as the Hendecad is a higher register of the Monad, and that the Hexad is a higher register of the Tetrad, we can say that the Decad is a higher register of the Pentad.  But…this is a little weird.  I mean, yeah, it logically follows, but we also know that the Decad is also a higher register of the Mēden, as both reflect a different state of Being.  I mean, right?  The Mēden is Being by Emptiness, where a thing that exists is empty of independent existence and relies entirely on all other things to exist; the Decad is Being by Wholeness, where a thing that exists is full of all things that exist, containing everything else.  And yet, the Decad is nothing more than the liminal point between one iteration of the full Tetractys counted out and another; just as we started with the Mēden before the Monad, we start with the Decad before the Hendecad.  In a sense, the Decad and Mēden are equals in their own relationship.

What of the Pentad, then?  The Pentad is the balance point between the Mēden and the Decad, and we associate the Pentad with the idea of Growth.  Growth is a distinct concept from any of Becoming, Variation, Accordance, and Structure, as it builds upon and enhances them all.  Consider that the Pentad is the only one of the numbers that can be formed in two distinct ways using distinct numbers in the sum: the Pentad can be formed by adding either the Monad with the Tetrad or the Dyad with the Triad.  All the other numbers in the Decad have only one way to use distinct numbers to form the sum (9 = 4 + 3 + 2, 6 = 4 + 2, etc.)  Even the Decad itself cannot lay claim to this little fact.  The only other number that can be considered as special is the Mēden, which isn’t even a number according to the Greeks; it has no sum because it has no value, because it is nothing.  Thus, in a sense, the Decad is conceptually equal to the Mēden, even if not arithmetically equal, because they are both Being in contraparallel ways.

The Pentad represents growth because it affords the cosmos a power of balance, reciprocity, distribution and flow in a way utterly unlike any other number.  It is neither static nor dynamic, neither oppositional nor reinforcing, neither varying nor assimilating, neither complete unto itself nor utterly and only part of everything else.  In a way, it is Growth (Pentad) and Being (Decad/Mēden) that are also part of their own relationship, and if we’re to be proper about it, we would say that the Decad is a higher register of the Pentad, and not that the Decad is a higher register of the Mēden, because the Mēden doesn’t actually exist except as everything else (being completely empty of independent existence, like a kind of hypostasis or substratum of all numbers, as it were).

So, let’s put this all together in a table for clarification, shall we?  As above, we can identify Individuation with Becoming, Relation with Accordance, Harmony with Accordance, and Form with Structure; thus, all these concepts have the same number.  However, we can distinguish between Individuation and Realization by saying that the former is “manifesting” and the latter “manifested”, like with our geomantic mental exploration of the Tetractys from before.

Concept
Ideal Manifesting Manifested
Monad Becoming Individuation Realization
1 9
Dyad Variation Relation Mixture
2 8
Triad Accordance Harmony Essence
3 7
Tetrad Structure Form Order
4 6
Pentad Growth Being
5 Emptiness Wholeness
0 10

All this is well and good, but how do we think of this in terms of a more practical manner?  I mean, it’s good to understand the numbers and their relationships for their own sake, but where does it get us?  Well, consider again the Gnosis Schema:

alchemical_planetary_tetractys_paths_circuit1

Every time we traverse one of the three systems on this schema (Hot, Cold, or Cosmic), although there are four distinct paths and four distinct sphairai, there are actually five different steps.  Consider the Hot System: we begin at Mercury, proceed to Jupiter/Air, then to Mars/Fire, then to Sun/Sulfur, and then back to Mercury.  We proceed from the Monad to the Dyad to the Triad to the Tetrad to the Pentad…which then becomes the Monad for the next system.  As we proceed from our starting point, we undergo a process of analysis and synthesis; as we return to our starting point, we complete this process and prepare ourselves for the next process.  This completion/initiation point is the liminal sphaira of Growth, the Pentad, which is hidden from but implied by the numerical structure of the Tetractys itself.

Okay, but then this leaves two issues.  The first is that the process of the Gnosis Schema doesn’t take four steps, nor does it take ten steps; it takes twelve.  To use the astrological correspondences of the sphairai:

  1. Mercury → Jupiter
  2. Jupiter → Mars
  3. Mars → Sun
  4. Sun → Mercury
  5. Mercury → Moon
  6. Moon → Saturn
  7. Saturn → Venus
  8. Venus → Mercury
  9. Mercury → Fixed Stars
  10. Fixed Stars → The One
  11. The One → Earth
  12. Earth → Mercury

The fourth, eighth, and twelfth steps are where we leave one system to return back to Mercury so as to proceed to the next system on the Gnosis Schema.  If we elide the first two of these steps by considering that we only “pass through” Mercury, we can get down to ten:

  1. Mercury → Jupiter
  2. Jupiter → Mars
  3. Mars → Sun
  4. Sun → (Mercury) → Moon
  5. Moon → Saturn
  6. Saturn → Venus
  7. Venus → (Mercury) → Fixed Stars
  8. Fixed Stars → The One
  9. The One → Earth
  10. Earth → Mercury

This way of reckoning the transitions between one system and the next as seamless might be considered ideal, thinking of the whole process of traversing the Tetractys as a Decad unto itself, although a bit forced in my opinion.  Yes, if we start at Mercury, then we may not need to consider it as a distinct sphaira that we need to reckon again.  However, this thought leaves a funny taste in my mouth.  If we undergo the process of analysis and synthesis within one system after leaving Mercury, then when we return, we’re not the same person anymore, and Mercury will have new lessons to teach us before we proceed on to the next system.  As we change, so do the lessons we must learn.  After all, παντα ρει.  Besides this, having twelve distinct steps to traverse the Tetractys is a pleasant echo of the twelve signs that the Sun passes through during the course of the year (and, additionally, is the fundamental thought behind associating these paths with the signs of the Zodiac and the rest of the letters of the Greek alphabet onto the paths of the Tetractys).

alchemical_planetary_tetractys_gnosis_paths

So much for that issue, which turned out to be moot in the end.  The other is actually more notable, and goes back to our analysis of the first four numbers of the Decad before the Pentad (Monad through Tetrad) as “manifesting” and the second set after the Pentad (Hexad through Ennead) as “manifested”, the Upper and Lower Tetractyes, respectively, and how they relate to the three systems.  Say that we start at Mercury, and proceed around the Gnosis Schema along the twelve paths.  We know that every time we complete a system, we have gone through five sphairai, beginning with and ending at Mercury.

  1. Hot System
    1. Mercury
    2. Jupiter
    3. Mars
    4. Sun
    5. Mercury
  2. Cold System
    1. Mercury
    2. Moon
    3. Saturn
    4. Venus
    5. Mercury
  3. Cosmic System
    1. Mercury
    2. Fixed Stars
    3. The One
    4. Earth
    5. Mercury

Note how we attain the Decad, the Wholeness of Being, after only having completed the second Cold System without having gotten to the third Cosmic System.  When we come back to Mercury after the Cosmic System, we end up at the Pendedecad, rank 15, which is not a completed decad.  This is awkward, since it means that one trip around the Gnosis Schema is not enough.  Additionally, if we consider that the upper “manifesting” tetractys numbers (Monad through Tetrad) and the lower “manifested” numbers (Hexad through Ennead) are different experiences, then it means that we’ve only experienced half of each system by going through it only once.  So, to be a completionist and perfectionist about this, we’d need to go through the Gnosis Schema twice:

  1. Manifesting Hot System
    1. Mercury
    2. Jupiter
    3. Mars
    4. Sun
    5. Mercury
  2. Manifested Cold System
    1. Mercury
    2. Moon
    3. Saturn
    4. Venus
    5. Mercury
  3. Manifesting Cosmic System
    1. Mercury
    2. Fixed Stars
    3. The One
    4. Earth
    5. Mercury
  4. Manifested Hot System
    1. Mercury
    2. Jupiter
    3. Mars
    4. Sun
    5. Mercury
  5. Manifesting Cold System
    1. Mercury
    2. Moon
    3. Saturn
    4. Venus
    5. Mercury
  6. Manifested Cosmic System
    1. Mercury
    2. Fixed Stars
    3. The One
    4. Earth
    5. Mercury

In this way, we get to experience both a manifesting and manifested version of each system, going through both the yin/yang, masculine/feminine, active/passive aspects of each force in turn.  The first pass through the Gnosis Schema has us go through the manifesting/yang/masculine/active Hot system, composed of active and hot sphairai, then through the manifested/yin/feminine/passive Cold system, composed of passive and cold sphairai, and then through the manifesting Cosmic system so as to bring about divinity in our lives and worlds.  However, this is only half the equation for a complete experience of everything.  We would then need to undergo, maybe even “undo”, what we’ve done by continuing on the paths: we’d then undergo the manifested Hot system, then the manifesting Cold system, then the manifested Cosmic system so as to complete the process, and allow the divinity we’ve accomplished to become fully realized both within, through, and by us.

I make this sound like going through the Gnosis Path once is pointless until you do it a second time, but it’s not.  As we complete one iteration of the Gnosis Schema, we have gone through the ten states of the cosmos, the ten sphairai of the Tetractys, and have brought about completion.  However, in doing so, we prepare ourselves by this very completion to continue along this path in another, more natural, more intuitive way.  It’s akin to what’s said about one attaining K&CHGA in modern Western traditions: once you are under the tutelage of your Holy Guardian Angel, you complete your initiatory phase and begin your actual Work, since your HGA would lead you henceforth as teacher and tutor.  What happens after that is continuing along the Lightning Path of the Tree of Life, but in different ways above the Veil of Paroketh that mimic what was done below it but in a greater, grander magnitude.

To offer a parallel about this, I propose to think that that the first iteration of one’s trip around the Tetractys on the Gnosis Schema is meant to intentionally manifest one’s paredos or Agathodaimon by undergoing initiation in the three Systems, and the whole cosmos generally.  It is only after that, under the direction of the Agathodaimon, that one allows what was intentionally manifested before outside oneself to naturally manifest within oneself, and vice versa, to the cumulative effect that one not only brings God down into this world (first iteration), but that we become God ourselves in all worlds (second iteration).  I mean, I only propose to think this; I don’t yet claim that that’s what would actually happen, but it’s a useful way to think about it.  If true Gnosis is to be attained, then one must experience both sides of all coins, not just the shinier side; the darker, more hidden side would be impossible to experience without the aid of the divinity we’ve worked to manifest, and to become manifested as divinity ourselves would be even less likely.  If the manifesting and manifested aspects of the Tetractys are different, then going through each of the systems in its different aspect is as important as returning to Mercury after each individual system, since we are ourselves different after each individual process of analysis and synthesis.

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.

Emanation in Qabbalah versus Mathesis

So, in the meantime of developing the Tetractys of Life and starting to use more Pythagorean and classical Neoplatonic ideas in my studies of the occult, I think I’ve finally found a word that accurately captures what I want to name this system.  The broader system in Hermeticism and Western occulture is qabbalah (or Jewish kabbalah or Christian cabala, to use different spellings to indicate different traditions).  All these words have the same root in Hebrew: קַבָּלָה‎, meaning “tradition” or “reception”.  I’ve been using a Greek transcription of this word, καμπαλα or “kampala”, to describe my Pythagorean-Neoplatonic system, but this is still basically the same word, and I’m developing it to a point where it doesn’t really fit into the qabbalistic scheme anymore.  After thinking about the thing I’m developing and going through some Greek dictionaries, I think I’ve found a word to name this new system of occult thought: μαθησις, or “mathēsis”, which means “the act of learning” or “obtaining knowledge”.  This word is related to our word “mathematic“, which itself comes from Greek meaning “scientific, disposed to learn”, itself from Greek μαθημα, or “that which is learnt”.  While this Tetractys of Life and everything are things to be learned, sure, they’re all tools to learn more.  Hence, the broader system I want to call is appropriately mathēsis, a term that’s been used before in the pre-modern and modern Western world by philosophers such as Descartes and Leibniz to describe a hypothetical universal science modeled on mathematics.  And, well, since Pythagoras established that everything is number and (in our modern sense) mathematical, this isn’t too bad a term.  To that end, I’ve gone through and labeled all the Towards a Greek Kabbalah posts (which are their own blog project in their own right) under the category of mathesis.

Alright, so, labels and terms are out of the way.  I want to talk about emanation in mathēsis and how it compares to qabbalah, because there’s a critical difference between the two that really should be understood.  While I originally set out to develop a qabbalah-like system based on Greek mathematical and grammatomantic principles that essentially shared the same ideas, I ended up with a much different beast of a cosmology than I had anticipated.  For instance, consider the idea of emanationism, where successively more complex forms of existence and reality develop or flow forth both within and from a higher and more primitive source.  This is distinct from creationism, where things are made as they are without successive steps by an external creator, and from materialism, where things come about from other things without a metaphysical origin.  The idea of emanationism is replete throughout many forms of the occult, not least in both Pythagorean, Neoplatonic, and mystic Jewish thought.  It can be seen in both the kabbalistic Tree of Life as well as in this new mathetic Tetractys of Life, but not in the same way.

For instance, consider the Tree of Life in qabbalah.  There are ten sephiroth, each assigned a particular number from 1 to 10 and descending from the top to the bottom.  Each sephirah represents a different attribute or aspect of the one God, or a different way God expresses his will.  There exists a particular set of paths, collectively termed the Lightning Bolt Path, that hits each sphere in sequence from Kether to Chokmah to Binah all the way down to Malkuth.  This describes the emanation of the cosmos from God in successive forms, ultimately culminating in our existence down here on Earth.  This also ties in (or perhaps founded?) the notion of an Idea of God descending through the many spheres of Heaven, hitting each planet in turn, building up more form and density until it hit our lowest Earth-plane, finally becoming a manifest Thing.  There is one Source and one Goal, clearly marked out with clearly defined stages in between.

The Tetractys of Life also describes emanation, but not in the same way.  Like the Tree of Life, there are ten spheres or units, each representing an aspect of creation in a different manner.  Like the Tree of Life, there is one Monad at the top, the undifferentiated and divinely simple source of all things.  Like the Tree of Life, the Tetractys of Life describes an emanatory or development of creation from the top down.  However, that’s where the similarities end.  Instead of having each sphere on the Tetractys represent a different emanation or stage in existence, the Tetractys shows emanation based on the rank of the Tetractys; instead of going One-Two-Three-…-Ten, it goes Monad-Dyad-Triad-Tetrad.  In other words, there are only four stages of emanation in the Tetractys compared to the ten in the Tree.  The emanatory dyadic principles of Light and Dark  occur simultaneously and as two parts of a whole, not in a sequence.  They are different, but they are in a kind of super-alchemical marriage as One, since they both come from One.  Likewise, the emanatory triadic reagents of Salt, Mercury, and Sulfur occur simultaneously as a result of the marriage between Light and Dark, as do the emanatory tetradic substances of the four elements from the harmony of the three reagents.  And, from these four substances, all of material creation is made.

Why is this significant?  Because we have different notions of a “starting point” when working with the Tree and with the Tetractys.  With the Tree, we can all safely agree that we’re down here in the tenth sephirah of Malkuth, and it’s our job to rise through the sephiroth in the reverse order compared to how we got here.  With the Tetractys, however, there is no single starting point; our starting point is below the Tetractys, in the unnumbered and implied pentad of all the things that exist, the symbol of which is the pentagram and which represents the Divine Proportion (φ).  In that sense, our starting point is below the Tetrad working within as a Pentad, itself not represented on the Tetractys.  The Tetractys is the source of life but is not itself life in the same sense that the Monad is the source of existence but is itself neither existence nor nonexistence.  We must first understand how the Pentad comes forth from the Tetrad, then the Tetrad from the Triad, then so forth back to the Monad.

tetractys_pentad

So, rather than thinking of each of the ten spheres in the Tetractys as a separate stage of emanation, it’s more proper to understand mathetic emanation as occurring in four stages (divine simplicity, differentiation, system, embodiment) compared to the qabbalistic ten.  And, within each stage, there are different forces at work that represent how that emanation of the cosmos takes place.  While the Tetractys of Life illustrates the different types of forces within each rank of the Tetractys, this is only an ideal representation, much as the Bohr representation of atoms is convenient to understand ideal spatial relationships between an atom’s nucleus and electrons, but in reality the electrons move in indeterminate electron clouds where either the speed or location of a subatomic particle may be known but not both at the same time.  In other words, Light and Dark take place at the same time and interchangeably within the Dyad, as do the three reagents within the Triad, as do the four elements within the Tetrad.  We may find it easy to focus on one element, reagent, or principle at the same time, but this is a hyperfocused and ultimately false distinction that isn’t true on a fundamental level.  That said, on a fundamental level, everything is already part of One and is One, much as the distinction between the sephiroth in qabbalah is only apparent from the point of view of the Created and not of the Creator.

So why am I clarifying the notion of emanation when studying mathesis in using the Tetractys of Life?  Because it requires a different sort of understanding of the cosmos than what we’re used to thinking based on the Tree of Life in qabbalah, which is arguably the starting point for much of Western occultism today.  Why does this matter?  Because I ran into the practical problem of trying to assign numbers from 1 to 10 to each of the spheres in the Tetractys.  I wanted to link the spheres on the Tetractys to the sephiroth in some way, or find some sort of numerical sequence for the forces in the Tetractys, so I could link these spheres to other types of magical technology and techniques.  For instance, consider magic squares, the qameas of the planets.  If the planet Saturn is corresponded to the sephirah of Binah, and Binah’s number in the order of emanation is three, then three is the qabbalistic number of Saturn.  Thus, the magic square or qamea of Saturn is a 3 × 3 grid of numbers from 1 to 9 (or 3²), upon which we can plot qabbalistic names and sigils of various spirits and concepts related to the sphere of Saturn.  I personally like the use of magic squares in magic, and I wanted to find a particular way to develop a set of magic squares to each of the forces in the Tetractys of Life.  However, after a good amount of reflection and late-night thinking, I couldn’t find a way to suitably number the spheres on the Tetractys outside their non-sequential lambdoma numbering.  Because I can’t (yet?) think of a way to sequentially number the spheres in the Tetractys, this makes it cut off from systems such as qabbalah and much of qabbalah-influenced magical tech; at the same time, trying to force on a numbering system like this seems ill-advised, like trying to square the circle when the two cannot be done except at a higher level.

In this case, if we have a collection of points that themselves are unordered, are we up Styx creek without a paddle?  Not at all.  The use of algebra and arithmetic weren’t the preferred means of mathematics back in Pythagorean thought, but rather geometry.  And, understanding the four ranks of the Tetractys to refer to geometric forms, we have a 0-dimensional figure as the Monad (a single point), a 1-dimensional figure as the Dyad (two points form a line), a 2-dimensional figure as the Triad (three points form a plane or a triangle), and a 3-dimensional figure as the Tetrad (four points form a solid or a tetrahedron).  Geometry, then, might be a better route to go to understand the various forces represented within each rank of the Tetractys than number squares or knocking on an altar a particular number of times.  The Tetractys is slowly but surely showing me a new way to understand the cosmos and how to apply myself within it and to it both theurgically and thaumaturgically; what new tech it’ll lead me to, I don’t yet know, but I’m excited to find out.