Data, Information, Knowledge

As an initiate in La Regla de Ocha Lukumi (a.k.a. Santeria), I’m trying to wrap my head around all the different things we do and the proper way to do them.  The most straightforward method for this is to simply show up to ceremonies, watch what’s done, listen to what’s said or sung, and follow along; in this manner, I learn the things we do, how to do them, and why we do them.  I learn primarily from my godfather when I’m in a one-on-one situation, and under his watch and guidance more generally when I’m in the broader community.  This is the simplest way for me to learn, but even then, there are so many complications in this alone.  For one, since we’re all learning, there are things my elders will occasionally shift when they find a better or more proper way to do things, so occasionally the things they show or tell me can change over time, which isn’t even bringing up the matter of things that I can’t formally know yet, based on my own experience or initiations within the religion, without which I formally can’t know about certain things without having undergone the mysteries thereof.  For another, there’s the issue of different houses within a lineage with their small variances, and different lineages within the religion with their larger ones, which becomes more evident when we have people from other communities visiting and participating in our ceremonies or vice versa.  There’s also the issue of the “stuff out there”, books and blogs and personal notes of other people in the religion, which really should be vetted thoroughly before even being given an ounce of credence since some of it may not apply to us and some of which may just be outright wrong.

Trying to take all that in and form a useful body of knowledge that I can use is…daunting, to say the least.  Thank God and the gods for my godfather, but even by his own admission, it can be bewildering and confusing even at the best of times.

The situation is a little different in Western occulture, but many of the same issues still apply.  Consider all the grimoires we have available to us nowadays from the medieval and Renaissance Solomonic traditions; heck, just consider the books Gordon over at Rune Soup goes over in in his grimoire course.  Each book, while still belonging more-or-less to the same overall tradition of magical study, has its own variations of practice, theory, and internal logic; some things are clear inventions that start with one grimoire and continue forward form there, while other things that were present from the beginning slowly fade out over time.  Then, based on all those texts, consider our modern (largely derivative) texts and how those vary both in philosophy and praxis due to the time and location wherein they were written.  Then, for an additional twist, throw in everybody’s UPG that they love to make dogmatic Truth far more often than is good for them (or us).  If one were to study magic, then, how would you go about reconciling all these differences?  Between all the details and variations, between all the similarities and commonalities, where does one even begin to make coherence out of the mess?

Let’s talk about how we come across such facts and tidbits in the world we live in.  I like to draw a threefold distinction here: data, information, and knowledge.  All have their role to play, but all are slightly different in terms of delivery and scope:

  • Data is a Latin word literally meaning “things that are given” (where, yes, the singular of data is datum, but I won’t fault you for using data as a singular noun in English).  Literally anything that exists or that is said, witnessed, or perceived is data.  The world is full of data, but much of it doesn’t make sense or even matter.  Literally the entire world, if you’re receptive to it all, is full of data.  Data is, in many ways, boring and meaningless without some sort of structure or methodology to process it by.  If data is a set of raw materials, then the form of raw materials produces information.
  • Information is, in the words of one of my old computer science professors that stuck with me, “data that makes a difference”.  Differences can only be shown when you have some sort of rule, method, structure, or form to pit two pieces of data against each other with.  Information is another Latin derivative meaning “to educate”, but more literally meaning “to give form to”.  Information is a structure of data that literally informs (builds within) a body of knowledge.
  • Knowledge is synthesized, coherent structures of information.  When we “know” something, we have a context to put information within, and we can link it to other bodies of information to see even bigger trends that connect both within and outside a single system of information.

To use an organic metaphor, consider an animal body, which is composed of organs, which are composed of cells, which are composed of chemicals.  Those individual chemicals at the lowest level are data, and they can occur anywhere both within an animal body and outside them.  When arranged in certain structures (such as nucleotides in a strand of DNA), you start to get cells.  When the cells are organized together according to function and purpose, you get organs.  When your organs are put together in a coherent, symbiotic way, you get a complete animal.  Similarly, our minds are composed of different bodies of knowledge, which are themselves composed of structures of information, which are themselves composed of data.  The data are arranged in certain ways to form information; the information are arranged and structured in certain ways to form knowledge; different bodies of knowledge are linked together to form our intelligible minds.

To give a more concrete example, consider a school of students.  At testing time, each test score of each student gives us a single point of data.  We can point and say that we know that Tom’s score is 74 and Abby’s score is 95, which is nice and all, but individual points of data don’t really mean anything.  We can see that 95 is a higher score than 74, but more than that, we can’t say anything unless we start looking at a broader picture, a structure to fit these data points within.  Consider Tom’s trends of scores across the school year; while 74 may not seem like a particularly great score, if we see that that’s his highest score across the entire year, then we can say that Tom is getting better, while Abby might be having an off day with 95 being her lowest score across the whole year.  We can evaluate how well Tom and Abby are doing amongst their peers by taking the average or median scores of their class, or the whole school, to see whether Tom’s situation is common compared to his classmates or whether he’s underperforming.  We can split the types of test up by subject and see whether these scores are indicative of Tom or Abby excelling in certain subjects but not others.  All these methods to analyze data produce information, which is “data that makes a difference”.  Going one step further, we can take how this given school performs on tests to our bodies of information about education methods generally that we might’ve picked up from our own classes, the psychology of children and adults in learning and performing on evaluations, how obscure the material is on the tests compared to both what is commonly known and what is specialized expertise in a given field, and other things that we’re informed of to come up with a general, broad-view understanding of the performance of the school and the context in which it takes place.  From that knowledge, we can make further judgments that we might not be able to make reliably when we’re focused only on one system of information, because we lack sufficient context or experience in order to extrapolate.

We need to understand two things about data, the things we encounter in the world:

  1. Any given data point is a fact on its own terms.  This doesn’t mean that every bit of data we have is true, but it is a fact in and of itself.  Consider this book on Santeria I have before me; it is a fact that the book says such-and-such about a particular orisha.  That is a data point, and it is a fact that the book says so.  Whether such a fact is true depends on other factors that cannot be validated on its own terms; if I have other bits of data that say the opposite of what the book says (such as what other santeros say, what my godfather says, what my own experience has validated, etc.), then I can consider the data in the book to be false, but the book still says it all the same.
  2. Any given data point may or may not be meaningful.  Consider a generator that produces random numbers or words.  No matter how you pick them, any given item from that random set is just that: random.  Nothing in it makes a particularly big difference either way, since any comparison you use between one item and another will be meaningless.  It’s only when data are structured together and compared can a trend be (possibly) produced; the data that produce that trend are meaningful, and the data that don’t may or may not be meaningful, depending on whether it’s an “exception that proves the rule”, a once-off exception that can be explained contextually, or another random result that doesn’t have any bearing one way or another on the trend.  When we talk about people having “bullshit thresholds”, this is what we mean: it’s a boundary above which we can accept data as meaningful, and below which we can consider it to be no better than random noise.

It’s the easiest thing in the world to amass a large set of data, but it’s correlating that data into information that’s difficult.  In order to produce information, we need some sort of guidance to arrange, compare, and distinguish the data we have available to us.  For this, we use models, structures of data, sets of axioms or rules, and reliable methods of comparisons.  While this sounds numerical and mathematical, it doesn’t necessarily have to be.  For me in my education in Santeria, I have the religious, philosophical, and practical models imparted to my godfather which he’s expanded on in his own way, which he has passed down onto me.  For instance, if a particular santero says X and Y (two pieces of data), and the model my godfather has established allows for X and not Y, then I can accept X into my information model but not Y.  By understanding the model, I can often see why X is allowed and not Y, and if I can’t understand the model’s rules well enough to account for those, then there’s something my godfather hasn’t yet told me or there’s some other limitation that hasn’t yet been conceived of yet in the model, whether it’s arbitrary or not.  For a run-of-the-mill Solomonic magician, those models might be produced by a combination of analyzing the commonalities between grimoires over the centuries and the accounts of their uses from other magicians, forming a set of rules of “here’s what’s essential, here’s the expected results, here’s what can be added to good effect, here’s what can be removed without harming the overall results, etc.”; based on this understanding of the grimoires, one can perform a ritual and see how the methods of the ritual impacted the result, what the result was, whether the result can be trusted, and so forth.

Knowledge is a little more difficult to sift through, because it’s more abstract than a single structure of information.  Information structures, moreover, tend to be coherent and consistent within themselves; they each have their own sets of rules that permit some data but not others.  However, when you have more than one structure of information, it can happen that they each have a set of rules that can conflict with other systems of information.  One example I can pick out in my own experience is the role of the planets in my life.  In the system of information I have regarding astrology and Western magic, the planets (and the objects of the celestial world generally) are paramount in effecting certain things in this world.  In Santeria, on the other hand, so far as I can discern (and that’s a big disclaimer!), there’s no such corollary to that; I haven’t yet found any astrological component to the religion, besides some associations of the Sun and the Moon and a few star-based images, but there’s no role for the planets, aspects, houses, signs, and so forth.  Astrology, simply put, doesn’t matter or even have a place in Santeria.  So, then, if in one system of information I can say that Mercury retrograde is a poor time to do ritual, but in another it’s a moot point because “wtf even is Mercury or a retrograde”, what should I do?  This is an example of a conflict between different systems of information within an overall broader body of knowledge.

According to Gödel’s incompleteness theorem, you can have a system of understanding based on rules that can be either consistent (anything that is provable by the system is true) or complete (anything that is true is provable by the system), but not both.  If you’re consistent, then you must be incomplete, where whatever you can prove is true, but there are true things that cannot be proved by the system itself.  If, on the other hand, you’re complete, then you must therefore be inconsistent, where the system can prove everything that is true, but will also necessarily prove things that are not true.  I find this a useful model for understanding how things work.  Any given system of information, for us, is almost always going to be consistent, and therefore incomplete.  Thus, we rely on other systems of information that are likewise consistent and incomplete to fill in the gaps left by any one system.  By linking them together by means of context, comparison, metaphor, and allusion, we can have an overall more-or-less (we hope) complete system of knowledge that is based on multiple systems of information.  Just like we have to pick and choose the data we use to create information, we have to sometimes limit ourselves to what information we choose to link together in order to form knowledge.

Eventually, our end goal should be having knowledge.  Data is easy to get, and information is almost as easy, but neither are entirely usable by a complete being such as ourselves.  It is knowledge that declares and defines the contexts of information, but how do we go about getting knowledge?  It’s a lifelong process and largely automatic for human beings, and different traditions and philosophies have written endlessly about this, so it’s probably best for me to not wade into that set of eternal debates here.  Still, there are a few questions that you might want to consider:

  • What are my models for understanding data as information?
  • From where do my information models come from?
  • How do my experiences relate to what I already know, both as information and as knowledge?
  • How do I evaluate data as meaningful for a given system of information?
  • How can I explain data that do not fit a system of information?
  • How can I refine my models of information to weed out more untrue pieces of data while permitting more true pieces?
  • How can I link one system of information to another?
  • What sort of knowledge can I get by linking one system of information to another?
  • In what context should I analyze a system of information as a whole?
  • What system of information is best to take in new data to produce useful knowledge?

I’ve never been one for the whole “nothing is true, everything is permitted” thing.  There are indeed things that are true, if not generally for all people than specifically for individual people or contexts, and those are useful in and of themselves.  It’s the problem of determining the false chaff from the true wheat that’s the problem, and the rules for that can fluctuate at any given moment depending on what system of information is most useful at that moment.  Plus, when dealing with a number of occultists, it’s hard to keep track of who’s reliably honest and useful in their results, who’s good but crazy, and who just exaggerates for the sake of self-aggrandizement; I know I’ve had that problem in figuring out where to set my bullshit thresholds with certain people, and I’m pretty certain most of my readers have, as well.  We filter data through our bullshit thresholds all the time, but it’s always worthwhile to recalibrate that threshold once in a while and analyze why it’s set where it is for us, and whether it’s too high or too low for our own needs.

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


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.


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:


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.

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:


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).


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.

Pondering the Dyad

I think that, of all the numbers I’ve encountered in the occult, and especially lately with my meditations on the Tetractys, the Dyad has to be the most confusing and hard to understand for me.  I mean, what’s so hard about it?  It’s just one more than the Monad, two, isn’t it?  Well…no.  Two Monads does not a Dyad make; two Monads are necessary, it’s true, but they are not sufficient to make the Dyad.  The Dyad is more than just a combination of two things, it’s a unity or union between two things.  You can’t analyze (take apart) the union without synthesizing (putting together) the ends, though it’s easy to see the two ends as separate and distinct from each other and, crucially though incorrectly, understand them as whole entities in and of themselves.  But consider:

  • What is music?  Music is a sequence of notes, yes?  But it’s also the rhythm, the timing, and the harmony produced between successive or concurrent notes that produces the music.  Music is not a just a sequence of notes, but it’s something more than that.
  • What is a fight?  A fight is the interaction between two fighters, yes?  But it’s also the flow, the connection, the respect or lack thereof between them where the fight itself takes place.  An individual fighter fights nobody on their own.
  • What is a sephirah?  A sephirah is an emanation of God that reflects one of His many attributes, yes?  But it’s also the connection and flow from God.  Without a connection, a sephirah has no means to be filled with God and becomes a husk.
  • What is love?  Love is the relationship and harmony between two individuals, yes?  But it’s not possible to have love without something to love, nor is it possible to love someone without reciprocity or knowledge and having love both around and in the recipient.  Without the connection, love devolves into lust or limerence.

The Dyad represents something that is not itself able to exist; it requires two, and the Dyad is the representation of the two co-existing.  That union is the Unit, the Monad present in a lower register, but the Monad is no longer in existence as soon as it makes existence, because then there is something that exists as Creator and something that exists as Creature.  The emptiness (and I’m using this in a Buddhist “interexistence” or “dependant existence” sense) that is formed between the two monads in the Dyad is the true Dyad, without which you just have a collection of monads.  I mean, consider the human body: the human body is a collection of organs, bones, and humours; going deeper, it’s a collection of molecules, atoms, and subatomic particles.  Yes, we are all just a collection of these things, but clearly there’s more to it than that to produce a cohesive unit, a complete whole.

Trying to comprehend the numbers on the Tetractys is different than simply counting how many spheres are in a rank, or the number One through Ten each dot represents.  If you do that, you’re just understanding each number as a collection of monads when there’s so much at work within each number.  It’s like, if you study energy work, if all you study is the seven chakras of the body, you neglect the fact that energy cycles throughout the body; focusing on the chakras alone treats the body as just the seven chakras when the body is a collection of major and minor chakras and all the medians and channels that connect them all.  Having a blockage of energy in the lower leg cannot itself be healed by focusing on any one of the chakras, but if you’re not trained to focus on the body holistically, then you aren’t going to be able to make much of an impact on the body.

I’ve noticed parallels between my lack of knowledge on the Dyad and one of the issues I currently have in learning aikido.  In my martial art, I’m starting to get the hang of the actual moves themselves, how to move my one-point around, how to roll the arm for a pin, how to step properly to allow myself enough safe space in attacking or being attacked.  Still, none of this is useful if I can’t apply the moves in practice against an opponent, and that’s where the matter of timing and connection comes in.  I can sense my own ki, and I can sense the ki of my opponent, but connecting the two together when the opponent is approaching to grab me is an issue.  Timing, the flow and blending of myself and the opponent, is something I’m still having to work on and it’s not clicking yet.  It’s not a matter of counting seconds or recognizing a limit of distance after which I can move my own body; I have to blend with the motions and ki of my opponent in order to make the technique work.  This timing, this connection between me and the other, is the “presence” of the Dyad in aikido; there is no such thing as attacker and attackee if I can’t properly engage or be engaged in attack.  It is only through the fluid and completely connected actions of myself and the other that aikido works, without which it’s just two people trying to put each other into pins and joint locks fruitlessly.

In the Tetractys, the rank of the Dyad is the first time we see a connection formed between two Monads.  It is the first time we have the opportunity for comparison or change between two otherwise indistinct and undifferentiated Monads; by the power of this connection, we can say that “this is and that isn’t” or “this changes into that”.  None of this is possible in the rank of the Monad, since there is by definition only ever One thing to compare or be compared to, and comparing something to itself is a tautology that makes anything and nothing true.  I mean, even the figure of the Monad itself, the circle with a point in its center, cannot itself be made by one thing alone.  It was made by an old-style geometer’s compass, making use of both its legs; one to stabilize it in the center, and one to give form around it.  With only one leg, it could only produce one point, but with two, it can make a shape, a circle, a neverending line enclosing an area.  It gives definition and the first possible comparison: what is in the circle and what is outside.  A point cannot be meaningfully compared to any other point without other notions of length or measure, but with a circle or a line (either being made from a connection between two points) we can do just that.

Aikido, at least in my style of Shin-Shin Toitsu Aikido (Aikido with Mind and Body Unified), there’re four principles of mind and body unification and five for the practice of aikido itself.  The last principle of the first set and the first principle of the last set are the same: “ki is extending”, meaning that ki flows constantly through ourselves and through the universe.  If we get in line with the flow of ki, aikido works; if we try to force things, aikido doesn’t work.  After this, to make aikido work, you need to know your opponent’s mind and respect their own flow of ki; you need to understand what they’re going to do and how they’re going to do it, and act accordingly to respect their actions and make them go where you want them to go.  If you know how to move around their ki, you know how they’re going to move their ki, so you know their mind; if you know their mind, you’re connected with them and letting ki extend properly.  This is the essence of timing, and is moreover the essence of all connections: knowledge.  Dyad is knowledge.

Even in the Hermetic text of the Poemander, it makes sense.  In the beginning, there was only Nous, the Mind, single and simple.  Literally everything only began when the Nous produced the Logos, the Word.  The Word is Thought, which is produced in the Mind.  Prior to the Logos (if there can conceivably be a “prior” in a world that does not experience time), there was only Mind without Thought.  Once Mind produces Thought, the Mind has something to think about, something other.  Even if the Logos is the Nous, the two are still separate and, thus, the Monad becomes a Dyad.  It is by relation can we think, can we ponder, can we consider, can we reflect, can we know.  Knowledge of the Other leads to a union, and in union things can happen.  In union we become a unity, reuniting the Logos with the Nous once more.  Music is the knowledge of  how different notes strung together form a pleasing melody, or when played at once form a harmony.  A fight is the knowledge of how two people interact to blend together in action.  A sephirah is the knowledge of how the light of God flows from the Source through different channels into yet other channels, transforming from some one thing raw into some one thing manifest.  Love is the knowledge of two hearts and minds acting as one.

Knowledge is the root of all action.  Knowledge is the root of all transformation.  Knowledge is the root of separation.  Knowledge is the key to union.  It’s the things to be known that change from situation to situation, but in knowledge all situations become different manifestations of the same cause.  I may not yet have a solid knowledge (heh) of the Dyad just yet, but at least something’s been opened.

49 Days of Definitions: Part X, Definition 7

This post is part of a series, “49 Days of Definitions”, discussing and explaining my thoughts and meditations on a set of aphorisms explaining crucial parts of Hermetic philosophy. These aphorisms, collectively titled the “Definitions from Hermes Trismegistus to Asclepius”, lay out the basics of Hermetic philosophy, the place of Man in the Cosmos, and all that stuff. It’s one of the first texts I studied as a Hermetic magician, and definitely what I would consider to be a foundational text. The Definitions consist of 49 short aphorisms broken down into ten sets, each of which is packed with knowledge both subtle and obvious, and each of which can be explained or expounded upon. While I don’t propose to offer the be-all end-all word on these Words, these might afford some people interested in the Definitions some food for thought, one aphorism per day.

Today, let’s discuss the forty-ninth and final definition, part X, number 7 of 7:

Therefore soul is an immortal essence, eternal, intellective, having, as an intellectual (thought), its reason endowed with Nous.  By understanding nature, it attracts to itself the intellect of (the planetary) harmony; then, once it is freed from this natural body, it remains alone with itself (and) is grieved, belonging only to itself in the intelligible world.  It rules on its reason.

After the last few definitions, which I feel were getting a little dramatic in how they were presenting the interaction between mortals on earth and immortals in heaven and how us who are Man should act, we wrap things up with this definition, which talks about the soul, which really is the centerpiece and focus of the entire Definitions.

First, we start of with a list of attributions of the soul, and here specifically that of Man.  It’s an essence, an underlying quality, which helps to define that which we are.  It is immortal; it does not die, nor is it born; while it may have been made by Nous (X.3), it was not generated in the same way bodies are (V.5).  The soul is eternal, which only confirms that it has always existed outside of time itself and experiences time only as much as God does or allows us to in our bodies; the soul truly is unbegotten, just as matter is (X.5).  It is intellective, able to think and reason with Nous, since that is what makes Man distinct from other creatures (IV.1, V.3).  Because of this, we can reason and understand the cosmos in a way that only God can, but it takes time, practice, skill, dedication, and perseverance to do so.  We can similarly choose to do none of those things and remain as, essentially, animals are; we can let our reason and minds stay catatonic and remain as animals do, or we can use reason just enough to get things done but in nowhere a complete way as we ought.

The way we understand things as we ought to is obtained by acting reasonably with the soul in the body (V.3).  This produces knowledge, true honest knowledge, which when obtained enough yields knowledge of everything: ourselves, all other things, and God itself (VII.5).  By understanding that which goes on around us, we understand everything as it works together: how bodies increase and decrease, by what means, and why they do this.  We understand the intelligible things that cannot be seen but we can still yet know, all the same.  However, we must continue to choose to do this, lest influences from the heavenly beings above sway us to do otherwise.  But even then, once we understand even a little bit of nature and the natural world, Man “attracts to itself the intellect of the planetary harmony”.  We begin to associate ourselves with the planets and other gods, and we begin to raise ourselves up into knowledge of systems far beyond that of the material plane of the earth.  As we attract ourselves to “the intellect of the planetary harmony”, we ascend into godhood, coming to know how all things work.  This is not the final stage of gnosis or perfection, but it’s certainly getting there.

After all, the soul stays in the body only as long as it needs to; then, once the soul reaches perfection, the soul leaves the body to die (VI.2, VI.3).  At this point, the soul is “freed from this natural body”, and, without a body, the soul becomes inert once more as it was beforehand.  Thus, it “remains alone with itself”, but it is also “grieved”.  After all, it has all the knowledge of the cosmos and of God at this point, yet it sheds its old skin, its old world, everything it had grown up knowing, and “grieves”.  This is an interesting point, since why should we grieve?  Sadness, after all, is an illness of the soul; without anything to expose itself to, how can the soul obtain anything?  After all, it remains “belonging only to itself in the intelligible world”.  It is without body, and it is now independent as a truly immortal being, a god, free from the sensible world in the infinity of God.  It rules, on its own and by its own, according to “its reason”, it’s Logos.

So why should there be grief?  All this work and perfection and godhood for…grief?  It doesn’t make much sense, I’ll agree, so there’s something missing, I’d think.  Jean-Pierre Mahé notes that the text is not only incomplete at this point, but that the rest of the text in several versions of the Definitions is spurious and an add-in from some other text dealing with astrological influences.  It’s kind of a let-down for the final definition, but let’s assume that the text is complete, and that this is the final and definitory definition of them all.  What follows is pretty much my interpretation, but this is going to be less logical and less based on the rest of the text than the other definitions.

The perfect soul, freed from the body,  rules on its reason in the intelligible world of God.  It, already possessing soul-Nous (VIII.4), has now also obtained divine Nous in its entirety, and thus becomes one with the knowledge of God and, thus, God.  By knowing all the beings, by knowing the self, by knowing Man, by knowing God, the soul becomes everywhere God is.  By ruling on its reason, which is now the Logos of the Nous, the soul acts according to the will of God without any external influence to sway it, and no unreasonable things to change its opinions or desires.  It belongs only to itself, but since itself is now effectively God, then it belongs to and exists within God perfectly in harmony.

The grief mentioned in this definition refers to it being separated from the material sensible world, which is odd when you consider the etymological root of “grief” to mean “weighty” in Latin.  The process of shedding the body for the soul may not be a very peaceful process, just as the process of birth for a human being is by no means easy or painless.  Perhaps, then, the grief of the soul is the final removal of its illnesses of sadness and joy, or the experiences it can no longer experience as a moving soul in a sensing and sensible body.  Yet, being joined in the knowledge of God, it already knows these things and experiences them intelligibly.  But it also knows that there are others that have not yet experienced this, and that they suffer in envy and jealousy and death when they don’t have to.  Why should they suffer?  God loves Man, after all, and Man loves God; if you saw a loved one in pain, you might also do what you could to relieve it.  As God, since that’s effectively what the soul is now, why wouldn’t you try to help out those who are suffering so that they wouldn’t need to suffer anymore?  If that’s what reason dictates, after all, why couldn’t you return to animate a new body, speak reasonably, act reasonably, lead others to act and speak reasonably, lead others to knowledge, and help perfect the souls of others that they too might be free?

Maybe this is an indication that the soul, ruling on its reason, may reason to return to the world; after all, since this soul is now God, we know that “God changes and turns into the form of man” for the sake of Man, so that others may become God as well.   In other words, to quote one of my favorite stories, perhaps the ending has not yet been written.