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.
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.