Realizing that the tetractys is pretty much the glyph I want to use for kampala wasn’t an immediate realization. I know I wanted something like the Tree of Life from kabbalah with its ten sephiroth so nicely arranged, but of course I didn’t want to appropriate it either without making sure it was what I needed. However, I recalled that the tetractys was another glyph of ten units that could easily describe the creation of the world, so I immediately switched to that. One part of the problem was solved; the next was how to arrange the emanations of creation on the tetractys itself. If the tetractys is a combination of ten units arranged into four rows, then there should be a way to describe the emanation of creation to each unit on the tetractys in an ordered way. Since the system of emanation I’m most familiar with involves the ten heavens (Earth, Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, Stars, and the Source-God-Good), I decided to try my hand at arranging them in a way similar to how they’re arranged on the Tree of Life, in a top down and ordered manner. Thus, if we assign the spheres of the cosmos to the units of the tetractys starting at the top and going down, left-to-right within a row, we get an image like this:
Simple and straightforward. However, there are significant problems with this. Sure, God is at the top, which fits the nature of God as Monad or Unity. The sphere of the fixed stars and that of Saturn are directly below, which is much like the positioning of their respective sephiroth of Chokmah and Binah on the Tree of Life. Beyond that, though, things get weird; the Sun is off to one side instead of in the center where it probably should be in this system, and Earth is way over in the bottom right corner of the tetractys. Honestly, nothing on this setup looked appealing to me, especially since it conflicted with other planetary relationships I had already known and studied, or even allowed for the possibility of. This was too bizarre to feel “right” in any sense.
Okay, so maybe that wasn’t the method I should’ve used. Let’s try another way, starting from a different perspective. Part of the tetractys’ appeal was due to its mathematical applications, one of which is known as Plato’s Lambda, or the Lambdoma, so named because it takes the form of a lambda (Λ). In Plato’s Timaeus, which is his treatise on Pythagorean cosmology, he describes the creation of the cosmos by a Demiurge by taking “strips” of creation and applying two mathematical sequences to it, the geometrical series based on 2 and the geometrical series based on 3.
If we start at 1 at the top and go left to 2, we keep doubling the next number in the sequence, so 1 becomes 2, 2 becomes 4, and 4 becomes 8. If we start at 1 at the top and go right to 3, we keep tripling the next number in the sequence, so 1 becomes 3, 3 becomes 9, and 9 becomes 27. The left side is a sequence of even numbers, and the right a sequence of odd numbers. The Pythagoreans considered even numbers female or passive and odd numbers male or active, which we can still see vestiges of in modern numerology (cf. the Tarot, where trump I is the Magician and II the High Priestess). However, 1 was neither odd nor even, so 2 was the first even number and 3 the first odd number, hence their use in starting their progressions. If we fill in the blanks, so to speak, in the Lambdoma with extra numbers based on the Tetractys, where a new number is the product of the two numbers above it, we get 6 in the third row (being the product of 2 × 3), and 12 and 18 in the fourth row (2 × 6 and 6 × 3, respectively):
The original lambdoma has seven numbers: 1, 2, 3, 4, 9, 8, and 27. Three of these are odd, three are even, and one is neither odd nor even. The number seven recalls the seven planets, and I’ve seen a system of dividing the planets where three are in one category, three are in another, and one is in neither group. This is called sect, which refers to whether a planet is more powerful in the sky or under the earth either in the daytime or at nighttime. This is a type of polarity much like femininity or masculinity of a planet, and the planets are divided into three groups like this:
- Diurnal: Sun, Jupiter, Saturn
- Nocturnal: Moon, Venus, Mars
- Hermaphroditic: Mercury
If diurnality is equitable to masculinity and nocturnality to femininity, then diurnal planets can be ascribed to odd numbers and nocturnal planets to even numbers. The Sun and Moon are the most diurnal and nocturnal, respectively, with Jupiter and Venus following them, and Saturn and Mars following them. Mercury, being neither diurnal nor nocturnal, adapts to either; it can be given a value of 1 in the lambdoma. Thus, if we use the original lambdoma to plot the seven planets, we get a figure like this:
However, that still leaves three slots in the tetractys to be filled in, and having everything come from Mercury at the top isn’t quite true, especially when Mercury can obtain a sect depending on whether it rises just before or just after the Sun. Thus, if we move Mercury down to where 6 is in the completed lambdoma (the combination of an even and an odd number, suitable for Mercury), we have an empty slot at the top for the Monad. This leaves two more slots at the bottom, which can be reserved for the Earth in slot 12 (2 × 2 × 3, more female than male) and the Stars in slot 18 (2 × 3 × 3, more male than female):
While this arrangement makes sense, having the Earth and Stars in the same row as Saturn and Mars still didn’t feel right, and trying to draw connections between everything felt wrong. Mercury being in the middle, being the communicator of the gods and a middling connecting force, felt right, as did the Moon on the left side and Sun on the right, but this doesn’t agree with the standard emanationist models I’m used to. After all, shouldn’t the sphere of the fixed stars, the ultimate barrier between this world and God, be higher than the Sun and Moon? Should the Sun and Moon, luminaries though they might be, be representative of the two principles of Duality? I was stumped, honestly. Further, Plato in the Timaeus groups the planets into two groups based on their relative speed: three that move roughly together (Sun, Venus, Mercury) and four that move with unequal motion to the first three and amongst themselves (Moon, Mars, Jupiter, Saturn). This was in the same section as the use of the lambdoma and mathematical progressions of 2 and 3, so surely a better grouping could be made that would exemplify this.
It was at this point that I started getting a headache and an odd itch on my back, and not just any itch, but something that didn’t feel too physical. I recalled what I had on my back: the Golden Chain of Homer, a tattoo that symbolically describes Man’s creation from and evolution to God using alchemy. It was when I realized that the Chain is a sequence of ten stages that I facepalmed and reinspected this tattoo I got a while back and thought it so important to be inscribed onto my mortal coil. I reread the book available to me on the Golden Chain, and that’s when I found this description of principles:
Would you look at that? It’s an organization of different alchemical principles: four elements, three reagents, two principles, and one source. Arranged in a one-two-three-four pattern, a tetractys. Who’d’ve thunk it, really. The realization that my tattoo was a key to the system I’m working on gave me a sort of nauseating tremble, but that’s revelation for you, I suppose.
So, maybe my trying to base a Tetractys of Life on planetary principles right off the bat was misguided; perhaps I should start from here, since this pretty much points out the path ahead. If, instead of using planetary principles to describe sequential emanation through the tetractys, I use the notion of different stages of development in different levels of manifestation, perhaps a more reasonable tetractys layout could be found. The diagram above needed some tweaking, however; Nitrum (Male, Light) and Fire were on the left side, while Salt (Female, Darkness) and Earth were on the right, and the Lambdoma has the two sides switched so that the left side was feminine and the right side masculine. Further, Mercury was on the male side when I feel it would more properly be in the middle, since (to me) Sulfur speaks more forcefully than Mercury, and mercury more than Salt. I’ve also seen other diagrams presenting Mercury to be completely feminine and Salt to be in the middle, so it would seem like these principles are still up for debate in alchemical terminology. To my mind and for my analysis, I’m establishing Mercury as between the purely active reagent and purely passive reagent. So, taking these alchemical principles together, I developed the following alchemical tetractys:
Note that in this diagram, the Sun symbol stands for Light, Activity, or Masculinity, and the Moon symbol stands for Darkness, Passivity, or Femininity, not their corresponding planets. Mercury stands for the alchemical reagent of Mercury, but we’ll get to more on that in a bit.
Okay, so now it might be more possible to assign the planetary spheres of the cosmos to the tetractys based on their corresponding alchemical forces. Obviously, the Monad would stay the Monad, and alchemical Mercury would likely best remain planetary Mercury. I didn’t like having the Sun and Moon remain representatives of the two principles of Light and Dark, but instead decided that they’d fit better as the alchemical reagents of Sulfur and Salt, respectively. In this way, we have the most Light of the planets, the most Dark of the planets, and the hermaphroditic Median of the planets, all together in the same row. This left six spheres left: the four Planets, Earth (or Mundus, to differentiate it from the element Earth), and the Stars. To me, having Mundus and the Stars represent the principles of Darkness and Light, or Female and Male, made more sense than using the Moon and the Sun; there’d be the lowest and passive receptacle of creation, compared to the highest and most ethereal initiator of creation. Thus, Mundus and Stars became the two principles at top.
This left the last four nonluminary planets to be given to the four elements. Saturn, being the darkest and coldest of the planets, seems fitting to be the natural progression from the Moon on the left (more feminine), so Saturn would be attributed to the element Earth. Likewise, Mars would be given to Fire, since Mars is the hottest of the planets and befits a more masculine progression from the Sun. This leaves Venus and Jupiter, the former of which is cooler than Jupiter according to Agrippa (book I, chapter 26 and chapter 28), even though they’re both airy planets (book II, chapter 7). Assigning Jupiter, a diurnal and masculine planet, and Venus, a nocturnal and feminine planet, to either Water or Air was something of a sticking point for me, since I could argue for either arrangement with a variety of reasons. I originally put Venus as Air to be paired with Mars as Fire, and likewise gave Jupiter to Water to be paired with Saturn as Earth. However, I realized that it’d be a better arrangement to have Venus as Water and Jupiter as Air, since although they’re equally moist in elemental terms, Venus is cooler than Jupiter, and since Venus is nocturnal, it had more in common with the Moon than the Sun; the converse case applied with diurnal Jupiter and the Sun.
So, in the end, after assigning the spheres of the cosmos to the tetractys based on alchemical principles, the Tetractys of Life is starting to have actual form:
(Note that, in this diagram, the alchemical representation of a sphere is in the upper-right half, and the planetary representation is in the lower-left half. The Mercury symbol, however, stands for both alchemical and planetary Mercury, and “Monad” represents, well, the Monad. The pentagram represents the sphere of the fixed stars, because typing takes up too much space, like my blog.)
It’s an interesting layout, but I like it. It represents another view of emanation that isn’t necessarily sequential but, in a sense, simultaneous; in the beginning, there is only God (Monad), but as soon as there’s Differentiation (Heaven and Mundus), there’s Process (Sulfur, Mercury, Salt) as well as Substance (Fire, Air, Water, Earth). Each of these forces can be related to a planetary sphere, but it’s not in a sequential order as in the Tree of Life. For instance, in kabbalah, the Lightning Bolt Path descends from God to the Fixed Stars to Saturn to Jupiter all the way down to Earth. On this tetractys, the Monad could descend into the Fixed Stars, but then into the Moon, Mercury, Sun, or maybe even Saturn or Jupiter, or even directly to Earth. It’s hard to assign a type of sequence to this tetractys, and indeed, even considering all possible paths that could be drawn on this setup between the spheres, it’d be impossible to draw a path that connects all the spheres in a direct sequence without passing through other spheres disrupting the order. Perhaps that’s a good thing, depending on the paths we assign and take and what the paths themselves mean.
Speaking of sequences, is there a way to sequentially number the spheres on the tetractys? In a simple way of ordering them from 1 to 10, not really; for convenience, I number them from top to bottom, left to right, such that the Monad is 1, Mundus is 2, Stars is 3, and so forth to Mars being 10. It makes more sense to use the Lambdoma numbering, personally, which is what I plan to base further exegesis and analysis on in the future, but for now, we’ll refer to the spheres on the tetractys by their alchemical or planetary assignment.
So, with all this at our fingertips and our disposal, what can we meditate on now? Plenty more, as if we needed more (we always do). Between the relationships that the tetractys indicates to all other things in existence, or the process of coming into existence, we now also have processes and principles that guide our meditations. We have relationships between principles, reagents, and elements with the planets, as well as with notions of masculinity/activity/light and femininity/passivity/darkness as well as with number and mathematics. Most importantly, we now have destinations between which we can start creating paths, and assigning to them the 24 letters of the Greek alphabet to tie those into our process of emanation and creation. We’ll talk about paths on the Tetractys of Life next.