As many of my readers know, as well as those in Western occulture generally, correspondences are a big thing for us. Based on our shared philosophical and educational lineages, we like to say that “A is like B”; we understand that the light of the Sun is much like the heat of fire, which itself is like the luster of gold based on certain shared properties. In recognizing these shared properties, we immediately come to a system of symbols, where one thing can stand in for another, as well as to a system of harmonic relationships, where two things can be used compatibly with each other because they share the same ideas. On a large scale, we call this system of symbolism one of correspondence, where something corresponds to something else. This is often used in emanationist frameworks, where these correspondences cross levels of manifestation. For instance, the Sun being an astrological planet is on a higher level than the element of Fire, which is itself on a higher element than actual fire or gold. However, we can use any of these things to represent or produce a harmony with the other since they’re all corresponded to each other.
Probably one of the most valuable resources for this comes from the Second Book of Occult Philosophy by Cornelius Agrippa, where Agrippa presents a set of correspondences that link various names of God, planets, choirs of angels, ranks of the blessed, elements, prophets, and the like to each other based on certain shared properties. Crucially, however, Agrippa organizes this by number. Thus, he has a Scale of Four (book II, chapter 7) to correspond things that are easily divisible into one of four groups, a Scale of Seven (chapter 10) for things grouped into sevens, a Scale of Ten (chapter 13), and so forth. Each of these are immensely useful for magicians, since they provide us with symbols and ritual ideas at a glance. Aleister Crowley’s famous Liber 777 and, more recently, Stephen Skinner’s Complete Magician’s Tables offer these but on a much grander scale, corresponding far more things together on a qabbalistic basis than Agrippa does in his Scale of Ten.
Of course, finding systems of correspondence is an old thing, and even back in classical and antique times do we see the foundations of these systems of correspondence set up and used. And, well, you can see where I’m taking this, aren’t you? The Tetractys, that venerable Pythagorean symbol, was seen to contain within itself the foundations of all life and existence in every conceivable form, and not just in a strictly emanationist way. Each rank of the tetractys, based on whether it related to the Monad, Dyad, Triad, or Tetrad, was associated to something else that formed part of the cosmos.
One good source for this comes from Iamblichus’ Life of Pythagoras, where he gives a good overview of the life of Pythagoras (duh) as well as a number of his teachings (though nowhere in depth as I’d like). The Taylor translation linked above, however, also contains an extensive collection of other Pythagoreans who followed Pythagoras and wrote down what the Teacher (ostensibly) said, as well as a set of notes where Taylor inspects the things Iamblichus says and expands on them where the original author was annoyingly terse to our modern readers. Part of this expansion is where Taylor talks about how the Tetractys wasn’t just a number but a graphical mnemonic, if you will, of various things
|Odd Geometry||Point||Open curve||Closed curve (circle)||Cylinder|
|Growth of Vegetation||Seed||Length||Breadth||Depth|
|Power of Judgment||Intellect||Science||Opinion||Sense|
|Parts of an Animal||Rational||Irascible||Epithymetic||Body|
|Ages of Man||Infancy||Youth||Adulthood||Old Age|
Well, would you look at that, it’s a table of correspondence along the same path as Agrippa’s Scale of Four. It’s not quite the same (Agrippa gives Summer, Spring, Winter, and Autumn instead of Pythagoras’ Spring, Summer, Autumn, Winter, and I’m personally in favor of using Agrippa’s associations or a variation thereof, especially considering how Athenians started their year at the summer solstice), and there are a few hard-to-understand terms and progressions, but for the most part it’s definitely something useful in seeing how emanation works in everything.
I mean, sure, the can of Monster energy drink next to me is something that emanated from the Source just as I did, but it has a different body and different contents than I do. Consider the body of the can, the metallic mostly-cylindrical shape the drink comes in. The can wasn’t born, so it can’t age in the way a human ages, but consider how soft drink cans are made for a bit. The cylindrical can was stretched out from a circular cut from a flat sheet of aluminum; from this, we got the tetrad-corresponded cylinder from the triad-corresponded circle. Of course, this circle itself has depth, since it’s a cutout from an aluminum sheet which is a body; all bodies have three dimensions (length, breadth, and depth), without any one of which it’d only be a two-dimensional shape. So, whence the circle itself? The circle itself is a form, not a body, an idea that can interact with others. Whence the form of a circle? The form of a circle is made from a curved line traveling around a point. After all, all circles only need two points for a definition: a center and a boundary. The curved line demonstrates motion and direction, both of which are relative concepts (in order to move, you need something to move from both in terms of location, speed, orientation, etc.). The curved line, then, comes from the single point, the Monad of all shapes and forms and bodies.
So why is the tetradic form of a circle a cylinder and not a sphere? After all, isn’t the sphere the thing most like a circle in the third dimension? Sorta, yeah, but a sphere is (according to Pythagoras and other Pythagoreans) a perfect body, and there is nothing we can make in the cosmos that is perfect due to the constant actions of Difference, Existence, and Sameness as well as the upheaval and drama in the four elements. Rather, the tetradic form of a circle is a circle with depth, the most straightforward of which is a stack of circles, forming a cylinder. It makes sense, though a little counterintuitive.
Between Agrippa and Taylor’s exposition of the correspondences of fourfold things to the Tetractys, a lot of intellectual work has already been cut out for us in studying how the Tetractys can relate to individual things. Then again, that’s just it; this kind of analysis is good for understanding individual things, and it’s the relationships of those things that are just as important, if not moreso. In fact, one of the more famous divisions of things is the Quadrivium, literally “four ways”: four types of mathematics used throughout the classical, medieval, and Renaissance worlds. In this, arithmetic is an understanding of bare number (Monad), followed by music (in the broad sense) as an understanding of relationship and modulation (Dyad), followed by geometry as an understanding of static form (Triad), followed by astronomy which is an understanding of moving bodies (Tetrad). Just as one can’t study astronomy without a knowledge of geometry, and geometry of music (for the study of proportions and ratios is a type of music in the classical, ideal sense!), and music of arithmetic, the Tetractys itself indicates that the relationships between things are where the real action lies in the cosmos.
After all, wasn’t that the whole point of my developing mathesis, anyway? To discover relationships more than units? To understand the changes between the different methods of manifestation rather than the methods themselves? Something is still missing, and that’s where mathesis becomes mathematic, in our modern sense of numbers and relationships. After all, if we’re still trying to analyze stuff as individual units, then we’re dealing with things as individual monads. A Dyad is more than just two monads put next to each other; it is a relationship between the two that makes two monads into a Dyad. That relationship is often called “music” in Pythagorean literature, but it’s not necessarily the music of instruments or sounds. Music, in this case, is the means of progression, movement, and patterns. It is not enough to study sheer quantity in the arithmetic sense, and it is yet too much to study harmony in the geometric sense. Another type of analysis-and-synthesis is needed for the Dyad.