Pythagorean Correspondences to the Tetractys

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

Monad Dyad Triad Tetrad
Number 1 2 3 4
Doubling Progression 1 2 4 8
Tripling Progression 1 3 9 27
Even Geometry Point Line Polygon Solid
Odd Geometry Point Open curve Closed curve (circle) Cylinder
Element Fire Air Water Earth
Platonic Solid Tetrahedron Octahedron Icosahedron Cube
Growth of Vegetation Seed Length Breadth Depth
Communities Individual Family Town State
Power of Judgment Intellect Science Opinion Sense
Parts of an Animal Rational Irascible Epithymetic Body
Seasons Spring Summer Autumn Winter
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.

Towards a Greek Kabbalah: Tetractys as Cosmic Framework

Alright, so now we understand the Greek letters as symbols of many things: zodiac signs, planets, elements, numbers, body parts, and any number of gods, images, and other concepts.  All this is in addition to their use as instruments of written language as glyphs and of spoken language as sounds and names.  While we’ve come a long way, we’re still only setting out our basic tools for further analysis.  We know of the Greek letters as units, single entities representing a single set of symbols.  To use them, we have to start seeing these letters as relationships, transferring and communicating information and power between other units.  It’s like a single word, such as “my” or “the”, being understood, but without meaning until it’s used in a sentence when it indicates relationships and distance between and among other concepts.  Within a word, letters act as relationships between the letters before and after it, but is there anything else bigger that we might have the letters act as a relationship between?

This is where we start thinking about things cosmically and from an emanationist perspective, and, to be honest, I have some catching up to do on Hermetic and Neoplatonic philosophical language to describe it accurately.  Suffice to say that, like Jewish kabbalah and Hermetic qabbalah, Greek kampala also describes the creation of the cosmos in a series of stages, but not necessarily in a clearly-ordered and sequential manner like the sephiroth do.  Rather, it is through providing multiple levels of understanding of the cosmos that we can better understand it.  The Greeks loved to divvy up stuff into smaller stuff, the foundation of the problem-solving technique “divide and conquer”, and that continues here.  With that, I propose we use the geometric diagram of the tetractys, the holy diagram of Pythagoras: Tetractys   The tetractys is a diagram consisting of four rows of points, each row having an increasing number of points starting at one and ending at four, arranged in an equilateral triangle.  This was considered to be the foundational blueprint for all of creation according to that mathematical and mystic hero of Greek thought, and was mathematically significant: it combined the Monad (unity), Dyad (two), Triad (three), and Tetrad (four) into a single unit.  These four numbers, representing the One, Power or Differentiation, Harmony, and Cosmos, compose all the things of the universe, as 1 + 2 + 3 + 4 = 10, the unity of a higher order, or the Decad.  All of these numbers were holy to the Pythagoreans, but ten most of all; given its fourfold structure, this diagram was called the Tetractys, and sometimes referred to by the Greek letter Delta (Δ).  The Pythagoreans saw it as so holy that they prayed to it and glorified it:

Bless us, divine number, thou who generated gods and men! O holy, holy Tetractys, thou that containest the root and source of the eternally flowing creation! For the divine number begins with the profound, pure unity until it comes to the holy four; then it begets the mother of all, the all-comprising, all-bounding, the first-born, the never-swerving, the never-tiring holy ten, the keyholder of all.

And, further, the Pythagoreans swore by the tetractys itself:

By that pure, holy, four lettered name on high,nature’s eternal fountain and supply,the parent of all souls that living be,by him, with faith find oath, I swear to thee.

The tetractys was considered to represent the fourfold nature of creation in eleven different ways, according to Iamblichus in his “Life of Pythagoras”.  Essentially, a single Monad (God, the Good, etc.) created a Duality of Two, which then created a Harmony of Three, which then created an Ordering of Four; by the interaction of these different forces, both within their own groups and across other groups, all other things are made.  In fact, by interpreting each row (with its difference) in different ways, we obtain something resembling Cornelius Agrippa’s Scale of Four (book II, chapter 7):

  1. According to the composition of numbers: 1, 2, 3, 4
  2. According to the multiplication of numbers: a point (0-dimensions), a side (1-dimension), a square (2-dimensions), a cube (3-dimensions)
  3. According to magnitude: a point (0D), a line (1D), a plane (2D), a solid (3D)
  4. According to simple bodies: fire, air, water, earth
  5. According to figures: pyramid, octahedron, icosahedron, cube
  6. According to things rising into existence through vegetative life: seed, length (shoot), breadth (leaf), depth (trunk)
  7. According to communities to form nations: individual, household, street, city
  8. According to judicial power: intellect, science, opinion, sense
  9. According to parts of the animal: rational, irascible, epithymetic (that which desires good), physical body
  10. According to the seasons of the year: spring, summer, autumn, winter
  11. According to the ages of man: infancy, youth, adulthood, senescence

The tetractys even helped to guide the Pythagorean musical system by taking ratios of the rows of dots:

  1. Rows 4 and 3, 4:3, perfect fourth
  2. Rows 3 and 2, 3:2, perfect fifth
  3. Rows 2 and 1, 2:1, octave
  4. Rows 1 and 1, 1:1, unison

In fact, so influential was the use of the Tetractys in Greek thought that it even influenced philosophical schools hundreds of years afterwards, even Jewish kabbalah and Hermeticism.  This can even be seen in one representation of the Tetragrammaton, the four-lettered name of God, represented in a tetractys-like form: Tetragrammaton Tetractys Plus, having ten units inside, parallels can be drawn between the tetractys and the Tree of Life, or ten sephiroth.  Dion Fortune in her “The Mystical Qabalah” even drew a comparison between the fourfold Tetractys and the first four sephiroth on the Tree of Life, especially with regards to the tetractys as demonstrator of physical space:

The point is assigned to Kether; the line to Chokmah; the two-dimensional plane to Binah; consequently the three-dimensional solid naturally falls to Chesed.

In terms of the four parts of the body, it might be better to restate tetractys #9 above (according to the parts of the human) in Agrippan terms as the Mind, Spirit, Soul, and Body.  These four parts of the human are that which links us to the divine (Mind, row 1), that which allows us to reason and intellectually understand the world (Spirit, row 2), that which feels and moves (Soul, row 3), and that which is moved and is felt (Body, row 4).  It is by the unification and purification of these four parts of the body do we practice ascension through and beyond ourselves back to the One, but that’s another topic for another day.  Suffice it to say that, through the cultivation and increasing of virtues in the four parts of ourselves, we ascend the Tetractys and the multiple parts of the world we find ourselves connected to.  If you want, give the excellent Summary of Pythagorean Theology by Apollonius Sophistes a read in the meantime, since that’ll be a huge thing for us later on.

The study and meditation of the Tetractys will become bigger and bigger later on, especially once we view it as a kampalic cosmic map much in the way that the Tree of Life functions for kabbalah and qabbalah.  As yet, we’ll leave the individual units of the tetractys unnumbered and unmarked, letting the structure speak for itself.  To let it do so, meditate on the structure and form of the tetractys, offering it the same devotion and glory the old Pythagoreans themselves would have done so.  Hold the image in your mind, and relate all the parts of the cosmos to its structure: the fourfold nature of things resulting from a threefold harmony resulting from a twofold differentiation resulting from a single Source.  To say much about the tetractys at this point would be premature, so I’ll leave it as an introduction on its own as a symbolic representation of what’s to come: first a seed, then a shoot, then a leaf, then a trunk.

Towards a Greek Kabbalah: Symbolism of the Greek Letters

From before, a letter has four parts: a name, a glyph, a sound, and a meaning.  The first three were discussed last time, along with a basic set of meditations to get us familiar with the first three of these parts.  We didn’t discuss the final part of the letters, however, which is the meaning of the letters.  Unlike the name, glyph, and sound for a letter, of which there tends to be only one of each, there are many layers of meaning for each letter: numerical, astrological, divine, oracular, Phoenician, Greek, and more.  This is what makes the divination system of grammatomancy so powerful, in that a whole world of knowledge can be unlocked with a single letter.  So, even though the meaning of a letter is the fourth part, there are many parts to the meaning of a letter.

What are some of those meanings?  Honestly, if I had to indicate all the meanings of the letters, this blog post would become a whole blog in and of itself, so I’ll simply list a few sets of meanings along with links or links to books for further reading, though my ebook on grammatomancy lists many of them:

  1. Numerical:  my page on isopsephy and gematria, Kieran Barry’s The Greek Qabalah
  2. Astrological: my page on stoicheia, Agrippa’s table of letters (book I, chapter 74, though I reverse how he arranges the planets to the Greek vowels)
  3. Oracular: Apollonius Sophistes’ Greek Alphabet Oracle
  4. Divine: a post linking the Greek gods to the letters for purposes of a lunar grammatomantic ritual calendar

Honestly, with all that down, we already have a wealth of knowledge at our fingertips, but there’s another way to give meanings to the Greek letters: their original Phoenician names, and Greek words related to the letters.  Even the Greeks were aware, to an extent, of the Phoenician origin of their alphabet, which doesn’t diminish its importance in the least for our purposes.  After all, the Phoenician script was the origin of many of the world’s writing systems (especially if you buy the argument, as I do, that it formed the origin of the Brahmic script in India, which connects it even to the Far Eastern Korean).  The diagram below shows Phoenician in the center column, Hebrew to the right of Phoenician and Arabic to the right of that, and Greek to the left of Phoenician and Latin to the left of that.  Letters of different scripts in the same color boxes show the origin of the letter, while arrows show derivations of other letters.

Origins of Letters from Phoenician


Phoenician script has 22 letters, the same 22 as modern Hebrew; there’s a 1-to-1 mapping between those two scripts.  The Ionian Greek script, however, got rid of three of the letters (digamma/waw, qoppa, san/sampi), added four (phi, khi, psi, omega), and moved the position of the derived form of Waw (which became Upsilon) further back in the alphabet.  Each of the Phoenician letters had their own name, many of which provided the names for their corresponding Greek letters.  These names referred to, in many cases, earlier Egyptian hieroglyphs or related words that provided a basis for what the letter looked like.  Many of these names were maintained in Greek, often in derived forms, such as Alpha from ʾĀlp, Bēta from Bet, Gamma from Gimel, and so forth.  For the Greek letters that have Phoenician origins, either in name of the letter or its form, their Phoenician meanings might include the following:

Letter Phoenician Meaning
Α ʾĀlp Ox
Β Bet House
Γ Gimel Throwing stick weapon, camel
Δ Dāleth Door
Ε He Window
Ζ Zayin Weapon, sword
Η Ḥeth Wall, courtyard, thread
Θ Ṭēth Wheel, good
Ι Yōdh Hand, finger
Κ Kaph Hand, palm of a hand
Λ Lāmedh Goad
Μ Mēm Water
Ν Nun Fish, serpent, whale
Ξ Simketh or Sāmekh Fish, tent peg, prop support
Ο ʿAyin Eye
Π Mouth
Ρ Rēš Head
Σ Form from Šin
Name from Simketh
Τ Tāw Mark, cross
Υ Wāw Hook
Φ Form from Qōph Back of the head, sewing needle, eye of a needle, monkey
Ω Form from Omicron

Of course, by the time the Ionian Greek script was adopted and spread throughout Greece, many of the letter forms were so far removed from their Phoenician counterparts (if any existed) that many of these meanings became meaningless or detached from the letters.  However, the Greeks themselves often found new symbolism for the names, often from a variety of sources.

  • Words or names that started with the letter itself
  • Images or concepts that bear a resemblance to the shape of the letter
  • Words that bear a strong resemblance or things that have a connection to the name of the letter
  • Assigning a letter to parts of the body, starting with Alpha at the head and going down to Mu at the feet, then starting again from Nu at the feet and going back up to Ōmega at the head (cf. the Body of Sophia)
Letter Meaning
Initial letter Graphical Importance Body
Α  Man, air, Apollo  Beginning, invention, source, God  Head
Β  King, help  Duality  Neck
Γ  Earth, birth  Shoulders and hands
Δ  God, ten  Breast
Ε  Build  Justice, Apollo  Diaphragm
Ζ  Life, Zeus  Back
Η  Hera  Belly
Θ  God, death, Mars  The world/universe  Thighs
Ι  Jesus, jot, single  Line, perfection, Rod of Moses  Knees
Κ  Lord, Caesar  Lower legs
Λ  Lion  Ratio, progression  Ankles
Μ  Mary, myriad  Middle  Feet
Ν  Feet
Ξ  Ankles
Ο  Circle, heaven  Lower legs
Π  Father, fire, five, Mars  Knees
Ρ  Thighs
Σ  Savior  Belly
Τ  Cross, crucifix  Back
Υ  Son  Moral choice, dilemma  Diaphragm
Φ  Voice, sound  Breast
Χ  Time, Christ  World soul, cross  Shoulders and hands
Ψ  Psyche, soul  Holy Spirit  Neck
Ω  Ocean, Orion  End  Head

You’ll note that I’ve started to include Abrahamic and Christian references; this is intentional, and not simply me copying entries blind from Kieran Barry’s “The Greek Qabalah”.  After all, as a Hermeticist, I’m not opposed to including Christian or Jewish references here (despite my trying to distance myself from Jewish kabbalah); rather, including them reaches back and allows for more access to much of Renaissance and Medieval development of Hermeticism as well as its classical and pagan origins.

So, where does all this leave us?  Between the graphical shapes and names of the letters, along with their oracular meanings, divine connections, numerical and isopsephic connections, and astrological or planetary or elemental connections, we have whole worlds of meaning for each of the letters.  These can all be incorporated into the meditations on the letters by visualizing or contemplating on them while intoning or repeating the letters.  The images and symbolism of the letters, coupled with their pronunciation, will further open up more doors in exploring the worlds and meanings of the letters and how they affect the world through their presence and, by their presence, the will and presence of the gods and God.

In fact, speaking of doors, let me share a method of scrying I like to use for deeply exploring a particular symbol.  Once the meanings and symbolism of the letters in all their complexity and layers have been learned and reviewed, and after meditating briefly to calm and clear the mind but before leaving the meditative state, I visualize a doorway with a particular symbol inscribed on it.  In our case, that symbol would be one of the letters of the Greek alphabet.  Knock on the door, mentally intoning the letter itself, and open it up.  Everything inside is a representation and symbol connected to that original symbol; explore the world, perhaps calling on the genius or spirit of the symbol to guide you or to send you a guide, or calling on your own HGA or personal tutelary spirit to guide you through it.  Explore the world as deeply as you care to, and when you’ve decided you’ve had enough, take the same route back through the world, passing by all the things you passed by before, and exit the same way you came.  Close the door, clear the mind again, and exit the meditative state.  I’ve used this skill to great efficacy before, notably on my meditations on the geomantic figures and the elemental archangelic kings, and it can be adapted to any number of symbols.  Using this method with the Greek letters can increase one’s deeper knowledge of them by exploring the deeper symbolism and worlds behind the letters which wouldn’t be apparent from simply reading up on their symbolism, and can indicate other symbols not listed above as well as connections to other letters that might not be apparent.  Further, the technique can be augmented by having it take place in one’s astral temple, or astrally projecting into the world itself.