Monday, September 5, 2011

Trigrammaton Qabalah

Do what thou wilt shall be the whole of the Law.

Note: 'Qabalah', as used here, refers to the practice of alpha-numerical mysticism in general; though the term's original use is with the Hermetic interpretation of the Hebrew Kabbalah, and the Greek language has the term 'Isopsephy,' and Latin has 'Arithmancy,' both to refer alpha-numerical mysticism in their own languages, the ubiquity of the term Qabalah makes it convenient to divorce the term from exclusive association with the Hebrew language.

So, what is 'alpha-numerical mysticism'? Essentially, a system of alpha-numerical mysticism grows up around a paradigm for relating the letters of an alphabet to numerical values, which gives words numerical values (that of their letters summed together) and thus creates a basis for associating words and attributing concepts and archetypes to numbers. In the Greek and Hebrew alphabets, all letters were given numerical value, and numbers were written using combinations of letters (in some cases along with a punctuation mark showing the letters indicated a number, to prevent ambiguity). The first nine letters were numbered one through nine, the second nine ten through ninety, and the last letters were used for the numbers 100 to 900. The decimal (base-10) number system was thus built into the way these alphabets were used even before the number '0' came into use.

The Hebrew Kabbalah and Greek Isopsephy have been used both in the interpretation of holy texts (namely the Tanakh and the Gospels, respectively) as well as generally for engendering an understanding of the way everything in connected, an understanding which has an important role in the foundation of any mystical perspective. They have also been used by magicians for the purposes of creating rituals and names which were much better understood by the initiated than by outsiders. As mentioned in an earlier post on this blog, Abrasax, gnostic god of the Sun, had a name that enumerated 365, thus containing the promise of the Sun's return from Winter.

However, since most of us are not fluent in Greek of Hebrew, these systems of mysticism are of limited use to us. Indeed, we can translate words and phrases into one of those languages and determine their numerical value that way, but it's less efficient than running the operating system that we really want to use in a virtual machine. A more direct system is needed for alpha-numeric mysticism to be truly accessible to English speakers without the prerequisite of fluency in an ancient language. Further, inspired texts written in English would have to first be mangled into the ambiguity of multiple possible translations for their qabalah to be understood. Even the Book of the Law mentions this need: "Thou shalt obtain the order and value of the English Alphabet; thou shalt find new symbols to attribute them unto." (AL II:55)

Fortunately, the work of R. Leo Gillis, standing on the shoulders of Aleister Crowley, has provided precisely what is needed. Gillis noted that Crowley had written a particular inspired text called Liber Trigrammaton (pdf warning), which contains 27 symbols similar to the 8 trigrams of the I Ching. The only difference was that, where the I Ching trigrams consisted of Yin and Yang (- and +, represented by a broken line and an unbroken line respectively), the Trigrammaton symbols also contained a Tao symbol (of neutral value, represented by a dot). In his later notes on this book, Crowley attributed the letters of the English alphabet to the first 26 of these symbols, and referred to the book as "the foundation of the highest theoretical Qabalah." However, Crowley never determined numerical values to associate with these figures, and thus he never solved the second half of the equation - the "value of the English Alphabet." (Ibid.)

This is where Gillis comes in. His brilliant realization was that the symbols of Liber Trigrammaton can be taken as numbers in ternary (base-3). Thus 0 was represented by three lines of Tao (visually, a column of three dots), 1 by two lines of Tao and one of Yang (two dots with an unbroken line below them), 2 by two lines of Tao and one of Yin (two dots with a broken line below them), 3 by a line of Yang between two dots of Tao, and so on. Representing Tao as 0, Yang as 1, and Yin as 2, the sequence from one to 10 would go:

Just like in the decimal system, where each place value represents a power of ten (1 = 10^0, 10 = 10^1, 100 = 10^2, et cetera), each place in the ternary system represents a power of three (1 = 3^0, 3 = 3^1, 9 = 3^2). Thus all natural numbers (including 0) under 27 can be written in three lines, and all under 729 can be written in six lines.

The beauty of this system of notation is that there are two operations that can be applied to any numbers to find a pair of numbers related to them, as well as an operation applied to any two to find a third number that relates the two together. The first two operations (which require only one number) are called antigram and reversal, and the operation which requires two numbers is called transition.

Antigram is a very simple operation. From the original number, you leave all 0 digits as they are. You turn every 1 digit (unbroken line) into a 2 digit (broken line), and vice versa. So (1) and (2) are antigrams, as are (23) and (16). Note that antigram relationships aren't at all obvious in base-ten notation; they arise specifically from Trigrammaton notation. Note also that (0) is its own antigram.

Reversal is somewhat more complex, because you have to have a set number of digits in mind (usually 3 or 6). Instead of swapping the values on lines like you do with antigram, you swap the order of lines, so that the first line is last, the second line comes before the last line, et cetera. For some examples, (21) and (5) are reversals, and so are (25) and (17). There are many trigrams that are their own reversals, such as (10), (26), and (16). Further, there are some trigrams whose antigrams are the same as their reversals, like . As with antigram, the properties of reversal are not obvious in decimal notation.

Transition is a more complex operation than antigram or reversal, but a couple examples should make it clear. Each example listed below is a transitional triad: given any two, the operation of transition can find the third.
, , .
, , .
, , .
, , .

To find a transitional trigram, work line by line through the pair of trigrams already given. If a particular line in both trigrams is Yin, Yang, or Tao, leave it as it is in the transitional trigram. If the value differs for the same line between the two trigrams, whichever of Yin, Yang, or Tao is not used in either trigram will be present in the transitional trigram.

Let's look at the first example triad:
1) , , .
This is a perfect example of the second rule. Notice that on each line, one trigram has Yang, one has Yin, and another has Tao. It doesn't matter that it's not the same trigram that has each, because they're all in the same transitional triad. If we were only given the first two trigrams, we could figure out the third like so: the top line is Yang in one and Tao in the other, so it must be Yin in the third; the middle line is Yin in one and Yang in the other, so it must be Tao in the third; the bottom line is Tao in one and Yang in the other, so it must be Yin in the third.

2) , , .
You see both rules in action with this one. The top line is Tao in the first two, so it must be Tao in the third. The middle line applies the second rule - since Tao is in the first trigram, and Yang is in the second, Yin must be in the third of the triad. The bottom line applies the first rule again - since Yang is present in the same line of two trigrams of the same transitional triad, it must also be present in the third.

3) , , .
Since there are no lines with the same symbol between any pair of trigrams, the second rule is all we need to figure this one out. Just like with the first example, Yang, Yin, and Tao are distributed across each line.

4) , , .
You know how we solved this one by now. However, it shows a neat property of transition. The third symbol in a transitional triad that contains two antigrams is always 0. The same is not true for reversal, however.

We looked at these three operations using only trigrams, but the same could easily be done with hexagrams (6-line ternary numbers).

Now, some magicians have taken issue with Trigrammaton, pointing out that a ternary system dealing with the permutations of positive and negative has been in existence at least since the dawn of the most recent Age of Pisces, known as the Tai Hsuan Ching. This system added, to the unbroken line and the once-broken line familiar from the I Ching, the twice-broken line. The three symbols (called T'ien, Ti, and Jen) together represented the unification of Heaven, Earth, and Man. The criticism linked is very good at demonstrating that Crowley's Trigrammaton is not this system. However, it does not purport to be. The genius of Trigrammaton is that it adds a symbol for 0, rather than for 3, to the symbol set.

However, m1thr0s does make one very good point in the link above - seeking to find a one-to-one correspondence between Trigrammaton and the Tree of Life or the Major Arcana of the Tarot is not something to be done casually. In the next post on this subject, we'll look at Crowley's attribution of the English alphabet to the trigrams, and consider other possible attributions for them.

Thank you for your time and attention.

Love is the law, love under will.


  1. Thanks. I want to get into the way it applies to Liber Legis and the other holy books of Thelema eventually, but gotta lay the groundwork first.