Trigram Divination

For the purposes of divination, one must be able to generate any number at random, and at will. There are several methods that can accomplish this, and one of them takes the tradition of the I Ching as an inspiration for creating the various types of lines, or digits, of the ternary numbers.

In I Ching, Yang lines can turn into Yin lines, and vice versa, or they can remain static and not change. This means there are four different possibilities. In Trigrammaton there is an extra line, the Tao, which can also turn into Yang or Yin, and vice versa. This means that all together there are 3 x 3 = 9 different types of lines, as shown below.

The simplest way to pick between 9 possibilites is to take 9 objects that signify the various lines, and choose one of them in a random fashion. M&M’s in 9 colors would do fine, (and you could eat the evidence afterward). But if you have 9 colors and 9 types of line to match them with, then there are 9! = 362,880 possible ways to color those 9 lines. Is there a way to be less arbitrary about it? There is, but it requires other numbers to do it.

A precise method of choosing 1 out of 9 possible lines is found by using the digits of the nine “bigrams” of Trigrammaton. The bigrams are all those numbers that are written using only two lines, or digits. These numbers, built from right to left, can be considered as representatives of those nine kinds of line, based on what the first and second digits are.

For example, 00, 11 and 22 are Tao static, Yang static, and Yin static, because they repeat the digit. But 5, which in ternary is ‘12’, represents Yin into Yang, because it starts with a Yin line and ends with a Yang line, (reading the digits from right to left).

Since any number can be reduced to a single digit, (e.g., 150 = 1 + 5 + 0 = 6), then any number can generate a type of line, (9s will count as 0s). When you have enough of these lines, you can make a new number. But how do we get those single digits in the first place? Any way you like. Use six words for their gematria values, throw darts at a magic square, or roll three dice and add them up. You might even play tic tac toe on this square:

As an example of this method we can use the word QELHMA, a six-letter word in Greek. The values of the separate letters are 9 – 5 – 30 – 8 – 40 – 1. We can arrange these as a set of six lines, reduce the digits of the letters, and then convert the reduced digit to a ternary bigram in the following manner:

Now using the Bigrams generated by the values of the individual letters, we can create the following pair of hexagrams, from the bottom line upward. The hexagram on the right is generated by the initial digits of the bigram, and becomes the hexagram on the left, (generated by the second digit of the bigram):

384 = a messenger unto that small dark orb.
147 = manifestation

So the letters of the word Thelema can be used to generate the 384 hexagram becoming the 147 hexagram. 384 is a very significant number; it is the number of lines in all 64 I Ching hexagrams, ( 6 x 64 = 384), and it is also the number of days in 13 lunations, (the 13 Full Moons of certain calendars).

This whole approach assumes an equal probability for all nine types of line. Next we will look at a method that uses a graduated scale that gives more weight to certain lines and less to others. This method is a bit more complicated to explain, but is simple in practice.

Both the systems of I Ching and Liber Trigrammaton rely on the basic trigrams to develop their explanation of the cosmic order. I Ching goes on to combine each of the 8 trigrams with one another to create the 64 hexagrams. Likewise Trigrammaton combines its 27 trigrams with one another to form a total of 729 hexagrams. These hexagrams are simply all the numbers from 0 to 728, and they establish the universe of discourse within which the qabalah of Trigrammaton develops.

This procedure for generating a particular ternary hexagram relies for its inspiration on the method used in I Ching. Since ancient times, one means of creating the Yang and Yin lines of the I Ching required a complicated manipulation of stalks from the yarrow plant. When this yarrow-stalk method of creating a line is used, there are 16 possible outcomes for each line cast. These possible lines are distributed in the following ratios:

7/16: static Yin; 5/16: static Yang; 3/16: moving Yang; 1/16: moving Yin

First we notice that the number of possibilities is the number of different lines to the second power: 4 x 4 = 16. 

Second, the four numerators of these ratios are the set of the first four odd numbers; 1, 3, 5, 7. 

Third, the overall chance of a Yang line being chosen is 8/16, and likewise for the Yin line. 

Fourth, a disparity is introduced in the ratios between the static and the moving lines. The static lines are three times more likely to appear than the moving lines, being a ratio of 12/16 for the static lines versus 4/16 for the moving lines.

This method of divining a hexagram of Trigrammaton will utilize these four aspects of the yarrow-stalk method, (as well as adding a couple more parameters).

One: the number of probabilities is the number of line-types (9), to the second power (81) 

Two: the numerators of the nine probability ratios are the set of the first nine odd numbers: 1, 3, 5, 7, 9, 11, 13, 15, 17. 

Three: there is equal probability of choosing a Tao, Yang, or Yin line (27/81 for each).

Four: there is a greater likelihood of static lines versus moving lines (45/81 versus 36/81). 
(There are two additional parameters necessary to isolate a single sequence): 

Five: the total sum of the changes created by the various lines is equal to zero. 
(This leaves 6 possible sequences. To decide between them requires a final parameter). 

Six: The 48th I Ching hexagram, “The Well”, determines the probability of 9/81

There are only two ways to subdivide the series of the first nine odd numbers such that each of the three subsets equals 27. These sets are: (17, 9, 1); (15, 7, 5); (13, 11, 3); or (17, 7, 3); (15, 11, 1); (13, 9, 5). 

The first group represents the probability of the “cast” lines of a hexagram, i.e., the line that is drawn, while the second group represents the probability of the “becoming” lines, i.e., what the cast line turns into. This relationship is most easily displayed on a magic square of 9 cells. The columns are the cast lines; the rows are the becoming lines:

The magic square of nine cells bears a close resemblance to the Chinese ideograph of the word “Ching”, which is the name of the 48th hexagram, The Well. This ideograph symbolizes the Chinese practice of laying out a village plan such that there are eight fields on the perimeter of a square, each held separately by the farmers, while the central field is the place for the Well, which all hold in common. The Well is the repository of Yin, the power of Water. And most important for the present purpose, this Well is in the center.

Since the value of 9 is found in the center of the magic square above, the probability of 9/81 is given to Tao changing into Yin. This shows that at the center of all things, in the Well of existence, is the Tao. The Tao mutates into Yin, and therefore becomes the water in the Well. The Tao is a constant, as is the Well. The Judgment of this hexagram states that “the Well is never depleted”. This is because the Well is always replenished by the Tao.

The probability of 9/81 is the center of the series. By using this hinge as the act of Tao becoming Yin, then the reverse, Yin becoming Tao, must have a probability of 3/81. 

This plays a role in the next step, the integration of the 81 probabilities with the 81 lines of the trigrams in Liber XXVII. The method used is to treat the trigram sequence as three sets of nine, and group the lines according to their occurrence in these three columns:

Tao static has the probability of 17/81. These are the 17 Tao lines of the left column.

Tao changing to Yin has a probability of 9/81. These are the 9 Tao lines that appear in the middle column.

Tao changing to Yang has a probability of 1/81. This is the sole Tao in the right column.

Yang static has a probability of 15/81. These are the 15 Yang lines in the left and middle columns.

Yang changing to Tao has a probability of 7/81. These are attributed to 7 Yang lines in the right column.

Yang changing to Yin has a probability of 5/81. These are attributed to the remaining 5 Yang lines of the right column

Yin static has a probability of 13/81. These are attributed to the 13 Yin lines in the left and middle columns.

Yin changing to Yang has a probability of 11/81. These are attributed to all the Yin lines in the right column, (except for the Final trigram).

Yin changing to Tao has the probability of 3/81. These are given to the three Yin lines of the Final trigram -- these three Yin lines all collapse back into the Tao, the Zero trigram.

The simplest way to choose one line among 81 different possibilities is to take a collection of 81 different objects and choose one from among them to indicate a particular line. The number 81 is easily accommodated by a deck of tarot cards, so long as there are three “wild” cards added to the 78 cards of the standard deck. 

These three cards will represent the Zero trigram. The other 78 lines of Liber XXVII can then be matched with the 78 cards of the tarot. The Major, Minor, and Court cards of the tarot are mapped onto the 81 lines, while at the same time these lines can distribute the 81 probabilities for divination.

The Trigram Sequence in Liber XXVII
 Attribution of the Tarot Cards to the 81 Lines--Probabilities for Divination