ONE
of the most enigmatic of the Holy Books written by Aleister Crowley is Liber
XXVII, entitled Liber Trigrammaton --- Being the Book of the Trigrams of the
Mutations of the Tao with the Yin and the Yang.
This work contains 27
Trigrams formulated by the use of three symbols in groups of three: a Tao,
represented by a point; a Yin, represented by a broken line; and a Yang,
represented by a solid line.
Crowley notes that Liber
XXVII describes the cosmic process, or the course of creation, on the basis of
three principles. The present work will
show that by using the Base Three system of mathematics, this cosmic process
can be decoded, and an entirely new qabalah, or mystical system, can be
established from it.
The
decoding of the Trigrams is a simple process.
In Base Three, there are only three numerals: Zero, One, and Two. These numerals correspond to the symbols for
Tao, Yang, and Yin. As with the
Hexagrams of I Ching, the Trigrams are analyzed starting from the bottom line
and moving to the top line.
In the decoding process,
the bottom line corresponds to the first digit of the Base Three system. This digit represents the Ones place,
inasmuch as 3 to the zero power equals 1.
The middle line of each Trigram corresponds to the second digit in Base
Three, which represents the Threes place, (where 3 to the first power equals
3). The top line of each Trigram
corresponds to the third digit in Base Three, which represents the Nines
place, (where 3 to the second power equals 9).
Each line may be occupied
by the number zero, one, or two, which designates how many ones, threes, and
nines go to make up the number.
According
to this system, a value can be generated for each Trigram by considering which
symbol is in which place, and converting those symbols into Base Three. These figures will then be translated into
Base Ten for easier comprehension.
For example, the Trigram
containing three Yang lines has a value of 1 for the Ones place, 1 for the
Threes place, and 1 for the Nines place.
The sum of 1 + 3 + 9 = 13, therefore that Trigram is an expression of
the number 13 in Base Three. The same
method is used for all the Trigrams, with the three symbols of Tao, Yang, and
Yin determining how many ones, threes, and nines are involved in each.
After
being decoded, the 27 Trigrams are seen to represent all the numbers from Zero
to Twenty-six. These 27 numbers are NOT
in serial order, making the sequence all the more fertile for creating a new
Qabalah.
For example the first Trigram contains a
zero value for every digit, and therefore equals 0.
The following six Trigrams all contain two
points, and designate this numerical sequence:
1,
2, 3, 6, 9, & 18. The total of all six
of these numbers is 39; this is the key number of Liber Trigrammaton.
The next 12 Trigrams all contain only one
point, and are in this order:
4,
5, 7, 8, 10, 11, 19, 20, 12, 15, 21, & 24.
The sum of this set of twelve numbers is 156.
The final set of eight Trigrams all
contain no points, and appear in this order:
13,
14, 16, 22, 17, 23, 25, & 26.
The sum of this set of eight numbers is also 156. Note that 156 = 4 x 39.
The sum of all the Trigrams, the numbers
from 0 to 26, is 351. This total is
split into three sections; the first section of seven Trigrams equals 39, and
the following two sections each equal 4 x 39.
Having established a
numerical identity for each Trigram, the next step in the creation of a new
Qabalah is to attribute various Elements, Zodiac signs, and Planets to these
Trigrams.
The initial Trigram,
valued at Zero, is attributed to the Element of Spirit.
The next four Trigrams in
the sequence are attributed to the four classical Elements:
Fire is 1, Water is 2, Air
is 3, and Earth is 6.
This is the Elemental
order that forms the basis for Crowleys Book of Thoth Tarot.
The next two Trigrams are
valued at 9 and 18. For reasons that
will be clear later on, these two receive no single attribution: they are the
neutral poles of the system.
The
next twelve Trigrams, containing two Tao lines, symbolize the 12 signs of the
Zodiac. These are attributed in the
traditional order, starting with Aries.
The final eight Trigrams
are attributed to the Planets. In the Book
of Thoth, Crowley has placed these Trigrams on the mystical Hebrew diagram
known as the Tree of Life. Here, the
Trigrams correspond to the Supernal Triad and the seven Sefirot below it. By using the planets associated with these
Sefirot in the Book of Thoth, the eight Trigrams are attributed to
Saturn, Mercury, Sun, Juppiter, Venus, Moon, Mars, and Earth, in that order.
One of the charts below
displays the absorption of the Trumps of the Tarot into the Trigrammaton
structure. It is important to note that
the Trigrams are not being attributed to the Tarot, it is the Tarot that is
being assimilated into the Trigrams.
The Trigrams are numbers, and all qabalistic interpretations ultimately
refer back to pure number. Not the
Zodiac, not the Tarot, not Hebrew letters, but pure number.
Once the qabalistic
attributes are determined for the Trigrams, it is a simple matter to absorb the
Tarot as well. There are 26 Trigrams
with an English letter and a qabalistic attribute, and these are cognate with
the 22 Trumps and the 4 Aces of The Book of Thoth Tarot:
The Aces are attributed to
the four Elemental Trigrams, having 2 Tao-lines each.
The Planetary Trumps are
attributed to the Planetary Trigrams, having no Tao-lines.
The Zodiac Trumps are
attributed to the Zodiac Trigrams, having one Tao-line each.
This leaves the Fool, the
Aeon, and the Hanged Man, which are attributed to the 0, 9 and 18 Trigrams.
The
Fool is attributed to the Zero Trigram according to Crowleys definition of the
card in The Book of Thoth: The really important feature of this card is
that its number should be 0. It
represents therefore the Negative above the Tree of Life, the source of all
things. It is the Qabalistic Zero. It is the equation of the Universe, the
initial and final balance of the opposites; Air, in this card, therefore
quintessentially means a vacuum.
The
Aeon is attributed to the 9, the positive, masculine pole of the system, while
the Hanged Man is attributed to the 18, the negative, feminine pole of the
system
The
most controversial step in the qabalistic process is to attribute a letter of
the alphabet to each Trigram. This step
will create a new gematria, a technique of translating words into numbers
based on the individual values of the letters in that word. In his commentary to Liber Trigrammaton,
Crowley has attributed the 26 letters of the English Alphabet to all of the
Trigrams, except the final one. Each of
these English letters is then given the Base Three value of its associated
Trigram.
This fulfills verse II:55 of Crowleys Book
of the Law: Thou shalt obtain the
order & value of the English Alphabet; thou shalt find new symbols to
attribute them unto.
In the Commentary to this verse Crowley states: The attribution
in Liber Trigrammaton is good theoretically, but no Qabalah of merit has arisen
therefrom. I contend that no Qabalah
arose for him because Crowley only solved the order half of the order & value equation. He arranged the order of the letters, but
did not decipher the correct values for each letter. It is only by obtaining the correct numerical values for the new symbols, which are the Trigrams,
that a Qabalah of merit can arise therefrom.
The present work follows Crowleys
original letter attributions, as these are the only indication he has left us
regarding the basis of an English-language Qabalah. These attributions to Liber XXVII were published in Crowleys
periodical The Equinox Vol. 1 # 7, March 1912, and subsequently in The Law
Is For All ed. Israel Regardie, and Magical and Philosophical
Commentaries on the Book of the Law, ed. Symonds & Grant.
Liber
Trigrammaton is one of the Holy Books of Thelema, a group of works that are
technically known as Class A documents.
By definition, a Class A document can not be changed, even by one
letter; thus the exegesis of the meaning and value of each letter is integral
to an understanding of such a document.
Since all of the Holy Books are written in the English language, such an
exegesis requires a Qabalah and a gematria based on the English Alphabet.
The Trigrams
of Liber XXVII
(Numbers are Trigram values in upper and lower positions of a
Hexagram.)
0
189
648
0 7 24
27 216 351
1
8 13
54 270 378
2 10 14
81 297
432
3
11 16
162
513 594
6 19 22
243 540
459
9
20 17
486 324 621
18
12 23
108 405
675
4
15 25
135 567
702
5 21 26
Further light is shed on these numbers
when one looks at the Trigrams in sets of opposite pairs, or Antigrams. A Trigrams opposite is determined by
switching Yang lines to Yin, and vice-versa.
The Tao has no opposite.
1 2 = 3
3
6 = 9
9
18 = 27
-----
Total 39
13 26 = 39
14 25 = 39
16 23 = 39
22 17 = 39
-----------
Total 156
The Zodiac Trigrams as Polarities
4 ^
8 a = 12
5 _
7 ` = 12
10 b 20 e = 30
11 c 19 d = 30
12 f 24 i = 36
15 g 21 h = 36
-----------
Total
156
The diagram above
demonstrates that all the Fire signs are opposite Water signs, while all the
Air signs are opposite Earth signs. This arrangement reflects the polarities of
the Elemental Trigrams.
The total value of the six Fire and Water
signs is 78, and these are all even numbers, (4, 8, 10, 20, 12, 24).
The total value of the six Air and Earth
signs is also 78, and these are all odd numbers, (5, 7, 11, 19, 15, 21).
Of the six Antigram pairs,
each possible combination of Cardinal, Fixed, and Mutable Zodiac signs is
present: (C-C, F-M, F-F, M-C, M-M, C-F).
The three similar pairs: C-C, M-M, F-F,
represent only Water and Fire signs, and their Trigrams total 78.
The Fire signs contain only Tao and Yang
lines, while the Water signs contain only Tao and Yin.
The three unlike pairs: F-M, M-C, C-F,
represent only Air and Earth signs, and their Trigrams also total 78.
All
of the Air and Earth signs have a combination of Tao, Yang, and Yin.
The pairs of opposite
numbers also show a unique set of relationships when the difference between two Antigrams is examined. The chart below shows that the 13 pairs
differ by each of the numbers from 1 to 13.
The initial set represents
the Elemental Antigrams.
The sequence of 1, 3, 9,
(the place-values of the three lines of a Trigram), is shown in this set.
The second set represents
the Zodiac Antigrams. All the
differences in this set are even numbers.
In the third set, the
differences between Planetary Trigrams are all prime numbers.
Antigrams
Difference Sum Product
1 &
2 1 3 2
3 &
6 3 9 18
9 & 18 9 27 162
4 &
8 4 12 32
5 &
7 2 12 35
10
& 20 10 30 200
11
& 19 8 30 209
12
& 24 12 36 288
15
& 21 6 36 315
13
& 26 13 39 338
14
& 25 11 39 350
16
& 23 7 39 368
22
& 17 5 39 374
135
+ 216 91 351 2691
The sum of the numbers 1-26, plus the
products of the Antigrams, equals 2 x 39 x 39.
For the pair 22 & 17, the total of
their difference, sum, and product is 418.
The sequence of Antigrams, arranged by
increasing value of their differences, is a key feature of base 3 mathematics,
and will be used below in the attribution of Hexagrams to the wheel of the
Zodiac. The reason this feature is so
important, is because there is one, and only one, pair of Antigrams that
correspond to a unique difference-value.
For example, 93 and 186 are the only pair of Antigrams that differ by
93, and so on for every other whole number.
The Four Special Groups of Hexagrams:
These are the 27 Reversible Hexagrams:
36 72 84 120 156 168
204 240 244 280 316 328
364 400 412 448 484 488
524 560 572
608 644 656
692 728 0
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These are the
27 Doubled-Trigrams
28 56 84 112 140 168