The Book of Mutations

1111 Pages·2009·18.55 MB·English

by  R. Leo Gillis

The Veils of the Tao

The Tao formulated the One.
The One exhaled the Two.
The Two were parents of the Three.
The Three were parents of all things.

All things pass from Obscurity to Manifestation,
inspired harmoniously by the Breath of the Void.

Tao Teh Ching Chapter XLII, translated by Ko Yuen

“We can refer everything in the Universe to the system of pure number whose symbols
will be intelligible to all rational minds in an identical sense...
This present attempt at a magical alphabet is, in fact, a projection, both intensive and
extensive, of this system to infinity. On the one hand, all possible ideas are referred by
progressive integrations to the pure numbers 0 to 10, and thence to 2, 1, and 0. On the
other, the connotations of 0, 1, and 2 are extended, by progressive definitions, to
include every conceivable idea on the plane of the Universe.”

On the Nature and Significance of the Magical Alphabet - Aleister Crowley
The Book of Mutations

Copyright 2009 by R. Leo Gillis

All rights reserved.
The author wishes to thank the following people:

Richard Kaczynski and Byron Bonikowski for catalyzing this work at the outset. Together
with the author, they comprise the “three poles” of the system.

Frater RIKB, who contributed greatly to the development of this material and designed
many of the graphics. His insight and friendship are greatly treasured.

Frater RVS, who was a pioneer in this field, and contributed important methods to the
furtherance of this work.

Fratres AMO, SRKT, Adityanath and Zalanes, James Barton and John DePompeo for their
ideas and inspiration that added to this work.

And L.A.Speed, who always knew it could be done.

This book is dedicated to my dear Tredici, the star that lights up my heaven.
The Book of Mutations -- Table of Contents

8 Introduction
14 Foreword: Techniques of Trigrammaton Qabalah
18 Liber Trigrammaton sub figura XXVII -- by Aleister Crowley

Part One -- The Standard Model
23 Liber Trigrammaton Decoded
27 The Trigram Sequence in Liber XXVII
28 The Trigrams as Polarities
31 Numerical and Trigrammaton Order of the Trigrams
32 Platonic Models of Trigrammaton

Part Two -- Divination
46 Divination Procedure for Casting a Hexagram of Trigrammaton
52 Trigram Sequence in Liber XXVII--Probabilities for Divination

Part Three -- The Hexagrams
54 The Hexagram Tables of Trigrammaton
55 Trigram Values in the Upper Position of a Hexagram
87 The Nuclear Hexagrams
88 The 81 Nuclear Hexagrams Arrayed by their Upper Trigrams
89 Transitional Hexagrams
91 Pairs of Antigram Values in Decimal Notation
96 Antigram-pairs, their differences, the solar calendar and the circle of the zodiac
97 Differences Between Antigrams, in Ordinal Sequence
109 Details of the Antigram Sequence
110 Lower Trigram Sequence
111 The Order & Value Pairs

Part Four -- Applied Magick
113 Trigrammaton and Astrology
116 The Hexagrams and the Circle of the Zodiac
119 Juppiter, the Zodiac Circle, and the Lines of the Hexagrams
120 The Trigrams and the Nakshatras
123 Pentagram of the Five Elements
129 Trigrammaton and Magic Squares:
130 The Kamea of Venus and the Kamea of Mercury
134 The 12 x 12 Magic Square of the Zodiac Trigrams
139 The Kamea of Luna and the 81 lines of Trigrammaton
142 The Kamea of Tunes and the Kamea of Ambergris
144 The Kamea of Baphomet in Decimal Notation
148 The Hexagrams and the Six-Dimensional Hypercube
149 The Tetraktys and the Types of Hexagrams
156 Hexagram Types on the Kamea of Baphomet
164 Gematria Poem on the Perimeter of the Kamea of Baphomet
168 The Magic Hexagon and the Trigrams
171 The Magic Triangle
174 Liber 110001
Part Five -- The Tree of Life
177 The Looking Glass Tree of Life
181 The Looking Glass Tree of Life – Numerical Data
189 The Transitional Triad Tree of Life
192 Thelema and the Tree of Life
198 The Tree of Life as a Multidimensional Template
199 The Alphabet of Liber AL on the Tree of Life
205 The New Naples Arrangement
216 The Lecce Ladder

Part Six -- The I Ching and Trigrammaton
219 Thelemic I Ching
252 I Ching Divination – The Sixteen System
254 The Gematria of the King Wen Sequence of Hexagrams
268 The Lama Govinda Sequence of the I Ching as a Book

Part Seven -- The Triform Energy Cascade
270 Charged Sets of the Trinity
277 Magickal Attributions to the Charged Sets of the Triform Energy Cascade
284 The Generation Tree of the Charged Sets of the Triform Energy Cascade
285 The Integration of the Trigrammaton Qabalah and the Triform Energy Cascade
286 The Family Tree of the Trigrammaton Qabalah
288 The Condensed Tetractys of the Trigrams
291 The Tree of Union
293 The Tree of Union in Three Dimensions
294 The Triform Energy Tarot
302 The Integration of the Tarot and the I Ching

Part Eight -- Commentaries on The Holy Books of Thelema
308 Preface to the Commentaries
310 A Commentary on Liber XXVII
318 A Further Commentary on Liber XXVII
337 Gematria equivalents of the verses of Liber Trigrammaton
339 TQ Commentary on Liber B vel Magi sub figura I
343 TQ Commentary on Liber Cheth vel Vallum Abiegni sub figura CLVI
346 TQ Commentary on Liber A'aSh vel Capricorni Pneumatici sub figura CCCLXX
350 TQ Commentary on Liber Tzaddi vel Hamus Hermeticus sub figura XC
354 TQ Commentary on Liber DCCCXIII vel ARARITA sub figura DLXX
368 TQ Commentary on Liber Cordis Cincti Serpente sub figura LXV
391 Addendum: The Coils of the Serpent
392 The Call of the Coil
393 TQ Commentary on Liber VII vel Lapidis Lazuli
Part Nine -- The Book of the Law

396 The Text of Liber AL vel Legis sub figura CCXX
405 Verse-totals from Liber CCXX in Numerical Order
406 Verse-totals from Liber CCXX in Sequential Order
407 A Comparison of the Verse-totals of the Chapters of Liber CCXX
409 Recursive Verses in The Book of the Law
410 A Trigrammaton Qabalah Commentary on The Book of the Law
411 The Formula of the First Verse of Liber CCXX
414 The Formula of the Ending of the Words
415 The Great Cipher of Liber AL vel Legis, chapter II, verse 76
417 Number Words in the Cipher
417 Digit Pairs in the Cipher
418 The Harmonic Mean in the Cipher
419 Pentagrams and the Cipher
420 The Glyphs of the Cipher Arrayed on a Cube
421 Splitting the Cipher into 143 and 208
422 Miscellaneous Aspects of the Cipher
423 The secret key of Liber AL, verse I:46
428 Pi, Chapter 2, and the Global Sum of Liber CCXX
430 The Word of Nuit and the Mathematics of Verses I:24-25
433 143 and the Sheets of the Holograph Manuscript
435 Thelema 93 and The Book of the Law
437 The Order of the Letters
439 The Gematria Range of the Text of Liber CCXX
441 The Trigrammaton Sequence in Liber CCXX
455 The Scribe and Prophet, Ankh-af-na-khonsu, the Holy Chosen One
458 Self-Identifications of Hadit
459 The Stele, the Kiblah, the Ka’aba, and the Cubical Number
461 Miscellaneous Number Mysteries in Liber CCXX
465 The Four Numerals in the Text of Liber CCXX
469 A Dialogue Concerning Nothing
471 The Secret of the 19th sheet of the Holograph
473 The Grid-page of the Holograph
482 Triangular Numbers and Liber CCXX
487 The Three Grades of Thelemites
491 Three Ordeals in One
493 The Four Ordeals of The Book of the Law
497 A Short Commentary on The Book of the Law

Appendices

501 The Holograph Manuscript of Liber AL
523 Gematria of Verses of the Holy Books of Thelema
555 Gematria of Words of the Holy Books of Thelema
640 Gematria Dictionary of the Holy Books of Thelema
825 The Master List of Ternary Hexagrams
844 Live and Die Daily – 365 Hexagram Meditations
Introduction

This book is an exposition of the Trigrammaton Qabalah, (TQ). The basis of the
TQ can be found in Liber Trigrammaton sub figura XXVII, Being the Book of the
Mutations of the Tao with the Yin and the Yang. This brief document, commonly known as
Liber XXVII, was penned by Aleister Crowley in 1907, and was called by him “the
foundation of the highest theoretical qabalah.”

The key to unlocking Liber XXVII is the realization that the 27 trigrams of this
Holy Book comprise all the numbers from 0 to 26, written in Base 3 notation.

Most of us are familiar with Base 2, or binary, mathematics. Most computers are
based on this principle of counting using only 0’s and 1’s.

In Base 3, there is a third possible digit, so that all numbers are written with 0s, 1s,
and 2s. In Liber XXVII, these digits are represented as Tao, Yang, and Yin. By taking
these three principles, or digits, three at a time, there are 27 possible “trigrams”, or figures
of three lines.

The first principle of the TQ: Tao = 0, Yang = 1, and Yin = 2.

The second principle: Tao is Neutral, while Yang and Yin are opposites.

In line with these two axioms, there is a single trigram that is completely neutral:
the Zero, which is composed of three Tao lines, or 000.

The other result of these axioms is that the remaining 26 trigrams form 13 pairs of
“opposites”, which we will call antigrams.

Antigrams: A pair of trigrams where one is comprised of a set of lines that are
the opposite of the other’s lines. For example, 11 and 19 are Antigrams:

 

11 19

The trigrams of the TQ are used as a classification scheme, to provide a framework
for the symbolism of both the Eastern and Western esoteric traditions. Astrology and
magic squares, the tarot and runes, divination and arithmology, the Tree of Life and sacred
geometry, Taoism and the I Ching, are all absorbed into the TQ system, and explored by
the use of the trigrams.
All of this activity derives from the abandonment of the old paradigm of decimal
mathematics, in favor of the new paradigm of Base 3 mathematics. Simply put, Base 3 is
the foundation for the mathematical mysticism, or qabalah, of the New Aeon.

Within the study of number mysticism, there is a large component devoted to the
“literal qabalah”. This aspect of the qabalah scrutinizes sacred texts in terms of their
numerical value. Traditionally, this is done with the use of three tools: temurah, notariqon,
and gematria.

Temurah is simply the rearrangement or replacement of letters in a word, based on
some formula. Notariqon is the use of letters in a word as anagrams. Neither of these plays
a significant role in the TQ.

The last category is gematria, which is the replacement of letters with numbers so
that words might be given a numerical value. Generally this is done by adding together the
assigned value of all of the letters in a word. This art plays a very large role in the TQ,
under the heading of the Trigrammaton English Gematria, or TEG.

TEG has its basis in the assignment of English alphabet letters to the trigrams,
which was first done by Crowley in his commentary to Liber XXVII, published in his
journal The Equinox in 1912. In this work, Crowley assigned the 26 letters of the English
alphabet to the 27 trigrams, with the exception of the last trigram in the series, which
represents a return into silence, or “the absence of letter”. To determine the value of each
letter, one simply takes the Base 3 value of the trigram to which that letter is attributed.

In Cairo Egypt, April 1904, Crowley penned his most important work, known as
The Book Of The Law. This book was dictated to him by a discarnate intelligence known
as Aiwass. In the second chapter of this work Aiwass says, “Thou shalt obtain the order
& value of the English Alphabet; thou shalt find new symbols to attribute them unto.”
(Hereafter all quotes from the Book of the Law will appear in red italics).

In order to fulfill this prophecy, (as he stated in his Old Comment to this verse),
Crowley assigned the English letters to the trigrams of his other book, Liber XXVII,
making this work the Key to the literal qabalah of The Book of the Law.

Crowley insisted throughout his lifetime that he did not author The Book of the
Law, also known as Liber CCXX. He was merely the scribe for the words uttered by
“Aiwass”. In order to prove this, he found many strands of esoteric knowledge hidden in
the text, and expected more to be found in the future, once the full Key had been
discovered. It would be fair to say he thought the super-human intellect responsible for the
book would be proven by the mathematical perfection of the text. In other words, he
thought that this book contained a message too complex and perfect for a human to have
authored it.

The TEG is an attempt to show that this complexity does indeed exist, and that it is
too perfect to simply pass off as a mere “coincidence”.
To begin a qabalistic exegesis of the text of The Book of the Law, one can start
with the gematria value of the entire book. In doing so, we use Buckminster Fuller’s
“Principle of Synergetic Advantage”, which says: to begin the study of a whole system,
start with the whole.

{The advantage is “synergetic”, because Fuller defines synergy as: “the behavior of
a whole system, unpredicted by the behavior of any of its parts considered separately.” In
this case the behavior of the “whole” can be described as the sum of all of its parts -- the
limit that can be reached by the simplest operation of gematria}.

The baseline of the study of The Book of the Law is the official, typescript version
published as Liber AL vel Legis sub figura CCXX, or simply Liber CCXX.

Using Trigrammaton English Gematria, the entire contents of Liber CCXX --
including all the English letters, numerals, verse-numbers and foreign letters -- is 267,696.
This number has some very interesting properties, and can be found hidden in the
sequence of trigrams in Liber XXVII.

The 27 trigrams of Liber XXVII, in the order in which they appear, have the
following decimal equivalents:

0, 1, 2, 3, 6, 9, 18, 4, 5, 7, 8, 10, 11, 19, 20, 12, 15, 21, 24, 13, 14, 16, 22, 17, 23, 25, 26.

The first three of these numbers are the trigrams of 0, 1, 2, or Tao, Yang, Yin.
These are the three fundamental digits of the Base 3 system, and form the first set. This
initial set will not be used in the calculation that follows.

The second set are the four trigrams that follow, each with only one Yang or Yin
line; these are the four elements of Fire (3), Water (6), Air (9), and Earth (18).

The third set are the next nineteen trigrams, representing the 12 Zodiac signs, the
Sun and six of his planets.

The last set is the final trigram, the one that has no English letter, the number 26.

Summing up the members of these sets, we have:

3, 6, 9, 18 = 36
4, 5, 7, 8, 10, 11, 19, 20, 12, 15, 21, 24, 13, 14, 16, 22, 17, 23, 25 = 286
26 = 26

We can then multiply these numbers and get an amazing result:

36 x 286 x 26 = 267,696