I'll demonstrate it to you in the following text.|
It might be necessary to give some short informations to a rather small book in Hebrew language, which is estimated to have appeared first in 1st - 5th century AD, called SEPHER YETZIRAH "Book of Creation or Book of Formation, produced by an anonymous writer. It might be (and it was) suspected, that parts of the given system of the Sepher Yetzirah are much older than the given date.
There have survived different versions of this text, ranging in their length from 1300 words until 2500 words. 4 different versions you can find in "Sepher Yetzirah" from Aryeh Kaplan, 1993.
The object of the book are "32 ways of wisdom" which with God created the world. 22 of this ways are connected to the Hebrew alphabet, 10 are connected to the socalled Sephiroth (the numbers from 1 to 10). Also involved are astrological symbols, parts of the human body, a sort of letter-combinatoric and someting, which looks a little bit like a linguistic Hebrew grammar. In the different versions of Sepher Yetzirah some attributions are not identical. The text concludes with the note, that the biblical Abraham received this teachings from God somehow claiming the author to be identical with Abraham (writing under the name of an idealized author was not uncommon at the given time for writers of mystical texts)..
The system shown in the book got a big career in the following Hebrew mystic, especially in the historical Kabbala, which started around 1170 AD. There are more than 50 old commentaries on the book. Its strong influence even reached the Western esoterical interpretation of the Kabbala, finally it was related to the Tarot game with its 22 major arcana by Eliphas Levi and the Golden Dawn in the 19th century. In this form it is still very active, as you can see it in the various forms of modern Tarot decks and their astrological attributions, which in most cases go back to the SY.
This is the basic sorting of the 32 ways:
10 Sephiroth (numbers):
- 3 "mothers", - connected to the elements fire, water, air
- 12 "simple letters" - connected to the signs of the zodiac
- 7 "double letters" - connected to the planets and to the six directions of space with the seventh letter presenting the center (so one must perceive this group in a 6+1-structure *)
* Sepher Yetzirah 4.4: "seven doubles ... up and down, east and west, north and south and the holy palace precisely in the center and it supports them all"
This results in the SY-formula:
- 1 element: "Breath of Living God" (Ruach Elohim)
- 3 elements: breath (= Ruach= air), water, fire
- 6 elements: directions of space
(3 + (6+1) + 12)
(1 + 3 + 6)
| Ways of Wisdom: |
= 22 + 10 = 32
Or simple: (3 + (6+1) + 12) + (1 + 3 + 6) = 22 + 10 = 32
In the following it will be demonstrated, that this same formula appears in the
mathematical structure of the I-Ching (only regarding the 64 hexagrams, not the
technic of divination and change). The appearance of this quality in both systems is not miraculous or an unusual "accident", but simply the result of the fact, that both systems use the same mathematical base conditions. The Sepher Yetzirah has its focus on the cube of space (with 6 sides or directions), the I-Ching doesn't focus "philosophically" the cube of space, but just 6 dimensions to explore the various possibilities of its philosophical dualism of Yin and Yang. The Sepher Yetzirah receives "32 ways of wisdom" by its way of mathematical contemplation, the I-Ching "64 hexagrams", which in a specific aspect include the 32 ways of wisdom.
You can connect I-Ching and SY,
- because both theories are based on the same mathematical structure
- because both theories touch each other in the philosophical meaning, both tend to be philosophical explanations, how multiplicity erased from oneness; so there is a similarity of intention.
- .... but naturally each of both is its own system, the I-Ching has elements, which are not part of the Sepher Yetzirah (for instance the divinatory aspects), and the Sepher Yetzirah has parts, which are not part of the I-Ching (for instance the Hebrew alphabet).
- Operation 1: Unite complementary hexagrams and you get 32 hexagram-pairs:
The objects of the I-Ching are the 64 hexagrams.
The objects of the SY are the 32 ways of wisdom.
You can transform the 64 hexagrams in 32 objects by uniting the complementary hexagrams (in my notation "1" shall present a yang-line, "0 " shall present a yin line, I write them horizontally, and the first 1 or 0 shall be the first line)
- Example: 111111 unites with 000000
- Example: 011111 unites with 100000
- Example: 001111 unites with 110000
- Example: 000111 unites with 111000
By this operation you gain 32 objects on both sides, 32 hexagram pairs meet 32 ways of wisdom.
- Operation 2: Form in the 32 hexagram-pairs two subgroups with 22 elements and 10 elements:
The Sepher Yetzirah parts the 32 symbols in a group of 22 letters and 10 Sephiroth.
The 32 I-Ching-hexagram-pairs are partable in a group with 22 "unbalanced
hexagramm-pairs" and 10 "balanced hexagram-pairs".
"Balanced" means, that the pair consists of 2 hexagrams, that have each 3 yang
and 3 yin
"Unbalanced" means that the pair consists of 2 hexagrams, that have different
numbers of yin- and yang-lines (6-0 or 5-1 or 4-2)
- Example: 111111 / 000000 is unbalanced
- Example: 111110 / 000001 is unbalanced
- Example: 111100 / 000011 is unbalanced
- Example: 111000 / 000111 <--- is balanced
- Example: 110000 / 001111 is unbalanced
- Example: 100000 / 011111 is unbalanced
Find out, that there are precisely 10 "balanced hexagram-pairs" and 22 "unbalanced hexagram-pairs".
- Operation 3: Find the subgroups, which are formulated by Sepher Yetzirah.
The SY now separates the 2 main groups in different parts:
22 = 3 + (6 + 1) + 12 (= 3 mothers, 6+1 doubles, 12 simple)
10 = 1 + 3 + 6 (= 1 Breath of God, 3 elements, 6 directions)
You can achieve now the same mathematical grouping, if you part the 32 hexagramm pairs by the following way. The instrument of generation is a "rolling process" (the last line or number (0,1) is repeated as the first line or number etc. in an endless cycling containing 6 steps.). This is the result of the "rolling process" - with one exemption (the 12 simple letters consist of two "merged" cycles, forming a new cycle with 12 elements):
| 1 center (double)
|| 6 directions (doubles)
|| 3 mothers
|| 12 simple
| 111111 / 000000
| 100000 / 011111
010000 / 101111
001000 / 110111
000100 / 111011
000010 / 111101
000001 / 111110
|100100 / 011011
010010 / 101101
100100 / 110110
| 110000 / 001111
101000 / 010111
011000 / 100111
010100 / 101011
001100 / 110011
001010 / 110101
000110 / 111001
000101 / 111010
000011 / 111100
100010 / 011101
100001 / 011110
010001 / 101110
1 Breath of God
101010 / 010101
010101 / 101010
111000 / 000111
011100 / 100011
001110 / 110001
000111 / 111000
100011 / 011100
110001 / 001110
101001 / 010110
110100 / 001011
011010 / 100101
001101 / 110010
100110 / 011001
010011 / 101100
All 64 hexagrams are used to form the "32 Ways of Wisdom"
I think, that the mathematical structure, which is used by I-Ching and SY, is a
very simple and natural one.
So it is not necessary to assume, that there had been any communicative
connection between the author of I-Ching and the author of SY. Both authors
simply used the same structure. But as the structure is the same and the
meditations of the authors followed in their ideas the underlying structure,
there is more than one similarity between the both systems.
The Tarot game was invented in 15th century in a different context. The reason
to chose the number 22 as number of the major arcana was different to the
intellectual model of the SY-author and the I-Ching-author.
When in 19th century Tarot was connected "artfully" to the SY, a new system
arose. From this point on one could assume a connection between I-Ching and
Tarot - but it is a creative game and the world is, what you want, that it is.
The I-Ching has no pictures, and by the way, the Chinese had no alphabet. And
the author of SY probably didn't thought of divination, although his probable
source, the priests of David, cared about it, and their binary use of Urim and
Tunnim (oracle stones) might have led them to adopt the same mathematical
Although the author of SY probably wrote in the centurys after Christ, the
author couldn't have invented the 22 letters and the 10 fingers. This simple
logic leads to the question, if the inventor of the Hebrew alphabet already had
the system in his mind, when he choose the number 22 as the ordering number of
his new invention. Then you are in a time around 1500 BC. Although there is the
possibility, that he accidently (or because of linguistic reasons) took this
number, the probability of an adoption of a scheme that was already known to
him from another context (maybe as a divination-scheme, maybe as a
memory-system) is high.
Actually Aleister Crowley or other authors active in Tarot probably didn't know
about the connection between I-Ching and SY or about the mathematical base of
Some of the kabbalists might have had knowledge about the mathematical base of
SY, but I consider, that - if - there had been only few and they were very
early in time. After the kabbala became famous and therefore connected to all
and everything, I think, people were not able to look at the very simple start
The use of the scheme is already detectable in Old Egyptia, also in the bible, also in Greek Mythology (although in a modified form). And in other cultures. It was just a very common structure in older times, but became in the Western world lost in later generations. It is a very good system, useful as divination tool or memory system. Divination systems and memory systems lost their meaning with the invention of Monotheism and scripture, this should be the reason, why this simple structure was mystified and lost in hiistory.
I detected the relationship myself in 1974 and since that time never found a book or an author, who really did understand it (although there were some, who explained to know something about it; for instance Crowley). Aryeh Kaplan, modern expert in Kabbala of some name and translator of the Sepher Yetzirah, claims, that the 5-dimensional hypercube explains the reason for the "32 Ways of Wisdom". This is, as demonstrated above, a technical error. The 6-dimensional hypercube explains the inner structure of the 32 ways of Sepher Yetzirah. And the 6-dimensional hypercube is nothing else but the mathematical body of I-Ching.