Preliminary - The I Ching reorganized

Abstract: The ancient I Ching is a set of 64 hexagrams which are all the possible unique combinations of the binary numbers 0 and 1 taken as sets of 6. I have renumbered the hexagrams using an octal numbering system. Instead of the classical decimal numbering 1 through 64, the hexagrams are numbered 0 through 77 in the octal numbering system. Since the hexagrams take their new octal numbers from the binary, and octal, digits of which they are comprised, the actual make-up of any hexagram can be ascertained by its octal number alone.

Brief Introduction:

Each six line or binary digit hexagram is composed of two, three line trigrams;

_____

(7)

__ __

(0)

__ __

_____

(4)

__ __

_____

__ __

(2)

_____

__ __

(1)

_____

__ __

(3)

_____

__ __

_____

(5)

__ __

_____

(6)

each line of which can be represented by the numbers 0 and 1, where _____ is 1, and __ __ is 0.

The binary representation of each octal number is;

0, 0, 0 = 0

0, 0, 1 = 1

0, 1, 0 = 2

0, 1, 1 = 3

1, 0, 0 = 4

1, 0, 1 = 5

1, 1, 0 = 6

1, 1, 1 = 7

Because the lines of I Ching hexagrams are constructed from the bottom up to the top line, the numbers beneath the trigrams above are the octal digit of that trigram.

Table of hexagrams

legend –

the number in the upper left of each square denotes the octal number of that hexagram. These numbers are 0-7, 10-17, 20-27, 30-37, 40-47, 50-57, 60-67, 70-77
the number in the lower right of each square denotes the ancient and still used decimal number of that hexagram
The text in each square gives the English name for the hexagram along with the ancient Chinese name
The lower legend gives the hexagrams lower trigram for the vertical column of hexagrams
The left side legend gives the upper trigram for that horizontal row of hexagrams
The octal numbers of the hexagrams are constructed from the binary digits from the bottom up in the same way the coins or yarrow sticks are thrown in the classic method of determining each 3 binary digit, octal digit, or trigram.

A few examples;

The lower left hexagram Standstill, Stagnation, P’i, ancient number 12 above has the octal number 07. It is comprised of the following lines;

_____

__ __

where _____ is one and __ __ is zero. From bottom to top the binary digits of this hexagram are 0, 0, 0, 1, 1, 1. Octally, that is, arranging each set of 3 binary digits as one octal number, the octal number of this hexagram is, therefore, 07.

In the lower left the hexagram octal 07, Standstill, Stagnation, P’i, ancient number 12.

Further study;

Marie-Louise von Franz, in 1968, was the first to publish that the mathematical structure of DNA is analogous to that of the I Ching. She cites the reference to the publication in an expanded essay Symbols of the Unus Mundus, published in her book Psyche and Matter.^--Marie-Louise von Franz Psyche and Matter (Shambhala, 1992) p.39-62. The reference is cited on page 44; she cites the reference as number 16 of the article: Dialog über den Menschen: Eine Fetschrift zum 75. Geburtstag von Wilhelm Bitter (Klett. Stuttgart, 1968).

I have the thought that because the Chinese language is pictographic and because the I Ching is a set of binary, or octally based diagrams that study of the I Ching might elucidate the seemingly different brain functioning of the classical Oriental mind.

If there is no relatively direct use of or numerological significance of the classical I Ching hexagram decimal numbers an octal numbering scheme presented is much more easily workable.