La suddivisione dei 64 esagrammi- Edward A. Hacker and Steve Moore

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Edward A. Hacker and Steve Moore
EDWARD A. HACKER, professor emeritus, Department of Philosophy and Religions,
Northeastern University. Specialties: the Yijing, Aristotelian logic, philosophy of science.
E-mail: a-omega@attbi.com STEVE MOORE, editor, The Oracle—The Journal of Yijing
Studies. Specialty: the Yijing. E-mail: steve@endymion.freeserve.co.uk
Journal of Chinese Philosophy 30:2 (June 2003) 219–221
© 2003 Journal of Chinese Philosophy

A BRIEF NOTE ON THE TWO-PART DIVISION
OF THE RECEIVED ORDER OF THE
HEXAGRAMS IN THE ZHOUYI

The received order of the hexagrams in the Zhouyi is divided into
two unequal parts. The first part contains thirty hexagrams and the
second contains thirty-four. The purpose of this note is to suggest a
simple solution for this asymmetrical division.
The suggested solutions to this unequal division seem to fall into
two categories: (1) the hexagrams were originally evenly divided into
two parts, but a mistake occurred that resulted in an uneven division,
and (2) the uneven division hides a deeper symmetry. Richard Rutt
falls into the first category. He states that at the time the sixty-four
hexagrams were divided into two parts, the Chinese wrote on bamboo
slats that were bound together by cords. He theorizes that the “fraying
of the cords might lead to jumbled slats, which could explain . . . the
unequal length of the two parts. . . .” Alfred Huang falls into the
second category. In a manner too complex to present in detail, he
attempts to show that the received order has been structured in terms
of yin and yang, the meanings, attributes, and familial aspects of the trigrams,
and so forth, to provide a “hidden balance” of yin and yang
throughout the order and between the two unequal halves. As a result
of this approach, based on traditional philosophical concerns, he
believes that the book has been divided unequally in order to demonstrate
this “hidden balance”. The authors of this article believe there
is too much “special pleading” in Huang’s approach to be convincing.2
The suggestion offered in this note is that, at the time the two-part
division was made, there was a way of “writing the hexagrams” such
that the hexagrams were equally divided, using eighteen in each part.
These thirty-six hexagrams represented the sixty-four hexagrams in
the received order. Such a compact way of writing the sixty-four hexagrams
is found in the Zhouyi Tushi Dadian (Encylopedia of Zhouyi
Diagrams)(3).

* The original is from the Zhouyi Qimeng Yizhuan by Hu
Yigui (b. 1247).
La figura si vede nell'articolo qui non la si può riprodurre

The table (which “reads” from right to left, beginning with qian at
upper right) contains two lines with eighteen hexagrams on each
line. The hexagrams are not numbered, but labeled by their names. If
the inverse of a hexagram differs from the original, then its name is
written upside down above it, indicating that one should turn the
hexagram upside down to read the name of its inverse. In this way,
one figure represents both the hexagrams in an invertible pair. There
are fifty-six hexagrams that may be represented as invertible pairs,
and these may thus be condensed to twenty-eight hexagram-figures,
their inverses being named when the table is turned upside down.
There are eight hexagrams that are not invertible in this way. In such
cases, they are paired by opposites. These pairs are 1/2, 27/28, 29/30,
and 61/62. All eight of these hexagrams have to occur individually in
the table, since their inverses are identical to their originals.When one
looks at the above table, thirty-six hexagrams are represented; turning
the table upside down reveals twenty-eight more hexagrams (36 + 28
= 64). However, it will be noted that there is an uneven distribution
of these opposite or non-invertible pairs: three pairs appear in the top
line of the table, and only one in the lower line. As a result, the top
line of the table represents hexagrams 1–30, as they appear in the
received edition of the Zhouyi text, while the lower line represents
hexagrams 31–64.
Our hypothesis is that the current division of the Zhouyi text
resulted from just such an exercise as that represented by Hu Yigui’s
tabulation. The eighteen hexagrams in the upper row (and their different
inverses) became part one of the received order, and similarly
the lower row became part two. Thus, there are eighteen hexagram
figures (compact version) in each part—symmetry has been restored.
It is also interesting to note that the number thirty-six (the number
of hexagram figures in the compact version) is a square, as is sixtyfour.(4)

We might speculate that writing on bamboo slats may have been a
motive for seeking compactness. However, knowing the Chinese penchant
for speculative manipulation of the hexagrams from at least as
early as the Han dynasty, it seems just as likely that we need look no
further than a “philosophical” diagram such as that of Hu Yigui for
the origin of text’s current division.

NORTHEASTERN UNIVERSITY
Boston, Massachusetts
ROYAL ASIATIC SOCIETY
London, England
Endnotes
1. Richard Rutt: Zhouyi: The Book of Changes (Richmond, Surrey: Curzon Press, 1996),
p. 105.
2. Alfred Huang: The Numerology of the I Ching: A Sourcebook of Symbols, Structures,
and Traditional Wisdom (Rochester,VT: Inner Traditions, 2000), Chapter 6, pp. 57–84.
3. Zhouyi Tushi Dadian [Encylopedia of Zhouyi Diagrams] (Beijing: Zhonguo gongren
chubanshe, 1994),Vol. 1, p. 601.
4. We should point out that Alfred Huang (op. cit., p. 63) is also aware that the two divisions
of the book can each be represented by eighteen hexagrams, although he seems
unaware of Hu Yigui’s tabulation. However, Huang draws an opposite conclusion to
the hypothesis presented here. He believes that because the received order is divided
into unequal parts according to his theoretical explanation, so, as a result, the unequal
parts can each be represented by eighteen hexagrams.
Chinese Glossary
Hu Yigui Zhouyi Qimeng Yizhuan
Qian Zhouyi Tushi Dadian
Zhouyi