KW Table

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the King Wen SEQUENCE

in tabular form

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KW Table

The King Wen Table The King Wen Sequence in Tabular Form

by József Drasny

Second, improved edition

Copyright © Drasny József , 2013

http://www.i-ching.hu

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KW Table

Summary

For over the last two thousand years, scholars have been unable to come into

accord on the meaning of the arrangement of the hexagrams in the traditionally received

(King Wen, KW) sequence. In fact, besides the connection of the odd and the

subsequent even numbered hexagrams, it is hardly possible to find any relation between

the content of a given sign and its place in the row. Beginning with the ninth wing of the

Yijing (the Xu Gua), many different explanations have been suggested on the possible

meaning of this arrangement. In the opinion of many scientists, the sequence hides some

kind of ancient astronomical, physical, mathematical, or other knowledge. Many others

say the sequence was generated randomly, and it is useless even to think about any

order in it. In short, there is no generally accepted theory that would explain the place of

each hexagram in the KW sequence.

In this short study a two-dimensional arrangement will be shown, the King Wen

Table. It has been generated from the KW sequence by the simplest way. In this table,

certain groups of related hexagrams can be discovered, having regular positions there.

In the sequence, however, these groups and their structure are not recognizable.

Consequently, the well structured KW Table can be rightly considered the direct

predecessor of the irregular sequence. If somebody wants to find any meaning or

significance in the arrangement of the hexagrams, it is also well worth to study this

table.

Still, based on the structure of the KW Table, a good guess can be made about

an earlier arrangement, the King Wen Array.

Throughout this argumentation, there are facts based on observations, and there

are assumptions based on these facts: The final hypothesis has at least one advantage

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KW Table

over the other explanations: it is in accordance with the rule of Ockham’s razor, using

the fewest and simplest assumptions.

In a former work, the author set forth a theory on the spherical arrangement of

the hexagrams, the Yi-globe.1 There, among others, he dealt with the development of the

KW sequence from the structural elements of this sphere. The Yi-globe, however, was

only a hypothetical form and originating the KW sequence from might also seem

conjectural. In this article, a more general solution will be demonstrated, based on the

positions of the hexagrams in the KW sequence alone, without any reference to the Yi-

globe at all.

The King Wen Sequence in Tabular Form

Regularities in the King Wen Sequence

In the traditional sequence, there are two well-known regularities:

a) In the sequence, each even numbered hexagram, except the eight symmetrical

ones, is followed by its reverse sign (twenty-eight pairs altogether).

b) The eight symmetrical hexagrams are in pairs with their complements (four

pairs).

With respect to the order of the pairs, opinion varies considerably. The main

views can be classified as follows. There are only two or three works given as examples

in each group. They are subjectively picked out from the vast literature, from scholarly

books to metaphysical websites, simply to demonstrate the diversity of opinions. A

more systematic and scholarly work on this this subject was published by Steve Moore.2

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KW Table

a) The traditional sequence comes from King Wen, and it is the only authentic

arrangement. There are close relations between the contents of the adjacent

hexagrams and pairs, and/or there are coherent groups in the sequence. For

example:

- The ninth wing of the Yijing contains explanatory notes on the

connection of each hexagram with the previous one in the sequence.3

- Liu I-ming took the hexagrams as successive steps along the way

towards perfect enlightenment.4

- Frank Kegan identifies six sets of ten successive hexagrams, each with a

particular function. In the sets, a special meaning is given to each place.5

b) There has to be some kind of regularity in the sequence but it is unknown and

waits for discovery. The representatives of this view usually propound a rule,

disclosed by them. For example:

- The monograph of Richard S. Cook “resolves the classical enigma. It

provides a comprehensive analysis of the hexagram sequence, showing

that its classification of binary sequences demonstrates knowledge of the

convergence of certain linear recurrence sequences.”6 (Citation from the

editor’s note on the book.)

- Based on the principles of his “Novelty Theory”, Terence McKenna

constructed a mathematical function, using numerical values derived

from the King Wen sequence. Using this “Timewave Zero” formula, he

predicted the “end of time” at December 21, 2012.7

c) There are different, new arrangements; some developed long ago, others more

recently, with additional meanings. They in many ways seek to compensate for

the lack of universality in the traditional sequence. Two of these inventions are

as follows:

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KW Table

- In the “natural” system of Shao Yong (1011–1077), the sequence starts

with the Creative. In the following signs the lines gradually change,

beginning from the upper line and down to the lowest one, according to a

definite rule. In fact, this arrangement is a kind of transcription of the

binary numbers (derived much later) from 111111 to 000000.8

- Andreas Schöter arranged the hexagrams in a lattice “by energy level,

from the least energetic at the bottom, to the most energetic at the top. …

In mathematical terms, this is a six-dimensional hypercube.”9

d) There is no order in the sequence, nor should we try to create one. This is the

view of most users and readers. They say the essence of the book is not in the

arrangement of the hexagrams but in their meaning separately and together. The

meaningful pairs are enumerated in the sequence at random, without any rule or

order among them.

- Bradford Hatcher thinks the pairs have been scrambled into a random

sequence, and the efforts of finding some order in this sequence are

simply a useless expenditure of time.10

The argument made in this paper partly belongs to group b above because it

discloses some kind of regularity in the traditional sequence. However, this order comes

from another, geometrical arrangement that has not been known up to the present.

Three regular groups in the King Wen sequence

In the Yijing literature, there are well-known short or longer sequences and

groups where the hexagrams are categorized according to the meaning or the

composition of the hexagrams. The following gives examples of such groups:

- The eight doubled trigrams, composed from two identical trigrams;

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KW Table

- Nine hexagrams that show the development of character;11

- The twelve sovereign (waxing and waning) hexagrams;

- Jing Fang’s “eight palaces” (or eight houses), with eight hexagrams in each.

Observing the twelve sovereign hexagrams and two other groups, so far

unknown relations can be found among their ordinal numbers in the KW sequence.

1. The ordinals of the sovereign hexagrams are: 1–2, 11–12, 19–20, 23–24, 33–34,

43–44.

2. The ordinals of the hexagrams in the sequence, created by exchanging the

trigrams in the sovereign hexagrams, are: 1–2, 11–12, 9–10, 15–16, 25–26, 45–

46.

3. A group where the hexagrams are composed from two opposite

(complementary) trigrams, in other words, from the opposite pairs of the Earlier

Heaven: 11–12, 31–32, 41–42, 63–64.

As it is easy to see, the differences between the ordinals in these groups are in

connection with the number ten (see the bold-faced numbers). These connections are

frequent enough to see them as an indication of some kind of regularity.

It will be useful to demonstrate this regularity in a table (Figure 1).

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KW Table

Figure 1. Three groups in tabular form

There are three rows in the table, one for each group:

- The pairs of the Earlier Heaven are in the first row.

- The sovereign hexagrams are in the second row. The Creative and the Receptive

(#1 and #2) are not included here because their places have been assigned to the

leading positions, probably in the long past. As for the pair #11–12, it has been

already placed in the first row.

- The third row contains of the opposite hexagrams of those in the second row

(with the exchanged trigrams).

In this arrangement, it is easy to find regularity among the elements. Each of the

four columns consists of the first three pairs of four consecutive decades respectively.

There are only three pairs not following this order; they have two asterisks (**) on

them.

- Column 1: #11–12, #19–20 (instead of #13–14), and #15–16.

- Column 2: #63–64 (instead of #21–22), #23–24, and #25–26.

- Column 3: #31–32, #33–34, and #9–10 (instead of #35–36).

- Column 4: #41–42, #43–44, and #45–46.

Putting to one side the three anomalies, Figure 1 seems to be the part of a greater

table in which all the hexagrams would be found (Figure 2).

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KW Table

Figure 2. The King Wen sequence in table form

The numbers in the cells proceed one another in order, ten (five pairs) in each

columns, and indicate the position of the given cell in the table. In the frame of double

order, the arrangement of the ordinal numbers visibly agrees that of the hexagrams in

Figure 1. That is, the cell No 11–12 holds the hexagrams #11–12, the cell No 31–32

holds #31–32, and so on. The cells No 21–22, 13–14, and 35–36 are exceptions,

corresponding to the three misfits in Figure 1.

The cells of the three hexagram sequences dealt with above are marked with

different colors. It can be well seen that each of these sequences has one definite region

in the table: they are the three rows in the frame. That is, these groups of hexagrams

have their own regions in the table, though one pair in each group stands separately and

there is an ‘alien’ hexagram on their places. Still, the regularity of this arrangement is

apparent and can be formed as follows.

There are three groups of hexagrams where the elements belong together in a

definite way (by form and content). Arranging the hexagrams into the table of

Figure 2 and in the cells corresponding to their ordinals, the elements of each

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KW Table

group remain together in adjacent cells, forming a separate region for the

group.

The question is whether could be this regularity applied to other groups of the

hexagrams. First, with a view to answering this question, it is necessary to examine

more exactly the common characteristics of the hexagrams in the three groups

mentioned above.

Group of the eight directions (DIR8)

Previously, the hexagrams of the first group were defined as comprising the

opposite pairs of the Earlier Heaven. They can be seen in Figure 3, in detail.

Figure 3. The four pairs of the Earlier Heaven (Group DIR8)

In this diagram, the hexagrams are in the order as they are placed in the cells of

Figure 2 (the KW sequence in table form), from No 11–12 to 41–42. Under the images

of the hexagrams, there are the names of the upper and the lower trigrams. The numbers

below are the ordinals in the KW sequence. The double lines indicate the boundary of

the region. Three pairs in the region contain the opposite (complementary) trigrams of

the Earlier Heaven; they are individually framed and shadowed. In the second cell,

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KW Table

however, the hexagrams (#21 and #22) are different. The missing pair of the group is

#63–64; it is shown outside the region.

In the eight hexagrams of this group, i.e. the hexagrams in the grey cells, the

upper and the lower trigrams are the complements of each other. In the circular diagram

of the Earlier Heaven, these trigrams are in opposition, and their connecting lines show

the eight directions of space. Hence, this is the group of the eight directions, DIR8 in

short.

Group of the sovereign hexagrams (SOV8)

The second row belongs to the group of the eight sovereign hexagrams. (As it

was noted above, two pairs of this sequence, #1–2 and #11–12 have already been placed

in other cells.) In this group, one trigram in the hexagrams is always the Qian or Kun,

and the other is one of the children, excepting the Li and Kan. The group is named

SOV8 after the eight hexagrams of the sovereigns.

In Figure 4, the hexagrams of this row are shown.

Figure 4. The eight sovereign hexagrams (Group SOV8)

The arrangement of this diagram is similar to that of Figure 3. Three pairs of the

eight sovereigns, #23–24, #33–34, and #43–44 are settled in the frame. The pair #13–

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KW Table

14, however, does not belong to the sovereign hexagrams but occupies a cell in the row.

The fourth pair of the sovereigns is #19–20, and it is outside this region, in the cell 19–

20. It is shown beside the region.

Group of the sovereign hexagrams with exchanged trigrams (SOVX)

The third sequence contains the opposites of the eight sovereign hexagrams in

the previous group (SOV8); the upper and the lower trigrams are exchanged in them.

They are shown in Figure 5. The pair #35–36 is the alien and the missing pair is the #9–

10; the latter stands outside the region.

The constitutive trigrams are the same as those in group SOV8: the Qian or Kun,

and one of the children, excepting the Li and Kan. This is the group of the eight

sovereigns with exchanged trigrams, SOVX in short.

Figure 5. The eight sovereigns with exchanged trigrams (Group SOVX)

Based on the above observations, it seems to be worthy to look for other regular

groups in the table. As it was formulated above, regularity means some groups of

hexagrams being coherent according to their upper and lower trigrams, and the distinct

regions for these groups in the table.

The next four regular groups in the King Wen sequence are as follows.

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KW Table

Group of the four cardinal trigrams (CPT4)

It was found that in the groups SOV8 and SOVX, in the majority of the

hexagrams, one trigram was the Qian or Kun, and the other was one of the ‘children’,

but the Li and Kan are excepted. A new regular group can be created from the

complementary hexagrams, where beside the Qian and Kun, the Li and Kan should be

the second trigrams.

In the first column of Figure 2, the first pair (#1–2), has an exceptional and

distinguished place, but below them the hexagrams #5–6 and #7–8 have the above

required qualities. The one is composed of the trigrams Qian and Kan, and the other

from the Kun and Kan, but the Qian–Li and the Kun–Li pairs are missing.

There are two pairs, however, with the combinations sought, in the cells No 13–

14 (Qian and Li) and in No 35–36 (Kun and Li), where apparently they do not belong to

the given group (see Fig. 4 and Fig. 5). These hexagrams (#13–14 and #35–36) will

make the first column complete, replacing #3–4 and #9–10 in their present cells. As a

matter of fact, the pair #9–10 obviously belongs to group SOVX, to the cell No 35–36.

Also #3–4 will find its correct place in another group and region.

All these pairs can be seen in Figure 6.

Figure 6. The hexagrams of the four cardinal points (Group CPT4)

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KW Table

After the necessary replacements, one trigram in these hexagrams always will be

Qian or Kun, and the other the Li or Kan. These characteristics make these four cells the

region of the four cardinal points of space. Thus, the group is termed CPT4.

Group of the children of same sex (SAMX)

Following the three rows in the middle of the table, the hexagrams in the fourth

and fifth row are shown (Figure 7).

Figure 7. The pairs of the children of same sex (Group SAMX)

Examining the eight pairs here, four of them can be found that are composed of

the same rule: #27–28, #37–38, #39–40, and #49–50. They are shadowed in the frame.

Their composing trigrams are the pairs of two different ‘sons’ (from the Zhen, Kan, and

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KW Table

Gen) or two different ‘daughters’ (from the Xun, Li, and Dui); there are no ‘mixed’

pairs. In addition, there are two pairs that correspond to this rule and belong to this

group but they are at other places in the table, in the cells No 3–4 and 61–62 (the

hexagrams #3–4 and #61–62). The irregular pairs are in the cells No 47–48 and 29–30,

and make the recognition of the regularity difficult.

The hexagrams #17–18 and #19–20 remain outside this group and the region.

This group will be marked SAMX, according to the combination of the

hexagrams from two children of same sex.

Group of the children of opposite sex (OPPX)

The complementary part of group SAMX contains the hexagrams with the

trigrams of opposite sex. These are at different places of the table as follows:

- Three pairs, #53–54, #55–56, and #59–60 are together in the sixth column, with

the double trigram #57–58 sandwiched between them.

- The pair #21–22 would join with these, in the cell 63–64. There, the pair #63–64

is alien because it belongs to DIR8 and its place is the cell No 21–22.

- The pair #17–18 resides separately, in cell 17–18.

- Also the pair #47–48 remains without a dwelling place. At present, the only

empty cell in an unfilled region is at 19–20, and it may go there.

- Still, three pairs in the first row (#11–12, #31–32, and #41–42) are composed

from the trigrams of opposite sex but they belong to a separate group of higher

rank, to the group of the Earlier Heaven (DIR8).

The six pairs enumerated above (the three pairs in group DIR8 not included) are

shown in Figure 8. Four of them are in the region of the last columns and two are in the

adjacent cells at the lower end of the second column.

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KW Table

As was the case with the other six groups, these hexagrams have common

qualities in terms of their composition. The twelve hexagrams contain the son–daughter

combinations of the trigrams. They will be named group OPPX, after the children of

opposite sex.

Figure 8. The pairs of the children of opposite sex (Group OPPX)

Group of the eight double trigrams (DBL8)

In terms of their composition, the double trigrams obviously belong together,

even though they are scattered in the table of the KW sequence. Only two pairs, #51–52

and #57–58 are together in the sixth column, although not in adjacent cells.

The places are shown in Figure 9.

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KW Table

Figure 9. The eight double trigrams (Group DBL8)

The reason for the separate place of the Creative and the Receptive (#1 and #2)

has already been offered. With respect to the fourth double pair, the Abysmal and the

Clinging (#29 and #30) do not have regular place in cell No 29–30, in the region of

group SAMX. Instead, their expected cell would be No 61–62, beside #51–52, at the top

of the last column. There, the pair #61–62 is alien and belongs to the group SAMX. In

this way, three pairs of the double trigrams would be close to each other, but only two

of them will be located in adjacent cells, in No 51–52 and 61–62. Their common region

is in the last two columns.

The group of the eight double trigrams will be named as DBL8.

The composition of the seven groups is shown in the next table (Figure 10). The

boldfaced numbers indicate the hexagrams that are within their corresponding region,

the other hexagrams are the aliens.

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KW Table

Figure 10. The composition of the seven groups

Now, the table of the KW sequence can be completed with all the groups and

regions (Figure 11).

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KW Table

Figure 11. The table of the KW sequence with the groups and regions

Here, the color of each cell designates the group to which the two hexagrams in the

given cell belong. Apparently, the majority of the hexagrams belong to definite regions of

adjacent cells in the table except for one or two alien (misplaced) pairs. In detail:

The table contains six regions, regularly arranged in the rows and columns. (The

sixth region consists of two separate parts: the last two columns and two adjacent

cells at the end of the second column.)

In each of these regions, a particular rule can be applied for the composition of the

majority of the hexagrams. In such a way, seven groups of hexagrams have been

created (two groups in the sixth region).

It is important to note that in the individual groups, all the possible opposite

hexagram pairs are present, i.e. the reverse and the inverted hexagrams, and the

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KW Table

hexagrams with exchanged trigrams. (The exchanged trigrams of group SOV8 are

separately in group SOVX.)

Based on these regularities, it can be supposed with reason that this tabular form

(or a very similar one) had been deliberately developed it was in use before the linear

KW sequence.

At some unknown time in the past, however, the table was extended in one row,

following the rules of Chinese reading (reading the columns from the top down). In

such a way, the adjacent hexagrams in the horizontal rows departed from each other,

and their connections became unrecognizable.

This kind of transformation of the table may have happened when the demand

occurred to make records of the hexagrams together with the associated judgments and

line texts. In the course of recording, the hexagrams were written at the top of a bamboo

slip (or other material) and the corresponding texts below. Each hexagram had one or

more bamboo slips and they all were tied together, one beside the other in a row. The

succession of the hexagrams mechanically followed their order in the table, i.e., it went

according to the rules of Chinese reading, from the top down and consecutively in the

columns. That is to say, the linear sequence of the hexagrams was only a formal

necessity, determined by the form of writing. By that time (before the second century

BC), the original sense of the arrangement had probably been forgotten and might not

be taken into account. Afterwards, the text and the linear arrangement served as the

basis of the canonized Yijing classics, and the sequence has remained unchanged until

today.

A similar case would occur if somebody read an English poem according to

Chinese practice, beginning with the first word of each line, then the second word, and

so on. In the end, the sense of the verse would completely disappear. This might happen

with the original tabular form of the hexagrams.

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KW Table

Changes in the table of the KW sequence

The hypothesis about the transformation of the table into the KW sequence

would be more easily acceptable if an explanation was found for the positions of the

hexagrams that lie outside the region in which one would expect to find them.

It is rather easy to find reasons for two changes that refer to the pair #29–30 (the

Abysmal and the Clinging) and #63–64 (After Completion and Before Completion). In

the Yijing, the hexagrams are divided into two parts, from 1 to 30 (Upper Canon) and

from 31 to 64 (Lower Canon). It can be supposed with reason that the two pairs above

were intentionally removed from their original positions in consequence of this

separation, on the occasion of the transformation of the table into the sequence.

In the table, the Abysmal and Clinging pair originally had to be in cell 61–62,

and not in 29–30, as they were shown in Figure 11. In the tabular arrangement, these

hexagrams might be among the other double trigrams, in the last columns. Similarly to

the Creative and the Receptive (#1–2) at the head of the first column, the Abysmal and

Clinging had to be at the top of the last one. These four hexagrams, in the diagram of

the Earlier Heaven, in their simple trigram form, represented the four cardinal points of

the universe. In the table form, they might have the same role; they marked out the

limits of the created world. In the linear arrangement and at its separation in two parts,

the Abysmal and the Clinging would have lost their distinguished position, ending up in

the insignificant penultimate place in the second part of the sequence. Not willing to

allow this to happen, they were removed to a similar, important position, at the end of

the Upper Canon, changing place with the Inner Truth–Preponderance of the Small

pair. Thus, in the sequence, they received the ordinal numbers 29–30 according to their

new positions.

A similar change-over may have happened at the places 21–22 and 63–64. In the

table, the functionally correct place of the After Completion and Before Completion pair

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KW Table

was in the cell 21–22 (see Figure 3). After the transformation and the partition, it was

also necessary to close the Lower Canon with one of the cardinal hexagrams, as

happened in the first part. For this reason, the two signs of Completion were removed to

the end of the sequence, changing places with the less important Biting Through–Grace

pair in cell 63–64. Thus, the two pairs, the Creative–Receptive and the After

Completion–Before Completion, as the symbols of the Heaven and the Earth, and the

Beginning and the End, provided a symbolic frame to the whole material, and got the

last two ordinals, No 63 and 64.

In such a way, a reasonable explanation may be given for the location of these

four misplaced or “deviant” pairs. Before these changes, the table might have had the

form of Figure 12. Here, in the cell 21–22, the hexagram pair #63–64 occupies its

correct place in the region of group DIR8, and the pair #21–22 is in the last column,

among the members of its own group OPPX. Similarly, the pair #29–30 is in its original

cell 61–62 at the top of the last column, and #61–62 occupies the cell 29–30 in the

region of group SAMX.

Figure 12. The table of the KW sequence just before the transformation

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KW Table

Replacing the ordinal numbers with the images of the hexagrams, the following

table will be developed (Figure 13). According to the hypothesis, this was the

arrangement just before the transformation. Also, it may be perfectly right to call it the

King Wen Table (after the King Wen Sequence).

Figure 13. The King Wen Table

Notes to Figure 13:

1. The numbers on the upper row denote the limits of the present KW ordinals of the

hexagrams in the corresponding column. (The exceptions are the #63–64 and #21–22 pairs,

and the #29–30 and #61–62 pairs, as was shown in Figure 12 above.)

2. In the diagram, the misplaced pairs are marked with small circlets. According to the

ordinal numbers, each of these pairs has a given position in the array but by composition it

belongs to another cell in another region. The color of the circlets shows the proper region

of the pair.

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KW Table

3. The vertical line X---X shows the plausible place where the table might have been

cut in half before the extension in the row.

Here, there are only six pairs that stand in wrong cells; each of them takes the

place of another pair of the six. It is rather easy to see the misplacements: the pair #9–10

has changed place with #35–36. The other four pairs have changed places successively,

from cell 3–4 to 13–14, from 13–14 to 19–20, from 19–20 to 47–48, and from 47–48 to

3–4. At present, no reasons can be found for these changes. These anomalies, however,

are so few in number and in proportion that the whole table can be regarded as a regular

design with a few incidental errors and not a random array with so many uniformities.

The series of the latter misplacements in the table might happen in another way.

The hexagram pair #35–36 originally might be in the cell 3–4 and not in cell 9–10 as it

was supposed in the above example. This meant six successive misplacements; the

hexagrams in the cell 3–4 were moved to the place 35–36, from 35–36 to 9–10, from 9–

10 to 13–14, from 13–14 to 19–20, from 19–20 to 47–48, and from 47–48 to 3–4. That

is, the whole process of the changes was carried out not at random, but in a cyclic way.

Still, there is a disturbing element in the KW matrix, where two pairs stand

separately, in the cells 17–18 and 19–20. They belong to group OPPX, according to the

composition of the hexagrams. It might have been the case that in an earlier variant of

the KW matrix, they were together with the other members of this group in the last

column, and their present cells were empty. This question will be discussed later.

To sum up, the formation of Figure 13 could be and indeed had to be the

arrangement of the hexagrams just before the development of the KW sequence. After

the extension of the columns in a row, the sequence was cut in half, and, at last, the

pairs #29–30 and #63–64 occupied their distinguished places at the ends of the Upper

and the Lower Canon respectively (see the arrows on Figure 14). This sequence has

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KW Table

remained unchanged until now, and has become the traditionally received, so-called

King Wen sequence (Figure 14). Later still, the ordinal numbers were added.

Figure 14. The King Wen sequence, just after the transformation

It is often said that the arrangement of the hexagrams in this sequence has been

made randomly. In the demonstration above, however, we have seen that each

movement of the hexagrams was a conscious choice, following their order in the table

and placing the hexagrams successively in the linear arrangement. From this point of

view, the KW sequence may be considered the regular extension of the King Wen

Table.

Conclusion

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KW Table

At the beginning of this article, it was shown that the arrangement of the

hexagrams in the KW sequence contained some traces of an order. This order became

visible when the hexagrams were arranged in a rectangular array of five rows and seven

columns. The transformation of the sequence into this form was very simple: ten

consecutive hexagrams (five pairs) went to each column. The last three cells remained

empty (Figure 2). Observing the compositions of the hexagrams and their positions in

the array, two rules might be established:

- The hexagrams were distributed in classes (groups), collating their ordinal

numbers and the constituent trigrams.

- A definite region (a rectangular area of adjacent cells) in the array was

associated with each group (Figure 13).

- There were only six pairs out of these rules.

The classification of the hexagrams, the arrangement of the regions, and the

strong relationship between the groups and the regions likely have resulted from the

conscious design of this table by one or more intelligent person at some point in the

distant past. In contrast, the hexagrams in the traditional King Wen sequence apparently

do not have any order other than the traces of the rectangular array.

The irregular KW sequence, in great probability, has been preceded by the

regular, two-dimensional King Wen Table.

Accepting the above hypothesis, the further guessing will be easier in connection

with the significance of the KW sequence. The sequence only seems to be the

simplified, mechanically extended variant of the KW Table. If somebody should want

to find some hidden meaning in the arrangement of the hexagrams or in their mutual

relations, he/she will have to search in this tabular form for it.

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KW Table

Supplement

On the basis of the conclusion above, I have made some speculations on the

possible arrangements of the hexagrams before the existence of the King Wen Table. I

supposed that this table had had an earlier variant where all the hexagrams were

regularly arranged and there were not any ‘deviant’ pairs.

Earlier arrangements

At present, there are rules for the classification of the hexagrams and there are

rules for the placements of the groups in the array. In the past, there had to be a

conscious mind that planned and elaborated these rules and they certainly were

applicable for all the hexagrams, without exceptions. The misplacements might be made

intentionally or at random but they had to happen in an originally regular arrangement.

Thus, knowing the rules, the original, regular array can be reproduced by

removing the deviant pairs to their determined correct positions (Figure 15).

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Figure 15. An early variant of the King Wen Table

Here, in accordance with the (supposed) intentions of the creator, still two

modifications have been made. The three pairs of the double trigrams in the last

columns were united in one region, and the six separated pairs of group OPPX received

a common area. The necessary changes were as follows:

- The hexagram pair #57–58 went up to the cell 53–54, adjoining #51–52. At the

same time, #53–54 and #55–56 got one step lower, to the cells 55–56 and 57–58

respectively.

- The pair #21–22 from the cell 63–64 moved to the next cell 65–66, and the two

pairs from cells 17–18 and 19–20 went to the empty cells at the end of the last

column. Thus, all the members of group OPPX came together in a rectangular

region at the end of the table.

- Three cells remained empty: 17–18, 19–20, and 63–64.

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The result of these modifications was an arrangement where every group,

including the DBL8 and OPPX groups, had its own, rectangular region in the array.

At this moment, one has to think about the occurrence of the arrays in real life.

The above tables (Figures 14 and 16) represent the sixty-four hexagrams in the plane as

they might have been arranged in the ancient past. Here, they are shown in the form of

modern drawings but in the past they could not been easily realized with the

contemporary tools. In fact, these arrangements probably were composed from discrete

objects (such as pieces of oracle bones, tortoise shells, bamboo slips, etc.) and laid out

on a table or on the floor. There, it was not necessary to have sixty-four pieces of them

because the reversed hexagrams could be simply shown by inverting the corresponding

hexagram upside down. Only the four symmetrical pairs (#1–2, #27–28, #29–30, and

#61–62) had to be made from two pieces each.

On this subject Larry J. Schulz referred to the essay of Lai Zhide (1525–1604).

He wrote:

Lai offered an explanation for the division of the Zhouyi into two sections of

unequal length. In his opinion, Wen Wang, the progenitor of the Zhou

dynasty, treated the inverted gua pairs as single six-line units when he

established the Zhouyi order. That is, if the second pair of gua Zhun and

Meng, and all others in invert pairs are counted as one unit and the eight

linear opposites … are counted individually, the result will be 18 units in the

“Former Section” and 18 in the “Latter”.12

Using this form of representation, the most expressive and the most probable

variant of the rectangular arrays can be visualized (Figure 16). Here, each cell only

contains one single hexagram that represents both members of the corresponding

reversed pair. The symmetrical pairs occupy two adjacent cells. Now it becomes

seemingly apparent why have the three cells remained empty just beside the

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symmetrical pairs in the former table (Figure 15): those are the places of the second

members of these pairs.

Figure 16. The King Wen Array

Looking at this array, I have to think about a wise man sitting on the floor,

taking the wood tables one by one out of a pile, and arranging them in rows and

columns before him. He carefully examines the images, contemplates the meanings, and

decides their places in the layout. If such a man had ever lived, he might have been Ji

Chang himself, the later King Wen, or somebody else whose work would have been

attributed to the King. Anyhow, I should call this arrangement the King Wen Array

because it is worthy of this name.

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This array might be very convenient for the daily use. It was easy to keep in

mind and to reconstruct it from memory. Owing to a lack of any recorded form,

however, in the course of centuries (from the era of King Wen to the first manuscripts),

the meaning of the arrangement might have been forgotten and the pieces of the

hexagrams were removed from their original places through ignorance or by accident.

The last corrupted variant might be the array of Figure 13, with relatively few changes

in it, in comparison with the elapsed time. Then, from that variant the known sequence

has been evolved.

When contemplating the King Wen Array, one also should find a rich

symbolism. In my imagination, for example, the rectangular array may represent a

house or a palace, supported by two pillars on the sides. The hexagram groups may be

the main building blocks and the cells are the bricks. Each element has its own meaning,

but its position in the array, the group to which it belongs, and the surrounding

hexagrams add much more significance to it. Others may find different interpretations;

all may lead to a better understanding of this old mystery.

Still, I thank Steve Marshall for reading my early manuscript and offering useful

and valuable remarks that changed my attitude to the subject.

Endnotes

1 Drasny József, A Ji King elfeledett világképe – A Ji-gömb (The forgotten worldview of the I Ching

– The Yi-globe). (Budapest: Szenzár Kiadó, 2005). 2 Steve Moore, Structural Elements in the King Wen Sequence of Hexagrams. Oracle Paper No. 1.

February 2005. Online: http://www.biroco.com/yijing/Moore_Structural_Elements.pdf. Retrieved on

January 11, 2013. 3 The Yijing. The Sequence of the Hexagrams (Xu Gua).

4 Liu I-ming, The Taoist I Ching, trans. Thomas Cleary (Boston: Shambhala, 1986).

5 Frank R. Kegan, “King Wen Sequence Explained for First Time since 1100 B.C.E.”, Stars-n -Dice.

Online: http://www.stars-n-dice.com/fluxtome.html. Retrieved on January 11, 2013.

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6 Richard S. Cook, Classical Chinese Combinatorics: Derivation of the Book of Changes Hexagram

Sequence (Berkeley: STEDT Monograph 5, 2006). 7 Terence McKenna, “Derivation of the Timewave from the King Wen Sequence of Hexagrams”,

Levity. Online:http://www.levity.com/eschaton/waveexplain.html. Retrieved on January 11, 2013. 8 Hellmut Wilhelm, “Change: Eight Lectures on the I Ching.” in Understanding the I Ching. The

Wilhelm Lectures on the Book of Changes, eds. Hellmut Wilhelm and Richard Wilhelm (Princeton:

Princeton University Press, 1995), pp. 114–119. 9 Andreas Schöter, “The Yijing as a Symbolic Language for Abstraction”, Yijing. Online:

http://www.yijing.co.uk/downloads/LoA.pdf. Retrieved on January 11, 2013. 10

Clarity – I Ching Community, Clarity.

http://www.onlineclarity.co.uk/friends/showthread.php?t=12850&page=2. Retrieved on January 11, 2013. 11

The Yijing, Xi Ci Zhuan, Part II, Chapter VII. 12

Schulz, L. J. (1990), “Structural motifs in the arrangement of the 64 gua in the Zhouyi. Journal of

Chinese Philosophy”, Journal of Chinese Philosophy, vol. 17: pp. 347–348. Online:

http://www.biroco.com/yijing/Schulz_Structural_Motifs.pdf. Retrieved on January 11, 2013.