The Image of the Cosmos in the I Ching: the Yi-globe (2011)

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V. The origin of the sequence of the hexagrams

(This chapter is a shortened version of the original manuscript.)

The rules of the canonical sequence
The development of the canonical sequence
The positions of the inverse pairs
The importance of the traditional sequence

In chapter II a structure was demonstrated, embracing the sixty-four hexagrams in one closed spatial system; it was the Yi-globe. Hereafter, it is not surprising that a question presents itself: whether there is any relation between the Yi-globe and the traditional, canonical sequence of the hexagrams?

In examining the canonical sequence it is striking that it is hardly possible to find any relation between the content of a given sign and its place in the row. Though the I Ching offers a short commentary  that concerns this subject  (Xu Gua: The Sequence of the Hexagrams), it is considered even by R. Wilhelm as an 'unconvincing explanation' [Baynes: 260]. The Taoist philosopher Liu Yiming (1734-1821) analyzed the I Ching in another way: in the aspect of the inner alchemy, considering the hexagrams as steps along the way towards perfect enlightenment (Liu Yiming: The Taoist I Ching). Other people found, or believed to have found, other theories explaining the origin of the sequence. As a matter of fact, however, there is not a single generally accepted theory among them that would justify this arrangement.

THE RULES OF THE CANONICAL SEQUENCE

As it has been demonstrated in the present book, there is a form – the Yi-globe – that fully expresses the message of the I Ching by means of the arrangement of the hexagrams. It is reasonable to suppose that the canonical sequence of the hexagrams originates from this ancient form and not from another, unknown source.

In accordance with this supposition, the rules found in this sequence can be taken as starting-points. These rules are:

a) Each hexagram constitutes a pair with its reverse.

b) Not having a reversed pair, the symmetric hexagrams are paired with their complement.

This pairing is visibly represented on the Yi-globe:

a) The reversed hexagrams are placed symmetrically to the north-south meridian plane.

b) The symmetric hexagrams are clearly isolated from the previous ones. Each of these eight signs is placed on the north-south plane (six on the meridians and two on the axis), each without a pair.

(See also chapter III.)

In addition, apart from these two correspondences, there is another interrelation between the two types of arrangements which is not so eye-catching at first view but is still essential. This relation can be recognized by rotating the Yi-globe by 90 degrees so as it was made in figure 26, and preparing its projected planar image. Here the meridians will be transformed into vertical lines and the parallels into horizontal ones (figure 46) – similarly to the cylindrical projection of the Earth, but here the western hemisphere remains behind the eastern one.

I-Ching: The planar projection of the Yi-globe

Fig. 46. The planar projection of the Yi-globe

In the projected image, the hexagrams at the front side of the globe would wholly cover their reversed pairs on the back side. To facilitate visibility, the back part of the hexagrams is removed in a slightly shifted position. The hexagrams constituting the treble groups on level III (on the Equator), and originally overlapping each other, are isolated, whereby here they form three separate rows. The signs, whose place is inside the globe, on the axis, are shown beside the main figure in order to avoid further multiple overlapping.

In this figure, the individual groups of the hexagrams that symbolically belong together are marked by capital letters and different colors to make the spherical elements easily recognizable. These groups are:

If the hexagrams in groups A through G are thoroughly examined, some kind of relation can be found among the ordinal numbers within the individual groups as follows:

Apparently the relation among the ordinal numbers in a group is always somehow connected with the number 10, hence it is called 'decimal rule'. This is the third rule interconnecting the canonical sequence with the structure of the Yi-globe.

The decimal rule:

THE DEVELOPMENT OF THE CANONICAL SEQUENCE

The presence of the main rule of the canonized arrangement, the pairing, in the Yi-globe provides for the basis in itself to suppose that there is a direct relation between the Yi-globe and the canonical sequence. The described 'decimal rule' supports this conception, and – as it will be demonstrated – also contains an indication to the structure of some intermediate states between the two forms.

In all probability, the sixty-four hexagrams have been rearranged some times during the thousands of years. The 'decimal rule' is just the means to demonstrate that the characteristic elements of the Yi-globe – the axis, the Equator, the Sun-line, etc. – remained recognizably present in the sequence of our days. Presumably, these re-arrangements did not occur at the same time, in one step, but during the gradual transformations of the forms. First, perhaps, the original three-dimensional structure had been simplified into a plane, then it underwent one or more transformations, split up, and mutated until it reached the present linearity. The passage below makes an attempt to outline the main stages of this process.

The canonical matrix

The 'decimal rule' offers the possibility to explore the arrangement directly preceding the canonical sequence. That is to say, one step can be taken backwards from the present form to the projected image of the Yi-globe.

It is very simple to make the 'decimal rule' visible if the hexagrams in the linear sequence will be distributed into groups of ten, or even better into five pairs. Then the groups have to be arranged into columns, and placed beside one another. Thus each fifth pair (and each tenth hexagram) will enter the same row (figure 47). Since this placement is made on the basis of the canonical sequence, it is called canonical matrix.

I-Ching: The canonical matrix (The King Wen sequence in matrix form)

Fig. 47. The canonical matrix

The groups and
their color:

The color codes

Thus a 5x7 matrix has been produced; consisting of 7 columns with 5 hexagram pairs per column (the last three cells of the 7th columns are empty). Each cell contains the ordinal numbers and the abbreviated names of the two hexagrams, and marked with the color of the corresponding element in the Yi-globe. In this arrangement the decimal rule clearly presents itself. The adjacent (or near) pairs belong together in a way which resembles the essential elements of the Yi-globe: the identical colors are grouped per column (in columns 1, 6 and 7) and per row (in the rows of columns 2-5). Thus the regions corresponding to the individual groups can be determined in the matrix:

Within the figure thick lines separate the regions corresponding to the individual groups.

The Yi-matrix

Based on the analysis of the canonical matrix, it appears that some time in the past an arrangement, similar to the one demonstrated in figure 47, had to exist. In this hypothetical arrangement the hexagrams were grouped in accordance with their positions in the Yi-globe. In the course of time, however, the place of some hexagrams has changed – maybe accidentally, maybe as a result of a new conception – and the canonical matrix took shape. Thereafter, the extension of this has yielded the recently known sequence.

This ancient arrangement can be achieved by the restoration of the canonical matrix; whereby the hexagrams which are in the 'proper' places – that is in the cells assigned for the corresponding group – remain there, while the 'strange' ones are transposed to their appropriate cells. In this new matrix, the hexagrams will be arranged in strict accordance with the elements of the Yi-globe. In reality,  this had to be the original, correct form of the canonical matrix. After the Yi-globe, this is called Yi-matrix.

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It can be stated that the Yi-matrix represents the essential connection – the missing link – between the Yi-globe and the present sequence of the hexagrams. On the one part it contains the basic elements of the Yi-globe in a recognizable, systematic form; on the other part it exactly follows each rule of the canonical sequence (the pairs and the decimal groups).

The origin of the Yi-matrix

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The transformations of the Yi-matrix

The logical deduction following the changes from the Yi-globe up to the canonical sequence, included a step – the transition from the Yi-matrix to the canonical matrix – which has to be attributed to the displacement of the signs.

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The passage below demonstrates that:

The three changes:

a.) The cyclic movement of six hexagram pairs

The majority of the misplaced hexagrams — six pairs — was removed together. This group is extracted and demonstrated separately (figure 50).

Six misplaced hexagram pairs in the King Wen sequence

Fig. 50. Six hexagram pairs taken out of the Yi-matrix

The positions of the selected cells in the matrix are indicated in the top row. The second row shows the hexagrams at their original places in the Yi-matrix, and in the third row they are removed into their new positions in the canonical matrix. It can be seen at once that the changes were carried out not at random, but in a cyclic way: the first hexagram pair in the Yi-matrix moved to the place of the second one, the second pair took the place of the third one and so on, and finally the sixth pair returned to the first place. That is to say actually only one series of movements occurred instead of six different changes. The arrows show the course of movements as well as the cells where the hexagrams moved to.

b.) The movement of the pair Gentle-Joyous

The hexagram pair Gentle-Joyous moved downwards by two places in the sixth column. As a result, the pairs below it: Development-Marrying Maiden and Abundance-Wanderer moved upwards by one place each.

c.) The movement of the pair Abysmal-Clinging

The hexagram pair Abysmal-Clinging being at the top of the last column exchanged place with the pair Inner Truth-Preponderance of the Small at the bottom of the third column.

It can be seen that the displacements in the Yi-matrix are limited to these three cases (a, b and c), and resulted in the canonical matrix. This matrix formed the basis for the canonical sequence, and the present numbering of the hexagrams.

Here a possibility presents itself, that any of the changes listed above could occur later, within the linear sequence itself. This is referred to by lama Govinda’s saying: 'By revealing the structure of the Book of Transformation, we found by chance certain irregularities — without even looking for them, though I darkly remembered Richard Wilhelm’s words that in the dim past some of the unbound pages of the book had been misplaced accidentally.' [Govinda: 169.] The opinion of lama Govinda, in a certain extent, confirms the theory that some of the hexagrams are not at their correct place at present.

The development of the canonical sequence (summary)

Figure 51 summarizes the process of the arrangements of the hexagrams in time.

The Yi-globe (decreased)
The Yi-globe

The planar projection of the Yi-globe
The planar projection of the Yi-globe

The Yi-matrix
The Yi-matrix

Displacements in the Yi matrix
Displacements in the Yi matrix

The canonical matrix
The canonical matrix

The disintegration of the canonical matrix
The disintegration of the canonical matrix

The canonical (King Wen's) sequence
The canonical (King Wen's) sequence

Fig. 51. The development of the canonical sequence

The 64 hexagrams took the following main structural forms during the series of transformations:

1.) The original, oldest form is the Yi-globe, which perhaps existed only imaginarily or in the subconscious. Still it had to exist, since each conception and each form can be derived from it. The two cardinal rules of the present sequence – the pairing of the reversed and the complementary hexagrams – already were presented in the Yi-globe.

2.) The projected planar image of the Yi-globe is only an explanatory illustration before the next matrix arrangement.

3.) In the Yi-matrix the hexagrams were represented in pairs, and reproduced on real, material carriers (bamboo strips, wooden plates etc.). Here the associated structural elements of the Yi-globe were still arranged in perfectly identifiable form, in rows and columns. Here the material representation and the physical separation of the hexagram pairs invited the danger of their misplacement.

4.) The canonical matrix, the direct predecessor of the 'traditional' sequence known of our time, has been developed from the Yi-matrix, by means of the displacement of the hexagrams. Fortunately, there occurred only three changes influencing eleven matrix positions altogether. As far as its structure is concerned, it is identical with the Yi-matrix, and the elements of the Yi-globe are recognizable within it despite the changes.

5.) The linear sequence has been developed by means of the disintegration (the extension of the columns) of the canonical matrix.

6.) Thus the original three-dimensional structure degenerated to a one-dimensional one, to the so-called King Wen's sequence, where the spatial connections among the hexagrams reveal themselves only in traces, in a hardly recognizable manner.

Consequently, based on the studies, it is highly probable that:

(11) The sequence of the hexagrams known in our days and considered as traditional is derived from the Yi-globe. This sequence is the one-dimensional, distorted variant of the Yi-globe; however, it embraces its elements in a latent form.


THE POSITIONS OF THE INVERSE PAIRS

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THE IMPORTANCE OF THE ORIGIN OF THE TRADITIONAL SEQUENCE

If it is supposed that the above described assumption aiming at the origin of the traditional, canonical sequence is correct, it makes further guessing needless in respect to the possible connotations implied in the sequence of the hexagrams. It seems that the meaning of the hexagrams as a whole lies not in their sequence but in the archetypal image, the Yi-globe. That is to say, the sequence itself is nothing but the simplified, one-dimensional variant of the Yi-globe. This variant is without space and time; the interrelations of the hexagrams are hardly recognizable. Moreover, the changes occurred in it in the course of time almost completely annihilated the little information that remained. Any other deduction made on the basis of this sequence can only lead astray.

Still, the canonical sequence has a vast importance, since — even in fragments and in a distorted form –  it has continued to exists for about two thousand years, embracing and transmitting to us the Yi-globe. Thereby it demonstrates that the sixty-four hexagrams enclose the totality of the world. Furthermore, at the same time, this sequence confirms the existence of the Yi-globe in the past.

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