(This chapter is a shortened version of the original manuscript.)Fundamental principles
The introduction gave a brief survey of different ancient worldviews, emphasizing their identical content: the whole known and pictured world. The symbolic representations of these early conceptions contain quite a few common elements. Also the I Ching includes 'the form and the scope of everything in the heaven and on earth', but its symbols, the hexagrams bear no resemblance to those of other peoples. The form of the aligned sixty-four hexagrams does not reflect the 'round' world, while the disorder of the hexagrams within the sequence contradicts ancient Chinese philosophy, according to which one single heavenly order rules the world.
The next discussions are based on the supposition that this lack of harmony between the content and the form is superficial only. It would contradict any cultural tradition that a worldview manifesting the essential subject with such an inherent disharmony could have been able to exist for thousands of years. It is well-founded to suppose that some interrelation ought to have existed among the hexagrams predestined to express the unity and the order of the world. Maybe this interrelation or order has lost or has been forgotten in the course of times; it is a mission of posterity to find it again.
For that matter, several indications can be found in the I Ching, confirming the existence of some sort of systematization among the hexagrams. Here is an example from the commentary Da Zhuan: 'Heaven is high, the earth is low; thus the Creative and the Receptive are determined.… Movement and rest have their definite laws.' [Baynes: 280.] Richard Wilhelm expounds this idea as follows: '…at the beginning of the world, as at the beginning of thought, there is the decision, the fixing of the point of reference. … The premise for such a decision is the belief that in the last analysis the world is a system of homogeneous relationships – that it is a cosmos, not a chaos. This belief is the foundation of Chinese philosophy, as of all philosophy.' [Baynes: 281.] According to Wilhelm the two fundamental hexagrams, the Creative and the Receptive are such points of reference; they determine a system of coordinates, 'into which everything else can be fitted.' [ib.]
Based on thorough consideration and literary indications, it can be trusted that if there is some kind of relationship or order among the hexagrams, it can be disclosed. This would not only be a formal result, but would also mean the revelation of latent content, if any, in the book, thereby enriching the I Ching with an additional set of associations.
The study of the book suggests that the order of the hexagrams has to be sought directly at the source, in the I Ching itself. Actually, the book discloses some important interrelations among the trigrams, and the extension of these relations over the hexagrams seems realizable. Thus, it can be expected to create a structure harmonious with the above ideas, perfectly expressing the spiritual contents of the I Ching .
The I Ching clearly describes the creation of the trigrams. The creators are the two major forces, the Creative (Qian, the father) and the Receptive (Kun, the mother): these opposing and at the same time co-operating powers. The scene of the creation is the space between them, between the heaven and the earth. It is exactly so as the Da Zhuan reads: 'Heaven is high, the earth is low. ... Events follow definite trends, each according to its nature.' [Baynes: 280.] In another classic, in the Dao De Jing (Tao Te Ching) Laozi says the same: 'Between the earth and sky / The space is like bellows, / Empty but unspent. / When moved its gift is copious.' [Laozi, Chp.5.]
Electromagnetic fields are often illustrated with field lines. Also the Heaven and the Earth are equal and opposite powers, and they mutually take effect on each other. Thus, the location of their interaction can be imagined as the symbolic picture of an electric field (figure 7).
Fig. 7. The field of force between the Qian and the Kun
The events of the I Ching are going on this field. In primordial times such an event was the creation of the trigrams. According to the commentary Shuo Gua the Receptive was conceived by the power of the Creative: 'The Receptive is the earth; therefore it is called the mother. In the trigram of the Arousing she seeks for the first time the power of the male and receives a son. Therefore the Arousing is called the eldest son.' [Baynes: 274.] This message can be rendered into the language of changes: the first change occurred when the lowest, yielding line of the Receptive changed into a firm one. Thus, the trigram Arousing (Zhen) was received. Similarly, the changing of the middle line created the Abysmal (Kan), and that of the upper one the trigram of Keeping Still (Gen). In the I Ching these three trigrams were called the eldest, the middle and the youngest son respectively (see Table 1), and, as it was shown, they all have come into being from the Receptive, by the changing of its yielding lines.
The other three trigrams, that is the Gentle (Xun), the Clinging (Li), and the Joyous (Dui), the three daughters were created in a similar way. Again, the Shuo Gua reads: 'In the trigram of the Gentle the male seeks for the first time the power of the female and receives a daughter. Therefore the Gentle is called the eldest daughter.' and so on. Here the firm lines of the Creative were transformed to yielding ones. Figure 8.a illustrates these changes in the field of force of the Creative and the Receptive. In the diagram the lines linking the trigrams show the paths of movement.
After their creation, the six offspring remained under the influence of their parents. As a result, the yielding lines in the female trigrams change to firm, and vice versa (figure 8.b). The sons and the daughters, however, had got own power; thus, these changes could be resulted from their interaction as well.
Fig. 8.a. The birth of the three 'sons' and the three 'daughters'
Fig. 8.b. The interactions of the 'sons' and the 'daughters'
In figure 8.b, the eight trigrams represent the whole world, with the Creative at the top, and the Receptive below to manifest the saying: 'heaven is high, the earth is low'. Forces operate between the two, inducing changes in 'the world under the heaven'. This diagram illustrates the creative forces, the location and the productions of the creation, and the laws of movement in this space. Consequently, it is well-founded to take this figure for the symbol of the changing world in the moment of the Creation. Thus, actually, the world’s genesis is manifested here in symbolic form (figure 9).
Fig. 9. Diagram of the Arising Heaven
This is a third worldview besides the Earlier Heaven and the Later Heaven (see fig. 5), and it presents the image of the world at the beginning of the times when the major powers arose; so there is every reason to call it Arising Heaven.
(Further analysis of the Arising Heaven: xxxxx)
Since this image of the changing world fully reflects the basic idea of the I Ching, it can serve for a means by which a similar arrangement can also be found for the hexagrams. It is supposed that the laws of movement of the trigrams can be extended to the hexagrams, whereby the original goal of constructing a cosmological image of the world can be achieved.
The system of the hexagrams — a preliminary overview
Here, the first 'son' is the hexagram Return (no. 24) with one firm line at the lowest place. The first 'daughter' is the Coming to Meet (no. 44) with one yielding line below and five firm lines above. There are six hexagrams altogether that contain only one single firm line, and they are interconnected directly with the mother, the Receptive. Likewise, the six daughters join to the Creative, the father. This arrangement is illustrated on figure 10.
Fig. 10. Image of the Arising Heaven (with the hexagrams of the I Ching)
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As it was established above, the Receptive has to be designated for the basis of the system of the hexagrams. The Receptive is the mother, who is conceived by the Creative and bears the children – elements of the existing world – to manifest herself in them.
The changing of one yielding line of the Receptive into firm produces the first elements of creation. Level I in figure 10 shows the resulting six hexagrams succeeding one another as their firm line moves gradually upwards. It should be noted, however, that this linear arrangement does not correspond to the environment of the hexagrams. The field of force between the Creative and the Receptive extends in all direction and surrounds the source points. Accordingly, the hexagrams have to be placed not in the plane but in space, in three dimensions (following the example of the electric fields). In the present case the Receptive is the mother, the source of energy, that generates all the forms – under the influence of the Creative. The best way to represent this cosmic process is to take the Receptive as the center, and the paths of change (like the field lines) branching out spoke-like from it and leading to the manifested ideas.
Demonstrating the Receptive and the six hexagrams in the above manner, a perfectly balanced, symmetric arrangement will be generated, exactly expressing the inner message in the language of traditional symbolism: the fact of creation and the order in it (figure 11).
Fig. 11. Hexagrams of level I, and the Receptive
a) Demonstration in the plane   b) Perspective demonstration
As it was shown, each hexagram on level I has one firm and five yielding lines. The changing of a yielding line into firm results in five new descendants for each sign. These new hexagrams contain two firm and four yielding lines, and there is fifteen of them altogether.
Fig. 12.a. Hexagrams of levels I and II (except for the doubled trigrams)
The location of the three doubled trigrams – the Abysmal (010.010, no. 29), the Arousing (001.001, no. 51), and Keeping Still (100.100, no. 52) – requires particular consideration.
Fig. 12.b. The doubled trigrams on level II
It should be noted here too that in reality the hexagrams are placed in three dimensions, and at different heights according to the number of the firm lines. Figure 12.c illustrates the spatial arrangement of the first two levels in perspective (the most of the connecting lines are omitted).
Fig. 12.c. Spatial image of levels I and II (sketch)
In figure 13.a, circle III holds the hexagrams derived from those of level II; they have three firm and three yielding lines. There is twenty such hexagrams altogether, but here only eighteen are located.
Fig. 13.a. Hexagrams of the first three levels
(except for the doubled trigrams and the signs of the Completion)
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The two hexagrams of the Completion – similarly to the doubled trigrams on level II – will come onto the same place, where they overlap one another.
The arrangement of the hexagrams on the upper levels goes on in the same way as on the lower ones.
The offspring of the Creative surround their father in the order as their only yielding line goes down (level V). The hexagrams of the next generation (with two yielding lines) are placed on level IV below: twelve signs at the outer circle and the three doubled trigrams (no. 30, 57, and 58) in the center. The hexagrams of the third level are originated in the signs of level IV. Eighteen hexagrams go to the circle and the two signs of Completion in the middle point. (Figure 14.a)
Fig. 14.a. Hexagrams of levels III, IV, and V
(except for the doubled trigrams and the signs of the Completion)
It is visible that in this case the groups of three at circle III have got their former positions (when level III was approached from below). Within the groups, however, only the middle hexagrams (on the main line) are on their proper place; the 'floating signs' at their sides changed place with each other. The positions can be equalized if all the three hexagrams of each group will be placed on the main line, overlapping one another there. In this case the floating signs will be perfectly balanced as well.
(Balancing the floating signs (detailed description): xxxxx
Uniting the five levels, a spatial map can be prepared – for the time being in a rough sketch only (figure 17).
Fig. 17. Spatial map of levels I to V (sketch)
Summarizing the outcomes presented up to now it can be established that the procedure of placing the hexagrams can be considered as complete, whereupon:
a) All the hexagrams are placed on five levels (I to V), according to the number of their firm lines.
b) The hexagrams of the adjacent levels are interconnected by paths of changes.
c) The place of each hexagram is exactly determined by the rules of balance and symmetry.
In order to receive the final form, figure 17 should be slightly reshaped.
Now the final form together with the hexagrams and the paths of change can be demonstrated (figure 19.a). Based on its contents and form, and its characteristics, this sphere has been called Yi-globe (after Yi Jing).
Fig. 19.a. The Yi-globe, with the paths of changes over the surface
It can be easily recognized that a closed net-like structure of spherical form has been developed with a vertical rotation axis represented by the Creative–Receptive line. This sphere includes all the 64 hexagrams (represented by small circlets) and the paths of change between them. The overlapping hexagrams are separated from each other. Here the lines between the surface and the axis are omitted – to avoid overcrowding.
A more clear view of the Yi-globe can be given without the paths of changes (figure 20). The connecting lines are easily traceable on other diagrams, e. g. on figures 13 and 14. Also, the overlapping hexagrams are more or less separated here from each other.
Fig. 20. The Yi-globe without the paths of changes
The enlarged version of figure 20, with the names of the hexagrams and the (King Wen) serial numbers (figure 20.b):
Fig. 20.b. The Yi-globe without the paths of changes (enlarged)
The next diagram shows an even simpler picture; here the hexagrams are substituted by small circlets (figure 21).
Fig. 21. The Yi-globe, with small circlets
The enlarged version of figure 21, with the names of the hexagrams and the (King Wen) serial numbers (figure 21.b):
Fig. 21.b. The Yi-globe with small circlets (enlarged)
For the sake of completeness the passage below lists the characteristic features of the Yi-globe in detail:
1) The two principal hexagrams, the Receptive and the Creative mark the vertical axis of the globe. The base of the axis – and that of the globe as well – is the Receptive, wherefrom changes, and thereby the whole creation starts, while the top is the Creative, whereto the ascending movements trend, where all the paths meet.
2) The circles of the individual levels (from I to V) resemble the parallels of the earthly coordinate system.
3) As it follows from the method of the design, and is apparently shown in figures 13 and 14, each hexagram – except for those on the axis – falls on the radius of the circles, branching at 30 or 60 degrees from one another. The connecting lines of the end points of these radii appear as meridians on the globe, keeping the intervals of 30 degree; thus there is 12 such meridians altogether.
4) 54 hexagrams are placed over the globe’s surface, in the points of intersection of the parallels and the meridians. They are distributed over the surface as follows:
5) Eight hexagrams have been placed along the axis of the globe, between the Creative and the Receptive:
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In summarizing the demonstrated structures and the pertaining data it can be established that the Yi-globe, without deep analysis, considering only its geometrical characteristics, expresses a fact which was not apparent in the former configurations of the hexagrams: the unity and completeness of the world. That is to say, it proved true that the signs of the I Ching, the hexagrams, can be related with another general world symbol, the sphere.
This outcome can be expressed in a thesis:
(1) If the hexagrams of the I Ching are arranged in the space between the Creative and the Receptive according to the laws of change – and following the principles of symmetry and balance – a sphere will be produced. This sphere represents the whole universe, similarly to other circular and spherical symbols found in the myths. This is the Yi-globe.
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