The Image of the Cosmos in the I Ching: the Yi-globe ( = I Ching Globe = Yijing Globe )
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II. The reconstruction of the Yi-globe - The spherical arrangement
(This chapter is a slightly shortened version of the original manuscript.)
Fundamental principlesThe five levels
Final compilation: The Yi-globe
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.
FUNDAMENTAL PRINCIPLES
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 creation of the trigrams – The Arising Heaven
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. In figure 6 the field around two equal and opposite electric charges is shown[*].
Fig. 6. Illustration of the electric field surrounding two opposite charges
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.
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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.
In this world the changes can pass in both directions. There are ascending movements when a yielding line changes to firm; they lead to higher positions ('Heaven is high.'). When a firm line transforms to a yielding one, the movement is directed downwards, and leads to a lower level ('The earth is low.'). Accordingly, there are superior and inferior places (levels).
(Further analysis of the Arising Heaven: .....)
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
The actions in the process of the creation of the hexagrams essentially are the same as they were in the case of the trigrams. Naturally, the Creative and the Receptive are the creators here too, as they were shown in the diagram of the Arising Heaven.
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)
After the arising of the first offspring, the creating process did not come to an end as in the Arising Heaven. The Creative manifested itself in the six sons yet: their five yielding lines changed to firm one by one; whereby five new hexagrams came forth from each of them. Having two firm lines, they are superior in comparison to the former six signs; they represent a higher level in the world (fig. 10, level II). These new descendants were conceived then again, and these changes led to an even higher level (level III). Similar changes were accomplished in the daughters and in their descendants under the influence of the Receptive, and resulted in the hexagrams of levels IV and III. This process of changes follows the derivation of each hexagram, thus symbolically the genesis of the created world. For picturing this development it is enough to put down the hexagrams on paper, in succession of the generations (the levels) applying the constructing principles of figure 9, and to demonstrate how the hexagrams originate from one another. The movements, shown in figure 10 schematically only, will be set forth in detail later.
It can be seen even now that in the course of the changes five levels take shapes in the space between the Receptive and the Creative. As it is shown, the hexagrams in level I have only one firm line; according to the rules of changes the second level is occupied by their 'successors' with two firm lines, and so on in the following levels.
Such a mode of development – started from one point and ended in the created things – is fully analogous with the cosmic evolution as represented by some religious symbols, for example the well-known mandalas and yantras in the Hindu and Buddhist tradition. In the yantras the centre is surrounded by simple figures or geometric forms arranged along concentric circles. Such a yantra symbolizes the universe and its inner structure as well as the manifestation of the elements by the creative (divine) power radiating from the centre. So a yantra is always a concentrically extending, closed form, while it is symmetric and balanced, according to the inherent features of the created world.
Balance and harmony represent the essential features of the universe according to the Chinese philosophic systems as well – first of all in the Taoist ideology. Opposite powers in the world – heaven and earth, fire and water, lightness and darkness, firmness and flexibility etc. – are in constant interaction, not for neutralizing each other, but for accomplishing balance and harmony. Since it is the earthly purpose of man to be in harmony and to be one with the universe, he is required to create inner balance and harmony. The Taoist anthology of the 13th century, the 'Book of Balance and Harmony' reads: 'Balance and harmony are the subtle functions of sensitive efficiency, the essential workings of response to change, the totality of the cyclic movement and stillness of the flow of production and growth spoken of the Yi Jing.' [Li Daoqun]
Comparing the present task – the reconstruction of the hexagrams' system – with the compilation of a yantra, it is obvious that in both cases a universe has to be built up where balance and harmony prevail. Consequently, it is well-founded and understandable to borrow formal solutions from the yantras representing this common content, in particular:
- starting the construction from one core (the centre),
- concentric expansion of the creative forces,
- balanced and harmonic arrangement.
THE FIVE LEVELS
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.
Level I
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
In the figure, each path bears the ordinal number of the line the change of which results in the creation of the new hexagram. For instance path 3 means that the changing (from yielding to firm) of the third line of the Receptive (000.000, no. 2) will bring about the hexagram of the Modesty (000.100, no. 15).
For technical reasons, further on the
hexagrams will be sometimes referred to in the above way, i.e. their binary
notation will be applied. Accordingly, each hexagram will be considered as a
six-digit binary number, where '1' corresponds to the firm lines, '0' to the
yielding ones, and the least significant bit stands for the bottom lines of the
hexagrams. (In the latter respect this method is the reverse of the
Leibniz-marking.)
Naturally, the movements between two
hexagrams can be accomplished in both directions. When a line changes from
yielding to firm, it means a movement outwards, from the centre to the outer
circle, and the changes from firm to yielding mean inward movements.
Level II
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.
It should be noted at this stage that each new sign can be derived from two different hexagrams. For instance the changing of the second line of the hexagram 000.001 (no. 24) results in the 000.011 (no. 19), and the same hexagram will come about if the first line of the 000.010 hexagram (no. 7) changes (see: the red lines on fig. 12.a). That is to say hexagram 19 is the common 'child' of no. 24 and no. 7, whereby it should be connected to both of them so as to be at equal distance from the two components to comply with the rule of balance. Following the above procedure, the placement of twelve hexagrams out of fifteen will simply and automatically come about. They will be located along the circumference of circle II outside of circle I, exactly between the two hexagrams they are derived from, constituting a completely symmetrical form, evenly distributed at 30 degrees from one another (figure 12.a).
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.
Each of the above-mentioned signs derives from two hexagrams placed on level I at the two end points of the circle diameter, which is opposite to one another. It is obvious that there is only one place where symmetry is best achieved and perfect balance is accomplished. This place is half-way between the two component trigrams, in the centre of the circle. This statement is true for all the three doubled signs, which means that their position is common: their appropriate place is in the centre of level II (fig. 12.b).
Fig. 12.b. The doubled trigrams on level II
(The secondary places of the doubled trigrams: .....)
As it is shown in the above figures, the arrangement of the hexagrams and the paths of change are totally balanced. The hexagrams are placed in concentric circles, symmetrically to each axis and to the centre as well, while the paths of change, evenly distributed, are conducted spoke-wise outwards. It seems that this structure, where the changes are followed, fully meets the requirements of balance and harmony.
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)
Level III
Figures 13 show the hexagrams of level III, together with the first two levels. Here the explanations are less detailed: the hexagrams are represented by their ordinal numbers (instead of their six lines) and the numbers on the connecting lines are omitted.
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)
The eighteen hexagrams along the circumference can be split into two groups:
a) There are six hexagrams — no. 11, 12, 31, 32, 41, and 42 — each of them deriving from three adjacent hexagrams of level II. Their place is evident: they are arranged symmetrically among the three creating hexagrams, that is to say, in the direction of the middle one (further on: in the 'main lines').
b) For the time being, the remaining twelve hexagrams (further on: the 'floating signs') are placed in the middle between their two components as shown in figure 13.a. (The third component is always a doubled trigram in the centre; it does not influence the placement.)
(.....)
Apart from the eighteen hexagrams described up to now, level III bears still two others: After Completion (010.101, 63) and Before Completion (101.010, 64). Hexagram 63 is derived from no. 39, 3, or 36; while in the case of hexagram 64 no. 35, 40, or 4 are the constituents. The hexagrams of these treble groups are placed at 120 degrees from each other along circle II, on the peaks of an equilateral triangle. According to the rule of symmetry, the derived hexagrams ought to be arranged so as to be at an equal distance from each of their three constituents. There is only one such point on level III: the centre of the circle. This statement is true for both treble groups, thus 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 (figure 13.b).
Fig. 13.b. The hexagrams of Completion and their connections with the signs of level II
The upper levels
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): .....)
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)
FINAL COMPILATION: THE YI-GLOBE
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, because there is a visible disharmony in it and its elimination seems to be obligatory. Since here a spatial form is in question, it is not enough to place the hexagrams symmetrically in the horizontal planes (on the individual levels); it is required to follow this arrangement in the vertical planes as well. It means that the vertical envelope of the whole structure has to be a circle as well, where the five levels are uniformly distributed. Namely, the angle heights should be ‑60, ‑30, 0, 30, and +60 degrees respectively. Getting through these modifications, figure 18 will be formed.
Fig. 18. Spatial image of levels I to V (final)
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; those parts of the globe are shown separately, on figure 19.b.
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The paths of change of the doubled trigrams |
The paths of change of the Completion | |
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Fig. 19.b. The paths of change inside the Yi-globe | ||
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. To compare the globe to the Earth, the position of the circles can be represented by the following coordinates (proceeding downwards from the top):
- circle V: parallel 60º N
- circle IV: parallel 30º N
- circle III: the Equator
- circle II: parallel 30º S
- circle I: parallel 60º S
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:
- circle V: 6 hexagrams, at 60 degrees from each other.
- circle IV: 12 hexagrams, at 30 degrees from each other.
- circle III: 18 hexagrams, in 6 treble groups, at 60 degrees from each other.
- circle II: 12 hexagrams, at 30 degrees from each other.
- circle I: 6 hexagrams, at 60 degrees from each other.
5) Eight hexagrams have been placed along the axis of the globe, between the Creative and the Receptive:
- level II: three doubled trigrams (29, 51, 52), overlapping each other on the axis,
- level III: After Completion and Before Completion (63 and 64), in the centre of the globe,
- level IV: a further three doubled trigrams (30, 57, 58), overlapping each other as well.
(.....)
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.
During this globe’s development, the hexagrams were located at the places determined by the changes, harmonically fitting to the configuration. The Yi-globe has been produced in this way with the different hexagrams placed over its surface and in its axis. Observing the placement of the hexagrams over the globe, it can be realized that the position of certain hexagrams is in accordance with their content; i.e. these hexagrams were placed on the globe where they exactly should be placed in the world according to their meaning. This means that the globe, and just this globe, not only in its totality but also in details, is in conformity with the I Ching. To demonstrate the above, the Yi-globe is going to be thoroughly analyzed based on the position of the individual hexagrams, to demonstrate how their place on the globe complies with their meaning as demonstrated in the I Ching.
It can be stated anyway that the original problem has been successfully solved: a traditional form was found, a globe that fully expresses the joint content of the sixty-four hexagrams, while perfectly accords with the circularly arranged eight elements of the Earlier Heaven.
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