News, Q&A, Addenda

[논둑길맨발로]

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

Introduction	Reconstruction	Analysis	Microcosm	Origin	Analogues	News
<−− Home	Contents				References	Contact

---

News, Q&A, Addenda

Addenda
    A-1.  The five levels of human existence in the Yi-globe
    A-2.  The I Ching and the double spirals – The Yi-spiral.
    A-3.  The origin of the King Wen sequence from a two-dimensional array (.pdf)
        (This writing has been outdated; it has a final, complete version. See the news of January 2013.)
Questions & Answers
News

ADDENDA (new ideas, amendments, etc.)

A-1.  The five levels of human existence in the Yi-globe

In the Yi-globe, the hexagrams are arranged in five levels (from level I to V) between the Heaven (the Creative) and the Earth (the Receptive); so there are seven levels altogether. The Receptive has no firm lines; each hexagram on level I has one firm line, those on level II have two firm lines, and so on, until level V; theCreative, at the top, has six of them (see e.g. figure 10 and figure 20 ). There is 1, 6, 15, 20, 15, 6, and 1 hexagram on each level respectively. Such kind of grouping follows a simple mathematical rule, and it is well known since long. See one of the oldest from Steve Marshall's scans. Oddly enough that while this distribution is widely known and often published, there are no observations on the common features of the hexagrams in the individual groups apart from their mathematical basis, though they may belong together by the meanings as well. (There is a short passage about this subject in chapter III. Here, I set forth this matter in detail.)

The Yijing (the commentary Shou Kua) refers to the Tao of heaven, the Tao of earth, and the Tao of man, and reads: "In ancient times the holy sages made the Book of Changes thus: ... They combined these three fundamental powers ..." That is, the Man is taken for a fundamental power too. This ternary of the powers is expressed in the lines of the hexagrams, as it is well known by the readers of the Book: "The two lowest places are those of the earth, the third and fourth are those of man, and the two at the top are those of heaven." [R. Wilhelm]

In the Yi-globe, the hexagrams between the Creative and the Receptive have to be regarded as the products of the interaction of the two primal powers; they stand for the myriad things, i.e. the elements of the manifested world. The man is the subject of this manifestation as well, and so, the five levels between the Heaven and Earth represent the Man too. That is, the same ternary (Heaven - Man - Earth) appears here in the Yi-globe as in the lines of the hexagrams. This arrangement perfectly corresponds to the words of The Doctrine of the Mean: "[The superior man] ... may with Heaven and Earth form a ternion." [Confucius]

Obviously, the levels have a natural hierarchical order according to the number of the firm lines in the hexagrams. Besides, studying the names and the judgments connected to the hexagrams of the middle five levels (from I to V), still another hierarchy can be observed. The hexagrams on a given level have some qualities in common with each other, and these qualities mostly correspond to the level where they are located. In other words, the meanings of the hexagrams are in close connection with the number of the firm lines in them. This means that the hexagrams of the lower levels have lower qualities than those of the higher levels.

In spite of not being a learned philosopher, I have tried to put into words my observations about these common features. The basis of my observations is rather limited: the names of the hexagrams and some judgments; the majority of the judgments and the line texts have not been taken into consideration. Nevertheless, I think there are some usable and interesting ideas here that worth of further studying.

The common qualities of the hexagrams on the respective levels (quotations are from Wilhelm/Baynes, if not marked otherwise):

• Level I.  Entrance into human existence
  

  

• The beginning and the end of the course of life
• Return (The Turning Point) (24)
  Judgment: "Going out and coming in without error."
  This is the very first manifestation of the two basic powers, this is the first son. He has just emerged from the pure softness and got a firm base below. Now, he can follow his way of life upwards on the Sun-line, ascending to the heaven (see: figure 26). Or, he can wander about the world through the elaborate network of the paths of changes ( figure 19.a), and return to the earth without reaching at the higher levels.
• Splitting apart (23)
  Judgment: "It does not further one to go anywhere."
  "Stripping - It emphasizes that eliminating what has been unusable is de adequate way to handle it." [Ritsema&Karcher]
  This is the last station when the man descends from the heaven on the back half of the Sun-line. Here his life cycle (around the Yi-globe) reaches the end; he eliminates his unusable burden and does not go anywhere but back to the earth.
• Basic qualities (collective)
• Holding Together (8)
  Judgment: "Holding Together brings good fortune."
• The Army (7) / (Multitude, at Wu)
  Judgment: "The army needs perseverance and a strong man."
• These signs embody the idea that man cannot live and act alone, but only in union with others. (Later on Aristotle said: "Man is a social animal.") Holding together is of prime importance for man to remain alive or in existence. The most of the communities - a society, an army, or other - have a central figure, a "strong man" who leads and holds the members together.
• Basic qualities (individual)
• Modesty (15) / (Humbling, at R&K and others)
  Judgment: "Modesty creates success. The superior man carries things through."
• Enthusiasm (16)
  Judgment: "It furthers one to install helpers and to set armies marching."
• These individual qualities are in close connection with the communities. "When a man holds a high position and is nevertheless modest, he shines with the light of wisdom; if he is in a lowly position and is modest, he cannot be passed by." That is, all of them have to submit to the common interests. "It is enthusiasm too that can unify mass movements", as an army in war, or a human society in peace.


• Level II.  Initial progress and obstacles / Youth
  

  

There are three doubled trigrams in the center of this level, on the axis of the globe. It seems that each of them dominates over one third of the hexagrams on the surface, on this level.
• The Arousing generates movements and activities aiming at the advance of the person.
  The hexagrams under the influence of the Arousing:
  Approach (19), Progress (35), Deliverance (40), Pushing Upward (46)
• The Abysmal means danger. It presents obstacles for the person on its way ahead.
  The hexagrams that mean obstacle and/or danger:
  Difficulty at the Beginning (3), Youthful Folly (4), Darkening of the Light (36), Obstruction (39)
• The Keeping Still shows the way out of the difficulties:
  Contemplation (20), Providing Nourishment (The Corners of the Mouth) (27), Gathering together(45), Preponderance of the Small (62)


• Level III.  The courses of life, events, tendencies / Adulthood
  

  

Two hexagrams, the After Completion and the Before Completion, do not belong to this level. They are the in the middle of the globe; they are the Center of the World, the alpha and the omega, the beginning and the end of everything.
The eighteen hexagrams on the surface represent the problems of the adult age, the different courses of life.
• The manners of behavior, the ways of life:
  Development (Gradual Progress) (53), Following (17), Influence (31), Duration (32), The Wanderer(56)
• Marriage:
  Marrying Maiden (54), and according to the judgments: Development and Influence (Wooing)
• Public life:
  The Well (48), Biting Through (21)
• Different directions, opposite chances:
  Increase (42) − Decrease (41)
  Dispersion (59) − Limitation (60)
  Work on What has Spoiled / (Corrupting, at R&K) (18) − Grace (22)
  Peace (11) − Standstill (12)
  Oppression (47) − Abundance* (55)
  (* Note: In fact, the Chinese character of hex. 55 - Feng - stands for a city and not forAbundance. See: The Mandate of Heaven by S. J. Marshall.)


• Level IV.  Greatness / The years of maturity
  

  

  There are three doubled trigrams in the center, the Clinging (Fire, Lightning) (30), the Gentle (57), and the Joyous (58). Apparently, it is the Clinging which has the greatest influence on the outer hexagrams. But the other two is effective in the outside world as well.
• The four firm lines give great strength and power to the next hexagrams:
  The Power of the Great (34), the Preponderance of the Great (28), the Taming Power of the Great(26).
• The firm lines have the quality of light as well. In consequence, the clean and clear qualities manifest themselves in the hexagrams as follows:
  Inner Truth (61), Innocence (25), and partly in the Caldron (50), the Family (37), and the Waiting(5).
• The greatness often encounters opposition. The feature of the Lightning comes out in the:
  Conflict (6), Opposition (38), and Revolution (49).
• The Retreat (33) is the opposite (inverted) pair of the Approach (19) on level II. While the Approachwas the second step upwards on the Sun-line, the Retreat is the second station on its descending branch. Thus, on this high level, it forewarns decline in the future.


• Level V.  Next to the Heaven
  

  

• Reaching and leaving the Heaven
• Break-through (43) / (Resolution, at others)
  The last station on the Sun-line, before the peak.
  The light lines have driven the dark lines out, except the topmost one. By a resolute action, the man can break through this blockade and ascend to the heaven, reaching his aim of total enlightenment.
• Coming to Meet (44)
  Judgment: "One should not marry such a maiden."
  The opposite (inverse) pair of the Return (24). According to R. Wilhelm: "The principle of darkness ... obtrudes again from within and below." Under the influence of this dark (female) element the man starts sinking down to the earth back.
  See the consecutive hexagrams on the way downwards: Retreat - Standstill - Contemplation- Splitting Apart - Receptive!
• High qualities
• Fellowship with Men (13)
  Judgment: "It furthers to cross the great water."
• Possession in Great Measure (14)
  Judgment: "Supreme success."
• These two hexagrams are in strong relation with the human communities as the Army (7) and the Holding Together (8) are on level II. These are, however, more favorable than those of the inferior level. Here the five firm lines indicate strength and clarity. The character of the unions is peaceful and not combating; the communities do not need strong leaders, the force that holds them together is within the individuals.
• Restraining the power
• The Taming Power of the Small (9)
• Treading (Conduct) (10)
• In these hexagrams one weak line restrains the power of the five strong lines. They refer to correct conduct in the communities: holding the mighty in check, through the gentle and cheerful.

I think the foregoing classification of the hexagrams satisfactorily demonstrates the connections between the height of a level and the quality of the hexagrams on it.

Still another conclusion can be drawn from these observations: the levels are in connection with the periods of time in human development too. The phenomena of level II chiefly represent starting, low positions and the ascending thence; they are related to youth or adolescence. The problems of late adolescence and early adulthood (marriage, choosing the way of life, etc.) accumulate in level III, while the hexagrams of level IV are characteristic of the years of maturity and old age. Level I and V do not belong directly to ages; the former refers to the inferior, earthly existence, the latter to the superior spiritual qualities. Thus, it can be told that the hexagrams on the five levels correspond to the different stages of human existence.

On the basis of the considerations above, perhaps new connotations can be added to the hexagrams when consulting an oracle. For example, the level of the hexagram can mean the level of existence of the questioner (mental abilities, spiritual state, maturity, etc.) or the condition of the situation (beginning, progressing, hindered, etc.)

A-2.  I Ching: the way of enlightenment – The Yi-spiral.  

In the previous addendum (The five levels of human existence in the Yi-globe) the presence of the ternary Heaven-Man-Earth in the Yi-globe was demonstrated. There, the five planes between the Creative (Heaven) and the Receptive (Earth) represented the five levels of human existence, in hierarchical order from bottom to top. This hierarchy was based on the number of the firm (light) lines in the hexagrams, and was also recognizable in the names and meanings of the hexagrams. It was shown, too, that the position of Man in the ternary, between Heaven and Earth, was also a general concept in both ancient Taoist and Confucianist teachings.

On the basis of these ideas, several new features of the symbolism of the Yi-globe were subsequently discovered and will be presented here.

Note: The following concept is not based on scholarly reasoning. It is merely a new, additional illustration of the rich, comprehensive symbolism of the Yi-globe.

The Way

Enlightenment, salvation, deliverance, liberation, self-realization, initiation, and getting closer to God are among the most essential aims of every tradition and religion. In a certain sense, all these ideas can be symbolically expressed as 'ascending from the earth to heaven'. According to Taoist teachings, by reaching a balance with the nature, i.e., by following the Way, one arrives at complete enlightenment and becomes united with the Tao. In connection with this, it is widely accepted that the investigation of the I Ching and the application of its principles is nothing other than the essential practice of the Tao. The Book of Balance and Harmony reads: "Sages are sages simply because of the application of the principles of the I Ching. Application of the I Ching is accomplished simply by openness and tranquility. ... If openness and tranquility are continued for a long time, one becomes spiritually illumined." [in Cleary: p. 10].

In the following pages, the veracity of these Taoist ideas will be visibly demonstrated. The symbol that comprises all the hexagrams of the I Ching – the Yi-globe (by its particular means) – actually shows a way from earth to heaven. This procedure is in complete agreement with Rene Guenon's symbolism: "[The axis]measures the distance between Heaven and Earth, that is, the very extent of the Cosmos in the vertical direction which marks the hierarchy of states of manifested existence while joining them one to other across this multiplicity of states, which appear in this respect as so many rungs by which a being on the way of return toward the Principle can raise itself from Earth to Heaven." [Guenon: p. 24].

On the Yi-globe, 'raising from Earth to Heaven' means ascending from the Receptive to the Creative. Here, the 'rungs' are the hexagrams on the surface which represent the distinct states of manifested existence. These hexagrams are arranged in five circles along the axis of the globe; each of these circles corresponds to a hierarchical level of existence in the given phase of spiritual development. The seeker of the Way has to live through these states, in reality or in contemplation. Once the aspirant has passed through all the states in a given circle, he can ascend to the next hierarchical level.

Over the proceeding passages this ‘way’ will be followed step by step. Figure A2/1 displays the scene.

Figure A2/1. The Yi-globe. View from East

1.) The first step, starting from the Receptive (hexagram 2), clearly leads to hexagram 24 (Return, Turning Point). In this hexagram, a light (firm, yang) line enters to the lowest place, under the pure dark (yielding, yin) lines, indicating the beginning of illumination.

2.) In the succeeding hexagrams, after the Return, the light line ascends to higher and higher places. Each step means the achievement of a higher spiritual state within the frames of the given hierarchical level, here on level I. Following the ascending line, the way moves clockwise in the circle. After arriving at the highest place in hexagram 23 (Splitting Apart), the light line returns down to where it started from (i.e., hexagram 24). Having gone through every state in the cycle, a second yang line is added below, indicating that the aspirant has deserved a higher level in the hierarchy. Thus, the way ascends to level II, to hexagram 19 (the Approach).

3.) On level II, from hexagram 19, the way goes in the same direction as before, while the two light lines one by one ascend to higher places. After arriving at the two highest places in hexagram 20 (Contemplation, the View), the light lines move down from the top to the first place and the way returns to hexagram 19. Here, the situation of level I repeats itself: a new yang line is added to the hexagram which leads the aspirant to a higher state of existence on level III, to hexagram 11 (the Peace).

4.) On level III, there are six groups of three hexagrams in the circle. In each group, the hexagrams are placed in the same position: on the corresponding main line. Now, if one wants to go through all the hexagrams one by one, it is necessary to separate them and to assign their sequence within each individual group. In this way, two arrangements can be made, depending on the location of the two 'floating signs' on the sides of the third hexagram, which is fixed in the middle place.

Note: The fixed hexagrams on the main line are the pairs 11-12, 31-32, and 41-42. For a detailed explanation of the 'fixed' and 'floating' hexagrams, see Chapter II, figure 13.a and the passage that follows it).

These two arrangements appeared in the course of reconstruction of the lower and the upper circles of the Yi-globe ( figure 13.a and figure 14.a , respectively). Then, the two sets of circles were interconnected and the floating signs moved to their balanced position on the main line, associating themselves with the fixed hexagrams that were already there. Figure A2/2 shows these two parts anew, but turned away by 90 degrees and without the paths of changes.

Figure A2/2. The lower and the upper circles of the Yi-globe

In the next diagram, the two different arrangements of Circle III are shown separately, and in a detailed form (figure A2/3).

Figure A2/3. Circle III with the two different sequences of the hexagrams

It is revealed from the reconstruction of the Yi-globe (Chapter 2, The Five Levels) that the hexagrams in one of the two groups have been arranged as the descendants of the Receptive (Circle I, II, and III) and in the other as those of the Creative (Circle V, IV, and III). According to the symbolic meanings of the Yi-globe (universe, macrocosm, microcosm), it is reasonable to refer to the first group as 'lower world' because the lower hemisphere has been formed from these circles and, similarly, the other group can be called 'upper world' as the circles of the upper hemisphere. On the way, a seeker of complete enlightenment has to learn both the lower and the upper world in their full integrity. Thus, at first, one has to circulate in Circle III as it is the last phase of the lower world, i.e., move clockwise, according to the sequence III.a (fig. A2/3); then, one goes in the opposite direction, in the same circle, as in the entrance phase into the upper world, i.e., counterclockwise, following the sequence III.b.

Summing up the above explanations, the way on level III proceeds in the following manner. Arriving at hexagram 11 (the Peace), the way continues to the left, and covers the full circle (sequence III.a). It then makes a turn of 180 degrees and follows the route according to the sequence III.b. Returning to hexagram 11 again, a fourth yang line arrives and elevates the way to level IV, to hexagram 34 (The Power of the Great).

5.) On level IV, one has to follow the ascending light lines again; so, from hexagram 34, one goes to the right, towards hexagram 5 (the Waiting), and the way keeps moving counterclockwise. From hexagram 34, the next step leads to level V (hexagram 43, Break-through).

6.) The last cycle, on level V, begins with hexagram 43; in this hexagram only a single dark line remains — on the top — on the sixth place. On this level, the ascending light lines gradually push this dark line down to the lowest place (hexagram 44, Coming to Meet). Closing the circle at hexagram 43, we have completed our wandering over the states of manifested existence.

7.) From hexagram 43, by adding a single light line, the aspirant arrives at the highest level, the Creative, to the pure yang state, the complete enlightenment. The way has come to completion.

The whole way is shown in figure A2/4.

Figure A2/4. The way of complete enlightenment through the hexagrams

Note: One must not mistake this way of enlightenment for the paths of changes, as received in divination. This is a symbolic course, mapped out on the Yi-globe by the light (firm) lines of the hexagrams.

The figure above is not entirely accurate in all aspects. Namely, the transitions from one level of the hierarchy to the other cannot be made by leaps, as they are indicated in the diagram. In every cycle, in every step, one light line ascends one place higher in the actual hexagram, which means a higher level of illumination. This increasing illumination can be symbolically shown in the diagram by raising the line of the route a bit higher in every step within the cycle. Thus, at the end of the cycle, the way approaches the height of the next level, and the transition between the two levels will proceed smoothly. Consequently, in a correct representation, the route of advancement shows a spiral on the surface of the Yi-globe (figure A2/5).

Figure A2/5. The way of enlightenment on the surface of the Yi-globe

Summing up, this curve symbolizes the way to complete enlightenment, i.e., the way from earth to heaven. Along the way, one's inner illumination gradually grows, while he passes through every states of human existence, until he arrives at his ultimate goal.

In fact, this curve is a double spiral, since its lower and upper halves coil in opposite directions. One half of this spiral follows a path along the lower hemisphere: it belongs to the 'lower waters' or to the 'lower worlds'. It coils outwards here, signifying the phase of evolution with birth as its beginning point. The other half is in the 'upper waters', i.e., in the 'upper worlds'. Coiling inwards, it signifies involution, withdrawal, and completion at the end.

In figure A2/5, the axis of the Yi-globe is highlighted. This is the symbol of the World Axis, clearly demonstrated in Chapter III. Here, it is shown as the scene of the first phases of Creation, before the manifestation of beings. This procedure of Creation is in full harmony with the Taoist ideas:

• Creation starts from the Great Ultimate; it is the Center of the Yi-globe here.
• Then, the yin and yang can be differentiated, though they remain together in the Center. This is represented by hexagram 64 (Before Completion) and hexagram 63 (After Completion), where the firm and yielding lines are arranged alternately, in balance and harmony. These are the Beginning and the End, the Alpha and the Omega.
• After this, the yin and the yang separate from each other; eight trigrams are created and doubled: these are the eight primal hexagrams.
• The pure yang and the pure yin hexagrams become the two poles of the universe, with the field of force between them. These are: hexagram 1 (the Heaven, the Creative) and hexagram 2 (the Earth, the Receptive).
• The other six doubled trigrams (marked with the six short, black lines on the axis) contribute to the variety of the manifested world (see: figure 19.b1 ).

There exists another, simpler route from the Receptive to the Creative, but one should not call it a 'way of enlightenment' because, in the upper hemisphere, it does not follow the ascending light lines. This is a simple spherical spiral as it is shown in figure A2/6.

Figure A2/6. Spherical spiral on the Yi-globe

(Later on, I shall return to this subject)

Spirals, double spirals

In order to reveal the multi-dimensional symbolic meanings of the previous spirals, a brief survey is given below about the general symbolism of spiral curves.

The spiral forms play universal and complex roles among traditional and religious symbols. In figure A2/7, a simple (Archimedean) spiral and a double spiral are shown.

Figure A2/7. Simple and double spiral

These and many similar forms primarily represent the following subjects:

• In general:
• way, route: lines of movement
• power, force: motive power/force
• spirit, breath, breathing
• time: cycles and periods (eras, solar year, lunar month, day)
• coiling outwards: creation, birth, growth, development – evolution
• coiling inwards: withdrawal, contraction, completion, death – involution
• Double spirals: two simple spirals of opposite character (left- and right-handed, coiling in- and outwards), connected to each other at one or at both ends:
• unity of opposite powers: action and reaction
• transition, transformation, inversion
• space and time: motion in space.
• Spatial (three-dimensional) spirals:
• the axis of the world
• connection between earth and heaven
• the path to God
• Decorative elements: all over the world, similar to other traditional symbols, spirals often occur as ornamental motifs. They have been known since prehistoric times, and are also used on objects of different kinds in the present day.

In China, the spirals, particularly the double spirals, are among the most widely known and most important symbols. Their origin goes back to the mythical era: spiral motifs have been found on carved stones and earthenware from the 3rd millennium BC, and from even before that time. More discoveries of painted pottery came from excavations in the vicinity of An-yang, dating from the 14-12th century BC [Bulling: p. 161]. Double spirals of the S-form type also occur in ancient ideography, forming different ideographs [ibid.].

The most frequently used double spiral can be seen, however, in the well-known yin-yang (taiji) diagram, as the boundary line between its two halves (figure A2/8).

Figure A2/8. The yin-yang (taiji) diagram

It is worth noting what the views of several philosophers are on this matter.

• "The double spiral represents the completion of the sigmoid line, and the ability of the sigmoid line to express the intercommunication between two opposing principles is clearly shown in the Chinese Yin-Yang symbol." [Cirlot: pp. 306-307].
• "From a cosmic point of view, the double spiral may be regarded as the flattened projection of the two halves of the egg of the world, ... or of the Upper and Lower Waters." [ibid.].
• "This double spiral ... which can be regarded as the planar projection of the two hemispheres of the Androgyne, offers an image of the alternating rhythm of evolution and involution, of birth and death." A citation from Elie Lebasquais [in Guenon: p. 31].
• "The two spirals can be considered as the indication of a cosmic force acting in opposite direction in each of the two hemispheres, which, in their broader application, are of course the two halves of the 'World Egg', the points around which the two spirals coil being the two poles." [Guenon: p.31-32].

An important conclusion can be drawn from the above citations:

The yin-yang diagram is an analogous, two-dimensional form of the World Egg (the 'cosmic egg', or the primordial 'Androgyne').

This idea was directly expressed by Guenon, in the following words: "It [the yin-yang diagram] is also, according to another and more general traditional symbolism, the 'World Egg'; whose two halves, when they separate, become Heaven and Earth respectively." [Guenon: pp. 29-30].

According to the analysis of the Yi-globe (see: Ch. III), the yin-yang diagram may be its planar representation. Assuming this analysis and the above statement are correct, another conclusion can be formed:

The Yi-globe is also an alternate form of the World Egg. Its lower and upper hemispheres correspond to the two halves of the latter.

These latter statements clearly express the close relationship between the Yi-globe and the other universal symbols of macrocosm (yin-yang diagram, World Egg). The presence of the spiral forms in Chinese tradition and the meanings of these forms yield new arguments in support of the method of the reconstruction of the Yi-globe in the field of force between the two primal powers (see: Ch. II). Also, the occurrence of different spirals as new, complex symbols, such as the 'way of enlightenment' and the forthcoming 'Yi-spiral' and 'Yi-circle', are not strange or unusual events in Chinese culture.

It is necessary to mention snakes or serpents again here, as they are among the spiral forms, and are frequently shown in the different symbols, coiled around themselves, and thus forming a spiral. In figure A2/6.b a spherical spiral can be seen on the surface of the Yi-globe, ascending uniformly from the beginning to the end. If this spiral were replaced by a serpent, and the Yi-globe considered the World Egg, a well-known symbol could be reproduced: the serpent surrounding an egg, which is the symbol of the creation of the world in many traditions (see: e.g. here).

There is yet another interesting opinion in connection with the meanings set forth above. As J. E. Cirlot demonstrates, the spiral is also associated with the idea of dance, "and especially with primitive dances of healing and incantation, when the pattern of movement develops as a spiral curve. Such spiral movements may be regarded as figures intended to induce a state of ecstasy and to enable man to escape from the material world and to enter the beyond." (my italics) [Cirlot: p. 306].

Note: This idea may have some relation to the 'Pace of Yu', i.e., with the stories of the strange, hopping gait of Yu the Great, the legendary founder of the Xia Dynasty (c. 21st cent. BC). There is a reference to the Pace of Yu as a dance, for example, in the book of S. Little who quotes Yuan Miaozung (early 12th cent. AD) as follows: "The Pace of Yu is a Taoist ritual dance, named for the mythic emperor Yu ... The dance serve many functions, including exorcism and purification." A diagram illustrates this dance, the last phase of which goes around the North Star in the form of a contracting spiral: three turns go clockwise and then, after a turn of 180 degrees, a fourth one goes counterclockwise. [Little: p. 200].

The double spiral arrangement of the hexagrams – The Yi-spiral

The Yi-globe itself is a rather complicated form, but taking its complex symbolism into consideration, it is still the best solution possible to convey all the knowledge about the hexagrams and about their roles in cosmology. With the double spiral on its surface, however, the whole structure has become much more complicated; it can no longer be represented in the usual ways.

To make things simpler, one has to prepare the planar projection of this three-dimensional spiral and to set the two halves next to each other and, then, to place the hexagrams on them in their proper positions. This form will be called Yi-spiral, on the analogy of the Yi-globe (figure A2/9).

Figure A2/9. The Yi-spiral

This diagram contains all the 54 hexagrams that are on the way of enlightenment, on the surface of the Yi-globe. Aside from this, it has preserved all the symbolic meanings which were enumerated above, and were present in the three-dimensional variant.

This arrangement also has quite a few qualities that are characteristic features of the Yi-globe: the presence of the two poles and their opposite characters; the direction of development (starting from the two poles); the circular and cyclic arrangement of the hexagrams; and the indication of the movements (the changes) and time, etc. Some important features however, are missing: First of all, those properties that originate in the spatial form: the sphere itself, the axis and the center, the hexagrams inside the sphere, and some others as well. Nevertheless, considering the form and meaning, the Yi-spiral can be taken not only as the 'way of enlightenment', but as a new, expressive arrangement of the hexagrams, and as the symbol of the manifested universe. The two hexagrams of Completion (hexagram 63 and 64) and the eight doubled trigrams do not have worldly manifestation, and so, they are separately shown as 'pivot hexagrams' (see figure A2/5).

The spiral of the 'way of enlightenment' can also be associated with snakes. Looking at figure A2/5 from above, a form can be seen, which is similar to a snake coiling around itself in two opposite directions (figure A2/10).

Figure A2/10. Snake in the form of a double spiral

This picture represents the same as figure A2/5. In the center, the tail and the head are the two poles, the Receptive and the Creative, respectively. The black, outwards winding spiral is the evolutionary phase of development, and the red, inwardly winding half stands for involution. The transition from one phase to the other goes unbroken.

Besides of this symbol, two other variants can be easily formed, also relating to this subject.

• a.) If the snake were shown with his tail in the mouth, as if swallowing it, it would be an 'ouroboros', representing the 'eternal return', the eternal circulation. The meaning of this symbol is that after attaining complete enlightenment, one can be united with the Supreme Ultimate in the Center, and then, according to his will, be reborn to the Earth.
• b.) A snake with two heads, that is one at the tail end as well, is an 'amphisbaena'. In such a form the two heads correspond to the two poles and the two directions of the opposite forces, making it a rather cosmic symbol.

A special double helix – The Sun-line

A double helix is a spatial curve that consists of two (typically congruent) helices with the same axis, differing by a translation along the axis. In science, this is commonly known as the structure of nucleic acids such as DNA, and RNA [Wikipedia: helix]. In symbolism, however, the two helices coil in opposite directions around a (vertical) axis or, when they are shown in the form of snakes, around each other. Their symbolic meaning is usually the same as that of the planar double spirals: duality, complementary opposition, movement, power, etc.

An example of the double helices is the two 'nadis' ('ida' and 'pingala') or subtle currents, known in traditional Indian medicine and yoga; they coil around the 'sushumna' nadi, the central canal of the subtle body. Another such a configuration is the two serpents of the 'caduceus' (the 'wand of Hermes'). Fu Xi, who is well-known by all the readers of the I Ching, can be seen in ancient pictures in a similar form, coiled together with his wife (and/or sister) Nuwa (see: Wikipedia, Fu Xi).

The Sun-line on the surface of the Yi-globe was already analyzed in Chapter III (figure 26). As it can be seen, it is composed from two parts. Each part is a single turn of a special helix; a left-handed one on the front (East) side of the globe, and a right-handed on the back (West) side. They are mirror copies of each other, and interconnected at the end points of the axis, forming a loop around it (figure A2/11).

Figure A2/11. The Sun-line on the Yi-globe. Perspective and top view

These helices are very special indeed. None of them have a central axis - they are curved around a hemisphere - nevertheless, their top view is a circle (see the figure above).

Note: Applying spherical coordinates, the equations of the two spirals are very simple:
r = R, and Θ = φ on the front side, where [0 ≤ φ ≤ Π], and
r = R, and Θ = 2Π - φ on the back side, where [Π ≤ φ ≤ 2Π].
Here the basic plane of the coordinate system is the equatorial plane, the azimuth reference line goes to the South, and R is the radius of the globe; r, Θ (inclination), and φ are the spherical coordinates.

It has already been demonstrated that the Sun-line represents the cyclic character of time and the visible annual motion of the Sun on the sky. On the basis of the present references to the double helices, it is easy to see that the Sun-line also represents the field of force between the two opposite powers, the Heaven and the Earth, where the elements of the universe have been manifested. Moreover, they also apparently show two paths: one from earth to heaven, and another in the opposite direction. In this way, this loop indicates a route of circulation that is, considering the symbolism of these paths, an ouroboros; this is another route of the eternal return (figure A2/12).

Figure A2/12. The circle of the eternal return – The Yi-ouroboros (view from South)

Summarizing the contents of the present addendum, the first sentence of the statement (9) from the end of chapter III (The Analysis) is repeated here:

The Yi-globe embraces all the cardinal metaphysical symbols of the peoples of the world, thereby also revealing that the hexagrams and the I Ching — apart from being unique Chinese creations — form an integral part of our universal tradition.

This statement has already been confirmed in this chapter. In addition, some other universal symbols – spirals of different kinds – though previously hidden within the structure of the Yi-globe have been henceforth revealed. Their symbolism may be considered a new contribution to the material of knowledge regarding the I Ching. The Yi-spiral, this new arrangement of the hexagrams, might well serve as a subject of contemplation.

References:

• BULLING, A: The Meaning of China's Most Ancient Art. E.J. Brill Pub.1952.
• CIRLOT, J. E., et al.: A Dictionary of Symbols. Philosophical Library. 1990.
• CLEARY, Thomas: The Taoist I Ching – Introduction. Shambhala, 1986.
• GUENON, Rene: The Great Triad. Sophia Perennis, 2002.
• LITTLE, Stephen; EICHMANN, Shawn: Taoism and the Arts of China. University of California Press, 2000.

QUESTIONS & ANSWERS

Q: How can you follow the changes of the hexagrams through the Yi-globe?
A: The Yi-globe contains all the hexagrams and all the paths of changes between them. For the sake of simplicity, however, these paths usually are not shown on the pictures of the sphere but they can be easily envisioned there or seen on the detailed circular diagrams. (See Chapter II, passage The Five Levels, figures from 11 to 14. E.g. figure 12a is here.)
Here is an example for the illustration of the movements:
Hexagram 36 (Darkening of the Light), changing lines: 2,3,5,6, resulting hexagram: 61 (Inner Truth)
−−− x −−−
−−− x −−−
−−−    −−−
−−−O−−−
−−− x −−−
−−−−−−−−
- The changing of the second line from yielding to firm (6 at the 2nd place: 6/2) leads to hex 11 (Peace)
- 9/3 in hex 11 leads to hex 19 (Approach)
- 6/5 in hex 19 leads to hex 60 (Limitation)
- 6/6 in hex 60 leads to hex 61 (Inner Truth)
The movements are shown on the next picture:

The succession of the changing lines is indifferent as regards the final situation. For example, in this case there are 24 different ways between the two end points, depending on the order of the four changing lines.
Note: When consulting the oracle, the in-between hexagrams have to be ignored! According to my slight experience, they have not any role in the course of divination. (But who knows?)

Q: How do you interpret an oracle by means of the position of the given hexagram?
A: This study does not deal with oracles or divination. The Yi-globe is the symbol of the Universe primarily, revealing its structure and operation.
Nevertheless, my conviction is that in the future the Yi-globe would become a useful tool for competent practioners of divination, because it implies new and valuable information for them.
According to my (maybe lay) opinion the following factors can be taken into consideration at first:

• The level of the actual hexagram.
  This may mean the level of existence for the questioner (mental abilities, spiritual state, age, etc.)
• Moving from one level to another, in the case of changing line(s).
  This is going closer to the Heaven or to the Earth, arriving at a higher or a lower level.
• The meridian of the actual hexagram.
  Four meridians show the four cardinal points of space and the four seasons (see figure 23 ). There is one meridian to the left and another to the right of each of them (thus twelve together), marking the direction or the time before and after the main points. The directions and the seasons have their particular meanings in Chinese symbolism which can be used in consulting the oracle.
• Moving from one meridian to another.
  Here the direction and the measure of the change in space and time (see the above question) can provide additional information.

Q: The King Wen sequence is expressing another point of view than the Yi-globe sequence.(?)
A: In reality, the King Wen sequence has not any explicit point of view or it is not known yet. There are a number of questions in connection with this subject: Was it King Wen who created this sequence? Had he any intention to include general ideas in it? Have the sequence remained unaltered during the three millenia? A lot of guesswork has been made already to discover some kind of order in this sequence or to find any explanation for its present form. It follows from the diversity of the opinions that only one of them (if any) can be true; but who can tell which one is that one?
The Yi-globe expresses the unity and the complexity of the Universe. This statement is confirmed by the spherical form, the positions of the cardinal hexagrams, the embedded traditional symbols, etc. It follows from this study as well that the King Wen sequence is nothing but the simplified, one-dimensional variant of the Yi-globe.
Consequently, it seems very probable that the "point of view" of the Yijing lies not in the lineal sequence of the hexagrams but in their archetypal image, the Yi-globe.

NEWS

A review by Steve Marshall
Steve Marshall published an extensive review on the Yi-globe in his site Yijing Dao.
(May, 2009)

A new thread in the Clarity site
A new thread has been started in the Clarity site among the "I Ching News" with the title The Yi-globe.
(May 9th, 2009>

The revolving Yi-globe
Chris Willmot has made a revolving Yi-globe which can be turned away by 10, 30, or 90 degrees, bringing the required hexagram to the foreground, and showing the directly connected (being at one bit distance) hexagrams conveniently. Besides, this globe has some other functions that help the orientation among the hexagrams and the oracles.
(July, 2009)

The human microcosm
From the beginning of this site, a good many people visited chapter 4 which dealt with the possible interrelations between the Yi-globe (i.e. the spherical arrangement of the hexagrams) and the human microcosm. I know well that the ideas in that chapter were mainly suppositions, and they were based only on some similarities in form (between the Yi-globe and the acupunctural meridians) and on the common principles of the two fundamental works (the Yi Jing and the Nei Jing) - though these conformities and analogies were very interesting and surprising (at least, I thought so). In my original manuscript I have had some more vague ideas on this subject that may be interesting for others. Thus, for the sake of the persons showing an interest in this subject, now I have added these, previously omitted passages to the site. Perhaps, somebody from the new readers would develop a new theory on the basis of this material.
(January 5th, 2010)

The Yi-yantra ( Yijing-yantra )
Chapter 6 (on the analogues of the Yi-globe) is an often visited part of this site, though until now it has been a rather short one. I think that a great part of the visitors was disappointed after having found the picture of the Yi-yantra without a detailed explanation. Thus, I decided to add some of my former ideas to this passage.
(January 10th, 2010)

The Teikemeier/Drasny Prism
Andreas Schoter, the author of many valuable papers on the I Ching, see here, analysed the geometry of the Yi-globe (together with Lothar Teikemeier's Iching-sphere). He found close connections between these spherical arrangements and his six-dimensional hypercube (formed by the Boolean lattice) and developed a new structure that he called the Teikemeier/Drasny Prism.
(November, 2010)

The new version of the Yi-globe
In the course of the past two years, based on new experiences, and using the opinions and critics received from the readers, I revised and rewrote the previous manuscript of the Yi-globe. Now, as I think, it looks like a real book.
It can be reached from the home page, click at the ’NEW VERSION’.
The contents is on the page: The Yi-globe: The Cosmos in the hexagrams of the I Ching (pdf).
The direct URL is http://www.i-ching.hu/pdf/yiglobe.pdf (yiglobe.pdf file, free download).
In addition to the original content, the modified chapter on the origin of the King Wen sequence has some points of interest. I found a new argument for the hypothesis and made the reasoning more understandable.
(October, 2011)

The new version on the SCRIBD
You can also read the new version of the book under the title The Cosmos in the I Ching - The Yi-globe.
Free download.
(February, 2012)

The King Wen Table and the King Wen Array
This is a new idea about the two-dimensional arrangements of the sixty-four hexagrams that existed before the traditional (King Wen's) sequence. This theory has been evolved from my former assumptions about the origin of the KW sequence (Chapter V, in the main site) but, at this time, I found a general solution, without references to the structure of the Yi-globe.
In May 2012, I put up the early draft of this writing here, as an addendum (A-3.The origin of the King Wen sequence from a two-dimensional array). By now, it has become redundant and needless to read. 
In January 2013, the writing has been completed and you can reach the text through the Home page
or by the direct URL: http://www.i-ching.hu/array/kingwen-array.htm
(January, 2013)
You can read and download the same writing in .pdf file from the SCRIBD, under the title The King Wen Table of the I Ching.
Free download.
(March 25, 2013)

Error corrected!
I am very sorry, but for a while, there was a regrettable error on the page of The King Wen Table. In Figure 16 (An early variant of the King Wen Table) some hexagrams were placed in wrong cells. On February 22nd, the diagram was corrected. 
(February 26, 2013)

NEW!  The Rectangular Predecessors of the King Wen Sequence 
This is a new edition of The King Wen Table and the King Wen Array of the last year. I have changed the title of the page, improved the wording at some places in the body, and removed the chapter Circular representations of the groups.
You can read the new text on the place of the old one: http://www.i-ching.hu/array/kingwen-array.htm
or through the Home page of this site.
You can read and download the same text in .pdf file from the SCRIBD, under the title The King Wen Table of the I Ching. Free download.
(February 13, 2014)

Analogues	TOP	References

All material on this web site is Copyright ⓒ by Jozsef Drasny, Budapest, 2007