Advanced I Ching Studies: Mutual Hexagrams (Zong Gua / Fan Gua / Jiao Gua)

Article 3 of Section I: Deeper Concepts in Hexagram Analysis

Difficulty Level: Advanced

Prerequisites: Familiarity with the 64 hexagrams, the eight trigrams, basic I Ching terminology, and concepts like Nuclear Hexagrams (Hu Gua) and Contrasting Hexagrams (Cuo Gua / Pang Tong Gua).

I. Introduction: Seeing from Another Angle

The I Ching offers multiple lenses to view a situation. Beyond the primary hexagram, its internal structure (Nuclear Hexagram), and its direct opposite (Contrasting Hexagram), a crucial perspective is gained by examining its “Mutual Hexagram.” This technique involves looking at the hexagram as if its structure were inverted or its component trigrams swapped, offering insights into reverse perspectives, hidden undersides, or the eventual outcome if the situation’s orientation were to flip.

Mutual Hexagrams, known by terms like Zong Gua (綜卦), Fan Gua (反卦), and Jiao Gua (交卦), challenge us to consider the situation from a different structural viewpoint, revealing inherent symmetries, consequences of a reversed approach, or the perspective of “the other side.”

II. Definition, Terminology, and Derivation

The concept of “Mutual Hexagrams” encompasses several related types of structural transformations based on inversion or reversal.

A. Key Terminology:

• Zong Gua (綜卦): Often used as an overarching term for hexagrams related by inversion. It translates to “Composite Hexagram,” “Synthesized Hexagram,” or “Overall Hexagram.” The character 綜 (zong) implies gathering threads or taking an overview. In the context of simple inversion, it means viewing the hexagram from the opposite end (upside down).

• Qian Gua (乾卦 or 潛卦): Often referred to as “Inverse Pairs.” This involves the vertical flip of a hexagram. Line 1 becomes line 6, line 2 becomes line 5, and so on.

• Jiao Gua (交卦): “Exchange Hexagrams” or “Reverse Pairs.” These are pairs of hexagrams that have the same component trigrams (Ba Gua), but with their positions reversed. The lower trigram of one becomes the upper trigram of the other, and vice versa.

• Fan Gua (反卦): Meaning “Reverse Hexagram” or “Anti-Hexagram.” This term can be ambiguous. Yu Fan (164-233 CE) used Fan Gua to describe hexagrams that are their own reverse pairs (i.e., symmetrical hexagrams or Chong Gua). More broadly, it can refer to various oppositional relationships.

• Dao Gua (倒卦): Meaning “Inverted Hexagram” or “Toppled Hexagram.” This descriptively refers to the action of turning the hexagram upside down, aligning with Qian Gua.

Relationship between Qian Gua and Jiao Gua:

For hexagrams that are not made of doubled trigrams (non-Chong Gua), the vertical flip (Qian Gua) results in the same hexagram as swapping the upper and lower trigrams (Jiao Gua). Thus, for these 56 hexagrams, the “Inverse” and “Reverse” are identical.

B. Derivation Methods:

1. Qian Gua (Inverse / Vertical Flip):

   • Line 1 of the primary hexagram becomes Line 6 of the Qian Gua.

   • Line 2 becomes Line 5.

   • Line 3 becomes Line 4.

   • Line 4 becomes Line 3.

   • Line 5 becomes Line 2.

   • Line 6 becomes Line 1.

     (This is the method we primarily referred to as Zong Gua in the initial explanation).

2. Jiao Gua (Reverse / Trigram Swap):

   • The lower trigram of the primary hexagram becomes the upper trigram of the Jiao Gua.

   • The upper trigram of the primary hexagram becomes the lower trigram of the Jiao Gua.

   • The lines within each trigram maintain their original relative positions (1,2,3).

C. Types of Resulting Hexagrams:

1. Different Hexagram is Formed (Asymmetrical Hexagrams):

   • Most hexagrams (56 of them, forming 28 pairs) will result in a different hexagram when inverted (Qian Gua) or when their trigrams are swapped (Jiao Gua). For these, Qian Gua = Jiao Gua.

2. The Same Hexagram is Formed (Symmetrical Hexagrams):

   • There are 8 hexagrams that remain unchanged after inversion (Qian Gua) or trigram swap (Jiao Gua). These are their own Qian Gua and Jiao Gua.

   • These include the six Chong Gua (hexagrams formed by doubling one of the eight basic trigrams):

     • #1 Qian (乾) - Heaven over Heaven

     • #2 Kun (坤) - Earth over Earth

     • #29 Kan (坎) - Water over Water

     • #30 Li (離) - Fire over Fire

     • #51 Zhen (震) - Thunder over Thunder (Its Qian Gua is different: #52 Gen. Zhen is not symmetrical in the Qian Gua sense. Correction based on re-evaluation: Zhen is not a symmetrical hexagram for inversion. The 8 symmetrical hexagrams for inversion (Qian Gua) are: 1, 2, 27, 28, 29, 30, 61, 62.)

     • #52 Gen (艮) - Mountain over Mountain

     • #57 Xun (巽) - Wind over Wind

     • #58 Dui (兌) - Lake over Lake

   • Correction: The 8 hexagrams that are their own Qian Gua (symmetrical upon vertical flip) are:

     • #1 Qian (乾)

     • #2 Kun (坤)

     • #27 Yi (頤)

     • #28 Da Guo (大過)

     • #29 Kan (坎)

     • #30 Li (離)

     • #61 Zhong Fu (中孚)

     • #62 Xiao Guo (小過)

   • The 8 hexagrams that are Chong Gua (doubled trigrams) are their own Jiao Gua (Reverse Pairs, as their trigrams are already identical). These are: 1, 2, 29, 30, 51, 52, 57, 58.

   • Note the overlap: Qian, Kun, Kan, Li are both symmetrical by inversion and are doubled trigrams.

D. Example of Derivation (Asymmetrical - Qian Gua / Jiao Gua are the same):

Hexagram 3, Zhun (屯) - Difficulty at the Beginning (Water ☵ over Thunder ☳).

• Qian Gua (Inversion): Results in Hexagram 4, Meng (蒙) - Youthful Folly (Mountain ☶ over Earth 坤 ☷), as detailed previously.

• Jiao Gua (Trigram Swap): Thunder ☳ (lower) becomes upper; Water ☵ (upper) becomes lower. Thunder over Water is Hexagram 40, Jie (解) - Deliverance.

  Correction: The initial document’s example for Zhun (H3) becoming Meng (H4) was based on Qian Gua (inversion). The Jiao Gua of Zhun (Water over Thunder) would be Thunder over Water (Hexagram 40, Jie). This highlights the importance of distinguishing the transformation type. Let’s stick to Qian Gua (inversion) as the primary focus for “Mutual Hexagram” as initially defined, and treat Jiao Gua as a distinct but related concept.

For clarity, this article will primarily focus on Zong Gua as Qian Gua (Inversion / Vertical Flip), while acknowledging Jiao Gua as another significant “mutual” relationship.

III. Reverse Perspectives: The Interpretive Value of Zong Gua (Inversion)

The Zong Gua (as Qian Gua/Inversion) offers several layers of interpretive insight:

A. The Other Side of the Coin / Process:

• Represents the natural consequence or next stage if the primary hexagram’s process is followed or seen from its endpoint. Ex: Hexagram 53, Jian (漸) - Development; its Zong Gua is Hexagram 54, Gui Mei (歸妹) - The Marrying Maiden.

• Can show the situation from the perspective of “the other party” or the “receiving end.”

B. Unseen Implications or Consequences:

• Reveals what happens if the current trajectory is reversed or assumptions are flipped.

• Highlights the eventual outcome or “bill to be paid.” Ex: Hexagram 11, Tai (泰) - Peace; its Zong Gua is Hexagram 12, Pi (否) - Standstill.

C. Inherent Symmetry or Asymmetry (based on Inversion):

• For Symmetrical Hexagrams (1, 2, 27, 28, 29, 30, 61, 62): Implies stability, self-containment, or a situation that looks the same from either direction. This can mean strength (Qian, Kun) or a cycle difficult to escape (Kan).

• For Non-Symmetrical Hexagrams: The difference highlights inherent directionality or evolution.

D. Time and Sequence:

• Often interpreted as representing a temporal sequence: what comes after.

• Can represent looking back at the beginning from the end, or vice-versa.

E. Interpretive Value of Jiao Gua (Trigram Swap / Reverse Pairs):

• Analyzing Jiao Gua provides insights by examining how the component trigrams operate when positioned in the lower (inner, subjective) place compared to the upper (outer, objective) place.

• This perspective helps in analyzing the objective applicability of subjective experience (inner to outer) or the internalization of objective experience to form an optimal attitude (outer to inner).

• This approach became an explicit dimension of interpretation by the Han dynasty, following the elaboration of the meanings of upper and lower trigram positions (Ban Xiang or Half-Images).

IV. Consequences and Challenges in Interpretation

A. Understanding the “Consequence” (for Zong Gua as Inversion):

• Not always negative; can be natural fulfillment, logical next step, or a different valid standpoint.

• Can represent cost, benefit, challenge, or opportunity of inversion.

B. Context is Key:

• Specific meaning depends on the primary hexagram and the question.

C. Distinguishing from Other Related Hexagrams:

• Cuo Gua (Contrasting): Polar opposite.

• Zong Gua (as Qian Gua/Inverted): Reversed viewpoint, other end.

• Jiao Gua (Reverse/Trigram Swap): Swapped trigrammatic perspective.

• Hu Gua (Nuclear): Inner core.

D. Symmetrical Hexagrams (Zong Gua as Inversion):

• Self-sameness implies a profound, all-encompassing, or inescapable nature. Points to a fundamental or archetypal state.

V. Broader Context and Related Concepts

The analysis of Mutual Hexagrams (both Zong Gua/Qian Gua and Jiao Gua) is part of a larger toolkit of structural dimensions within Yijing studies.

A. Other Key Structural Dimensions:

• Pang Tong Gua (Opposite / Contrasting Hexagram): Diametrically opposed in the sequence or by line-for-line inversion (also Cuo Gua).

• Hu Gua (Nuclear Hexagram): Interior trigrams (lines 2,3,4 and 3,4,5).

B. Historical Development and Foundational Role:

• The idea of “invertible or positional pairing” (Zong Gua and Jiao Gua relationships) is considered a basic “building block” for the standard King Wen sequence of hexagrams.

• Early teaching methods, attributed to Zhou Gong, involved presenting figures in pairs, including opposite pairs and pairs of inverts, suggesting an ancient foundation.

• These structural analyses developed over time, with distinct dimensions recognized in the original Zhouyi, the Ten Wings, Han Dynasty Yiweishu (apocrypha), and later Post-Han commentaries.

C. The Za Gua (Tenth Wing) and Hexagram Pairs:

• The Za Gua (Miscellaneous Notes on the Hexagrams) briefly defines each hexagram, often by contrasting two of them. It reviews 32 structurally meaningful pairs.

• Some discussions of the Za Gua note that 56 hexagrams (the asymmetrical ones) are arranged in upright and inverse pairs.

D. Changing Lines, Ben Gua, Zhi Gua, and Fan Yao:

• A major structural dimension is that a Changing Line Text (Yao Ci) acts as an interpolation in meaning between the original Hexagram (Ben Gua) and the Resultant Hexagram (Zhi Gua).

• The concept of reversal also appears at the line level with Fan Yao (反爻 - Reverse Line). This links the meaning of a specific changing line to a reverse perspective, often within the context of the Zhi Gua. For example, the sources might connect the changing 5th line of Hexagram 7 (leading to Hexagram 29 as Zhi Gua) to the Fan Yao of Hexagram 29, line 5.

E. Alternative and Complex Methods for Relating Hexagrams:

• Numerical Methods: The Ten Wings mention subtracting a hexagram’s line values from 55 to find a “related hexagram” (e.g., H54 relates to H38; H3 to H8). This is distinct from structural symmetries.

• Complex Inter-Hexagram Relationships: Advanced interpretations can involve analyzing relationships between a given hexagram/line and multiple other hexagrams computationally.

F. Early Analysis of Trigram Interaction:

• The Warring States period text Shifa (Method of milfoil divination) shows early methods for interpreting upper and lower trigrams and their interactions within a cluster of hexagrams, indicating ancient roots for analyzing relationships based on trigram components.

VI. Practical Application and Exercises

A. Methodology Review (for Zong Gua as Inversion):

1. Identify the primary hexagram.

2. Derive its Zong Gua by inverting the lines.

3. If different, consider its name, image, and meaning relative to the primary. If same, reflect on the symmetry.

4. Ask: How does this reverse perspective illuminate? What consequence or outcome? If a process, what about later stages? If interaction, what about the other’s perspective?

5. Integrate insights.

B. Practice Exercises:

1. Derive the Zong Gua (Inversion) for Hexagram 7, Shi (師) - The Army. Its Zong Gua is also Hexagram 7 Shi (as it is symmetrical for trigram positions, but not for line-by-line inversion unless the trigrams are identical and symmetrical themselves. Correction: H7 Shi is Earth over Water. Its Zong Gua/Inversion is Water over Earth, H8 Bi). How does Bi (Holding Together) offer a reverse perspective to Shi?

2. Consider Hexagram 27, Yi (頤). It is symmetrical by inversion. What does this suggest about nourishment?

3. Take a hexagram from a reading. Determine its Zong Gua (Inversion). How does this add to your understanding?

VII. Conclusion

Mutual Hexagrams, particularly the Zong Gua (as Qian Gua/Inversion) and the related Jiao Gua (Reverse Pairs/Trigram Swap), provide vital alternative perspectives in I Ching analysis. By inverting the hexagram or its trigrams, we consider unfolding time, opposing viewpoints, or structural consequences. These techniques, situated within a rich historical and methodological context that includes other structural analyses like Cuo Gua and Hu Gua, and concepts like Fan Yao and the Ben Gua/Zhi Gua relationship, deepen our understanding of the Yijing’s multifaceted wisdom. They encourage a comprehensive view, acknowledging that every process has multiple facets, every action a reaction, and every standpoint an alternative.