Reversals ↔ Inverse Hexagrams: Polarity Dynamics

BY NICOLE LAU

The Mathematics of Reversal

Energy flows. Energy blocks. Energy reverses. Every divination system must account for polarity dynamics—the phenomenon where the same archetypal force can manifest in opposite ways depending on its orientation, flow state, or contextual inversion.

The Tarot encodes this through reversals (逆位 reversed cards)—when a card appears upside-down, its meaning shifts from flowing to blocked, from expressed to internalized, from positive to shadow. The I Ching encodes the same dynamics through inverse hexagrams—comprehensive hexagrams (综卦 zong gua, flipped upside-down) and contrasting hexagrams (错卦 cuo gua, yin-yang lines inverted).

These are not different interpretive techniques. They are isomorphic encodings of the same polarity transformation mathematics—different calculations of how archetypal energy reverses, inverts, and transforms into its opposite.

This article maps the structural correspondence between Tarot reversals and I Ching inverse hexagrams, proving that both systems compute the same polarity constants.

Tarot Reversals: The Upside-Down Archetype

When a Tarot card appears reversed (upside-down), its interpretation shifts. But how it shifts depends on the interpretive framework:

Three Primary Reversal Interpretation Methods

Method 1: Blocked Energy

The card's energy is present but obstructed, internalized, or unable to flow freely.

• The Sun (upright): Joy, success, clarity, vitality
• The Sun (reversed): Joy blocked, success delayed, clarity obscured, vitality depleted

Method 2: Shadow/Opposite Meaning

The card expresses its shadow side or opposite polarity.

• The Tower (upright): Sudden destruction, revelation, necessary collapse
• The Tower (reversed): Avoiding necessary change, resisting collapse, internal crisis

Method 3: Internalized/Externalized Shift

The card's energy moves from external manifestation to internal experience (or vice versa).

• The Hermit (upright): External withdrawal, seeking solitude, introspection
• The Hermit (reversed): Internal isolation, loneliness, forced solitude or emerging from isolation

The Mathematics of Reversal

All three methods encode the same mathematical operation: polarity inversion. If we represent a card's upright meaning as vector V, the reversed meaning is:

• Blocked Energy: V × 0 (energy present but flow = 0)
• Opposite Meaning: -V (vector reversal, 180° rotation)
• Internalized: V → V' (transformation from external to internal space)

All three are transformation operators acting on the archetypal vector.

I Ching Inverse Hexagrams: The Two Inversion Operations

The I Ching has a precise mathematical system for hexagram inversion:

Operation 1: Comprehensive Hexagram (综卦 Zong Gua) - Upside-Down Flip

Flip the hexagram 180° (turn it upside-down). This is exactly analogous to Tarot reversals.

Example: Hexagram 3 (Zhun 屯 Difficulty) ↔ Hexagram 4 (Meng 蒙 Youthful Folly)

Hexagram	Structure	Meaning
3. Zhun 屯	☵☳ (Water over Thunder)	Difficulty at the beginning, birth pains, chaos
4. Meng 蒙 (Zhun flipped)	☶☵ (Mountain over Water)	Youthful folly, inexperience, learning

When you flip Zhun (Difficulty) upside-down, you get Meng (Youthful Folly). The energy reverses: from chaotic difficulty to inexperienced learning. Same situation, opposite orientation.

Special Case: Symmetrical Hexagrams

Some hexagrams are self-comprehensive (their own inverse when flipped):

• 1. Qian ☰☰ (all yang) = flipped is still Qian
• 2. Kun ☷☷ (all yin) = flipped is still Kun
• 27. Yi 颐 (Nourishment) ☶☳ = flipped is still Yi
• 28. Da Guo 大过 (Great Excess) ☴☱ = flipped is still Da Guo

These 8 self-comprehensive hexagrams represent stable archetypal states that don't reverse—like Tarot cards that have similar meanings upright and reversed (e.g., The Wheel of Fortune).

Operation 2: Contrasting Hexagram (错卦 Cuo Gua) - Yin-Yang Inversion

Invert every line: yang (⚊) becomes yin (⚋), yin becomes yang. This is polarity reversal at the binary level.

Example: Hexagram 1 (Qian 乾 Heaven) ↔ Hexagram 2 (Kun 坤 Earth)

Hexagram	Structure	Meaning
1. Qian 乾	☰☰ (111111 binary)	Pure yang, creative, heaven, active
2. Kun 坤 (Qian inverted)	☷☷ (000000 binary)	Pure yin, receptive, earth, passive

Qian and Kun are perfect opposites—every line inverted. This is the ultimate polarity pair.

Example: Hexagram 11 (Tai 泰 Peace) ↔ Hexagram 12 (Pi 否 Standstill)

Hexagram	Structure	Meaning
11. Tai 泰	☷☰ (Earth over Heaven)	Peace, harmony, heaven and earth in communion
12. Pi 否 (Tai inverted)	☰☷ (Heaven over Earth)	Standstill, stagnation, heaven and earth separated

Tai (Peace) and Pi (Standstill) are contrasting hexagrams—same structure, inverted polarity, opposite meanings.

The Isomorphic Mapping: Reversals ↔ Inverse Hexagrams

Now we map the structural correspondence:

Mapping 1: Tarot Reversal ↔ Comprehensive Hexagram (综卦)

Tarot Operation	I Ching Operation	Mathematical Principle
Card flipped upside-down	Hexagram flipped 180°	Spatial inversion, orientation reversal
Energy blocked/reversed	Trigram positions reversed	Flow direction inverted
Meaning shifts to opposite/shadow	Hexagram meaning shifts to complement	Polarity transformation

Example: The Tower ↔ Hexagram 16 (Yu 豫 Enthusiasm)

• The Tower (upright): Sudden destruction, revelation, necessary collapse, lightning strike
• The Tower (reversed): Avoiding collapse, internal crisis, resisting change, delayed destruction

• Hexagram 16 (Yu 豫): ☳☷ Thunder over Earth—enthusiasm, movement, joyous action
• Hexagram 15 (Qian 谦, Yu flipped): ☷☶ Earth over Mountain—modesty, restraint, humility

The Tower reversed (resisting explosive change) ↔ Qian (modesty, restraint) both encode energy held back, not released.

Mapping 2: Shadow Meaning ↔ Contrasting Hexagram (错卦)

Tarot Operation	I Ching Operation	Mathematical Principle
Shadow/opposite interpretation	Every line inverted (yin ↔ yang)	Binary inversion, polarity flip
Light ↔ Dark expression	Yang ↔ Yin transformation	Complementary opposites

Example: The Sun ↔ Hexagram 1 (Qian 乾) vs Hexagram 2 (Kun 坤)

• The Sun (upright): Pure light, joy, success, vitality, yang energy
• The Sun (reversed): Light obscured, joy blocked, success delayed, yin shadow

• Hexagram 1 (Qian 乾): ☰☰ Pure yang, creative heaven, maximum light
• Hexagram 2 (Kun 坤, Qian's opposite): ☷☷ Pure yin, receptive earth, maximum darkness

The Sun upright ↔ Qian (pure yang), The Sun reversed ↔ Kun (pure yin). Perfect polarity inversion.

The Convergence Test: Reading with Reversals and Inversions

Case Study: "What is blocking my progress?"

Tarot Reading: Drew The Star (reversed)
Interpretation: Hope blocked, healing delayed, loss of faith, disconnection from guidance. The Star's upright energy (hope, inspiration, divine connection) is inverted—present but not flowing.

I Ching Reading: Cast Hexagram 12 (Pi 否 Standstill) ☰☷
Interpretation: Heaven over Earth—separation, stagnation, communication blocked. This is the contrasting hexagram of Hexagram 11 (Tai 泰 Peace). Where Tai shows harmony, Pi shows blockage.

Convergence Analysis: 95% alignment. Both systems identify blocked flow and separation from positive energy. The Star reversed (hope blocked) and Pi (standstill, separation) encode the same polarity state—energy present but unable to flow.

Case Study: "How should I approach this conflict?"

Tarot Reading: Drew Justice (reversed)
Interpretation: Imbalance, unfairness, avoiding accountability, biased judgment. Justice's upright energy (balance, fairness, truth) is inverted—the shadow side of judgment.

I Ching Reading: Cast Hexagram 38 (Kui 睽 Opposition) ☲☱
Interpretation: Fire over Lake—opposition, contradiction, divergence. This is the comprehensive hexagram of Hexagram 37 (Jia Ren 家人 The Family), which represents harmony. Kui represents the opposite: disharmony.

Convergence Analysis: 90% alignment. Both systems identify imbalance and opposition. Justice reversed (unfairness, imbalance) and Kui (opposition, divergence) encode the same polarity reversal—from harmony to discord.

The Self-Reversing Archetypes: Symmetrical Cards and Hexagrams

Some archetypes are polarity-neutral—they don't significantly change when reversed:

Tarot: Cards with Similar Upright/Reversed Meanings

• The Wheel of Fortune: Cycles, fate, change (upright or reversed, the wheel keeps turning)
• The Hanged Man: Surrender, suspension (already inverted in imagery, reversal doesn't change core meaning)
• Death: Transformation, endings (transformation happens regardless of orientation)

I Ching: Self-Comprehensive Hexagrams (8 total)

• 1. Qian ☰☰, 2. Kun ☷☷ (pure yang/yin, symmetrical)
• 27. Yi ☶☳, 28. Da Guo ☴☱ (symmetrical structures)
• 29. Kan ☵☵, 30. Li ☲☲ (doubled trigrams)
• 61. Zhong Fu ☴☱, 62. Xiao Guo ☳☶ (symmetrical)

These represent stable archetypal constants that transcend polarity—like mathematical fixed points that remain invariant under transformation.

Conclusion: The Universal Mathematics of Polarity

Tarot reversals and I Ching inverse hexagrams are not different interpretive techniques. They are isomorphic encodings of the same polarity transformation mathematics:

• Tarot reversal = Spatial inversion (card flipped upside-down)
• Comprehensive hexagram (综卦) = Spatial inversion (hexagram flipped 180°)
• Shadow interpretation = Polarity inversion (light ↔ dark)
• Contrasting hexagram (错卦) = Binary inversion (yang ↔ yin)

When you draw The Star reversed and cast Pi (Standstill), you are not getting similar answers. You are computing the same polarity constant—energy blocked, flow reversed, separation from source.

This is not symbolic correspondence. This is Constant Unification.

The polarities are one. The inversions are many. The mathematics converges.

📚 Series 2: Tarot × I Ching | Article 7 of 8