Part IV: Concept Index¶
Cross-reference by operational principle
The Principle¶
Characters cluster by the operations they encode. This index organizes by WHAT THEY DO, not by how they're spelled or what radical they contain.
Use this index to find all characters encoding a given principle.
π-Operation Characters¶
Principle: The arc that completes what straight lines cannot. O→G→π→P.
| Character | Pinyin | What It Encodes | Chapters |
|---|---|---|---|
| 利 | lì | Scythe arcs through field | 8, 11, 22, 56, 81 |
| 曲 | qū | The curved path itself | 22 |
| 輪 | lún | Continuous 2π rotation | 11 |
| 反 | fǎn | Return arc completing 2π | 25, 40 |
| 復 | fù | Return to root (recursive reset) | 16, 28, 52, 64 |
| 歸 | guī | Return home | 16, 28, 34 |
Guodian validation: 利 (A01), 反/返 (A37), 復 (A24). The π-operation is ~300 BCE core.
Boundary Management Characters¶
Principle: The six operations that produce 玄同 (mysterious sameness).
The Chapter 56 Sequence¶
| Character | Pinyin | Operation | Effect |
|---|---|---|---|
| 塞 | sāi | Block | Close input channels |
| 閉 | bì | Shut | Close gates |
| 挫 | cuò | Blunt | Reduce edge sharpness |
| 解 | jiě | Untangle | Dissolve complexity |
| 和 | hé | Harmonize | Soften brightness |
| 同 | tóng | Merge | Unify with field |
Pattern: First four REDUCE (塞閉挫解). Last two INTEGRATE (和同).
Guodian validation: Complete sequence appears in A27-A28.
Non-Occupation Characters¶
Principle: 弗居 (doesn't dwell). Not claiming, not possessing, not defending position.
| Character | Pinyin | What It Encodes | Chapters |
|---|---|---|---|
| 弗 | fú | Not (action-negative) | Throughout |
| 居 | jū | Dwell/occupy | 2, 34, 51, 77 |
| 恃 | shì | Rely on/claim | 2, 10, 51, 77 |
| 持 | chí | Hold/maintain | 9, 64 |
| 執 | zhí | Grasp/cling | 29, 64 |
| 積 | jī | Accumulate | 9, 81 |
| 爭 | zhēng | Contend/compete | 3, 8, 22, 66, 68, 81 |
The Non-Occupation Formulas¶
| Formula | Translation | Chapter |
|---|---|---|
| 弗居 | Doesn't dwell | 2 |
| 弗恃 | Doesn't claim | 2, 51 |
| 不執 | Doesn't grasp | 64 |
| 不積 | Doesn't accumulate | 81 |
| 不爭 | Doesn't contend | 8, 22, 68, 81 |
Guodian validation: 弗居, 弗恃 in A17-A18. Non-occupation is ~300 BCE core.
Self-Organization Characters (自X)¶
Principle: What emerges from a system's own nature without external imposition.
| Character | Pinyin | What It Encodes | Chapters | Guodian? |
|---|---|---|---|---|
| 自化 | zì huà | Self-transform | 37, 57 | ✓ A13 |
| 自定 | zì dìng | Self-settle | 37 | ✓ A14 |
| 自然 | zì rán | Self-so (spontaneous) | 17, 23, 25, 51, 64 | ✓ A12 |
| 自均 | zì jūn | Self-equalize | 57 | ✓ A19 |
| 自富 | zì fù | Self-prosper | 57 | ✓ A31 |
| 自正 | zì zhèng | Self-correct | 57 | ✓ A32 |
| 自樸 | zì pǔ | Self-simplify | 37 | ✓ A32 |
The Chapter 57 Cascade¶
我無為而民自化，我好靜而民自正， 我無事而民自富，我無欲而民自樸。
"I non-impose and people self-transform, I prefer stillness and people self-correct, I don't busy and people self-prosper, I don't desire and people self-simplify."
Pattern: Ruler's 無X → people's 自Y.
Co-Emergence Characters (相X)¶
Principle: What arises together through the act of distinction. Drawing a boundary creates both poles simultaneously.
| Character | Pinyin | What It Encodes | Chapters | Guodian? |
|---|---|---|---|---|
| 相生 | xiāng shēng | Mutual arising | 2 | ✓ A15 |
| 相成 | xiāng chéng | Mutual completing | 2 | ✓ A16 |
| 相形 | xiāng xíng | Mutual shaping | 2 | ✓ A16 |
| 相盈 | xiāng yíng | Mutual filling | 2 | ✓ A16 |
| 相和 | xiāng hé | Mutual harmonizing | 2 | ✓ A16 |
| 相隨 | xiāng suí | Mutual following | 2 | ✓ A16 |
The Chapter 2 Sequence¶
有無之相生也，難易之相成也， 長短之相形也，高下之相盈也， 音聲之相和也，先後之相隨也。
Each pair demonstrates co-emergence in different domains: - 有/無: existence - 難/易: difficulty - 長/短: extension - 高/下: position - 音/聲: sound - 先/後: sequence
Guodian validation: Complete sequence in A15-A16. Co-emergence algebra is ~300 BCE core.
Void/Function Characters¶
Principle: 無之以為用 (emptiness provides function). The hub, the pot, the room.
| Character | Pinyin | What It Encodes | Chapters |
|---|---|---|---|
| 虛 | xū | Empty/void | 3, 5, 16 |
| 沖 | chōng | Hollow/pour | 4, 42 |
| 用 | yòng | Function/use | 4, 11, 35, 40 |
| 谷 | gǔ | Valley (receptive void) | 6, 15, 28, 32, 39, 41 |
| 淵 | yuān | Abyss/deep pool | 4, 8 |
| 牝 | pìn | Female (generative opening) | 6, 10, 61 |
The Chapter 11 Demonstrations¶
| Object | 有 Component | 無 Component | Function |
|---|---|---|---|
| Wheel | Spokes, rim | Hub hole | Rolling |
| Pot | Clay walls | Interior hollow | Containing |
| Room | Walls, roof | Door/window openings | Dwelling |
Formula: 有之以為利，無之以為用 - 有 provides 利 (constraint, structure) - 無 provides 用 (function, capacity)
Return/Reversal Characters¶
Principle: 反者道之動 (reversal is pattern's movement). The 2π completion.
| Character | Pinyin | What It Encodes | Chapters |
|---|---|---|---|
| 反 | fǎn | Reversal/return | 25, 40, 65, 78 |
| 復 | fù | Return to root | 16, 28, 52, 64 |
| 歸 | guī | Return home | 16, 28, 34 |
| 還 | huán | Circle back | — |
| 迴 | huí | Revolve | — |
The Chapter 25 Cycle¶
大 → 逝/潰 → 遠 → 反 Great → Overflows → Far → Returns
Guodian variant: Uses 潰 (overflow/burst dam) instead of 逝 (depart). More hydraulic, more geometric.
Completion Characters¶
Principle: What happens at the finishing point. The 幾成 (near-completion) vulnerability.
| Character | Pinyin | What It Encodes | Chapters |
|---|---|---|---|
| 成 | chéng | Complete/accomplish | 2, 9, 17, 34, 64 |
| 全 | quán | Whole/intact | 22, 45 |
| 終 | zhōng | End/finish | 16, 64 |
| 始 | shǐ | Begin/start | 1, 14, 64 |
| 敗 | bài | Ruin/fail | 29, 64 |
Chapter 64's Completion Teaching¶
民之從事，常於幾成而敗之。 慎終如慎始，則無敗事。
"People's affairs constantly at near-completion ruin them. Careful at end as at start, thus no ruined affairs."
The vulnerability: 幾成 (almost-done) is where attention drops. The prescription: 慎終如慎始 (end-care equals beginning-care).
Constancy Characters¶
Principle: 知常曰明 (knowing the constant is called clarity). Frame-independent invariance.
| Character | Pinyin | What It Encodes | Chapters |
|---|---|---|---|
| 常 | cháng | Constant/invariant | Throughout |
| 恆 | héng | Constant (Guodian form) | Throughout |
| 久 | jiǔ | Lasting/long-time | 7, 16, 59 |
| 固 | gù | Solid/certain | 59 |
The Constancy Formulas¶
| Formula | Translation | Chapter |
|---|---|---|
| 常道 | Constant pattern | 1 |
| 常名 | Constant name | 1 |
| 知常曰明 | Knowing constant = clarity | 16 |
| 知和曰常 | Knowing harmony = constant | 55 |
Knowing Characters¶
Principle: 知 as targeted articulation. Arrow + mouth = directed attention.
| Character | Pinyin | What It Encodes | Chapters |
|---|---|---|---|
| 知 | zhī | Know (targeted) | Throughout |
| 明 | míng | Clarity | 16, 33, 52, 55 |
| 智 | zhì | Cleverness | 18, 19, 33, 65 |
| 惑 | huò | Confused | 22, 44 |
| 愚 | yú | Foolish (structurally) | 20, 65 |
The Knowing Hierarchy¶
| Term | What It Is | Valence |
|---|---|---|
| 明 | Clarity (seeing constant) | Positive |
| 知 | Knowing (targeted) | Neutral |
| 智 | Cleverness (surface) | Cautionary |
Chapter 33: 知人者智，自知者明 "Knowing others = clever; self-knowing = clear"
Yielding Characters¶
Principle: 柔之勝剛 (soft overcomes hard). What arcs vs. what breaks.
| Character | Pinyin | What It Encodes | Chapters |
|---|---|---|---|
| 柔 | róu | Soft/yielding | 43, 76, 78 |
| 弱 | ruò | Weak/yielding | 40, 76, 78 |
| 剛 | gāng | Hard/rigid | 76, 78 |
| 強 | qiáng | Strong/forceful | 30, 33, 55, 76 |
Chapter 76's Formula¶
| At Birth | At Death |
|---|---|
| 柔弱 (soft, yielding) | 堅強 (hard, stiff) |
Structural reading: Life = what can arc. Death = what can't arc.
Water Characters¶
Principle: Chapter 8's supreme demonstration. Water IS 無為 in physical form.
| Character | Pinyin | What It Encodes | Chapters |
|---|---|---|---|
| 水 | shuǐ | Water itself | 8, 78 |
| 淵 | yuān | Deep pool | 4, 8 |
| 江 | jiāng | Great river | 32, 66 |
| 海 | hǎi | Ocean | 32, 66 |
| 清 | qīng | Clear | 15, 45 |
| 渾 | hún | Murky | 15, 25 |
Why Water¶
Water demonstrates all principles: - Finds lowest path (處眾人之所惡) - Cuts paths without forcing (利萬物) - Takes shape of container (外其身) - Returns in cycles (反) - Soft overcomes hard (柔之勝剛)
Pattern/Alignment Characters¶
Principle: 道 and 德 as the core relationship.
| Character | Pinyin | What It Encodes | Chapters |
|---|---|---|---|
| 道 | dào | Pattern/way | Throughout |
| 德 | dé | Alignment/power | 38, 51, etc. |
| 法 | fǎ | Method/law | 25 |
| 理 | lǐ | Principle | — |
The Chapter 51 Formula¶
道生之，德畜之 "Pattern generates, alignment nurtures"
| Function | What Does It |
|---|---|
| 道 (pattern) | Generates (生) |
| 德 (alignment) | Nurtures (畜) |
德 is not virtue. 德 is structural alignment with 道—like a spoke maintaining correct angle to hub.
Summary: Index by Function¶
| Functional Domain | Key Characters | Core Chapter |
|---|---|---|
| π-operation | 利, 曲, 輪, 反 | 22, 11 |
| Boundary management | 塞閉挫解和同 | 56 |
| Non-occupation | 弗居, 不爭, 不積 | 2, 81 |
| Self-organization | 自化, 自然, 自正 | 37, 57 |
| Co-emergence | 相生, 相成, 相形 | 2 |
| Void/function | 虛, 沖, 用, 谷 | 11, 4 |
| Return/reversal | 反, 復, 歸 | 40, 16 |
| Constancy | 常/恆, 久 | 1, 16 |
| Yielding | 柔, 弱 vs. 剛, 強 | 76, 78 |
This is Part IV of the Structural Lexicon. Part V (Pinyin Index) provides alphabetical lookup.