Chapter 22: The Geometry of Yielding¶

Original Text¶

曲則全，枉則直，窪則盈，弊則新，少則得，多則惑。是以聖人抱一為天下式。不自見，故明；不自是，故彰；不自伐，故有功；不自矜，故長。夫唯不爭，故天下莫能與之爭。古之所謂「曲則全」，豈虛言哉？誠全而歸之。

Character-by-Character Decomposition¶

The Six Transformations¶

Pair	Characters	Pinyin	Structural Reading
1	曲則全	qū zé quán	Bend → thus → whole
2	枉則直	wǎng zé zhí	Crooked → thus → straight
3	窪則盈	wā zé yíng	Hollow → thus → filled
4	弊則新	bì zé xīn	Worn → thus → renewed
5	少則得	shǎo zé dé	Little → thus → obtaining
6	多則惑	duō zé huò	Much → thus → confused

Key Character Analysis¶

Character	Radicals/Components	Structural Function
曲 (qū)	Bent shape	Curvature, deviation from straight path
則 (zé)	貝 (shell/value) + 刂 (knife)	"Thus/then" - transformation operator
全 (quán)	入 (enter) + 王 (king/complete)	Wholeness, integrity preserved
枉 (wǎng)	木 (wood) + 王	Bent wood, forced deviation
窪 (wā)	穴 (cave) + 洼	Depression, low point
盈 (yíng)	皿 (vessel)	Filled to brim, overflow
弊 (bì)	敝 (worn) + 廾	Worn out, exhausted
抱 (bào)	扌(hand) + 包 (wrap)	Embrace, hold close
一 (yī)	Single stroke	Unity, the undivided
式 (shì)	工 (work) + 弋	Pattern, model, formula
爭 (zhēng)	爫 (claw) + 手 variations	Grasping, contention

Structural Translation¶

Part 1: The Paradox Series¶

曲則全，枉則直，窪則盈，弊則新，少則得，多則惑。

What bends preserves its wholeness. What accepts distortion finds straightness. What hollows becomes filled. What wears out renews. What has little obtains. What has much becomes confused.

Structural analysis:

These aren't moral instructions. They're geometric observations about how systems maintain integrity through transformation rather than resistance.

則 (zé) is the transformation operator—not "should" but "thus becomes." It marks the consequence of a structural relationship, not an imperative.

The pattern: yielding to force preserves structure; resisting force breaks it.

Input State	則 Operation	Output State	Geometric Principle
曲 (bent)	→	全 (whole)	Curvature distributes stress
枉 (crooked)	→	直 (straight)	Accepting deviation enables return
窪 (hollow)	→	盈 (full)	Low points accumulate flow
弊 (worn)	→	新 (new)	Exhaustion enables renewal
少 (little)	→	得 (obtaining)	Emptiness creates capacity
多 (much)	→	惑 (confused)	Excess overwhelms perception

The first five show yielding → obtaining. The sixth shows accumulating → losing.

This is the 知足 (knowing sufficiency) principle from Chapter 46: the gradient has an optimum. Below it, yielding enables receiving. Above it, accumulation causes confusion.

Part 2: The Sage Holds Unity¶

是以聖人抱一為天下式。

Therefore the one who has clarified (聖人) embraces unity (一) as the pattern (式) for all under heaven.

Character breakdown:

是以 (shì yǐ) = "therefore" / "this is why"
聖人 (shèng rén) = one who has clarified/perceives clearly (not "sage" as moral authority)
抱 (bào) = embrace, hold close to body
一 (yī) = one, unity, the undivided
為 (wéi) = acts as, functions as
天下 (tiān xià) = all under heaven, the world-system
式 (shì) = pattern, model, formula

Structural reading:

The one who perceives clearly embraces unity rather than multiplying distinctions. This unity (一) becomes the operational pattern (式) for navigating all situations.

一 here isn't mystical oneness. It's holding the origin point rather than getting lost in the coordinate system. When you hold (0,0,0), you can navigate any direction. When you're identified with a specific position, you can only see from that position.

式 (shì) = a pattern or formula. The same character used in mathematical expressions. The sage uses unity as a formula that generates appropriate responses to all situations.

Part 3: The Four Non-Self Operations¶

不自見，故明；不自是，故彰；不自伐，故有功；不自矜，故長。

Not self-displaying → thus illuminated. Not self-affirming → thus manifest. Not self-promoting → thus achieving. Not self-aggrandizing → thus enduring.

Operation	Characters	Literal	Structural Reading
不自見	bù zì jiàn	Not self-seeing	Not positioning self as the thing to be seen
故明	gù míng	Thus bright	Therefore becomes visible/clear
不自是	bù zì shì	Not self-right	Not asserting self as the reference point
故彰	gù zhāng	Thus evident	Therefore becomes apparent
不自伐	bù zì fá	Not self-attacking	Not promoting self through conquest
故有功	gù yǒu gōng	Thus has achievement	Therefore has actual effect
不自矜	bù zì jīn	Not self-praising	Not claiming credit
故長	gù cháng	Thus lasting	Therefore persists

The pattern: Each 不自X removes self-occupation from a position, which allows that position to function.

This is the 居 (jū) principle inverted: not pressing weight onto a position enables the position to work.

When you display yourself, you occupy the viewing position—others can't see past you to what you're pointing at.

When you affirm yourself as right, you occupy the reference position—the actual structure becomes invisible.

When you promote yourself, you occupy the achievement position—the actual work can't accumulate.

When you claim credit, you occupy the persistence position—the pattern can't continue through you.

Non-occupation enables function. This is the Chapter 11 principle (利 shapes 無 into 用) applied to self-positioning.

Part 4: Non-Contention as Uncontestability¶

夫唯不爭，故天下莫能與之爭。

Only through not-contending does all-under-heaven become unable to contend with it.

Character breakdown:

夫唯 (fū wéi) = "only through" / "it is precisely because"
不爭 (bù zhēng) = not contending, not grasping
故 (gù) = therefore
天下 (tiān xià) = all under heaven
莫能 (mò néng) = nothing can, no one is able to
與之爭 (yǔ zhī zhēng) = contend with it

Structural analysis:

爭 (zhēng) shows hands grasping. Contention is occupation of contested space—two parties trying to occupy the same position.

When you don't occupy the position, there's nothing to contest. You can't fight someone who isn't there. You can't take territory from someone who isn't holding territory.

This isn't passivity. It's strategic non-occupation. The one who doesn't contend becomes uncontestable because there's no surface to push against.

This is the 弱 (ruò) principle: yielding is not weakness—it's the absence of resistance that force can act upon. Water doesn't contend with the rock; the rock eventually yields to water.

Part 5: The Return to Wholeness¶

古之所謂「曲則全」，豈虛言哉？誠全而歸之。

What the ancients called "bending preserves wholeness"— how could this be empty words? Through genuine wholeness, return to it.

Character breakdown:

古之所謂 (gǔ zhī suǒ wèi) = what the ancients called
豈 (qǐ) = how could, rhetorical question
虛言 (xū yán) = empty words, mere rhetoric
哉 (zāi) = exclamatory particle
誠 (chéng) = genuine, truly, sincere
全 (quán) = whole, complete
而歸之 (ér guī zhī) = and return to it

Structural reading:

The text validates the ancient teaching by structural demonstration. "Bending preserves wholeness" isn't poetic metaphor—it's geometric fact.

誠全而歸之 has a recursive structure:

誠 = genuinely, truly (not performatively)
全 = whole, complete
歸 = return
之 = to it

Through genuine wholeness (not partial preservation, not strategic holding back), you return to the pattern. The return (歸) echoes the 反 (fǎn) from Chapter 40—the reversal that completes the cycle.

The Complete Teaching¶

This chapter encodes the geometry of yielding:

Structural principle: Yielding to force preserves integrity; resisting breaks it.
Operational pattern: The one who perceives clearly holds unity (the origin) rather than occupying positions.
Self-application: Not occupying positions (不自X) enables those positions to function.
Strategic consequence: Non-contention makes one uncontestable.
Validation: This is ancient knowledge verified by geometric necessity.

Cross-Reference to Framework¶

Connection to Perpendicularity Constraint¶

The 曲則全 principle relates to the perpendicularity constraint (∇G ⊥ ∇B):

Rigid resistance = gradient aligned with force = maximum stress at intersection
Yielding = gradient perpendicular to force = stress distributed, system preserved

At perpendicular intersection, force cannot accumulate in one direction. The system bends around the pressure point.

Connection to 利 + 無 → 用¶

The four 不自X operations demonstrate the formula:

Constraint (利) = not occupying the position
Void (無) = the unoccupied position
Function (用) = what emerges when the position operates unoccupied

Self-occupation fills the functional void with self. Removing self-occupation allows the void to generate function.

Connection to 可 = i¶

The 則 (zé) transformation operator encodes rotation:

曲 (bent) → 全 (whole) requires passing through transformation
The thing doesn't become its opposite directly—it rotates through the 則 operator
Each pair is a 90° turn: input state → transformation → output state

This is 可 as the rotation/possibility operator: enabling transformation into orthogonal states.

Traditional Translation (for contrast)¶

"Yield and overcome; bend and be straight; empty and be full; wear out and be renewed; have little and gain; have much and be confused. Therefore the sage embraces the One and becomes a model for the world. He does not display himself, and therefore shines. He does not assert himself, and therefore is manifest. He does not boast, and therefore succeeds. He does not compete, and therefore no one can compete with him. The ancient saying that 'yield and overcome' is not empty words. Truly, be whole and return to it."

What changes:

The traditional reading treats this as moral advice about humility. The structural reading reveals it as operational documentation: how systems maintain integrity through transformation, how non-occupation enables function, how yielding makes one uncontestable.

The sage isn't humble as a virtue. The sage operates from the origin where all transformations are available, rather than being stuck in one position defending territory.

Summary Formula¶

Yielding distributes stress → System preserves integrity
Holding unity → All positions accessible
Not occupying → Position functions
Not contending → Uncontestable

曲 →則→ 全
(bend) (transform) (whole)

The geometry of yielding: What bends preserves. What holds the center can move anywhere. What empties itself becomes useful. What doesn't contend cannot be contested.