三十輻

Chinese Text

三十輻共一轂，當其無，有車之用。 埏埴以為器，當其無，有器之用。 鑿戶牖以為室，當其無，有室之用。 故有之以為利，無之以為用。

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Translation

三十輻共一轂，當其無，有車之用。 Thirty spokes share one hub; Where it is nothing, there is the cart’s function.

埏埴以為器，當其無，有器之用。 Knead clay to make vessels; Where it is nothing, there is the vessel’s function.

鑿戶牖以為室，當其無，有室之用。 Carve doors and windows to make a room; Where it is nothing, there is the room’s function.

故有之以為利，無之以為用。 Therefore: Substance provides the harvest-capacity (the π-operation), Emptiness provides the operational function (the void that enables motion).

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Key Terms

Character	Pinyin	Structural Reading
輻	fú	spoke (radiates from void to rim)
轂	gǔ	hub (contains the axle-void)
無	wú	void, nothing (generative, not absence)
用	yòng	function, capacity (what void provides)
埏	shān	knead (working substrate)
埴	zhí	clay (malleable earth)
器	qì	vessel (openings guarding emptiness)
鑿	záo	carve (subtract material)
室	shì	room (space you can arrive into)
利	lì	harvest-capacity, π-operation (scythe arc)
有	yǒu	substance, form, presence

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The 利 Correction

利 lì = 禾 hé (standing grain) + 刀 dāo (blade)

Previous translations: “advantage,” “profit,” “benefit” — abstract nouns

Structural reading: The scythe operation — the arc that sweeps through the field

Reading	Operation	Result
Knife	Linear push	One stalk at a time, exhausting
Scythe	π-sweep	Swath per stroke, completing

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The Formula

有之以為利 = Structure provides harvest-capacity
             (the blade that can execute π-operations)

無之以為用 = Emptiness provides operational function
             (the void through which arcs sweep)

有 → 利 → 無 → 用
Structure → cut → void → function

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Three Demonstrations

Object	有 (form)	無 (void)	用 (function)
Wheel	Spokes	Hub	Rotation
Vessel	Clay walls	Interior	Containment
Room	Walls	Carved space	Dwelling

All demonstrate the same principle: Structure exists to perform the cut that maintains the void.

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See Chapter 11 Essay for extended analysis.