Source

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。

Glossary

之

it

共

converge at

利

benefit

器

vessel

埏

knead

埴

potter's clay

室

chamber

戶

door

故

therefore

有

what is present

無

emptiness

牖

window

用

function

當

where there is

輻

spoke

轂

hub

鑿

chisel out

三十

thirty

以為

to make

Translation Notes

1. "Thirty spokes converge at one hub; where there is Emptiness, there is the use of the cart" (三十輻，共一轂，當其無，有車之用) — Alternatives considered: …where there is emptiness, there is the wheel’s use. · …when there is emptiness, use is provided. · …where emptiness exists, the vehicle is used. · Chose present rendering because To preserve (1) the locative-conditional force of 當其無, (2) the technical emptiness enabling function, and (3) the practical scope indicated by 車.
2. "Mold and knead clay to make a vessel; where there is Emptiness, there is the use of the vessel" (埏埴以為器，當其無，有器之用) — Alternatives considered: …knead clay to make a container; emptiness is what makes it useful. · …shape sticky clay into a utensil; at its void, it has use. · Chose present rendering because To maintain the chapter’s parallelism and its craft-grounded metaphysical argument about functional emptiness.
3. "Carve doors and windows to make a room; where there is Emptiness, there is the use of the room" (鑿戶牖以為室，當其無，有室之用) — Alternatives considered: …cut out openings in a wall to make a dwelling; emptiness is what makes it useful. · …make a chamber by carving apertures; it is at emptiness that it has use. · Chose present rendering because To preserve the rhetorical concreteness and the parallel architecture-to-function logic.
4. "Therefore, what is present brings benefit, and Emptiness provides use" (故有之以為利，無之以為用) — Alternatives considered: Therefore being yields benefit, and non-being yields use. · Therefore what exists brings profit, and what is absent brings use. · So presence gives advantage; emptiness gives function. · Chose present rendering because To preserve (1) the sharp parallel antithesis, (2) differentiation between 利 and 用, and (3) the logical force of 故 in the concluding maxim.

Footnotes

1. "Thirty spokes converge at one hub" (輻／轂) — The Daodejing’s triadic structure (wheel—vessel—room) is realized here through the fixed image pair 輻 (“spokes”) and 轂 (“hub/nave”), where function depends on a hollow center. Classical dictionaries gloss 轂 as the place where the spokes gather (輻所湊), i.e., the “nave” of the wheel rather than the entire wheel. Wang Bi (not required by the prompt but representative) and later commentators generally take the “emptiness” (無) as the functional void within designed form; see also Han Feizi’s language about usefulness arising from intentional gaps (cf. “blank space” reasoning in later Legalist texts).
2. "where there is Emptiness, there is the use of the cart" (當其無) — 無 (“Emptiness”) here is not merely negation (“there is nothing”); it functions as a technical philosophical term for the void/hollow space that makes an artifact operational. The pattern 當其無 (“at that point/where there is emptiness”) locates the functional condition precisely within the constructed object. In Daoist reception, this aligns with the broader conceptual contrast of 有 and 無 as complementary rather than mutually exclusive: what is present yields tangible benefit (利), while what is empty/absent yields use/function (用). For later debates on how to construe 無 as “non-being” versus “emptiness,” see modern scholarship; within classical exegesis, the emphasis tends toward a functional emptiness rather than metaphysical annihilation.
3. "Mold and knead clay to make a vessel" (埏埴／器) — 埏埴 refers to potter’s processes involving moistened earth/clay and shaped clay bodies. Translating it as “mold and knead clay” preserves both the technical handwork and the sense that a vessel is made by forming clay into a hollow container, in which the effective “use” comes from the interior void. The character 埏 (often explained as moistening/working earth for shaping) and 埴 (sticky potter’s clay) are both technical in the artisan imagery of this chapter. 器 in this context is the vessel/container itself; however, the term also has extended classical senses (ability/talent). Here, the immediate craft context strongly favors “vessel.”
4. "Carve doors and windows to make a room" (鑿戶牖／室) — The architectural terms 戶 and 牖 denote entry openings: 戶 is a door, and 牖 a window/opening in a wall. Retaining the door/window pair is important because the argument hinges on intentional cutouts that create inhabitable and functional space. 室 is the room/chamber created by architectural enclosing; in Daoist reading, the room is “made” (以為室) by carving and framing, yet its usability depends on openness—again tied to the technical sense of 無 (“emptiness/void”) as functional condition. On how later traditions explain 戶牖 together as a functional configuration of openings within walls, see general architectural glossary in pre-Qin and early imperial textual traditions (e.g., ritual and building-related vocabularies).
5. "Therefore, what is present brings benefit, and Emptiness provides use" (有…利；無…用) — 故有之以為利，無之以為用 is the chapter’s culminating antithesis: 有 (“what is present”) yields 利 (“benefit/advantage”), while 無 (“emptiness”) yields 用 (“use/function/utility”). The pairing matters: 利 focuses on tangible advantage accruing from form and material presence, whereas 用 denotes operational functionality enabled by emptiness within designed structure. The structure “有之…無之…” uses 之 as a pronominal/structural particle referring back to the crafted artifacts and the conditions described in the preceding three examples. Comparative philosophical context: similar reasoning about usefulness arising from intentional lack appears in other pre-imperial texts, where carved hollows, gaps, and voids enable a tool’s/space’s function.
6. "Daoist principle of complementary function between material form and emptiness" (老子（Lǎozǐ）／道德經) — This chapter is traditionally labeled Daodejing (道德經) chapter 11 (數 say it is “Chapter 11 of the received Daodejing”), part of the core corpus associated with Laozi (老子, Pinyin: Lǎozǐ). While the text is commonly attributed to Laozi, modern scholarship generally treats the Daodejing as having undergone compilation and editorial layering. The conceptual core of this passage—often summarized as “usefulness of emptiness” (emptiness enabling use)—is a hallmark of early Daoist thought and becomes a recurring philosophical motif in later Daoist and non-Daoist commentarial traditions. Because different editions sometimes vary in punctuation or minor wording, translations typically follow the received text but remain attentive to variants; major classical editions place this line as the chapter’s closing maxim.

Glossary References

無

Emptiness · A technical Daoist term in this chapter: the void/hollow space that makes an artifact or space functional (e.g., hub void, vessel interior, room openness). In this translation, rendered consistently as “Emptiness” (capitalized) to preserve philosophical weight.

有

what is present · Complementary to 無 in this chapter: the material/form aspect of crafted objects that yields tangible benefit (利). The translation renders 有 as “what is present” to keep the antithesis with Emptiness.

利

benefit · In the final maxim, 利 contrasts with 用. It denotes tangible advantage accruing from material presence and formed structure.

用

use · In the final maxim, 用 denotes functionality/utility—what the object can do—which depends on the designed emptiness (無).

當其無

where there is Emptiness · A locative/conditional phrase: not temporal “when,” but “at/where emptiness is located,” indicating the functional condition within the constructed artifact/space.

之

(structural/pronominal suffix) · In “有之…無之…,” 之 refers back to the conditions/artifacts described immediately above. Here it is left implicit in English while the construction’s sense is carried by the surrounding syntax (e.g., “there is the use of …”).

輻／轂

spokes / hub · Technical wheel terms: 輻 = spokes; 轂 = hub/nave where the spokes meet. The chapter’s argument depends on the functional importance of the hub’s void. ---

Context

This passage is chapter 11 of the received Daodejing (Tao Te Ching), traditionally attributed to Laozi and usually situated in the late Spring and Autumn or Warring States intellectual milieu, though the text almost certainly reached its present form through compilation and editorial layering. It belongs to the foundational corpus of early Daoist thought. The chapter develops a characteristic Daodejing insight: practical efficacy depends not only on material presence but on absence, emptiness, or non-being (無). The examples of wheel hub, vessel, and room illustrate an ontological and political-philosophical principle found throughout the text: what seems insubstantial or lacking is precisely what makes things function.

The images are drawn from ordinary premodern material culture familiar to early Chinese audiences: the spoked wheel of carts and chariots, pottery shaped from clay, and house construction involving doors and windows. These are not ornamental examples but craft-based demonstrations of a metaphysical claim. The passage assumes a world in which utility is grasped through use in concrete artifacts. It also reflects a broader classical Chinese discourse contrasting 有 and 無, terms that can mean presence/absence, being/non-being, or substantiality/emptiness depending on context. In Daoist usage here, 無 should be treated as a technical concept rather than merely simple negation.

Themes

1. Utility of emptiness The central claim is that emptiness, hollowness, or non-being is what enables function. A wheel works through the empty hub, a vessel through its hollow interior, and a room through open spaces.
2. Interdependence of being and non-being The passage does not deny the value of material form; rather, it argues that material presence and emptiness work together. What exists provides tangible benefit, while emptiness provides functional use.
3. Daoist reversal of ordinary values The chapter exemplifies the Daodejing's habit of reversing common assumptions by showing that what appears lacking, vacant, or insubstantial is in fact indispensable.
4. Metaphysics grounded in everyday craft Abstract philosophical insight is conveyed through familiar technologies and artisanal processes, linking ontology to practical life.

Idioms

1. 有之以為利，無之以為用 One of the most famous formulations from the Daodejing. It states that what is present gives advantage or benefit, while emptiness or non-being gives use or function. The line is frequently cited in philosophical, aesthetic, and design contexts.
2. 當其無，有…之用 This repeated pattern is not an idiom in the later fixed-expression sense, but it is a memorable formula from the chapter. It means that precisely where there is emptiness, the use of the object resides.
3. 三十輻，共一轂 A well-known opening line often quoted as a synecdoche for Daoist thinking about relational structure: many components converge on an empty center that makes coordinated function possible.

Literary Devices

1. Parallelism The chapter is built from three tightly parallel examples: wheel, vessel, and room. Each follows the same structure, creating cumulative argumentative force.
2. Analogical reasoning Concrete objects are used as analogies to demonstrate a broader philosophical principle about being and emptiness.
3. Enumeration The passage lists three crafted objects in sequence, moving from transportation to utensils to habitation, broadening the scope of the claim across everyday life.
4. Antithesis The final sentence balances 有 and 無, establishing a concise conceptual opposition whose force depends on their complementarity rather than absolute contradiction.
5. Compression Like much of the Daodejing, the wording is extremely concise, allowing multiple layers of ontological, practical, and political interpretation.

Translation Challenges

1. 三十輻，共一轂 — The syntax is elliptical: the spokes 'share' or 'converge upon' one hub. English must supply a verb naturally without overexplicating. 轂 is specifically the hub or nave of a wheel, not the entire wheel; technical precision matters because the argument depends on the empty center.
2. 當其無，有車之用 — 無 here is not mere 'nothing' in a casual sense; it refers to the empty space at the hub that enables the wheel's function. 當其無 is compact and can mean 'at the point where there is emptiness' or 'in its emptiness there is'. The translator must preserve both the locative and functional sense. 車之用 may mean the use of the cart/wheel assembly rather than simply 'the wheel's use'; context-sensitive phrasing is needed.
3. 埏埴以為器 — 埏埴 refers to kneading or shaping clay; the exact verbal texture can be rendered as 'mold clay' or 'knead clay'. 器 can mean vessel, utensil, implement, or container. 'Vessel' often fits the philosophical register best, but the choice shapes tone.
4. 鑿戶牖以為室 — 戶牖 means doors and windows; some translations flatten the pair into 'openings', but the concrete architectural imagery should ideally be preserved. 室 can mean room or house/chamber; the scale should be chosen consistently with the example.
5. 故有之以為利，無之以為用 — This is the philosophically decisive line. 有 and 無 must be rendered consistently with the preceding examples and with Daoist terminology. 利 and 用 are related but distinct: 利 is benefit, advantage, or profit; 用 is use, function, or utility. The distinction should not be blurred. 無之以為用 should not be weakened into a vague 'what is not there is useful'. The wording should preserve the technical sense of emptiness or non-being as the condition of function. Because the line is aphoristic and balanced, English should remain compact and antithetical without losing philosophical precision.

Technical Terms

1. 有無 (yǒu-wú) (Taoist philosophy): Complementary Taoist concepts: '有' (Being) is the tangible form providing benefits, while '無' (Non-Being/Emptiness) is the functional space enabling utility. - Translation: Always render as a pair. Consistent terminology crucial: 'presence/emptiness', 'being/non-being', or consistently philosophical terms. Capitalization may denote conceptual weight (e.g., 'Being' and 'Emptiness').
2. 無 (wú) (Taoist philosophy): Void or absence that functionally enables material artifacts. Central Taoist principle opposing pure materialism. - Translation: Must be rendered as 'emptiness', 'void', or 'non-being' — avoiding weakly descriptive phrases (e.g., 'what is not there'). Consistency in parallel examples and final couplet is critical. Reviewer feedback explicitly requires strengthening this rendering.
3. 有 (yǒu) (Taoist philosophy): The concrete form or substance of artifacts that grants practical advantages. - Translation: Translates as 'what is there', 'material presence', or 'being'. Consistency with '無' required to maintain philosophical tension.

Ambiguous Terms

1. 當 — 90% confidence - Possible meanings: `at` · `when` · `confront` · `equal` · `appropriate` - Resolution: In the context of '當其無', '當' functions as a preposition meaning 'at', 'in the presence of', or 'just where'. It establishes the condition under which function arises.

Glossing Notes

This chapter from Laozi (Tao Te Ching, Ch. 11) uses parallel concrete examples to demonstrate the Taoist principle of complementary function between material form ('有') and emptiness ('無'). Special care must be taken for '無' — it is a technical philosophical term requiring consistent rendering as 'emptiness' or 'non-being' (capitalization optional, but must be consistent within the text). The three examples (wheel hub, pot, room) share identical grammatical structure, which should be preserved in translation. The final aphorism ('故有之以為利，無之以為用') encapsulates the core teaching: material provides advantage, while emptiness enables function. Note: There are no direct allusions to other classic texts; this is foundational Taoist metaphysics.

Translation Principles

1. Preserve the threefold parallel structure across wheel, vessel, and room; the repeated syntax is part of the argument, not mere ornament.
2. Render 無 consistently as a technical term such as 'emptiness' or 'non-being' where context allows, especially in the concluding line; avoid weakening it into merely 'what is not there'.
3. Maintain the distinction between 利 and 用: the first concerns benefit or advantage, the second use or function.
4. Keep the imagery concrete and artisanal: spokes, hub, clay, vessel, doors, windows, room. Do not over-abstract the examples.
5. In the repeated phrase 當其無, use consistent phrasing throughout so that the recurrence of the concept of emptiness is audible in English.
6. Retain the aphoristic brevity of the final maxim. The conclusion should sound balanced and memorable, not discursive.
7. If capitalization conventions are adopted for technical philosophical terms, apply them consistently; otherwise use lower-case consistently. In either case, preserve 無 as a recognizably technical concept.

Segmentation

1. 三十輻，共一轂，當其無 `sentence`
2. 有車之用 `clause`
3. 埏埴以為器，當其無 `sentence`
4. 有器之用 `clause`
5. 鑿戶牖以為室，當其無 `sentence`
6. 有室之用 `clause`
7. 故有之以為利，無之以為用 `sentence`

Segmentation Notes

Segmentation follows strong grammatical cues and parallelism: each '當其無' marks a conditional/adverbial clause introducing 'emptiness', followed by a result clause '有…之用'. The final sentential couplet is anchored by '故' and the parallel structure '有之以為利 / 無之以為用', with '以為' functioning uniformly as a purpose/result marker and '之' as a referential linker to what is being constructed and its functional contribution. No segment is ambiguous at the boundary level because the repeated '當其無' and '有/無 …之用' patterns provide clear clause demarcation.

Tone & Style

Calm, aphoristic, and quietly paradoxical. The passage begins with concrete, almost instructional examples and culminates in a succinct philosophical conclusion whose tone is authoritative but understated.

Classic Daodejing style: highly compressed, formulaic, and analogical prose with strong parallelism and conceptual antithesis. The register is simple on the surface but philosophically dense, inviting both practical and metaphysical readings.

None.

Terminology

無

Emptiness

有

Being

有無

Being and Emptiness

用

function

Terminography Notes

For this Laozi-style technical aphorism, the critical issue is consistent conceptual rendering of 無 (functional emptiness/non-being) and its pairing with 有. The glossary explicitly treats 無 as critical and warns against weak paraphrases; therefore register 無 and the 有/無 conceptual pair and align the final clause’s 用 with a functional-technical sense (function) rather than a generic “use.” Capitalization for Emptiness/Being should be maintained consistently within the project to prevent lexical drift in the repeated parallel pattern 當其無／當其無… and the final couplet 故有之以為利，無之以為用.