Translation: Thirty spokes converge upon a single hub; precisely because the hub is hollow at its center, the cart has its function of carrying loads.
Analysis: This is the most widely accepted interpretation. The wheel can rotate because of the round hole at the center of the hub — the axle passes through this hollow space, enabling the wheel to turn. If the hub were solid, it could not accommodate the axle and the wheel could not rotate. This is the first concrete illustration of "the usefulness of nothingness" — the tangible spokes and hub (being/有) provide the structure, but what truly makes the cart functional is the emptiness at the center of the hub (non-being/无).
Similar views: Heshanggong ("毂中空虚，轮得转行，舆中空虚，人得载其上也" — "The hub is hollow and empty, so the wheel can turn and travel; the carriage is hollow and empty, so people can ride upon it").
Translation: Thirty spokes (modeled on the days of the month) converge upon a single hub; precisely because of that "nothingness," the cart possesses its marvelous function.
Analysis: Heshanggong draws upon numerological symbolism — the thirty spokes correspond to the thirty days of a lunar month, implying natural law. Wang Bi, on the other hand, approaches the matter from an ontological perspective — the hub is able to "unify the many" because it receives things through "nothingness." This interpretation elevates the concrete wheel analogy to the philosophical plane: all forms of "being" are able to fulfill their respective functions only because behind them operates a unifying "nothingness."
Similar views: Wang Bi ("以其无能受物之故，故能以实统众也" — "Because nothingness is able to receive things, it can thereby use substance to unify the many").
Translation: Thirty spokes converge upon a single hub; it is precisely at that hollow center that the cart's function resides. Those who cultivate themselves should likewise empty their hearts so as to receive the Tao and Virtue.
Analysis: Heshanggong extends the cart analogy to self-cultivation: "治身者当除情去欲，使五藏空虚，神乃归之" — "Those who cultivate the self should eliminate emotions and desires, making the five organs empty and void, so that spirit will return to dwell therein." Just as the hollow hub enables the wheel to turn, an empty heart enables one to receive the Tao. This is a leap from the analogy of material objects to the cultivation of body and mind — the "emptiness" within is not mere hollowness but rather the capacity to contain all things.
Similar views: Heshanggong ("治身者当除情去欲，使五藏空虚，神乃归之" — "Those who cultivate the self should eliminate emotions and desires, making the five organs empty, so that spirit will return to dwell therein").
Translation: Clay is kneaded and shaped into a vessel; precisely because the vessel is hollow inside, it has the function of holding things.
Analysis: The second analogy. A jar or a bowl can hold things not because of the clay itself, but because of the space enclosed by the clay. If a vessel were made solid, it would have no capacity for holding anything. "Nothingness" (the hollow interior) is where the vessel's true value lies.
Similar views: Heshanggong ("器中空虚，故得有所盛受" — "The vessel is empty and hollow inside, and therefore it can hold and receive things").
Translation: Clay is kneaded and shaped to make an object; precisely because of that "nothingness," the object gains its practical function.
Analysis: This interpretation extends "器" (vessel) from a specific earthenware container to all tangible things. Laozi uses the clay vessel as an analogy to demonstrate that all created things owe their usefulness to the "emptiness" within them. This is not merely physical empty space but implies that the function of all "tangible" things originates from the "intangible" — metaphysical "non-being" is the fundamental condition for physical "being" to serve its purpose.
Similar views: This echoes Chapter 40: "天下万物生于有，有生于无" — "All things under heaven are born from being, and being is born from non-being."
Translation: Doors and windows are cut out to make a room; precisely because there is the openness of the doorways and windows and the empty space within, the room has the function of providing shelter.
Analysis: The third analogy. The function of a room derives from two levels of "nothingness": first, the openings of the doors and windows — which allow people to enter and exit and light to come in; second, the empty space within the room — which gives people a place to dwell and move about. If the walls were sealed shut and the interior were filled solid, the room would lose its function as a dwelling.
Similar views: Heshanggong ("户牖空虚，人得以出入观视；室中空虚，人得以居处，是其用" — "Doors and windows are open and empty, allowing people to come and go and to see; the room is empty within, allowing people to dwell — this is their usefulness").
Translation: Doors and windows are cut out to make a home; precisely because of that emptiness, the dwelling has its function.
Analysis: The three analogies (cart, vessel, room) progress in an ascending sequence — from a vehicle for transport to a utensil for daily use to a dwelling for habitation — encompassing the basic necessities of human life. Each analogy demonstrates the same truth: "being" constitutes the form; "nothingness" provides the function. Taking "室" in the sense of "home" implies that the very foundation upon which one establishes one's life also lies in maintaining inner emptiness and openness.
Similar views: An extension of Heshanggong's self-cultivation theory.
Translation: Therefore, "being" provides convenience, while "nothingness" is what truly serves the function.
Analysis: The summation of the entire chapter. A generalization drawn from the three analogies — the spokes, the clay, and the walls (tangible things) provide the material conditions and structure (convenience/利), but what truly enables the cart to travel, the vessel to hold, and the room to shelter is the emptiness within (function/用). There is a subtle distinction between "利" (convenience) and "用" (function): "利" refers to the concrete advantageous conditions, while "用" refers to the actual efficacy that is brought into play.
Similar views: The standard interpretation found in the received commentaries.
Translation: Therefore, "being" provides the material conditions, while "nothingness" is the fundamental source of marvelous function.
Analysis: This elevates the conclusion to the ontological level. Wang Bi systematically elaborates: "有之所以为利，皆赖无以为用也" — "The reason 'being' can serve as a benefit is that it entirely depends on 'nothingness' to serve as the function." "Being" presupposes "nothingness" as its prerequisite; without "nothingness," "being" could not fulfill any function whatsoever. This established the core thesis of Wei-Jin "Dark Learning" (玄学): "taking nothingness as the root" — nothingness is the ground of being, and being is the manifestation of nothingness.
Similar views: Wang Bi ("有之所以为利，皆赖无以为用也" — "The reason 'being' can serve as a benefit is that it entirely depends on 'nothingness' to serve as the function").
Translation: Therefore, "being" provides its conveniences precisely because "nothingness" is at work within — being and non-being complete each other, and neither can be neglected.
Analysis: This reading emphasizes the inseparable relationship between being and non-being. Laozi does not deny the value of "being" but rather points out that "being" and "nothingness" each has its own role. "Being" provides the structural conditions; "nothingness" provides the functional space — the two are indispensable to each other. This is consistent with the thought of Chapter 2, "有无相生" — "Being and non-being give rise to each other." Without spokes (being), there would be no cart either; it is simply that people ordinarily see only "being" and overlook "nothingness," so Laozi specifically highlights the value of "nothingness."
Similar views: Chapter 2, "有无相生" — "Being and non-being give rise to each other," and Chapter 40, "有生于无" — "Being is born from non-being."
Translation: Therefore, tangible institutions and facilities (being) provide the conditions for governance, but the way of non-action (无为) (nothingness) is the fundamental source of effective rule.
Analysis: Heshanggong extends the entire chapter to the domains of governance and self-cultivation: tangible palaces, vessels, carts, and horses (being) form the material foundation for the functioning of a state, but what truly enables a state to enjoy lasting peace and order is "emptiness and nothingness" — an empty heart, a tranquil disposition, and governance through non-action (无为). Just as "the Tao is emptiness" (道者空也) — the great Tao takes emptiness as its substance and the myriad things as its function. A belly that houses the spirit fears the body's destruction; a room that shelters people fears the building's collapse — the key lies in preserving that "empty" essence.
Similar views: Heshanggong ("虚无能制有形。道者空也" — "Emptiness and nothingness can govern the tangible. The Tao is emptiness").
This chapter contains 11 interpretation combinations.
[Core Divergences]
Chapter Eleven is one of the most vividly illustrative chapters in the Tao Te Ching. Using three everyday objects — the wheel, the clay vessel, and the dwelling — as analogies, it demonstrates the functional value of "nothingness." The chapter is structured with impeccable clarity: three parallel analogies (cart, vessel, room) each conclude with the formula "当其无，有X之用" ("it is the nothingness that provides the function of X"), and the whole is crowned by the philosophical summation "故有之以为利，无之以为用" ("Therefore, being provides the conditions; nothingness provides the function"). The core idea operates on two levels: (1) the level of material objects — emptiness is not a defect but a prerequisite for function: without the hollow center of the hub the wheel cannot turn, without the hollow interior of the vessel nothing can be held, without the empty space within the room no one can dwell; (2) the philosophical level — "being" and "nothingness" are not opposed but rather "being" depends on "nothingness" to fulfill its function. From this, Wang Bi derives the "Dark Learning" (玄学) thesis of "taking nothingness as the root": "以其无能受物之故，故能以实统众也" — "Because nothingness is able to receive things, it can thereby use substance to unify the many." Heshanggong, meanwhile, extends the idea to self-cultivation: if the human heart can remain empty, it is like the hollow hub — capable of containing the Tao and Virtue and governing the entire body. This chapter echoes the discussion of being and non-being in Chapter One — "无名天地之始，有名万物之母" ("The nameless is the beginning of heaven and earth; the named is the mother of the myriad things") — but is far more intuitive and accessible. Using the most homely of everyday experiences to reveal the most profound of philosophical truths is the hallmark of Laozi's literary style.