卅輻同一轂 當其无 有車之用也
[sa4] [fu2] [tong2] [yi1] [gu3] [dang1] [qi2] [wu2] [you3] [che1] [zhi1] [yong4] [ye3]
30 spokes [of a wheel] become [come together as] a hub, but what is missing [empty] gives the carriage its usefulness
三十輻共一轂，當其無，有車之用。
[san1] [shi2] [fu2] [gong4] [yi1] [gu3]， [dang1] [qi2] [wu2]， [you3] [che1] [zhi1] [yong4]。
30 spokes [of a wheel] become [come together as] a hub, but what is missing [empty] gives the carriage its usefulness
A solid wheel works, but is heavy. A properly spoked wheel is lighter than a solid wheel, but is equally strong. The “empty” or “missing” part of the wheel is what makes the wheel so useful, that is, the lack of weight makes the wheel lighter and therefore better suited for any kind of vehicle or carriage. What is “missing” from the item has defined its usefulness.
We could argue that the item itself is designed in this way, but this entire section serves to redefine Yin and Yang in a way that shows how the two exist at all levels. We can then argue that the item is designed this way because Yin and Yang require it in order to be useful. The following examples drive this point home.
埴而爲器 當其无 有埴器之用也
[zhi2] [er2] [wei2] [qi4] [dang1] [qi2] [wu2] [you3] [zhi2] [qi4] [zhi1] [yong4] [ye3]
[Mixing or shaping] clay to become a vessel, but what is missing [empty] gives the vessel its usefulness
埏埴以為器，當其無，有器之用。
[shan1] [zhi2] [yi3] [wei2] [qi4]， [dang1|dang4] [qi2] [wu2]， [you3] [qi4] [zhi1] [yong4]。
Mixing [or shaping] clay to become a vessel, but what is missing [empty] gives the vessel its usefulness
When clay is shaped into some kind of vessel, the value is in what it holds. A block of clay is useless as a vessel. What is missing defines the usefulness again. We can again argue that the shaping is what makes the vessel, but the shaping must be done in order to create a missing or empty part to make the vessel in any way useful. The clay by itself is only part of the equation.
鑿戶牖 當其无 有室之用也
[zao2] [hu4] [you3] [dang1] [qi2] [wu2] [you3] [shi4] [zhi1] [yong4] [ye3]
Making [lit. chiseling] doors and windows, but what is missing [empty] gives the room its usefulness
鑿戶牖以為室，當其無，有室之用。
[zao2] [hu4] [you3] [yi3] [wei2] [shi4]， [dang1|dang4] [qi2] [wu2]， [you3] [shi4] [zhi1] [yong4]。
Making [lit. chiseling] doors and windows to create a room, but what is missing [empty] gives the room its usefulness
A room without doors or windows is just a box. One must chisel or otherwise cut these bits out in order to make any use of a potential room or building. The accessibility and airflow is what makes the room or building have any real value as a room or building. We start with creating something, but finish out the creation with “destruction” in order to get a useful product. Both must exist in order to have useful creation.
故有之以爲利 无之以爲用
[gu4] [you3] [zhi1] [yi3] [wei2] [li4] [wu2] [zhi1] [yi3] [wei2] [yong4]
Thus, what exists is for profit, but what is missing [empty] is for its use
故有之以為利，無之以為用。
[gu4] [you3] [zhi1] [yi3] [wei2] [li4]， [wu2] [zhi1] [yi3] [wei2] [yong4]。
Thus, what exists is for profit, but what is missing [empty] is for its use
The actual thing has to exist for it to be worth anything, but what is missing, removed, or empty actually gives it the usefulness. A wheel must have something to be a wheel, but the emptiness between the spokes is what gives it its value. A clay vessel requires clay, but it is useless without being worked to have material removed or shifted to create an emptiness to hold something. You must have walls and a roof to have a room, but empty spots or missing spots in the walls which make doors and windows are also essential to actually have a useful room.
This entire section basically reiterates the Yin and Yang of the world. You must have both sides in order to have anything. The clay is one side, but the shape and spot where clay has been pushed down or removed is what makes the clay into the desired vessel instead of a brick. The spoking of a wheel makes the wheel useful, but the lack of solid material between the spokes makes the wheel light and defines its usefulness. A room or building must have doors and windows to be functional.
This can all be reiterated more simply in terms of design, but the specific phrasing is used to highlight the permanence and permeation of Yin and Yang. When a clay vessel is being worked, we start with a lump of clay and beat it and work it adding water and similar to shape it. The shape is influenced by what must missing from the original in order to create a vessel. This emptiness completes the equation. A solid wheel still works, but a spoked wheel does the same with less material and in a much easier way. Without knowing what must be “removed” from what has been “added”, one makes either something inefficient or otherwise useless. The balance must exist for the creation’s design to be useful.