(Translated, with comments, by William P. Coleman)
Thirty spokes unite at a hub;
it’s the emptiness there that makes the wheel usable.
Shape clay to make a bowl;
it’s the empty space inside that makes the bowl usable.
Cut out doors and windows;
their emptiness makes the room usable.
the ways a thing exists make it have benefit;
the ways it doesn’t exist make it usable.
|<– Chapter 10
||Chapter 12 –>|
It’s easy to get so involved with the spokes in the wheel that you don’t notice the value of the hole in the middle that allows you to fix the wheel to an axle: How can something that isn’t there be one of the working parts of the wheel?
With doors and windows, the problem is the opposite: you notice the emptiness right away and you home on in the fact that the emptiness is what you want.
About the bowl though, who knows? Which is the part you want — the bowl or the empty space inside it?
The German philosopher Immanuel Kant once wrote a beautiful sentence that captures the idea of the necessary interaction of positive and negative exactly. Kant was discussing Plato’s theory of Ideas, and he had the notion that Plato thought the ideas are the only reality and they exist in some separate realm far from everyday objects. I personally do not think that’s what Plato thought at all: in fact, I believe that Plato thought he has reduced such notions to absurdity and refuted them. (See also my comments on Rupert Brooke’s Tiare Tahiti and on Plato’s Phaedo.)
But, regardless of whether Kant understood Plato correctly or not, his remark about what he thought Plato thought is expressive and enlightening:
Die leichte Taube, indem sie im freien Fluge die Luft teilt, deren Widerstand sie fühlt, könnte die Vorstellung fassen, dass es ihr im luftleeren Raum noch viel besser gelingen werde.
A light dove, parting the air in free flight, feeling its resistance, could get the idea it would succeed even better in a space with no air.— Immanuel Kant;
Kritik der reinen Vernunft 
For the dove to be able to fly and to feel that lightness, the air has give just the right resistance. If it resists too much, the bird cannot make headway. If it resists too little, there is nothing to hold the bird up and it falls.
We’ve seen in previous chapters this idea that “much” is not intrinsically good — and “little” isn’t intrinsically good either. What’s good is meeting the world exactly: what’s good is reality.
This idea is also important in the lines from Lao Tzu’s Chapter 1 that I’ve translated as:
So, we clear ourselves of passion, to see natures;
just as we’re passionate too, to see appearances.
These are the same, but are called differently as they arise.
As I discuss in the Inroduction to my translation, many translators are convinced a priori that passion is bad and clearing yourself of it is good. Therefore, they translate this to mean that if you clear yourself of passion (good) you’ll see appearances, but it you’re passionate (bad) you see merely an empty outer shell instead of the inner reality. (This interpretation would require ignoring Lao Tzu’s explicit statement that both are the same.)
I think that Chapter 11 throws light on Chapter 1. The “natures” you get from clearing passion and the “appearances” you get from embracing it are like the bowl and the emptiness inside it — or like the spokes and the emptiness at their hub: they’re useless without each other — they don’t even make sense separately. Neither solidity alone nor emptiness alone is any good.
For comparison, I’m including the translation by Lin Yutang, which I always love and respect, even when I disagree:
11. The Utility of Not-Being
Thirty spokes unite around the nave;
From their not-being (loss of their individuality)
Arises the utility of the wheel.
Mold clay into a vessel;
From its not-being (in the vessel’s hollow)
Arises the utility of the vessel.
Cut out doors and windows in the house (-wall),
From their not-being (empty space) arises the utility of the house.
Therefore by the existence of things we profit.
And by the non-existence of things we are served.