The Taoist concept of wu-wei -- action through inaction -- has long puzzled me. The idea is well represented by the old George Harrison song "The Inner Light" (which is derived from Chapter 48 of the Tao Te Ching):
Without going out of my door
I can know all things on earth
Without looking out of my window
I can know the ways of heaven
The farther one travels
The less one knows
Arrive without traveling
See all without looking
Do all without doing
Come on, how is that supposed to work? Do all without doing?
Recently, I was reading a bit about the psychology of musical performance and it hit me: wu-wei is about what people call "visioning". If you envision the performance in the way that athletes do, then you're acting it out without taking action, doing it without engaging in the deed itself -- action through inaction.
I don't know if this kind of visioning is part of Taoist practice, but for me thinking about it this way helps to make sense of wu-wei.