Control, Inflection, Breath, Chance, and Concept.

Compare these two ideas:
"When I hear what we call music, it seems to me that someone is talking. And talking about his feelings, or about his ideas of relationships. But when I hear traffic, the sound of traffic—here on Sixth Avenue, for instance—I don't have the feeling that anyone is talking. I have the feeling that sound is acting. And I love the activity of sound [...] I don't need sound to talk to me."- John Cage

An artistic medium is used to clarify and intensify events based on people's inherent psychological needs and desires.
-Paraphrasing Zettl's theory of applied media aesthetics

If you look at the work that Zettl studies and praises, it is incredibly controlled, such as Citizen Cain. Today my composition teacher, Josh Goldman, brought up the movie Citizen Cain, saying that the idea of being clever is very dangerous, and that when being clever becomes the focal point of the work, that the idea of a work shifts from the experience of the art to the process of the art, and puts the art back into the characteristic-oriented way of seeing things rather than the profound. He did, however, very much enjoy Citizen Cain regardless.
John Cage's statement is offering a thought-out relinquishment of control. He has asked himself the question of what he wants to hold onto and what he wants to let go of.
Often human cleverness can make the details of something too sharp, "intensify and clarify" something too much and one begins to destroy the natural experience of it. A piece can become overworked. The wonderful part about this though, is that this process doesn't prevent you from asking the question of adding something. As long as you know, in some abstract, creative, sense why you put something somewhere, not only will the places that you intensify be all the more real and clear, but the emptiness of the piece will ring truer, and all in all the music is sure to be more expressive and sincere.
Music is a process of thought, but not thought that only refers to doing. It can also refer to leaving something up to a chance process like John Cage, or even to leaving something empty, either using silence or letting the parts layered below speak. My room-mate Joe is a Jazz Studies major and he said "We study Miles for the notes he didn't play." Miles Davis is almost everyone's favorite.
I am saying this as a composer but really it is true of all things. Putting thought into something doesn't necessarily mean adding things, it means considering the possibility of a thing, or of taking something away, and developing abstract structure and inflection to guide the process of what speaks and what recedes in order to guide the breath and life of a piece, and say only as much as needs to be stated, but no less. When this process is complete, when the intent has been translated into a communication through sensory experience, a piece may be called complete.