These have always been among my favorite comments about composition and influence. The first comes from Lutoslawski Profile, a collection of in-depth interviews with the Polish composer, by Balint Andras Varga.
It was in  that I heard an excerpt from [Cage’s] Piano Concerto and those few minutes were to change my life decisively. It was a strange moment, but I can explain what happened.
Composers often do not hear the music that is being played; it only serves as an impulse for something quite different–for the creation of music that only lives in their imagination. It is a sort of schizophrenia–we are listening to something and at the same time creating something else.
That is how it happened with Cage’s Piano Concerto. While listening to it, I suddenly realized that I could compose music differently from that of my past. That I could progress toward the whole not from the little detail but the other way around–I should start out from the chaos and create order in it, gradually. That is when I started to compose Jeux Venitiens.
And this from Anthony Braxton:
Since coming into academia, I came to understand very early that I would have to build an alternative system to help me, because in academia you’re constantly talking about your music and that’s dangerous. You’re constantly talking about the science of the music in a two-dimensional way. So I started to move the ray of focus in my model into the poetic logics, as a way to not know what I’m doing. Because I’m not interested in a music that’s two-dimensional, that I can talk about as being the “it” of the music. By that I’m saying that I want the undefined component of my music to be on an equal par with the defined component.