Forming a model might not involve precise thinking, it often involves lateral thinking, at least with me.

I heard that computer science was more of a subset of music than math.

Higher math requires a great deal of lateral thinking. Also, music an math are often closely related but I don't see the connection between music an say computer vision.

Computer vision practitioners do mostly math, are we calling them computer scientists also? Sheesh :). Whenever I get in the same room with one, we are talking completely different languages (and we do have a sizeable computer vision team in our lab).