The left-brain/right-brain dichotomy is an extreme oversimplification. However, your point is well-taken. Creativity is in fact often unconscious -- once we set our mind to working on something, we're actually thinking about it without realizing it. This is why ideas seem to suddenly come to us out of nowhere. Margaret Boden's The Creative Mind is a very good explanation of this. Probably as close as we can get with current cognitive models, anyway.