As Shunryu Suzuki says: "in beginner's mind there are many possibilities, in expert's mind there are few". Concept of "shoshin" in zen buddhism.
As you said invention (creativity) is mostly about simply connecting the dots. Look at the way lots of artists and creative people work. They just get two (or even more) things that usually have no relation at first look. Then they find a relation between them through anything they can find like smallest similarity in shape or color, or their mutual relation to something else...
Have you ever played the game say the same thing?
Your post inspired me to write something about the process of creativity in my own life. I may write it soon. Thank you.