The concept of a commutator is it is an experiment. With a high level of control.
As a little kid you would find a vhs tape on the floor. You don't want to watch that movie, and for some odd reason you actually go to put it back in the box. You open the case and find that another video is in the box. You take it out Putting the correct vhs in the box. Then you take that movie and put it in its correct box, which of course has another wrong video inside. You take that swap the two and decide if this is the one you want to watch or not. You go from there.
Eventually you will sort out all the videos into the correct cases. Your problem is solved. Likewise with a cube, you take the lone piece, put it where it belongs, then now you have that cubie in its place. You then put that cubie where it belongs. Then take care of a few cubies at a time.
Likewise, you don't move or touch that movie until you find the right movie box. You rearrange the movies so they are in the correct boxes. Then you of course make sure to put them in order on the shelf like they should be.
Its random and silly. but it makes sense, I hope...