It's only different for sports because all the coordinating (like of old the activites of hunting and war) applies to a single focus, the body is all maneouvere

It's only different for sports because all the coordinating (like of old the activites of hunting and war) applies to a single focus, the body is all maneouvered to the same mind state. In dance, you have to coordinate subtle muscles in precise ways. In sports, the precision is about the particular result you want (a stroke, a kick), but in dance, there are many goals and you need to mind whether your thigh muscle is holding up in just the proper, beautiful way, because the teacher and a knowing audience can tell, much like in musical performances, whether you are really achieving the coordination or faking, or being a beginner. The coordination in dance is of several (and I mean tens of body parts or muscles at the same time) parts having different purposes (supporting the movement, getting balance, showing off, giving impulse, etc) and the brain having to watch them all, all at once. It's much harder to dance beautifully than to swim or run or jump and throw a basketball beautifully, because in dance aesthetics is the primary source of goals for all those body parts, they have different roles or different relationships to the same melodies and harmonies playing over the dance.