It may come as a surprise to those of you who know me for more cerebral reasons, but I am actually a very physical person.
And one of the things I've had cause to reflect on is the curious relationship between martial arts and dancing. It's a connection with history; classical dance and fencing, for example, have stolen footwork from each other for a long time. You've probably heard of football players taking ballet to improve their performance in that violent sport; you may even have heard of capoeira, which blurs the line between dance and martial arts.
I've taken modern dance classes and danced recreationally - international folk, contra, and swing at one time or another, and it seemed I was always following choreography in high school chorus. Being a male who could carry on loudly and on pitch while moving around meant I was indispensable in many numbers. I took tae kwon do into my teenage years, and then fenced in college.
Dancers and martial artists share many of the same warmups and stretches, more than typical for two different kinds of athletes; flexibility, balance, and coordination are are crucial in both pursuits. The key difference is not in the types of movement used; every basic building block that is used in one can be used in the other. (Well, almost. En pointe in ballet is, I suspect, an exception, but I can think of few others.)
The most basic difference lies in the treatment of rhythm. When you dance, you dance with the rhythm. When you spar, you fight against the rhythm. The skilled martial artist constructs rhythms in order to break them; the point is to become the unexpected, to surprise your opponent with carefully controlled timing. When you dance with a partner, the point is to communicate and telegraph your timing as much as possible; in dance, you must master gluing yourself to a rhythm so intimately that even should you slip, you will move with the rhythm.
To be masterful in either, one must master rhythm - but in two completely different opposed ways.