"Me: It's awful hard to take you seriously when you complain about someone else's physics, and you get something as simple as speed wrong. You're talking about a change in velocity. Speed doesn't have a direction, it only has a quantity. So, speed *can* increase, while changing direction."
Why don't you try doing the vector sum of the horizontal and vertical velocities to calculate the body speed? I already know the answer, but you apparently don't.
In fact, I was not talking about the velocity across the floor; I was instead talking about the velocity in the instantaneous direciton of movement, because that is the velocity that counts for kinetic energy and momentum purposes. You perhaps haven't realized it yet, but there is a very elegant interchange between kinetic energy during the moving phase and gravitational potential energy during the slower risen phases.
"Additionally, velocity, which is the direction of travel combined with the speed of travel, will change with a change of direction. Your velocity in one direction will lessen, while your velocity in another direction will increase."
Yes. But the way you change direction EFFICIENTLY is to first convert much of your kinetic energy in the original direction into the potential energy of rise altitude - which has no direction across the floor, since gravity is "down". Then you convert this back into kinetic energy in the new direction.
If you go and examine all of the characeristic figures of the "swing" or "body flight" dances in the context of this insight, you'll see how elegantly it all works out.
In my experience, all of the truly masterful dancers exhibit this knowledge intuitively in their dancing, though probably only a few of them could state it as a physics student would. But many of the merely succesful dancers do not exhibit this, and regularly break from this elegance of movement. When you get to see the two versions side by side - the energy conversvation version vs. the merely musuclar one, you realize how much role this plays in keeping the merely ordinary couples merely ordinary, instead of remarkable.