Nice example. To really bring it home, try making the circle while thinking about last night's dinner or all the appointments you have coming up next week. Keeping one point, to borrow an analogy from baseball, is nothing more than keeping your eye on the ball.
The more you can reduce the time interval between perception and action the more closely mind and body are coordinated. And while you can never reduce the interval to zero, it can approach zero without limit.
It's a little more complex than a state of mind since the body is involved as well. Call it a state of mind/body. And you're right when you state that it can be "recognized, isolated, and trained to deeper levels."
Yeah, just to be clear and make sure I don't unwittingly steer conversation into a certain philosophical gutter, what I was analogizing was indeed an elaboration of what is at base a body state, then gradually progresses more and more towards working with the mind. It wasn't meant to imply a "no mind" thing - you could sit on your butt and meditate for 3 lifetimes and you will never get that state - just like you won't learn to play violin by taking up Zen. There are basic body mechanics that are learned first, like how to actually express those linear forces that lead to that circle, since the way the untrained body will do it is just decades of bad movement habits. But after you've passed that state, symbolic reasoning/visualization/etc. imposes a cap on performance that must be removed to go farther. Moving in a circle is tough.