walking on thin ice

Had another one of those "in the dojo, as in real life" moments whilst teaching. We were working on moving from the hips. It has lots of names: namba-aruki, musoku-ho, nijiku, etc. but the basic idea is to move from the center, and move the whole body as one unit. There are all kinds of comments about twisting, rotating, turning, pivoting, kicking-off, floating, and a million other magical/physiological explanations that make no sense to me. Basically, I try to move as effortlessly as possible, simple economics of motion. I try not to move my arms and legs first, nor independently from the rest of my body. Instead of extending the arm to reach forward, half the work can be done by moving the body forward. Given that the arm is connected to the body, moving the body moves the arm. Net result is that the arm gets to where it's going faster/easier than relying on just the arm itself.
So we were working on walking, moving forward, and keeping centered; keeping the shoulders are trunk over the hips. More accurately, generally what happens is when moving forward the upper body tends to lean in, and the legs kick alternately, but the hips are left behind, with the butt sticking out. So we try moving from the hips first, keeping the shoulders over the hips, and the legs, connected to the hips, have to come along as well.
I was trying to explain the feeling of keeping the knees bent, sinking the hips forward/down to sort of fall into the forward movement, not locking the legs stiff, which just ends up precariously thrusting the body up, unbalanced. And I remembered when I was walking across the icy sidewalks with Elvis. I was having trouble balancing, because no matter how carefully I picked up and placed my feet, I would invariably find some hidden spot, or some uneven surface, and I would lose my balance. So instead of trying to adjust so much with my feet and legs, I just pushed forward from the hips, flexed the knees, and in a right foot forward stance, slid across the ice. Flex knees, hips forward, slide. Repeat.
So back in class I was trying to explain how to do the same thing from a sitting position. Great thing about seiza techniques is that they are designed to force you to move from the hips. You can't use your legs; you're sitting on them. So I was thinking about the ice, and friction, and Elvis and I tried something.
He held onto my hips and I simply sat UP: I pushed up and against his grip and, he being in a dominant position, my legs simply slid out from under me as the force rebounding from his iron grasp easily overcame the static friction of my cotton uniform on the smooth wood floor.
So then I tried sitting IN: instead of trying to push with my legs, I tried to extend my hips forward as if I was moving into the cut. This time he got pushed back and over, whereas my legs stayed firmly under me.
I don't know the mathemati-physical explanation of opposing forces and static friction, but I know that when I move from my hips, my legs aren't stressed and pushing, and I move IN considerably more than up (or down or any other direction.) Obviously my legs and feet are pushing against the floor, otherwise I'd never move relative to the floor, but it must be significantly less force than when I purposefully kick off with my feet and legs. I think this may be one of the big differences between "normal" walking and moving from the hips in a more budo way.
I know I am not particularly good at whatever it is I am supposed to do, and I'm not even sure when I think I do it right that I am even doing the right thing, but sometimes it feels effortless and looks as right as I can tell, and the cut is strong, clean, and true. And then I slip on the ice!

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