<snip> My own perspective is that, I find that when I relax deeply with awareness, my breathing seems to naturally match with the other person's breathing, but the later is my own realization not a method I was taught. Relaxation being the key to the natural matching that I am referring to. I do not attribute that to any one teacher nor do I think that it is the best way or the only way - just something I noticed.
Does that make sense?
Sorry to butt in.
Richard, I understand full well the vagueness that comes together with the Japanese term of "breathing," but I think what Mike is gunning for is more a "what happens" when you breathe.
How does breathing in or breathing out contribute to power, how does it aid the body, or what effects do certain types of breathing have on the body.
The answer, at least from my own experience, isn't some vague answer that deals with relaxation, "matching", etc etc
There's a more practical effect on the body, mainly in terms of conditioning. Course, you have to have a certain amount of conditioning to feel it...if you don't then (and that "you" is not aimed at "you," I meant it generally) you won't be able to feel it.
Case in point, the one demo that you gave with the student gripping the end of the sword as the teacher raises and lowers it, while the student is unable to punch/kick, seems pretty easy, given someone with enough conditioning in the body (not of muscle tho).
Launching the guy on the downswing should be fairly easy for anyone conditioned enough, and could be indicative of someone that's trained to use the breath to store and release power.