Re: Defining Kokyu
Well I would think that one can just take the opposite of what I said in order to get at what I would think is a "normal push."
For example, (pushing against a wall):
Not being in line with the principles or laws of Nature would be something like attempting to push a wall when barefooted and while standing on a large slate of ice (i.e. attempting a thrusting action with no friction to support it). Many people do things very akin to do this in their waza (i.e. attempting a thrusting action without an engaged based of support that can offer friction to the energy moving away from one's center of mass). A lack of coordination of body would be for example a loss of Directional Harmony -- having one part of the body going one way (e.g. the hips) and one part going the other way (e.g. the arms or hands); such that the body overall is "fighting" against itself and thus directing energy away from pushing the wall. A lack of coordination of mind would be for example an attachment or preoccupation with a subjective experience and/or idea (through things like fear, pride, and ignorance) such that one loses awareness of the total present moment; such that they cannot be totally present in the act of pushing the wall. Etc.
When one or more of these things (or things like them) are present, one is just pushing the wall (i.e. not pushing the wall with kokyu-ryoku).
Outside of these parameters, I am not too keen on saying, "To push a wall with kokyu-ryoku, you push it like this." As abstract as my "qualities" may sound, or as contrary as these descriptives may be in comparison to a list of step-by-step directives (if that is indeed what you are looking for), for me they remain very universal and thus very concrete. Moreover, for me, I do not feel that one can really offer a list of step-by-step descriptives to aid anyone with developing kokyu-ryoku. So I am not at all sure what such a list would even look like. As you can see, in my understanding of kokyu-ryoku I have included a reconciliation of the subject/object dichotomy. This aspect (among others) is not at all supported by any kind of listing of directives.
Having looked up some stuff since my last postů I would say that things like the "cool ki tricks" are not kokyu-ryoku -- as understood by my definition. If anything, they entail only certain aspects of the totality of kokyu-ryoku. Just as a set of descriptives (e.g. put your foot here, bend your knees like this, extend your arm thusly, etc.) might get someone to demonstrate certain aspect of a coordination of body, such "tricks" can only assist someone with some of the aspects of a coordination of mind (e.g. relax) -- not all of them. Thus, personally, I do not see Tohei's tests as simple kokyu demonstrations (the one's I now know of). I see them more as addressing relaxation, which, for me, is part of kokyu-ryoku but not all of it. However, I would conced that if someone can employ kokyu-ryoku they should be able to perform such simple tests of relaxation. By extension, again for me, kokyu-ryoku, if one was to attempt to identify it or to put it up for examination, is best witnessed under spontaneous training conditions.