In lieu of the recent surge of claims about science ("science can't do this" and "this is beyond the scope of science" and so forth) I was considering how one might approach testing something that, hypothetically for our purposes, exists but is difficult to reproduce the effects of.

Extra Sensory Perception and aspects of magical practice have been somewhat popular around here, so we can use one of these as an example. If we say that, for instance, I can actually effect the reality around me by being conscious of it and "feeling things at it" (this would be the unproven but true reality that we wouldn't know is true), but that the effects of imposing my will were unpredictable, can it or can it not be tested and verified through any method we know about? Furthermore if the very nature of the ability was to be somewhat unpredictable (as in, based on many variables beyond our control) what does that imply about our capacity to verify real things with complex, unpredictable behavior? How does that effect our perceptions of what we consider possible or probable?

Have at me.