NOTE: my Karma has been nuked, so unfortunately I will be unable to continue this discussion after this posting.
Well, that depends on what you'd want to study. I tend to be of the school of thought that you want like treatments for like causes, not necessarily like treatments for like effects. Thus, if there are N ways to get a headache, I would expect N treatments. In other words, I would expect that if I looked at the underlying cause (which will presumably be electrical, chemical and/or blood pressure related, where any possible magnitude and permutation of those is entirely valid) that if two people had absolutely identical underlying causes that the treatment would always be absolutely identical (ie: the treatment isn't random) and that if I monitored that underlying cause, there would be a change in state between before treatment and after treatment.
Okay, good -- a concrete example. I was at a party once, and a German guy got drunk and walked into a low beam. In the morning he was in terrible head pain but there was no obvious damage. I offered to give him healing. He reluctantly accepted. I put my hands on his head. I saw that the energetic form of his head had been pushed in -- broken in almost. I called as much power as I could muster, and in a couple of minutes I saw that it had popped out and returned to its original form. I asked him how he felt, and he said the pain had all gone. Job done! (It is not often this quick.) However, he had a new problem -- he couldn't believe what had just happened. I left as quickly as was polite because I didn't want to get involved as he tried to make sense of it all.
So, now we want to study this scientifically. So we need to create a category: "Damage to the energetic form of the head". Then all cases of this type, we can group together and give the same treatment, and do our statistical analysis of the outcome. But already we have a problem because science will not accept the diagnosis of the practicioner, nor the reality of this state of "damage to the energetic form". It is currently unmeasureable by science, and very easy to ridicule: "Where is the proof!?". However, we could indeed conduct the study regardless, assuming we accept the diagnosis of the practicioner. But you can see that in order to study these treatments, you need to get inside them, which is very uncomfortable for many scientists, because it means suspending judgement.
In the case of my witch-doctor friend (a curandero), even after 5 years studying on and off with him, I still don't understand what he sees, i.e. I can't even do the first stage of categorisation of cases by cause according to his method of treatment and world-view. By the time I can do that categorisation, I will be a curandero just like him. Only then could I conduct my scientific study. Now do you see the problem?
Chinese medicine has the 6 pulses read at the wrist. This is the method of diagnosis for a part of Chinese medicine. Once you have learned to take those pulses correctly (I haven't), your diagnosis will agree with that of other practicioners, and then there is a common basis for measuring progress. Now imagine the ridicule of doing a scientific study using 6-pulse-readings as a basis. "Homeopathy! Homeopathy!" they will shout. But what other approach is feasible given that there is as yet no instrument other than a human capable of accurately measuring the six pulses? Even if the study were successful it would likely be buried as most scientists would find neither the method nor the result acceptable.
Also you assume that it is possible to give identical treatment once the cause has been diagnosed. This may be the case with certain Chinese remedies, where a quantity of a physical agent is given (herbs, whatever). This is not possible when the treatment is energetic. I can say that I performed procedure "X", but generally the procedures are very broad, and the treatment is in cooperation with the patient (at some subtle level), i.e. there is a feedback loop, so it is impossible to give the same treatment twice. This makes it problematic for scientific study, unless you get into the fine details, which as I say are generally unmeasurable with current instruments, and nonsensical to anyone who is not willing to at least "entertain the possibility" that they may be part of a valid world-view. So it remains outside of scientific study, through no genuine fault of its own.
Now to go back to your other point:
But just to point out that human perception is all that we've got. It is our only direct input, despite its flaws. Everything else is second- or third-hand.
To some extent, I've covered this in discussing the level of directness (or lack thereof). However, it is worth examining this point a little closer. Yes, as Descartes (and indeed R. D. Laing) noted, human perception is indeed all that we've got. Furthermore, indirectness (as noted) increases the number of places errors can be introduced. As a result, you want to keep things as direct as possible.
Equally, though, quantitative data can be more precisely compared than qualitative data. When comparing qualities, you introduce all kinds of other types of error.
I agree completely. It is so much easier to study something that can be quantified. This is why science gets so uncomfortable studying qualitative things. Really the scientific method is not so well suited to these cases.
You are defining 'exists' as something that is measurable by a physical instrument. To me the only thing that exists is my direct perception, and everything else is secondary, for example it is derived from perception through reason and model-fitting in my imagination.
Ah, well here we'll need to agree to disagree. In part because I don't believe people directly perceive anything (I regard the senses as feeding an internal virtual reality in which the consciousness resides, where there is no guaranteed relationship between the senses and the VR representation)
I think we are agreeing. There is 'reality' (whatever that means), then there is "perception of reality", which is reality plus all the confusion of the human mind, one step away from reality. Then there are all the things that we build on top of it, hoping to get closer to 'reality', but in fact we are TWO steps away from reality, reality plus human confusion plus consensus and model-fitting and estimation of likelihood, for example. We are now two steps away although we hope we are at a reasonable approximation of zero steps away. All being well (e.g. in cosmology, general relativity, etc) we probably are reasonably close to zero steps away, but if the confusion+consensus+model-fitting/etc process doesn't work out too well, we may be SO far away from reality that we have no idea how confused we are. If we are not aware of the weaknesses of this process of perception we may believe we are zero steps away and impose that belief on others, not realizing how transparent is the error to those who have experienced different perceptions during their lifetime.
but also because I hold that mathematics holds primacy, that all physics across all multiverses [...] The whole point of multiverse theory is that they aren't. Which means that you can prove that the mathematics in the universe is necessary but is NOT sufficient to model itself since it is NOT sufficient to model the universe and the two are equivalent sets.) That, however, gets rather esoteric.
As I say, you can have the last word now because I won't be able to reply to due to my destroyed Karma.