You’re making really good points, but unfortunately I mainly agree with them. That is, you’re arguing against something I did not argue.

i.e., whether it "would be" good medicine or not is completely irrelevant, because we're talking about a treatment that doesn't fit at all within scientists' observation of the universe.

Whether it’s good medicine is an observation of the universe. If it worked and violated models, the models would have to change. If you disagree with this, then we really do disagree.

Many drugs have been used successfully before their mechanism was fully understood. They have, on occasion, driven arguably fundamental discoveries. They were in one sense outside our models, although our models were known to be incomplete. Our models of the behavior of water are also known to be incomplete. p != 0 that something odd could be going on there. We know that the particular odd thing that homeopathy claims does not occur in any significant way, but we only knew that when we tested it. (Of course all the smart money would have been on its not working. But expert opinion is not exactly the same as science.)

Can you put a categorical upper bound on liquid water information storage over time that’s lower than a categorical lower bound on the information needed to, say, lower blood pressure? I doubt anyone can yet. Could be wrong. Until then, it will be possible to put forward a million loopy theories – microcrystals, whatever – that do not obviously violate specific laws, but which can still be shown, by experiment, to have nil predictive power. And the smart money, obviously, will be overwhelmingly against all of them. But that by itself is not a scientific principle. It’s just how science works.

Your point about science as a refining process is quite true in the sense you use it, but it’s not really addressing the sentence you quoted. If you want a broader picture that synthesizes what you’re saying with what I’m saying, you might try Wikipedia’ing Karl Popper’s theories as a starting place and following the various derivative and competing ideas. Believe it or not (are you hinting you’re a working scientist?), how scientific knowledge progresses in practice is a topic of much interest from the outside.

The proposed mechanisms for homeopathy […] require a complete contradiction of its very foundations.

Two points. First, what is the contradiction? I’m curious, because in my amateur’s understanding it’s not obvious. Second, that’s actually a slightly different point from the sentence I objected to. The original said that for it to work, it would have to violate etc. You’re saying that for it to work in the way claimed, it would have to violate etc. That’s significantly narrower. (Back to drugs that have worked with incompletely understood mechanisms.)

I don't even know how you could put those two sentences next to eachother.

Because my whole point is that theories follow data (in principle, not in time). Water molecules behave in ways that we cannot yet derive perfectly from our theories alone. So we’re not in a position to categorically rule out certain kinds of behavior – even if, in casual speech, we say we know they cannot happen. Disproof is hard except by statistical methods like clinical trials. That’s another key sentence where if you disagree then we really do disagree ;). So I think you’re confusing having an accurate theory with having a proven theory.

Every example I've seen of the "1 = 0" proof contains a very subtle mistake which violates mathematic principles.

[Squints, scratches head.] Perhaps you thought I said “can’t” instead of “can” in the sentence you quoted? If not, I’m afraid I completely miss your point there.

if we were to argue that water could contain "memory", we would have to try to figure out how

Scientists would have to. Doctors merely ought to.

Your debunking of water memory by vibration is good, but you had to propose a pseudo-plausible mechanism to debunk. Someone else could propose another one. When you say “any known mechanism” (my emphasis), I think you’re departing from falsifiability. (If not, again, I’m curious. My known unknowns about chemistry are large.)

Eventually, in practice, we’ll want to come at the issue from the other end and check results as well as principles. This is what a clinical trial does. Homeopathy failed. And so I’m saying that describing homeopathy as something with no results is rhetorically stronger than describing it as something with no known mechanism.

If someone isn't a doctor, biologist, chemist, or physicist, then I don't see how that person could say, "...but I think they might be wrong!"

Oh dear. I get the sense that you’re trying to cure me of mistrust in the scientific process. There’s no need. I’m not trying to say that I know better than qualified experts. I’m criticizing a detail of a cartoonist’s phrasing. “X doesn’t fit some unspecified principle” is not as strong to me as “X does not work”. That’s all.