There are many recurrent themes when debating with apologists for homeopathy; one of these is their repeated assertion that if we (the skeptics) were to read and understand this long list of scientific studies, then we would understand that it works.

I am willing to risk a small wager: I bet I know more about how homeopathy works than the people who make this claim.

Here’s what I know:

1. There has never been any credible generalised proof of the fundamental law of homeopathy, the so-called law of similars. I have asked many homeopaths to cite any such proof and none has ever been provided. All they do is link (again) the same long list of “scientific studies”, to which I will return in a moment. I am willing to go double or quits on this one: I bet no homeopath actually has in their possession anything which amounts to a proof of this fundamental tenet of their belief system, other than the word of Samuel Hahnemann – a word which, it turns out, is based on a generalisation from a single data point. I do not think there is any even remotely rigorous proof of this. It is this reliance on the word of one man, taken as unchallenged truth, which marks homeopathy out as a religion and not a scientific endeavour.
2. There has never been any credible generalised proof of the homeopathic principle known as potentisation. I have asked many times and have been offered a veritable smorgasbord of unconnected and often conflicting pieces of work cherry-picked from sources of wildly varying credibility. Of these a few notable examples are:
• The work of Luc Montaigner, which is self-published not peer reviewed, and describes an effect which even it it were replicated independently (which it has not been) would be restricted to certain classes of compounds, to the extent that Montaigner himself says it cannot be extended to cover the materials used in homeopathy, and in any case has a duration measured in picoseconds. Homeopaths love Montaigner because he is a Nobel laureate. Science does not recognise the Nobel prize as conferring infallibility; even Einstein was wrong when he famously said that “God does not play dice“.
• The work of Jacques Benveniste, which purported to show a water memory effect, but which was finally shown to have been the result of deliberate error on the part of his assistant. Benveniste always disputed these findings, denouncing measures such as taping labels to the ceiling to prevent fraud, and homeopaths continue to accept them without question, but the scientific consensus is that his implausible results were down to error, deliberate or not.
• Some effects of nanodomains in water; nanodomains are real enough but their supposedly extraordinary properties in water are almost exclusively the province of pseudoscience (cf. polywater). No homeopath in my experience understands what nano means in this context, and none has ever shown any proper understanding of the difference between 10^-9 and 10^-30, which homeopaths call 15C. There’s a nice demolition of this line of argument at “Water Cluster Quackery“.
• Arm-waving references to “quantum” or even “quantum entanglement“, which any physicist will tell you is not observable at the macro scale. There is no explanation why these supposed effects are not visible in other contexts such as semiconductor fabs  where scientists routinely control the placement of individual atoms. There is no recorded instance where this effect, supposedly achievable by any backyard homeopath using nothing more specialised than plain water and a leather cushion, has been objectively measured by the most sensitive instruments known to man.
• Papers such as “Domains of Water Molecules Provide Mechanisms of Potentization in Homeopathy” which begins: “In homeopathy, high potentization means such high dilution that there is no longer even one molecule of the original active agent per gram of the mixture. Nevertheless such high dilutions apparently remain effective. We develop a possible mechanism for homeopathic potentization to explain this phenomenon.” This is the logical fallacy of begging the question: to start by assuming that the effect you are investigating exists, without citing any credible source for that claim, is to head down the path of tooth-fairy science. In this case a question tot he editor revealed that he values an “open mind” above rigorous peer-review, which would never allow such sloppiness.
3. No paper has ever convincingly refuted the null hypothesis of placebo effect plus observer bias. Meta-analyses such as that by Shang et. al. show that the more carefully you control for bias, the more likely you are to end up showing that homeopathy = placebo. Lining up all the data points which underpin this conclusion – for example by listing large numbers of poorly designed studies which show effect beyond placebo – only reinforces the conclusion, as does the occasional well-conducted piece such as “Homeopathy has clinical benefits in rheumatoid arthritis patients that are attributable to the consultation process but not the homeopathic remedy: a randomized controlled clinical trial” (scientists do come up with such catchy titles!).
4. Homeopathy cannot and does not self-correct. I have asked many times for a single concrete example of homeopathy self-correcting for error. Not one has ever been advanced. And it won’t be, I think, because of the way homeopathy operates. It can’t self-correct because it has no mechanism for self-correction. If two homeopaths disagree they simply form different strands of homeopathy (such as those who accept versus those who reject remedies based on nosodes or ephemera such as the light of venus or “shipwreck”) or – bizarrely – accept both conflicting versions as equally valid. Here again there is more of religion than of science. Christianity finds space for those who believe in transubstantiation and those who do not, but science only accepts one or the other when two possibilities are mutually exclusive, and only one mechanism for establishing which is which, the scientific method. One of the longest-running and most closely fought battles in science was between the wave and the particle theory of light, and even now physicists are vexed by the fact that it is not fully settled, only nailed down tot he point that we know which will work in any given situation. Imagine what would happen if scientists, like homeopaths, could not even agree on whether you have to take a strictly measured centessimal dilution, or whether you can just pour everything down the drain and refill (the Korsakovian method). Homeopathy can only survive because it is subjective and lacks any empirically verifiable principles, or any proper mechanism for weighing competing claims. The scientific method is a negative feedback system, where measurement of the results is used to correct the input, and homeopathy is a positive feedback system, where each result is accepted as implicitly valid and new results built on it. Negative feedback systems are inherently stable, positive feedback systems are inherently unstable. The former converges on the correct output, the latter drives away from it.

Now, I do not claim to be omniscient, or a great scientist, or utterly certain of anything, but I know that these four things are true: there is no proof of the fundamental homeopathy principles of similars and potentisation, no homeopathy study has ever convincingly refuted the null hypothesis, and homeopathy, unlike science, lacks a mechanism for self-correction. These foru things are my form conclusions based on the evidence I have read.

What’s interesting here is that in understanding these things, within the limits of an interested non-specialist anyway, I think I can show greater understanding of homeopathy than most if not all practitioners, because I have yet to encounter one who can offer satisfactory proof of similars or potentisation, who can understand why the null hypothesis is important and how their cherry-picked collections of anecdotes fail to refute it, or the importance of self-correction and the implications of its absence in homeopathy.