If I were to tell you that I can correctly predict the result of tossing a coin, would you believe me? Probably not: you'd want to see pretty good evidence. How good? Suppose I do so correctly four or five times in succession: will you believe me now? After all, there's only a 1 in 20 chance I could have got it right by luck. But, no, you still won't believe me: after all, such a claim is so far removed from our everyday conception of the possible that you want much more than this level of evidence. One friend's response was to require me to keep going 'all day' -- which seems a little harsh, since I reckon the chance I could carry on successfully all day by sheer luck is only about 1 in 10^3000 (which is a one followed by 3000 zeros, though that's not a helpful way to think about it).
So if I now tell you that homoeopathy works, will you believe me? Let me say that there are several trials, with unimpeachable experimental methodology, which show significant positive results (There are plenty of others which don't, but let's leave those aside for the moment.) Perhaps that's enough for you.
It shouldn't be. The conventional measure of scientific success is that there should be less than a 1 in 20 chance that positive results could happen by luck. That's perfectly good for a one-off trial of something for which you have no biased expectation one way or the other, but, as we saw above, it's nowhere near good enough to convince you of something profoundly surprising, something which throws into doubt everything you know about how the world works. Furthermore, if many such trials are being conducted, then 1 in every 20 will apparently show positive results.
But why is homoeopathy in this category? Let's compare it with herbal medicine. If you take a herbal remedy, you're taking a complex cocktail of mostly-unidentified chemicals, perhaps one or two of which are known to have particular short-term effects. No-one understands the rest, still less the ways in which they interact with each other, and it's no surprise that such a cocktail can have all sorts of effects on the human body (and mind!). Science can happily accommodate the effectiveness of such remedies, though it will find them very difficult to analyse. If, in contrast, you take a homoeopathic remedy, you are generally ingesting -- well, nothing, or at least none of the ingredient the practitioner believes gives the remedy its efficacy. The point is that this chemical has been diluted so much in the preparation that not a single molecule is left in the dose. (This is noticed by relating the number of molecules in typical everyday quantities with the number of dilutions required by homoeopathy -- a calculation which was not understood at the time the latter was fixed.) Now, perhaps some scientific mechanism can be imagined which allows the inert ingredients to retain some memory of the chemical which was once among them. (None ever has been imagined, however; our understanding of the physics of the molecular-scale world is pretty good.) But certainly you should allow scientists to require a much higher standard of proof in this case than for a herbal remedy.
Practitioners often claim that scientists are biased against complementary and alternative medicine because they ask for much higher standards of proof (much more 'significant' evidence) than for conventional therapies. Well, of course they do; a therapy's being 'conventional' means precisely that its action is consistent with what we (the scientific community) understand of the way the world works. Just as with one's everyday belief that it's impossible to predict the toss of a coin, scientists won't lightly accept the existence of an effect which would require them to start again, from scratch (well, from the mid-19th century), re-inventing the sciences that correctly predict so much of the world around us.
Niall MacKay, August 2002