Before the advent of evidence-based medicine, a huge variety of quack nostrums and dubious cures flourished. Many of these have faded away with time - and in cases like radioactive water, this was almost certainly for the best. However, some superstitious treatments that predate scientific medicine are still being used today. One of the most prominent is homeopathy.

Invented by Samuel Hahnemann in the early 1800s, homeopathy claims that "like cures like": a substance that produces symptoms of disease in a healthy person will cure those same symptoms in a sick person. (By this principle, one would assume that the homeopathic cure for a person who has been shot is to shoot him again.)

However, it's not as simple as just administering these substances to the sick person. Instead, they must be successively diluted - adding one part remedy to nine parts water, mixing, adding one part of the resulting solution to nine parts water, and so on - repeating this process many times until, by our subsequently acquired understanding of atoms and molecules, there is not even one molecule of the original substance left. Not to worry, though, because homeopaths claim that the water "remembers" what used to be dissolved in it, so that the process of dilution actually increases rather than decreases the remedy's effectiveness. (Incidentally, homeopathy also claims that that all illness comes from internally originating "derangement of the vital force's normal harmonious vibratory frequency", and that the "vibrational pattern" of the remedy is what gets the body back into shape.)

There is absolutely no rational basis by which this could work. Everything we have learned in the last two hundred years about how the world works rules this out, and if homeopathy could be shown to have significant curative effects, then practically everything we thought we knew about the laws of physics and the human body would have to be thrown out. However, there is no such effect. Large, well-designed studies routinely find that homeopathy is useless. Skeptico, for example, links to a Lancet review of 110 clinical trials which concluded that homeopathy does no more good than a placebo.

I don't know for certain how Hahnemann came up with the idea of homeopathy, but based on how it's claimed to work, I think I can offer a plausible speculation. Here's what probably happened:

Searching for a new method of curing diseases, Hahnemann at first guessed that a toxic substance which produced symptoms in a healthy person would cure a disease with those same symptoms in a sick person. This approach did not work, and naturally it had terrible side effects. In a bid to remove these side effects while keeping the presumed curative effects, he tried a variety of experiments. One of these experiments entailed successively greater dilutions of these substances. Unbeknownst to him, he had actually diluted his formulas to the point where none of the active ingredient was left. (Avogadro's work on molarity and molecules was not published until over fifty years later.) But when he administered the result to patients, they showed improvement without showing any of the harmful side effects.

Knowing what we now know, it is obvious why this worked. The side effects ceased because none of the harmful substance was left. The improvement occurred because of his patients' belief in the treatment, the same improvement that often occurs in people receiving care that they believe will help them. In other words, what Hahnemann actually discovered was the placebo effect. Believing he was on to something, he never compared the effectiveness of his "potentized" solutions of water against doses of ordinary water not prepared using any special method at all, which would have shown him his error.

Nevertheless, homeopathic medicine was a hit, and it is easy to see why. In Hahnemann's era, the scientific approach to medicine was rudimentary at best. Treatments were based on old, discredited superstitions such as the theory of the four bodily humors, and many of them, such as bloodletting, were actively harmful. Compared to these, Hahnemann's approach was an improvement because it simply did nothing, allowing the body's natural recuperative powers to work without interference.

Of course, we now have far more effective treatments that do not cause unnecessary harm, so there is no longer any good reason to rely on homeopathic medicine. And in any case, the idea that water "remembers" what substances it has come in contact with was absurd from the beginning. It is a particularly silly bit of magical thinking, and the logical gaps in the idea should have been obvious even in Hahnemann's day.

For example, during the process of preparation, how does the water "know" which substance it is supposed to concentrate? In addition to whatever the homeopath chooses to add to it, any reasonable volume of water, no matter how pure or filtered, is bound to contain at least minute quantities of all kinds of toxins and contaminants - bacterial proteins, viruses, insect secretions, human and animal skin cells, heavy metals, natural radionuclides, pesticides, fertilizers, arsenic, asbestos, industrial byproducts, and so on. (See this list from the EPA). Are we to believe that water can somehow tell the difference between the one remedy the homeopath adds to it and all the other dissolved molecules it contains, and selectively amplifies only the former?

On the other hand, what if the homeopathic preparation of water does indeed amplify the curative properties of every substance dissolved in it? In that case, the probability is very good that any reasonably sized body of water will naturally have come in contact with some or all of homeopathy's chosen remedies at some point in the past. By homeopathic principles, the more dilute the remedy, the more concentrated its curative effect. Therefore, it follows that any glass of water must be a homeopathic panacea, already containing an extremely dilute and therefore highly effective version of any "remedy" one would care to name. It seems pointless, therefore, for homeopaths to waste their time and money stocking medicine cabinets with specially prepared remedies for different types of disease. Whenever they feel ill, all they should have to do is drink a glass of tap water, and they should be cured of whatever afflicts them. But this would not generate much revenue for homeopathic practitioners, so it is probably not surprising that they do not talk about this.

Other posts in this series:

• Popular Delusions

Consumers, be advised! When you want to know the future or ward off bad fortune through the invocation of magical power, don't trust just any fake dime-store psychic. Be sure to choose only the best fake psychics for all your supernatural needs.

Such is the message of a bulletin issued recently by the United Kingdom's official consumer-protection agency:

The UK's Office of Fair Trading (OFT) has warned consumers not to fall for scams perpetrated by bogus clairvoyants, fortune tellers and healers.

Fake psychics had been mailing UK households saying "something bad" would happen to them if they did not buy a lucky charm or send money, the consumer protection agency said this week.

I have called before for consumer-protection groups to take action against individuals making extravagant and unproven supernatural claims, and this cannot help but be a step in the right direction. However, I fail to see why the Office of Fair Trading took action against only this psychic scam and not others. The only important difference between these psychic claimants and the other, more prominent ones is the directness with which they promise magical help in exchange for money.

Is it that these scams seem to be threatening consumers, whereas the so-called "genuine" psychics never stoop to such explicitly extortionate tactics? But how could that be? Everyone experiences both good and bad fortune in their lives, and a genuine psychic would surely be able to foretell both and tell customers how to avert the latter. If the more prominent media psychics never warn people about threats to come, surely that must mean that they are also scammers. They're merely running the opposite scam: telling people what they want to hear for money, as opposed to telling people what they don't want to hear and then demanding money to nullify their own prediction.

In fact, the OFT appears to take action against garden-variety scammers doing this very thing:

Others had offered Money Creating Scarabs of the Pharos (sic) and Parchments of the Sacred Olive Branch, claiming to bring good fortune, the OFT said.

Again, if this is illegitimate, why are the more prominent psychics and mediums who do very much the same thing not subject to liability?

But the most ironic part of the article must surely be the following:

Den Jones, a spokesman for the Spiritualists' National Union, the largest organization of healers and mediums in the U.K., said consumers shouldn't respond to mass mailings.

"If one is looking for a spiritualist healer or medium, there are qualified ones and unqualified ones," he said. People wishing to use one should only go to people certified by his organization, he said.

For the record, here is how to become a member of the Spiritualists' National Union. The major hurdles, apparently, are twofold: gaining the sponsorship of two existing members, and paying an annual application fee.

The procedure is that the appropriate application form is completed and returned by the applicant with the appropriate remittance to the Union's Head Office: if it is received in correct form, i.e. correctly sponsored and the correct amount of subscription and joining fee enclosed, the applicant will be accepted immediately into provisional Class B membership for a period of twelve months...

Notably absent on that page is any mention of actual testing or examination to see if the applicant possesses any genuine psychic power as a precondition of membership. If customers go to a psychic claimant who is a member of the Spiritualists' National Union, the only thing they are assured of is that they are consulting a person who has paid his membership dues to the Spiritualists' National Union. There is no formal test whatsoever to ensure that the applicant has any psychic abilities at all. The SNU does claim to conduct tests on its members, but it makes it plain that these are strictly voluntary and carry no penalties for failure:

One important facility which the Union offers to members is the provision of an educational scheme which provides courses in the various aspects of the movement: it conducts examinations for those who wish them and makes awards to successful candidates.

Of course, if this organization were to establish an actual test of competence for membership, one that ruled out the possibilities of subjectivity and fraud, there would almost certainly be no members left. The fact that James Randi's million-dollar prize has gone unclaimed for years is good evidence for that.

In other news, the Princeton Engineering Anomalies Research lab is closing its doors after 30 years of operation. Set up to study claims of human psychic ability, the lab's major (in fact only, as far as I know) experiment consisted of having volunteers stare at a random number generator and try to alter its output through willpower alone. The results? After three decades, the lab's director claims, his data shows a deviation from pure randomness by 2 or 3 parts out of 10,000. In other words, the PEAR lab claims to have shown that, in a run of 10,000 coin flips, participants can on average produce 2.5 more heads than would be expected by chance alone. How many millions of dollars have gone into producing this result?

As Robert Park has written, one of the sure signs of pseudoscience is an effect that can be found only at the very limits of detection, hovering at the boundary where results fade into statistical noise, and cannot be amplified. This is just what we would expect from a self-deceived scientist misinterpreting occasional fluctuations in randomness as data, which is almost certainly what has happened here. The PEAR lab has had more than enough time to produce a genuine result, and they have failed to do so. It's about time that they close down so that those resources can be redirected to areas of real importance where there are actual discoveries waiting to be made.