You may bend over backward to defend your pet “alternative” remedy—herbal medicines, acupuncture, Chinese traditional medicine, tribal witchdoctor cures—whatever it is. If the evidence supports it, your pet remedy deserves to be embraced by orthodox medicine. But homeopathy is in a class of its own. Not only does it not work, but—with a reservation to be entered below—it cannot work. Or, putting it at its mildest, if homeopathy is your personal favorite quackery, you are going to have to bend over backward a massive lot further than for any other branch of alternative medicine.

Homeopaths believe effectiveness increases the more you dilute the putatively active ingredient. They measure dilution on a logarithmic so-called C-scale. 30C—which is recommended as a good, effective dose—corresponds to a dilution of one part in 10^-60. The late James Randi calculated that this is equivalent to one molecule of the active ingredient in a volume of water equal to the volume of the solar system. In other words, there is no active ingredient at all.

Critics often say there is no good evidence that homeopathy works. But that misses the point. What would such evidence look like? What could it look like? There’d have to be a double-blind control trial in which patients were treated either with the homeopathic dose or with a control substance, say water. Because both the experimental and control doses are identical—water—the experiment cannot yield a positive result. With the reservation mentioned, it follows that there can be no evidence in favor of homeopathy.

Actually, neither the experimental nor the control dose is pure water anyway. At the levels of dilution we are talking about, both doses contain traces not only of the allegedly active ingredient but of everything else as well—including Oliver Cromwell’s urine. Such conclusions follow from the following familiar calculation (I’m not sure who first made it, but I got it from Lewis Wolpert’s The Unnatural Nature of Science): There are many more molecules in a glassful of water than there are glassfuls of water in the world, including the sea. The same applies to bladders. So every time you have a cup of coffee, you are probably imbibing a component of the urine of Cromwell (or it was once sucked into the trunk of the last mastodon, or circulated in the blood of Christ, etc.).

I said there is a reservation. Homeopaths have a get-out, or they think they have. Water is endowed with “memory.” When homeopaths prepare a medicine, they don’t just dilute it multiple times. It is subject to succussion—shaking in a special, ritualized way. Succussion takes place at every one of the stages of dilution. The molecular shape of the active ingredient somehow imprints itself on the water and is replicated, via succussion, in all the water of subsequent dilutions. Nobody knows what the actual mechanism of water memory is. If it exists, it is something entirely unknown to science. That is not impossible. The homeopath who demonstrated it would win not only the Nobel Prize for Medicine but the Nobel Prize for Physics as well. You’d think that with such dazzling incentives, they’d all be beavering away trying to demonstrate, once and for all, the memory in water. Instead, all they do is tell anecdotes about patients who recovered—as they probably would have anyway.

You don’t even have to do the physics. A purely medical trial would suffice to demonstrate, to any desired level of statistical confidence, that homeopathy really works. It’s not difficult to set up the necessary experiment. Here is my design.

Take a number N (the larger the better) of patients suffering from a complaint that homeopaths agree is suitable to be cured by some particular potion when it is diluted to the 30C level. If possible, match the patients in pairs: same sex, roughly similar age, etc. Matching pairs are not essential, but they increase the chance of a positive result. One of each pair will receive the control dose, the other the homeopathic, determined at random. Of course, the patients mustn’t know which dose they receive, nor should any doctors, homeopaths, nurses, or indeed anyone else who comes in contact with the patients. The knowledge is locked away in the form of secret numerical codes to which nobody has access until the experiment comes to its predetermined end.

So much is standard double-blind procedure. I happen to have chosen a matched pairs design, but other designs would work fine as well. Now, however, for the special concession to homeopathic succussion theory. It is laborious but necessary. Every patient must have their own fully succussed dose. The control water must be succussed in exactly the same way as the homeopathic water. The only difference is the small quantity of substance—or water—that is added at the start of the procedure. Why must every patient have their own separately succussed dose? Why not prepare a large vat of homeopathically succussed water that you dip into for half the patients and another large vat of control succussed water that you dip into for the other half of the patients? Because there might be a difference between the vats, their temperature, how close they are to the window, perhaps an insect fell in one of them, perhaps the succussion was slightly different; it doesn’t matter what. If the succussion procedure is undertaken separately for each individual patient, there is no possibility of such confounding error.

The succussion itself may be done by professional homeopaths, and they can be as biased as you like—they have no way of knowing whether they are succussing control or homeopathic water. The judgment as to whether each patient’s health has improved can also be done by professional homeopaths or by conventional doctors, any of whom can be biased. It doesn’t matter who does it, or what their biases might be, so long as neither they nor anybody else knows which dose was which. Nobody must know until the codes are broken and the experiment ended. The statistical analysis will then reveal whether the homeopathic treatment worked.

This experiment has not been done. Other experiments have taken place, but none of them, as far as I know, have taken the crucial step of succussing control water as well as homeopathic water separately for each patient. If this experiment is properly done and yields a positive result, I’ll eat my hat—but not before raising it to homeopathy.

The Center for Inquiry is suing retailers who display homeopathic remedies alongside evidence-based medications.