Is Homeopathy Really As Implausible As It Sounds?

We look into the mathematics of alternative medicine.

The new British minister of health has recently become the target of scorn and mockery, after a science writer with The Telegraph noted that he supports homeopathy, a branch of alternative medicine most health experts view as quackery. But just how quackish is it?

Quick as Western doctors are to equate alternative medicine with utter nonsense, there’s a difference between something that hasn’t been proven to work and something that couldn’t possibly work. The tools available for understanding the body are largely blunt, and some alternative theories have gained traction as those tools sharpen. Improvements in brain imaging technology, for example, have shown that meditation—a practice long dismissed by Western doctors as pure mysticism—can improve both the structure and function of the brain.

The form of alternative medicine known as Homeopathy was developed by a German physician around the turn of the 19th century. For two and a half centuries, it has sustained a solid following: According to the National Center for Homeopathy, over 100 million people worldwide use homeopathic medicine. There are—according to the Center’s website—eighteen homeopathic doctors within a ten-mile radius of Popular Science’s office in New York. Could it be that the practice of homeopathy is simply untested and unfairly stigmatized, or is it truly implausible?

To answer that question, let’s first set aside some of the more philosophical/hypothetical principles of homeopathy. Let’s ignore, for example, the homeopathic notion that illness is caused by a disturbance in an individual’s “vital force” rather than something external, like a bacterium or virus. Let’s focus instead on what matters most: whether or not the medicine makes people better. Homeopaths do, after all, use medicines, often in the familiar form of tablets and pills.

Those medicines are formulated according to a number of what we may loosely call “laws.” The first of those laws states that “like cures like” — an agent that causes certain symptoms in a healthy person will cure anybody suffering from those same symptoms. The theory behind why the law works is pretty mystical in nature, but the basic idea is central to mainstream medicine: most vaccines consist of at least part of the thing they’re meant to vaccinate against.

Another thing homeopathy has in common with Western medicine is its strict attention to how treatments are dosed. All homeopathic remedies are available in a huge range of concentrations. But there’s a big difference: those concentrations are really small. In homeopathy, less is more, so homeopaths think of a large dose as a high dilution, instead of a high concentration.

The idea that a lower dose of a drug has a bigger effect than a high dose runs contrary to what western medicine has found. The contradiction is troubling, but it doesn’t totally kill homeopathy’s plausibility. The fatal flaw lies in just how much homeopathy says to dilute things.

Most homeopathic remedies are available at a maximum concentration (or minimal dilution) of 6X. A remedy at this concentration contains only about 1 microgram of active ingredient. To put that in context, here’s how a 6X dose of remedy compares to some other known substances:

There are substances out there whose effects can be felt in amounts tinier than a 6X dilution. Botulinum toxin—a protein produced by the bacterium Clostridium botulinum and frequently injected into human skin to reduce the appearance of wrinkles—is lethal (when ingested) at a dose of just 80 nanograms, or about 4% of the 6X homeopathic remedy. And the human body produces miniscule amounts of several chemicals whose effects remain a mystery to medical science.

The trouble is, most homeopathic remedies are sold at much higher dilutions than 6X. On one popular homeopathic website, for example, sulphur is available in 13 different dilutions. The third-lowest dilution is 30X, which is well past the point where plausibility breaks down:

In fact, most available treatments are sold at even more absurd dilutions. Oscillococcinum, a popular flu remedy derived from duck liver and made by Boiron, a French manufacturer of homeopathic cures, comes in a standard dilution of 400X.

At this low concentration, to ensure you actually did ingest one molecule you would have to swallow about 10380 pills—many, many more pills than there are atoms in the universe.

And that’s pretty implausible.