Homeopathy is a kind of alternative medicine from Germany. It uses small sugar balls called remedies. People make them by adding water to a substance again and again. They say, "The more you dilute it, the stronger it becomes."

But a common remedy, 30C, is diluted 100 times, thirty times over. After that, not one molecule of the substance is left. Big studies found it works no better than a fake pill.

Homeopathy was developed by a German doctor, Samuel Hahnemann, more than 200 years ago. It is based on two ideas: a substance that causes certain symptoms can treat them, and the more the substance is diluted, the stronger it becomes. Many remedies are labeled "30C," which means they were diluted one hundred times, thirty times in a row.

Calculations show that by about 12C, it is very unlikely that even one molecule of the original substance remains. In 2005, Swiss researchers compared 110 homeopathy trials with 110 trials of conventional medicine. When they looked at large, high-quality trials, the effects of homeopathy could not be distinguished from those of a placebo. People may still feel better because of the placebo effect or because they recover naturally.

Homeopathy, devised by the German physician Samuel Hahnemann in the late eighteenth century, rests on two principles: "like cures like," and the claim that repeated dilution, combined with vigorous shaking, increases a remedy's potency. The second principle collides with basic chemistry. A remedy labeled 30C has been diluted a hundredfold thirty times, and Avogadro's number implies that by around 12C the chance of a single molecule of the original substance remaining is close to zero.

Supporters therefore appeal to a supposed "memory of water," an idea that has never been reliably demonstrated. Clinical evidence points the same way. In a 2005 Lancet study, Shang and colleagues compared 110 placebo-controlled homeopathy trials with 110 conventional-medicine trials. Smaller, lower-quality studies tended to show larger effects, but once the analysis was restricted to large, rigorous trials, homeopathy was indistinguishable from placebo. The study's selection of trials drew criticism, yet later reviews have reached broadly similar conclusions.

Why, then, do users report improvement? The placebo effect, the natural course of illnesses such as colds, and long, attentive consultations all play a part. The greatest danger lies not in the sugar pills themselves but in using them instead of effective treatment.