Homeopathy’s “Law of Infinitesimals”

Stephen Barrett, M.D.
March 20, 2002

Homeopathic products are formulated by taking a sample of a substance and repeatedly diluting it with water, water/alcohol, or milk sugar. The products are derived from minerals, plants, zoological substances, microorganisms, and several other sources. If the allegedly medicinal substance is soluble, 1 part is diluted in either 9 or 99 parts of distilled water and/or alcohol and “succussed” (shaken) vigorously; if insoluble, it is finely ground and “triturated” (pulverized) in similar proportions with powdered lactose (milk sugar). One part of the diluted medicine is diluted, and the process is repeated to reach the desired concentration, after which it may be bottled or used to impregnate sugar granules.

Dilutions of 1 to 10 are designated by the Roman numeral X (1X = 1/10, 2X = 1/100, 3X = 1/1,000, 6X = 1/1,000,000). Similarly, dilutions of 1 to 100 are designated by the Roman numeral C (1C = 1/100, 2C = 1/10,000, 3C = 1/1,000,000, and so on). Most remedies today range from 6X to 30C, but some carry designations as high as 200C.

Advocates claim that the lower the concentration of a substance, the more potent it becomes. This concept, often referred to as the “Law of Infinitestimals,” is the equivalent of saying that the less sugar you put into a cup of coffee, the sweeter it will become. This is just the opposite of the dose-response relationship that pharmacologists have demonstrated.

The laws of chemistry state that there is a limit to the dilution that can be made without losing the original substance altogether. This limit, which is related to Avogadro’s number (6.023 x 1023), corresponds to homeopathic potencies of 12C or 24X (1 part in 1024). Modern proponents claim that even when the last molecule is gone, a “memory” of the original substance is retained. A 30X dilution means that the original substance has been diluted 1,000,000,000,000,000,000,000,000,000,000 times. Assuming that a cubic centimeter contains 15 drops, this number is greater than the number of drops of water that would fill a container more than 50 times the size of the earth and a 30C solution would require a container more than 30 billion times the size of the Earth.

For practical purposes, this means that “30X” and “30C” solutions do not actually exist, because it is not possible to create a solution in which one molecule of an original substance is dissolved in a container of water bigger than the Earth.

Oscillococcinum, a 200C product “for the relief of colds and flu-like symptoms,” involves “dilutions” that are even more far-fetched. Its “active ingredient” is prepared by incubating small amounts of a freshly killed duck’s liver and heart for 40 days. The resultant solution is then filtered, freeze-dried, rehydrated, repeatedly diluted, and impregnated into sugar granules. If a single molecule of the duck’s heart or liver were to survive the dilution, its concentration would be 1 in 100200 This huge number, which has 400 zeroes, is vastly greater than the estimated number of molecules in the universe (about one googol, which is a 1 followed by 100 zeroes).

Homeopathy’s founder (Samuel Hahnemann, M.D.) himself realized there was virtually no chance that an original molecule would remain after extreme dilutions. But he declared that vigorous shaking (“succussion”) or pulverizing between dilutions would leave behind a spirit-like essence that cures by reviving the body’s “vital force.”

Modern chemistry, which has developed understanding of the molecular nature of matter, and of the size of molecules, has found no “spirit-like” essence that could be left behind following dilutions past Avogadro’s number.

Modern proponents postulate that the solution retains a “memory” of the substance. If this were true, every substance encountered by a molecule of water, alcohol, or milk sugar might imprint an “essence” that could exert powerful and unpredictable medicinal effects. Moreover, water is never 100% pure, and impurities can enter the solution from the container or surrounding air. So if a few molecules could determine how a remedy acts, there is no reason to assume that the original substance will prevail over the impurities encountered along the way.

Many proponents allege that homeopathic products resemble vaccines because both provide a small stimulus that triggers an immune response. This comparison is not valid. The amounts of active ingredients in vaccines are much greater and are measurable. Immunizations produce measurable antibodies, but highly dilute homeopathic products have no measurable active ingredients and produce no measurable response. In addition, vaccines are used preventively, not for curing symptoms.

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This article was posted on March 20, 2002.