Homeopathic dilutions

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In homeopathy, homeopathic dilution (known by practitioners as "dynamisation" or "potentisation") is a process in which a substance is diluted with alcohol or distilled water and then vigorously shaken in a process called "succussion". Insoluble solids, such as quartz and oyster shell, are diluted by grinding them with lactose (trituration). The founder of homeopathy, Samuel Hahnemann (1755–1843) believed that the process of succussion activated the "vital energy" of the diluted substance,[1] and that successive dilutions increased the "potency" of the preparation, although other strands of homeopathy disagree[which?].

The idea is pseudoscience, because at commonly used dilutions, no molecules of the original material are likely to remain.

Potency scales[edit]

Several potency scales are in use in homeopathy. Hahnemann created the centesimal or "C scale", diluting a substance by a factor of 100 at each stage. The centesimal scale was favored by Hahnemann for most of his life. A 2C dilution requires a substance to be diluted to one part in one hundred, and then some of that diluted solution diluted by a further factor of one hundred. This works out to one part of the original substance in 10,000 parts of the solution.[2] A 6C dilution repeats this process six times, ending up with the original material diluted by a factor of 100−6=10−12. Higher dilutions follow the same pattern. In homeopathy, a solution that is more dilute is described as having a higher potency, and more dilute substances are considered by homeopaths to be stronger and deeper-acting.[3] The end product is often so diluted that it is indistinguishable from the dilutant (pure water, sugar or alcohol).[4][5][6]

There is also the continued flow mode of dilution that is measured on MFC.

Hahnemann advocated 30C dilutions for most purposes (that is, dilution by a factor of 1060).[7] In Hahnemann's time it was reasonable to assume that preparations could be diluted indefinitely, as the concept of the atom or molecule as the smallest possible unit of a chemical substance was just beginning to be recognized. We now know that the greatest dilution that is reasonably likely to contain one molecule of the original substance is 12C, if starting from 1 mole of original substance.

This bottle contains Arnica montana (wolf's bane) D6, i.e. the nominal dilution is one part in a million (106).

Some homeopaths developed a decimal scale (D or X), diluting the substance to ten times its original volume each stage. The D or X scale dilution is therefore half that of the same value of the C scale; for example, "12X" is the same level of dilution as "6C". Hahnemann never used this scale but it was very popular throughout the 19th century and still is in Europe. This potency scale appears to have been introduced in the 1830s by the American homeopath Constantine Hering.[8] In the last ten years of his life, Hahnemann also developed a quintamillesimal (Q) or LM scale diluting the drug 1 part in 50,000 parts of diluent.[9] A given dilution on the Q scale is roughly 2.35 times its designation on the C scale. For example, a preparation described as "20Q" has about the same concentration as one described with "47C"g.[10]

Potencies of 1000C and above are usually labelled with Roman numeral M and with the centesimal 'C' indicator implied (since all such high potencies are centesimal dilutions): 1M = 1000C; 10M = 10,000C; CM = 100,000C; LM (which would indicate 50,000C) is typically not used because of confusion with the LM potency scale.

The following table is a synopsis comparing the X and C dilution scales and equating them by equivalent dilution. However, the homeopathic understanding of its principles is not explained by dilution but by "potentisation", hence one can not assume that the different potencies can be equated on the basis of equivalence of dilution factors.

X Scale C Scale Ratio Note
1X 1:10 described as low potency
2X 1C 1:100 called higher potency than 1X by homeopaths
6X 3C 10−6
8X 4C 10−8
12X 6C 10−12
24X 12C 10−24 Has a 60% probability of containing one molecule of original material if one mole of the original substance was used.
26X 13C 10−26 If pure water was used as the diluent, no molecules of the original solution remain in the water.
60X 30C 10−60 Dilution advocated by Hahnemann for most purposes: on average, this would require giving two billion doses per second to six billion people for 4 billion years to deliver a single molecule of the original material to any patient.
400X 200C 10−400 Dilution of popular homeopathic flu preparation Oscillococcinum
Note: the "X scale" is also called "D scale". 1X = 1D, 2X = 2D, etc.


Serial dilution of a solution results, after each dilution step, in fewer molecules of the original substance per litre of solution. Eventually, a solution will be diluted beyond any likelihood of finding a single molecule of the original substance in a litre of the total dilution product.

The molar limit[edit]

If one begins with a solution of 1 mol/L of a substance, the dilution required to reduce the number of molecules to less than one per litre is 1 part in 1×1024 (24X or 12C) since:

6.02×1023/1×1024 = 0.6 molecules per litre

Homeopathic dilutions beyond this limit (equivalent to approximately 12C) are unlikely to contain a single molecule of the original substance and lower dilutions contain no detectable amount. ISO 3696 (Water for analytical laboratory use) specifies a purity of ten parts per billion, or 10×10−9 ― this water cannot be kept in glass or plastic containers as they leach impurities into the water, and glassware must be washed with hydrofluoric acid before use. Ten parts per billion is equivalent to a homeopathic dilution of 4C.


Critics and advocates of homeopathy alike commonly attempt to illustrate the dilutions involved in homeopathy with analogies. The high dilutions characteristically used are often considered to be the most controversial and implausible aspect of homeopathy.

A popular homeopathic treatment for the flu is a 200C dilution of duck liver, marketed under the name Oscillococcinum. As there are only about 1080 atoms in the entire observable universe, a dilution of one molecule in the observable universe would be about 40C. Oscillococcinum would thus require 10320 more atoms to simply have one molecule in the final substance.[11]

Another illustration of dilutions used in common homeopathic preparations involves comparing a homeopathic dilution to dissolving the therapeutic substance in a swimming pool.[12][13] There are on the order of 1032 molecules of water in an Olympic-size swimming pool and if such a pool were filled with a 15C homeopathic preparation, to have a 63% chance of consuming at least one molecule of the original substance, one would need to swallow 1% of the volume of such a pool, or roughly 25 metric tons of water.[14][15]

Proposed explanations[edit]

Homeopaths maintain that this water retains some "essential property" of the original material, because the preparation has been shaken after each dilution.[16] Hahnemann believed that the dynamisation or shaking of the solution caused a "spirit-like" healing force to be released from within the substance. Even though the homeopathic preparations are often extremely diluted, homeopaths maintain that a healing force is retained by these homeopathic preparations.[15] Modern advocates of homeopathy have proposed a concept of "water memory", according to which water "remembers" the substances mixed in it, and transmits the effect of those substances when consumed. This concept is inconsistent with the current understanding of matter, and water memory has never been demonstrated to have any detectable effect, biological or otherwise. The claim often given to support "water memory" is that science does not fully understand water. In fact a great deal is known about the structure and properties of liquid water, from both theoretical and experimental studies, because of its importance in biochemistry, its relative molecular simplicity and the quantum mechanical nature of hydrogen bonding which make it a popular substance to study in theoretical chemistry.[17] The actual memory of water can be measured experimentally and is found to be around 50 femtoseconds, which is 0.00000000000005 seconds.[18] Generally considered to be pseudoscience by the scientific community, one disputed study into the so-called memory of water, conducted by Jacques Benveniste, claims to have demonstrated that water can be energetically imprinted upon.[19][20][21] Another such study, published in 2003 by Swiss chemist Louis Rey, claims to have found that homeopathically diluted solutions of sodium chloride and lithium chloride have a very different hydrogen bond structure from normal water, as measured by thermoluminescence.[22][23]

Dilution debate[edit]

Not all homeopaths advocate extremely high dilutions. Many of the early homeopaths were originally doctors and generally used lower dilutions such as "3X" or "6X", rarely going beyond "12X"; these dilution ("trituration") levels were still popular in the late 20th century with advocates of Wilhelm Heinrich Schüßler's 12 biochemic tissue salts, for example. The split between lower and higher dilutions followed ideological lines. Those favoring low dilutions stressed pathology and a strong link to conventional medicine, while those favoring high dilutions emphasised vital force, miasms and a spiritual interpretation of disease.[24][25][26] Some products with both low and high dilutions continue to be sold, but like their counterparts, they have not been conclusively demonstrated to have any effect beyond the placebo effect.[27][28]


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  2. ^ In standard chemistry, this produces a substance with a concentration of 0.01%, measured by the volume-volume percentage method.
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