Homeopathic dilutions

From Wikipedia, the free encyclopedia
Jump to: navigation, search

Homeopathy involves a process known by practitioners as "dynamisation" or "potentisation" whereby 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 remedy.

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 remedies.[3] The end product is often so diluted that it is indistinguishable from the dilutant (pure water, sugar or alcohol).[4][5][6]

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 remedies 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 remedy described as "20Q" has about the same concentration as a "47C" remedy.[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 due to 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 based on 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 allowable concentration of arsenic in U.S. drinking water[11]
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 remedy Oscillococcinum
Note: the "X scale" is also called "D scale". 1X = 1D, 2X = 2D, etc.

The problem of homeopathic dilution[edit]

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 10-fold 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.

1 bottle of poison in Lake Geneva[edit]

Hahnemann is reported[by whom?] to have joked that a suitable procedure to deal with an epidemic would be to empty a bottle of poison into Lake Geneva, if it could be shaken 60 times.

1 pinch of salt in the Atlantic Ocean[edit]

One example given is that 12C solution is equivalent to a "pinch of salt in both the North and South Atlantic Oceans", which is approximately correct.[12]

1/3 of a drop in all the waters of the Earth[edit]

One third of a drop of some original substance diluted into all the water on earth would produce a remedy with a concentration of about 13C.[13][14]

Duck liver 200C in the entire observable Universe[edit]

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 universes to simply have one molecule in the final substance.[15]

Swimming pool[edit]

Another illustration of dilutions used in common homeopathic remedies involves comparing a homeopathic dilution to dissolving the therapeutic substance in a swimming pool.[16][17]

One example, inspired by a problem found in a set of popular algebra textbooks, states that there are on the order of 1032 molecules of water in an Olympic-size swimming pool[18] and if such a pool were filled with a 15C homeopathic remedy, 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.[19][20][21]

30C: 1 ml in 1,191,016 cubic light years[edit]

Yet another illustration: 1 ml of a solution which has gone through a 30C dilution is mathematically equivalent to 1 ml diluted into 1054 m3 - a cube of water measuring 1,000,000,000,000,000,000  (1018) metres per side, which is about 106 light years. When spherical, then it would be a ball of 131.1 light years in diameter. Thus, homeopathic remedies of standard potencies contain, almost certainly, only water (or alcohol, as well as sugar and other nontherapeutic ingredients).

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.[22] 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 remedies are often extremely diluted, homeopaths maintain that a healing force is retained by these homeopathic preparations.[21] 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. However one disputed study into the so-called memory of water, conducted by Jacques Benveniste, claims to have demonstrated that that water can be energetically imprinted upon.[23][24][25] 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.[26][27]

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". 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.[28][29] 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.[30][31]


  1. ^ Kayne SB (2006), Homeopathic pharmacy: theory and practice (2 ed.), Elsevier Health Sciences, p. 53, ISBN 978-0-443-10160-1 .
  2. ^ In standard chemistry, this produces a substance with a concentration of 0.01%, measured by the volume-volume percentage method.
  3. ^ "Glossary of Homeopathic Terms", Creighton University Department of Pharmacology http://altmed.creighton.edu/Homeopathy/Glossary.htm, retrieved 2009-02-15  Missing or empty |title= (help).
  4. ^ "Dynamization and Dilution", Complementary and Alternative Medicine, Creighton University Department of Pharmacology, retrieved 2009-03-24 .
  5. ^ Smith T (1989), Homeopathic Medicine, Healing Arts Press, pp. 14–15 .
  6. ^ "Similia similibus curentur (Like cures like)", Creighton University Department of Pharmacology http://altmed.creighton.edu/Homeopathy/philosophy/similia.htm, retrieved 2007-08-20  Missing or empty |title= (help).
  7. ^ Hahnemann S (1921), The Organon of the Healing Art (6th ed.), aphorism 128 .
  8. ^ Robert ED (1853), Lectures on the theory & practice of homeopathy (PDF), London: B. Jain, pp. 526–7, ISBN 81-7021-311-8 .
  9. ^ Little D, "Hahnemann's advanced methods", Simillimum.com, retrieved 2007-08-04 .
  10. ^ If a dilution is designated as q on the Q scale, and c on the C scale, c/q=log10(50,000)/2=2.349485.
  11. ^ "Arsenic in drinking water", United States Environmental Protection Agency http://www.epa.gov/safewater/arsenic/index.html  Missing or empty |title= (help).
  12. ^ A 12C solution produced using sodium chloride (also called natrum muriaticum in homeopathy) is the equivalent of dissolving 0.36 mL of table salt, weighing about 0.77 g, into a volume of water the size of the Atlantic Ocean, since the volume of the Atlantic Ocean and its adjacent seas is 3.55×108 km3 or 3.55×1020 L : Emery KO, Uchupi E (1984), The geology of the Atlantic Ocean, Springer, p. 1086, ISBN 0-387-96032-5 .
  13. ^ The volume of all water on earth is about 1.36×109 km3: "Earth's water distribution", Water Science for Schools, United States Geological Survey, 28 August 2006 .
  14. ^ Gleick PH, Water resources, In Schneider SH, ed. (1996), Encyclopedia of climate and weather 2, New York: Oxford University Press, pp. 817–823 ).
  15. ^ Robert L. Park (2008), Superstition: Belief in the Age of Science, Princeton University Press, pp. 145–146, ISBN 0-691-13355-7 
  16. ^ Review, critique, and guidelines for the use of herbs and homeopathy, James Glisson, Rebecca Crawford and Shannon Street, Nurse Practitioner, April 1999.
  17. ^ An Open Letter to ABC News 20/20 with Barbara Walters and John Stossel
  18. ^ Assuming an Olympic swimming pool contains 2.5 × 106 liters of water, there are about 8.3403 × 1031 molecules of water in an Olympic swimming pool.
  19. ^ Section 5.3, Beginning Algebra, 10/E, Margaret L. Lial, John Hornsby, Terry McGinnis, Addison-Wesley, Copyright: 2008, Published: 01/02/2007, ISBN 0-321-43726-8
  20. ^ The description in the algebra textbook suggests that there are about 100 molecules of therapeutic material remaining in the pool after 15C dilution, which is a reasonable assumption. However, the textbook incorrectly states that to expect to consume one molecule of the original substance, a person has to imbibe 1% of the pool's volume. Unfortunately, this claim is somewhat careless about probabilities; for example, to have a 95% probability of ingesting at least one molecule of the original material, a person has to drink about 3% of the pool, or about 75 metric tons of water (assuming that after dilution, 100 molecules of the original material remain). In general, consuming a fraction r of N molecules leads to a probability of approximately 1 − enr of consuming at least one of the n molecules of the original substance, where N is assumed to be a large number. A 15C dilution prepared using one liter of original substance will produce a volume-volume concentration of 10−30 liters of original material per liter of diluent, or 10−27 milliliters of original substance per liter of diluent. In a 2.5×106 liter pool, there is therefore 2.5 × 10−21 milliliters of original material. If the original material has a molar mass of M (in grams/mole) and a density of D (in grams/ml), then there will be 2.5 × 10−21 D/M moles of original material in the pool, or n=1505.535 D/M molecules of the original material. The textbook example assumes that D/M of the original material is about 0.0664 (for comparison, water has a value of D/M of about 0.0554).
  21. ^ a b "Dynamization and Dilution". Retrieved 2007-07-24. 
  22. ^ Resch, G; Gutmann, V (1987), Scientific Foundations of Homoeopathy, Barthel & Barthel Publishing 
  23. ^ "When to believe the unbelievable", Nature 333 (6176), 1988: 787, Bibcode:1988Natur.333Q.787., doi:10.1038/333787a0, PMID 3386722 
  24. ^ Maddox, J.; Randi, J.; Stewart, W. (1988). ""High-dilution" experiments a delusion". Nature 334 (6180): 287–291. Bibcode:1988Natur.334..287M. doi:10.1038/334287a0. PMID 2455869.  edit
  25. ^ Sullivan W (1988-07-27), "Water That Has a Memory? Skeptics Win Second Round", The New York Times, retrieved 2007-10-03 
  26. ^ Rey, Louis. "Thermoluminescence of ultra-high dilutions of lithium chloride and sodium chloride". Physica A: Statistical Mechanics and its Applications 323: 67–74. doi:10.1016/S0378-4371(03)00047-5. 
  27. ^ Milgrom, Lionel (11 June 2003). "Icy claim that water has memory". New Scientist. Retrieved 11 October 2014. 
  28. ^ Wheeler CE (1941), Dr. Hughes: Recollections of some masters of homeopathy, Health through homeopathy .
  29. ^ Bodman F (1970), The Richard Hughes memorial lecture, BHJ, pp. 179–193 .
  30. ^ "HeadOn: Headache drug lacks clinical data", ConsumerReportsHealth.org, Consumers Union, retrieved 2009-03-25 .
  31. ^ "Analysis of Head On", James Randi's Swift, retrieved 2006-07-27 .