Homeopathy 2007; 96(03): 202-208
DOI: 10.1016/j.homp.2007.03.008
Copyright © The Faculty of Homeopathy 2007

The octave potencies convention: a mathematical model of dilution and succussion

David J. Anick

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Further Information

Publication History

Received22 February 2007

accepted27 March 2007

Publication Date:
13 December 2017 (online)

Several hypothesized explanations for homeopathy posit that remedies contain a concentration of discrete information-carrying units, such as water clusters, nano-bubbles, or silicates. For any such explanation to be sustainable, dilution must reduce and succussion must restore the concentration of these units. Succussion can be modeled by a logistic equation, which leads to mathematical relationships involving the maximum concentration, the average growth of information-carrying units rate per succussion stroke, the number of succussion strokes, and the dilution factor (x, c, or LM). When multiple species of information-carrying units are present, the fastest-growing species will eventually come to dominate, as the potency is increased.

An analogy is explored between iterated cycles dilution and succussion, in making homeopathic remedies, and iterated cycles of reseeding and growth, in bacterial cultures. Drawing on this analogy, the active ingredients in low and medium potency remedies may be present at early dilutions but only gradually come to ‘dominate’, while high potencies may develop from the occurrence of low-probability but faster-growing ‘mutations.’ Conclusions from this model include: ‘x’ and ‘c’ potencies are best compared by the amount of dilution, not the amount of succussion; the minimum number of succussion strokes needed per cycle is proportional to the logarithm of the dilution factor; and a plausible interpretation of why potencies at approximately regular ratios are traditionally used (the octave potencies convention).

  • References

  • 1 Anick D.J. Stable Zwitterionic water clusters: the active ingredient in homeopathy?. J Am Inst Homeop. 1999; 93: 129-135.
  • 2 in: Schulte J., Endler P.C. Ultra High Dilution. 1994. Dordrecht: Kluwer Academic Publishers;
  • 3 Roy R., Tiller W.A., Bell I., Hoover M.R. The structure of liquid water; novel insights from materials research; potential relevance to homeopathy. Mater Res Innovation 2005 09/04 93-124.
  • [4] Anick D.J., Ives J.A. The silica hypothesis for homeopathy: physical chemistry. Homeopathy 2007; 96: 189-195.
  • 5 Hahnemann S. Organon of Medicine. Fifth and sixth editions. New Delhi: Jain Publ. Pvt. Ltd.; reprinted 1995 (transl: Dudgeon RE and Boericke W).
  • 6 Edelstein-Keshet L. Mathematical models in biology. SIAM Classics Appl Math 2004; 46.
  • [7] Bhatia M. Homeopathic Potency Selection. Hpathy Ezine, April 2004: ⟨http://www.hpathy.com/philosophy/bhatia-potency-selection2.asp⟩.
  • [8] Thomas AL, Homeopathic Posology. Similima 18: ⟨http://www.similima.com/org18.html⟩.
  • 9 Demangeat J.-L., Gries P., Poitevin B., Droesbeke J.-J. et al. Low-field NMR water proton longitudinal relaxation in ultrahighly diluted aqueous solutions of silica-lactose prepared in glass material for pharmaceutical use. Appl Magn Reson 2004; 26: 465-481.
  • 10 Walach H., Jonas W.B., Ives J. et al. Research on homeopathy: state of the art. J Alternative Complementary Med 2005; 11: 813-829.
  • 11 Webb G.F., Blaser M.J. Dynamics of bacterial phenotype selection in a colonized host. Proc Natl Acad Sci USA 2002; 99: 3135-3140.
  • 12 Milgrom L.R. Are randomized controlled trials (RCTs) redundant for testing the efficacy of homeopathy? A critique of RCT methodology based on entanglement theory. J Alternative Complementary Med 2005; 11: 831-838.