September 2010|Vol 7|Issue 9

September 2010 | Volume 7 | Issue 9


Challenges on the Law of Infinitesimals


Dr.Smita Brahmachari
A/L-177 Vimatangi
Kapil Prasad, P.O. Old Town
Bhubaneswar,Orissa, Pin: 751002
Mobile: 9178738156

    Abstract :
        The Paper aims at considering all important aspects of the scientific framework of homoeopathic practice, looking at the levels of scientific evidence of high dilutions in an objective way, through an extensive review of literature. It will provide scientific explanation of the action of high potency homoeopathic remedies having no molecule of the original drug in the prescribed dose to the patient. It will thus establish the fact that Homoeopathy has been wrongly disregarded as ‘unscientific and placebo therapy’ largely because of the conceptual inadequacy of the contemporary science. Conclusions are clear: Homeopathy must stay within the framework of medical practice, and it is even a necessity for public health.

        The infinitesimal homoeopathic doses always remain the point of controversy since its inception as they cannot be measured by the present scientific instruments and techniques and on the basis of Avogadro’s number, the presence of material in the homoeopathic medicine beyond the molar concentration 10 or 12 becomes negative. Homoeopathy is closely associated in the public mind with the supposedly “illogical” principle that the power of a medicine increases with dilution and with the corollary of this principle: that the greatest power is to be found in the small or infinitesimal dose. These have been major points of criticism by the non-homoeopathic physicians. More recently the most reputed medical journal ‘Lancet’ published a controversial article in its Volume 366 August 27th, 2005, “Are the clinical effects of Homoeopathy Placebo effects? Comparative study of placebo controlled trials of Homoeopathy and Allopathy” by Aijing Shang et al. This is just an example particularly at a time when there is a paradigm shift from the conventional therapy to Homoeopathy, owing to its low-cost, harmless and effective medicine. Let us clear the point of controversy step wise.


    1. Evidence for the infinitesimal dose
        The “infinitesimal” dose was only an empirical discovery by Hahnemann. When he administered medicines according to the law of similars, he found that the patients reacted very violently and he reduced his doses in order to moderate the patient’s reaction. Allopathic medicine should not be amazed at the homoeopathic small doses, since the power of minute quantities is recognized today outside homoeopathy as well as inside it. A milligram of acetylcholine dissolved in 500,000 gallons of blood can lower the blood pressure of a cat; even smaller amounts will affect the beat of a frog’s heart1. Florey reported in 1943 that pure penicillin will inhibit the development of sensitive microbes in vitro at dilutions of 1:50,000,000 to 1:100,000,000; morphological effects on streptococci were seen at dilutions of 1:250, 000,000. Zinsser found that sensitization could be achieved with 1/1,000,000 of a cc of horse serum, and smaller quantities of egg albumin. The human body manufactures 50-100 millionths of a gram of thyroid hormone per day, and the concentration of free thyroid hormone in the normal blood is one part per 10,000 million parts of blood plasma.
    Hahnemann was a contemporary of Amadeo Avogadro who discovered that the number of molecules in one mole of any substance is 6.0253 × 1023. Once the existence of this Avogadro constant had penetrated the medical consciousness, orthodox physicians turned from the criticism of the homoeopathic small doses to criticism of ultra molecular dose, since it became clear that medicines diluted beyond 10-23 i.e., the 12C or 24X dilutions – fell outside the range within which it could be expected that single molecule of the original medicinal substance remained in the dilution.

    2. Biochemical Investigations
        The most striking experiment conducted under homoeopathic auspices to demonstrate the power of the “high dilutions” was that of William Boyd in Edinburgh, published in 1954. In the early 1930’s V.M.Persson in Leningrad had investigated micro dilutions (upto 120X) of mercuric chloride for their effect on the fermentation of starch by salivary amylase and on the lysis of fibrin by pepsin and trypsin, obtaining significant results in controlled studies. In 1933 he repeated the experiments and published new confirmatory observations. The purpose of Boyd’s experiment was to confirm Persson’s results. The micro dilutions used were mercuric chloride 61X (10-61) which, by the present physical theory, should contain no molecules of the original mercuric chloride but only distilled water as diluents. The experiment showed that addition of mercuric chloride 61X accelerated the rate of hydrolysis of starch with diastase, studied colorimetrically with an absorptiometer, and since the results showed biological scatter, the frequencies of the differences were analysed statistically which showed statistically significant results. Boyd conducted more than 500 comparisons, in several series from 1946 to 1952. Analysis was done by independent statisticians who reported that they showed significance (P less than 0.001). The outcome of this experiment was reported in The Pharmaceutical Journal (September 11, 1954). Reports also appeared in British newspapers.

    3. Botanical Investigations
        i) Kolisko, in 1932, soaked wheat seeds and others in micro dilutions (upto 10-30) of such substances as iron sulphate, antimony trioxide and a double salt of copper, found that growth was promoted by lower dilutions, then inhibited with higher dilutions, and then again stimulated at even higher dilutions. A full report of her experiments was published in 1959.

    ii) Joseph Roy, in 1932, made micro dilutions of barley stems, the soaked barley seeds in these dilutions before planting them. He found that the 3C, 6C, 9C, 12C, and 18C microdilutions each gave a different weight of barley shoots as compared with the controls.

    iii) Netien, Boiron and Marin performed experiment with pea plants impregnated with copper sulphate, showing that addition of copper sulphate micro dilutions to the growth medium intensified the excretions of copper by the plants.

    iv) Wannamaker performed experiment measuring the effect of boron micro dilutions on onion growth. She concluded that the weight and length of the plants are affected, as well as their boron and sulphur contents.

    4. Bacteriological Investigations
    i) H. Junker investigated the effect of various micro dilutions on paramecia cultures. He added micro dilutions, upto 10-27 of atrophine sulphate, caffeine, acetic acid, uric acid etc., and found that differences measured in terms of daily changes in the growth of each paramecia culture in the function of the degree of dilutions of the substance added – took the typical sinusoidal form found by other investigators.

    ii) Patterson and Boyd in 1941 reported alteration of the Schick test from positive to negative following per oral administration of alum precipitated toxoid 30C or Diphtherinum 201C (made from diphtheria bacillus).

    5. Zoological Investigations
    i) Stearns, in 1925, added arsenic trioxide (Arsenicum album), mercuric nitrate and triturated tumor material, in microdilutions of from 6X to 400X, to cultures of Drosophila melanogaster (fruit flies) of a strain in which approximately half of all males died of an inherited tumor. Addition of microdilution caused a reduction in the male death rate from inherited tumor, the difference being 4 times greater than in controls.

    ii) In 1951 Jarricot reported success in experiments altering neuromuscular excitability of isolated frog and turtle heart through perfusion with 18C to 118C dilutions of Iberis Amara and the 60X dilution of Veratrine sulphate.

    iii) Julian and Launay were able to inhibit and modify the effects of a physiologic dose of reserpine (in mice) by the preliminary 7C and 9C injections of Rauwolfia serpentine. The same experiment was performed successfully with Cicuta virosa.

    iv) In 1976 Van Mansvelt and Amons reported on the effect of mercuric chloride, at dilutions as low as 0.9 × 10-25, on the proliferation of a mouse lymphoblastic strain; growth inhibitor was detected down to a level of 0.9 × 10-17 but the curve instead of being flat as expected, had peaks of toxicity at 10-5, 10-6, 10-16, and 10-17. The author explains this substantial indication towards unconceived phenomenon which needs further study.

    6. Investigations using the techniques of Physics
        Wurmser and Loch in 1948 investigated the effect of micro dilutions on the wavelength and intensity of light from a fixed source. They filtered the light to permit passage of wavelengths from 3800 to 4200 A; this was passed through a receptacle filled with solution, changes being registered by a photoelectric cell. They found measurable changes for quinine sulphate, Taraxacum and Aesculus hippocastanum at dilutions from 24X to 30X.
    It is needless to argue on the issue that effects of homoeopathic medicines are not placebo response. These medicines act favourably, as evident from some of the following Research reports of the highest scientific standards published in the medical journals of international repute during the last two decades

    1. Three Orthodox Scientists J.Klijnen et al. published their review of homoeopathic clinical research with conclusion, “The amount of positive evidence even among the best studies came as a surprise to us. Based on this evidence we would readily accept that homoeopathy can be efficacious, if only the mechanism of action were more plausible”.

    2. The final report “COST Action B4 Unconventional Medicine”(1999) and its supplement submitted to the European Commission concerning use and development of Complementary and Alternative Medicine, states that the available clinical trial evidence suggests that homoeopathy has an effect greater than placebo.

    3. A multicentric trial in four independent laboratories in four different European countries in 1999 showed that higher dilutions of histamine inhibit anti-IgE induced basophil degranulation. The results showed statistically significant inhibition.

    4. A Randomized Double Blind Placebo Controlled Trial conducted by CCRH under the Dept. of AYUSH, Govt. of India of homoeopathy medicine in HIV infection showed statistically significant increase in CD4 T-cell count in medicine group in comparison to the placebo group.

    5. M. Taylor et al. at the University of Glasgow while performing a meta-analysis of all the data from four studies on allergic conditions, found the results so significant (P=0.0004) that they concluded either homoeopathic medicines work or controlled trials do not. Since modern science is based on controlled trials, it is more likely a conclusion that the homoeopathic medicines are effective.

        The recent research report to be added in this list is Jonathan Leake, A Nobel laureate who discovered the link between HIV and AIDS has suggested there could be a firm scientific foundation for homoeopathy. Professor Luc Montagnier, a French virologist, stunned his colleagues at a prestigious international conference when he presented a new method for detecting viral infections which bore close parallels to the basic tenets of Homoeopathy. Although fellow Nobel Prize winners who view Homoeopathy as quackery were left shaking their heads, Montagniers comments were rapidly embraced by homoeopaths in UK eager for greater credibility. Montagnier told the conference that solutions containing DNA of pathogenic bacteria and viruses, including HIV, could emit low frequency radio waves that induced surrounding water molecules to become arranged into nanostructures. These water molecules, he said, could also emit radio waves. He suggested that water could retain such properties even after the original solutions were massively diluted, to the point where the original DNA had effectively vanished. In this way, he suggested, water could retain the memory of substances with which it had been in contact - and doctors could use the emissions to detect disease. For the lay person such claims may sound technical but uncontroversial. For scientists they are highly provocative because they embody principles which are extremely similar to those said to underpin homoeopathy. Homoeopathic medicines work on the principle that a toxic substance taken in minute amounts will cure same symptoms that it would cause if it were taken in large amounts.

        Montagnier’s claims come at a sensitive time, with British Medical Associations annual conference last week calling for the National Health Service to stop spending 4million a year on Homoeopathy.

        One more research paper I want to present before the readers which appeared in the esteemed newspaper Hindu 11th July 2010 edition that is Homoeopathic medicine Belladonna is effective in preventing Japanese Encephalitis (JE). A recent study conducted by the Kolkata-based School of Tropical Medicine has shown. Belladonna is derived from a plant A.belladonna which is also source of the drug atropine. Conducted in collaboration with the Central Council for Research in Homoeopathy (CCRH) under the Department of AYUSH, researchers claim to have found a probable role for Belladonna in preventing JE virus infection. The results of the study are published in the latest issue of the American Journal of Infectious Diseases. The outcome of the study was presented by Principal Investigator Bhaswati Bandopadhyay, Assistant Professor of Virology at the Clinical Virology Symposium, in April last year at Florida. Japanese Encephalitis presents a significant risk to humans and animals, particularly in South East Asia (including India) where around 50,000 cases and 10,000 deaths occur per year, particularly affecting children below 10 years. The statistics reveal that about 50 per cent of the patients who develop JE suffer from permanent neurological defects and 30 per cent of them die due to the disease

        The lists of scientific evidences speaking in favour of homoeopathy are endless. But it is important for all of us to work more meticulously with great zeal, dogged determination, commitment to establish Homoeopathic system as the first choice of treatment option and perseverance, on scientific parameters, without jeopardizing the tenets of Homoeopathy, so that our studies leave no gaps when such analyses are repeated.

    1. Science 72 (1930), 526.
    2. British Medical Journal, 1943 (ii), 634.
    3. Zinsser, Enders, Fothergill, op. cit., 344.
    4. Starling and Lovatt Evans, op. cit., 1493-94.
    5. W.E. Boyd, “Biochemical and Biological Evidence of the Activity of High Potencies” British Homoeopathic Journal, 1954.
    6. W.M. Persson, “The Principle of Catalysis in Biochemistry and Homoeopathy”, Journal of the American Institute of Homoeopathy 23 (1930), 1055-1090.
    7. W.M. Persson, “Effects of very small amounts of Medicaments and chemicals on Urease, Diastase and Trypsin”, Archives International de Pharmacodynamic et de Therapie 46 (1933), 249-267.
    8. L. Kolisko, Physiologischer and Physikalischer Nachweis der Wirkasamkeit kleinster Entitaeten, 1923 -1959.
    9. Joseph Roy, “La Dilution Homoeopathique, sa Justification Experimentelle”, Le Bulletin Medical 46 (1932), 528-31.
    10. Hermann Junker, “Die Wirkung extremer Potenzverduennungen auf Organismen”, Pflueger’s Archiv 219 (1928), 647-72.
    11. Paterson and W.E.Boyd, “A Preliminary test of the Alternation of the Schick test by a Homoeopathic Potency”, British Homoeopathic Journal 31 (1941), 28-29.
    12. G.B.Stearns, “Experiments with Homoeopathic Potentised Substances Given to Drosophila Melanogaster with Hereditary tumours”, The Homoeopathic Recorder 40 (1925).
    13. J.Jarricot, L’Infinitesimal des Homoepathes (Lyon: Editions des Laboratoires P.H.R., 1951).
    14. O.A.Julian and J.Launay, “Psycho-Pathological Test on Animals by Reserpine and Cicuta virosa, According to the Homoeopathic Laws of Analogy and Identity,” Journal of the American Institute of Homoeopathy 59 (1966), 155-64.
    15. James Stephenson, “A Review of Investigations into the action of substances in dilutions greater than 1×10-24 micro dilutions” Journal of the American Institute of Homoeopathy 48 (1955) 327 - 335.
    16. Klienjen et al., “Clinical trials of Homoeopathy” British Medical Journal, Vol.302, Feb. 1991, 316-323.
    17. European Commission, Directorate – General Science Research and Development: COST Action B4, Unconventional Medicine, Final Report of the Management Committee 1993-1998.
    18. Belon al. Inhibition of human basophil degranulation by successive histamine dilutions results of a European multicentre trial, Inflammation research 48, Supplement 1 (1999) S17 – S18.
    19.,134 ,
    20. http://www.thehindu .com/todays- paper/tp- national/ article510105. ece,.