Homeopathy ‘research’: scienciness sans science – Part Un (dilutions)

The “alternative medicine” modality called homeopathy is popular in some parts of the world, especially some European countries (including Germany, where it was invented in the late 18th century; France; the UK), and in India and its neighbors in the subcontinent. Many Indian homeopaths are well-known amongst the global homeopathy-aficionado community, and there were over 250,000 registered homeopaths in India in 2010 – which is not surprising, considering that homeopathy enjoys official government patronage in India and is recognized as a valid system of medicine in that nation.

Long-time readers of this blog are aware of my views on homeopathy; let me say it again categorically: homeopathy is bunkum, quackery, sham, and nonsense, a pretend-medicine, or medicine-wannabe. There is zero physiological basis behind the principle of homeopathy, zero physico-chemical basis behind homeopathy formulations, and zero systematic evidence of its efficacy. And yet, it seems to enjoy wide popularity in more than 60 different countries of the world, and people anecdotally claim to feel better after seeing a homeopath for treatment. Professor Edzard Ernst, a former homeopath, has written extensively (and still does) on this phenomenon, for which ancillary explanations such as confirmation bias, placebo effect, and so forth have been proposed.

Why – you may well ask – am I so adamant that homeopathy is nonsense? It is because, above all, homeopathic formulations – sometimes referred to as “serially diluted and agitated (SAD) drugs” – are physico-chemically implausible. Let me explain, in the next few paragraphs, how homeopathic dilutions attempt to defy the fundamental laws of physics and chemistry.

Substances are made of units such as molecules, atoms or charged ions depending upon their nature. A mole of such a substance is a fundamental quantity that is related to the atomic or molecular mass of the substance. A mole of any substance contains a fixed number of those units, and that number is called the Avogadro number, roughly equal to 6.02 x 1023 (“roughly”, because I have shortened the decimals for simplicity). For example, atomic mass of Carbon is 12; one mole of Carbon-12, containing 12 grams of carbon, consists of 6.02 x 1023 carbon atoms. One mole of Oxygen, which has a greater mass than carbon at 16, contains 16 grams of oxygen, made up with the same 6.02 x 1023 oxygen atoms. The Avogadro number (or the related Avogadro Constant) is one of the fundamental properties of matter. One mole of any substance made of multiple atoms and molecules will have a mass that is a sum total of the masses of the constituent atoms and molecules, and will contain 6.02 x 1023 units.

Now consider the process of dilution. Say 1 gram (gm) of a substance is measured, and put in 1 liter (L) of water, yielding a concentration of 1 gm/L. Once the substance completely dissolves in the water, its molecules are dispersed evenly amongst the molecules of water. At this point, if 10 milliliters (i.e. a smaller volume that is only 1/100th of the original volume) of that solution is taken out, by mathematical probability that smaller volume will contain a proportionately smaller amount of the substance, 1/100th of a gram, or 10 milligram (mg). Now, consider that this small volume (10 ml) is put in another container of water that contains 990 ml of fresh water, so that the final volume in container 2 becomes 990 + 10 = 1000 ml (or 1 liter). However, the amount of the substance that was transferred from the first container to the second is the 10 mg that came out with the 10 ml. The resultant concentration of the substance in the container 2, therefore, is 10 mg in 1 L, or 10 mg/L. This is called a hundred-fold, or 1:100 dilution (1 gm/L, which is same as 1000 mg/L original » 10 mg/L).

If the same process is repeated from the second container to a third, from the third to a fourth, and so forth, this is called a serial dilution, and in this case, a serial hundred-fold dilution. Similarly, it is possible to do a ten-fold or 1:10 serial dilution, in which each the substance in each container is 10-times more concentrated than in the next one. As one can understand, with each dilution, the amount of the substance in the resultant solution continues to decrease proportionally. Let me illustrate this with a blue dye, which I serially dilute in water.

dilution effects on dye

When the amount of substance gradually decreases, it doesn’t require a stretch of imagination to understand that the number of fundamental units that make up that substance also decreases. In the above example, let’s consider a hypothetical substance whose molecular weight expressed in grams is 10 gms. So 10 gms of the substance represents a mole of it, and contains 6.02 x 1023 molecules. If these 10 gms are dissolved in 1 L of water, the concentration is 10 gm/L. A 10-fold serial dilution of this solution would produce, sequentially, solutions of concentration 1 gm/L, 100 mg/L, 10 mg/L, 1 mg/L, 100 microgram (µg)/L, and so forth. Therefore, the number of molecules of the substance present in the successive solutions would decrease by the same proportion, as 6.02 x 1022 (in 1 gm/L), 6.02 x 1021 (in 100 mg/L), down to 6.02 x 1018 molecules (in 100 µg/L), and further. It’s a simple mathematical progression.

It’s easy to see how, after the 22nd ten-fold dilution in series (10-22 dilution), the 23rd solution would contain only about 6 molecules. If the dilutions are carried on further, from the 24th solution onwards, the mathematical probability of finding even 1 molecule of the original substance in the solution becomes small, tending to zero (60, 6, and 0.6% probability at, respectively, 10-24, 10-25, and 10-26). Similarly, if 100-fold serial dilutions are carried on, after the 11th dilution (100-11 dilution), the 12th (as well as any subsequent) solution likely contains none of the original substance, and the probability of finding one molecule is rapidly reduced (60, and 0.6% probability at, respectively, 100-12, and 100-13).

The so-called SAD drugs used in homeopathy frequently breach this limit set by the Avogadro number. Ten-fold serial dilutions are designated ‘X’, and 100-fold dilutions, ‘C’, in homeopathy. Using these designations, any dilution of a drug-like substance beyond 22X or 11C cannot possibly contain even a single unit of the substance. And yet, in homeopathic practice, it is quite common to encounter dilutions such as 30X, 30C, 200X, 200C and so forth.

Therefore, even if one sets out at the beginning with medicinally-active, valid herbally-sourced substances, at the end of the SAD process, nothing of those substances can remain. It is important to understand this distinction, because homeopathic preparations deliberately use the name of the corresponding herb or a mineral substance or organic material – producing a false projection that they are imbued with putative pharmacological properties of such herbs or minerals or organic product. For example, see homeopathic preparation Digitalis purpurea (purportedly related to the eponymous Foxglove plant), Ferrum Phos (purportedly related to Ferrous or ferric phosphate, an Iron-containing salt of phosphoric acid), Apis Mel (purportedly related to the sting venom of Apis mellifera, the European honeybee), and so forth.

It is not that most homeopaths don’t know about this theoretical limit. But in order to explain this magical system of ‘alternative medicine’, modern homeopaths have invented science-y sounding terms like “super-Avogadro dilutions” or “ultradilutions”, and so forth, and for the longest time, homeopathy aficionados, especially in countries endemic for homeopathy, have been trying to show that something of the drug – some impression, perhaps – is retained in these dilutions that go well beyond the Avogadro limit.

I recently stumbled across few such papers which represent such efforts. The claims therein were pretty tall, and prodigious use of scientific terms and concepts introduced just the right degree of scienciness into the texts; but sadly, the science therein, without fail, appeared to be quite sketchy. If I get enough time, I shall try to discuss the scientific contents of a few of these papers. Watch this space.


  1. Mona Albano

    I look forward to it!

    Your explanation is very clear and the small, small steps should help people to understand. I have this argument with my friend: she says it’s like vaccination, using just a small amount. I tell her that in vaccination you do have a couple of micrograms of the antigen to work with, not the magical memory of the last molecule!

    • Kausik Datta

      Thank you, Mona. The purported similarity between homeopathy and vaccination is often a deliberate misrepresentation pushed by… you guessed it, homeopaths. But as you have correctly indicated, homeopathy is ‘not just a small amount’; it’s actually no amount, for the majority of the dilutions at which their preparations are sold and used. The link to the second essay in this series is HERE; hope you like it.

  2. SavvySkeptic

    The article is extremely well researched.

    Part Un – is focused on the concepts on homeopathy. The author has carefully explained why scientific community thinks homeopathy is bunkum, quackery, sham, and nonsense, a pretend-medicine, or medicine-wannabe. The explanation is accessible to a common man as well.

    Part Deux – I loved this. This is an in-depth analysis of a paper that was published out of research at IIT Kharagpur, India. This paper has been used by homeopaths in India to claim that research at IITs endorse homeopathy. In India, this single paper has done so much harm. Author has shown how the game is played and sciency words are introduced in research papers on homeopathy.

    The fact this sort of poor quality paper got through peer review raises concerns about the peer review system. More importantly, it raises concerns about level of research in India, if prestigious institutes like IITs engage in such poor quality work which is not only bad science but in a country like India has very bad social impact as well.

    I will forward the articles to relevant people at IITs and try to elicit a response.

    • Kausik Datta

      Thank you for your kind comments. This is the third (or fourth) paper published based on work done at an IIT. IITs are prestigious educational institutions, but their focus is more on engineering and technology – which is perhaps why the basic science research work done therein sometimes turns out to be sub-par. This, unfortunately, tarnishes the image of scientific research done elsewhere in the country.

  3. tibetti

    If something is crap then that allopath and the crimal nexus between allopath and pharma industry.
    No amount of stupid articles like the one u wrote will help you allopaths, dogmatic thinking does not help. Curing is more important through any branch of medicine either Ayurved, homeopathy TMI etc etc.
    Mine is bigger than urs attitude wont help 🙂

    Raymond Rice, Gerson list goes on and on, shows true colors of the allopath doctor and pharma industry criminal nexus.

    • Kausik Datta

      So, in other words, you have nothing substantial to address the basic questions I raised, and yet you decided to parrot some bog-standard altmed aficionado lines nonetheless. Typical.

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