Homoeopathy is a field of alternative medicine based on the belief that highly diluted ingredients which cause certain symptoms in healthy individuals will cure those symptoms in sick ones. Some common homoeopathic remedies include arsenic for diarrhoea, anthrax for acne and duck liver for colds and flu. To remove the risk of poisoning or even killing patients, the remedies available for sale in pharmacies have been prepared by repeatedly diluting and shaking the mixture with water between each stage of dilution, to the point where not only the toxicity, but in many cases even the last remaining molecule of the active ingredient disappears completely. Homoeopathic drops and pills are therefore likely to contain only the solvent (mostly water) and sometimes sugar or the ‘carrier’ substance in the case of tablets. For this very reason, homoeopathic remedies are often not controlled and tested for safety like real evidence-based medicine, which occasionally allows a potentially dangerous substance to slip through the cracks of general ignorance.
Homoeopaths freely admit to these facts, but for very obvious financial reasons you are not likely to find it explicitly spelled out like that on the little boxes and bottles of water and sugar-pills for sale as ‘medicine’ at your local pharmacy. Instead, they use a special notation for the dilution factor next to the active ingredients (which are almost always described in Latin), which is likely to be seen as just another complex chemical term or symbol by average users.
Very, very few people who see the words Anas Barbariae Hepatis et Cordis Extractum 200CK on their flu ‘medicine’ will know that it means a homoeopath took some duck liver and heart extract, mixed it with 100 times as much water, emptied the container of 99% of its content, filled it up with water again, threw out 99%, filled it up with water and then repeated this process 197 more times, before finally taking the by then pure water left in the container after the 200th step, and selling it as something that will cure colds and flu. Oh, and don’t forget that the container was shaken during each step. So, not only was the original ingredient a disgusting medieval witches’ brew of duck innards, but ironically the final product people pay for does not contain anything but water or inert carrier material.
Given the Latin names and cryptic dilution shorthand, it’s almost as if homoeopaths are trying to hide something, isn’t it? When pressed to explain the supposed healing mechanism that pure water will have for anything from dandruff to AIDS, they will revert to waffling about healing spirits and scientifically invisible ‘energies’ that their shaking is supposed to charge the water with. Natura South Africa even states flat-out (my bold) on their website that:
The remedy is prepared by repeatedly diluting and succussing (shaking) the substance between each stage of dilution. This process is known as ‘potentisation’. After each stage of dilution, the remedy becomes less chemically active and more energetically active. Eventually the remedy will contain no molecules of the original substance and will only be energetically active.
No further explanation is given for ‘energetically active’ water, and naive readers will be mislead into thinking that it is an accepted relevant scientific term. This method is almost identical to that described by an 18th century physician named Samuel Hahnemann, who invented homoeopathy based on a single atypical reaction when he developed fever after taking some quinine. Homoeopathy is considered quackery or pseudoscience by mainstream medical science, and this post is an attempt to explain the reasons for this skepticism without citing the usual credible medical research that can find no differences between the effects of homoeopathic remedies and placebo.
Instead, my purpose is to put the incredible effects of serial dilution into perspective by computing the size of a gel capsule needed to deliver just one molecule of the original ingredient in some commonly available homoeopathic remedies. I recently had an argument about homoeopathy with a friend who claimed to have taken a popular homoeopathic flu remedy called Oscillococcinum. When I told him that he actually took only pure water, he insisted that I must be wrong, since the packaging clearly shows Anas Barbariae Hepatis et Cordis Extractum 200CK as the active ingredient. Like so many others, he had been mislead by packaging that mimics real medicine, and although this post wont convince any homoeopaths that their claims are just wishful thinking with some water, it may surprise a few people who thought they knew what they were paying for.
After some mildly interesting maths and a little first-year chemistry, I was able to derive the following formula for the length of a standard-proportion gel capsule in metres, given the factor used to dilute the original substance in X-notation.
Results
| Dilution Factor | Length of gel capsule required to deliver 1 molecule of the active ingredient |
Comparable to |
| X24 (C12) | 7.49 cm | A Bic cigarette lighter. |
| X30 (C15) | 7.49 m | Roughly the size of a large fuel lorry tank. ![]() |
| X60 (C30) | 74899919 km | About half the distance between the Earth and the Sun.![]() |
| X400 (C200) | More than a long scale billion billion billion billion billion billion billion billion times the size of the observable universe.![]() |
The last dilution factor is used for Oscillococcinum, sold by a company called Boiron. It is made from duck livers and hearts (at least it starts off with that), and has been the topic of a very interesting study undertaken by the Cochrane collaboration. The section “Risk of bias in included studies” in that document is typical of homoeopathic studies that claim to show results better than placebo – shoddy methodology, small sample sizes and other statistical tricks used to skew results.
These results should speak for themselves; homoeopathic remedies at these dilution factors contain nothing but water, and any claims about efficacy made by true believers can only be the result of simple placebo or confirmation bias due to regression to the mean, i.e. getting better like they would have even if they had not taken the homoeopathic water. The ‘healing energy’ or ‘healing spirits’ claimed by homoeopaths can not be measured, and probably does not exist.
For anyone interested in checking my maths, feel free to read on.









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