Homeopathic Dilutions

Much Ado About Nothing

After realising that giving sick people substances that caused the very symptoms he was trying to cure, Hahnemann realised that something needed to change. Instead of deciding that his principle of “like cures like” was perhaps wrong, Hahnemann decided that instead what he needed to do was dilute his remedies.

Hahnemann went further than simple dilution, however. His idea involved serial dilutions, with each step punctuated by a vigorous shaking of the dilution container. According to Hahnemann this shaking, known as “succussion”, would activate the “vital energy” of the substance1. It is here that homeopathy essentially became magic.

According to homeopathy, this process of serial dilution and succussion would prevent a substance from causing the symptoms that it could be expected to cause when given to a healthy person but still allow it to cure those symptoms via the (incorrect) principle of “like cures like”.

The claim becomes even more scandalous when you realise just how far homeopathic remedies are diluted. Each step of a serial dilution is generally a dilution of 1 in 10 or 1 in 100. The number of steps, size of each step and sometimes the method used are labelled on the remedy. The number of steps comes first, followed by the size of each step represented by a roman numeral. For example, a dilution of 30C (a common homeopathic dilution) consists of 30 steps of a 1 in 100 dilution.

Let me say that again. A common homeopathic dilution involves diluting the original substance by 1 in 100 30 times. As an example, let’s imagine a homeopathic dilution of gold (which was one of the common remedies listed on ABC Homeopathy – listed as “Aurum Metallicum”), starting with an enormous but simple amount of one mole. From Avogadro’s constant, which was unknown during homeopathy’s inception, we know the number of atoms or molecules in one mole. For gold, this amount would weigh about 200g; if it were a cube would be just over 2cm across.

After 10 dilutions of 1 in 100, we would expect to have just over 6000 atoms remaining. After 12 dilutions, we’re almost just as likely to have a single atom left as we are to have none at all. After all 30 dilutions, the probability that there is even a single atom remaining is astronomically low. So low, in fact, that for all intents and purposes it should be considered to be 0.

Now, let’s take another approach to our thought experiment. We know that the total number of atoms in the visible universe is likely to be somewhere between 1078 and 1082. Taking the liberal estimate of 1082, we can estimate the same dilution of 30 serial dilutions of 1 in 100 on the entire known universe. At the end, we would expect to have around 1022 atoms left, which is about 1/60th of 1 mol – the number of molecules in 0.3 mL of water. And that’s from the entire universe! Homeopathic dilutions that go so far as 200C are far from unheard of, either.

The idea that homeopathic remedies supposedly become stronger as they become more diluted (when dilution is accompanied by succussion) goes directly against the dose-response relationship. There has never been a plausible mechanism put forth by which shaking a solution can impart any properties of the diluted substance to the diluent. What’s more, the claim that such a phenomenon exists at all has not held up to rigorous scientific testing.

However, the fact that homeopathic remedies rarely contain any of the original active ingredient likely won’t bother many homeopaths. The reason for this is that, supposedly, the act of succussion at each dilution step “releases and concentrates the spirit-like, healing essence of the substance derived from its animal, botanical or mineral source”1. Basically, this process of “Dynamization” removes all material trace of the original medicinal substance and leaves behind only its “spirit-like, healing essence”. To quote Hahnemann himself2:

The homœopathic healing art develops for its purposes the immaterial (dynamic) virtues of medicinal substances

It isn’t usually marketed this way, but homeopathy can be placed squarely in the pseudoscientific category of so-called “energy healing”.


  1. Glossary of Homeopathic Terms. Omaha: Creighton University School of Medicine [updated 03 August 2009; cited 04 April 2012]. Available from: http://altmed.creighton.edu/Homeopathy/Glossary.htm
  2. Hahnemann, Samuel “§ 11”, “§ 270” Samuel Hahnemann’s Organon of Homœopathic Medicine. New York: William Radde, 1849. 99, 217. Google Books. Web. 04 April 2012.

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