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Samuel Hahnemann (1755 – 1843) was the originator of homeopathy. He was clearly a well-intentioned man.. There is good reason to believe that he thought dilution could not go on for ever, but he died 22 years before it became possible to calculate that his favourite 30C dilution already contained nothing at all.

The bible of homeopaths is Hahnemann’s Organon der rationellen Heilkunde, “Organon of the Medical Art”. His views on dosage, as expressed in the six editions of this book are almost as self-contradictory as the other bible. Hahnemann’s writing about ‘vital spirits’ sounds very silly now, but it is language that was quite common at the end of the 18th century, before much was known about medicine or physiology. But his interest in chemistry was entirely sensible.

Before 1800 Hahnemann started out with the very high doses that were conventional at the time. Unlike most of his contemporaries, he was smart enough to realise that giving 50 g of antimony was killing people so he kept reducing the dose until it was no longer toxic. Unfortunately he (like almost everyone else at the time) didn’t know about controls so he mistook lack of toxicity (because the dose was zero) for a beneficial effect. Nonetheless, for most of his life he did not advocate the extreme dilutions that many modern homeopaths use routinely.

In The Life and Letters of Dr Samuel Hahnemann by Thomas Lindsley Bradford, M.D.(or see Google books edition of the Organon), there is an interesting passage. According to the edition here pp. 237 – 238), this was a note attached to para. #283 in the first edition of the Organon.

” The doctrine of the divisibility of matter teaches us that we cannot make a part so small that it shall cease to be something, and that it shall not share all the properties of the whole.”

Here Hahnemann refers to the doctrine of divisibility, but appears to be saying that dilution can go on for ever. But he also says something that directly contradicts this view (Organon, Dudgeon’s translation see also here, page 239 ). The emphasis is mine.

“I must say that these procedures seem to show chiefly how high one can go with the potentized attenuation of medicines without their action on the human health becoming nil.

Although this claims that you can dilute a lot, it also admits that if the dilution goes too far the effect would eventually vanish, contrary to the usual homeopathic “principle” that it should keep getting stronger and stronger. and contrary to Hahnemann’s suggestions in other places that he thought matter was infinitely divisible.

This passage shows quite clearly that Hahnemann did not believe that his medicines would work if they were diluted so much that that there were no molecules left. That he believed this is confirmed by a letter that Hahnemann wrote in a letter to a Dr Schreter dated September 13th, 1829. This letter reprimanded Schreter for advocating extremely high dilutions.

there must be some limit to the thing. It cannot go on to infinity

The original German version was

“Es muss ein Ende geben, es kann nicht bis ins Unendliche weitergehen”

This confirms that Hahnemann was aware of, and accepted, that matter was not infinitely divisible and his medicines would not work if they contained nothing of the original material.

This attitude is actually not at all surprising, because Hahnemann was an educated man and he had a particular interest in chemistry. He cannot have failed to be aware of Dalton’s atomic theory, which was published between 1805 – 1810, while Hahnemann was writing the first edition of the Organon.

Peter Morrell, in Hahnemann and Homeopathy, says

“These were obviously developments that Hahnemann could not have failed to know about and indeed, was thoroughly excited about, It is clear from many of his asides that he regarded chemistry as the most important science.”

What is astonishing is that I can find no example of Hahnemann ever having mentioned Dalton or Avogadro. Perhaps he was a bit scared by the implications of their suggestions that molecules could not be divided without changing their nature.

The first edition of the Organon was published in 1810. but in the 5th edition appeared 1833, ten years before his death, These dates turn out to be important.

John Dalton (1776 – 1844) was able to estimate relative atomic masses of various molecules, the smallest unit that a chemical can exist in without losing irs identity. His values were soon improved by Amadeo
(1776 – 1856), in 1811. Avogadro made the very important proposal that the volume of a gas (strictly, of an ideal gas ) is proportional to the number of atoms or molecules that are present. More precisely, the relationship between the masses of the same volume of different gases (at the same temperature and pressure) corresponds to the relationship between their respective molecular weights. Hence, the relative molecular mass of a gas can be calculated from the mass of a sample of known volume.

BUT neither Avogadro nor Dalton knew how many molecules there were in a given mass of a substance

This is absolutely crucial because it means that, although Hahnemann realised that there was a limit to the dilutions that could be used, he had no way of knowing what that limit was,

The answer to that question was discovered only in 1865, 22 years after the death of Hahnemann.  It was discovered not by Avogadro, but by Johann Josef Loschmidt (1821 – 1895). It is Loschmidt, not Avogadro, who discovered the crucial numerical value of ‘Avogadro’s number‘, and in the German literature it is known, properly, as Loschmidt’sche Zahl.

This number is 6.022 x 1023 molecules per mole. One mole of a pure compound is its molecular mass in grams. The molecular mass of carbon (relative to hydrogen) is 12, so 12 grams of carbon contain 6.022 x 1023 carbon atoms. The molecular mass of of strychnine is 334.4 so 334.4 grams of strychnine contain 6.022 x 1023 strychnine molecules.

Armed with the numerical value of Avogadro’s number, it is easy to calculate that a 30 C homeopathic dilution contains nothing whatsoever. More precisely, it would contain, on average, a single molecule in spherical pill with a diameter equal to the distance from the earth to the sun.

But Hahnemann could not have known that. If had lived another 25 years he would almost certainly have renounced the idea of using 30 C dilutions.

He had a good excuse for getting it wrong. He was dead before the knowledge existed to do the calculation

But modern homeopaths have no excuse whatsoever for believing the impossible.

Hahnemann would have thought they were nuts, I suspect. He was too intelligent to believe that medicines that contain no medicine could be effective. In his words, “It cannot go on to infinity”.


I very grateful to ‘ Lindy’ for help in checking the references that are cited here, and for helpful discussions.

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10 Responses to Hahnemann would have thought modern homeopaths were barmy

  • “Hahnemann was aware of, and accepted, that matter was not infinitely divisible and his medicines would not work if they contained nothing of the original material.”

    I wonder how the homeopathic community will take this? I’m guessing they will deny Hahnemann ever said it. Or simply respond by saying, “ah, but it works in my practice – I’ve seen it with my own eyes”. Or pretend that Lohschmidt is wrong. Modern homeopaths have no excuse whatsoever for believing the impossible, but I don’t think that having no excuse will stop them – nothing else has.

  • I’ve no doubt that you are right about homeopaths. Rational argument never worked before and I don’t suppose it will now,

    The aim really has to hope to influence a few officials in the Department of Health, or a few vice-chancellors. To my mind, they are the villains. All the homeopaths I’ve met seem to believe totally in their myths. VCs presumably don’t, but promote it anyway.

  • The THES thread DC mini-blogged, relating to UCLan’s latest degrees in magic, and Mike Eslea’s open letter, might be a useful place to catch some VC’s attentions. While I am sure VCs are too busy to read the THES, I would imagine their cadre of PAs and apparatchiks do.

  • I thought this was a particularly useful and balanced piece. It doesn’t simply dismiss Hahnemann as a nutcase, but points out that there are reasons why he held the beliefs that he did, and why those beliefs are no longer tenable.

  • Thanks wilsontown. It is dangerous to try to judge personality and motive after 200 years. It is also quite hard to imagine what it must have been like to try to think about medicine in an age when hardly anything was known about physiology, and microbiology didn’t exist.

    I get the impression of a man eager to do good, and interested in science (in the form of chemistry) who, in later life, became a victim of his own dogmas.

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