Alternative Medicine I – The Ultimate Dilute: Homeopathy

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Homeopathy. One of the most popular alternative medicines in the Western world, and perhaps the most widely misunderstood. The science against homeopathy, like the skeptics, is unequivocal. The British Homeopathic association list homeopathy as a possible treatment for long-term chronic problems such as eczema, chronic fatigue syndrome, asthma, migraine, IBS and depression, but numerous healthcare bodies agree there is no evidence that homeopathy is effective in treating any health condition.

What is Homeopathy?

First of all, let’s clarify what exactly we’re talking about. According to the British Homeopathic Association, homeopathy is about “treating like with like” – homeopathy is “based on the principle that … a substance taken in small amounts will cure the same symptoms it causes if it was taken in large amounts”. Fine. That’s not unreasonable at all. In fact, this principle has been exploited by modern medicine in the treatment of allergies, and even vaccinations work by a similar principle (although vaccines are treated first so as to make sure that the damaging effects of the live virus are not longer present). But there is a second key part to homeopathic medicine; that the medicinal effects of these normally toxic substances are increased with increasing dilutions. Homeopathy employs the technique of succession, in which a substance is repeatedly mixed and diluted.

Defying Avogadro

It’s this serial dilution that raises red flags for most skeptics. Or, rather, BIG, NEON FLASHING flags – homeopathic treatments are diluted so many times that there is essentially no chance that the medicine contains even one molecule of the supposedly medicinal substance. This isn’t just a throw away statement. Homeopathy defies avagadros limit – the maths of homeopathic succession makes it quickly apparent how absurd the idea is.

A 1X dilution of a substance means that it has been diluted to a tenth of its original concentration. That’s one drop of the original substance to 10 drops of water (1:10). A 2X dilution (or 1c in homeopathic lingo) means a 1:100 dilution, 3X means 1:1000 dilution and so on. Although it starts out sounding innocent enough (1 in 10 is roughly the concentration of the glass of squash I’m drinking), it quickly escalates. Because the homeopathic dilution scale is exponential, it goes from quite a reasonable amount of the substance floating about, to essentially nothing, very rapidly. In fact, when I say essentially nothing, I mean nothing. Homeopathic dilutions greater than 12c (which is most of them, frankly), have been diluted beyond avagadro’s limit, meaning that there is almost no chance at all that even a single molecule of the original substance exists in the final dilute. Let’s take a closer look at this.

Avagadro was a 19th Century chemist, and his limit (also known as his number and his constant) is one of the fundamental laws of chemistry. His constant is the number of particles (atoms or molecules) in one mole of a substance, which is roughly 6.022 ×1023. How much a mole is (in grams) depends upon the atomic mass of the constituent parts, but that’s another story, and I’m not a Chemist. The point is, that, if you dilute a substance beyond 1023, the chances are that you’ve diluted out every single remaining molecule. If you’ve taken one mole (1023 molecules) of your active ingredient, and diluted it 1:1024 (a 24X or 12c dilution), then you’ve got 1 part of your original substance to 100,000,000,000,000,000,000,000 parts water. That’s way beyond dilute squash. That’s way beyond ‘trace amounts’. At this stage, butting up against avagadro’s limit, we’re now stuck calculating the probability that even a single molecule of the original substance remains. At 12c, it’s 10%. Go beyond the limit and each subsequent dilution reduces the chances that any molecules remain by a power of 10. So at 25X (12.5c), you’ve got a 1% chance of finding a molecule of the active ingredient, at 26X (13c) you’ve got a 0.1% chance and so on, getting less and less likely the further we go.


Concentrations like this are many orders of magnitude below the safe limits for the most toxic chemicals. There is more uranium in your breakfast cereal than there is ‘active ingredient’ in a 12c homeopathic remedy. But most homeopathic remedies rest somewhere in the 30c – 200c range. Even at the lower end of that, 30c, there is only a 0.00000000000000000000000000000000001% chance that even a single molecule of the original substance exists in the final dilute. The water required to dilute 1ml of a solution to 30c would fill a sphere 131 light years in diameter. Light years.

X Dilution Scale C Dilution Scale Ratio Chance of Having at Least
One Molecule Left
1X 1:10 100%
2X 1C 1:100 100%
6X 3C 1:1000000 100%
10X 5C 1:10000000000 100%
20X 10C 1:100000000000000000000 100%
24X 12C 1:1000000000000000000000000 10%
30X 15C 1:1000000000000000000000000000
50X 25C 1:10000000000000000000000000000000
100X 50C 1:1000000000000000000000000000000000000
200X 100C 1:10000000000000000000000000000000000000000000
400X 200C 1:10000000000000000000000000000000000000000000

It is the fact that homeopathy defies basic laws of chemistry that makes many people so incredulous about the idea that homeopathy might do anything at all, other than hydrate you. Almost all homeopathic remedies are, statistically and practically speaking, just water. So if you’re trying to treat dehydration, great! Go for homeopathy*. Or you could just have that glass of squash. It’ll probably taste better!

* Actually don’t because according to representatives from the World Health Organisation, homeopathy is not even an effective treatment for dehydration.

The Memory of Water

So why on Earth are we even still talking about this? Well, despite its logical flaws, millions of people continue to use and swear by homeopathic remedies. So, assuming that ultradilute solutions of usually toxic substances can treat certain ailments, how might it work?

One explanation that homeopaths have put forward to explain how their treatment works despite containing none of the active ingredient at all, is through the ‘memory of water’. This idea basically claims that water molecules are in some way altered by the substances that have been dissolved in them previously, changes that are evident even when no molecules of the original substance remain. Somehow, water has been changed, structurally or otherwise, through its encounter with the active ingredient, and the medicinal properties of that ingredient transferred in the process. This is where the succussing or shaking of homeopathic remedies appears to be key – many homeopaths believe that serial dilution, punctuated by vigorous shaking, is important in stimulating the memory of water.

Several studies have tried to demonstrate the memory of water, and provide scientific explanations for how this might work. For example, one study published in 2007 explained that “the nanoheterogenous structure of water can be determined by interactive phenomena such as epitaxy … temperature–pressure processes during succussion, and formation of colloidal nanobubbles containing gaseous inclusions of oxygen, nitrogen, carbon dioxide, and possibly the remedy source material”. Whether that is true or not remains unclear, however, as the study in question (although reporting positive results) had serious methodological flaws, and is, either accidentally or deliberately, misleading in multiple places. The paper has been heavily criticized (see Wilson and Hebbern 2007) and almost universally rejected. Studies such as this one have tried to show detectable differences between different homeopathic remedies in terms of their structure properties in different conditions, however none have conclusively shown differences for dilutions below 12c. (For a full review of these papers and why they are misleading, see here and here.

Another piece of commonly cited evidence for the memory of water comes from Samal and Geckeler (2001), who showed that water molecules tend to ‘clump’ around dissolved substances. What this has to do with homeopathy isn’t really clear though, since the paper says nothing about dilution. Dilution would, as it happens, have exactly the same effect whether the water is clumped around the dissolved substance or not – with successive dilutions beyond avagadro’s limit these clumps would be lost, just as the individual molecules would.

So, there is no solid evidence available yet for the memory of water. And any hypothesis that attempts to explain it also crucially needs to explain how and why the memory of water also appears to be selective. In our daily lives we constantly mix different substances with water, and frequently these substances undergo serial dilution and vigorous motion – just think what happens when you flush your toilet. Thus, the water we drink could be viewed as an ultradilute solution of urine, faecal matter, food and paper, not to mention thousands upon thousands of toxic chemicals used in industry. In fact, tap water must also be an ultradilute solution of all soluble pharmaceutical drugs as well. So why is it that water apparently ‘remembers’ the active ingredients of homeopathy, but conveniently forgets all of our waste materials?

The Evidence

I found a total of 33 papers investigating homeopathy – 14 presented the results of new trials and 19 statistically analysed the results of many trials (meta-analysis). Obviously, even the most casual observer will realise that this indicates that I’ve not found all of the trials on homeopathy. This doesn’t matter too much – meta-analyses are far more meaningful, and they’ve done the hard work for me. But still, lets begin by looking at some of the empirical studies I found.

No. Studies: 14
Placebo-Controlled Studies: 11
No. Reporting Significant Results: 9 (6 placebo-controlled)
No. Meta-analyses: 19
No. Reporting Significant Results: 6

Only 11 of the 14 research papers I found were informative – the others failed to include an adequate control group or randomisation procedure and so I excluded them on the basis that their results will not be reliable.

I found studies investigating the effectiveness of homeopathic treatment for a remarkable range of ailments including: severe sepsis, haemophilia, migraine, muscle soreness, arthritis, asthma, ADHD, diarrhoea and hay fever. Several studies (five) reported significant positive effects of homeopathy compared to a placebo, suggesting that homeopathy is an effective treatment for these ailments. However, I believe several of these are red herrings. For example, one study reporting a positive effect of homeopathy for haemophilia patients included no baseline measures for the condition – it simply compared people treated first with homeopathy and then with the placebo. Meanwhile, around half of all studies (5/11) failed to find any significant positive effect of homeopathic treatment. One study, investigating muscle soreness actually found that the placebo was more effective than the homeopathic remedy! For childhood asthma, childhood acute ear infections, migraines, and mental fatigue, studies were unable to find a statistically significant effect of the homeopathic remedy tested.

One interesting study on rheumatoid arthritis compared the effect of homeopathic treatment with the effect of just homeopathic consultation, and found that the consultation itself products a significant benefit, but the treatment was no more beneficial than the placebo. This reiterates a point I made in the introduction – alternative therapies may be effective because the practitioners have more time and money to offer a pleasant and reassuring consultation to their patients.

Ok, so, that’s still fairly inconclusive. My literature search was not exhaustive, nor was it statistically rigorous – so let’s turn to some meta-analyses, which are both. Meta-analyses take results from many separate studies and analyse them together to obtain a picture of the overall trend.

I found 20 meta-analyses on homeopathic treatment, 6 of which surveyed homeopathy in treating any illness, the others focused on psychiatric conditions, influenza (2 studies), irritable bowel syndrome, migraines, delayed onset muscle soreness, dermatitis caused by cancer treatment, induction of labour, hot flashes, ADHD, chronic asthma and post-operative ileus. Of these, 13 / 20 failed to find a positive effect of homeopathy. Among them were some large-scale studies conducted by highly reputable organisations. For example, the Cochrane collaboration reviewed the evidence for homeopathic remedies for influenza and found no statistically significant effect of homeopathy, and the NHMRC in 2014 failed to find a positive effect of homeopathy for any of 61 different conditions. Shang (2005) compared 110 conventional and homeopathic clinical trials and found strong effects for pharmaceutical treatments, but only very small effects for homeopathy, leading the authors to conclude that homeopathic remedies elicit no more than a placebo effect.

Never the less, 7 studies reported significant results, although most complained that very few methodologically sound studies were available. A 1991 meta-analysis of 105 papers found that overall more conditions showed a positive trend than a negative one, however the authors refused to draw conclusions about the efficacy of homeopathy because of the paucity of good quality results. More recently, Linde (1997) reviewed 89 studies on homeopathy and found that although no single condition showed a significant benefit from homeopathic treatment, averaging across all conditions did show a small beneficial effect. Even more recently, Davidson and colleagues (2011) analysed 25 academic papers and found that somatic syndromes responded positively to homeopathy, while other psychiatric conditions did not. However, many studies complained about the low methodological quality of research on homeopathy, and Ernst and Barnes (1999) report that randomized trials tended to produce non-significant results while non-randomised trials (ie, biased trials) were the ones that showed a significant benefit. This effect is not an uncommon one, and is often a good indicator that the placebo effect is at work – studies with small sample sizes, poor randomization procedures or badly designed placebos are more likely to falsely detect an effect when in fact none exists. Similarly, a year later, Cucherat and colleagues reported that their meta-analysis of 16 academic papers showed a significant overall effect of homeopathy, however this effect disappeared when the authors began removing the poorest quality studies one by one.

One study that seems to be more solidly in favour of homeopathy, published by Kassab (2009), showed that across eight studies, topical applications of calendula extract had a significant positive effect on dermatitis resulting as a side effect of cancer treatment. These studies, however, all used ‘material doses’ of calendula – not diluted beyond avagadro’s limit – which would be reasonably likely to contain at least some of the extract in the final treatment. Furthermore, in 1997 Barnes and colleagues reported that amongst 6 studies testing homeopathic remedies for postoperative ileus (bowel obstruction), significant benefits were obtained only in studies with material doses – 12C or lower. Of the other studies I reviewed, most used dilutions between 30c and 200c, well beyond avagadro’s limit. Many others simply did not report the dilution, or determined it on a patient-by-patient basis. Thus, it is hard to tell to what extent positive effects of homeopathy are isolated to material-dose studies, however it is clear that not all ‘homeopathic remedies’ studied are ultradilute (which makes them considerably more believable as viable treatments), and it is extremely difficult to make meaningful comparisons between papers that use such a wide range of different doses.

The Verdict

Overall, the weight of scientific evidence suggests that homeopathic remedies do not confer significant benefits over and above the placebo effect. Those studies that have reported a significant effect are often plagued by methodological flaws, and the overwhelming message from the literature is that there is a lack of good-quality studies available to consider. Further, it is ultimately quite difficult to study homeopathy because one of its key features is the development of individualized treatments, making controlled studies very difficult. The wide variety of different treatments and dilution regimes further makes it hard to compare between studies. However, the verdict for homeopathy doesn’t look good.

Kassab’s 2009 study on the use of calendula for dermatitis seems promising however, and warrants further investigation. Using material doses of calendula seems to improve the symptoms of dermatitis for patients undergoing cancer treatment. This makes sense – calendula has been known for centuries to have medicinal effects, and pharmaceutical studies have confirmed that Calendula extracts can have antiviral, antigenotoxic and anti-inflamatory properties, making it ideal for treating dermatitis, especially in cancer patients. A better understanding of how this natural extract can be used to treat dermatitis could allow us to develop more effective drugs and treatments.


An Academic Consensus

Ultimately, my little review pales in comparison to the volume of reports, articles and blog posts on the topic of homeopathy. Of all the alternative medicines, homeopathy may be the most widely rejected. If you’d like to read more, you’ll find excellent reviews here, and here… oh, and here. Also, this video says everything, really. And check out Ben Goldacre’s superb book Bad Science for a comprehensive review of how the wool is pulled over our eyes both by alternative and conventional medicine.

Hundreds of academics, scientific figures and other learned folk have repeatedly and succinctly debunked the science of homeopathy. Publically, in 2010 over four hundred skeptical British citizens took part in a nationwide homeopathic overdose ( as part of the 10:23 project (so named after avagadro’s constant, 1023). Nobody was harmed during the mass overdose, despite consuming and entire bottle of their chosen homeopathic pills.

Reports by the NCCIH, the House of Commons Science and Technology Committee and the NHMRC all concluded that there was no reliable evidence for medicinal benefits of homeopathy for any condition. When asked whether the UK Government had any credible evidence that homeopathy works beyond the placebo effect, Minister Mike O’Brien replied “the straight answer is no”.

There is little evidence to support homeopathy as an effective treatment for any specific condition
– National Centre for Complementary and Integrative Health, USA

In our view, the systematic reviews and meta-analyses conclusively demonstrate that homeopathic products perform no better than placebos
– House of Commons Science and Technology Committee, UK

There is no good-quality evidence that homeopathy is effective as a treatment for any health condition
– National Health Service, UK

Homeopathic remedies perform no better than placebos, and that the principles on which homeopathy is based are “scientifically implausible”
– House of Commons Science and Technology Committee, UK

There were no health conditions for which there was reliable evidence that homeopathy was effective
– The National Health and Medicines Research Council, Australia

Our evidence-based WHO TB treatment/management guidelines, as well as the International Standards of Tuberculosis Care (ISTC) do not recommend use of homeopathy
– World Health Organisation, International

Some products labeled as homeopathic can contain substantial amounts of active ingredients and therefore could cause side effects and drug interactions
– National Center for Complementary and Integrative Health, USA

The Government should stop allowing the funding of homeopathy on the NHS
– House of Commons Science and Technology Committee, UK

Although there have been many research studies into homeopathy there is no scientific or medical evidence that it can prevent cancer or work as a cancer treatment
Cancer Research UK

Several key concepts of homeopathy are inconsistent with fundamental concepts of chemistry and physics
– National Center for Complementary and Integrative Health, USA

If There’s Nothing There, It’s Harmless, Right?

Surely there’s no harm in homeopathy, though? Well, homeopathy does seem to be cheaper than conventional medicine (I should hope so, since it mostly doesn’t have anything in it!). And, given its love of diluting the active ingredient entirely out of the treatment, homeopathy seems to at least be one of the more harmless of the alternative medicines. Right? I mean, how could water possibly cause side effects? Well, placebo treatments can just as easily have side effects, if you’re expecting them to be there – it’s a phenomenon known as the nocebo effect, the placebo’s evil twin.

Homeopathy has some other pretty nasty consequences. For instance, in 2006, BBC Newsnight exposed homeopaths in London recommending that their patients refuse pharmaceutical anti-malarial medication in favour of homeopathy, advice that could be lethal. Of the ten homeopaths included in the undercover program, seven failed to ask about the patient’s medical background before prescribing a treatment (risking possible drug interactions or aggravating existing medical conditions), and all ten were prepared to advise homeopathic malaria prevention instead of conventional pharmaceutical treatment. The incidence of malaria in travellers returning to the UK has increased steadily over the last twenty years and is commonly attributed simply to a lack of anti-malaria medication. Homeopathy and other complimentary medicines have also been implicated in a significant minority of parents refusing vaccination for their children, which has recently led to a resurgence of measles, mumps and Whooping cough in the US. In response to an email enquiry about vaccination, only 2 out of 77 homeopaths advised immunization of a child against measles, mumps and rubella. Not so harmless.

Herbal Medicine

I’d like to take a short moment to side-step from homeopathy over to the wonderful world of herbal medicine. Again, this is a huge, all-emcompassing term that includes hundreds of different treatments, ancient and modern, taken from cultures and civilisations around the world, and featuring over 12,000 different plants and natural extracts. It is essentially impossible to empirically evaluate herbal medicine as a whole – each ‘treatment’ must be evaluated on its own.

Last Words

Ok, back to my point. Natural, herbal, even non-existent treatments can still have serious negative effects on your health, on the health of others, and on the natural world. There is no evidence, overall, that homeopathy is beneficial in treating any health condition. A few individual treatments appear promising (at doses above avagadro’s limit), and should be the focus of further research to isolate the active ingredient with the aim of improving efficacy and safety. Guidance from homeopaths can sometimes be inaccurate and even dangerous, and following homeopathy can promote pseudoscientific or ‘magic’ explanations that dampen scientific curiosity and ultimately leave us all poorer.

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