IT WAS the titan of science Carl Sagan who said extraordinary claims require extraordinary evidence – yet this logical axiom is jettisoned whenever people indulge in the dubious and ill-founded promises of alternative medicine.

King among all these outlandish claims is homeopathy, proposed by Samuel Hahnemann in 1807. This is the belief that “like cures like”; that a substance that causes similar symptoms to a certain disease in a healthy person will cure that disease in an unhealthy person.

This is in no way an empirical law of nature, but rather a hunch Hahnemann wished to entertain. He also decreed that the more dilute the remedy is, the more potent it is. This is the antithesis of what is observed in nature, where the potency of any solution is proportional to the active ingredient in that substance. But these dilutions are incredibly extreme. Homeopathy solutions are typically diluted to 30C – akin to having just one particle in a collection of 10^60 particles, where 10^60 is 1 followed by 60 zeros.

This is a tiny fraction and is contrary to physical chemistry, which precludes this level of dilution actually being possible on Earth. In fact, it’s easy to prove that to have this solution with just one active atom would require a “planet” of water 15,000 times the mass of the sun and 28 times its size.

When Hahnemann proposed this he could perhaps have been forgiven, as the existence of atoms was not proposed and proven until almost a century later – making it seem perhaps plausible that there would be no limit to how much you could dilute something.

However, modern science cannot take a position so clearly divorced from reality. The homeopathic community claims water has the ability to somehow “remember” what it has been in contact with.

This concept is called water memory, but has long since been debunked; polar bonds in water persist for no more than a few million billionths of a second. Given that all water on Earth in a closed system and every molecule of water in existence will undoubtedly have seen quite an amount of effluent, we should perhaps be somewhat grateful for this liquid amnesia.

Yet despite this, homeopaths sell “remedies” diluted up to 200C, which would require 10^320 (a number equal to 1 followed by 320 zeros) universes to have a single active molecule. This is most inconvenient, given that as far as modern cosmology can ascertain we have only one. In general, it’s a good rule of thumb that any treatment that would have to violate the laws of physics to be viable is probably unlikely to be biologically effective. There is simply no way around the fact that homeopathic medicines are quite simply just water and sugar.

Apart from the physics problem, there is also the intractable fact that large-scale studies of homeopathy have shown it works no better than placebos; while homeopaths often claim to have positive trial data, examination inevitably shows the only positive data stems from poorly controlled trials with high drop-out rates, small sample groups or from dedicated homeopathic publications.

In medicine, trial outcomes are weighed and scored in a powerful process called meta-analysis, which consistently shows homeopathy does not work beyond a placebo effect.

It may therefore sound like harmless quackery – after all, people have been buying snake-oil from devious charlatans or elixirs from well-meaning but misguided folk for years, and surely it’s merely a harmless indulgence? Well, sometimes, but it is not always that simple.

Many homeopaths shun conventional medicine and inform their clients it is dangerous. As they are often unqualified to practise medicine, they frequently miss glaring warning signs and delay or caution against conventional medical intervention.

This has led to many patient deaths, most tragically of children whose parents were advocates of alternative medicine. Indexes such as whatstheharm.netlist thousands of cases where patients have died or suffered at the hands of inept homeopaths and other alternative practitioners.

Worse again, many homeopaths are profoundly against medical vaccination, yet still sell homeopathic and clinically useless “vaccines” for killer diseases such as malaria and measles – this is deeply dangerous, totally unregulated and utterly misguided.

People choose homeopathy because it panders to the naturalistic fallacy that asserts naturally occurring things are good, while synthetic or pharmaceutical things are bad. But fallacy is an apt term for this: arsenic, uranium and hydrochloric acid are also naturally occurring, but it would be foolish to sprinkle them on your breakfast cereal.

There is also a fear of the side-effects of pharmacological interventions and practices, and this is perfectly valid and often well-founded. It does not, however, make homeopathy valid.

Homeopathy is at best useless and at worst positively damaging, not just medically but to our collective understanding of science.

By clinging to delusion, belief in alternative medicine denigrates the very wonder of science and medicine and the massive strides we as a species have made over the last century or so in understanding the world around us, and how our bodies work.

Granted, science doesn’t know everything, and there are still many mysteries about the human body. But it will not be superstition and archaic ritual that shed light on these mysteries but rather methodological research, conducted with a sceptical attitude through the scientific method that brings new advances and understanding.

Dr David Robert Grimes is a physicist and cancer researcher at Oxford University. His science and medicine blog is at davidrobertgrimes.com