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Before we go any further into homeopathy, and look at whether it actually works or not, there is one central problem we need to get out of the way.

Most people know that homeopathic remedies are diluted to such an extent that there will be no molecules of it left in the dose you get. What you might not know is just how far these remedies are diluted. The typical homeopathic dilution is 30C: this means that the original substance has been diluted by one drop in a hundred, thirty times over. In the ‘What is homeopathy?’ section on the Society of Homeopaths’ website, the single largest organisation for homeopaths in the UK will tell you that ‘30C contains less than one part per million of the original substance.’

‘Less than one part per million’ is, I would say, something of an understatement: a 30C homeopathic preparation is a dilution of one in 100³⁰, or rather 10⁶⁰, or one followed by sixty zeroes. To avoid any misunderstandings, this is a dilution of one in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000, or, to phrase it in the Society of Homeopaths’ terms, ‘one part per million million million million million million million million million million’. This is definitely ‘less than one part per million of the original substance’.

For perspective, there are only around 100,000,000,000,000,000,000,000,000,000,000 molecules of water in an Olympic-sized swimming pool. Imagine a sphere of water with a diameter of 150 million kilometres (the distance from the earth to the sun). It takes light eight minutes to travel that distance. Picture a sphere of water that size, with one molecule of a substance in it: that’s a 30C dilution.*

At a homeopathic dilution of 200C (you can buy much higher dilutions from any homeopathic supplier) the treating substance is diluted more than the total number of atoms in the universe, and by an enormously huge margin. To look at it another way, the universe contains about 3 × 10⁸⁰ cubic metres of storage space (ideal for starting a family): if it was filled with water, and one molecule of active ingredient, this would make for a rather paltry 55C dilution.

We should remember, though, that the improbability of homeopaths’ claims for how their pills might work remains fairly inconsequential, and is not central to our main observation, which is that they work no better than placebo. We do not know how general anaesthetics work, but we know that they do work, and we use them despite our ignorance of the mechanism. I myself have cut deep into a man’s abdomen and rummaged around his intestines in an operating theatre—heavily supervised, I hasten to add—while he was knocked out by anaesthetics, and the gaps in our knowledge regarding their mode of action didn’t bother either me or the patient at the time.

Moreover, at the time that homeopathy was first devised by Hahnemann, nobody even knew that these problems existed, because the Italian physicist Amadeo Avogadro and his successors hadn’t yet worked out how many molecules there are in a given amount of a given substance, let alone how many atoms there are in the universe. We didn’t even really know what atoms were.

How have homeopaths dealt with the arrival of this new knowledge? By saying that the absent molecules are irrelevant, because ‘water has a memory’. This sounds feasible if you think of a bath, or a test tube full of water. But if you think, at the most basic level, about the scale of these objects, a tiny water molecule isn’t going to be deformed by an enormous arnica molecule, and be left with a ‘suggestive dent’, which is how many homeopaths seem to picture the process. A pea-sized lump of putty cannot take an impression of the surface of your sofa.

Physicists have studied the structure of water very intensively for many decades, and while it is true that water molecules will form structures round a molecule dissolved in them at room temperature, the everyday random motion of water molecules means that these structures are very short-lived, with lifetimes measured in picoseconds, or even less. This is a very restrictive shelf life.

Homeopaths will sometimes pull out anomalous results from physics experiments and suggest that these prove the efficacy of homeopathy. They have fascinating flaws which can be read about elsewhere (frequently the homeopathic substance—which is found on hugely sensitive lab tests to be subtly different from a non-homeopathic dilution—has been prepared in a completely different way, from different stock ingredients, which is then detected by exquisitely sensitive lab equipment). As a ready shorthand, it’s also worth noting that the American magician and ‘debunker’ James Randi has offered a $1 million prize to anyone demonstrating ‘anomalous claims’ under laboratory conditions, and has specifically stated that anyone could win it by reliably distinguishing a homeopathic preparation from a non-homeopathic one using any method they wish. This $1 million bounty remains unclaimed.

Even if taken at face value, the ‘memory of water’ claim has large conceptual holes, and most of them you can work out for yourself. If water has a memory, as homeopaths claim, and a one in 10⁶⁰ dilution is fine, then by now all water must surely be a health-giving homeopathic dilution of all the molecules in the world. Water has been sloshing around the globe for a very long time, after all, and the water in my very body as I sit here typing away in London has already been through plenty of other people’s bodies before mine. Maybe some of the water molecules sitting in my fingers as I type this sentence are currently in your eyeball. Maybe some of the water molecules fleshing out my neurons as I decide whether to write ‘wee’ or ‘urine’ in this sentence are now in the Queen’s bladder (God bless her): water is a great leveller, it gets about. Just look at clouds.

How does a water molecule know to forget every other molecule it’s seen before? How does it know to treat my bruise with its memory of arnica, rather than a memory of Isaac Asimov’s faeces? I wrote this in the newspaper once, and a homeopath complained to the Press Complaints Commission. It’s not about the dilution, he said: it’s the succussion. You have to bang the flask of water briskly ten times on a leather and horsehair surface, and that’s what makes the water remember a molecule. Because I did not mention this, he explained, I had deliberately made homeopaths sound stupid. This is another universe of foolishness.

And for all homeopaths’ talk about the ‘memory of water’, we should remember that what you actually take, in general, is a little sugar pill, not a teaspoon of homeopathically diluted water—so they should start thinking about the memory of sugar, too. The memory of sugar, which is remembering something that was being remembered by water (after a dilution greater than the number of atoms in the universe) but then got passed on to the sugar as it dried. I’m trying to be clear, because I don’t want any more complaints.

Once this sugar which has remembered something the water was remembering gets into your body, it must have some kind of effect. What would that be? Nobody knows, but you need to take the pills regularly, apparently, in a dosing regime which is suspiciously similar to that for medical drugs (which are given at intervals spaced according to how fast they are broken down and excreted by your body).