The Law of Infinitesimals

Three weeks ago, I mentioned a book I was reading, How Mumbo-Jumbo Conquered the World: A Short History of Modern Delusions, by Francis Wheen, which is about…exactly what it sounds like it’s about.  The essential premise of the book is that the Age of Reason ushered in by the Enlightenment is under assault, that the forces of ignorance, superstition, and philistinism are everywhere.

Three weeks ago, I was pretty glib about this assault on reason.  I was only about halfway through the book, and I think I basically concluded that, because of a spin class I once took, everything was just fine.

I was wrong!  I’ve finished the book, and I’m frankly terrified.

Here is but one scary and demoralizing example:

Have you heard of Hahnemann’s ‘Law of Infinitesimals’?  It is one of the three laws invented by Samuel Hahnemann in the late 1700’s, and it remains one of the foundational tenets of homeopathic medicine.

Hahnemann’s Law of Infinitesimals states that the more you dilute a medically active substance in a medically inert solution (like milk or water), the more potent it becomes.

I’m going to repeat that very slowly, just so we’re all clear:

The more you dilute a substance (so, the less of it there is per unit solvent), the more potent it becomes.

Let me put that another way:

Let’s suppose you have two cups of water, Cup A and Cup B, and into Cup A you put 100 molecules of Medicine X, and into Cup B you put 1 molecule of Medicine X.

The Law of Infinitesimals

Cup A                           Cup B

According to one of the cardinal principles of homeopathy, Cup B will be the more powerful medicine.  Not the correct dose, not the more medically advisable, the more powerful.

Some homeopathic remedies are sold at dilutions so high that they almost certainly contain no molecules of the original “medical” substance.

(Of course, it would be very difficult to say this for sure of any given container of diluent; however, Avogadro’s Limit is generally held to be the dilution at which no more original substance remains.  Avogadro’s Limit is around 13C (1 x 10²⁶) if 1 mole of the original substance were used in first dilution.  Hahnemann apparently advocated 30C as the best “usual” dilution of homeopathic remedies, and one remedy, Oscillococcinum, is famously sold at 200C.  Since every ‘C’, or “centesimal dilution” is one part substance diluted by 99 parts solvent, that would mean that a 200C solution (one part into 99 parts, then one part of that into 99, then one part of that into 99, 200 times) would have one molecule of active ingredient for approximately every 100²⁰⁰ molecules of diluting solution (that would be 10 with 400 zeroes after it).  Since that is way, way more than all the molecules in the universe, it is very unlikely that that one molecule is in your dose.)

No problem, say homeopaths!  Even if your bottle of Oscillococcinum has zero molecules of Oscillococcinum in it and is, in actuality, a bottle of water, no matter: the water “remembers” the Oscillococcinum, and that’s just as good.  No, scratch that – it’s even better.

This is so stupid I can’t believe that anyone believes it.

First of all, heaven help us all if water molecules “remember” other substances with which they’ve come into contact.  Worse still if, through that “memory”, water can impart the properties of those substances to the drinker.  Because, if that is the case, when you drink that Oscillcoccinum, or even when you down a bottle of Poland Spring, you’re also drinking all the things all the water molecules in that bottle have ever touched: feces, dirt, rotten flesh, every manner of poison and putrescence that has burped out of the surface of the earth in the gadzillion-odd years it’s been roiling around.

But failure to see that is merely failure of imagination, a failure of which we are all guilty.  Active belief in the Law of Infinitesimals, on the other hand, is an almost deliberately perverse misreading of actual principles of medicinal dosing.  It is a committed idiocy.

It also violates the sort of everyday experience that informs common sense:

If you’re making margaritas, and you make one with a single shot of tequila, and one with two shots of tequila, which will be the stronger drink?  Is there a single homeopathic consumer on the planet, no matter how credulous and stupid, who would accept the Law of Infinitesimals from their bartender?

I live in a country where a frightening percentage of the population refuses to believe in Evolution.  Where there is a movement against vaccines, the enormous benefit of which has been demonstrated well beyond reasonable doubt.  My countrymen are so skeptical that they literally pose a threat to themselves and to their own children.

But they believe in this, in Memory Water and the Law of Infinitesimals.

And the angels wept.

If the sight of serial dilutions makes you want to curl and weep, Wikipedia actually has surprisingly good and clear information on homeopathic doses.  Their basic article on homeopathy is also pretty informative.

Featured image is not of Hahnemann, who I’d love to kick in the shins right about now and so will not feature here and who looks like a tool (see the Wikipedia page on Homeopathy if you don’t believe me), but of Amedeo Avogadro, who might not have been a looker, but was right.  It is taken from his Wikipedia page.

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