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.

“One Half the World Fools and the Other Half Hypocrites”

A Disgression on ‘ How Mumbo-Jumbo Conquered the World: A Short History of Modern Delusions‘, by Francis Wheen.

I’m reading a genuinely scary book: How Mumbo-Jumbo Conquered the World: A Short History of Modern Delusions, by Francis Wheen.  It’s a catalog of the absurdities and errors which, according to the author, characterize the thinking of modern Western man: post-structuralism, catastrophism, Reaganonimcs, alternative medicine, &c.

Two years ago, this book would have made me feel smug.  I suffer from none of the pernicious un-reasons which afflict the men and women in this book, despite the fact that many of them are actually smarter than I am.  I try to be empirical, and I think I largely succeed (but, then, again, obviously, everyone thinks they’re empirical).

Two years ago, I would have read How Mumbo-Jumbo Conquered the World and shaken my head in self-satisfied dismay about how stupid and gullible other people are.  But that was before I took a spin class.

I’ve taken one spin class, a little over a year ago.  I really enjoyed that one spin class I took, although I would never describe it as pleasant.  It was in a small dark room filled with bikes armed with excruciating sharp little seats.  The music was thumpy and very loud and there was an extremely fit woman in the front shouting at us.

But it was encouraging shouting.  This woman with insanely muscular arms kept yelling at me that I was beautiful, that I was killing those hills, that I could definitely do another, that I was looking really great today.

These were all lies, or at least, none of these things were objectively true.  I didn’t look beautiful or even great – I looked horrible, like a sweating person in bad pain who wasn’t going to be able to sit comfortably for a week.  And I was not “killing” the “hills”  – I was lurching up them in near-despair.

Nevertheless, I believed everything the woman screamed at me that day.  Somehow the dark and the music and the numbing pain and the arms and the yelling combined to make me love that shrieking woman, and I would have followed her into battle if she had asked me.  Yet I remember that somehow, in the dank thrumming spin room, it managed to occur to me how cultish my feelings were.

I didn’t care at all – I was having a blast.  But it was humbling: I was susceptible to spin class-level manipulation, which is not, let’s face it, super-sophisticated.  And I knew I was being manipulated, and it still didn’t matter to me: feeling pumped in that moment was worth more than occupying my precious intellectual high-ground.

I don’t think I betrayed the Enlightenment by enjoying my spin class.  But we all abandon the strict precepts of reason every once in a while to make our world a little more comfortable.  That doesn’t make it right, and it doesn’t make it admirable: ideally, we would all be empirical all the time.  We would be data-driven: we would not believe what is not true, and when we do not possess sufficient data, we would remain agnostic.

But someone who actually did that would be insufferable.  We must act on what we believe we know and we must, in a world of contradictions, at some point choose to believe something: I chose to believe in that moment that I was a hill-crushing goddess.  I think that the best that we can reasonably do is change our minds when new information requires it: when I saw myself in the mirrors in the hallway after class, I quickly revised my estimation.  We’re all going to turn out to have been wrong about much of what we believe, whether we like it or not – in the meantime, we might as well spin.

Title quotation by Thomas Jefferson. Featured image, from Thomas Paine’s Age Of Reason, taken from