Wart remedies and snake oil

[unixronin]

Wen the Eternally Surprised has a major outbreak of highly persistent warts on her fingers.  We've tried all the over-the-counter remedies, and they've been frozen twice with liquid nitrogen to no avail.  As a last possible resort while we wait for the dermatologist appointment (the dermatologists are booked up four months ahead), the pediatrician suggested we try something called "thuja", a tree extract.

Well, I finally found the stuff today, at the health food store.  It turns out to be packaged as a homeopathic remedy, in half-ounce vials at either 12C or 30C "strength" (read: dilution).  This is probably a good thing, as it is generally stated that the primary active ingredient in "oil of thuja" is thujone.

Now, let's stop here a moment and do some simple math.  The molecular formula for thujone is C₁₀H₁₆O, and its molecular weight is 152.23.  Let's assume, just for the moment, that oil of thuja were actually pure thujone.  (It isn't, but the assumption gives us some actual numbers to work with instead of ballpark guesses.)  Using our old friend Avogadro's number (6.023x10²³), we can calculate that a half-ounce vial — call it 14 grams — of thujone contains about 5.5x10²² thujone molecules ... before dilution.  But remember those cryptic strength ratings?

Well, it turns out that 1C means a 100:1 dilution.  And it's geometric.  2C is 10000:1; 3C is 1000000:1.  Doing the math, 12C "strength" is a dilution of 10²⁴:1.

But wait!  We only started out with 5.5x10²² thujone molecules in the first place.  That means that, statistically speaking, there is a chance fractionally better than 1 in 18 that any given 14-gram vial of 12C oil of thuja extract contains a single molecule of thujone.

But wait!  It gets better!  There's a 30C strength!  At 100:1 dilution each time, that is an additional 10³⁶:1 dilution.  That means there's roughly one thujone molecule for every 5.5x10³⁷ 14g vials of the 30C extract.  That's such a huge number that not only are there not enough 14g vials on the entire planet for any one of them to have a statistically significant probability of containing a single thujone molecule, but I think I can say with good confidence that there is not anywhere on the planet a 14g vial of 30C homeopathic thujone extract that contains a single molecule of alcohol (thujone is soluble in alcohol, but not in water) that has ever been in the same container of any size with even a single molecule of thujone.

So the 30C, and even the 12C, thujone preparations are pure alcohol with a slight chance, at the 12C dilution, of being contaminated by a thujone molecule.  But then even that is processed and made into pellets.  Well, you can't make alcohol into a pellet; it's a volatile liquid.  I'd wager those pellets don't even contain any more than residual traces of the alcohol solvent — I'd bet they're composed entirely of binders and other non-active ingredients with possible trace impurities left behind by the alcohol.

The essence of snake oil, huh?  So why do I say this is probably a good thing?

Well, you see, thujone is reported to be "toxic to both brain and liver cells", and is widely classified as a neurotoxin.  So aren't you glad that when you buy the stuff for your health, you aren't actually getting any of it?