published 1/30/09, updated 6/06/10

Warning!

May cause famous magicians to make fun of you.

The Power of Avogadro Compels You!

James Randi and Alexa Ray Joel try to poison themselves — one of them deliberately and the other accidentally making homeopathy look 10X sillier than it already did

by Paul Ingraham, Vancouver, Canada MORE
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Credentials and qualifications

I am a writer and retired Registered Massage Therapist (unusually well-trained for a massage therapist, a 3000-hour program). I’m almost done with a Bachelor of Health Sciences degree. I am a peer reviewer for The Natural Standard, and a copyeditor for Science-Based Medicine. My most important qualification is more than a decade of workaholic post-graduate study, clinical experience, and constant conversations with readers from around the world, including many experts who have provided countless suggestions and criticisms.

For more information, see: Who Am I to Say? More information about my qualifications, credentials and professional experiences for my readers and customers.

Homeopathic medicines are diluted medicines. What most people don’t realize is just how diluted. It’s one thing to believe that low concentrations of a substance can have an effect on a person. But a substances that’s been diluted out of existence? Some people believe that’s a bit much. This article explores some of extreme mathematics of homeopathic dilutions, using two impressive examples from dramatic effect: two celebrities who have tried to kill themselves with homeopathy, one for the purposes of demonstration, and the other quite deliberately. I’ll start with Mr. Randi and end with Ms. Joel.

Demonstration #1: James Randi’s death-defying overdose

I was delighted see James Randi here in Vancouver (January 26, 2009). Mr. Randi is the patron saint of debunkery and reason (a post shared with Carl Sagan, perhaps). His lecture made good use of stage magic to demonstrate how — and how easily — people are fooled into believing things, and it was pretty entertaining.

I picked up one interesting new piece of interesting knowledge: Avogadro’s limit (or constant, or number). I knew of the idea, but I had never made the connection with homeopathy.

Randi started out his lecture by consuming an entire bottle of Calms Forté, a popular homeopathic “sleep aid,” which had a warning on the bottle to seek medical assistance in case of overdose.

Needless to say, Mr. Randi was not poisoned. He didn’t even slow down!

So, just how “potent” can Calmes Fortés be? And why is the manufacturer putting a warning on the bottle when I have seen with my own eyes that the whole bottle can be swallowed with no more harm than a bitter taste?

(Regardless of what you might believe or think about homeopathy, you have got to admit that it’s rather fishy that there would be a false toxicity warning on the bottle!)

The Amazing Randi not being poisoned by Calmes Fortés. (Photo: Fred Bremmer)

This isn’t a full homeopathy debunking, by the way

Homeopathy has been called nonsense by an incredible variety of bright people already. Wikipedia has an excellent review of homeopathy that is more complete and authoritative than anything I can pull together. NCCAM, the biggest pro-alternative-medicine institution in history, publishes a page summarizing homeopathic issues but admits that “there is little evidence to support homeopathy,” despite their well-funded mandate to produce that evidence. And don’t miss the most important homeopathic scandal of the last decade: the BBC’s 2006 exposé of homeopaths in London who lethally told patients not to take genuine anti-malarial medications. And, best of all, take a look at one of the funniest YouTube videos ever produced about any kind of questionable medicine: learn by laughing! Dr. Steven Novella called this “more compelling in a couple of minutes than everything I’ve ever written about homeopathy.”

Extreme dilution delusion

What I learned from Randi’s lecture was some of the specific chemistry and mathematics of homeopathic dilution (and I went on to study it much more). A 1X dilution of the active ingredient — caffeine in the case of Calms Forté — means that it’s diluted to a tenth of its original concentration. A 2X dilution is one hundredth of its original concentration, 3X is a thousandth, and so on (powers of ten). But 1X, 2X and 3X are at the very lowest end of homeopathic dilutional extremes! Homeopathic dilution goes further — much further.

Most homeopathic medicines are diluted way1 past “Avogadro’s limit.” Amedeo Avogadro was a 19th Century Italian savant and chemist, and his “limit” is one of the laws of chemistry. It is somewhat like the folding limit, which states that you can only fold a piece of paper a few times, no matter how thin it is.2 Avogadro’s limit basically says you can only dilute so far before you lose the original substance altogether. The standard homeopathic dilution, advocated by the founder of homeopathy for most purposes, is not 3X, not 6X, not 10X, but 60X or 1 in 10⁶⁰, an absurdly big number. A 60X dilution is supposed to mean a concentration of 1 part per:

1,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000

But this is chemically impossible.

Beyond Avagadro’s limit

If you’re diluting something, you’ll hit Avogadro’s limit somewhere around 24X — nowhere close to 60X. By this point, you’re already dealing in concentrations vastly less than “trace amounts.” By the time you’re playing with Avogadro, your substance is so dilute that you have to do the math in terms of probabilities of finding individual molecules. But homeopathy cruises right past this and just keeps on diluting ... even though there’s nothing left to dilute.

Like diving into a black hole, things get weird and mathy past Avagadro’s limit. For each additional dilution past the limit, the chance of finding a molecule of the original substance drops by a power of ten. At 24X you’ve got only a 10% chance of finding a single molecule — that’s the practical limit. At 25X, your chances of finding that molecule drop to only one in a hundred. At 25X, one in a thousand. Such concentrations are much, much lower than completely safe levels of the nastiest chemical contaminants. There’s literally more uranium in your breakfast cereal than the “active” ingredient in a 25X homeopathic preparation.

And at 60X dilution …? Wikipedia explains such dilution “would require giving two billion doses per second to six billion people for 4 billion years to deliver a single molecule of the original material to any patient.” Wow.

There are many other amusing analogies for the extremity of homeopathic dilutions.

And a single molecule is not actually anything more than a theoretical concentration. It’s not actually possible using any technology to directly detect concentrations anywhere close to Avogadro’s limit.

More amazing analogies

There are numerous other amusing analogies for the extremity of homeopathic dilutions. James Randi explained it to us this way (I paraphrase):

“I called a friend of mine, a mathematician, and gave him the dosage size and dilution factor for Calms Forté, and asked him to work out how many pills I would have to take to be sure that I have gotten at least one molecule of active ingredient.”

The answer? Thirteen averaged-sized swimming pools full of them. For one molecule. Of caffeine. Such is the silliness of homeopathy. Here’s another fun analogy to finish this off (hat tip to Jonathan B., for the second time in two days):

Q: Dump a half litre vial of the most vile toxic substance you can imagine into the ocean. Wait ten years for it to completely diffuse throughout the waters of the world. Then take a random half-litre sample of ocean water from anywhere. How many molecules of the toxic substance will you find in the sample?

A: About 5000.

Maybe 5000 sounds like a lot to the average reader, but you have to compare that to how many other atoms are in there (an absurdly greater number). 5000 toxic molecules, no matter how toxic, are completely lost in a litre of water, actually undetectable in a half-litre sample, and you could drink the water in complete safety.

And yet this concentration is therefore about 5000 times higher than a 24X homeopathic remedy!

Perhaps the silliest thing about homeopathic dilution is that it ignores the fact that everything we drink and eat and breathe is harmlessly “polluted” with more thousands more molecules of countless substances than any homeopathically diluted ingredient. A homeopathic ingredient is always greatly outnumbered, in any sample, by countless other substances in an incredible variety of concentrations — all of which, in theory, should have an effect just like the homeopathic ingredient.

10X crazier

Homeopathic true believers aren’t bothered by any this mere science of course, because they actually like the idea that “less is more,” and that you don’t actually have to have any molecules of active ingredient at all, because the remedy “remembers” the “energetic imprint” of the ingredient and can still work therapeutic miracles even when it’s not there.

(What does water “remember” about all the other substances that have contaminated it at far higher concentrations, I wonder?)

However, believing that zero molecules can be therapeutic is at least 10X more crazy than believing that one molecule can be, which is pretty crazy itself. Before Randi explained Avogadro’s limit, I already knew that homeopaths believe that incredibly low (near nil) concentrations of an ingredient can have a therapeutic effect, but I was not aware that they believe that actually nil concentrations are just as good.

Now that I know, I am 10X happier to make fun of homeopathy.

A couple hours after the show, James Randi turned up at the Railway Club to visit with the BC Skeptics Society. Meeting in downtown Vancouver. Some of my best friends were there (like Kennedy, immediately to his left, and Brian waaaay at the back left). Alas, I had been dropped off at home because I was “tired” and didn’t want to go out to the pub! D’oh! (Photo: Fred Bremmer)

Demonstration #2: Alexa Ray Joel’s honest-to-goodness suicide attempt

Alexa Ray Joel, somehow still with us after trying to kill herself with an unbelievably teensy dosage of arnica and other herbs.

I could not make this up. Truth really is stranger than fiction — and funnier, too!

Back in December, Billy Joel’s daughter Alexa Ray tried to kill herself, probably because she heard “Piano Man” one too many times. She did a poor job of it. She tried to kill herself homeopathically. And not just any homeopathy — she took Traumeel.

That’s my turf.

Traumeel is (mostly) a homeopathic preparation of the herb arnica and allegedly good for “aches and pains.” It contains ingredients that would be modestly toxic (probably not lethal) … if they weren’t so diluted, of course. Alexa Ray’s “over”-dose led to about .00000000000000001% of her death. The crazy math of it being quite familiar to skeptics around the world, we all blew milk out their noses and slapped our thighs crimson when we heard this precious news item.

You could get more arnica montana by licking the plant — once. Hell, a hundredth of a lick would probably be a higher dose. Given the nature of Traumeel — not all that diluted by homeopathic standards, well below Avogadro’s limit but still extremely dilute — Alexa Ray’s suicide method was less dangerous than a single cigarette, or inhaling new car smell. It would be (much) easier (and more fun) to kill yourself with light beer. Death by Nerf bat would have been considerably more efficient.

Last year I wrote a comprehensive analysis of Traumeel that rose to the top of the Google charts, and there it remains — usually second in the listings only to traumeel.com itself. It is a polite article. It is a careful article. One does not want to step directly on the toes of those who profit from Traumeel. My aspersions are … diluted. The article does not ever say that Traumeel does not do anything, it just implies it.

And so does Alexa Ray’s failure to kill herself.

Obviously, you can’t kill yourself with Traumeel, no matter how hard you try. I promise. Alexa tried, and she is with us still.

This isn’t a safety feature of homeopathy. What’s more likely: that homeopathy doesn’t work at all? Or that homeopathy is potent medicine but not potent enough to hurt you in overdose? Just how wishful can thinking get?

The only thing this pathetic Joelian incident demonstrates is that the ingredients of Traumeel are so epically diluted that … that it … that it doesn’t … no, I’m not going to say it. You know how the sentence ends. I will just close with this:

“A leading toxicologist said it would be nearly impossible to overdose on the homeopathic medicine Traumeel,” reported the Daily News.

Um … “nearly”?

Notes

Way, way, way, way, waaaaaaaaaay. Return to text.

The paper-folding limit was long believed to be 7, but this was debunked by a high school student who proved that the real limit is 12 (see Wikipedia). This was memorably dramatized by the Mythbusters TV show. Return to text.