Homeopathy or how to misapply evidence based medicine – Part 1

Solar system final

Somewhere out there (not to scale)

In the late 18th century Samuel Hahnemann (a German physician) proposed that “like cures like” [1]. He proposed that if a substance causes disease in a healthy person then a very small amount of the same substance can help a sick person [1].

“Hmm, hold on”, you might say “isn’t this sort of what we do with vaccines?”

Well, let’s look at some chemistry (if you don’t want to see all the math, skip to the conclusion below):

1. How much vaccine is there in each “shot”? 

A conjugated polysaccharide vaccine can have a molecular weight anywhere between 10,000 g/mol – 100,000 g/mol [2, 3].

There are 25 micrograms of each polysaccharide isolate in Pneumovax 23 [4]. That’s 23 x 25 = 575 micrograms (or 0.000575 g).

Let’s take 100,000 g/mol as the weight of the polysaccharide (that’s fairly consistent with weight required to make a polymer).

0.000575 g / 100,000 g/mol = 5.75 x 10^-9 mol

How many molecules of vaccine are there in each vaccine “shot”? Avogadro’s number is 6.0221413 x 10^23/mol, so…

(5.75 x 10^-9 mol)(6.0221413 x 10^23/mol) = ~3.5 x 10^15 (that’s 3,500 TRILLION molecules).

So, perhaps “like” can “cure like”, but you still need some molecules to be present. Ok, you need 3,500 TRILLION molecules.

2. Can homeopathic remedies match this chemistry? 

Let’s look at a preparation called “China 30” because this product will make another appearance in a later post.

China stands for Cinchona officinalis which is a medicinal plant [5].

The “30” means it has a “potency” of 30C. A potency of 1c is when you take 1 part of something and dissolve it in 100 parts diluent (making a 1:100 dilution). So you repeat this process 30 times. The result is a dilution of 10^-60. Not sure what the Cinchona officinalis preparation itself entails, but I’m going presume there’s some quinine in it. Also not sure how much of the original substance is used, but to be very generous, let’s say they use 1 kg (1000 g) and then dissolve that (which I doubt, but I’m feeling generous today). Quinine HCl salt has a solubility of about 1g/ml in warm water and alcohol [7].

So, quinine’s MW is 396.91 g/mol (quinine hydrochloride [7]). Take 1 kg and you have 2.5 moles of quinine.

2.5 moles would contain (2.5 x Avogadro’s number) 1.5 x 10^24 molecules.

But we had a dilution of 10^-60, so we have to multiply:

1.5 x 10^24 molecules x 10^-60 = 1.5 x 10^-36 molecules/liter. But, there’s no such thing as a 10^-36 of a molecule. Molecules either are or aren’t. So how many liters of this “30C” preparation would you have to drink to get just 1 molecule of quinine? Well…

1 liters / 1.5 x 10^-36 molecules/liter = 6.7 x 10^35 liters.

That seems like a large volume, but how large? Well, there are about 1.4 x 10^21 liters of water on Earth (that’s ALL the water on Earth; oceans, lakes, underground, everything!) [8].

So to get just ONE molecule of quinine from a “30C” preparation of China 30, you would need to drink all the water on Earth 482 TRILLION times. That’s still very hard to imagine.

Ok, the volume of the solar system filling all the space from the Sun to Mercury would be 8.2 x 10^35 liters (I got this by calculating the volume of a sphere with a radius of the distance from the Sun to Mercury, which Google and Wikipedia tell me is 58 million kilometers) [9]. So with a “30C” dilution you would need to drink as much of that preparation as would fill all the space from the Sun to Mercury!

3. What can we conclude about the basic chemistry of homeopathic preparations?

“Like” can “cure like” but you still need some real drug in the preparation. One shot of a Pneumovax 23 vaccine contains TRILLIONS of molecules of the drug and saves countless lives. On the other hand to get ONE molecule of drug from China 30 into your body, you would need to drink so much of it that it would fill all the space between the Sun and Mercury! I guess if you want quinine from China 30, you better get drinkin’!

P.S. If you’re wondering what this has to do with evidence based medicine (EBM), I promise you, I’m getting there.

1. Briggs J.P., Straus S.E. (2012). Chapter e2. Complementary, Alternative, and Integrative Medicine. In A.S. Fauci, D.L. Kasper, J.L. Jameson, D.L. Longo, S.L. Hauser (Eds),Harrison’s Principles of Internal Medicine, 18e.

2. Mallick J. (2009). Extraction and purification of capsular polysaccharide from streptococcus pneumoniae and Escherichia coli for conjugate vaccines preparation – Thesis Paper. [Link to PDF]

3. Ellis RW and Brodeur BR (Eds). (2003). New Bacterial Vaccines (Medical Intelligence Unit). Springer. [Google book link]

4. Lexi-Comp Online (TM). Hudson, Ohio: Lexi-Comp, Inc.; June 02, 2013.

5. Rajan A, Bagai U. SEM studies on blood cells of Plasmodium berghei infected Balb/c mice treated with artesunate and homeopathic medicine China. J Parasit Dis. 2011 Oct;35(2):134-9. Epub 2011 Aug 10. [PubMed Link]

6. Morgan J. Homeopathic Pharmacy. [Link to PDF]

7. The Merck Index. 14th edition.

8. USGC. How much water is there on Earth? http://ga.water.usgs.gov/edu/earthhowmuch.html

9. Have to admit, I just Googled this one.


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