Homeopathic Dilutions

Through history homeopaths have been hailed as saviors of modern medicine and/or demonized as quacks.  I will take a mathematical look at homeopathic dilutions.

Homeopathic dilutions are supposedly able to cure all sorts of illnesses and ailments by using strange and sometimes deadly substances in highly diluted forms.  'this concept has proven effective in some areas, particularly in the field of allergic reactions to things like bee venom and peanuts.  However, homeopathic dilutions are far more diluted than anything used in viable research studies.

Homeopathic dilutions are diluted to extreme amounts.  But just how extreme?  We will take a look.

When you get a homeopathic dilution, it is often tagged with some dilution amount like 10X, 100X or even 300X.  These numbers are geometric progressions of dilution rates.  These are essentially the exponents of the dilution base of 10.  So this is to say a 1X dilution is `10^1=10` times diluted.  Basically it is 9 parts "carrier" and 1 part "cure."

A 2X dilution would be `10^2=100` times diluted, or 99 parts carrier and 1 part cure.  

As you can see, this dilution rate gets really big, really fast.

I can tell you that a 100X dilution is ridiculously diluted. A 300X dilution is not even possible. I will go even further and say 100X dilutions are meaningless.  AS are anything over 80X.  Why?  because there are `1.32*10^80` particles in the observable universe.  To be guaranteed you get a single molecule of the "cure" you would have to consume a quantity of the "carrier"  the size of the observable universe.

But lets look a the dilutions that are more believable.  We will assume both the "cure" and the "carrier" are Hydrogen.  This will give us the smallest possible mass to be consumed.  Just remember, the REAL volume will be much larger than what we calculate.

The mass of a Hydrogen atom is `1.67*10^-24` grams.  An easy conversion is that a 24X dilution would require you to consume 1.67 grams of the dilution to get a single atom of the cure.  While this doesn't sound too bad, bumping that up to a 25X dilution would require you to consume 16.7 grams.  A 26X would require 167 grams to be consumed.  A 27X would require 1.67 kg to be consumed.  

We aren't even to the homeopathic regions yet.  We can keep going.  28X would require consumption of 16.7 kg, 29X would require 167 kg and finally, a 30X dilution would require you to consume 1,670 kg of the carrier, to get a single atom of the cure.

For an American, that is more than 3,681 pounds.  

We can go a bit further, just in case you are wiling to consume over a metric ton of this "remedy" 3 times a day.  31X would be a cool 18 tons.  32X would be 180 tons.  At 46X you would have to consume 3 Earth-masses to get a single atom of cure.  at 51X you would have to consume a mass of nearly 84% of the Sun.

As a result, homeopathic remedies are mathematically proven to be quackery.