Please note; there is math ahead performed by someone (me) with the loosest grasp possible on arithmetic and chemistry. Please, if my numbers are off by any degree, let me know and I’d gladly correct them. Thanks. 

I once thought that the way to make money from homeopathic tinctures was through buying distilled water, and putting it into nice bottles with pretty labels, and selling those little bottles for $10 each. I’d even include a warning stating that the bottles contained absolutely no medicinal properties, and contained 100% distilled water. It would be a positive gold mine, even without the warning, as there is no way of testing a homeopathic remedy for effective ingredients, and so fraud could never effectively be proved in a court of law. However, I think that the real money is in ‘pure’ sea water, though, as it’s positively loaded with infinitesimal quantities of all sorts of things; maybe I’d even go with a name like Deep Sea Homeopathic Holistic Water.

I know people who purchase homeopathic products, and I was trying to come up with a good example to try to lay out the pure numbers on this, to try to show that what they’re buying is little more than diluted snake oil, with very little actual snake oil in it. I’ve seen proofs on web pages, but they tend to rely on numbers that other people have given, accepting them as gospel, and I wanted to know exactly how many atoms of something were in each bottle of 200C Snake Oil. I’m really surprised at just how little there is, and I think that the best example I can use to illustrate this is by turning the entire volume of Earth’s oceans and seas into a homeopathic cure. After all, covering 70% of the surface of the planet has to be a pretty visible metaphor.

“One approach is to use homeopathic remedies to target the tumors themselves. In this case, the homeopath selects remedies which match the symptom picture of the tumor itself (e.g. Conium Maculatum for hard immovable tumors that develop slowly). Homeopaths using this approach might also consider other symptoms (such as the individual’s food cravings, disposition, etc), but their primary focus is to target the tumor and reverse its growth. Some physician homeopaths also give remedies at the tumor site itself (in the form of an injection) to more aggressively stimulate a response. ” — The Cancer Cure Foundation

Conium Maculatum might be more recognizable to people as Poison Hemlock; the state poison of ancient Greece. Now, hemlock does have sedative and antispasmodic properties in small doses, so it’s not all about killing philosophers.

“To produce different remedy potencies, the mother tincture is diluted in an alcohol/ water mixture according to one of two scales, the decimal (x) and the centesimal (c). Between every stage of dilution the diluted tincture is succussed (shaken vigorously) in the decimal scale the dilution factor is 1:10 and in the centesimal it is 1:100. To produce a 1c potency of the allium remedy for example, one drop of the mother tincture is added to 99 drops of an alcohol/water mixture and succussed. To produce a 2c potency, one drop of the 1c mixture is added to 99 drops of an alcohol/water mixture and succussed. The number of a homeopathic remedy shows how many times it has been diluted and succussed, for example, Allium 6c has been diluted and succussed six times.” — Healthy New Age

ABCHomeopathy.com lists a 15mL, alcohol-diluted bottle of “3X” Hemlock for $8.99 and explains the different potencies of dilutions “Chronic illnesses should be treated with high potencies (30x-200c) and acute conditions with low potencies (6x or 6c)… Really high potencies such as 200C.” See, the more you dilute something, the stronger it is. The lower the chance that there is even an atom of Hemlock in that bottle, the more powerful it is…

“DECIMAL – potency based on the ratio of 1 part substance to 10 parts dilution. Designated with a X (in Europe designated with a D) after the remedy name. X potencies are considered low potencies. X potency is often used for children, sudden illness and first aid treatment.
CENTESIMAL – potency based on the ratio of 1 part substance to 99 parts dilution. Designated with a C (or left blank in Europe) after the remedy name. C potencies are considered medium potencies. C potency is often used for seasonal problems and chronic conditions.
MILLESIMAL – potency based on the ratio of 1 part substance to 1000 parts dilution. Designated with a M after the remedy name. M potencies are considered high potencies. M potency is used by practitioners for constitutional treatment.”Elixirs.com

Back to sea water. Using numbers from a 1968 publication, it appears that there are 0.0009 ppm of Copper, 0.021 ppm of Barium, and 0.0026 ppm of Arsenic in your average sample of sea water (Sea Friends – a part per million can be seen as mg / L); these are all valuable homeopathic tintures on their own, and would likely need to be diluted even further in order to approach the “potency” of a 200C mixture.

So, for the “C” scale, the Mother Tincture is a 1:100 mixture of water and/or alcohol to the essential ingredient. Let’s just say we start with a gram of the active ingredient and it’s diluted in a Liter of liquid; 1g/L. This isn’t exactly how the dilutions are made, as they tend to refer to “drops” of the tincture to solvent, but as you’ll see in a second, once the numbers get to where they are going, the difference in volume between a 1 mL ‘drop’ and a full Liter are insignificant. Even a kilogram of product diluted into a Liter of water to make the Mother Tincture, were it even possible, would yield little more effective compound in the 200C dilution.

Nevertheless, (in my experience) in cases of deep pathology (such as cancer), most patients have a profound level of resistance to feeling their feelings. Usually this is because of a built-in survival mechanism which protects them from feeling feelings which could destablize them and/or be more destructive than the disease itself (e.g. suicidal feelings). As a result, patients with deep pathology will tend to either have very moderate reactions to homeopathic remedies (because of the built in protective mechanism), or the remedies will release thoughts, emotions, and memories which are extremely toxic and destabilizing. In either case, there is strong initial resistance to the release process.

When patients are able to release suppressed toxic emotions (via homeopathy or other means), the optimal scenario is for the patient to work with accompanying practitioners (psychotherapists, counselors, healers, etc). Some homeopathic practitioners will provide some support, but often other professionals are needed. ” — The Cancer Cure Foundation

C indicates a power of 100, and X indicates a power of ten. 6X actually refers to a 10⁶ dilution, not the 1:6 most people would assume. As 10⁶ and 100³ are mathematically identical, a 6X dilution is scientifically, atomically, identical to the 3C product.

Assuming that you take the full 1 Liter of Mother Tincture and produce the absolute maximum volume you can of a 200C solution, you’re looking at a huge resulting volume.

1C dilution is the mother Tincture diluted by 1:100; resulting in 100L of solution
2C is diluted from 1C at 1:100 to yield 10,000L (100²)
3C is diluted from 2C at 1:100 to yield 1,000,000L (100³)
200C is the same thing again, 198 steps later, where we’re now at 100²⁰⁰ L of solution

That’s 100²⁰⁰, or a google², or with all the zeroes;

10,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000 L

All of the world’s oceans and seas contain an estimated 1.370 * 10²¹ L of water, or

1,370,000,000,000,000,000,000 L (Encarta)

What if we were to take that gram of initial product and dilute it to fill merely all of the world’s oceans? The resulting mix could be labeled as approximately “10.5C”, as 1.370* 10²¹ is mathematically the same as 1.370 * 100^10.5.

100¹⁰ == 100,000,000,000,000,000,000 L
100¹¹ == 10,000,000,000,000,000,000,000 L

Diluting that gram of initial product to somewhere between 10C and 11C would referred to as a medium or high potency dilution according to sources I’ve found.

1.370 * 10⁹ km³

1.370 * 10²¹ L

1 cubic kilometer = 1,000,000,000,000 (10¹²) L

By way of explanation, let’s take something inert like sand and make that into a homeopathic remedy to cure… oh, I don’t know. Let’s say this dilution will cure sun burns, because those have been seen to occur on sandy beaches.

We’ll use a gram of pure Silica sand, finely ground of course, with the chemical formula SiO₂; composed of 1 Silicon atom, and 2 Oxygen atoms.

How much does this molecule weigh? Well, Silicon weighs 28 atomic units, and Oxygen weighs 16 atomic units, for a total of 60 atomic units

Thanks to high school chemistry and the periodic table, we know that there are 6.023 x 10²³ atomic units in a gram. From there we can find that there are 6.02 x 10²³ / 60 = 1.00 x 10²² SiO2s in a gram, or 3 x 10²² atoms in a gram. Of course, when those atoms break down beyond the groups of three that make up SiO₂,

30,000,000,000,000,000,000,000 atoms. that’s plenty, right?

If we were to dissolve that gram of sand in all of the water that comprises all the Earth’s oceans and seas, complete with agitation and re-dilution again and again, and assuming absolutely perfect distribution of the sand atoms, we would see

(3 x 10²² atoms) / (1.37 x 10²¹ L == 21.8978102 atoms per L in all of the world’s oceans. If you look at the huge number above for 200C, you can readily see that a small amount of water such as that contained in all of the Earth’s oceans would need to be diluted many many more times at 1:100 to yield the full volume of 200C. Once we have surpassed 22 times the oceans’ volume, we have dropped past the point where you might statistically be able to expect a single atom to exist in a Liter of water, but yet this is a very strong product?

(3 * (10²²))atoms / (1.37000 * (10²¹)) Liters = 21.8978102 atoms / Liter if that one gram of silicon were spread equally throughout the world’s oceans and seas. That’s pretty impressive, actually, considering that that one little tiny gram of sand could be spread throughout the entirety of the world’s oceans. One might even be able to see seven full SiO₂ molecules in that Liter if you were lucky.

The problem comes that we’re dealing with a relatively small amount of solvent (water) as far as homeopathy is concerned. This is only 10²¹ L of water, not the 10⁴⁰⁰ L of water that a proper dilution to 200C would require. With the sample of sand, we’re limited to 3×10²² atoms; any dilution past that point becomes problematic. Once you have 10⁴⁰⁰ L of dilution,

(3 * 10²² atoms) / (1 * 10⁴⁰⁰ L) == 3 / 10³⁷⁸

There are only enough atoms to have THREE of them in 10³⁷⁸ L of water. Three individual, effectively indivisible (no amount of simply shaking the water is going to split them up, anyhow), atoms. How many 15mL bottles would you have to consume to statistically be able to say you had consumed 3 whole atoms worth of active ingredient to get both your Silicon and Oxygen atoms? Had we started with one kg per L of product, we’d still only have 1000 times as much product, or 3/ 10³⁷⁵; statistically insignificant difference, as you’d still need to consume the world’s oceans many times over to be certain that you had consumed your handful of atoms.

Interesting volumes that don’t come close to being large enough to hold a fully diluted 200C elixir;

Earth’s volume is roughly 1.0832 * 10²⁴ L

The Sun which we orbit is said to be able to contain 1.3 * 10⁶ Earths, for a total volume of 1.4082 × 10³⁰ L

That’s not much volume either, so how about a sphere that has a radius that’s a full light year?

1 light year = 9.4605284 × 10¹⁸ decimeters

(4 / 3) * PI * ((9.4605284 * (10¹⁸))³) = 3.54678441 * 10⁵¹ L

Not even close, but imagine that single gram of sand, held in your hand, with its 3 x 10²² atoms. See how not every Liter in that massive sphere that is so massive it would take light from the center a full year to escape the orb could contain even one single atom of the original material? Not even close.

Water doesn’t have memory, or it would be able to remember all the fish crap it had in it over the years; that couldn’t possibly be good for you. To believe that zero quantity of a medicine is effective in curing what ails you is to believe in real magic. Expelliarmus! Hmmm… nope.