Homeopathy is a great topic for dividing society along faith lines. One camp claims that it is very effective and proves with countless personal experiences that the preparations are useful against certain symptoms and diseases. The other camp denies on scientific grounds that the memory of a vagabond active ingredient molecule in a diluent could have any effect. It is also a faith like the first one, only in a different way. The scientific group believes that when examined with the methods of science, homeopathy is no better than the placebo effect (the effect of a preparation without an active ingredient on a psychological basis). At the same time, scientific studies show that the placebo effect should not be underestimated, as it can have a detectable positive and, in certain cases, a negative effect.
So the teams supporting and opposing homeopathy are not arguing about whether the effect exists, but what the original cause was. However, the scientific methods for establishing this are less mature, since often only a correlation can be established between statistical data, but that does not even remotely mean the discovery of the cause.
I wouldn’t even want to get into such a debate, only homeopathic remedies provide a great opportunity to illustrate exponential and logarithmic functions, since the numbers on the product labels show the dilution of the active ingredient, namely in the form of a logarithm.
If you are not familiar with the essence of homeopathy, I recommend that you get information from a reliable source, I would just summarize that homeopathy is based on the assumption that highly diluted preparations of certain active ingredients are attributed with curative and disease-preventing effects. The mentioned very strong dilution is a great mental playground for those who like mathematics.
The basis of the production of homeopathic preparations is that, based on a suitable active ingredient, the preparation is diluted multiple times (to 10 or 100 times) with some neutral diluent (water, alcohol, sugar). If, for example, I diluted a solution 100 times 3 times in a row, the original concentration of the active ingredient is first reduced to one hundredth, then to that hundredth, and finally to that hundredth. At the end of such an exercise, only 1/1000,000 fold concentration remains. This seems quite thin, but no worries, the main thing is that the active ingredient is still there, maybe even a tiny sample is enough for our body to have a beneficial effect. Anyone who learned about atoms and Avogadro’s number (6,02214086 × 1023 , so many piece of protons or neutrons would weigh exactly one gram) at school starts to frown when the degree of dilution becomes so great that the quantity of the product we buy theoretically does not contain a single molecular active ingredient. This ratio occurs roughly at the 12th 100-fold dilution, which in homeopathy is not considered an extreme value at all, the usual labeling convention would designate such a preparation with C 12 or C 12H. The letter C indicates that it is a series of 100-fold dilutions, and the number indicates the number of times the dilution was repeated. If the number in question is greater than 12, then every further whole-number jump means another 100-fold dilution beyond the fact that we have practically said goodbye to the last molecule of the active ingredient. The higher the number after the letter C, the less active ingredient in the preparation.
For those who would like to calculate the markings, there is a simplified and an advanced calculation method for understanding the C XX marking:
Simple calculation: write down the ratio of the solvent to the active ingredient (for example, 10,000:1 gram of solvent per gram of active ingredient), then take half the number of zeros in this ratio. (10 000 -> 2; 1 000 000 -> 3 and so on).
A more correct calculation: we take the logarithm base 100 of the ratio of the solvent and the active ingredient. This is the same as the value obtained with the calculator’s logarithm function ln() divided by ln(100), i.e. 4.605.
It’s a good exercise for our brains to try to imagine something mundane, say diluting sugar, to give us a point of reference.
The sugar content of carbonated soft drinks is more the more well-known its advertising is (red labels, doping drinks in preference), roughly 10% sugar content is the upper limit, from there extra sugaring would be at the expense of the taste. If I throw 3 sugar cubes into a liter of clean water (roughly 3×3.7 grams), the solution is around 1%. If this had a homeopathic designation, it would be C1 (diluted 1 time 100-fold). If I pour this very slightly sugary water into a bathtub full of clean water, I have diluted it another 100 times, which would earn my bath water the C2 homeopathic designation. Now I fill a 1 l bottle with this solution and think about where I can pour it. If I were to pour the contents of the bottle into the lake Balaton (the water volume of Lake Balaton is approximately 1.9 km3, i.e. 1.9 * 1012 liters, let us assume clean water), then I would have done approximately 6 more 100-fold dilutions, so the dilution changed from C2 to C8. Now this is getting homeopathic.
If I were to drop the 3 sugar cubes for my morning tea into pure water equal to the volume of the entire globe (1,100,000,000,000,000,000,000,000), I would get a roughly C13 homeopathic sugar solution. I am sure that even the harshest poisons could not have any effect in such a dilution.
The strongest known poison is Botulinum toxin. If I consume 100 nanograms (0.0000001 grams) of botulinum toxin, it will probably kill me. Ladies, this is the stuff of Botox, I think you are prettier and healthier without it! If I drink this mixed with a small glass of water, the lethal dilution is equivalent to a homeopathic dilution between C4 and C5. C3 (more concentrated) will definitely kill me, a C6 dilution would be 100 times the lethal dose, maybe I’ll get away with unpleasant symptoms. I don’t think my eyelashes would twitch from any poison in a C10 dilution, but I don’t want to prove this in practice on my own body, but I would gladly accept comments from knowledgeable professionals on this matter.
However, there are also homeopathic preparations with C20, C30 and C200 dilutions. This is extremely reassuring in that if the dilution is done correctly, I don’t think it could cause any harm in the case of any random active ingredient.
I can no longer take the C200 dilution seriously, because it would mean a much greater dilution than when a single molecular active ingredient is dissolved with multiples of all the substances in the known universe.
It is not the first time that homeopathy advocates have heard such and similar calculations, and they believe that highly diluted preparations are not effective due to the presence of the active ingredient – because the active ingredient is practically no longer in them – but the positive effect is triggered by the “memory” of the carrier diluent. This is an argument that is difficult to refute scientifically, since although today’s science does not really offer a mechanism in the physical model of materials to which such a thing could be attributed, a new discovery could come at any time that could change this. The history of science is, after all, the history of the faulty assumptions that science refutes with its own methods and puts on new foundations. Therefore, the most unscientific statement about something can be that “there is no such effect”. We tend to use our faith for similar uncertain situations, and it is much freer than science.
I can now choose between two beliefs freely:
1: I don’t believe that a completely diluted substance would cure me anyway due to the memory of its active ingredient. No problem, I don’t buy homeopathic products, I get upset when my doctor offers one and I find it outrageous that pharmacies charge gullible people high prices for useless preparations. For those who did benefit from the product, I think it was all because of their faith (the placebo effect exists and should not be underestimated).
2: I believe that the effect of a C20, C30 or even C200 preparation is because a fraction of it once partied with a good-natured molecule and the memory of that had a good effect on it. I, as a person, remember my countless charismatic teachers and colleagues who may no longer be alive, but who taught me something. Why not in the world of molecules?
However, there are always two sides to the coin: what do I do with the thought of how many other molecules that preparation may have encountered during its production, which may not have such a good effect. When I decide to take some globuli to keep my throat from hurting, I roll a few in my palm and pop them in my mouth. As I swallow, the last week runs through my head, wherever I went, who I met, how many door handles I touched. Of course, I also wash my hands regularly, especially since Covid, but even the best hand wash only washes off, say, 99.99% of the materials stuck to my hands. This is exactly a C2 dilution 😊! Where did the water I wash my hands come from? After cleaning through a pipe system originally from the Danube. You can see what the water of the Danube is like (I think C2..C8 dilution of all kinds of impurities, I can only guess it, after cleaning I hope everything I don’t like is in a stronger dilution than C4). All in all, the drinking water that we regularly drink is “full” of arsenic, nitrate, boron, ammonium, and the residues of all kinds of agricultural chemicals after water purification. I only looked at the usual concentration for arsenic in Hungary: 1 to 10 micrograms per liter. This in itself is a C4-C5 homeopathic arsenic preparation, but in some settlements the situation is much worse, public official data is available on the internet (https://www.antsz.hu/felso_menu/temaink/ivoviz , you can surely find such data for your area).
When I look at the world like this, I have an idea:
Now I take a completely imaginary homeopathic pellet as a projection of my phantasy, touch it with very thoroughly washed hands, I swallow it and then rinse it off with a glass of “clean” tap water. With this, I practically performed on myself an extremely extensive homeopathic treatment package with a combination of a large number of different active ingredients, worth thousands of euros, and I didn’t even have to spend a single cent.
This second faith is more sympathetic to me now because I feel that I made a very good business.
This article is an opinion-based piece with a homeopathic dose of real facts. My goal with it is that everyone can form their own beliefs and support them with calculations made with data from reliable sources in peaceful discussions. Such calculations can be done on paper, with a pocket calculator or using the DockCalc program, which I developed for such purposes and offer to all curious people. You can download the program and the calculations for the article here. You can see an overview of the above calculations here: