Very-Related Question:
Typical homeopathic dilutions are 10^(-60). On average, this 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.
Could one argue that if we administer a homeopathic pill of vitamin C in the above dilution to every living person for the next 3^^^3 generations, the impact would be a humongous amount of flu-elimination?
If anyone convinces me that yes, I might accept to be a Torturer. Otherwise, I assume that the negligibility of the speck, plus people’s resilience, would make no lasting effects. Disutility would vanish in miliseconds. If they wouldn’t even notice or have memory of the specks after a while, it’d equate to zero disutility.
It’s not that I can’t do the maths. It’s that the evil of the speck seems too diluted to do harm.
That’s not really the point. The “dust speck” just means the mildest possible harm that a person can suffer; if you don’t think a dust speck with no long-term consequences can be harmful, you should mentally substitute a stubbed toe (with no long-term consequences) or the like.
Could one argue that if we administer a homeopathic pill of vitamin C in the above dilution to every living person for the next 3^^^3 generations, the impact would be a humongous amount of flu-elimination?
Easily. 3^^^3 = 3^^27 = 3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3 is so much larger than 10^60 that it is almost certain that many people will receive significant doses of vitamin C. Heck, 3^3^3^3^3^3 ~= 8.719e115 >> 10^60, and that’s merely 3^^6. If there is any causal relationship at all between receiving a dose of vitamin C and flu resistance (which I believe you imply for the purposes of the question), then a tremendous number of people will be protected from the flu—much, much in excess of 3^^26.
almost certain that many people will receive significant doses of vitamin C
Not what I said.
Each person will receive vitamin C diluted in the ratio of 10^(-60) (see reference here). The amount is the same for everyone, constant. Strictly one dose per person (as it was one speck per person).
But the number of persons are all people alive in the next 3^^^3 generations.
If there is any causal relationship at all between receiving a dose of vitamin C and flu resistance
...which wouldn’t mean it is linear at all. Above a certain dose can be lethal; below, can have no effect.
Does it sound reasonable that if you eat one nanogram of bread during severe starvation, it would retard your death in precisely zero seconds?
Does it sound reasonable that if you eat one nanogram of bread during severe starvation, it would retard your death in precisely zero seconds?
No. You use energy at some finite rate (I’ll assume 2000 kilocalories/day, dunno how much starvation affects this). A nanogram of bread contains a nonzero amount of energy (~2.5 microcalories). So it increases your life expectancy by a nonzero time (~100 nanoseconds). A similar analysis can be performed for anything down to and including a single molecule.
But each patient receives less than 10^60 molecules—one must assume some probability distribution on the number of molecules if we are to suppose any medication is delivered at all. Assuming the dilutions are performed as prescribed in a typical homeopathic preparation, a minuscule fraction will randomly have significantly more than the expected concentration, but even so at least the logarithm of the fraction will be on an order of magnitude with the logarithm of 10^-60 -- and therefore will still multiply to a tremendous number in 3^^^3 cases.
That said, even if you assume that the distribution is exactly as even as possible—every patient receives either zero or one molecule of vitamin C—there will be a minuscule probability that the effect of that one molecule will be at the tipping point. Truly minuscule—probably on the order of 10^-20 to 10^-25, a few in one Avogadro’s number—but this still corresponds to aiding 1 in 10^80 to 10^85 people, which multiplies to a tremendous number in 3^^^3 cases.
Mathematically, I have to agree with your reply: you either have no molecules or at least one. And then, your calculations hold true. And I’m wrong.
Physiologically, though, my argument is that the “nanoutility” that this molecule would add would have such a negligible effect that nothing would change in the person’s life measured by any practical purposes. It will pass completely unnoticed (zero!) — for each person in the 3^^^3 generations.
I assume a fuzzy scale of flu, so that no single molecule would turn sure-flu to sure-non-flu. As I assumed with the specks.
Even if you perform the more sophisticated analysis, the probability of the flu should shift slightly—and that slightly will be on the order of 10^-23, as before. And that times 3^^^3...
Very-Related Question: Typical homeopathic dilutions are 10^(-60). On average, this 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.
Could one argue that if we administer a homeopathic pill of vitamin C in the above dilution to every living person for the next 3^^^3 generations, the impact would be a humongous amount of flu-elimination?
If anyone convinces me that yes, I might accept to be a Torturer. Otherwise, I assume that the negligibility of the speck, plus people’s resilience, would make no lasting effects. Disutility would vanish in miliseconds. If they wouldn’t even notice or have memory of the specks after a while, it’d equate to zero disutility.
It’s not that I can’t do the maths. It’s that the evil of the speck seems too diluted to do harm.
Just like homeopathy is too diluted to do good.
That’s not really the point. The “dust speck” just means the mildest possible harm that a person can suffer; if you don’t think a dust speck with no long-term consequences can be harmful, you should mentally substitute a stubbed toe (with no long-term consequences) or the like.
Easily. 3^^^3 = 3^^27 = 3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3^3 is so much larger than 10^60 that it is almost certain that many people will receive significant doses of vitamin C. Heck, 3^3^3^3^3^3 ~= 8.719e115 >> 10^60, and that’s merely 3^^6. If there is any causal relationship at all between receiving a dose of vitamin C and flu resistance (which I believe you imply for the purposes of the question), then a tremendous number of people will be protected from the flu—much, much in excess of 3^^26.
Not what I said.
Each person will receive vitamin C diluted in the ratio of 10^(-60) (see reference here). The amount is the same for everyone, constant. Strictly one dose per person (as it was one speck per person).
But the number of persons are all people alive in the next 3^^^3 generations.
...which wouldn’t mean it is linear at all. Above a certain dose can be lethal; below, can have no effect.
Does it sound reasonable that if you eat one nanogram of bread during severe starvation, it would retard your death in precisely zero seconds?
No. You use energy at some finite rate (I’ll assume 2000 kilocalories/day, dunno how much starvation affects this). A nanogram of bread contains a nonzero amount of energy (~2.5 microcalories). So it increases your life expectancy by a nonzero time (~100 nanoseconds). A similar analysis can be performed for anything down to and including a single molecule.
But each patient receives less than 10^60 molecules—one must assume some probability distribution on the number of molecules if we are to suppose any medication is delivered at all. Assuming the dilutions are performed as prescribed in a typical homeopathic preparation, a minuscule fraction will randomly have significantly more than the expected concentration, but even so at least the logarithm of the fraction will be on an order of magnitude with the logarithm of 10^-60 -- and therefore will still multiply to a tremendous number in 3^^^3 cases.
That said, even if you assume that the distribution is exactly as even as possible—every patient receives either zero or one molecule of vitamin C—there will be a minuscule probability that the effect of that one molecule will be at the tipping point. Truly minuscule—probably on the order of 10^-20 to 10^-25, a few in one Avogadro’s number—but this still corresponds to aiding 1 in 10^80 to 10^85 people, which multiplies to a tremendous number in 3^^^3 cases.
Mathematically, I have to agree with your reply: you either have no molecules or at least one. And then, your calculations hold true. And I’m wrong.
Physiologically, though, my argument is that the “nanoutility” that this molecule would add would have such a negligible effect that nothing would change in the person’s life measured by any practical purposes. It will pass completely unnoticed (zero!) — for each person in the 3^^^3 generations.
I assume a fuzzy scale of flu, so that no single molecule would turn sure-flu to sure-non-flu. As I assumed with the specks.
Even if you perform the more sophisticated analysis, the probability of the flu should shift slightly—and that slightly will be on the order of 10^-23, as before. And that times 3^^^3...