X(0)) is a smaller value of anti-utility than X(1)), absolutely. I do not, however, know that the decrease of one second is non-negligible for that measurement of anti-utility, under the definitions I have provided.
There are about 1,5 billion seconds in 50 years, so let’s define X(n) recursively as torturing ten times more people than in scenario X(n-1) for time equal to 1,499,999,999⁄1,500,000,000 of time used in scenario X(n-1).
That math gets ugly to try to conceptualize (fractional values of fractional values), but I can appreciate the intention.
since pain is difficult to measure, let’s precisely define the way torture is done
This is a non-trivial alteration to the argument, but I will stipulate it for the time being.
At approximately n = 3.8 10^10, X(n) means taking 10^(3.810^10) people and touching their skin with a hot needle for 1⁄100 of a second (the tip of the needle which comes into contact with the skin will have 0.0001 square milimeters). Now this is so negligible pain that a dust speck in the eye is clearly worse.
“Clearly”? I suffer from opacity you apparently lack; I cannot distinguish between the two.
Now this seems paradoxical, since going from X(n) to X(n+1) means reducing the amount of suffering of those who already suffer by a tiny amount, roughly one billionth, for the price of adding nine new sufferers for each existing one.
The paradox exists only if suffering is quantified linearly. If it is quantified logarithmically, a one-billionth shift on some position of the logarithmic scale is going to overwhelm the signal of the linearly-multiplicative increasing population of individuals. (Please note that this quantification is on a per-individual basis, which can once quantified be simply added.)
This is far from being a paradox: it is a natural and expected consequence.
“Clearly”? I suffer from opacity you apparently lack; I cannot distinguish between the two.
Then substitute “worse or equal” for “worse”, the argument remains.
I do not, however, know that the decrease of one second is non-negligible for that measurement of anti-utility, under the definitions I have provided.
Same thing, doesn’t matter whether it is or it isn’t. The only things which matters is that X(n) is preferable or equal to X(n+1), and that “specks” is worse or equal to X(3.8 * 10^10). If “specks” is also preferable to X(0), we have circular preferences.
If it is quantified logarithmically, a one-billionth shift on some position of the logarithmic scale is going to overwhelm the signal of the linearly-multiplicative increasing population of individuals.
So, you are saying that there indeed is n such that X(n) is worse than X(n+1); it means that there are t and p such that burning p percent of one person’s skin for t seconds is worse than 0.999999999 t seconds of burning 0.999999999 p percent of skins of ten people. Do I interpret it correctly?
Edited: “worse” substituted for “preferable” in the 2nd answer.
So, you are saying that there indeed is n such that X(n) is worse than X(n+1); it means that there are t and p such that burning p percent of one person’s skin for t seconds is worse than 0.999999999 t seconds of burning 0.999999999 p percent of skins of ten people. Do I interpret it correctly?
X(0)) is a smaller value of anti-utility than X(1)), absolutely. I do not, however, know that the decrease of one second is non-negligible for that measurement of anti-utility, under the definitions I have provided.
That math gets ugly to try to conceptualize (fractional values of fractional values), but I can appreciate the intention.
This is a non-trivial alteration to the argument, but I will stipulate it for the time being.
“Clearly”? I suffer from opacity you apparently lack; I cannot distinguish between the two.
The paradox exists only if suffering is quantified linearly. If it is quantified logarithmically, a one-billionth shift on some position of the logarithmic scale is going to overwhelm the signal of the linearly-multiplicative increasing population of individuals. (Please note that this quantification is on a per-individual basis, which can once quantified be simply added.)
This is far from being a paradox: it is a natural and expected consequence.
Then substitute “worse or equal” for “worse”, the argument remains.
Same thing, doesn’t matter whether it is or it isn’t. The only things which matters is that X(n) is preferable or equal to X(n+1), and that “specks” is worse or equal to X(3.8 * 10^10). If “specks” is also preferable to X(0), we have circular preferences.
So, you are saying that there indeed is n such that X(n) is worse than X(n+1); it means that there are t and p such that burning p percent of one person’s skin for t seconds is worse than 0.999999999 t seconds of burning 0.999999999 p percent of skins of ten people. Do I interpret it correctly?
Edited: “worse” substituted for “preferable” in the 2nd answer.
Yes.