I have argued in previous comments that the utility of a person should be discounted by his or her measure, which may be based on algorithmic complexity. If this “torture vs specks” dilemma is to have the same force under this assumption, we’d have to reword it a bit:
Would you prefer that the measure of people horribly tortured for fifty years increases by x/3^^^3, or that the measure of people who get dust specks in their eyes increases by x?
I argue that no one, not even a superintelligence, can actually face such a choice. Because x is at most 1, x/3^^^3 is at most 1/3^^^3. But how can you increase the measure of something by more than 0 but no more than 1/3^^^3? You might, perhaps, generate a random number between 0 and 3^^^3 and do something only if that random number is 0. But algorithmic information theory says that for any program (even a superintelligence), there are pseudorandom sequences that it cannot distinguish from truly random sequences, and the prior probability that your random number generator is generating such a pseudorandom sequence is much higher than 1/3^^^3. Therefore the probability of that “random” number being 0 (or being any other number that you can think of) is actually much larger than 1/3^^^3.
Therefore, if someone tells you “measure of … increases by x/3^^^3″, in your mind you’ve got to be thinking ”… increases by y” for some y much larger than 1/3^^^3. I think my theories explains both those who answer SPECKS and those who say no answer is possible.
I have argued in previous comments that the utility of a person should be discounted by his or her measure, which may be based on algorithmic complexity. If this “torture vs specks” dilemma is to have the same force under this assumption, we’d have to reword it a bit:
Would you prefer that the measure of people horribly tortured for fifty years increases by x/3^^^3, or that the measure of people who get dust specks in their eyes increases by x?
I argue that no one, not even a superintelligence, can actually face such a choice. Because x is at most 1, x/3^^^3 is at most 1/3^^^3. But how can you increase the measure of something by more than 0 but no more than 1/3^^^3? You might, perhaps, generate a random number between 0 and 3^^^3 and do something only if that random number is 0. But algorithmic information theory says that for any program (even a superintelligence), there are pseudorandom sequences that it cannot distinguish from truly random sequences, and the prior probability that your random number generator is generating such a pseudorandom sequence is much higher than 1/3^^^3. Therefore the probability of that “random” number being 0 (or being any other number that you can think of) is actually much larger than 1/3^^^3.
Therefore, if someone tells you “measure of … increases by x/3^^^3″, in your mind you’ve got to be thinking ”… increases by y” for some y much larger than 1/3^^^3. I think my theories explains both those who answer SPECKS and those who say no answer is possible.