MagnetoHydroDynamics comments on Torture vs. Dust Specks - Less Wrong
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I don't see that it's necessary -- or possible, for that matter -- for me to assign dust specks and torture to a single, continuous utility function. On a scale of disutility that includes such events as "being horribly tortured," the disutility of a momentary irritation such as a dust speck in the eye has a value of precisely zero -- not 0.000...0001, but just plain 0, and of course, 0 x 3^^^3 = 0.
Furthermore, I think the "minor irritations" scale on which dust specks fall might increase linearly with the time of exposure, and would certainly increase linearly with number of individuals exposed to it. On the other hand, the disutility of torture, given my understanding of how memory and anticipation affect people's experience of pain, would increase exponentially over time from a range of a few microseconds to a few days, then level off to something less than a linear increase with acclimatization over the range of days to years. It would increase linearly with the number of people suffering a given degree of pain for a given amount of time. (All other things being equal, of course. People's pain tolerance varies with age, experience, and genetics; it would be much worse to inflict any given amount of pain on a young child than on an adult who's already gone through, say, Navy S.E.A.L. training, and thus demonstrated a far higher-than-average pain tolerance.)
Thus, it would be enormously worse to inflict X amount of pain on one individual for sixty minutes than on 60 individuals for one minute each, which in turn would be much worse than inflicting the same pain on 3600 individuals for one second each -- and if we could spread it out to a microsecond each for 36,000,000 people, the disutility might vanish altogether as the "experience" becomes too brief for the human nervous system to register at all, and thus ceases to be an experience. However, once we get past where acclimatization inflects the curve, it would be much worse to torture 52 people for one week each than to torture one person for an entire year. It might even be worse to torture ten people for one week each than one for an entire year -- I'm not sure of the precise values involved in this utility function, and happily, at the fine scale, I'll probably never need to work them out (the empirical test is possible in principle, of course, but could only be performed in practice by a fiend like Josef Mengele).
There's also the fact that knowing many people can and have endured a particular pain seems to make it more endurable for others who are aware of that fact. As Spider Robinson says, "Shared joy is increased, shared pain is lessened" -- I don't know if that really "refutes entropy," but both of those clauses are true individually. That's part of the reason egalitarianism, as other commenters have pointed out, has positive utility value.
If getting hit by a dust speck has u = 0, then air pressure great enough to crush you has u = 0.
Nope, that doesn't follow; multiplication isn't the only possible operation that can be applied to this scale.