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 dust specks have a value of 0, then what’s the smallest amount of discomfort that has a nonzero value instead? Use that as your replacement dust speck.
And of course, the disutility of torture certainly increases in nonlinear ways with time. The 3^^^3 is there to make up for that. 50 years of torture for one person is probably not as bad as 25 years of torture for a trillion people. This in turn is probably not as bad as 12.5 years of torture for a trillion trillion people (sorry my large number vocabulary is lacking). If we keep doing this (halving the torture length, multiplying the number of people by a trillion) then are we always going from bad to worse? And do we ever get to the point where each individual person tortured experiences about as much discomfort as our replacement dust speck?
If dust specks have a value of 0, then what’s the smallest amount of discomfort that has a nonzero value instead?
I don’t know exactly where I’d make the qualitative jump from the “discomfort” scale to the “pain” scale. There are so many different kinds of unpleasant stimuli, and it’s difficult to compare them. For electric shock, say, there’s probably a particular curve of voltage, amperage and duration below which the shock would qualify as discomfort, with a zero value on the pain scale, and above which it becomes pain (I’ll even go so far as to say that for short periods of contact, the voltage and amperage values lies between those of a violet wand and those of a stun gun). For localized heat, I think it would have to be at least enough to cause a small first-degree burn; for localized cold, enough to cause the beginnings of frostbite (i.e. a few living cells lysed by the formation of ice crystals in their cytoplasm). For heat and cold over the whole body, it would have to be enough to overcome the body’s natural thermostat, initiating hypothermia or heatstroke.
It occurs to me that I’ve purposefully endured levels of discomfort I would probably regard as pain with a non-zero value on the torture scale if it was inflicted on me involuntarily, as a result of working out at the gym (which has an expected payoff in health and appearance, of course), and from wearing an IV for two 36-hour periods in a pharmacokinetic study for which I’d volunteered (it paid $500); I would certainly do so again, for the same inducements. Choice makes a big difference in our subjective experience of an unpleasant stimulus.
50 years of torture for one person is probably not as bad as 25 years of torture for a trillion people.
Of course not; by the scale I posited above, 50 years for one person isn’t even as bad as 25 years for two people.
If we keep doing this (halving the torture length, multiplying the number of people by a trillion) then are we always going from bad to worse?
No, but the length has to get pretty tiny (probably somewhere between a millisecond and a microsecond) before we reverse the direction.
And do we ever get to the point where each individual person tortured experiences about as much discomfort as our replacement dust speck?
Yes, we do; in fact, we eventually get to a point where each person “tortured” experiences no discomfort at all, because the nervous system is not infinitely fast nor infinitely sensitive. If you’re using temperature for your torture, heat transfer happens at a finite speed; no matter how hot or cold the material that touches your skin, there’s a possible time of contact short enough that it wouldn’t change your skin temperature enough to cause any discomfort at all. Even an electric shock could be brief enough not to register.
The idea that the utility should be continuous is mathematically equivalent to the idea that an infinitesimal change on the discomfort/pain scale should give an infinitesimal change in utility. If you don’t use that axiom to derive your utility funciton, you can have sharp jumps at arbitrary pain thresholds. That’s perfectly OK—but then you have to choose where the jumps are.
I think that’s probably more practical than trying to make it continuous, considering that our nervous systems are incapable of perceiving infinitesimal changes.
Yes, we are running on corrupted hardware at about
100 Hz, and I agree that defining broad categories to make first-cut decisions is necessary.
But if we were designing a morality program for a super-intelligent AI, we would want to be as mathematically consistent as possible. As shminux implies, we can construct pathological situations that exploit the particular choice of discontinuities to yield unwanted or inconsistent results.
It could be worse than that: there might not be a way to choose the jumps consistently, say, to include different kinds of discomfort, some related to physical pain and others not (tickling? itching? anguish? ennui?)
I might have to bring it up to a minute or two before I’d give you that—I perceive the exponential growth in disutility for extreme pain over time during the first few minutes/hours/days as very, very steep. Now, if we posit that the people involved are immortal, that would change the equation quite a bit, because fifty years isn’t proportionally that much more than fifty seconds in a life that lasts for billions of years; but assuming the present human lifespan, fifty years is the bulk of a person’s life. What duration of torture qualifies as a literal fate worse than (immediate) death, for a human with a life expectancy of eighty years? I’ll posit that it’s more than five years and less than fifty, but beyond that I wouldn’t care to try to choose.
Let’s step away from outright torture and look at something different: solitary confinement. How long does a person have to be locked in a room against his or her will before it rises to a level that would have a non-zero disutility you could multiply by 3^^^3 to get a higher disutility than that of a single person (with a typical, present-day human lifespan) locked up that way for fifty years? I’m thinking, off the top of my head, that non-zero disutility on that scale would arise somewhere between 12 and 24 hours.
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 dust specks have a value of 0, then what’s the smallest amount of discomfort that has a nonzero value instead? Use that as your replacement dust speck.
And of course, the disutility of torture certainly increases in nonlinear ways with time. The 3^^^3 is there to make up for that. 50 years of torture for one person is probably not as bad as 25 years of torture for a trillion people. This in turn is probably not as bad as 12.5 years of torture for a trillion trillion people (sorry my large number vocabulary is lacking). If we keep doing this (halving the torture length, multiplying the number of people by a trillion) then are we always going from bad to worse? And do we ever get to the point where each individual person tortured experiences about as much discomfort as our replacement dust speck?
If dust specks have a value of 0, then what’s the smallest amount of discomfort that has a nonzero value instead?
I don’t know exactly where I’d make the qualitative jump from the “discomfort” scale to the “pain” scale. There are so many different kinds of unpleasant stimuli, and it’s difficult to compare them. For electric shock, say, there’s probably a particular curve of voltage, amperage and duration below which the shock would qualify as discomfort, with a zero value on the pain scale, and above which it becomes pain (I’ll even go so far as to say that for short periods of contact, the voltage and amperage values lies between those of a violet wand and those of a stun gun). For localized heat, I think it would have to be at least enough to cause a small first-degree burn; for localized cold, enough to cause the beginnings of frostbite (i.e. a few living cells lysed by the formation of ice crystals in their cytoplasm). For heat and cold over the whole body, it would have to be enough to overcome the body’s natural thermostat, initiating hypothermia or heatstroke.
It occurs to me that I’ve purposefully endured levels of discomfort I would probably regard as pain with a non-zero value on the torture scale if it was inflicted on me involuntarily, as a result of working out at the gym (which has an expected payoff in health and appearance, of course), and from wearing an IV for two 36-hour periods in a pharmacokinetic study for which I’d volunteered (it paid $500); I would certainly do so again, for the same inducements. Choice makes a big difference in our subjective experience of an unpleasant stimulus.
50 years of torture for one person is probably not as bad as 25 years of torture for a trillion people.
Of course not; by the scale I posited above, 50 years for one person isn’t even as bad as 25 years for two people.
If we keep doing this (halving the torture length, multiplying the number of people by a trillion) then are we always going from bad to worse?
No, but the length has to get pretty tiny (probably somewhere between a millisecond and a microsecond) before we reverse the direction.
And do we ever get to the point where each individual person tortured experiences about as much discomfort as our replacement dust speck?
Yes, we do; in fact, we eventually get to a point where each person “tortured” experiences no discomfort at all, because the nervous system is not infinitely fast nor infinitely sensitive. If you’re using temperature for your torture, heat transfer happens at a finite speed; no matter how hot or cold the material that touches your skin, there’s a possible time of contact short enough that it wouldn’t change your skin temperature enough to cause any discomfort at all. Even an electric shock could be brief enough not to register.
The idea that the utility should be continuous is mathematically equivalent to the idea that an infinitesimal change on the discomfort/pain scale should give an infinitesimal change in utility. If you don’t use that axiom to derive your utility funciton, you can have sharp jumps at arbitrary pain thresholds. That’s perfectly OK—but then you have to choose where the jumps are.
I think that’s probably more practical than trying to make it continuous, considering that our nervous systems are incapable of perceiving infinitesimal changes.
Yes, we are running on corrupted hardware at about 100 Hz, and I agree that defining broad categories to make first-cut decisions is necessary.
But if we were designing a morality program for a super-intelligent AI, we would want to be as mathematically consistent as possible. As shminux implies, we can construct pathological situations that exploit the particular choice of discontinuities to yield unwanted or inconsistent results.
It could be worse than that: there might not be a way to choose the jumps consistently, say, to include different kinds of discomfort, some related to physical pain and others not (tickling? itching? anguish? ennui?)
In other words, it follows that 1 person being tortured for 50 years is better than 3^^^3 people being tortured for a millisecond.
You’re well on your way to the dark side.
I might have to bring it up to a minute or two before I’d give you that—I perceive the exponential growth in disutility for extreme pain over time during the first few minutes/hours/days as very, very steep. Now, if we posit that the people involved are immortal, that would change the equation quite a bit, because fifty years isn’t proportionally that much more than fifty seconds in a life that lasts for billions of years; but assuming the present human lifespan, fifty years is the bulk of a person’s life. What duration of torture qualifies as a literal fate worse than (immediate) death, for a human with a life expectancy of eighty years? I’ll posit that it’s more than five years and less than fifty, but beyond that I wouldn’t care to try to choose.
Let’s step away from outright torture and look at something different: solitary confinement. How long does a person have to be locked in a room against his or her will before it rises to a level that would have a non-zero disutility you could multiply by 3^^^3 to get a higher disutility than that of a single person (with a typical, present-day human lifespan) locked up that way for fifty years? I’m thinking, off the top of my head, that non-zero disutility on that scale would arise somewhere between 12 and 24 hours.
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.