A Torturous Dilemma

In light of the recent discussion about torture around here, this little thought experiment seems appropriate and perhaps informative. If you don’t think that torture is ever a good choice, then read to the end of this post — you will change your mind:

If neither event is going to happen to you personally, but you still had to choose one or the other:

Would you prefer that one person be horribly tortured for fifty years without hope or rest, or that 3^^^3 people get dust specks in their eyes?

I think the answer is obvious. How about you?

Eliezer Yudkowsky, author of the dilemma, explains the number of people to receive dust specks (written as 3^^^3) as this:

3^^^3 is an exponential tower of 3s which is 7,625,597,484,987 layers tall. You start with 1; raise 3 to the power of 1 to get 3; raise 3 to the power of 3 to get 27; raise 3 to the power of 27 to get 7625597484987; raise 3 to the power of 7625597484987 to get a number much larger than the number of atoms in the universe, but which could still be written down in base 10, on 100 square kilometers of paper; then raise 3 to that power; and continue until you’ve exponentiated 7625597484987 times. That’s 3^^^3. It’s the smallest simple inconceivably huge number I know.

So the choice is between 50 years of torture for one person, or dust specks in the eyes of an unfathomably large number of people. You as an omnipotent being personally unaffected by either event must choose between the two. Would it surprise you to learn that a good number of rational, sentient and non-sadistic people would choose torture? I’m guessing it would.

If it doesn’t surprise you, then you’re probably a utilitarian (and perhaps a statistics geek). If instead you think specks are the obvious answer, then consider the following and see if it changes your mind:

Prometheus(1) It is literally impossible for you to comprehend in any meaningful way a number as large as 3^^^3.

(2) If you aggregate the amount of suffering from getting a barely perceptible dust speck in the eye for such an impossibly large number of people, then you must have an impossibly large amount of suffering caused by such event.

(3) If you wish to have a have a world where there is the least amount of suffering (N.B. which assumption is what makes this a moral dilemma), then the best choice is to opt for the enormous, yet conceivable, amount of suffering (i.e. torture) over the unfathomably large amount of suffering.

Still not convinced? OK, fair enough. The natural inclination is to consider the two choices as the end points on a continuum — i.e. that a dust speck in your eye is the least bad thing that can happen, while torture for 50 years is the worst. However, comparing an impossible-to-conceive scenario (3^^^3 dust specks) to one that is at least conceivable is not symmetrical. If we want to make the extremes true opposites, we would have to come up with a torture scenario that is approximately as inconceivable as the dust speck one.

Therefore, instead of the 50 years of torture, let’s instead consider a combination of the fates of Prometheus and Sisyphus. Suppose that one person (let’s call him Promephus) is chained to a boulder, which he must push up a hill from dawn to dusk, only to have the boulder roll back down the hill at the end of the day dragging him with it. Upon the boulder coming to a rest, an eagle swoops down, claws out and devours his liver. For the sake of congruity, let’s say that Promephus must suffer this fate for 3^^^3 days.

You’re even more convinced now that dust specks is the way to go. Even though the total amount of suffering is equal regardless of the choice, it still seems intuitively correct that dust specks are the least bad alternative.

OK. But what happens if we start moving these two extremes towards each other? By that I mean that we gradually lessen the suffering, although the amount of total suffering for each side will remain equal. Accordingly, the dust speck alternative is made a little worse but for fewer and fewer people, and the torture alternative is made a little better (in increments of 1/3^^^3 of course), all the while the amount of suffering is theoretically equal on each side. For example, at some point maybe there are (3^^^3 - n) number of people have a toe smashed with a hammer, while Promephus must suffer unrelenting torture for 1000 years.* Let’s then assume that (3^^^3 - n) is still a very large number. In fact, let’s just remove one exponent and say that this number of people getting their toes smashed is equal to 3^^3, or 7,625,597,484,987 people. This is still a sufficiently large enough number of people to approximate Promephus’ torture (think of it as the number of seconds in a little more than 240,000 years), yet the amount of suffering is becoming more and more conceivable.

Then assume that we have a device which could measure suffering (a “sufferometer” or “SOM”) in units of disutility (”DU’s”) the two amounts of suffering would be precisely equal in DU’s.Sisyphus

We continue to reduce the amount of suffering equally on both sides, getting smaller and smaller DU readings on our handy dandy SOM. For each DU of change, therefore, the amount of suffering by one person is lessened, while the amount of suffering for x people is decreased, and at certain intervals x will decrease as well. As we decrease x, however, we will also be magnifying the type of suffering so that in the aggregate x people continue to register the same DU reading on the SOM as Promephus. But overall, the total amount of suffering is ever decreasing. If we continue in this vein, at what point does it become obvious that torture is the best choice, even though, as stated before, from a utiltarian perspective the choice is irrelevant?

For example, let’s then say that there are an equal number of DU’s in 10 years of Promephus being unrelentingly tortured, as there are in 100,000 people being killed by a gunshot to the stomach.

Or that, reducing DU’s further, 1 year of Promephus’ torture = 10,000 people being killed by a dirty bomb blast.

Or that, 1 week of torture = 2,974 people being killed in a terrorist attack.

Keeping in mind that choosing one alternative prevents the other, how many of you are choosing torture as the best choice now?


[* Note: We could simply remove one dust speck sufferer for each day of Promephus’ suffering. At some point, however, we will have one dust speck sufferer and one day of Promephus suffering, which are not equal in the amount of suffering. That then requires a whole new way to close the gap in the type of suffering. Suddenly we are back to increasing the number of sufferers on the least-bad side in order to equal the amount of Promephus’ suffering.]

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2 Responses to “A Torturous Dilemma”

  1. on 02 Nov 2007 at 6:53 pm Lance

    I love Overcoming Bias. When I first started this thing I expected I would spend a lot of time doing similar kinds of things, but then Overcoming Bias exists so I don’t have to.

  2. on 03 Nov 2007 at 2:22 am MichaelW

    I must admit that I haven’t spent much time there, but when I took a jaunt over to the site recently I was thrilled by the mental gymnastics going on. I can’t really follow a lot of what’s being discussed, but the hypo (I and the others it spawned) are fascinating to think about.

    The subject of this post was the very first thing that came to mind when I first read the scenario. I really had to think about it a great deal before I was able to write it, rewrite it, and finally post it. Such a simple thought exercise can be (and, to Eliezer’s credit, probably will be) fodder for a great many other challenges to intuitive thinking.

    Simply because we have been discussing waterboarding recently, I found the exercise to offer some rather counter-intuitive insights. I’m really curious if anyone else sees what I do, but I’m afraid that almost nobody will ever read this post.

    C’est la vie ;)

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