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Naturally the T(s) function I posted earlier was wrong. It should have been T(s)=1576800000-0.0002(s-1). However, that doesn't change my question.
The torture decreases linearly simply because there's no reason to decrease it by more; the number of people increases in the way that it does because of the nature of 3^^^3 (i.e. the number is large enough to allow for this)
I don't see how that follows. Even the progression from the first setting to the second setting seems arbitrary. You've established a progression from one scenario (torturing a person for 50 years) to another (3^^^3 dust specks) but to me it just seems like one possible progression. I see no reason to set up the intermediate stages like you have.
The more we can increase it at each stop, the more obvious it is that we shouldn't move the lever at all, but rather we should leave it at torturing 1 person 50 years.
That's only true up to a certain point. If I had to make a graph of the harm caused by the settings it would probably look like a parabola with what would look almost like an asymptote near setting 1.
Btw, I got the 0.0002 constant by finding the number number of seconds in 50 years and dividing by 7,625,597,484,987 (assuming 365 days per year). It's rounded. The actual number is around 0.00020678.
It has 7,625,597,484,987 settings. On setting 1, 1 person is tortured for 50 years plus the pain of one dust speck. On setting 2, 3 persons are tortured for 50 years minus the pain of (50-year torture/7,625,597,484,987), i.e. they are tortured for a minute fraction of a second less than 50 years, again plus the pain of one dust speck. On setting 3, 3^3 persons, i.e. 27 persons, are tortured for 50 years minus two such fractions of a second, plus the pain of one dust speck. On setting 4, 3^27, i.e. 7,625,597,484,987 persons are tortured for 50 years minus 3 such fractions, plus the pain of one dust speck....
Once again, on setting 7,625,597,484,987, 3^^^3 persons are dust specked.
Any particular reason why the lever scales like that? Given a setting s we have the torture time defined by T(s) = 50-0.0002(s-1) and the number of people being tortured defined by P(s) = 3^P(s-1) where P(1) = 1. I see no reason why the torture time should decrease linearly if the number of people being tortured increases super-exponentially.