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 lik... (read more)
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... (read more)
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.