So there is some number of 0.394 intensity pains such that no number of 0.393 intensity pains can ever be worse, despite the fact that these pains differ by 0.001, stipulated by Doug to be the pain of a dust speck.
In terms of the constants, it comes out to NT > -a*ln(1-I1/I2), where I1 is the lesser pain and I2 is the greater pain. This does strike me as somewhat undesirable; I would prefer that the required NT go to infinity when I1 and I2 are sufficiently close but not sufficiently far. Unfortunately, I can’t do this and still be consistent; the limit can’t depend on the difference between I1 and I2. I either have to accept a preference function in which all pains aggregate to the same limit, or there exits two pains arbitrarily close together such that a finite amount of one is worse than a Nearly Infinite amount of the other.
I’m not confident in my constants or in my ability to calculate I(brain state), but yes, I think I can “bite the bullet” on this one. I hereby declare that, for any two pains, if I1 > I2, then there is an amount of I1 pain that is worse than a Nearly Infinite amount of pain I2.
However, I believe that we live in a finite universe, so hopefully I don’t have to deal with Nearly Infinite quantities of anything. ;) You’d best keep me well away from that button that destroys the world, because I find it very, very tempting.
Let’s see just what that number is...
0.394(1-e^(-NT/100 personyears) > 0.393
1-e(-NT/100 personyears) > 0.998
e^(-NT/100 personyears) < 0.002538
-NT/100 personyears < −5.976
NT > 597.6 person*years
In terms of the constants, it comes out to NT > -a*ln(1-I1/I2), where I1 is the lesser pain and I2 is the greater pain. This does strike me as somewhat undesirable; I would prefer that the required NT go to infinity when I1 and I2 are sufficiently close but not sufficiently far. Unfortunately, I can’t do this and still be consistent; the limit can’t depend on the difference between I1 and I2. I either have to accept a preference function in which all pains aggregate to the same limit, or there exits two pains arbitrarily close together such that a finite amount of one is worse than a Nearly Infinite amount of the other.
I’m not confident in my constants or in my ability to calculate I(brain state), but yes, I think I can “bite the bullet” on this one. I hereby declare that, for any two pains, if I1 > I2, then there is an amount of I1 pain that is worse than a Nearly Infinite amount of pain I2.
However, I believe that we live in a finite universe, so hopefully I don’t have to deal with Nearly Infinite quantities of anything. ;) You’d best keep me well away from that button that destroys the world, because I find it very, very tempting.