"What's the worst that can happen?" goes the optimistic saying. It's probably a bad question to ask anyone with a creative imagination. Let's consider the problem on an individual level: it's not really the worst that can happen, but would nonetheless be fairly bad, if you were horribly tortured for a number of years. This is one of the worse things that can realistically happen to one person in today's world.
What's the least bad, bad thing that can happen? Well, suppose a dust speck floated into your eye and irritated it just a little, for a fraction of a second, barely enough to make you notice before you blink and wipe away the dust speck.
For our next ingredient, we need a large number. Let's use 3^^^3, written in Knuth's up-arrow notation:
- 3^3 = 27.
- 3^^3 = (3^(3^3)) = 3^27 = 7625597484987.
- 3^^^3 = (3^^(3^^3)) = 3^^7625597484987 = (3^(3^(3^(... 7625597484987 times ...)))).
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.
Now here's the moral dilemma. 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?
Now, do you have any actual argument as to why the 'badness' function computed over a box containing two persons with a dust speck, is exactly twice the badness of a box containing one person with a dust speck, all the way up to very large numbers (when you may even have exhausted the number of possible distinct people) ?
I don't think you do. This is why this stuff strikes me as pseudomath. You don't even state your premises let alone justify them.
You're right, I don't. And I do not really need it in this case.
What I need is a cost function C(e,n) - e is some event and n is the number of people being subjected to said event, i.e. everyone gets their own - where for ε > 0: C(e,n+m) > C(e,n) + ε for some m. I guess we can limit e to "torture for 50 years" and "dust specks" so this generally makes sense at all.
The reason why I would want to have such a cost function is because I believe that it should be more than infinitesimally worse for 3^^^^3 people to suffer than for 3^^^... (read more)