don’t know the exact values of N and T
For one thing N=1 T=1 trivially satisfies your condition…
I’m not sure what you mean by this.
I mean, suppose that you got yourself a function that takes in a description of what’s going on in a region of spacetime, and it spits out a real number of how bad it is.
Now, that function can do all sorts of perfectly reasonable things that could make it asymptotic for large numbers of people, for example it could be counting distinct subjective experiences in there (otherwise a mind upload on very multiple redundant hardware is an utility monster, despite having an identical subjective experience to same upload running one time. That’s much sillier than the usual utility monster, which feels much stronger feelings). This would impose a finite limit (for brains of finite complexity).
One thing that function can’t do, is to have a general property that f(a union b)=f(a)+f(b) , because then we just subdivide our space into individual atoms none of which are feeling anything.
Well, within the 3^^^3 people you have every single possible brain replicated a gazillion times already (there’s only that many ways you can arrange the atoms in the volume of human head, sufficiently distinct as to be computing something subjectively different, after all, and the number of such arrangements is unimaginably smaller than 3^^^3 ).
I don’t think that e.g. I must massively prioritize the happiness of a brain upload of me running on multiple redundant hardware (which subjectively feels the same as if it was running in one instance; it doesn’t feel any stronger because there’s more ‘copies’ of it running in perfect unison, it can’t even tell the difference. It won’t affect the subjective experience if the CPUs running the same computation are slightly physically different).
edit: also again, pseudomath, because you could have C(dustspeck, n) = 1-1/(n+1) , your property holds but it is bounded, so if the c(torture, 1)=2 then you’ll never exceed it with dust specks.
Seriously, you people (LW crowd in general) need to take more calculus or something before your mathematical intuitions become in any way relevant to anything whatsoever. It does feel intuitively that with your epsilon it’s going to keep growing without a limit, but that’s simply not true.