Monotonicity of relative entropy under partial trace says that
S(ρABC||σABC) ≥ S(ρAB||σAB). (*)
The relative entropy on the left is bigger than the relative entropy on the right.
S(ρABC||σABC) = S(ρABC||ρA⊗ρBC) = I(A,BC) = SA + SBC – SABC
S(ρAB||σAB) = S(ρAB||ρA⊗ρB) = I(A,B) = SA + SB – SAB
When σ is obtained from ρ by ignoring some correlations, the relative entropy reduces to a mutual information, which is a sum of entropies.
So the monotonicity inequality, (*), becomes a monotonicity of mutual information. Or equivalently, it becomes strong subadditivity.
SAB + SBC ≥ SB + SABC.
To speak of all judgements in mind-configuration space is to speak of the uncountably infinite. Therefore, human philosophical sentiments presuming small-world atheism such as: naive antinatalism, discrete-valued negative utilitarianism, and even any current form of consequentialism with regard to conscious experiences are all strictly non-sensical.
sin(x) hides in tan(x). It makes no sense to speak of which is more than the other. Judgements are approximate factors in a blob of amplitude distribution. –And that’s just the level III multiverse (completely ignoring what the seeming incompatibility of conscious experience with the physical fact of eternalism may imply.)
In layman’s terms, a monotonic infinite series is one which shows a single behavior such as always decreasing or always increasing. It cannot be the case that you belong to something which is bad or good (regardless of how these are defined within the parameters of Constructor Theory). Experiences are not discrete entities, disembodied from a physical process, but part of an entropic flow. And an entropic flow cannot have monotonic attributes ∀ attributes in an uncountably infinite context.
In so far as anyone disagrees with this:
A. They have discovered new mathematical truths.
B. They do not understand the math/logic.
C. They do not care about the math/logic, but their behavior is instead akin to expressing their own hurt and/or signaling conscientiousness.
A combination of B and C accounted for my previous strong negative utilitarian sentiments. I had hidden motives that I was not aware of, and confused them for being a realist. Now that I have put more leg-work towards an accurate picture of reality, consequentialism makes no absolute sense. An agent can create arbitrary enclosures to play in, but these do not add up or subtract out items from ground ontology.