Our sense-experiences are "unitary" (in some sense which I hope we can agree on without defining rigorously), so of course we use unitary measure to predict them. Branching worlds are not unitary in that sense, so carrying over unitarity from the former to the latter seems an entirely arbitrary assumption.
A finite number (say, the number of particles in the known universe), raised to a finite number (say, the number of Planck time intervals before dark energy tears the universe apart), gives a finite number. No need for divergence. (I think both of those are severe overestimates for the actual possible branching, but they are reasonable as handwavy demonstrations of the existence of finite upper bounds)
I don't think the point you were arguing against is the same as the one I'm making here, though I understand why you think so.
My understanding of your model is that, simplifying relativistic issues so that "simultaneous" has a single unambiguous meaning, total measure across quantum branches of a simultaneous time slice is preserved; and your argument is that, otherwise, we'd have to assign equal measure to each unique moment of consciousness, which would lead to ridiculous "Bolzmann brain" scenarios. I'd agree that your argument is convincing that different simultaneous branches have different weight according to the rules of QM, but that does not at all imply that total weight across branches is constant across time.
I didn't do this problem, but I can imagine I might have been tripped up by the fact that "hammer" and "axe" are tools and not weapons. In standard DnD terminology, these are often considered "simple weapons"; distinct from "martial weapons" like warhammer and battleaxe, but still within the category of "weapons".
I guess that the "toolish" abstractions might have tipped me off, though. And even if I had made this mistake, it would only have mattered for "simple-weapon" tools with a modifier.
This is certainly a cogent counterargument. Either side of this debate relies on a theory of "measure of consciousness" that is, as far as I can tell, not obviously self-contradictory. We won't work out the details here.
In other words: this is a point on which I think we can respectfully agree to disagree.
It seems to me that exact duplicate timelines don't "count", but duplicates that split and/or rejoin do. YMMV.
I think both your question and self-response are pertinent. I have nothing to add to either, save a personal intuition that large-scale fully-quantum simulators are probably highly impractical. (I have no particular opinion about partially-quantum simulators — even possibly using quantum subcomponents larger than today's computers — but they wouldn't change the substance of my not-in-a-sim argument.)
Yes, your restatement feels to me like a clear improvement.
In fact, considering it, I think that if algorithm A is "truly more intelligent" than algorithm B, I'd expect if f(x) is the compute that it takes for B to perform as well or better than A, f(x) could even be super-exponential in x. Exponential would be the lower bound; what you'd get from a mere incremental improvement in pruning. From this perspective, anything polynomial would be "just implementation", not "real intelligence".
Though I've posted 3 more-or-less-strong disagreements with this list, I don't want to give the impression that I think it has no merit. Most specifically: I strongly agree that "Institutions could be way better across the board", and I've decided to devote much of my spare cognitive and physical resources to gaining a better handle on that question specifically in regards to democracy and voting.
Third, separate disagreement: This list states that "vastly more is at stake in [existential risks] than in anything else going on". This seems to reflect a model in which "everything else going on" — including power struggles whose overt stakes are much much lower — does not substantially or predictably causally impact outcomes of existential risk questions. I think I disagree with that model, though my confidence in this is far, far less than for the other two disagreements I've posted.
Separate point: I also strongly disagree with the idea that "there's a strong chance we live in a simulation". Any such simulation must be either:
Unlike my separate point about the great filter, I can claim no special expertise on this; though both my parents have PhDs in physics, I couldn't even write the Dirac equation without looking it up (though, given a week to work through things, I could probably do a passable job reconstructing Shor's algorithm with nothing more than access to Wikipedia articles on non-quantum FFT). Still, I'm decently confident about this point, too.