since this-Omega simulates counterfactual-me and counterfactual-Omega simulates this-me
Does syntacticism work if you know Omega likes simulating poor you, and each simulated rich you is counterbalanced by many simulated poor yous? Or only in special cases like you mentioned?
Yes, it still works, because of the way the subjective probability flow on Tegmark-space works. (Think of it like PageRank, and remember that the s.p. flows from the simulated to the simulator)
It is technically possible that the differences between how much the two Universes simulate each other can, when combined with differences in how much they are simulated by other Universes, can cause the coupling between the two not to be strong enough to override some other couplings, with the result that the s.p. expectation of “giving Omega the $100” is negative. However, under my current state of logical uncertainty about the couplings, that outcome is rather unlikely, so taking a further expectation over my guesses of how likely various couplings are, the deal is still a good one.
Actually, in my own thinking I no longer call it “Tegmark-space”, instead I call it the “Causality Manifold” and I’m working on trying to find a formal mathematical expression of how causal loop unfolding can work in a continuous context. Also, I’m no longer worried about the “purer and more elegant version” of syntacticism, because today I worked out how to explain the subjective favouring of regular universes (over irregular ones, which are much more numerous). One thing that does worry me, though, is that every possible Causality Manifold is also an element of the CM, which means either stupidly large cardinal axioms or some kind of variant of the “No Gödels” argument from Syntacticism (the article).
Does syntacticism work if you know Omega likes simulating poor you, and each simulated rich you is counterbalanced by many simulated poor yous? Or only in special cases like you mentioned?
Yes, it still works, because of the way the subjective probability flow on Tegmark-space works. (Think of it like PageRank, and remember that the s.p. flows from the simulated to the simulator)
It is technically possible that the differences between how much the two Universes simulate each other can, when combined with differences in how much they are simulated by other Universes, can cause the coupling between the two not to be strong enough to override some other couplings, with the result that the s.p. expectation of “giving Omega the $100” is negative. However, under my current state of logical uncertainty about the couplings, that outcome is rather unlikely, so taking a further expectation over my guesses of how likely various couplings are, the deal is still a good one.
Actually, in my own thinking I no longer call it “Tegmark-space”, instead I call it the “Causality Manifold” and I’m working on trying to find a formal mathematical expression of how causal loop unfolding can work in a continuous context. Also, I’m no longer worried about the “purer and more elegant version” of syntacticism, because today I worked out how to explain the subjective favouring of regular universes (over irregular ones, which are much more numerous). One thing that does worry me, though, is that every possible Causality Manifold is also an element of the CM, which means either stupidly large cardinal axioms or some kind of variant of the “No Gödels” argument from Syntacticism (the article).