That all makes sense and you put it more clearly than I’ve seen before, but I dispute the implication that finding that our local universe is the result of a compact generator implies very much about the large-scale structure of an ensemble universe. For example imagine pockets of local universes that look all nice and neat from the inside yet are completely alien to aliens in a far-off universe pocket—”far off” being determined by the Turing languages for their respective universal priors, say. For a slightly more elegant variation on the idea I made the same argument here. Such an ensemble might be “uniform” and even devoid of any information content—see Standish’s Theory of Nothing—yet could look very rich from the inside. Does your reasoning eliminate this possibility in a way that I’m not seeing?
Edit: I was assuming you mean “ensemble” when you say “universe” but you might not have actually been implying this seemingly much stronger claim?
I don’t understand your objection. I would take “ensemble” to roughly map to what I meant by “domain”. Certainly the whole ensemble has little or no information content. You can’t really look at an ensemble from the inside, only your own universe. Does any of that clarify anything?
“far off” being determined by the Turing languages for their respective universal priors, say.
You are raising the objection that the Solomonoff prior takes the language as a parameter? True, but I’m not sure how that can be helped; in practice it amounts to only a small additive constant on program complexity, and in any case it’s not like there’s any competing theory that does the job without taking the language as a parameter. Besides, it doesn’t affect the point I was making.
You can’t really look at an ensemble from the inside, only your own universe. Does any of that clarify anything?
I think so, in the sense that I think we basically understand each other; but I’m not sure why you agree but seem uninterested in the idea that “certainly the whole ensemble has little or no information content”. Do you think that’s all there really is to say on the matter? (That sounds reasonable, I guess I just still feel like there’s more to the answer, or something.)
Well, I am interested in it in the sense that one of the things that attracted me to the multiverse theory in the first place was its marvelous economy of assumption. I’m not sure there is anything much else specifically to be said about that, though.
That all makes sense and you put it more clearly than I’ve seen before, but I dispute the implication that finding that our local universe is the result of a compact generator implies very much about the large-scale structure of an ensemble universe. For example imagine pockets of local universes that look all nice and neat from the inside yet are completely alien to aliens in a far-off universe pocket—”far off” being determined by the Turing languages for their respective universal priors, say. For a slightly more elegant variation on the idea I made the same argument here. Such an ensemble might be “uniform” and even devoid of any information content—see Standish’s Theory of Nothing—yet could look very rich from the inside. Does your reasoning eliminate this possibility in a way that I’m not seeing?
Edit: I was assuming you mean “ensemble” when you say “universe” but you might not have actually been implying this seemingly much stronger claim?
I don’t understand your objection. I would take “ensemble” to roughly map to what I meant by “domain”. Certainly the whole ensemble has little or no information content. You can’t really look at an ensemble from the inside, only your own universe. Does any of that clarify anything?
You are raising the objection that the Solomonoff prior takes the language as a parameter? True, but I’m not sure how that can be helped; in practice it amounts to only a small additive constant on program complexity, and in any case it’s not like there’s any competing theory that does the job without taking the language as a parameter. Besides, it doesn’t affect the point I was making.
I think so, in the sense that I think we basically understand each other; but I’m not sure why you agree but seem uninterested in the idea that “certainly the whole ensemble has little or no information content”. Do you think that’s all there really is to say on the matter? (That sounds reasonable, I guess I just still feel like there’s more to the answer, or something.)
Well, I am interested in it in the sense that one of the things that attracted me to the multiverse theory in the first place was its marvelous economy of assumption. I’m not sure there is anything much else specifically to be said about that, though.