I suspect the more fundamental difference of perspective here is about metaphysics. I feel like I can always fall back on “it doesn’t really matter, I’m only talking in terms of physics because talking in terms of simulations causes people to go funny in the head”, but my impression is that you’re skeptical of such naive computationalism? (I don’t think the hard problem has been at all solved and I have a real appreciation for the difference between syntax and semantics—I’m something of a property dualist?---but I still don’t understand what may or may not be your opposing intuitions. (I’m sort of suspicious of SL4 folk I guess, I lump folk like Eliezer and a few others into the “never acclimated to SL5 and got left behind” crowd but only very tentatively.))
(But philosophical natter won’t help with making actual progress, won’t get you anywhere. Having concluded that physical world and the domain of decision theory are fundamentally mathematical, the next step is to master what people know about mathematical thinking, and perhaps physics. Fluency in commonly useful mental tools, just short of becoming specialized in anything in particular in order to complete this stage in reasonable time, like 10 years.)
Sans les mathématiques on ne pénètre point au fond de la philosophie. Sans la philosophie on ne pénètre point au fond des mathématiques. Sans les deux on ne pénètre au fond de rien. — Leibniz [Without mathematics we cannot penetrate deeply into philosophy. Without philosophy we cannot penetrate deeply into mathematics. Without both we cannot penetrate deeply into anything.]
(Perhaps we should taboo “philosophical”. Speculative technical discussion often leads to actual progress. I don’t yet believe in math, but I know that I need to hang out a lot with people who do believe in math if I’m to stay on track, and that’s what I do. (Though not enough.))
Let’s just ignore questions of consciousness entirely and think in terms of decision-making systems, which may or may not be conscious, and which have sensory inputs, some self-knowledge or introspective capacity, a capacity to make causal world-models, etc (all those things can be given a purely functionalist definition).
What then does “talking in terms of simulations” mean? It means that the decision-making system needs to consider, in choosing a world-model, worlds where it (the decision-making system) exists at the physics level—at the lowest possible level of implementation, in a given ontology—and worlds where it exists at a level somewhere above lowest possible—that is, in a simulated physics several layers of abstraction removed from a fundamental physics.
I strongly doubt that you’re going to be able to derive the Born rule by just thinking about a decision theory that worries about whether you’re an nth-level simulation, and doesn’t concern itself too much with the nature of physics at the bottom level. Back on Earth, we didn’t derive the Born rule from any sort of apriori, it was chosen solely on the basis of empirical adequacy. But if you are going to derive it by reasoning about your possible place in an apriori multiverse (think Tegmark level 4), then you simply have to concern yourself with the distribute of possible bottom-level physical ontologies. Even if it turns out that simulations, and simulations of simulations, are frequent enough in the multiverse, that you must give those possibilities significant consideration, I don’t see how you can get to that stage without going through the stage of thinking about bottom-level physical ontologies.
Agreed, you need something like a basement to get a baseline, at the very least a logical basement as a Schelling point. There’s not a non-circular obvious decision theoretic reason why you or why cosmological natural selection would ‘pick’ the squared modulus as a Schelling point. But it’s sort of like property rights; we emerged out of Hobbesian anarchy somehow, and that somehow can be at least partially “explained” with game theory, social psychology, or ecology. Ultimately those all feed into each other, but I wouldn’t consider it fruitless to choose one approach and see how far it takes you. Does this analogy fail in the case of deriving the Born rule?
Deviations from the Born rule should be derived from timelessness-cognizant game theory for multipartite systems in order to find equilibria from first principles.
that would make more sense to me, though I still don’t believe that timeless equilibria have much to do with anything. The relationship between simulatee and simulator is completely asymmetric, the simulatee is at the mercy of the simulator in the Vast majority of cases.
As for the origin of the Born rule itself, I certainly don’t believe it has an origin in terms of multiverse-appropriate decision theory. Quantum mechanics is incomplete, it’s a type of statistical mechanics that arises from some class of more fundamental theory that we haven’t yet identified, and the Born rule—that is, the feature that probabilities come from the product of a complex number with its complex conjugate—specifically results from features of that more fundamental theory; that’s how I think it works.
But doesn’t statistical mechanics also fall out of decision theory? Or are you saying that perspective is not a useful one in that it doesn’t explain the arrow of time? (I’m really tired right now, I apologize if I’m only half-responding to the things you’re actually saying.)
Yup. Bayesian agents aren’t good at thinking about themselves, and if you can’t think about yourself you’re in trouble when someone starts offering you bets. I feel like there must be a way in which the whole thing is ironic in a philosophically deep way but I can’t quite put my finger on it.
Basically there is ontology that reifies decision theory as fundamental and reasons about everything in terms of it. It’s a powerful ontology, and often it is a beautiful ontology. Even better it’s still inchoate and so it’s not yet as beautiful as it someday will be.
I suspect the more fundamental difference of perspective here is about metaphysics. I feel like I can always fall back on “it doesn’t really matter, I’m only talking in terms of physics because talking in terms of simulations causes people to go funny in the head”, but my impression is that you’re skeptical of such naive computationalism? (I don’t think the hard problem has been at all solved and I have a real appreciation for the difference between syntax and semantics—I’m something of a property dualist?---but I still don’t understand what may or may not be your opposing intuitions. (I’m sort of suspicious of SL4 folk I guess, I lump folk like Eliezer and a few others into the “never acclimated to SL5 and got left behind” crowd but only very tentatively.))
(But philosophical natter won’t help with making actual progress, won’t get you anywhere. Having concluded that physical world and the domain of decision theory are fundamentally mathematical, the next step is to master what people know about mathematical thinking, and perhaps physics. Fluency in commonly useful mental tools, just short of becoming specialized in anything in particular in order to complete this stage in reasonable time, like 10 years.)
(From Chaitin’s home page:
)
What did “philosophie” mean in Leibniz’s time? (For Newton, e.g., “natural philosophy” was the usual term for what we now call “physics”.)
(Perhaps we should taboo “philosophical”. Speculative technical discussion often leads to actual progress. I don’t yet believe in math, but I know that I need to hang out a lot with people who do believe in math if I’m to stay on track, and that’s what I do. (Though not enough.))
Let’s just ignore questions of consciousness entirely and think in terms of decision-making systems, which may or may not be conscious, and which have sensory inputs, some self-knowledge or introspective capacity, a capacity to make causal world-models, etc (all those things can be given a purely functionalist definition).
What then does “talking in terms of simulations” mean? It means that the decision-making system needs to consider, in choosing a world-model, worlds where it (the decision-making system) exists at the physics level—at the lowest possible level of implementation, in a given ontology—and worlds where it exists at a level somewhere above lowest possible—that is, in a simulated physics several layers of abstraction removed from a fundamental physics.
I strongly doubt that you’re going to be able to derive the Born rule by just thinking about a decision theory that worries about whether you’re an nth-level simulation, and doesn’t concern itself too much with the nature of physics at the bottom level. Back on Earth, we didn’t derive the Born rule from any sort of apriori, it was chosen solely on the basis of empirical adequacy. But if you are going to derive it by reasoning about your possible place in an apriori multiverse (think Tegmark level 4), then you simply have to concern yourself with the distribute of possible bottom-level physical ontologies. Even if it turns out that simulations, and simulations of simulations, are frequent enough in the multiverse, that you must give those possibilities significant consideration, I don’t see how you can get to that stage without going through the stage of thinking about bottom-level physical ontologies.
Agreed, you need something like a basement to get a baseline, at the very least a logical basement as a Schelling point. There’s not a non-circular obvious decision theoretic reason why you or why cosmological natural selection would ‘pick’ the squared modulus as a Schelling point. But it’s sort of like property rights; we emerged out of Hobbesian anarchy somehow, and that somehow can be at least partially “explained” with game theory, social psychology, or ecology. Ultimately those all feed into each other, but I wouldn’t consider it fruitless to choose one approach and see how far it takes you. Does this analogy fail in the case of deriving the Born rule?
If you had said
that would make more sense to me, though I still don’t believe that timeless equilibria have much to do with anything. The relationship between simulatee and simulator is completely asymmetric, the simulatee is at the mercy of the simulator in the Vast majority of cases.
As for the origin of the Born rule itself, I certainly don’t believe it has an origin in terms of multiverse-appropriate decision theory. Quantum mechanics is incomplete, it’s a type of statistical mechanics that arises from some class of more fundamental theory that we haven’t yet identified, and the Born rule—that is, the feature that probabilities come from the product of a complex number with its complex conjugate—specifically results from features of that more fundamental theory; that’s how I think it works.
But doesn’t statistical mechanics also fall out of decision theory? Or are you saying that perspective is not a useful one in that it doesn’t explain the arrow of time? (I’m really tired right now, I apologize if I’m only half-responding to the things you’re actually saying.)
I don’t see how.
Are you using decision theory to refer even to the process whereby you decide what to believe, and not just the process whereby you decide what to do?
Yup. Bayesian agents aren’t good at thinking about themselves, and if you can’t think about yourself you’re in trouble when someone starts offering you bets. I feel like there must be a way in which the whole thing is ironic in a philosophically deep way but I can’t quite put my finger on it.
Basically there is ontology that reifies decision theory as fundamental and reasons about everything in terms of it. It’s a powerful ontology, and often it is a beautiful ontology. Even better it’s still inchoate and so it’s not yet as beautiful as it someday will be.