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.
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.