I think that you’re leaning too heavily on AIT intuitions to suppose that “the universe is a dovetailed simulation on a UTM” is simple. This feels circular to me—how do you know it’s simple?
The intuition I get from AIT is broader than this, namely that the “simplicity” of an infinite collection of things can be very high, i.e., simpler than most or all finite collections, and this seems likely true for any formal definition of “simplicity” that does not explicitly penalize size or resource requirements. (Our own observable universe already seems very “wasteful” and does not seem to be sampled from a distribution that penalizes size / resource requirements.) Can you perhaps propose or outline a definition of complexity that does not have this feature?
I don’t think a superintelligence would need to prove that the universe can’t have a computable theory of everything—just ruling out the simple programs that we could be living in would seem sufficient to cast doubt on the UTM theory of everything. Of course, this is not trivial, because some small computable universes will be very hard to “run” for long enough that they make predictions disagreeing with our universe!
Putting aside how easy it would be to show, you have a strong intuition that our universe is not or can’t be a simple program? This seems very puzzling to me, as we don’t seem to see any phenomenon in the universe that looks uncomputable or can’t be the result of running a simple program. (I prefer Tegmark over Schmidhuber despite thinking our universe looks computable, in case the multiverse also contains uncomputable universes.)
I haven’t thought as much about uncomputable mathematical universes, but does this universe look like a typical mathematical object? I’m not sure.
If it’s not a typical computable or mathematical object, what class of objects is it a typical member of?
An example of a wrong metaphysical theory that is NOT really the mind projection fallacy is theism in most forms.
Most (all?) instances of theism posit that the world is an artifact of an intelligent being. Can’t this still be considered a form of mind projection fallacy?
I asked AI (Gemini 2.5 Pro) to come with other possible answers (metaphyiscal theories that aren’t mind projection fallacy), and it gave Causal Structuralism, Physicalism, and Kantian-Inspired Agnosticism. I don’t understand the last one, but the first two seem to imply something similar to “we should take MUH seriously”, because the hypothesis of “the universe contains the class of all possible causal structures / physical systems” probably has a short description in whatever language is appropriate for formulating hypotheses.
In conclusion, I see you (including in the new post) as trying to weaken arguments/intuitions for taking AIT’s ontology literally or too seriously, but without positive arguments against the universe being an infinite collection of something like mathematical objects, or the broad principle that reality might arise from a simple generator encompassing vast possibilities, which seems robust across different metaphysical foundations, I don’t see how we can reduce our credence for that hypothesis to a negligible level, such that we no longer need to consider it in decision theory. (I guess you have a strong intuition in this direction and expect superintelligence to find arguments for it, which seems fine, but naturally not very convincing for others.)
Putting aside how easy it would be to show, you have a strong intuition that our universe is not or can’t be a simple program? This seems very puzzling to me, as we don’t seem to see any phenomenon in the universe that looks uncomputable or can’t be the result of running a simple program. (I prefer Tegmark over Schmidhuber despite thinking our universe looks computable, in case the multiverse also contains uncomputable universes.)
I don’t see conclusive evidence either way, do you? What would a phenomenon that “looks uncomputable” look like concretely, other than mysterious or hard to understand? It seems many aspects of the universe are hard to understand. Maybe you would expect things at higher levels of the arithmetical hierarchy to live in uncomputable universes, and the fact that we can’t build a halting oracle implies to you that our universe is computable? That seems plausible but questionable to me. Also, the standard model is pretty complicated—it’s hard to assess what this means because the standard model is wrong (is there a simpler or more complicated true theory of everything?).
The intuition I get from AIT is broader than this, namely that the “simplicity” of an infinite collection of things can be very high, i.e., simpler than most or all finite collections, and this seems likely true for any formal definition of “simplicity” that does not explicitly penalize size or resource requirements. (Our own observable universe already seems very “wasteful” and does not seem to be sampled from a distribution that penalizes size / resource requirements.) Can you perhaps propose or outline a definition of complexity that does not have this feature?
Yes, in some cases ensembles can be simpler than any element in the ensemble. If our universe is a typical member of some ensemble, we should take seriously the possibility that the whole ensemble exists. Now it is hard to say whether that is decision-relevant; it probably depends on the ensemble.
Combining these two observations, a superintelligence should take the UTM multiverse seriously if we live in a typical (~= simple) computable universe. I put that at about 33%, which leaves it consistent with my P(H).
My P(Q) is lower than 1 - P(H) because the answer may be hard for a superintelligence to determine. But I lean towards betting on the superintelligence to work it out (whether the universe should be expected to be a simple program seems like not only an empirical but a philosophical question), which is why I put P(Q) fairly close to 1 - P(H). Though I think this discussion is starting to shift my intuitions a bit in your direction.
What would a phenomenon that “looks uncomputable” look like concretely, other than mysterious or hard to understand?
There could be some kind of “oracle”, not necessarily a halting oracle, but any kind of process or phenomenon that can’t be broken down into elementary interactions that each look computable, or otherwise explainable as a computable process. Do you agree that our universe doesn’t seem to contain anything like this?
If the universe contained a source of ML-random bits they might look like uniformly random coin flips to us, even if they actually had some uncomputable distribution. For instance, perhaps spin measurements are not iid Bernoulli, but since their distribution is not computable, we aren’t able to predict it any better than that model?
I’m not sure how you’re imagining this oracle would act? Nothing like what you’re describing seems to be embedded as a physical object in spacetime, but I think that’s the wrong thing to expect, failures of computability wouldn’t act like Newtonian objects.
The intuition I get from AIT is broader than this, namely that the “simplicity” of an infinite collection of things can be very high, i.e., simpler than most or all finite collections, and this seems likely true for any formal definition of “simplicity” that does not explicitly penalize size or resource requirements. (Our own observable universe already seems very “wasteful” and does not seem to be sampled from a distribution that penalizes size / resource requirements.) Can you perhaps propose or outline a definition of complexity that does not have this feature?
Putting aside how easy it would be to show, you have a strong intuition that our universe is not or can’t be a simple program? This seems very puzzling to me, as we don’t seem to see any phenomenon in the universe that looks uncomputable or can’t be the result of running a simple program. (I prefer Tegmark over Schmidhuber despite thinking our universe looks computable, in case the multiverse also contains uncomputable universes.)
If it’s not a typical computable or mathematical object, what class of objects is it a typical member of?
Most (all?) instances of theism posit that the world is an artifact of an intelligent being. Can’t this still be considered a form of mind projection fallacy?
I asked AI (Gemini 2.5 Pro) to come with other possible answers (metaphyiscal theories that aren’t mind projection fallacy), and it gave Causal Structuralism, Physicalism, and Kantian-Inspired Agnosticism. I don’t understand the last one, but the first two seem to imply something similar to “we should take MUH seriously”, because the hypothesis of “the universe contains the class of all possible causal structures / physical systems” probably has a short description in whatever language is appropriate for formulating hypotheses.
In conclusion, I see you (including in the new post) as trying to weaken arguments/intuitions for taking AIT’s ontology literally or too seriously, but without positive arguments against the universe being an infinite collection of something like mathematical objects, or the broad principle that reality might arise from a simple generator encompassing vast possibilities, which seems robust across different metaphysical foundations, I don’t see how we can reduce our credence for that hypothesis to a negligible level, such that we no longer need to consider it in decision theory. (I guess you have a strong intuition in this direction and expect superintelligence to find arguments for it, which seems fine, but naturally not very convincing for others.)
I don’t see conclusive evidence either way, do you? What would a phenomenon that “looks uncomputable” look like concretely, other than mysterious or hard to understand? It seems many aspects of the universe are hard to understand. Maybe you would expect things at higher levels of the arithmetical hierarchy to live in uncomputable universes, and the fact that we can’t build a halting oracle implies to you that our universe is computable? That seems plausible but questionable to me. Also, the standard model is pretty complicated—it’s hard to assess what this means because the standard model is wrong (is there a simpler or more complicated true theory of everything?).
Yes, in some cases ensembles can be simpler than any element in the ensemble. If our universe is a typical member of some ensemble, we should take seriously the possibility that the whole ensemble exists. Now it is hard to say whether that is decision-relevant; it probably depends on the ensemble.
Combining these two observations, a superintelligence should take the UTM multiverse seriously if we live in a typical (~= simple) computable universe. I put that at about 33%, which leaves it consistent with my P(H).
My P(Q) is lower than 1 - P(H) because the answer may be hard for a superintelligence to determine. But I lean towards betting on the superintelligence to work it out (whether the universe should be expected to be a simple program seems like not only an empirical but a philosophical question), which is why I put P(Q) fairly close to 1 - P(H). Though I think this discussion is starting to shift my intuitions a bit in your direction.
There could be some kind of “oracle”, not necessarily a halting oracle, but any kind of process or phenomenon that can’t be broken down into elementary interactions that each look computable, or otherwise explainable as a computable process. Do you agree that our universe doesn’t seem to contain anything like this?
If the universe contained a source of ML-random bits they might look like uniformly random coin flips to us, even if they actually had some uncomputable distribution. For instance, perhaps spin measurements are not iid Bernoulli, but since their distribution is not computable, we aren’t able to predict it any better than that model?
I’m not sure how you’re imagining this oracle would act? Nothing like what you’re describing seems to be embedded as a physical object in spacetime, but I think that’s the wrong thing to expect, failures of computability wouldn’t act like Newtonian objects.