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.
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.