In principle, analogously to how Laplace’s demon would be able to perfectly predict the future and retrodict the past by knowing the position and momentum of all particles in the universe, an infinitely intelligent agent would be able to correctly answer any question — even, say, questions about the molecular structure of a perfectly effective and safe treatment for COVID-19 — pretty much by reasoning from the law of non-contradiction.
Even an infinitely intelligent agent is limited by the amount of empirical data it has. Sample complexity is a limitation even if computational complexity is unbounded. From the perspective of the Tegmark multiverse, there are different universes in which the molecular structure is different, and you don’t know in which one you are. By making observations, you can rule some of them out, but others remain.
Moreover, we need to assume a probability measure over universes to be able to conclude anything, otherwise you can always imagine a universe matching our observations so far and producing anything whatsoever after that. There is nothing logically inconsistent about a universe which is just like our own, except that a pink unicorn materializes inside my house after I click “submit”. It’s just that the unicorn universe much higher description complexity than the universe in which no such thing will occur. Having assumed such a probability measure, we get a probability measure over predictions: but these probabilities are not 0 and 1, there is still uncertainty!
Even an infinitely intelligent agent is limited by the amount of empirical data it has. Sample complexity is a limitation even if computational complexity is unbounded. From the perspective of the Tegmark multiverse, there are different universes in which the molecular structure is different, and you don’t know in which one you are. By making observations, you can rule some of them out, but others remain.
Moreover, we need to assume a probability measure over universes to be able to conclude anything, otherwise you can always imagine a universe matching our observations so far and producing anything whatsoever after that. There is nothing logically inconsistent about a universe which is just like our own, except that a pink unicorn materializes inside my house after I click “submit”. It’s just that the unicorn universe much higher description complexity than the universe in which no such thing will occur. Having assumed such a probability measure, we get a probability measure over predictions: but these probabilities are not 0 and 1, there is still uncertainty!