Yes, AIXI being uncomputable means that Omega can’t simply run the equation for itself, but there is no need for a perfect prediction here. On the whole, it just needs to be able to come up with a well-reasoned argument for why AIXI will take a particular action, or perhaps run an approximation of AIXI for a while.
This opens up the possibility that AIXI figures out that Omega is going to mispredict it, which would make TwoBoxing the best decision.
Moreover, anyone in this thread arguing for either one-boxing or two-boxing has already implicitly agreed with this assumption.
I think it is generally assumed that, even if Omega is not a perfect predictor, the agent can’t outsmart it and predict its errors. But if Omega is computable and the agent is uncomputable, this doesn’t necessarily hold true.
This opens up the possibility that AIXI figures out that Omega is going to mispredict it, which would make TwoBoxing the best decision.
I think it is generally assumed that, even if Omega is not a perfect predictor, the agent can’t outsmart it and predict its errors. But if Omega is computable and the agent is uncomputable, this doesn’t necessarily hold true.