If I initially divide the state space into solid colours, and then Omega asks if the bead could be striped, then I would say that’s a form of new information—specifically, information that my initial assumption about the nature of the state space was wrong. (It’s not information I can update on; I have to retrospectively change my priors.)
If you’re going to update based on what omega asks you then you must believe there is a connection that you have some information about.
If we don’t know anything about omega’s thought process or goals, then his questions tell us nothing.
I think our only disagreement is semantic.
If I initially divide the state space into solid colours, and then Omega asks if the bead could be striped, then I would say that’s a form of new information—specifically, information that my initial assumption about the nature of the state space was wrong. (It’s not information I can update on; I have to retrospectively change my priors.)
Apologies for the pointless diversion.
An ideal model of the real world must allow any miracle to happen, nothing should be logically prohibited.