Setting aside the (rather plausible sounding) hypothesis that the writing might not be entirely truthful…
The scenario you describe is a perfectly valid use of Bayesianism to use evidence from the past (“I woke up again in this room” + “the writing on the wall says…”) to make an informed prediction about the future (what color I’ll see the outside of the door is when I go look). Nothing in it involves using Frequentist-thinking to construct an invalid causality-violating Bayesian prior and then act impressed when that starts emitting acausal predictions.
Well, you can imagine you updating on all the evidence as it went in, in series. Like when you are a child and learn for the first time what year it is.
Setting aside the (rather plausible sounding) hypothesis that the writing might not be entirely truthful…
The scenario you describe is a perfectly valid use of Bayesianism to use evidence from the past (“I woke up again in this room” + “the writing on the wall says…”) to make an informed prediction about the future (what color I’ll see the outside of the door is when I go look). Nothing in it involves using Frequentist-thinking to construct an invalid causality-violating Bayesian prior and then act impressed when that starts emitting acausal predictions.
Well, you can imagine you updating on all the evidence as it went in, in series. Like when you are a child and learn for the first time what year it is.
You get similar situation overall.