What we could do is create a predictor—an algorithm that looks at the previously generated bits, tries to find all possible patterns in them and predict the most likely following bit—and then actually output the opposite. Keep doing this for every bit.
i think a (simplicity-biased) predictor would narrow in on the situation described: that {the rule generating the sequence} contains {a copy of the predictor}, making them irresolvably mutually-dependent, similar to the mutual dependence in the classical halting problem.
in such a case, the predictor is not predicting a 1 or a 0, but a situation where neither can be yielded. so, to be a true implementation of said predictor, it would need to be able to output some third option representing irresolvable situations.
you’d get some string of bits before the predictor considered [irresolvable-mutual-dependance exception] most probable though! what that string is (for some prediction-narrowing procedure) sounds like a fun question
i think a (simplicity-biased) predictor would narrow in on the situation described: that {the rule generating the sequence} contains {a copy of the predictor}, making them irresolvably mutually-dependent, similar to the mutual dependence in the classical halting problem.
in such a case, the predictor is not predicting a 1 or a 0, but a situation where neither can be yielded. so, to be a true implementation of said predictor, it would need to be able to output some third option representing irresolvable situations.
you’d get some string of bits before the predictor considered [irresolvable-mutual-dependance exception] most probable though! what that string is (for some prediction-narrowing procedure) sounds like a fun question