Inductive inference can be framed as predicting the next bit in an endless sequence of 0s and 1s. This turns learning problems into a shared prediction task and motivates seeking a more principled universal prior. section 9.1.2
Imagine an unknown coin producing a stream: it might be fair, biased, or follow a fixed pattern. Bayesian updating increases trust in sequence-generating programs that fit the observed history. A predictor can follow its most trusted program or combine their next-bit predictions in a Bayes mixture, weighted by past performance. section 9.1.2
