We present two phenomena which were discovered in pure recursion-theor
etic inductive inference, namely inconsistent learning (learning strat
egies producing apparently ''senseless'' hypotheses can solve problems
unsolvable by ''reasonable'' learning strategies) and learning from g
ood examples (''much less'' information can lead to much more learning
power). Recently, it has been shown that these phenomena also hold in
the world of polynomial-time algorithmic learning. Thus inductive inf
erence can be understood and used as a source of potent ideas guiding
both research and applications in algorithmic learning theory.