  Solomonoff's inductive learning model is a powerful, universal and highly
elegant theory of sequence prediction. Its critical flaw is that it is
incomputable and thus cannot be used in practice. It is sometimes suggested
that it may still be useful to help guide the development of very general and
powerful theories of prediction which are computable. In this paper it is shown
that although powerful algorithms exist, they are necessarily highly complex.
This alone makes their theoretical analysis problematic, however it is further
shown that beyond a moderate level of complexity the analysis runs into the
deeper problem of Goedel incompleteness. This limits the power of mathematics
to analyse and study prediction algorithms, and indeed intelligent systems in
general.
