Active Information in Metabiology

Metabiology is a fascinating intellectual romp in the surreal world of the mathematics of algorithmic information theory. In this world, halting oracles hunt for busy beaver numbers and busy beaver numbers unearth Chaitin’s number, knowledge of which in turn allows resolution of numerous unsolved mathematical problems, many of whose solutions would earn large cash bounties. All this, despite the fact that halting oracles can’t be implemented on a computer, a computer can never make a list of busy beaver numbers, and Chaitin’s number, always a positive real number less than one, is proven to be unknowable. The fun of metabiology is the application of these ideas to illustrate Darwinian evolution. When metabiology’s evolutionary process is stripped of the glitter of algorithmic information theory, however, what remains is a procedure similar to that used in other attempts to model Darwinian evolution, like the ev and AVIDA computer programs. Metabiology, like ev and AVIDA, succeeds because available sources of knowledge about the solution being sought can be mined. We show the mining of information from a halting oracle has striking similarities to mining information from a simple Hamming oracle. Unlike a halting oracle, however, Hamming oracles can be implemented on a computer. We demonstrate that for both oracles, information can be mined by search strategies that are analogous in some respects even though the methods differ; in both cases the search strategy used greatly influences the result. Because metabiology’s process relies on unknowable numbers and infinite resources, its reported relative performance measures can only be expressed asymptotically. That is, the results of metabiology are only proven to be true on the largest possible scale. In fact, simple simulations using bounded resources suggest the asymptote is not always approached quickly, indicating that metabiology results may only hold for scales larger than any practical system.