Large predicting and complexity theory

Here we turn onto the predicting task. The purpose of this paper is much of the setting the task correctly. It's just the case when the correctly formulated task is half of its solution. It's showed that the measure of complexity on the set of dynamical systems is needed. And firstly Affine maps (Markov chains) must be endowed with this measure. This complexity corresponds to the complexity of modeling or the complexity of calculating dynamic system. Suggested approach includes a lot of special cases — linear, harmonic and quantum approximations.