Factlike rather than lawlike character of the physical irreversibility principle expressed by means of Bayes' principle, and considered as a boundary condition for integrating the macroscopic evolution equations. The Ritz-Einstein controversy reexamined and J. von Neumann's irreversibility of quantum measurements reworded: one to one connection between the principles of statistical irreversibility and of wave retardation in the theory of quantized waves. Factlike time asymmetry and lawlike time symmetry in the cybernetic context.