Abstract The recognition activity of biomacromolecules based on quantum non-demolition measurements is regarded as the basis of information processing. Reflective arrows in the set of mappings appearing from quantum measurements correspond to the Gödel numbers created inside a system overcoming its incompleteness. Temporal evolution is a consequence of contradictory statements about the whole system in which a reflective arrow is both an element of the system and its signification. It results from the solution of a paradox in which the system generates new descriptions non-deducible from its previous states. The active combinatorial process of self modification of information, being an internalized language game, allows a system to create Gödel numbers. The whole system is constructed according to percolating coherent events, providing `vertical' self-assembly that is predetermined by the encoding and internal language games.