Abstract Purpose A deeper understanding of cognitive development in the situation of a neither‐nor‐dilemma is the purpose of this paper. Design/methodology/approach The approach is an evaluation of experimental studies of Montessori, Lewin, Piaget and my own studies of mental development under conditions of neurological and psychological syndromes with the help of von Foerster's mathematical models. Von Foerster suggested the use of specialized knowledge of mathematics and natural sciences – but without their methods of reduction – to solve the hard problems in humanities. One of the hardest problems in humanities is the question: How does a new pattern arise in the mind of an observer? Piaget theoretically influenced von Foerster and agreed with von Foerster's order‐from‐noise model as a principle of explanation for the equilibrium of cognitive structures. Findings The finding is an improved game‐theoretical simulation of Piaget's equilibrium theory: a remarkableness matrix. This matrix shows the way, in which a new cognitive pattern – or in other words: a new worldview – can arise by the reiteration of always the same experience. Research limitations/implications The research implication is a new way of mathematical description of this process. Practical implications The practical implications are improvements of educational settings and a basic research for a diagnostic manual for Eigen‐behaviors. Originality/value The newness of this paper is the connection of von Foerster's deductive simulation of Eigen‐behavior with Piaget's inductive probability model. The results may be helpful for educators, therapists, psychologists and other researchers in the field of cognitive sciences.