Abstract We accord with Mike Long’s rejection of fossilization as a concept able to describe or explain second language acquisition. And we share his bewilderment (Long, 2003, p. 512f.) that since most studies of fossilization make reference to explanatory factors external to language and cognition, “[s]urprisingly, no one seems to have considered the possibility that if fossilization is, as Selinker (1972) claimed, a cognitive mechanism producing the non-target end-state also called ‘fossilization’, there is no need for other explanations …”. In this paper we take up Mike’s proposition that stabilization might be a more viable alternative to fossilization and propose exactly what Mike asked for, a cognitive mechanism. We demonstrate that in SLA, linguistic simplification, one aspect of stabilization, is a dynamic process that follows its own regularities. We show that it can be modeled in an AI simulation of SLA using the mathematical formalisms of dynamical systems theory that are implied in agent-based modeling. In doing this we show that the formal, mathematical architecture of dynamical systems theory is particularly well suited for a simulation of the cognitive stabilisation mechanism that Mike Long asked for, because agent-based modeling can operate entirely on the basis of the internal dynamics of identifiable stabilization mechanisms, and they can lead to tipping points at which the system may abruptly change direction. Differing from the postmodern DST metaphors that are currently popular among some applied linguists (e.g., Larsen-Freeman, 2006), we have followed Long’s (2003) call for an operationalized concept that is testable. In this chapter, our agent-based model is fully operationalized and tested against longitudinal empirical data. Our chapter spans a period of four decades during which the first author and Mike interacted. Many of these interactions left traces in the research described here. Contextualising this research in its ‘historical’ background may be helpful in tracing the development of ideas that lead up to the AI simulation of SLA reported in this chapter. As the reader will see, many of these ideas were intentionally or unintentionally inspired or provoked by Mike’s critique, comments, suggestions and the presence of his critical mind.