The aim of this article is to present a very basic dynamic systems model of L2 learning based on a number of basic principles 1) at any moment in time, a learner’s L2 proficiency is a distribution of potentialities (possible levels of L2 production), 2) the distribution changes as a result of experienced L2-events such as conversations, 3) L2 proficiency and L2 events are represented on the same underlying array of linguistic proficiency (from 0, i.e., inexistent, to 1, i.e., maximal under the currently available linguistic resources); 4) learning processes are “normative” in the sense that they are governed by a process of convergence on the language spoken by a particular L2 community, this process depends on an optimum between familiarity and novelty; 5) the parameters governing the systems dynamic differ among individual learners and L2 learning contexts (e.g., highly adaptive versus non-adaptive communicative interactions with native L2 speakers).