computer—to the myriad reaches to objects that mount up over weeks, months, and years. These four concepts have been extended to a variety of phenomena probing processes that underlie complex action systems and a host of topics in motor development (eg, Corbetta & Thelen, 1996; Kelso, 1995; Schöner, 1995; Thelen & Ulrich, 1991). But even early in the development of these concepts a central issue arose: What about cognition? Early explorations of this question led to a strong, antirepresentationalist stance and to a central challenge—to rethink cognition without using static/rigid symbols (Townsend & Busemeyer, 1995; van Gelder et al., 1998). In this sense, the dynamical systems community had much in common with connectionist ideas taking hold at the time (Rumelhart, McClelland, & PDR Group, 1986). In addition, there was a move to think of cognition as embodied, that is, always intimately tied to sensorimotor systems. This line of thinking resonated within the developmental science research community apropos fundamental questions about the origin of cognitive systems (Smith & Thelen, 1993; Thelen & Smith, 1994). Recent work has demonstrated that embodiment plays a central role in adult cognitive activity, as well, including the neural bases of thought (Barsalou & Wiemer-Hastings, 2005; Damasio & Damasio, 1994; Spivey, 2007). Although some researchers have made strong arguments in defense of embodiment (Glenberg, 1997) and dynamical systems approaches to cognition, there was, at the time, no formal theory for how such interactions could arise. The reason: There are some fundamentally challenging issues that lie at the heart of this appealing idea that perception, action, and cognition are all intimately intertwined. The initial challenge is that sensorimotor systems evolve continuously in real time, but cognition can jump from one state to another, that is, from one thought to another. Consider both sides of this challenge. First, in what sense