In higher animals such as mammals, complex collective behaviors emerge from the microscopic properties of large structured ensembles of neurons. I will describe a model example of emergent computational dynamics, based on old-brain cortical properties. This collective (or emergent) description is derivable from the dynamical activity of neurons but has a completely different mathematical structure from the underlying neural network dynamics. The utility of understanding collective dynamics will first be illustrated by showing how it generates a natural solution to the ‘time-warp’ problem that occurs in recognizing time-varying stimulus patterns having a substantial variation in cadence (e.g. spoken words). The model of emergent dynamics will be shown to be capable of producing goal-directed motor behavior, object-based attention, and rudimentary thinking.