This paper addresses the key question of this book by apply- ing the chaotic dynamics found in biological brains to design of a strictly sequential artificial neural network-based natural language understand- ing (NLU) system. The discussion is in three parts. The first part ar- gues that, for NLU, two foundational principles of generative linguistics, mainstream cognitive science, and much of artificial intelligence -that natural language strings have complex syntactic structure processed by structure-sensitive algorithms, and that this syntactic structure deter- mines string semantics- are unnecessary, and that it is sufficient to pro- cess strings purely as symbol sequences. The second part then describes neuroscientific work which identifies chaotic attractor trajectory in state space as the fundamental principle of brain function at a level above that of the individual neuron, and which indicates that sensory process- ing, and perhaps higher cognition more generally, are implemented by cooperating attractor sequence processes. Finally, the third part sketches a possible application of this neuroscientific work to design of an a se- quential NLU system.