Intelligent behavior is characterized by flexible and creative pursuit of endogenously defined goals. Intentionality is a key concept by which to link neuron and brain to goal-directed behavior through brain dynamics. An archetypal form of intentional behavior is an act of observation in space-time, by which information is sought for the guidance of future action to explore unpredictable and ever-changing environments. These acts are based in the brain dynamics that creates spatiotemporal patterns of neural activity, serving as images of goals, of command sequences by which to act to reach goals, and of expected changes in sensory input resulting from intended actions. Prediction of the sensory consequences of intended action and evaluation of performance is by reafference. An intentional act is completed upon modification of the system by itself through learning. These principles are well known among psychologists and philosophers. What is new is the development of nonlinear mesoscopic brain dynamics, by which the theory of chaos can be used to understand and simulate the constructions of meaningful patterns of neural activity that implement the process of observation. The design of neurobiological experiments, analysis of the resulting data, and synthesis of explanatory models require an understanding of the hierarchical nature of brain organization, here conceived as single neurons and neural networks at the microscopic level; clinically defined cortical and subcortical systems studied by brain imaging (for example, fMRI) at the macroscopic level, and self-organizing neural populations at an intermediate mesoscopic level, at which synaptic interactions create novel activity patterns through nonlinear state transitions. The constructive neurodynamics of sensory cortices, when they are engaged in pattern recognition, is revealed by learning-dependent spatial patterns of amplitude modulation and by newly discovered radially symmetric spatial gradients of the phase of aperiodic carrier waves in multichannel subdural EEG recordings.