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The aim of this tutorial is to document a novel approach to brain function, in which the key to understanding is the capacity of brains for self-organization. The property that distinguishes animals from plants is the capacity for directed movement through the environment, which requires an organ capable of organizing information about the environment and predicting the consequences of self-initiated actions. The operations of predicting, planning acting, detecting, and learning comprise the process of intentionality by which brains construct meaning. The currency of brains is primarily meaning and only secondarily information. The information processing metaphor has dominated neurocognitive research for half a century. Brains certainly process information for input and output. They pre-process sensory stimuli before constructing meaning, and they post-process cognitive read-out to control appropriate action and express meaning. Neurobiologists have thoroughly documented sensory information processing bottomup, and neuropsychologists have analyzed the later stages of cognition top-down, as they are expressed in behavior. However, a grasp of the intervening process of perception, in which meaning forms, requires detailed analysis and modeling of neural activity that is observed in brains during meaningful behavior of humans and other animals. Unlike computers, brains function

We present results from numerical studies of supervised learning operations in recurrent networks considered as graphs, leading from a given set of input conditions to predetermined outputs. Graphs that have optimized their output for particular inputs with respect to predetermined outputs are asymptotically stable and can be characterized by attractors which form a representation space for an associative multiplicative structure of input operations. As the mapping from a series of inputs onto a series of such attractors generally depends on the sequence of inputs, this structure is generally noncommutative. Moreover, the size of the set of attractors, indicating the complexity of learning, is found to behave non-monotonically as learning proceeds. A tentative relation between this complexity and the notion of pragmatic information is indicated. 1 1

The key tenet for understanding brain and mind is that all knowledge of the world derives from perceptions that are created by anticipatory neural activity emerging in the brain. That activity moves the body through the environment while simultaneously predicting the changes in sensory input that accompany actions. Brains learn about the world by assimilating to the sensory consequences of their self-organized intentional actions. The essential problem for neurobiologists is to describe the synaptic mechanisms by which neurons interacting in massive numbers create the patterns of anticipatory neural activity that control behavior. Three mechanisms of pattern creation in neurodynamics are described. First, a transient from perturbation by a stimulus drives cortex from its prestimulus operating point in state space without changing cortical dynamics. This is explicit breaking of symmetry by an imposed forcing function. The pattern of relaxation on return to the prestimulus state gives the evoked or event-related potential. Second, a change in cortical dynamics is induced by a stimulus accompanied