We can now understand how "solutions" to problems of perception and the robustness of those solutions are necessarily related. Also, we can understand the process of mental development as an essentially inductive process. That is to say, it is the implicit order of the objects and phenomena of the world around us, their patterns, symmetries and invariance in space and time, that form the necessary conditions for the formation of solitons or traveling waves in the brain. The persistence of these solutions depends upon the persistence of the implicit "order" associated with the objects of perception. Thus, the robustness of cognitive states and all biological processes is a complimentary aspect of the fact that they make explicit the implicit ontology of the environment that they mediate as part of the catalytic process. It is not what can be calculated from the structure of the environment that is important, but rather, what can persist by uniting energy and structure (invariance, symmetry) in the form of a nonlinear continuous dynamic. The brain strengthens synaptic junctions according to how often they are stimulated (Hebbian learning). Once a dynamic solution to a perceptual "problem" is established, the consequence of synaptic strengthening will ensure the emergence of a similar dynamic given the same stimulus. So, similar to the way that a bacterium may change its metabolic state depending upon the availability of raw materials and the changing thermodynamics of its environment, the brain changes its cognitive state depending upon the stimulus.
This general approach is to be applied to all mental processes including behavioral processes. For example, the "solution" to the problem of coordination for an animal is implicit in the structure of the animal itself. The symmetries or invariance implicit in the structure of an animal enable traveling-wave solutions that both provide paths for energy dissipation and also make explicit these invariance as a continuous solution. For evidence of this, we can look to the locomotion of creatures like millipedes to observe solitonic solutions. As a millipede crawls, the waves of activity of its many legs represent a continuous solution to the boundary conditions embodied by its structure. There is evidence that these waves are solitons .
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