Grand Unified Theories of the brain need better understanding of behavior: the two-tiered emergence of function.

Over the last few decades, neuroscience, and various associated disciples, has expanded enormously in terms of output, tools, methods, concepts and large-scale projects. In spite of these developments, the principles underlying brain function and behavior are of yet only partially understood. We claim that brain functioning requires the elucidation of the rules associated with all possible task realizations, rather than targeting the activity underlying a specific realization. A first step into that direction was taken by approaches focusing on dynamical structures underlying task performances, as exemplified by Coordination Dynamics. Theoretically, this approach is founded on Haken’s Synergetics, which provides a mechanism through which the degrees of freedom associated with high-dimensional systems may be effectively reduced to one or a few functional ones. This dimensionality reduction, however, is only valid in the vicinity of phase transitions, which severely limits the framework’s domain of explanation. This limitation does not hold for the recently advanced framework of Structured Flows on Manifolds (SFM), which is similar in spirit yet complementary to Synergetics. Following novel theoretical work on the onset, propagation, and offset of epileptic seizures, we expand the SFM framework, and propose that the resulting two-tiered fast-slow dynamics may be a generic mathematical organization underlying and linking brain and behavior.