Cognitive complexity and the structure of musical patterns

Patterns are fundamental to all cognition. Whether inferred from sensory input or constructed to guide motor actions, they betray order: some are simple, others are more complex. Apparently, we can erect a simplicity-complexity dimension along which such patterns may be placed or ranked. Furthermore, we may be able to place the sources of patterns—such things as mental models, neural modules, growth processes, and learning techniques—along a parallel simplicity-complexity dimension. Are there psychological forces pushing us along this dimension? Seemingly so. The drive to simplify and regularize is seen in familiar Gestalt ideas of pattern goodness and Prägnanz, which hold in many situations. The drive towards complexity can be seen in the accretional processes of individual development, or the incremental sophistication of many cultural behaviours such as systems of musical design (e.g. musical harmonies in mid to late 19th century Europe), or new scientific methodologies (e.g. increasing sophistication in brain imaging techniques). Quite beyond this, the handling of complexity is a central issue in human skill and learning, providing the drive to efficiency in resource-limited processes like memory, attention, or multi-tasking. It has parallel implications in systems engineering, organization management or adaptive neural network design problems. In these cases, complexity is something to be circumscribed by various informationmanagement strategies while functional performance specifications are maintained. Yet another picture of complexity is as an emergent property, one embodying sophisticated implicit order springing up as a cumulative consequence of simple, typically iterative nonlinear processes operating in certain ranges of their control parameters. This is an approach derived from dynamical systems theory, and it has been used to model phenomena as diverse as social interactions, development, perception, motor skills, and brain organization, to say nothing of areas outside of psychology. I aim here to examine the utility and reconcilability of these different aspects of the concept of complexity. This is to be done by examining some central questions: