Computational Complexity and the Function-Structure-Environment Loop of the Brain

At present, the brain is viewed primarily as a biological computer. But, crucially, the plasticity of the brain's structure leads it to vary in functionally significant ways across individuals. Understanding the brain necessitates an understanding of the range of such variation. For example, the number of neurons in the brain and its finer structures impose inherent limitations on the functionality it can realize. The relationship between such quantitative limits on the resources available and the computations that are feasible with such resources is the subject of study in computational complexity theory. Computational complexity is a potentially useful conceptual framework because it enables the meaningful study of the family of possible structures as a whole-the study of ". the brain," as opposed to some particular brain. The language of computational complexity also provides a means of formally capturing capabilities of the brain, which may otherwise be philosophically thorny.