Our experimental work in computational neuroanatomy has uncovered distinctively efficient layout of wiring in nervous systems. When mechanisms are explored by which such “best of all possible brains” design is attained, significant instances turn out to emerge “for free, directly from physics.” In such cases, generation of optimal brain structure appears to arise simply by exploiting basic physical processes, without the need for intervention of genes. An idea that physics suffices here – of some complex biological structure as self-organizing, generated without genomic activity – turns attention to limiting the role of the genome in morphogenesis. The familiar “nature/nurture” alternatives for origins of basic internal mental structure are that it arises either from the genome or from invariants of the external environment. A third alternative is explored for the neural cases here, a non-genomic nativism.