Neurogeometry and entoptic visions of the functional architecture of the brain

The realization of a special issue on ‘‘Neurogeometry and Visual Perception’’ may be seen as a particular challenge. It may indeed be surprising for a general scientific audience to find out that a Journal specialized in systems neuroscience, such as The Journal of Physiology (Paris), publishes a series of papers focused on mathematical approaches aiming at understanding the brain in the light of abstract and formal geometry. Biologist readers may be shocked at the view of the first analytical equation and the concept of ‘‘contact bundle’’. Perplexity may invade the mind of theoreticians when forced to dive into the structural and functional diversity of the living brain. Both breeds of potential readers might find the interdisciplinary exercise practiced to the limit of their respective background culture. Our intention here, with the help of Jean Petitot and Jean Lorenceau who are the guest-Editors for this special issue, is to go beyond the question marks and eyebrows raised at a first pass, and to take the readers where they would normally not wander, most probably because of cultural habits or prejudice. The aim of our enterprise is to illustrate successful attempts in a theoretical field, such as Geometry, to take advantage of the complexity of brain organization and to open a new explanatory referential. We hope to succeed in showing the efficiency of geometrical tools and concepts in unraveling structural aspects of thought and brain association processes from the sole reading of the relational architecture inside the ‘‘black box’’. Computer scientists may be skilled enough to retrieve some of the built-in purposes of computing machines by looking at the wiring diagram of the connection boards and the identity of electronic sub-components, but will remain unable to touch the essence of the software running on the brain-dead machines. One reason for which mathematically based introspection of the inner architecture of the brain might be expected to be more successful, may be that the organizational complexity of neural networks is achieved both through phylogeny and developmental processes: evolution and on-going adaptation result in the constantly updated selection of