Brain's geometries for movements and beauty judgments. A contribution of Topos geometries

Daniel Bennequin^1*Lain Berthoz^2*

• ¹Université Sorbonne Paris Cité, Paris, France
• ²Collège de France, Paris, Ile-de-France, France

We present a theory on the neural basis of aesthetic experience, and judgement of beauty. It is based on both empirical facts concerning brain mechanisms and theoretical mathematical theories. We first recall previous evidence that the brain uses several non-Euclidian geometries for perception and action at different scales of space (personal, peri-personal, near locomotor, environmental, imaginative). This is supported by neuroscience data (brain imaging, neuropsychology, movement control, etc..). For example, the movement of drawing obeys specific kinematic rules, that reflect the control by Euclidian and affine geometries. We already formulated the corresponding geometries in brain's networks by using Topos and Stacks theory of the mathematician Alexander Grothendieck. The present article extends the previous proposals by suggesting that a meta-geometry provides the binding between these specialized geometries, by using known higher structures and dynamics (like n-Topos and n-Stacks) for joint perceptions and movements, and other modalities, as concepts, memories or emotions, at different spatial scales domains. We suggest that a form, an object, a movement, an environment, an event, an idea, is perceived as beautiful if the data provided by the senses and programs are embedded in these higher geometries, providing a sort of dynamic recognition, through relations of generalized proportions.