“Elements of Neurogeometry. Functional architectures of vision” by Jean Petitot
This book describes in detail certain geometric algorithms implemented by the functional architectures of vision found e.g. in primary visual area V1. Its main concern is therefore the internal neural origin of external spatial representations, and this is why the author coined the term neurogeometry to name its field of investigation. Neurogeometry thus deals with the ‘internal’ and ‘immanent’ geometric algorithms that allow the visual system to build the ‘external’ and ‘transcendent’ geometry of our surrounding world.
The internal geometry ‘immanent’ in neural infrastructures corresponding to external ‘transcendent’ space can greatly clarify what is meant in philosophy by the ‘synthetic a priori’ character of this space, in other words contemporary cognitive neuroscience supports many tenets of transcendental philosophy: there are neurophysiological roots for what Kant called ‘pure intuitions’.
The book describes several mathematical models of the primary visual cortex, referring them to a vast ensemble of experimental data and putting forward an original geometrical model for its functional architectures using concepts as wavelet analysis; contact, symplectic, and sub-Riemannian geometry, it provides a systematic interpretation of a number of important neurophysiological observations in a welldefined mathematical framework.
More information (in particular the Table of contents) can be found on the following web pages: