Chuck Grimes writes: "Cassirer's point was that there seemed to be something innate about perception, particularly the basic cluster that comprises the kinesethic perception of the body that shares a primary affinity with some spatial representations of abstract finite groups, in particular the Euclidean Group or E(8)."
Doyle Innate? In perception? symmetrical transformations of the body in space are acted upon in the cerebellum. What is your evidence there is an innate E(8) in the cerebellum?
Doyle I would guess you mean that certain kinds of transformations are possible to describe with mathematical methods and the cerebellum seems to be the body knowledge source which would fall under the category of such transformations. Such mathematical rules in the brain as innate or hard wired would be big news I'm sure. There are of course inherent structures to the brain, but the neural networks don't seem to have much built in with respect to hardwired mathematical rules. That is why Chomsky has so many gnats swarming around his theories, because he proposes innate structures where the neural networks don't seem to have them. Instincts for certain kinds of activities seem there, but nothing I've heard of like E(8). This seems to be a product of selection due to human dependence upon language. In other words mathematics is external where it belongs.
Doyle Some kinds of perception such as in vision in the optic nerve track seem to a common "ruled" structure to humans. The structure which is inherented seems to mediate seeing color, and other generalized qualities of vision, and I could accept an inheritence of the these structures. Mathematics in the brain needs to demonstrated in the material of the brain for me to accept such a claim. regards, Doyle Saylor