Concept Representation and the Geometric Model of Mind

Current cognitive architectures are either working at the abstract, symbolic level, or the low, emergent level related to neural modeling. The best way to understand phenomena is to see, or imagine them, hence the need for a geometric model of mental processes. Geometric models should be based on an intermediate level of modeling that describe mental states in terms of features relevant from the first-person perspective but also linked to neural events. Concepts should be represented as geometrical objects that have sufficiently rich structures to show their properties and their relations to other concepts. The best way to create such geometrical representations of concepts is through the approximate description of the physical states of neural networks. The evolution of brain states is then represented as a trajectory linking successful concepts, and topological constraints on the shape of such trajectory define grammar and logic.