Mathematical modeling and the neurobiology of metaphor

We look at a characterization of metaphor from cognitive linguistics, extracting the salient features of metaphorical processing. We examine the neurobiology of dendrites, specifically spike timing-dependent plasticity (STDP), and the modulation of backpropagating action potentials (bAPs), to generate a neuropil-centric model of cortical processing based on signal timing and reverberation between regions. We show how this model supports the basic features of metaphorical processing previously extracted. Finally; we model this system using a combination of euclidean, projective, and hyperbolic geometries, and show how the resulting model accounts for this processing, and relates to other neural network models.