Minding the gap between artificial and biological computing paradigms for biologically loyal AI

The theoretical foundation of neuroscience differs from that of artificial intelligence, and to bridge this gap with AI, we would need a new computing paradigm that describes both fields well. The gap came from mathematicians' invention of computability theory, which was deliberately narrower than cognition and yet became a cornerstone of computer science and cognitive science. It has resulted in circular logics for computational biology and biological computing: the computability model of human mathematical activities can limit the sort of technology we build, and in turn, the engineering constraints on our technologies can limit our understanding of brain systems. Here we study several important mathematical and biological activities that computability neglects, helping to bridge the gap between neurobiology and (aspirational) AGI. One such activity is mathematicians' producing proofs of theorems that lie outside artificial computers' logic. Another is neurons' functions that are more complex than transistors, informed by recent neurobiological findings. We end by surveying candidates and inspiration for a new synthesis of AGI with neurobiology, presenting the hypothesis that a new paradigm would have to thoroughly integrate cognition and motion.