Abstract
At its substratum, brain/mind organization requires both synaptic firings and non-synaptic events. Synaptic firings organize the pattern of non-synaptic events. Non-synaptic events organize the pattern of synaptic firings. The processes are related in a bizarre hierarchy. Comparing these processes to electric circuits, it is as if we have two circuits that each continuously and simultaneously update the topology, and consequently, the dynamical laws of the other. Since either can be seen to be rebuilding the other, from its own perspective each process appears higher than the other in a hierarchy. This same kind of hierarchy is found in a hyperset structure. Interpreted as a directed graph, the nodes in a hyperset form a hierarchy in which, from the perspective of any node in the hierarchy, that node is at the top. This organizational structure violates the Foundation Axiom. Algorithmic computation strictly complies with the Foundation Axiom. Thus, an algorithm organized like a hyperset is a contradiction in terms. Does this contradiction mean are we precluded forever from implementing brain-like activities artificially? Not at all! An algorithm is incapable of doing the job, but nothing prevents us from constructing interacting analog processes that update each other's dynamical laws on the fly.
