Neural algebra on “how does the brain think?”

Abstract

The mathematical model employed in this essay attempts to explain how complex scripts of behaviour and conceptual content can reside in, combine and interact on large neural networks. The neural hypothesis attributes functions of the brain to sets of firing neurons dynamically: to sets of cascades of such firings, typically visualised by imaging technologies. Such sets are represented as the elements of what we call a neural algebra with their interaction as its basic operation. The neuro-algebraic thesis identifies “thoughts” with elements of a neural algebra and “thinking” with its basic operation.We argue for this thesis by a thought-experiment. It examines examples of human thought processes in proposed emulation by neural algebras. In particular we analyse problems such as controlling, classifying and learning. In neural algebras these may be posed as algebraic equations, whose solutions may lead to extensions of a neural algebra by new elements. The modelling of such extensions consists of formal analogues to familiar faculties such as reflection, distinction and comprehension which will be mades precise as operations on the algebra.An advantage of our approach is that this modelling leads directly to brain functions. From the cascades of such functions we obtain the neurons involved in them and their connective structure, and mathematically describe their behaviour.