Part 2-The firings of many neurons and their density; the neural network its connections and field of firings

This paper is concerned with the firing of many neurons and the synthesis of these firings to develop functions and their transforms which relate chemical and electrical phenomena to the physical world. The density of such functions in the most general spaces that we encounter allows us to use linear combinations of them to approximate arbitrarily close to any phenomenon we encounter, imagine or think about. Absence of the technology needed to represent all the senses and the mathematical difficulty of making geometric representations of functions of a complex and of more general division algebra variables make it difficult to validate the mathematical outcome of this approach to neural firings. But we think that this problem will be solved in the not-too-distant future when at least the senses of smell, taste and touch would have been so mathematized that it is possible to instill these qualities in robots in some fashion. (C) 2016 Elsevier Ltd. All rights reserved.