Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 53

m=0: “Sherrington” element (linear characteristic)

mª0.2: “Weber-Fechner” element (logarithmic characteristic)

mÆ1: “All or Nothing” element (step-function characteristic).

With these and the other elements as specified in the previous paragraph,
the McCulloch element and the Ashby element, we are now prepared to
discuss the behavior of networks that incorporate these elements as their
basic computer components.

4. Some Properties of Computing Networks

Of the myriad networks that are not only theoretically possible but are
indeed incorporated into the neural architecture of living organisms, space
and ignorance will permit only a small glimpse into their vast richness. In
addition, the large variety of solutions that evolution has provided in
different species for their specific cognitive problems makes it difficult to
present this topic from a single ordering point of view, except that here we
are dealing with networks. However, in the last decades a number of general
principles have been carved out from this large complex of problems and
in the following an attempt will be made to do justice to some of them by
briefly suggesting their conceptual framework and by giving some exam-
ples to illustrate the underlying ideas.
We shall open our discussion with two paragraphs which represent
extremes in the spectrum that goes from the concrete to the abstract. The
first paragraph shows the possibility of orderly behavior in a “mixed” net,
the neuromuscular net in the sea urchin, where within elements of their
own kind no interaction takes place, but where each kind uses the other for
integrated action. The second paragraph touches briefly the McCulloch-
Pitts theorem which, in a sense, ends or starts all discussions about networks.
The next paragraphs discuss the development of cognitive networks, first,
in which cellular identity is recognized, while the subsequent considerations
are based solely on the localizability of groups of cells, but their individu-
ality is lost. The chapter concludes with a brief account of stability and
immunology of neural networks and with some remarks on adaptive nets
and how they store information.

4.1. A Neuro-muscular Net
Fulton (1943) opens his comprehensive treatise on neurophysiology with a
brief account of the early evolutionary stages in the development of the
nervous system. Rightly so, because the appreciation of these early stages
leaves no doubt as to the ultimate purpose of this system, namely, to serve
as a computer that links detection with appropriate action. Following
Parker (1943) we give in fig. 17 schematically the three decisive steps which