Computation in Neural Nets - Understanding Understanding: Essays on Cybernetics and Cognition - page 44

FIGURE 13. Ashby element computing
recursive functions.
such a minimal element an “Ashby element”. The mathematical machinery
that goes along with such elements is called recursive function theory, hence
elements of this general form may be called recursive elements.
We have as yet discussed elements with two inputs only. However, it is
easily seen that McCulloch's concepts can be extended to neurons with
many inputs as fig. 9 may remind us. However, the number of logical func-
tions that cannot be computed by using only a single neuron increases
rapidly—2 out of 16 for two inputs, and 152 out of 256 possible functions
for three inputs (Verbeek, 1962)—and networks composed of several
elements have to be constructed. These networks will be discussed in the
following chapter.
In the preceding discussion of the operations of a McCulloch formal
neuron a tacit assumption was made, namely, that the information carried
on each fiber is simply its ON or OFF state. These states have to be simul-
taneously presented to the element, otherwise its output is meaningless with
respect to these states. A term like “input strength” is alien to this calculus;
a proposition is either true or false. This requires all components in these
networks to operate synchronously, i.e., all volleys have not only to be fired
at the same frequency, they have also to be always in phase. Although there
are indications that coherency of pulse activity is favored in localized
areas—otherwise an E.E.G. may show only noise—as long as we cannot
propose a mechanism that synchronizes pulse activity, we have to consider
synchronism as a very special case. Since this article is not the place to argue