What Is Memory that It May Have Hindsight and Foresight as well? - Understanding Understanding: Essays on Cybernetics and Cognition - page 116

t

D ln 2

() = () ◊

yt

y0 e

where y(0) is the initial size of the colony, i.e., its size at time t = 0. The
methods of solution are of no concern to us here, the point I wanted to
make is only to assure you that a recursive definition of a function is as
good as any other and, in some cases, may be even more powerful than an
explicit expression (e.g., compare the terse recursive definition of above
with the cumbersome explicit expression).
If we now go back to our original problem of finding an appropriate
description for a system that acts according to the outcome of previous
actions, then it seems—at least to me—that the conceptual tool of recur-
sive function theory is just tailor-made for this purpose.
I shall now discuss the minimal case that corresponds to the “mnemonic”
part of Young's mnemon. Figure 5 shows a three-element system (F,T,D)
whose functional correspondence with the mnemonic features of the sub-
system (A,A + ) of Figure 3 will emerge in a moment.
Box F stands for the mechanism that computes the function* Y = F(X,Y¢)
on its two arguments X and Y¢. The argument X is an explicit function
of time X(t), and is called the “input proper”. The argument Y¢ is a repre-
sentation of the “output” Y of mechanism F at an earlier time, say t -D,
and is called the “recursive input”. In order that F can be informed about
its previous output—or action—the intensity of this action has to be mea-
sured by an element, T, which translates this intensity into a signal that is
accepted (“understood”) by F, and feeds this information with a delay D
back to F.
The functional correspondences of these elements with some of the phys-
iological features in Young's mnemon seem to be clear. D corresponds to
a cumulative synaptic delay that “holds” the whole picture of this system's
output activity for a while, D, before it informs the cell aggregate in A of
this activity. T represents the motoneuron's collaterals or terminations
of sensory afferents that generate the information of A's activity. F is, of
course, the aggregate (A,A + ), as yet without input of an eigen-state (+)
(-), but with an input proper, X, which represents the signal from the
classifying cell (cl.c.).
Let us now watch this three-element system in operation. Foremost, we
wish to know its output Y(t) at time t for a given input X(t) at that time.
Since F is given, we have

() =

{

() (

D ,

)

Yt

F Xt,Yt -

* According to standard notation, capital letters X,Y represent a set of components
(x 1 ,x 2 ...x n ), (Y 1 ,y 2 ...y m ), the value of each component representing, say, the stim-
ulus or response intensity along a corresponding fiber. In other words, X and Y rep-
resent the activity along whole fiber bundles and not necessarily that of single fibers.