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FIGURE 6. Stochastic action network.
Consequently, the multiplicity of connections will grow with
p
k
-1
, while the
connection scheme remains invariant.
This observation, which at this level may have the ring of triviality, will
later prove to be of considerable utility when we consider variable amounts
of an “agent” being passed on from element to element. This again requires
a concept of what happens at the site of the elements, a question which
leads us, of course, straight into the discussion of “What is a neuron”?
Before we attempt to tackle this quite difficult question—which will be
approached in the next chapter—we owe our patient reader an explanation
of the term “connection of two elements” for which we offered only a sym-
bolic representation of an “oriented line”, along which we occasionally
passed a mysterious “agent” without even alluding to concrete entities
which may be represented by these abstract concepts. We have reserved this
discussion for the end of this chapter because a commitment to a particular
interpretation of the term “connection” will immediately force us to make
certain assumptions about some properties of our elements, and hence will
lead us to the next chapter whose central theme is the discussion of pre-
cisely these properties. In our earlier remarks about networks in general
we suggested that the statement “element
e
i
is actively connected to
element
e
j
” may also be interpreted as “
e
i
acts upon
e
j
” or “influences
e
j
”.
This, of course, presupposes that each of our elements is capable of at least
two states, otherwise even the best intentions of “influencing” may end in
frustration*. Let us denote a particular state of element
e
i
by
S
i
(l)
, where
the superscript l:
l=123
, , ,...,
s
j
.
labels all states of element
e
i
, which is capable of assuming precisely
s
i
dif-
ferent states. In order to establish that element
e
i
may indeed have any influ-
ence on
e
j
we have to demand that there is at least one state of
e
i
that
produces a state change in
e
j
within a prescribed interval of time, say D
t
.
This may be written symbolically
* An excellent account on finite state systems can be found in Ashby (1956).
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