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Although this formalism does not specify any mechanism capable of per-
forming the required computations, it provides us, at least, with an adequate
description of the functional organization of memory. Access to “past expe-
rience” is given here by the availability of the system's own
modus operandi
at earlier occasions, and it is comfortable to see from expression (47) that
the subtle distinction between an experience in the past (
f
y
(
i
)
*), and the
present experience of an experience in the past [p
i
(
f
y
(
i
)
*)]—i.e., the distinc-
tion between “experience” and “memory”—is indeed properly taken care
of in this formalism. Moreover, by the system's access to its earlier states
of functioning, rather than to a recorded collection of accidental pairs {
x
i
,
y
i
} that manifest this functioning, it can compute a stream of “data” which
are consistent with the system's past experience. These data, however, may
or may not contain the output values {
y
i
} of those accidental pairs. This is
the price one has to pay for switching domains, from states to functions and
back again to states. But this is a small price indeed for the gain of an infi-
nitely more powerful “storage system” which computes the answer to a
question, rather than stores all answers together with all possible questions
in order to respond with the answer when it can find the question (Von
Foerster, 1965).
These examples may suffice to interpret without difficulty another prop-
erty of the finite function machine that is in strict analogy to the finite state
machine. As with the finite state machine, a finite function machine will,
when interacting with another system, go through initial transients depend-
ing on initial conditions and settle in a dynamic equilibrium. Again, if there
is no internal function change (
f
z
¢=
f
z
=
f
0
) we have a “trivial finite function
machine” with its “goal function”
f
0
. It is easy to see that a trivial finite func-
tion machine is equivalent to a nontrivial finite state machine.*
Instead of citing further properties of the functional organization of finite
function machines, it may be profitable to have a glance at various possi-
bilities of their structural organization. Clearly, here we have to deal with
aggregates of large numbers of finite state machines, and a more efficient
system of notation is required to keep track of the operations that are per-
formed by such aggregates.
2. Tesselations
Although a finite state machine consists of three distinct parts, the two com-
puters,
f
y
and
f
z
, and the store for
z
, (see Fig. 3a), we shall represent the
entire machine by a single square (or rectangle); its input region denoted
white, the output region black (Fig. 6). We shall now treat this unit as an
elementary computer—a “computational tile,”
T
i
—which, when combined
with other tiles,
T
j
, may form a mosaic of tiles—a “computational tessela-
* In the case of several equilibria {
f
oi
}, we have, of course, a
set
of nontrivial finite
state machines that are the outcomes of various initial conditions.
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