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2. Interacting Machines
We shall now discuss the more general case in which two or more such
machines interact with each other. If some aspects of the behavior of an
organism can be modeled by a finite state machine, then the interaction of
the organism with its environment may be such a case in question, if the
environment is likewise representable by a finite state machine. In fact, such
two-machine interactions constitute a popular paradigm for interpreting
the behavior of animals in experimental learning situations, with the usual
relaxation of the general complexity of the situation, by chosing for the
experimental environment a trivial machine. “Criterion” in these learning
experiments is then said to have been reached by the animal when the
experimenter succeeded in transforming the animal from a nontrivial
machine into a trivial machine, the result of these experiments being the
interaction of just two trivial machines.
We shall denote quantities pertaining to the environment (
E
) by Roman
letters, and those to the organism (W) by the corresponding Greek letters.
As long as
E
and W are independent, six equations determine their destiny.
The four “machine equations,” two for each system
=
(
)
Eyfxz
:
,
(24a)
y
¢=
(
)
zf
xz
,
(24b)
z
=
(
)
Wh xz
:
f
,
(25a)
h
¢=
(
)
(25b)
z
f
x z
,
z
and the two equations that describe the course of events at the “recep-
tacles” of the two systems
=
()
=
()
xxt
; xx
t
(26a, b)
We now let these two systems interact with each other by connecting the
(one step delayed) output of each machine with the input of the other. The
delay is to represent a “reaction time” (time of computation) of each system
to a given input (stimulus, cause) (see Fig. 4). With these connections the
following relations between the external variables of the two systems are
now established:
x
¢=h=
u
¢; x¢ =
y
=
v
¢
(27a, b)
where the new variables
u
,
v
represent the “messages” transmitted from
WÆ
E
and
E
ÆWrespectively. Replacing
x
,
y
, h, x, in Eqs. (24) (25) by
u
,
v
according to Eq. (27) we have
¢=
(
)
¢=
(
)
vf
uzuf
,;
v
,
z
y
h
¢=
(
)
¢=
(
)
zf
uz
,;
z
f
v
,
z
(28)
z
z
These are four recursive equations for the four variables
u
,
v
,
z
, z, and if
the four functions
f
y
,
f
z
,
f
h
,
f
z
are given, the problem of 'solving” for
u
(
t
),
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