[From Rick Marken (940207.1300)]
Jim Dundon (940206.2345) --
A lot of interesting questions for Bill P. I'll take the liberty
of trying to answer just the last one:
List all axioms [of PCT]
I would say that PCT is based on three axioms and one observation.
Axiom 1: Organismic outputs, o, are a function of perceptual
inputs, p:
(1) o = f(p*-p)
p* defines the zero point of the perceptual variable.
Observation 1. Organismic inputs, i, are a function of organismic
outputs, o and the state of the environment, d. We can see, for example,
that the image on the retina, an organismic input, is influenced by the
position of the eye, o, (an organismic output) and by the position of
objects in the environment, d.
(2) i = g(o) + h(d)
Axiom 2: Perceptual inputs are a function of organismic inputs:
(3) p = t(i)
Axiom 2 is needed to complete the loop. It just says that the inputs
that are an observed function of outputs are the same inputs that cause
those outputs. It also means that we can re-write equation (1) as
(1') o = f'(i)
where f'() is a function that includes both the system function, f(),
and the perceptual function, t(). Equation (1'), taken on its own,
characterizes the basic model of behavior in scientific psychology:
behavior, o, is a function of environmental input, i. In cognitive
psychology the function f'() is thought to be very complex, involving
a lot of "information processing". But all behavioral theories are based
on the same assumptions about behavior, viz., variations in an
independent variable, i, lead to variations in a dependent variable, o,
via processes inside the organism, f'(). This is "bread and butter"
behavioral science.
Axiom 3: The sense of the feedback in the loop implied by the
simultaneous existence of relationships (2) and (3) is negative.
This just means that increases in (p*-p) lead to outputs, o that
decrease the value of (p* - p).
Given equation 1 (axiom 1) and equation 2 (observation 2) and assuming
axiom 2 (which says that the equations are linked) and axiom 3 (which
says that the feeback relationship in the loop defined by equation
1 and 2 is negative) we get the two main theorms of PCT (from
simultaneous solution of equations 1 and 2):
(T1) p = p*
(T2) o = 1/g(p*-h(d))
Where the equals signs should be taken as approximation signs, with the
closeness of the approximation being dependent on loop gain.
T1 is the biggie: it says that, in a closed negative feedback loop,
the perceptual signal is kept equal to a reference value for that
signal -- the perceptual signal is under control and it is the only
variable in the loop that IS under control.
T2 is also a biggie because it spells the end of behavioral science
as we know it. The current assumption in the behavioral sciences is
given in equation 1' -- organismic output, o, is assumed to be a
function of environmental input (stimuli), i. The function, f'()
is the "psychology" of the organism; it's what makes the organism act
the way it does. Psychological experiments aim to discover the nature of
f'() through manipulation of independent variables, i, to determine
their effect on dependent variables, o. The observed relationships
between i and o should reveal something about the organism's "psychology",
viz. the function f'(). But T2 shows that this is not the case when you
are dealing with a closed loop system. The relationship between o
and i in such a system depends on two functions, g() and h() which are
properties of the organism's ENVIRONMENT, NOT of the organism
itself. The relationship between o and i also depends on p*, which IS
an important psychological property of the organism (it's the organism's
preferred state for its perception); but the contribution of this
variable to the variance of o is completely masked by the contribution
of d to o.
The fact that the relationship between o and i (in a closed negative
feedback loop) depends mainly on characteristics of the environment
is the so-called "behavioral illusion". People who believe that there
is information about the disturbance in perception have succumbed
(understandably) to this illusion. From the PCT point of view,
all behavioral science continues to labor under the illusion that
behavioral outputs are caused, guided, informed, afforded, etc by
enviromental or mental "stimuli". Of course, from the point of view of
conventional behavioral science, PCT is missing the point completely
because we don't see what MUST be true -- that behavior MUST be caused
by SOMETHING. But, in a causal loop, every variable is a cause of the
value of every other variable, including itself; what is important in a
closed-loop system is not what is caused but what is CONTROLLED.
Given the axioms of PCT, what an organism controls is its PERCEPTION,
a conclusion that has been confirmed by quite a bit of PCT research.
A somewhat more rigorous presentation of the axioms of PCT is
given in Powers' "Living Control Systems", pp. 129-165.
Best
Rick