[From Rick Marken (960114.1445)]
Bill Powers (960114.0915 MST) --
I'm afraid that Rick Marken hit you with a gotcha.
I wasn't going to be mean and claim a "gotcha" but since
you brought it up:-)
Bruce's "proof" that
X(n) = k1*k2*X(n-1) = g*X(n-1)
defines a closed loop system is flawed in a way that, I think,
is a good example of "real world" control of perception. I believe
that Bruce (like 99.99% of everyone else who gets interested in
PCT) is controlling for a perception of PCT as essentially compatible
with conventional psychology. I have seen this in Bruce's defense of
conventional methodology and conventionally obtained data. I see
it now in Bruce's apparent failure to grasp the essential and
crucial difference between an open and a closed loop system.
Open loop, sequential change equations, like X(n) = g*X(n-1), are common
in conventional psychology so I would guess that someone with the goal
of seeing PCT as compatible with conventional psychology would like to
imagine that a closed loop system could be charaterized by such a
familiar open loop equation.
Here's Bruce's proof that X(n) = g*X(n-1) characterizes a closed
loop system:
(5) X(n) = k1*Y(n-1), and
(6) Y(n) = k2*X(n-1)
But the same result can be given by
(7) X(n) = k1*k2*X(n-1) = g*X(n-1)
The proof is obtained by substituting equation (6) into equation (5); the
equation describing Y(n) is substituted for Y(n-1) in equation (5). Of
course, this is wrong since Y(n) is not Y(n-1); but doing this produced
the perceptual result (equation (7)) that would be desired by someone
who wanted to see X(n) = g*X(n-1) as the equation for a closed loop system.
I'm emphatically not saying that Bruce did anything bad or malicious;
he (like any control system) was (I believe) just doing whatever was
necessary to perceive what he wanted to perceive (consistency of PCT
with conventional psychology).
Because we are all perceptual control systems we all make mistakes like
this (I am CERTAINLY no exception; I made such a mistake when we were
discussing the reinforcement data and Bruce's discovery that response
rate is apparently constant _regardless_ of the reinforcement schedule;
I was controlling for the idea that rats vary their press rate to
compensate for the schedule change and keep food input rate nearly
constant; but Bruce showed that the appearance of variation in response
rate as a function of schedule was most likely an artifact; rats are
not controlling their food input at all in these experiments; I was
doing all kinds of weird (and embarassing and incorrect) things to
show that this could not be true -- simply because I didn't _want_
it to be true).
The lesson here is that perceptual control systems don't care what
they "do" (what actions they take to produce desired results); they
only care about getting the desired results (perceptions). People will
do whatever is necessary (including violate the known rules of algebra)
if doing so doesn't significantly disturb other controlled perceptions
and produces the results that are wanted (and, therefore, expected).
I hate to admit it, since Rick has started sounding like Alfonse
D'Amato going after Hillary Clinton
I may have sounded like scumbag D'Amato going after Hillary
but I felt more like Dominick Dunne going after the red herring-
pulling, obfuscation slinging OJ (read "conventional psychology")
defense team;-)
Best
Rick