Control of perception, D'Amato and Dunne

[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

[Martin Taylor 960115 14:00]

Rick Marken (960114.1445)

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.

Well, Bruce is wrong, but Rick is wronger. The equations deal only with
computational simulation steps, not with real analogue loops, so let's
consider them in that light. The equivalent equations for real loops have
to have time as an argument. These have computational step "n" instead.

So:

(5) X(n) = k1*Y(n-1)

says that the value of X that you have to use at computational step n is
based on the value of Y that you found at computational step n-1. It can't
be the value of Y that you are going to find at computational step n, because
you haven't found it yet. One happens before the other, and the "=" sign
is not a mathematical equivalence, but a substitution operator (Pascal :=).

(6) Y(n) = k2*X(n-1)

says that the value of Y you use at step n is based on the value of X that
you found at step n-1. Since the value of "n" is not part of the definitions
of these equations (they are symmetric with respect to translation of the
step number), you can rewrite (6) as Y(n-1) = k2*X(n-2).

Now it is legitimate to substitute (6) into (5), which was not the case
the way Bruce did it. You get:

7a. X(n) = k1*k2*(X(n-2) = g*X(n-2).

Whatever Rick may think, this is a characteristic form for a closed-loop
system: X(t) := f(X(t-delta),....). The present value of a variable affects
its later development, not its present value (as it seems Rick would require
in order to consider a loop to be closed).

Incidentally, equation 7a illustrates the Nyquist sampling problem. The
values of X for n odd are totlaly decoupled from the values for n even,
and it is possible to get wild oscillations. A negative feedback loop
might have k1*k2 any value less than zero, but equation 7a shows that if

k1*k2| > 1, X will grow beyond any bounds, oscillating between positive

and negative for sample moments 2, 4, 6, 8... and independently for sample
moments 1, 3, 5, 7...

The real analogue negative feedback system with high gain will behave very
differently.

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).

Apparently so.

Martin