Behavioral Illusion Confusion

[Dag Forssell (930918 0025) Rick Marken (930917.1100)

Thank you for your post, clarifying your questions and remarks on
control.

I think this may turn into a rather fruitful exchange. I will
persist with some observations and questions.

I don't understand. Do you think that dynamic variations of p
about r are not orders of magnitude smaller than the potential
range of p or r? What makes you think that I "assumed" an
idealized control system in my comment? I just pointed out that
the variations in p can be very, very small and still there will
be control.

That is not the way I read you. You also said:

  in a good control system the size of the variations of p around
r be so small that they are undetectable by the instruments used
to measure p.

    An aside:

    >From now on I will try to remember to use a tilde (~) to mean
    >"approximately equal"; so, in a control loop p~r, with the
    >approximation varying with loop gain.

    Good idea.

So Michael was talking about a bad control system. I certainly read
your statement as a rejection of Michael's observation. You
proceeded to ask him as you say:

The reason I responded to Michael's statement above as I did
(aside from the fact that I'm a high gain control system) is
because, as I said in my post to Michael:

Your statement above suggests that you believe that the dynamic
deviations of p from the reference level, r, are what drive
(cause?) the outputs of the control system. That is, dynamic
(temporal) variations in (r-p) are the cause of the temporal
variations in the outputs that affect p, keeping p near r. Is
this what you think is going on in a control loop?

A good interpretation of Michael and an innocent question. You
proceeded to argue against it, without any qualifying transition,
which I interpreted as you saying that Michael is a half-baked
idiot for thinking so. This created a large disturbance in me.
Your clarification does nothing to change my impression.

I don't know if this is what Michael meant. Perhaps he didn't --
and I should have ignored it. But it caught my attention because
this is the basic mistake made by the "other" control theorists --
the psychologists who apply control theory to manual control. They
assume that the observed relationship between output and

                                               ^^^^^^

perceptual input (or r-p) is a reflection of causal mechanisms in

^^^^^^^^^^^^^^^^ ^^^

the organism that transform input into output. PCT shows that this
is an illusion -- the "behavioral illusion". The relationship
between variations in o and r-p depends on the feedback function
(outside of the organism) that relates o to p, not on the organism
function that relates r-p to o.

Would you please clarify what you have typed above. Is perceptual
input equivalent to the error signal e = r-p?

Apparently this behavioral illusion is quite seductive because you
yourself (Dag) seem to have fallen for it. You say (in response to
my comment above):

This certainly is what I think. The temporal deviations of p from
r create an error signal e, which _contains information_ used by
the output function (again, see video script p. 11).

This part is basically true -- the error signal tells the output
how much to change, that's true, but these changes are being
produced in a loop; so the cause of the changes in o (e) is itself
caused by the changes it caused. In our simulations, these causes
are propagated around the loop by time integration(s). The result
is that, in a functioning control loop, o~1/g(r-p) rather than
o~f(r-p), where g is the feedback function and f is the "organism
function".

So the only thing Michael said is true. But in a loop it loses its
validity? I don't think so.

I am aware of the behavioral illusion. I have always thought that
the illusion is to think that there is a direct causal relationship
between input p and output o (ignoring r). Have you perceived that
this is what Michael and I mean when we write about a direct causal
relationship between the error signal r-p and output o?

One way to reveal the behavioral illusion is by creating a
situation where there is NO relationship between p (or r-p) and o,
even though p is controlled (p~r). I just did this with my little
Hypercard control simulator. A scatter plot of temporal variations
in (r-p) against temporal variations in o looks like this:

     > x
     > x x
  o | x x
     > x x x
     >________
        r-p

Not all points are plotted but this gives a representative picture
of the shape of the whole plot. The x's represent paired values of
p and o at different times. The relationship between r-p and o is
a cloud, not a function -- ie. there is no causal relationship
between r-p and o. ...

Again, I am puzzled by your equivalence between p and (r-p).

I did this simulation in response to your comment:

Rick, as I read your further argument in this post, the best I
can figure is that you write about some idealized conception of
a control system which takes an error signal as an instruction to
output any which way (which after trial and error proves
successful). You deny the obvious existence of a real,
demonstrable control system in the here and now, arguing instead
for an ivory tower, unspecified function f() with unreal
properties, including the full effect of reorganization over a
long time period

Here, I was thinking of, and thought you perhaps was thinking of:

  Romeo wants Juliet as filings want a magnet; and if no obstacles
  intervene he moves toward her by as straight a line as they. But
  Romeo and Juliet if a wall be built between them do not remain
  idiotically pressing their faces against its opposite sides like
  the magnet and the filings with the [obstructing] card. Romeo
  soon finds a circuitous way by scaling the wall or otherwise of
  touching Juliet's lips directly. With the filings the path is
  fixed; whether it reaches the end depends on accidents. With the
  lover it is the end which is fixed), the path may be modified
                                       ^^^^^^^^^^^^^^^^^^^^^^^^
  indefinitely. (James 1890 p. 7)
  ^^^^^^^^^^^^

  Marken, Richard S. (Ed.). (1990). Purposeful Behavior: The
  Control Theory Approach. American Behavioral Scientist, 34(1).
  Thousand Oaks, CA: Sage Publications. 11 articles on control
  theory. (Priced lower for individuals than companies).

When we talk about people as one control system, [a gross
simplification of an enormous hierarchy with reorganization] we
observe that the action varies all over the map. But to understand
control, we both agree that we study one single control system.

In fact, I write about real control systems that really work -- in
ivory towers or park benches. Note that there was no trial and
error in this simulation; this was just a plain vanilla, non-ivory
tower control system. Nevertheless, it produced the results above;
in fact, the cloud of points is an accurate representation of the
varying environmental (feedback) function relating o to p. There
was no magic; no mystery. This result was obtained from a model
that computed o deterministically from a single program statement:

o := o + k * (r-p) * dt

The only variables in this statement are o and p. Clearly, it is
the integration that makes it possible to have different o's on

     ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

different occasions with the same p. o is "caused" by (r-p) as you
suggest but it is also caused by "itself" -- that is, the
integrated effects of previous errors (r-p). The result of the
simulation shows that, when you measure temporal variations in
(r-p) and o as they vary dynamically in the control loop the
relationship between these variables approximates the inverse of
the feedback function that transforms o into effects on p rather
than the system function that actually transforms (r-p) into
effects on o.

This is very helpful to me. Suddenly, I think I see where the whole
argument resides. Allow me to digress for a moment. This will
clarify some differences in thinking habits.

Even though I am a mechanical engineer and learned more than my
share of calculus in school, I have used very little math in my
professional life. I think that what has happened is that I have
internalized and visualize all kinds of physical interactions and
properties including a general sense of orders of magnitude of
variable quantities without resorting to actually formulating
equations and doing formal calculations. I am very comfortable
knowing that I can derive and solve all the control equations, but
have not bothered to do so.

I have developed my entire program to teach PCT on the basis of
graphic illustrations and reasoning with physical examples. I
believe it would be a mistake for me to start showing equations.

In Durango last year, Bill flirted with a revised sequence of the
lower levels of perception. We are used to talk about:

A) 1 intensity, 2 sensation, 3 configuration and 4 transition.

Bill considered 3 transition and 4 configuration, but dropped it.

In Durango this year, someone came up to me after my presentation
and pointed out that my chart showed:

B) 1 intensity, 2 sensation, 3 transition and 4 configuration.

I am inclined to think that A) is valid for the derivation of
visual and other perceptions, but that B) is valid for perception
and control of muscles. I see a perfect correspondence with

2 force/acceleration, 3 velocity, and 4 position (of a limb).

I expect to show both on charts and discuss the reasons. If you
apply a force (muscle fiber contraction) to a limb, it accelerates,
depending of course on its mass. When you integrate the
acceleration over time, you get velocity. When you integrate
velocity over time, you get position.

Let us now discuss your example, as demonstrated with your
hypercard stack, in terms of the rubber band demonstration. I am
much more comfortable if we can keep this entire argument at a
physical level, using the physical equivalents as a reality check.

I am sure we agree that the "knot over the dot" is r, and the
perceived actual "knot in relation to dot" is p. Error e = p-r
tells you which way the dot is from the target, on a momentary
basis. You said this is "basically" true.

If by output you mean the momentary muscle contractions and
therefore hand acceleration, I think Michael's and my notion of a
direct causal relationship between r-p and o holds very well
indeed. (If you do the rubber band demonstration in "slow motion",
you can sort of see it, because the distances get large and you
hold back on acceleration. Velocity (direction at least) begins to
track r-p. This parenthesis is not intended to be rigorous).

If by output you mean the momentary hand velocity, one integration
removed, I will grant you that r-p is not directly related to o.
Careful observation of the rubber band experiment shows this.

If by output you mean the momentary hand position, two integrations
removed, I will agree that there is even less relationship between
r-p and o. The rubber band experiment makes this quite obvious.

As I now read you, you are basically saying something equivalent
position. Output is not related to r-p. Agreed. If you wish, claim
to say that your output in the rubber band demonstration is your
hand velocity. Still agreed.

I think I have now caught on to why you mention p and r-p together
in your posts.

I think most people would intuitively think that their output is
their muscle contraction -- the way they try to move the hand. This
I expect to be directly proportional to r-p, with suitable lags, of
course.

Please run your hypercard again and confirm my expectation that r-p
is linearly related to the derivative of o, o'. If not, try the
second derivative. It occurs to me as I review this, that the
dimensions of "knot over dot" and "knot perceived against dot" are
both position. If my output is muscle contraction and therefore
acceleration, it is two integrations away from position.

What does this all mean? It means that, philosophy aside, the
observed relationship between p or r-p and o reveals nothing about
the nature of whatever causal processes lead from p (or r-p) to o.

If my understanding is correct, it does if you go to the
derivatives of o. There is no important point to be made here, is
there? You are right about o, of course. But you are wrong to
bring r-p into the illusion. Excessive dependence on equations,
without thinking through the physics, leads to hollow arguments.

It is important to me to try to get this across because it is the
basis for my claim (based on PCT) that traditional methodology in
psychology cannot possibly reveal (except by chance) anything
about the properties of the organism that are responsible for the
organism's observed behavior (behavior being actions or results of
action -- o or q.i). I think that psychologists will continue to
pursue this fruitless methodological course (even if they end up
liking PCT) until they finally grasp "the behavioral illusion". As
long as there is a thread of hope that there is some degree of
lineal causal dependence of organismic outputs [o] on perceptual

                             ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^

inputs [p] (even if it is only thought to occur or be noticeable

^^^^^^

when the deviations of p from r are large) there will be an
inclination to continue on the hopeless course of traditional
psychological methodology (because it is familiar and
institutionalized).

I agree completely, o versus p is the basis for the behavioral
illusion. And the integration is not the issue you make it.
Correlation of r-p with o is not an issue that is central to the
behavioral illusion. More than that: It has nothing to do with it.

It also agrees with the PCT lesson that people resist
disturbances.

Mea culpa.

Thank you. Never again? <:)
I certainly did the same to you. Got your attention.

Please consider applying your understanding of PCT and reconsider
your reply to Michael.

My reply to Michael was a question: "Is this what you think is
going on in a control loop?" I was (and am) seeking understanding;
I'm trying to understand what Michael is saying.

It was more than that. My request still stands but may now be moot.

I am kind of surprised by your reaction to my post (Marken
[920915.2330]) to Michael. All I was trying to do was discuss the
"behavioral illusion". I took the liberty of doing this because I
think it is a rather significant component of the PCT approach to
understanding behavior. The behavioral illusion was discovered
mainly because Bill P. got the relationship between a control
architecture and a living system's architecture correct. The
behavioral illusion could have been discovered by the "other"
manual control theorists (and rescued psychology long ago from
it's deathly addiction to IV-DV research). It wasn't simply
because they got the mapping of control theory to living systems
wrong (they had the control theory part right but they put r in
the environment; small difference, big consequence). So discovery
of the "behavioral illusion" distinguishes PCT from other
applications of control theory to behavior -- and I thought it was
worth discussing it again on the net.

Are you less surprised now? I think it is highly worth while to
clarify the behavioral illusion. But let us be very clear about
what it is. I look forward to your careful reply and clarification
to my questions in this post. So far, I think your points alert me
to an incomplete (in terms of math only - number of integrations,
specifically) understanding on my part. I hope I have alerted you
to a mistaken emphasis and some confusion on yours. Be that as it
falls out. The important thing is that our understandings are
correct when we are done.

Best, Dag

ยทยทยท

From: A Science of Purpose, by Rick Marken.
to: Your output in the rubber band demonstration is your hand