MCT <> PCT

CSGnet Archive CSG1997
1

[Hans Blom, 970224b]

(Bill Powers (970221.1230 MST))

If you look at the program I posted, you will see that no time-
indices are used, because the operations are simply performed in
sequence.

Explicit use of time-indices in formulas is known to avoid confusion.
In programs they are not required, of course.

Thence the MCT expression would be
u(t) := [r(t+dt) - x(t+dt)]*G
with a suitably chosen (model-derived) G.

Now it seems to me that you're violating your own rules. u(t) refers
to the value at time t; how can it be derived from the _next_ values
of r and x, which have not occurred yet? You are using the variables
on the right side to compute the value of the variable on the left
side.

You pinpoint the basic difference between PCT and MCT! In formula

  u(t) := [r(t+dt) - x(t+dt)]*G

x(t+dt) refers to an _anticipation_ or _prediction_ rather than a
value that is already available. In the MCT literature, such a "one
step prediction" x(t+dt) is usually denoted as x(t+dt | t), where x
ought to have a hat as well, indicating an estimate rather than a
measurement, and where the symbol "|" stand for "given". Thus the
interpretation of x(t+dt) in the formula above should be: the (best
possible) estimate of what x is going to be a time dt into the future
given only observations upto time t (where these past observations
are "summarized" in the model).

I hope that you have no trouble with the controller specifying the
_next_ value of the reference level r(t+dt). In stabilization, we
would have a steady value of the reference level, i.e. r(t+dt) = r(t)
= r(t-dt) = ... Not so, of course, in regulation, where the reference
level changes in time. But in either case "wanting something" does
not refer to the present (which is already fixed) but to a future
state of affairs: the future is still flexible and can be influenced
(controlled?) by our present actions.

I don't think this problem is very important; when you program the
equations, you naturally write them in the right sequence, and the
indices take care of themselves.

Not using indices has obviously hidden the most basic difference
between MCT and PCT. One could say that, basically, a PCT system is
error-driven -- that is, the output of a PCT controller is based on
the _momentary_ error. An MCT controller, on the other hand, attempts
to minimize the _predicted_ or _anticipated_ error and, as a result,
will have zero error if its model -- and thus its anticipation -- is
accurate. The practical difference -- in the formulas "nothing but" a
difference in time indices! -- will be especially noticeable after
rapid reference value changes such as steps: a PCT controller will
usually have an exponential decrease of the ensuing error (as you
have described in the past), a predictive controller might have no
appreciable error at all (if its model is accurate). Consult your and
Rick's MCT program that you described last week, give it a square
wave reference and see how it behaves...

Let's switch to using the cruise control as the example.

No, let's not change horses in mid-stream. Exactly the same
differences would show up again.

The reason I want to switch is that the cruise-control example
doesn't involve a lot of awkward assumptions.

All right, have it your way. Although assumptions are impossible to
avoid (we're modeling, aren't we?), they might be less "awkward" in a
different example.

Let's get to the "model-based" aspect of model-based control. Exactly
_what_ is the model a model of? What is modeled is in PCT called the
"environment", resulting in an "environment equation" that describes
that environment. In MCT, this equation is considered to be a "model"
of the environment, because it is at best an approximation of the
"true" environment. So let's make this deal: give me an "environment
equation" that satisfies you -- any relation between an "input" (i.e.
the controller's "action") and an "output" (i.e. the controller's
"perception"), expressed as a formula -- and I'll demonstrate how to
build a model-based controller using that "environment equation"/
model. In doing so, we skip the phase of "model building" by the
controller (which is a different subject that we must postpone),
because you do that instead. No objections, please, that you are a
much better modeler than a dumb MCT controller. That might be true,
or it might not. We shall see. But that is not the issue now...

How's that?

Greetings,

Hans

2

[From Bill Powers (970225.0530 MST)]

Hans Blom, 970224b --

You pinpoint the basic difference between PCT and MCT! In formula

u(t) := [r(t+dt) - x(t+dt)]*G

x(t+dt) refers to an _anticipation_ or _prediction_ rather than a
value that is already available. In the MCT literature, such a "one
step prediction" x(t+dt) is usually denoted as x(t+dt | t), where x
ought to have a hat as well, indicating an estimate rather than a
measurement, and where the symbol "|" stand for "given". Thus the
interpretation of x(t+dt) in the formula above should be: the (best
possible) estimate of what x is going to be a time dt into the future
given only observations up to time t (where these past observations
are "summarized" in the model).

I don't know why you're suddenly latching onto "one step prediction" as the
"basic difference" between PCT and MCT. There's no reason that "one step
prediction" can't be used in PCT too; in fact, it's a very old idea and part
of traditional control theory. It's called a "phase advance network" if
you're an old analog man. Phase advance networks per se are not a preferred
mode for stabilizing control systems, because they make noise a larger part
of the signals. This is especially true if you try to compensate
second-order and higher systems (differential equations) this way, because
you have to compute second derivatives, third derivatives, and so on, each
time greatly increasing the sensitivity to noise. But they have been used
for a long time, especially when all that's wanted is a mild tweaking of
performance to get an extra few percent of dynamic response.

Here is an analog circuit for prediction of this sort:

                     --/\/\/\/\----
                    > >
          Input ----| |-------- output
                    > > > > \
                     -----| |------ /
                          > > \
                                        /
                                        \
                                        >
                                     ground

And of course there is a large variety of other circuits with
characteristics that, in effect, produce a "one-step-predicted" signal.

The basic difference between PCT and MCT has nothing to do with one-step
prediction, and everything to do with controlling an imagined environment
instead of the real one. It has to do with the (apparently devout) belief of
MCTers that no matter how complex the mathematical computation, the brain
can carry it out without any problem, and with all the accuracy and speed
required. It has to do with the necessary belief that any kind of
disturbance can be anticipated and simulated. It has to do with coordinating
computations in different parts of the brain so that the computation in one
network is a precise reflection of a computation in a physically different
network. And above all, it has to do with the high precision with which
digital computers can carry out mathematically-exact operations of unlimited
complexity.

So far, all I have seen by way of practical applications of this approach
have to do with achieving slight improvements of performance in comparison
with standard analog control methods (and sometimes, as in the crane-control
paper, _in addition_ to standard analog methods). I am far from convinced
that if an equal design effort had been devoted to improving the same system
by standard methods, or even just by empirical methods, the same degree of
improvement could not have been achieved. It seems to me that proponents of
this new approach often promise mountains of benefits, and produce molehills.

Let's get to the "model-based" aspect of model-based control. Exactly
_what_ is the model a model of? What is modeled is in PCT called the
"environment", resulting in an "environment equation" that describes
that environment. In MCT, this equation is considered to be a "model"
of the environment, because it is at best an approximation of the
"true" environment.

Obviously, you expect the brain to be able to produce a model of the
environment that is as exact as the best mathematical models we can produce.
In that case, the "environment model" and the "internal simulation" will be
identical, and what you say will make sense. But I seriously question this
assumption -- that, for example, if the environment consists of a mass on a
spring driven by force outputs of the system, the brain can construct a
model that predicts the behavior of this mass with an accuracy of a few
hundredths of a percent over a period of minute or hours, as we can do with
accurate measurement and good mathematical models.

My assumption is always that our physical model of the environment
represents its response to actions several orders of magnitude better than
any model the brain might produce. How else could we speak of "errors" in
control? When we observe people controlling things, they do NOT control them
perfectly, and the imperfections are easy to observe. If the brain is so
good at making models, why does it deliberately create a model that fails to
match the environment? I know what you're going to say -- in the eyes of God
it's an optimal design no matter how imperfect it may seem to our mortal
eyes. But I consider that hogwash.

In the PCT model, the environment is its own model; no approximations are
involved. And despite your protestations, the PCT model does NOT contain a
simulation of the environment. I have often wondered whether you really
understand how a PCT control system can maintain a control accuracy of 1
percent while the sensitivity of its output function to error signals varies
by 50 percent or even much more. I wonder if you know what I mean by a loop
gain of -10,000. Of course you keep telling me that you went through this
long ago and know all about these things, but what you say about control
systems doesn't seem to show this knowledge. In your wholehearted conversion
to MCT and the digital-computer approach, you seem to have forgotten what
the old-fashioned kind of control system can do, and in a far, far simpler way.

One thing I have noticed in trying to read textbooks about control theory
and control system design: Even in the old-fashioned texts where Laplace
transforms and frequency-domain methods are used, there is essentially no
introductory level of discussion. In the first chapter you see a flush
toilet and perhaps a motor attached to a potentiometer, and in the second
chapter you plunge into Laplace transforms. There is essentially no attempt
to help the student develop an intuitive feel for control processes, and to
learn how to devise control systems of the simplest possible kinds. My
impression is that the authors of the textbooks simply dive into the middle
of a control problem and then start adding patches to it to make the design
work. This leads to elaborate block diagrams that give no impression of
order or forethought, and equations that convey no sense of how the system
operates.

Unless the classroom work is entirely different from what is in the
textbooks, I simply don't see how a student can develop an intuitive
understanding of control. The student is taught, at least in the textbooks,
to rely on mathematical manipulations exclusively, without connecting the
parts of the equations to the corresponding physical processes. This gets
especially bad when discussion of the actual operation of the physical
system is replaced by transforms and plots in complex space, which (for me
at least) totally destroy any sense of the real system. I have never seen a
single textbook in which the author pauses to explain that control systems
control their own input signals. I had to learn that from a book on analog
computing.

So let's make this deal: give me an "environment
equation" that satisfies you -- any relation between an "input" (i.e.
the controller's "action") and an "output" (i.e. the controller's
"perception"), expressed as a formula -- and I'll demonstrate how to
build a model-based controller using that "environment equation"
model. In doing so, we skip the phase of "model building" by the
controller (which is a different subject that we must postpone),
because you do that instead. No objections, please, that you are a
much better modeler than a dumb MCT controller. That might be true,
or it might not. We shall see. But that is not the issue now...

All right. Since you are still reluctant to abandon the theolodite example,
let's go back to it, but use the right equation:

J*(d2x/dt^2) = u(t) + d(t), where
  J = moment of inertia
  x = pointing angle
  u(t) = driving torque (output of control system).
  d(t) = disturbing torque (arbitrary waveform)

We can assume no friction and no restoring force, and that the output torque
can be generated directly, as required (no motor acceleration to contend with).

You solve this problem in the standard MCT way, and I will solve it using
analog computing elements. I will use a disturbance that is a one-shot
square-wave occuring at some random time during the simulation run.

Let us, just to make sure we're talking about exactly the same problem, use
the following values:

Duration of run = 9 seconds

J = 100 n-m^2

ref angle = 0 for first 3 seconds
            1 radian for 3 seconds
            0 for remainder of run

disturbance magnitude = 10 newton-meters, duration = 2 seconds.

commencement of disturbance at 4.5 +/- 3 seconds, randomly selected.
initial value of x = 0.

I think this set of conditions will make points that we're each trying to
make. We can always add or change conditions after the first trial.

Best,

Bill P.

···

How's that?

Greetings,

Hans

3

[Hans Blom, 970226b]

(Bill Powers (970225.0530 MST))

I don't know why you're suddenly latching onto "one step prediction"
as the "basic difference" between PCT and MCT. There's no reason
that "one step prediction" can't be used in PCT too; in fact, it's a
very old idea and part of traditional control theory. It's called a
"phase advance network" if you're an old analog man.

MCT depends on "model-based" (often "one step", if no observations
are missing) prediction. A phase advance network and its discrete
counterpart -- use of a derivative term -- also use a model, one
could indeed say. But that model is crude and can represent only
linear extrapolation. The difference is that MCT models can be
arbitrarily complex and hence can give a better prediction.

The basic difference between PCT and MCT has nothing to do with
one-step prediction, and everything to do with controlling an
imagined environment instead of the real one.

Do you really think you -- or a controller -- perceives (all aspects
of) the "real" environment in terms of our human goals? This is
required in the comparator that compares a goal with ..., with what?
In _all_ cases, our sensory equipment is severely limited in this
sense. One would like to control for ultimate happiness, I guess, but
a "happiness sensor" is, regrettably, unavailable. Thus, if we would
like to control for maximum happiness, we need to do this in terms of
the perceptions that _are_ available. As you demonstrate in B:CP,
this type of "indirect" control, which depends on "indirect
measurements" -- on what I call a model, in PCT expressed as
"perceptual input functions" -- happens at all levels of the
hierarchy except at the lowest, "intensity" level.

It has to do with the (apparently devout) belief of MCTers that no
matter how complex the mathematical computation, the brain can carry
it out without any problem, and with all the accuracy and speed
required.

That is putting the problem upside down. Remember that we are trying
to model what goes on in the brain. To me, that modeling is mostly in
terms of functionality. You require, in addition, specific mechanisms
such as rather _literal_ subtraction (in a comparator). That is not
(yet) a concern for me.

It has to do with the necessary belief that any kind of disturbance
can be anticipated and simulated.

Can be _modeled_, Bill. At least to some extent. Only white noise
cannot be modeled at all. And not controlled away, whatever type of
controller. Any other type of disturbance can be modeled, making it
predictable to some extent, where only the non-predictable part that
is left after modeling is white noise-like and cannot be controlled
away.

It has to do with coordinating computations in different parts of
the brain so that the computation in one network is a precise
reflection of a computation in a physically different network.

I find the assumption that different parts of the brain cooperate and
coordinate their work quite plausible.

And above all, it has to do with the high precision with which
digital computers can carry out mathematically-exact operations of
unlimited complexity.

This is an incorrect inference. Note that in my theodolite MCT
controller I modeled the disturbance with an extremely simple
assumption, a zero order hold, i.e. the assumption that the future is
much like the past. That happens to be optimal (accidentally...) with
the disturbance that you specified, but it is also pretty good with
any low frequency type of disturbance. Approximate models may give
impressively good control behavior!

So far, all I have seen by way of practical applications of this
approach have to do with achieving slight improvements of
performance in comparison with standard analog control methods ...

Slight improvements seem to have driven biological evolution. In the
economical sense this happens as well: a 1% improvement of control
quality may generate many millions of dollars extra profit in an oil
refinery, for instance. Within a few years one will thus see the
disappearance of the earlier, less efficient, species of controllers.
I'm not saying that primitive control systems have fully disappeared
in organisms; but where the brain biology could support more complex
control schemes, I have no doubt that they will have had a good
chance of coming into being.

It seems to me that proponents of this new approach often promise
mountains of benefits, and produce molehills.

Once again, molehills of improvement may be decisive in an
evolutionary, economic or paradigmatic race. Einstein's formulas
offer an invisible improvement over Newton's in almost all cases of
interest, to mention a scientific example.

Let me pose this as a final question: you have admitted frequently
that model-based control must exist at least in the higher levels of
the hierarchy. Are you not ready to study those and their possible
mechanisms? In other words: why do you object so strenuously ("slight
improvements", "molehills") against the value of models?

Greetings,

Hans

4

[From Bruce Gregory (979226.1715 EST)]

[Hans Blom, 970226b]

In _all_ cases, our sensory equipment is severely limited in this
sense. One would like to control for ultimate happiness, I guess, but
a "happiness sensor" is, regrettably, unavailable. Thus, if we would
like to control for maximum happiness, we need to do this in terms of
the perceptions that _are_ available. As you demonstrate in B:CP,
this type of "indirect" control, which depends on "indirect
measurements" -- on what I call a model, in PCT expressed as
"perceptual input functions" -- happens at all levels of the
hierarchy except at the lowest, "intensity" level.

The truth at last. Perception = Model. No wonder we have had
trouble understanding one another. Now that we know this,
everyone can see that MCT _is_ HPCT. Now perhaps we can move on....

Bruce Gregory

5

[From Bill Powers (970226.1935 MST)]

Hans Blom, 970226b--

Do you really think you -- or a controller -- perceives (all aspects
of) the "real" environment in terms of our human goals? This is
required in the comparator that compares a goal with ..., with what?
In _all_ cases, our sensory equipment is severely limited in this
sense. One would like to control for ultimate happiness, I guess, but
a "happiness sensor" is, regrettably, unavailable.

Etc. Etc.

Let's stick to discussing the modeling. I think that is as close as we will
ever get to understanding each other's points of view.

Best,

Bill P.

6

[From Rick Marken (960727.2100)]

Me:

I suggest that one good way to compare these theories is in terms of the
insights they provide about the nature of human nature.

Hans Blom (960726) --

Some good questions. Let me try to give some preliminary answers. It
will not surprise you that the answers of MCT are not too different
from those of HPCT.

Again, thanks for your answers to my questions, Hans. You say that I will
not be surprised to find that the MCT answers don't differ much from
those of HPCT. In fact, I would have been VERY surprised if the MCT
answers hadn't differed considerably from those of HPCT. As it turns out,
I'm not surprised at all because your MCT based answers are about as
different from the HPCT answers as they can be.

Rather than evaluate the merits of the MCT answers, I will try to review
these answers in terms of their similarily to what HPCT might say. My goal
is simply to show that the implications of MCT and PCT regarding the nature
of human nature are quite different. Of course, I also think the data show
clearly and overwhelmingly that PCT is a much better model of human nature
than MCT. But it's hard to tell that this is the case if one doesn't even
know that the models are different -- WAY different. So my goal here is
just to point out this difference in terms of what the models have to say
about the nature of human nature.

For those who want to cut down on their reading, I have rated (on a 0 to
10 scale) each of Hans' MCT based views of human nature in terms of its
similarity to the PCT view: 10 = very similar, 0 = no simliarity.

Me:

What would you say are the essential insights about human nature
that come from looking a people from the MCT perspective?

Hans:

One: Learning comes before control. If learning does not succeed,
there can be no control. Babies. Schizophrenics.

Is there any theory of behavior that doesn't say something like this? PCT
is no exception, though PCT does suggest that it is _possible_ to have
control before learning; some control systems (like those that operate at
the cellular or molecular level) may be ready to go right out of the box
(right after a cell division, say). MCT says that control is based on
building up a "world model" so learning is essential; PCT says that control
is based on the existence of perceptual, comparison and output functions
and the connections between them; if these functions and connections exist
in a negative feedback loop with the appropriate gain and dynamic
characteritics then there will be control. How any one of these systems
comes into existence is a matter for research, but learning is not
absolutely necessary -- though it is probably involved in most cases of
control at the behavioral level.

1. Similarity Rating: 5

Two: We are all different, because our circumstances (perceptions and
actions) have been different. Our "internal models", that say how we
perceive the world and what we can do, are partly innate (DNA pre-
scribed hardware), partly based on our individual history. Ask any
therapist.

Again, is there _any_ theory that says we are _not_ all different? So MCT and
PCT are, indeed, similar in viewing people as different. But you are making
things up when you imply that MCT says people are differnet because they have
different "internal models". The "internal models" in MCT are models of the
laws of physics, not perceptual representations of external variables. MCT,
therefore, has to predict that people who live in the same environment
would _have to_ build the same internal models of that environment or
they could not control at all. In fact, MCT says nothing about the
importance of the perceptual function in control (find me a diagram in
a MCT text which includes the perceptual function explicitly). So the
implications of MCT is that people who live in the same environment
are all the _same_ in terms of their internal models. They may control
different perceptual aspects of that environment (a possibility that is
not explicitly represented in MCT) but they would do it using the same
internal model of that environment.

2. Similarity Rating: a very generous 5

Three: Uncertainties play a major role in how we view the world, but
much less in how we act... A world view can be crazy or underdeveloped,
whereas the individual may still function pretty well in society. Just
look around ;-).

It seems to me that uncertainties play the opposite role in PCT as they
do in MCT. Since disturbance variable values are unpredictable (and
usually undetectable) they play much less of a role in how we view
the world than in how we act. My uncertainties about road, wind and engine
conditions affected the actions I took to get to Flagstaff; but they had
nothing to do with my world view (the fact that I was on my way to Flagstaff
and that that's where I wanted to go).

3. Similarity Rating: 0

Four: There are a great many (sub)goals at any one time. Actions will
attempt to control for all of these goals at the same time, as far as
possible. This point of view pretty much dooms The Test ;-).

Up until the last statement things were going along fine. Since we have
successfully done The Test over and over again, any theory that says The
Test can't be done has real problems. Anyway, MCT and PCT certainly seem
to differ on this matter.

4. Similarity Rating: 0

Five: All subgoals serve one topmost goal. The question is: what is
it?

PCT would say that many subgoals could (and probably do) serve several topmost
goals. We have also written models to show how simply and elegantly this
hierachical control of perception system can be implemented.

5. Similarity Rating: 0

Six: Control is best in a fully predictable world.

PCT and MCT agree here, but for different reasons. Still, the general
statement has to count as true for both theories.

6. Similarity Rating: 10

Seven: Because the world is not fully predictable, it needs to be explored
continuously. Explorations reestablish the up-to-date-ness of the model.

PCT shows that no world model is necessary for control.

7. Similarity Rating: 0

Eight: Exploration and control require different types of action:

random versus "computable".

This is not at all like the PCT perspective. Exploration per se isn't
necessary to tune a world model becuase there is no world model.

8. Similarity Rating: 0

Nine: Developing correct perception is much more important than
developing correct action.

This makes no sense from a PCT perspective. There is no such thing as a
"correct" perception. In order to control, we have to construct perceptions
that can be influenced in all relevant dimensions.

9. Similarity Rating: 0

Ten: There are no "unused" perceptions. _All_ perceptions tune the
model, although some may be discarded AFTER it has been established
that they cannot be fit into the model.

PCT suggests that some perceptions are controlled; some are not.

10. Similarity Rating: 0

Corollary of the above: All behavior is optimal.

If "optimal" corresponds to "minimum possible error in all control
systems" then PCT suggests that in many cases behavior (control) is not
optimal; these are the cases where there is conflict between control
systems. When there is conflict, the organism is operating with more
error than necessary given the current organization of the control
hierarchy.

Farfetched?

Yes.

It is what the theory says!

Then the theory is missing something VERY important. But don't let that cause
you any conflicts;-)

11. Similarity Rating: 0

Another corrolary: Every second part of an optimal trajectory is
itself an optimal trajectory. The past does not matter

Well, this is pretty vague but, I've gotta admit that PCT leads to
the same conclusion.

12. Similarity Rating: 10

Me:

Why, according to MCT, do people have problems?

Hans:

People have to solve the riddle of how to live optimally.

Just above I see that a corollary of MCT is "All behavior is optiimal". It
sounds to me like people have solved the riddle of how to live optinally
as soon as they start behaving. So behaving people have no problems,
according to MCT. PCT says that people do have problems; the source of
these problems is conflict ybetween control systems.

13. Similarity Rating: 0

Me:

Why do people fight with one another?

Hans:

Because one person does not understand how he/she can "control" the
other. A person is like a rock or a chain saw or a chemical plant in
that he/she/it can be controlled only if we get to know how he/she/it
functions...Fighting is suboptimal behavior.

PCT says that one reason people fight is because they don't realize that
they can't control each other (arbitrarily): interpersonal control is
conflict. Sounds like a _big_ difference between MCT and PCT to me. Also,
if fighting is suboptimal behavior, then, according to MCT, it must not
exist. So, based on what MCT said earlier, people don't fight.

Are you sure you're not just making this stuff up as you go?

14. Similarity Rating: 0

Me:

What can people do to get along with others and themselves?

Hans:

Build better models. Get to know others better.

So such models would allow you to control people better, just as a better
model of the physical parameters of a wheelbarrow and the surface on
which it rides will let you control it better. PCT would say that this is
_exactly_ the wrong way to go. The first thing to do to get along with
people is to realize that people are control systems and that, therefore,
they cannot be controlled arbitrarily. You have to be willing to negotiate
in order to resolve conflicts over controlled variables.

15.Similarity Rating: 0

···

-------

Ok. That's it for this group. There were a total of 15 answers; the
highest possible similarity score is, thus, 150. I gave MCT a total
similarity rating of 30 yielding an average similarity value of 2
out of 10 between MCT and PCT (assuming all answers are equally
important).

MCT may be the greatest thing since sliced bread (I'll take the sliced
bread, thanks) but it is DEFINITELY not PCT.

Best

Rick

7

[Hans Blom, 960729]

(Rick Marken (960727.2100))

Rather than evaluate the merits of the MCT answers, I will try to review
these answers in terms of their similarily to what HPCT might say.

Would your answers have been different if you had evaluated the
merits of MCT independently?

My goal is simply to show that the implications of MCT and PCT
regarding the nature of human nature are quite different.

Good! Then they have different perspectives to contribute!

Of course, I also think the data show clearly and overwhelmingly
that PCT is a much better model of human nature than MCT.

How does PCT explain that different people prefer different models?

... The "internal models" in MCT are models of the laws of physics,
not perceptual representations of external variables.

I'm sorry that you got this impression. What you say is, of course,
absurd. Instead, the "internal models" in MCT are models of HOW WE
PERCEIVE the laws of physics. Sometimes this leads to the "laws of
nature" being incorporated into our models, if we guess right or
deduce correctly. Sometimes not. But even then, surprisingly, we seem
not to be so stupid that we design a model that is completely off the
mark. And that is usually good enough to have control of at least
SOME quality.

What IS correct in what you say is that the emphasis in MCT is much
more on law (relationships between perceived variables) than on
representation of external variables. In fact, MCT shows that many
different representations will lead to identical control behavior.
Think of this as a new choice of coordinates -- any coordinates will
do. So even if you have found a perfect representation, MCT will show
that there is an infinity of similarly perfect representations. This
demonstrates that it is not the representation that matters (here
many A.I. adherents make a mistake), but some of the properties of
representations.

MCT, therefore, has to predict that people who live in the same
environment would _have to_ build the same internal models of that
environment or they could not control at all.

Far too black and white. Whence the "not control at all"? You are
right about controllers: if their hard- and software is the same,
they will perform identically if "brought up" with identical
perceptions. For people this cannot be completely true: even
identical twins usually do not live in the same (psychological)
environment. But if they do, they show remarkably identical behavior.

In fact, MCT says nothing about the importance of the perceptual
function in control (find me a diagram in a MCT text which
includes the perceptual function explicitly). So the implications
of MCT is that people who live in the same environment are all the
_same_ in terms of their internal models.

MCT says that the perceptual function changes over time. It starts
out as an initial given, and is subsequently modified according to
what happened in the environment. And indeed, the more the same the
environment, the more alike will model and behavior be. We see this
at the scale of cultures.

What makes it more difficult for you is that MCT only infrequently
uses diagrams, because they are not precise enough. But when _you_
analyze a system, you also need the formulas, not (only) the diagram.
Given the MCT formulas, you could derive a diagram. They tend to get
a bit tangled, if you expand them to scalar pathways, because so
much relates to so much. But I do realize that you are at a real
disadvantage here, when you insist on diagrams. When one sees
diagrams in the MCT literature, diagrams of the loop show vectors and
matrix operations. That is good because all MCT systems can be
described by a common diagram. That is bad, as Bill Powers notes,
because you cannot see individual signals.

They may control different perceptual aspects of that environment
(a possibility that is not explicitly represented in MCT) but they
would do it using the same internal model of that environment.

In MCT, this statement is nonsense. MCT says that if the internal
model is the same, the same perceptual aspects of the environment
will be controlled. What do you think a model is? The perceptual side
of the model (if we make this conceptual "split" for a moment) tells
which of the perceptions is important to reach which goals. The
action side of the model tells which actuators need to be activated
in order to reach a certain desired outcome.

Up until the last statement things were going along fine. Since we have
successfully done The Test over and over again, any theory that says The
Test can't be done has real problems.

Tell me about the outcomes of your Tests. What are the invariants?
Have you discovered any goals that persons control for _at all
times_, the things that are _really_ important? If so, what are they?

>Seven: Because the world is not fully predictable, it needs to be explored
>continuously. Explorations reestablish the up-to-date-ness of the model.

PCT shows that no world model is necessary for control.

How does PCT explain exploration? Or is there no such thing in your
opinion?

PCT says that one reason people fight is because they don't realize that
they can't control each other (arbitrarily): interpersonal control is
conflict. Sounds like a _big_ difference between MCT and PCT to me. Also,
if fighting is suboptimal behavior, then, according to MCT, it must not
exist. So, based on what MCT said earlier, people don't fight.

The term "optimal behavior" must be confusing from a PCT perspective,
because PCT does not have something similar. Let me explain it
briefly.

1. The behavior of an optimal controller is, as the name says, optimal
always. But that "optimal" is contingent on its hardware (genetics)
and its environment (upbringing). For the environment that it found
itself in, each human has developed optimal behavior. That is (I
hope) what every therapist will tell his clients when they enter
therapy.

2. What is optimal changes over time. Because of learning, perform-
ance improves. So what is optimal at time T1 will be different from
what is optimal at T2 <> T1. If not, a problem exists that we will
have to explain.

3. Because optimal is contingent on the environment and its history,
placing an individual in a new (test) environment may show up as
behavior that is severely suboptimal _for that test environment_.
Note that this is how we usually evaluate people or organisms.

MCT tells what the major developmental problems are: an environment
in which perception is not possible, an environment in which action
is not possible, and growing up in an environment that is too
different from the "test" environment (daily life, where we are
members of a common culture).

Particularly obsidious is having been brought up in an environment
where it was forbidden to perceive certain things or to act in
certain ways. This results in severely limited models, either the
perceptual side (less perceptions available than possible) or the
motor side (less action patterns available than possible). Have you
ever met people who do not look at you during a conversation? They
miss clues. Have you met people who do not state their opinions
openly? They get poor feedback. Have you met people who cannot
listen? Although they get feedback, they do not use it. Such people
have, earlier in their lives, learned "optimal" behavior which
perfectly suited their situation but that is now, in a "new"
environment, very probably far from optimal.

Note that "optimal" is used here in two different senses: what is
"optimal" for the person himself and what is "optimal" for an outside
observer. The first is meaningless, since for the person himself his
behavior is always -- by definition -- optimal. So the term is
(almost) always used in the second meaning. It is this second meaning
of optimality that is the concern in therapy: how can someone be
brought to relinquish outdated beliefs and habits, which are not
appropriate anymore in his new environment. In MCT models, "therapy"
can be achieved by simply changing some parameter values which have to
do with how reliable the model thinks its knowledge (other parameter
values) is. Simply said: it has to forget. But what invariably shows
up is a period of "crisis", very bad control behavior; the old model
is being relinquished but the new one is not well tuned yet.

Patients often experience this as being caught on a local maximum.
Every path leads downward, and that is painful and prevents people
from exploration. Yet they know deep down that, somewhere, there must
be a higher mountain where they truly belong. It is this intuitive
"faith" or "hope" that allows some people to endure the crisis, pass
through it, and reach their higher mountain top.

Can a PCT model explain this phenomenon?

Are you sure you're not just making this stuff up as you go?

I wonder what you mean by this. I tried to make sense of this
question by thinking about its opposite. Did I quote God? No. Did I
cite the Pope or some other infallible authority? No. Did I give a
short, subjective impression of how I think the mathematics of the
theory and the pragmatics of real life relate? Yes. So I guess that
I'm just making stuff up as I go. Don't you?

A thought experiment: Assume for a moment that everybody just makes
stuff up as they go. Would that make a difference in how you see the
world?

A question: Who are the people that you trust _not_ to make things
up? You yourself? Who else?

So such models would allow you to control people better, just as a better
model of the physical parameters of a wheelbarrow and the surface on
which it rides will let you control it better. PCT would say that this is
_exactly_ the wrong way to go. The first thing to do to get along with
people is to realize that people are control systems and that, therefore,
they cannot be controlled arbitrarily. You have to be willing to negotiate
in order to resolve conflicts over controlled variables.

15.Similarity Rating: 0

I don't see a conflict. Realizing that people are control systems is,
of course, a requirement if you want to model them correctly. But does
that matter? A central heating thermostat is a control system as
well. Can't it be controlled?

Ok. That's it for this group. There were a total of 15 answers; the
highest possible similarity score is, thus, 150. I gave MCT a total
similarity rating of 30 yielding an average similarity value of 2
out of 10 between MCT and PCT (assuming all answers are equally
important).

MCT may be the greatest thing since sliced bread (I'll take the sliced
bread, thanks) but it is DEFINITELY not PCT.

We knew that already, Rick. What score would you have liked? A high
score would have told you that MCT has nothing additional to offer,
because it doesn't change the way you interact with the world. A low
score makes it incorrect for you, I presume. At which score would you
have said that both theories might learn something from exposition to
the other?

My opinion is -- but that cannot be new to you either -- that PCT
might profit by studying some of the learning mechanisms that have
been discovered to work extremely well (under some circumstances) by
a different theory. MCT might profit by systematically studying how
a hierarchy of layers might be useful to functionally separate tasks
that are now only kludges at the same level. The result? HMCT? HMPCT?

The thing is: MCT can "explain" some of what we see happening around
us, which PCT cannot (yet). If that is the case, it is in my nature
to pick the best of both worlds and see if the combination makes an
even better world. In biology, that is called recombination. It is
one of the processes that have led to the "invention" of ever more
complex "higher" organisms.

Greetings,

Hans

8

<[Bill Leach (960729.1918 EDT)]

[Hans Blom, 960729]

How does PCT explain that different people prefer different models?

Does MCT demonstrate this?

MCT says that the perceptual function changes over time. It starts
out as an initial given, and is subsequently modified according to
what happened in the environment. And indeed, the more the same the
environment, the more alike will model and behavior be. We see this
at the scale of cultures.

Hans while your assertions here "are reasonable" that is all that they are.
Indeed further down in your message you point out that different models can
provide exactly the same observed behaviour.

Tell me about the outcomes of your Tests. What are the invariants?
Have you discovered any goals that persons control for _at all
times_, the things that are _really_ important? If so, what are they?

I suppose that this is a bit sarcastic but PCTers are presently accepting
the idea that the "_really_ important questions" fall into three catagories:
Questions that seem to be irrelevent in a control theory view of life,
questions that are too vague to be phrased in testable terms, and finally
questions that are clearly beyond our present capability to address
rigorously (including the use of generative models of course).

Hans:

Seven: Because the world is not fully predictable, it needs to be explored
continuously. Explorations reestablish the up-to-date-ness of the model.

Rick:

PCT shows that no world model is necessary for control.

Hans:

How does PCT explain exploration? Or is there no such thing in your opinion?

I'll start with; does MCT "explain" "exploration" other than through a bunch
of impressive hand waving?

Of course more seriously, what is, in a rigorous sense, "exploration"? Are
you asking if PCT explains /why/ the behaviour of organisms sometimes seems
to fit some criteria for which there is a general agreement to call
"exploration"? Are you asking /what/ the organism so engaged is doing?

1. The behavior of an optimal controller is, as the name says, optimal
always. But that "optimal" is contingent on its hardware (genetics)
and its environment (upbringing). ...

Hans this does not really say anything.

3. Because optimal is contingent on the environment and its history,
placing an individual in a new (test) environment may show up as
behavior that is severely suboptimal _for that test environment_.
Note that this is how we usually evaluate people or organisms.

and this was worse since it contradicts 1.

MCT tells what the major developmental problems are: an environment
in which perception is not possible, an environment in which action
is not possible, and growing up in an environment that is too
different from the "test" environment (daily life, where we are
members of a common culture).

Obviously I have not read anything on MCT but while Perceptual Control
Theory does not "tell us" these same things, one would have to be a much
more "simple" fellow than even Rick claims to be to not draw the same
conclusion based upon experimentation with PCT's generative models.

Particularly obsidious is having been brought up in an environment
where it was forbidden to perceive certain things or to act in
certain ways. This results in severely limited models, either the
perceptual side (less perceptions available than possible) or the
motor side (less action patterns available than possible). Have you
ever met people who do not look at you during a conversation? They
miss clues. Have you met people who do not state their opinions
openly? They get poor feedback. Have you met people who cannot
listen? Although they get feedback, they do not use it. Such people
have, earlier in their lives, learned "optimal" behavior which
perfectly suited their situation but that is now, in a "new"
environment, very probably far from optimal.

This reads like an awful lot of "concluding". There is generative model test
data to support all of these assertions yes?

Patients often experience this as being caught on a local maximum.
Every path leads downward, and that is painful and prevents people
from exploration. Yet they know deep down that, somewhere, there must
be a higher mountain where they truly belong. It is this intuitive
"faith" or "hope" that allows some people to endure the crisis, pass
through it, and reach their higher mountain top.

Can a PCT model explain this phenomenon?

Hans even though my perception of what I think that you mean by what you
said is "pretty much OK" as far as I am concerned (not fact but
"reasonable"). On the other hand, what you wrote /reads/ like a religious
mantra. Lots of "flowery" words that actually do not say anything specific:
"local maximum"? maximum what?, Every path leads downward... What is a path
and what is downward? Surely you don't mean like an Escher picture? What is
painful and why? Why are you so sure that this pain prevents "exploration"? etc!

I don't see a conflict. Realizing that people are control systems is,
of course, a requirement if you want to model them correctly. But does
that matter? A central heating thermostat is a control system as
well. Can't it be controlled?

No! You can "trick it", you can mechanically overwhelm it but if you don't
mechanically alter it (that is do not make it something different from what
it currently is) you can not control it in the sense of making do something
other than control its' perception to the reference value.

My opinion is -- but that cannot be new to you either -- that PCT
might profit by studying some of the learning mechanisms that have
been discovered to work extremely well (under some circumstances) by
a different theory. MCT might profit by systematically studying how
a hierarchy of layers might be useful to functionally separate tasks
that are now only kludges at the same level. The result? HMCT? HMPCT?

Hans this could be true but the convincing is in conducting reproducable
experiments on learning with living systems and then modeling that learning
using generative model of the MCT design.

The thing is: MCT can "explain" some of what we see happening around
us, which PCT cannot (yet). If that is the case, it is in my nature
to pick the best of both worlds and see if the combination makes an
even better world. In biology, that is called recombination. It is
one of the processes that have led to the "invention" of ever more
complex "higher" organisms.

You have made quite a few assertions that are no less impressive than are
made by many "giants" of the behavioural sciences. The problems are that
these grand assertions of your appear to be no more quantifiable and
testable by you than they are as presented by the psych folks.

bill leach
b.leach@worldnet.att.net
ars KB7LX