Gods and fish and PCT

CSGnet Archive CSG1995
1

[From Rick Marken (950901.1400)]

Martin Taylor (950901 11:40) --

1. Is it possible to show that there CAN BE any model-based control system
whose behaviour cannot be reproduced in exact detail by a non-model-based
perceptual control system?

I don't see why not. I think experiments where people lose (and then regain)
a controlled perception are the kind that might provide data that can only be
handled by a model-based controller.

Bill's Artificial Cerebellum improves control some, when the output function
learns a specific model of the feedback function.

I don't think the Artificial Cerebellum actually learns a feedback function;
I think it learns an output (and an input?) function (and connections between
functions if there is a hierarchy of systems) that allows the control system
to control in the environment (characterized, in part, by the feedback
function) in which it exists.

Bruce Abbott (950901.1045 EST) --

What I _was_ trying to communicate (apparently not very well) is that a
group of autonomous control systems might in fact behave (under the right
conditions) in precisely the way that the physicists' model describes,
because at the right level of abstraction, such "particles" would interact
in much the same way that ferromagnetic atoms interact, though for very
different reasons.

I think it's the "different reasons" that are important. In the William James
piece that Tom quoted, James explained how to distinguish the superficially
similar behavior of a metal filing moving toward a magnet and a lover moving
toward his love; you introduce a disturbance (a card between the magnet and
the filing; a wall between the lover and his love). When you do this, you see
the difference between a cause-effect system (the particle) and a control
system (the lover). If James had had control theory, psychology would have
taken a very different course in 1895. It's now 1995 and psychology is still
crippled by it's failure to grasp what James seemed to grasp intuitively 100
years earlier -- that organisms are input control systems.

I think we can agree that drivers on the road are autonomous control
systems and that the vast majority of those systems attempt to keep their
vehicles on the road, on the correct side of the road, and try to maintain
space between their vehicles and the others (i.e., avoid collisions).

I agree.

Yet in the aggregrate, it is possible to learn some important lessons about
traffic flow if one simply imagines that each car is a particle responding
to "forces" impressed on it by the particles around it (e.g., a repulsive
force falling off with the square of the distance to the particle ahead, to
take a simple case).

I guess I don't see how we can really learn important lessons about traffic
flow by using the wrong model to describe what's going on. Whatever we learn
is bound to be misleading. Under certain circumstances the wrong model will
produce behavior that looks like what we see; the laws of electromagnatism
that explain the behavior of 100 filings moving toward and gathering around
a magnetic pole might also seem to explain the behavior of 100 Romeos moving
toward and gathering around Juliet. Indeed, there might be all kinds of
circumstances under which the electromagnetic model matches the Romeos'
behavior. But there will be many, many other situations where the
elctromagnetic model of the Romeos doesn't work. So the important lessons we
get from the elctromagnetic model are just a result of coincidence -- one
that could lead to delusion (like the cause-effect delusion that currently
grips psychology).

The laws of fluid dynamics then apply, and you can predict traffic jambs
around construction sites (restrictions to flow), standing waves, and even
multiple-car pileups by applying these laws to the right set of initial
conditions... It [fluid dynamic model] may provide a useful description so
long as it is not taken too literally.

I don't think literality is the problem. The problem is correctness. I agree
that you can probably predict many aggregate control phenomena with some
level of accuracy using an external causation model. But it seems like there
would be many (most?) circumstances where the external causation model would
make very inaccurate predictions. I think an external causation model could
handle some kinds of disturbance to control systems (assuming they all were
controlling for the same variables at nearly the same levels) by adding ad
hoc assumptions about the effects of environmental variables on the
individuals (for example, you could add a special term to the electromagnetic
model that caused Romeos to be pushed around and past obstructing walls);
what might create a problem is the situation where the actual individual
entiites have very different references for a variable or where they control
for quite different variables.

Actually, what might be interesting is to see how well these external
causation models of aggregate phenomena actually do when the phenomena they
model involve living systems. I think it would be useful to look for (or
create) situations that might distinguish external causation from aggregate
control models (like CROWD).

Tom Bourbon (950901.1420) --

The claim that knowing PCT, in and of itself, will necessarily lead to a
person becoming a better person, or to the world becoming a better place,
has a lineal-causal ring to it, wouldn't you say?

It sure does, now that you mention it. I'm glad to add another data point
to the "control" column though I'm sorry that my existential rejection of
lineal cause-effect sometimes has such a disturbing effect on others.

Best

Rick

2

[Martin Taylor 950905 19:00]

Rick Marken (950901.1400)

+Bill Powers (950901.1430 MDT)
=Hans Blom, 950904

In response to my two questions, I thank Bill and Rick for responding, but
I don't think that they really approached an answer.

···

Martin Taylor (950901 11:40) --

1. Is it possible to show that there CAN BE any model-based control system
whose behaviour cannot be reproduced in exact detail by a non-model-based
perceptual control system?

I don't see why not. I think experiments where people lose (and then regain)
a controlled perception are the kind that might provide data that can only be
handled by a model-based controller.

+
+Yes. A model which can continue behaving in an approximately right way
+when the perceptual system is arbitrarily turned off for a short time.

Am I quite wrong in thinking that one can turn off the perceptual input
for a while in Rick's spreadsheet demonstration, and have it lose track
only slowly (as in a model-based controller)?

+ 2. Is it possible to show that there CAN BE any perceptual control
+ system whose behaviour cannot be reproduced in detail by some
+ model-based control system?
+
+Yes. A perceptual control system that can counteract the effects of
+arbitrary independent disturbances with an accuracy greater than the
+theoretical accuracy with which the disturbance could be deduced and
+extrapolated into the future by any means of prediction.

You are asserting here that the model must function without input data.
I don't regard that as a reasonable restriction. I'm quite prepared to
accept that without observing the state of the world, no conceivable
mechanism could maintain that state at a desired level. If by "perceptual
control system" you mean "a control system that uses observations of the
world," then there is no issue.

What I'm hoping for is some kind of a theorem, not verbal arguments that
can appear to make points when the hidden assumptions are not examined.
But verbal arguments are OK if they are explicit enough to allow their
truth to be judged.

The questions relate to the difference between a complex hierarchic perceptual
control system of simple loops, and a simply structured (perhaps single
level) control system involving explicit modelling of the environment.

A model is supposed to duplicate the input-output relationships in the
real system, isn't it?

No. It is supposed to map them in some way. Just as your Artificial
Cerebellum does, in effect generating an inverse function to the feedback
function. A map need not be one-to-one, and need not have the same shape
as the original. The "standard" map of the London Underground is an excellent
model, but you could never overlay it onto the street map of the city.
The contents of a whole mess of memory registers in a computer with an
appropriate program may be a fine model of the dynamics of a control system,
but they hardly look like the control system itself. It's just a mapping
that preserves some useful structure of the original.

You are using the term "model" in such a vague and elastic way that it
hardly has any meaning left.

I used it in two ways, as I made explicit in my original posting (or so
I thought). The questions refer to a model1 in which there is explicit
description (representation, if you like) of some aspect of the outer
world. In further discussion, I suggested that one could regard the
structure of a control system to be a kind of distributed model2 of the
range of environments within which it could control. The two kinds are
quite distinct, I think.

The difference between the two kinds of model is analogous to the difference
between an AI system (in which rules and data are stored in accessible
memory locations that can be examined and assessed individually), and
a neural network (in which the same information is held in a distributed
fashion across the weights and links of the network.) In this second sense,
the term "model" is indeed "vague and elastic." It is in the first sense
that I asked the two questions.

My point was to question whether the distribution or explicit representation
of the "model" made an intrinsic difference, or whether the two ways of
constructing control systems could not IN PRINCIPLE be told apart by
observing their effects in the environment.

Now back to question 1: Both Rick and Bill seem to assert that NO perceptual
control system can retain ANY control when the perceptual input momentarily
goes away, and that this distinguishes perceptual control systems from
model-based control systems, which can. Is this a true statement of your
intent, Bill and Rick?

If it is, then I would like to see a proof of that fact. But in view of
much earlier interchange in CSG-L, I doubt that my statement reflects
either a truth of perceptual control systems, or the intentions of Rick
and Bill.

---------------------

I would like to dissociate myself (as a CSG participant) from Marc Abrams'
disgusting posting to Oded Maler.

Martin