# Rosy gefilltefish; PCT and Control theory

[From Bill Powers (931203.1500 MST)]

Martin Taylor (931203.1045) --

This may be another rosy gefilltefish, but at least today I think
I have an idea, and wish to chew on it a little longer.

What is an amplifier? It isn't just something that increases
the energy coming from a power source. It is something that
modulates a larger energy flow at its output than the energy
flow at its input.

Yes. But this modulation process (as you pointed out earlier
yourself in re the vortex) could work either by adding energy to
the larger energy flow, or subtracting from it. The change in the
larger energy flow is not necessarily in the same direction as
the change in the modulating flow. Consider sending a morse-code
message to someone by intermittently pressing an ice-cube against
his skin. You are transmitting a message into the system by
periodically removing heat energy from it. Modulation or not, the
flow of physical energy is travelling opposite to the direction
in which the message is going.

This means that you can't analyze the relationship between
incoming energy and outgoing energy in a signal-handling system
in the same way you would do it for a physical system in which
energy is conserved. In the physical analysis, the bookkeeping is
literal: the same energy that is taken out of the source shows up
in the sink. All the energy is accounted for, and it retains its
identity throughout (there is no other source and no other sink
than the ones represented in the energy equations).

The physical laws applying to energy transfer -- and to physical
entropy -- rely on energy conservation for their meaning. When
formulae that happen to have the same form as those used in
dealing with physical energy are applied in a situation where
conservation laws do not hold, then the meaning of those formulae
becomes completely different. To me this means that the proposed
relationship between physical entropy and information is
spurious. A similarity of mathematical forms does not indicate a
similarity in the underlying processes. It's just a pun; it's
like saying that a bad medical school is like a duck because they
both emit quacks. Or on a higher plane, it's like saying that a
control system and a mass on a spring are alike because they are
both describable with a second-order differential equation.

A similarity in mathematical descriptions is no basis for
assuming that two physical processes have anything in common.
That assumption leads to absurdities whether the description be
mathematical or verbal.

This is particular the case for analyzing the apparent flow of
information through a nonconservative signal handling system.
Depending on the internal organization of the system, you can
observe any apparent input-output relationship imagineable -- one
that seemingly satisfies physical laws of energy transfer, or one
that grossly violates them, as a "power amplifier" seems to do. A
literal application of physical formulae to such a situation is a
blunder.

ยทยทยท

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Oded Maler (931203) --

A heartwarming post. Not only that, but it takes us another step
toward mutual understanding.

The (simplified) world picture of Control is that of a plant (
= an open dynamical system) with two input channels (one for
disturbances, one for control) and one output channel
(observations of the state of the system). The controller is
another dynamical system plugged into the plant, taking the
observation on the plant as its input, and its output signal
enters the control channel of the plant.

So far so good. This is the objective picture of a control
process. It is the way engineers see the situation, and when we
are building models of behavior, the way PCTers approach it, too.

A controller is good if for all/almost all/all-reasonable
possible disturbance, the trajectories of the plant state over
time will have such and such properties (e.g., temperature
always around 22 degrees). An ECS in PCT, for example, is good
if for all reasonable disturbances, the CEV (which is a
function of the plant's state variables) is most of the time
near its reference value.

Here is where PCT begins to diverge from control engineering. But
I'll accept this as part of the objective view of what "good"
control is. The slight divergence showing up here is in who
decides that control is good, and what criteria are used. But
let's go on.

Usually Control systems are discussed and analyzed using
"objective" terminology (Boss reality). It is the state of the
plant that is "controlled for" although the observation
function (perception) is all that can serve as a basis for the
control law. The reason is that we design such systems to
achieve something in Boss reality (at least in the shared
consensus about it), so the CEV, height-of-airplane is what is
important for the analysis, not the "inner feeling" of the
controlling computers and sensors.

In this type of control, what is important for us is what is
controlled, and it is generally the "principal aspects" of the
plant (this is a vague term, I'll try to explain). The state
variables of the airplane as a plant, include height, velocity,
etc., and they are what is controlled. The sensored are
designed that way, and the effector indeed affect these
variables.

Ah, the "usually" alerts me to the possibility that you are going
to offer a different interpretation, possibly the one that PCT
requires. Go on, go on!

If however we extend the boundaries of the plant to include not
only the spatio-temporal neighborhood of the airplane at a
given moment, but include a much larger region including
changes in weather, light, etc., we will see that the
controller controls a tiny portion of the
plant/world/environment, and moreover, viewed from a global
point of view, this part is not fixed but moves along as the
airplane advances. The part of the world that is controlled is
carried away by the moving controller via its sensors.

The analogy with resepect to a living control system in the
world is clear. Such a system is also a controller but the tiny
part of the world that it controls is not fixed (from Boss
reality point of view).

Whoa! You have veered off in a totally unexpected direction. This
isn't where I thought you were headed. You have given me the
chance, however, to explain my view by taking a different path.

In the conventional view, as you say, what's important about what
is controlled "is generally the "principal aspects" of the
plant ...". But this is not what is important to a living control
system. It's important in one sense, in that an observer who can
see both the environment and the insides of the control system
can see that it is probably important for the control system to
make sure that certain effects in the plant take place. The
observer can see, for example, that it would be best for the
control system not to back itself or the plant off the edge of a
cliff.

But put yourself in the place of an organism that can know the
environment ONLY in the form its feedback sensors provide to it.
There is no engineer to tell this control system what the actual
state of the plant is. All that the organism knows is the state
of its sensor signals, which represent limited aspects of both
external and internal variables. So the organism has to learn to
control NOT the plant, but its perceptions. This means that it
basically doesn't care what happens to the so-called plant. As
long as its experiences are under control, it neither knows nor
cares about what its actual effects on the environment are.

The only way the organism can know what it is doing to its
environment is through reflected effects on the organism. It does
not know anything about physical laws except what it can learn
through experience with its perceptions. The actual physical
characteristics of the plant are unknown. If control is poor, and
the controlled variable is important to the organism, that will
be revealed only when something happens to the organism that it
senses as undesirable. And all adjustments of its methods of
control must be made by the organism blindly, simply on the basis
that certain adjustments make it feel better and others make it
feel worse.

This picture is in stark contrast to the engineering approach, in
which each part of the environment and the control system is
represented as a collection of properties and relationships that
are known and measured, and in which optimal control is achieved
by solving equations that show the best settings for all
parameters. This is not how organisms learn to control what
happens to them -- with the single and almost irrelevant
exception of engineers who have learned certain techniques for
calculating how to build devices that will control a few
variables at a time. Even the engineers, when not designing
control systems, control thousands of variables simultaneously,
which they learned to control in a very different way. And of
course the engineers, before they went to school, were already
controlling all those other variables, and animals which
completely lack calculational skills and analytical abilities go
through their whole lives controlling all those thousands of
variables without any abstract understanding of their
environments.

What is "optimal control" from the standpoint of an organism? It
is control that results in getting fed, keeping warm, producing
offspring, and other such things that directly affect the
organism or its species. I suspect that evolution has supplied
many detailed indicators of the state of the organism, which I
call intrinsic reference signals; these define the criteria of
optimality. But these are criteria that no engineer uses; the
engineer thinks more in terms of minimum-time error correction,
minimum use of energy, and so on -- objective criteria that have
objectively definable correlates, outside the control system,
important perhaps to the customer who wants to use the control
system but of no concern to the control system itself. Such
criteria are of no use to an organism; what happens to its
environment has no directly knowable effect on what the organism
experiences of its own state. There is no customer to satisfy but
the organism itself.

The challenge in understanding living control systems is in
figuring out how they come to control as well as they do without
using any of the knowledge that engineers use. To meet this
challenge we have to take the viewpoint of the controlling
system, knowing only what it knows, and trying to see how that
could be sufficient to account for what we see it doing.
------------------------------------------------------------
Best to all,

Bill P.

[Martin Taylor 931205 12:30]
(Bill Powers 931203.1500)

and (Rick Marken 931204.1030)

(Rick)

If I'm wrong, I'm happy to be corrected.

Oh, would that it were true!

(Bill)

...this modulation process (as you pointed out earlier
yourself in re the vortex) could work either by adding energy to
the larger energy flow, or subtracting from it. The change in the
larger energy flow is not necessarily in the same direction as
the change in the modulating flow. Consider sending a morse-code
message to someone by intermittently pressing an ice-cube against
his skin. You are transmitting a message into the system by
periodically removing heat energy from it. Modulation or not, the
flow of physical energy is travelling opposite to the direction
in which the message is going.

Yes. But just ponder for a moment how a refrigerator works, considered
as a heat engine. The interesting part of the flow isn't the main one,
from the power station to the fridge, but the heat loss from the contents
of the fridge. The point is that it doesn't matter where the primary
power source might be. But it has to be there, and you can't have
thermodynamic efficiencies greater than unity. All calculations of
things like "gain" apply to signals that are imposed on this main flow.
Modulated, to use another word. Whether the physical energy goes the
same way as the signal is immaterial. When you put the ice cube on the
skin, the energy flow through the skin is momentarily increased. When
you take it off, the flow is decreased. That change is the modulation
signal, and it is observable anywhere between the source and the sink.

This means that you can't analyze the relationship between
incoming energy and outgoing energy in a signal-handling system
in the same way you would do it for a physical system in which
energy is conserved. In the physical analysis, the bookkeeping is
literal: the same energy that is taken out of the source shows up
in the sink. All the energy is accounted for, and it retains its
identity throughout (there is no other source and no other sink
than the ones represented in the energy equations).

The physical laws applying to energy transfer -- and to physical
entropy -- rely on energy conservation for their meaning. When
formulae that happen to have the same form as those used in
dealing with physical energy are applied in a situation where
conservation laws do not hold, then the meaning of those formulae
becomes completely different.

This I really don't understand. Are you saying that Carnot's analysis
of heat engines has been shown to be wrong because heat comes in at a higher
temperature than it goes out? We are dealing with non-equilibrium flows
so we can't even achieve the Carnot efficiency, but the formulae don't
care. Energy differences are what they are, and so are entropy differences.

It's hard to respond coherently to this paragraph, I'm afraid, because
it doesn't make any sense to me. I don't imagine my response does to you,
either.

Let's try a different tack. Early in my acquaintance with PCT, I felt
that the notion of "control system" was a metaphor for something, but it
was hard for me to see what it might be a metaphor for. Gary, specifically,
put me straight, that the PCT "control systems" were exactly normal
everyday engineering control systems working in the real world. Now
that made everything make sense. One could bring to bear all the tools
that apply to control systems operating in the real world. They really
have to work. No fancy stuff. Just testing against Boss Reality. In
our scientific culture we have quite a lot of coherent beliefs about
the way physical systems work. For example, nothing can have effects
before it happens (a belief denied by clairvoyants and astrologers, but
I hope a belief accepted by PCT researchers).

I'm operating with a set of beliefs that may change as I learn, but the
base belief is that our understanding of physics is the best we can currently
do. The laws of thermodynamics apply, for example. If I accept that
control systems operate in the Real World described by physics, then they
are subject to the laws of thermodynamics.

We know something about what happens in non-equilibrium situations. Not
as much as we would like, perhaps, but a lot more than we did even 20 years
ago. Control systems originally developed within a strong non-equilibrium
energy flow, and it seems probable that the evolution of control systems
is likely to occur in most similar situations if the flow is sustained
enough. Why? I think it is because of the inherent negative feedback
that induces structural stabilities in such flows (we call the result
"self-organization;" the word itself implies feedback, which has to be
negative if the structure is to be stable). In the interactions among
such structurally stable negative feedback systems, other stabilities
will occur (through negative feedback), and it seems almost inevitable
that some of these will by chance come to pass through the mutual
alteration of the stable points of the loops--setting reference signals.
At THAT point, and not before, I would call what is happening "control."

There is no metaphor here. I'm trying to deal with systems operating
in a real world as best it is known to (classical) physicists. My
knowledge of physics is imperfect at best, so I may make mistakes. But
one mistake I am not making is

A similarity in mathematical descriptions is no basis for
assuming that two physical processes have anything in common.
That assumption leads to absurdities whether the description be
mathematical or verbal.

or

This is particular the case for analyzing the apparent flow of
information through a nonconservative signal handling system.
Depending on the internal organization of the system, you can
observe any apparent input-output relationship imagineable -- one
that seemingly satisfies physical laws of energy transfer, or one
that grossly violates them, as a "power amplifier" seems to do. A
literal application of physical formulae to such a situation is a
blunder.

It is not a blunder, because the system IS a physical system, and the
physical formulae MUST literally apply, unless we are claiming to haul
down the entire edifice of physics.

Power amplifiers don't in the least seem to violate any laws of physics,
once you realize that what is amplified is a modulation, not the energy
flow.

I do hope that this side-trail dragged by a little kipper will meet up
with the main trail some time. Only some of the hounds were "faulted."
The rest ignored this digression on energy, all initiated by a single
word on a diagram. If I had used "fed back signal" instead of "fed back
energy" would any of this discussion have occurred?

Has anybody's understanding of the physics of negative feedback been
altered? I doubt it.

Martin