Ignorance: pros and cons

[From Oded Maler 971127]

Posting in the middle of doing something else does not always result
in the proper choice of words, so I would like to clarify what I said
in my previous post. The background was a dispute between Hans (a
control engineer) and Bill P. about "who is the teacher".
Bill claimed that Hans is not really trying to learn PCT while
Hans claimed that Bill is not trying to go beyond very basic and old
genre of control theory. Now, the common usage (that is, everywhere
outside this group) of the term "control theory" is for a body of
mathematical and engineering techniques for making systems reach certain
states. Incidently I have received an announcement of a web site with
the abstracts of a major conference in the domain:
     http://master.ceat.okstate.edu/conference/cdc/cdc97.html

When I say that someone is ignorant in X, it is not meant to be a
prejorative. Each of us is ignorant in 99% of the "things" in the
world, and the only question is whether X is relevant to what one
is doing. PCT, although concerned with the same phenomenon called
"control", has some particular aspects:

1) It is interested in models that *explain* existing systems,
not in building new systems.
2) These systems have evolutionary, developmental and other particular
hardware constraints.
3) The theory is "sensor-centered", in that it emphasizes that from the
point of view of the controller, the goal is to put *perception* in a certain
state, rather than to control the "objective" state of the system. (This
aspect is treated in control theory as observation functions, but the
primary object *is* the objective state of the plant, and the change of focus
is important).

In another, ideal world, Bill and other PCTers would have known the
math, the techniques and the vocabulary developed in control theory
(and in theoretical computer science) during the last 50 years, so
that they could sort out the 99% which are irrelevant to PCT, and pick
and use the rest. In this actual world everyone does with what he/she
knows. The fact that PCT is put forward using old terminology and
techniques is not a-priori an "objective" reason to reject (neither to
accept it). It has its advantages in avoiding some complex models and
red herrings which are irrelevant to the particularities of PCT, and
disadvantages in, perhaps, missing some useful insights. On the
subjective side, this restriction has effects: almost all the attempts
to make control people look at PCT fail because they perceive it as
naive. On the other hand, had the theory been more developed
mathematically, the circle of PCTers who understand the technicalities
would have become even smaller.

Le voila,

--Oded

[From Bill Powers (9711256.0744 MST)]

Oded Maler 971127 --

Posting in the middle of doing something else does not always result
in the proper choice of words, so I would like to clarify what I said
in my previous post.

I haven't received your "previous post" yet, but this one is and excellent
commentary on the problems that exist between MCT and PCT. As you say,

Now, the common usage (that is, everywhere
outside this group) of the term "control theory" is for a body of
mathematical and engineering techniques for making systems reach certain
states.

This is correct; you can add "reach certain states by any means within the
engineer's abilities." This includes the use of operations that require
extensive quantitative knowledge of the environment as well as accurate
models of the environment (in form, although the parameters are left for
the system to adjust by itself). It also requires knowing what events in
the environment are going to affect the variables under control. And it
assumes that the system perceives the objective states of variables in the
environment. Perhaps most important, it assumes that the control system can
do mathematical computations of great complexity with perfect (symbolic)
accuracy, such as computing the inverses of functions as they are being
modified.

It's certainly to the modern control theorist's credit that he or she can
work out computational methods of this kind to produce control systems that
can adapt to (slowly) changing environments and maintain good control.
However, I find it extremely unlikely that a spinal-reflex control system
would depend on such calculations, especially those that require taking
inverses, and _most_ especially in cases where there are no unique
inverses. I find it unlikely that a cockroach could perform those
calculations, not just because it probably can't do symbolic mathematics,
but because there is simply not enough neural material present to do all
that would be required even to _evaluate_ the equations. And cockroaches
locomote in much the same way that all legged organisms do.

PCT, although concerned with the same phenomenon called
"control", has some particular aspects:

1) It is interested in models that *explain* existing systems,
not in building new systems.
2) These systems have evolutionary, developmental and other particular
hardware constraints.
3) The theory is "sensor-centered", in that it emphasizes that from the
point of view of the controller, the goal is to put *perception* in a
certain state, rather than to control the "objective" state of the system.
(This aspect is treated in control theory as observation functions, but the
primary object *is* the objective state of the plant, and the change of
focus is important).

Very nicely said. The MCT approach uses a naive-realist epitemology: the
variables in the objective system are really there, and the control system
simply senses them directly. Optimization is simply a matter of the
engineer's choosing objective criteria such as minimizing some function of
squared errors, without regard to _why_ that is assumed to generate some
optimum result. In PCT, we must use more indirect methods, based on the
idea that controlling perceived variables does have objective (side-)
effects on the organism, and that these effects are also under control (the
idea of the reorganizing system). All criteria of optimality trace back to
basic variables in the organism that must be maintained near specific
states in order for the system to continue functioning. All criteria
involved in performing or altering behavior, in other words, are internal
to the organism.

In another, ideal world, Bill and other PCTers would have known the
math, the techniques and the vocabulary developed in control theory
(and in theoretical computer science) during the last 50 years, so
that they could sort out the 99% which are irrelevant to PCT, and pick
and use the rest.

That is the core of the problem. Most of what I understand of MCT is
irrelevant to the model that I think applies to organisms. If it were
relevant, and I couldn't do the math, I could find someone who can do it
and boil it down to something I can understand. The real problem is the
_architecture_, in which a world-model of the environmental feedback
function is used as a simulation of the environment and the short-term
action of the system is always open-loop. The outcome of this approach is a
system that is very heavy on the computation side, so much so that it
starts to look impractical as soon as one considers any realistic environment.

In this actual world everyone does with what he/she
knows. The fact that PCT is put forward using old terminology and
techniques is not a-priori an "objective" reason to reject (neither to
accept it). It has its advantages in avoiding some complex models and
red herrings which are irrelevant to the particularities of PCT, and
disadvantages in, perhaps, missing some useful insights. On the
subjective side, this restriction has effects: almost all the attempts
to make control people look at PCT fail because they perceive it as
naive. On the other hand, had the theory been more developed
mathematically, the circle of PCTers who understand the technicalities
would have become even smaller.

There is a real break-even point here which we haven't reached. If good
mathematicians could be persuaded of the basic architectural soundness of
PCT as a model of organisms, the mathematical development of PCT would
rapidly become respectable. The problem with MCT is that is is based on one
particular architecture which, once you buy into it, leads you along
inevitable paths of development that become as complex and sophisticated as
the thinking that goes into it. Once you decide that the problem is that of
calculating the output that will produce the desired reference state, most
of the rest follows. You _have_ to compute inverses; you _have_ to deduce
the states of all possible disturbances; you _have_ to have an internal
model of the environment. If you want to compute output in this way, you
have no choice. This is very much the hard way to achieve control, yet if
you have enough patience and mathematical skill, and fast enough computers,
you can do it.

If the same resources of mathematical skill and ingenuity were applied to
the PCT approach, I'm sure the picture would be very different. The Kalman
Filter, after all, has been around since the early 1960s. What it it had
been applied to the self-organization of perceptual systems and hierarchies
of control, instead of to the problem of predicting and calculating
outputs? If there were 20,000 references to it in that context, PCT would
be on a very different footing.

Thanks for a most useful post.

Best,

Bill P.