PCT and system dynamics

[From Bill Powers (931118.1430 MST)]

Oded Maler (931118) --

But what in the rules of the world (including the perceptual
machinary) makes this particular high-dimensional dynamical
system converge to a state (more precisely a region of the
state-space) where the signal matches its reference. This the
*why* I referred to.

The answer, I think, is right under your nose in PCT. Nothing
MAKES the dynamical system converge to a particular state -- that
is, nothing external that is acting on the system. The objective
final state of a living control system is of no concern to the
control system; only to someone else who can see only the
objective outsides of the system and its environment. And what
that someone else thinks is irrelevant to what makes the control
system work or its reasons for working.

This is why I keep objecting to treating the reference signal as
just another input to the system. It is not just another input:
it is a very special input, made so by the nature of the
organization that is receiving it. It is an input that defines a
perceptual state of affairs that IS TO BE BROUGHT ABOUT BY
BEHAVIOR. If you think of this state of affairs as something
external to the system, some objective consequence of its
behavior, and try to explain why that objective consequence comes
to its final state, you will have posed a problem that's
impossible to solve. Why does the objective coffee get to the
person's lips to be swallowed? There is no law of nature, no
combination of laws, that decrees that outcome. There is only one
explanation, the one that Mary offered: because the organism
wants that state of affairs, as it is perceived, to come into
existence.

And where does the reference signal defining that want come from?
It comes from another level of control system that wants
something else, of which the goal of drinking the coffee is only
a subgoal, a means. And where does that reference signal come
from? Still deeper inside the organism. Ultimately we reach the
basic system that creates organization, and its reference signals
come not only from inside the organism but from the first
assembly of matter that became alive, 3 or 4 billion years ago.
Those reference signals have been inherited and modified and
inherited and modified until life has progressed to constructing
whole modern organisms as a way of controlling what happens to
itself.

The real answer is in that first proto-organism, the one that
took control of some critical substance in its vicinity and thus
increased its own accuracy of replication, and from then on
dominated the world of organic chemistry. This proto-organism
took the first step toward controlling what happens to itself,
nullifying natural influences in its vicinity in the process of
doing so. From then on, in ever more powerful ways, living
systems began to divert the course of the nonliving physical
world from the paths it would have taken if organisms didn't want
things.

When you don't see the fundamental difference between a closed-
loop control system and an open loop input-driven system, you
completely miss the point of PCT. Focusing on the objective
outcomes of behavior is one excellent way to overlook this basic
difference. Doing that makes it seem that a feedback control
system is just a special case of the more general idea of a
dynamical system. You start looking for the same kinds of
explanations whether the system is open-loop or closed-loop. You
ask "Why does this organism end up in the kitchen drinking coffee
instead of in the living room watching television?" And to answer
that question, you look around for causes -- for inputs which,
acting on the system, would cause it to behave in one way rather
than another. If you were speaking of an open-loop dynamical
system, that would be the proper approach because open-loop
systems are driven by their inputs and have no wants, no
preferences, no intentions regarding what the inputs will be. But
a closed-loop system is in the business of controlling its own
inputs; the whole point is that the external world no longer has
much influence over those inputs, compared with the amount of
influence the closed-loop system itself has, through its actions.

A control system is not JUST one form that a dynamical system
could take. It is surely one of the forms. But it has a status
entirely different from all other forms. It is a freak. It does
something that no other kind of dynamical system can do, and that
difference makes all the difference. It makes the difference
between a living system and a nonliving one.

The difference is that the living closed-loop control system
controls its own most important inputs. It alone, among all other
kinds of organizations, acts with a purpose. It alone creates
outcomes that are not simply balances of blindly-applied forces,
but are regulated, aimed at a particular outcome that the system
senses and for which the system has set a specific reference
level.

In the equations relating to optimal control that you posted a
couple of days ago, a closed-loop control system was hidden. But
all kinds of other systems were hidden there, too, depending only
on what values of the coefficients you chose. When you bury a
control system in an overgeneralized set of equations, there is
nothing to call your attention to it as a particularly
interesting case. You tend to treat that case in the same way you
treat all the others -- for one thing, you focus on explaining
the objective situation x(k) rather than the perceived situation,
y(k), because that is the relevant outcome for all cases except
that of the closed-loop control configuration. The reference
signal is just an input to all those other systems, whether the
coefficients result in negative feedback or not. So there doesn't
seem to be anything special to explain.

If there is nothing special to explain about a particular choice
of coefficients, then you start looking for a general way of
understanding the equations, a way of speaking about what they do
no matter what the coefficients are. This means you start looking
for overall principles to explain why inputs cause outputs to
converge to particular patterns. Whether those are controlled
patterns or not makes no difference any more. And so the
startlingly different mode of behavior of a closed-loop control
system becomes submerged in what seems a continuum of cases, no
one of them inherently more interesting than any other. That is
the penalty for overgeneralizing: you miss the significance of
the one special case that is radically different from all the
others. And inevitably, you apply the same sort of explanation of
outcomes to the control system case that you would apply to all
the other cases -- you even call them all "control systems."

That is what I call missing the point. Wake up and smell the
coffee.

···

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Best,

Bill P.

[From: Oded Maler (931123)]

(Bill Powers (931118.1430 MST):

* If you think of this state of affairs as something
* external to the system, some objective consequence of its
* behavior, and try to explain why that objective consequence comes
* to its final state, you will have posed a problem that's
* impossible to solve. Why does the objective coffee get to the
* person's lips to be swallowed? There is no law of nature, no
* combination of laws, that decrees that outcome. There is only one
* explanation, the one that Mary offered: because the organism
* wants that state of affairs, as it is perceived, to come into
* existence.

I disagree. It is a partial explanation. Laws of control-less
life-less universe are not sufficient - with this I agree.
But to claim that they disappear from the interaction when
there is control is again solipsism. The rules of physics
cooperate with the control system (and resist it when it is
poor - I have a lot of examples of resistance). Why a good
control system works in the world is still an open question
(to my mind). Of course, I accept the general story of evolution
of control from the proto-organisms etc., but controlling
chemicals within a substance is another story than controlling
the world of objects via neuro-muscular devices. Maybe "control"
is the underlying *principle* in all levels, but the details
are completely different (unless there is some secret in the
structure of the world).

--Oded

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--

Oded Maler, VERIMAG, Miniparc ZIRST, 38330 Montbonnot, France
Phone: 76909635 Fax: 76413620 e-mail: Oded.Maler@imag.fr