On disturbances

[From Bill Powers (930325.1530)]

Rick Marken (930317.1000 ff) --

Your excellent diagram makes it clear that we have to redefine
the disturbing variable. To call an external variable that
affects (potentially) a CEV a "disturbing" variable is to assert
that the organism has a reference level for the state of the CEV.
A noncommittal way to speak of such cases is to speak merely of
independent variables, or distal variables.

In your diagram there is one information path which shows the
"disturbing" variable being perceived but without any reference
signal or comparator. In that case, the perception is simply that
the CEV exists. A perceptual function creates an CEV, but only a
complete control system creates a controlled CEV.

A statement made by someone can therefore be perceived and
translated into a meaning without constituting a disturbance. It
is just a perception. Only when there is a preferred state for
the meaning of that perception and a means for comparing the
actual state with the preferred state can there be any error
signal, and only when the error signal is translated into an
effect on the source of the perception can we talk about a
disturbance.

Martin Taylor, some time ago, proposed an "alerting system," a
proposal that I drew back from, not seeing how it would operate.
Now perhaps I understand a little more of what he meant. If we
say that an alerting system is simply a control system without
its output connected, then we can imagine reference signals
defining preferred states of the environment, and error signals
that indicate a departure of the environment from that preferred
state, but which in fact result in no action. If something does
occur as a consequence of such error signals, we can only
conclude that the error signals themselves are being monitored by
some other system, which acts by changing the complement of
active control systems, perhaps bringing some of the "alerting"
systems into action by connecting their outputs as appropriate,
and disconnecting others. This is a possible mode of hierarchical
control that needs further clarification so we can try to model
it.

ยทยทยท

--------------------------------------------------------------
Allan Randall (930325) --

RE: perceived disturbances

Rick's objection to this term, and mine, is that it is too loose.
Do you mean that there is a perceptual signal that specifically
represents the amount of a change in a CEV, rather than the total
magnitude of the CEV (or its perceptual representtion)? If there
is a perceptual signal with a magnitude of 100 units, and an
independent variable in the environment changes so as to make the
perceptual signal become 110 units, a "perception of the
disturbance" would indicate 10 units, not 100 or 110.

Why can I not call variations in the CEV "disturbances" to a
fixed CEV?

You can, using an informal meaning of disturbance (the effect).
But if you're going to propose that these "variations" are
themselves perceptions, you have to propose a perceptual function
that specifically reports variations. If you have a control
system that works in terms of the total magnitude of the CEV, it
is not reporting the CEV in terms of changes, but of magnitude.
To get a perception of changes, you have to bring in a different
kind of input function, one sensitive to first derivatives or
that continually compares values of the CEV at time t with values
at time t-tau. That yields a perception of change -- but would be
useless for controlling magnitude.

What you can't do, in the spirit of modeling, is to speak of an
unexplained or arbitrary change in the CEV. If the CEV changes,
something must have changed it; otherwise it would not have
changed. This is precisely the same principle that Newton
expressed as his first law of motion. This is why I keep
insisting on the external independent variable and its physical
link to the CEV. A CEV doesn't just change. It changes as a
result of something acting on it. When you include an independent
environmental variable as one contributor to the change, you also
provide a handle by which an experimenter can apply influences to
the control system without breaking the control loop. In a model,
every change in every variable must be accounted for in some way,
either as a function of other dependent variables or as a
function of independent variables -- which themselves are
eventually accounted for as experimenter actions or as the
actions of higher control systems.

In modeling, you can't say "let variable b have the value of 10"
if variable b depends on the states of other variables. You have
to look for the independent variables and propose influences on
the system through manipulating those variables. Otherwise you're
simply violating the definition of the model. Variable b, if
dependent on other variables, is an unknown in the system
equation, for which you can solve if you know or specify the
states of the independent variables.

The state of a CEV depends on two variables: the output of the
control system, and a representative external independent
variable that I call the disturbing variable.

While I do not see why you are as opposed to this term as you
are, I have no problem with dropping it.

I would much rather you understood the opposition. I hope the
above explanation helps you understand.
---------------------

The point is that the disturbance d(t), if separated out from
o(t), is not a meaningful quantity to the ECS.

Whenever you see d(t) in one of Rick's equations, or D in one of
my diagrams, you should think of it as an environmental variable
outside the feedback loop, connected to the CEV as one end of the
rubber bands is connected to the knot. It does not EVER mean "an
arbitrary change in the CEV." d(t) could be varying between plus
and minus 100 units, while the CEV remains within 1 unit of its
reference level and is varying in a waveform that has no
resemblance to the waveform of d(t). All of this would be so much
easier to understand if you would just run one of our simple
tracking experiments and look carefully at the data!

d(t) is ALWAYS "separated out from o(t)." It's a physically
distinct variable. And d(t) and o(t) are physically distinct from
the controlled variable.

By drawing an arrow marked d(t) you are talking about something
the ECS has no direct access to.

Yes, this is correct. But d(t) is not the arrow; it is the
variable at the start of the arrow. The arrow merely indicates
the connection that gives d(t) an influence on the variable at
the head of the arrow. We would associate with the arrow,
perhaps, a constant of proportionality -- but not a variable. The
constant of proportionality written over the middle of the arrow,
times the value of the variable at the start of the arrow, is the
magnitude of the influence on the variable at the head of the
arrow.

Unfortunately, this convention holds in the environmental part of
a control-system diagram but not inside the control system.
Inside the control system, the boxes labeled "input function" and
so on contain the transformations, while the arrows indicate the
variables -- signals traveling from one place to another,
carrying the magnitudes of the outputs of the boxes. I have
thought many times of making the conventions uniform inside and
outside, but have never done so because in the environment, it
seems to me, the variables are associated with physical places
where we could measure them, while the arrows express the
invisible physical laws that connect the visible variables.
Inside the nervous system, the variables are associated with the
signals that go from one place to another, while the functions
are performed in specific physical locations (distributed or
not). It would be very nice to be able to express processes
inside and outside of the system in the same way. But maybe there
is a fundamental difference that the present convention
acknowledges.

The external observer who sees the "disturbance" as separate
from the output nonetheless needs to know about what the
control system is controlling for to define disturbance.
Disturbance is defined partially from an internal and partially
from an external point of view. This is fine, but it must be
recognized.

I agree, and it's good to have this pointed out explicitly. The
external observer here is not a naturalist or a behaviorist, but
a modeler. The variable affected by the disturbing variable and
by the output of the system is, in the eyes of the modeler, more
than just one variable caught between two others. It is the
visible entry-point to a control system, and the output is the
visible exit point. What goes on between entry and exit is
imagined, but carefully. Without that model of the control
system, there would be no reason to characterize one variable as
a disturbing variable and the other as an output. They would both
just be physical variables with effects on many other variables,
including the one between them.

I was thinking more of the disturbance being a result of past
outputs.

Do you mean in general? In general this isn't true, although it
might be true (the transient following complete removal of all
external sources of disturbance).

In general a disturbing variable is like the wind affecting the
path of a car. The disturbing variable, the wind, changes
completely independently of the path of the car and the steering
efforts of the driver.

The wind velocity (the disturbing variable) is converted by the
laws of aerodynamics (the arrow) into an influence on the path of
the car (at the head of the arrow).

You are suggesting, if I read you correctly, that we include
all past effects of the output into the disturbance. You are
considering the instantaneous output of the control net as
separate from the disturbance, but that is all.

No, this is not what Rick or I would mean. Is the reason becoming
clearer? By disturbance we do not mean the change in the
controlled variable itself, although there's many a slip in
trying to stick strictly to the proper meaning. We mean a
variable physically distinct from both the output and the
controlled variable, which acts through some environmental link
on the controlled variable at the same time that the output is
acting, through a different link, on the same variable.

Past effects of the output are still part of the closed negative
feedback loop. The disturbing variable is not in the negative
feedback loop.

I sure hope this is getting across. When you see exactly what we
mean here, I believe that all this confusion will melt away.

I'm not going to get into the probabilistic stuff. I'm having a
hard enough time sorting it out in private conversations with
Martin.
---------------------------------------------------------
Bruce Nevin (930325.1215) --

I don't mean to ignore your communiques. Despite my quibbles I
like what you're doing and believe that you're working your way
toward a real PCT understanding of linguistics -- individual and
social. But I've run out of brain cells -- there are too many
conversations going on, and I feel that you and I have no
argument over basic principles. I'm gradually working my way back
into the area where my competence lies: modeling. I'm trying to
drag others in the same direction, but basically I just want to
get back into it myself and do something real.
-----------------------------------------------------------
Best to all,

Bill P.