CTdiagram; causes

[From Bill Powers (930921.1230 MDT)]

Hans Blom (930921) --

A standard quick 'n dirty analysis of what a control system
controls for is obtained by setting both inputs to the
comparator (in my diagram the first part of the COA block)
equal to each other. This is similar to the well-known analysis
technique in electronics of assuming an ideal op-amp.

One of the inputs to the comparator is the perceptual signal. The
perceptual signal is some function of variables outside the
control system. Don't you have to know the form of that function
before you can say what the control system is controlling? For
example, if the input function is an integrator with an input x
and an output p, when you set p = r you're saying that the system
controls the first derivative of x (from the standpoint of an
external observer who can see the input x but not p). You
couldn't say that just by looking at the perceptual signal.

Note that in my diagram there is a split between target and r,
because you might want, for instance, to position the cursor one
(invisible) inch to the left of a presented (visible) line on
the screen.

How does the reference signal get added to the target position
before the target position has been perceived?

Note also that this "true" reference t is mathematically
equivalent to minus the "true" perception c, which is itself a
combination of two handle positions and a noise source. This
implies that an offset in c is equivalent to the same offset --
but with a negative sign -- in the reference.

I don't follow this. Why is 't', the target position, a reference
signal at all? Why isn't it just another perception? I find your
analysis very confusing, with things added together any old place
where it's convenient. It would be much plainer if you would make
the perceptual function explicit. Let's get rid of the second
handle to make the diagram simpler:

                        >> >
                 --- || -------- |r
      Handle -->| | || | | ---- |
      Dist ---->|(+)|--c -->| input | | | | O
                 --- || | |--- p --->|COMP|-e->| ....
                        >> >function> > > > A
                  t ------->| | ---- |
                        >> > (-) |
                        >> --------
                        >>

This represents the physical situation more closely -- each
element in this diagram can be put into correspondence with a
physical element in the behaving system or its environment. The
handle position and disturbances are added (in the environment)
to produce the visual cursor position on the screen. The visual
target position on the screen is caused to vary by some
generator, not shown. The target and cursor positions on the
screen are both inputs to the visual perceptual system, which
produces a perceptual signal representing the difference between
target and cursor positions. This perception is compared with a
reference signal (inside the organism) indicating the desired
difference in positions. The error signal goes into the output
function (with or without adaptation) to affect handle position
(connection not shown).

The vertical double line is the input boundary of the control
system. In organisms, reference signals originate to the right of
this boundary (and inside the output boundary, not shown). To the
left of the input boundary we have the environmental stuff,
outside the organism, that determines how c and t will behave,
given the handle position.

Mathematically, you can jumble up this diagram any way you please
and come out with the same equations. But you don't represent the
physical situation correctly if you put the reference signal in
the environment, adding to the target position before the
information gets into the control system. Why not add (or
subtract) the reference signal to the cursor position or the
handle position or the disturbance? The math would be the same.
There has to be some rationale for laying out the diagram other
than just to get the right operations shown. It makes a
difference when you try to match the diagram to the real system.

···

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

Please specify "essentially acausal". Is this a subjective
"acausal", something that exists only in the eyes of the
beholder?

Do we agree that the algebraic representation of a control system
(ignoring transients) is acausal? The simultaneous solution of
the algebraic (steady-state) equations doesn't make reference to
causation, as the entire system is in equilibrium at all times.
In the dynamic representation, transients and time-delays appear,
but in a stable system they disappear quickly after a transient
disturbance, leaving the system in the same state that the
algebra shows. It's in that sense that I say the system is
"essentially", meaning for all practical purposes, acausal.

In some applications of control theory to behavior, an "acausal"
system is defined as one in which an internal generator produces
behavior rather than the behavior depending on external events.

But really, who cares? Cause and effect are very old-fashioned
terms, like "humour" and "principle", that used to occupy
philosophers before the days of systems analysis. If you can
define the system and solve the equations, what does it matter if
you put the label "cause" into the diagram somewhere? There's a
network of variables which all change at the same time, and with
the solution of the system equations we can plot their behavior
against time. We can see how all the variables are changing and
how they are related to each other at every moment. What more is
needed?

I think that your "acausal" means something like "(often) too
complex for analysis".

No, that's not what I meant. Basically, I mean that you can't
pick out any variable as "the cause" of behavior, because there
isn't any such variable. The whole system is interacting
continuously with its environment, and "causation" is simply not
the right word for what is happening.

These considerations make that I usually can live with an S-R
characterization of a system, especially in higher level
systems that have a very long delay time, which is either
internal (mentation is a slow process) or in the outside world
(the perceptual results of some actions -- such as the pursuit
of happiness -- do not rapidly become available).

I think you're forgetting about environmental disturbances. A
system can't just "emit" a reliable consequence: in the real
world, actions have to vary from one instance to another of doing
the same thing, so the "R" part of S-R simply doesn't work. Can
you give an example of an S-R situation in which that formulation
does work in a real environment?
-----------------------------------------------------------------
Best,

Bill P.