[From Bill Powers (930318.1015)]
Wolfgang Zocher (930318) --
(response to private post)
Sorry about that very nasty illness. I hope you will give a
higher priority to getting well than to writing programs! I'm
sure I convey the hopes of everyone else on CSGnet that you will
recover soon. Two weeks of pneumonia is no joke.
···
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Allan Randall (930317) --
So my version of the challenge would take Ashby's compensatory
and error-driven control systems and, assuming they were both
designed to control, make a prediction concerning which would
control better.
OK. For ideal components and linear channels, the prediction is
pretty clear. But I will be interested to see the analysis you
use for the error-driven system, in which E is partly a function
of itself (via R).
Once you have the analysis for the two cases done, it would be
useful to derive the real-world requirements on both systems for
achieving a certain degree of regulation in the presence of
noise. One channel common to both arrangements is that from R to
T. How much difference would it make to each system if the output
of R contained some specifiable amount of random variation?
Outside the scope of this challenge, there is a factor that Ashby
didn't take into account: the possibility of disturbances that
act directly on E, and are not detected by R. Under those
conditions, disturbance-driven regulation is impossible, while
error-driven regulation continues as before.
Meeting the "challenge" is less important than producing an
actual analysis that I might be able to use! Keep in mind that I
am only a humble engineer, and need to have everything spelled
out in babytalk.
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Hans Blom (930317) --
So sensory input is a dependent variable. I take this to mean
that sensory input has no degrees of freedom of its own; its is
dependent UPON some- thing, and that something is the reference
signal.
What we say about dependent and independent variables is always
in the context of the particular model we are proposing. In a
single elementary control system in the PCT model, the perceptual
signal is ALWAYS a one-dimensional scalar. If there is a
multidimensional external quantity being controlled, in our model
the way it currently stands more than one control system would be
needed to keep all its degrees of freedom under control. I think
we all recognize that this conception has some failings --
handling sideways interactions among control systems of the same
level would be very awkward, for example. But at our present
stage of experimental sophistication, this simple model seems to
handle everything we can understand with satisfactory precision.
So having reduced the problem to one dimension per control
system, we can ask what determines the state of a single input
variable for a single control system. By definition, the input
variable has no way of altering itself. As per Newton's laws, it
changes only when the sum of all effects on it is nonzero.
There are two determinants of an input variable: the sum of all
independent environmental physical effects acting directly on the
variable (of which the variable is a function), and the output of
the control system. As we are dealing only with one-dimensional
variables, this means that no matter how many independent
disturbances there are and by what paths they affect the input
variable, we can always express the result as a single equivalent
disturbance acting through a single equivalent path. This leaves
only two influences on the input variable: "the" disturbance, and
the control system's output. The net disturbing influence is
arbitrary and independent of the operation of the system. All the
variables in the loop, including the output quantity and the
input variable, can be solved for using the closed-loop equations
-- they are all dependent variables. As you note, the reference
signal is also an independent variable relative to the control
loop, and hence relative to the input variable.
Is this the same as saying that the reference signal controls
the perceptions?
Yes, given that the control system is capable of maintaining its
error signal very small. The action of the system will almost
completely cancel the effects of independent environmental
disturbances on the sensory input, and at the same time force the
sensory input to track the varying reference value established by
a varying reference signal.
Originally, the title "Behavior: the control of perception"
gave me the impression that all perceptions are controlled. Now
I understand that there are also uncontrolled perceptions. Is
it therefore "Behavior: the control of SOME perceptions"?
That wouldn't have made a very catchy title, but you're right.
Behavior controls only some perceptions, those that can be
systematically affected by output actions and for which the
organism has reference signals and control systems. The remainder
can be controlled in trivial ways (not looking at the moon keeps
the perception of the moon at zero), but for the most part simply
make up the world within which the things we care about happen.
Now, if some perceptions are controlled and some are not, are
there also intermediates like:
- some perceptions are sometimes controlled, but not at other
times;
- some perceptions are partially or approximately controlled;
- some perceptions are controlled in some degrees of freedom
(dimensions) but not in others?
In this model, an elementary control system does not decide
whether or not to control. It simply controls. If some variables
are controlled only part of the time, the explanation has to be
sought at a higher level in the hierarchical model. As part of a
higher-level control process, a higher-level system may change
which lower-level control systems it is using to control its own
(derived) perceptions. It must have some way, therefore, of
turning lower systems on and off. There are several ways, which
have different implications. But the main thing is that when a
control system is turned on, it controls ALL of the time. It
can't turn itself on or off: something else must do that. That's
just my basic design principle. If the external part of the loop
is lost, the control system will frantically crank up its output
trying to correct the error. It will continue to do this until a
higher-level system notices something amiss and makes the
required adjustments. Rick Marken has shown that when the sign of
the external feedback is reversed, the control system that had
been tracking runs away on an exponential curve -- for about half
a second. The curve closely matches that of the model when
feedback is reversed. Then (according to the model), a higher-
level system reverses the sign of the control system's error or
output connection and it regains control.
As to partial or approximate control, that is only a question of
how well the control system works. There is a complete spectrum
of control ranging from hardly any to very precise. If we make
the reasonable assumption that control systems evolved because it
was in the species' interest to determine for itself how certain
parts of the local environment behave, we can assume that the
less error is allowed by a control system, the greater the
advantage to the organism.
On the other hand, there are specific circumstances in which very
tight control could be a disadvantage -- a waste of energy, for
example, considering the benefit to be gained. You have mentioned
something like this. Once again, my basic design principle
applies. A control system does not decide for itself how well to
control (assuming there is any choice). If its loop gain is
lowered under certain circumstances, a higher-level system is
doing the adjustment of gain, as part of maintaining control of
higher-order perceptions.
A specific example of this appeared in my model of operant
conditioning three or four years ago. One level of control had a
reference signal set by a control system for body weight. The
reference signal specified the level of a perception of short-
term nutritional state that was immediately affected by the rate
at which food was ingested (body weight was a long-term function
of average nutritional input). This short-term state decayed
fairly rapidly with time. The action of the system was to vary
the frequency at which a bar was pressed, producing food input
through a schedule of reinforcement and thus maintaining the
perception of nutritional input level matching its given
reference signal from the weight-control system.
Another higher-level control system, acting at the same time,
compared a cost of bar-pressing proportional to the rate of
pressing with a benefit of nutritional input proportional to the
rate of ingesting food. As the cost rose above the benefit, the
output gain of the bar-pressing system was lowered to keep the
benefit at least as high as the cost. I'm sure you'll recognize
this as a primitive form of optimal control (a one-way control
system in this case).
This model did very well in fitting the bar-pressing behavior of
rats over a wide range of schedules of reinforcement and two
conditions of body-weight (forced by withholding food between
experiments in the real studies).
I was more or less forced into this model, because no matter how
I tried to make the bar-pressing control system vary its own gain
with nutritional input (still remaining an elementary control
system), I could not reproduce the double-valued function
relating the schedule of reinforcement (bar-presses per reward,
which ranged from 1 to 160) to the rate of bar-pressing. Only
when the cost-benefit control system was introduced was I able to
make the curve reverse at the right place. Then the model came
very close to all the data points from the real rats.
Is behavior FULLY in the service of the control of perceptions
or could there also be behavior that is not?
One has to wonder (a) why an organism would learn to produce
behavior that never had any feedback effects on that organism,
and (2) how any organized behavior could reliably be produced, in
a variable environment, without feedback control. My hunch is
that essentially all behaviors (that is, outputs) are learned in
order to control some perception -- that in organisms there is no
open-loop behavior of any significance.
It's possible that evolution might have created some spontaneous
emission of actions without any feedback effects on the organism
doing the acting, as a benefit to the species. But such open-loop
acts would have to be very simple and noncritical, because to
reproduce the effect of any act in a normal environment would be
almost impossible without feedback from the actual effect
created. This is not to say that a feedback control action
couldn't be inherited because of a side-effect it has on other
organisms, with evolutionary consequences. To reproduce that
side-effect in a variable environment, however, the organism
would have to control for the effect of motor acts, not the acts
themselves. There's just too much chaos and interference out
there to make any totally open-loop behavior feasible. When a
peacock spreads his tail, the actual spreading must be a control
process, and perhaps even the subsequent response of a mate is
also controlled for -- but I'm sure that the side-effect of
making more peacocks is NOT a controlled variable.
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Peter Cariani (930318) --
Hi, Peter, long time no hear.
I'm afraid I don't see how anyone could call Bohr's approach
"invoking magic", when what he was calling for was the primacy
of (verifiable) results of observations and calculations over
tacit images of the nature of an underlying "Reality".
I don't come down on either Bohr's side or Heisenberg's. Bohr's
view is extreme, and teeters on the edge of solipsism.
Heisenberg's is naive, attributing uncertainty to the wrong
entity. I think control theory gives us a third alternative,
which I'm surprised has not shown up in physics (maybe it has).
We can easily say that our perceptions of reality (read:
instrument readings and interpretations) are a formal system that
we made up ourselves, based only on what we can perceive, not on
any objective "reality." But we don't have to stop there as Bohr
did. We also can act, produce outputs (read: experimental
manipulations). The effects of our actions are related to the
perceptions we get back only in the most indirect way. But such
effects DO OCCUR, even though we can't perceive how our output is
affecting our input. Furthermore, our perceptions often change
when we have performed no act: there are agencies out there.
To me this is a proof of existence: there is a reality out there
and it contains active agents. Unfortunately, we have to guess at
its details -- propose models of what MIGHT be there that would
account for the effects our actions have on our perceptions and
predict new effects of new actions. This guessing game works
extraordinarily well when the demands on models are exacting
enough: namely, that prediction errors should be no worse than
measurement errors. It works so well that one can reasonably
suppose that the resulting models are not inconsistent with what
is really going on. This doesn't mean they're isomorphic to
reality; it means only that something true is captured in them.
An epistemology that is based on observation alone can't lead to
such a conclusion. When you include action in the picture, and
close the loop, something different emerges.
So much of contemporary mathematical physics (and the current
wave of pop-physics pulps), having adopted a platonic-realist
approach, no longer seriously attempts to connect theory with
observation. One of the great intellectual tragedies of the
late 20th century has been this infusion of platonic mysticism
(following Godel, the later Carnap, and Tarski) into
philosophy, the foundations of mathematics, physics,
linguistics, and the cognitive sciences. We are still dealing
with the wreckage.
Platonic mysticism! Bravo. But the other side is anti-platonic
scholasticism, the triumph of pure reason over experiment. The
antidote to both sides is to include action in the picture as
well as perception.
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Best to all,
Bill P.