[From Bill Powers (960425.0100 MDT)]
Hans Blom, 960425 --
When you trivial- ize the importance of the influence of external
disturbances on the values of the internal reference levels, you
undermine the whole concept of hierarchical control. Let me show
you why.
...
Assume for a moment that goals are not modulated by disturbances
but that all goals at all levels of the hierarchy are fully
determined from above, by yet higher levels of the hierarchy. That
would effectively freeze the whole hierarchy into rigidity with
respect to the outside world, and that would make the control
hierarchy superfluous (except maybe as a set of connections); the
situation would be like having a lot of one-dimensional control
systems (at the lowest hierarchical level) WITHOUT ANY MUTUAL
INTERACTION AT ALL.
I think you have a mental picture in which all the levels of control
deal with the same type of perception (I've had this argument with
Martin Taylor, too). If you will scan over my proposals for levels of
perception, inadequate as they may be, you will see that each new level
deals with a new KIND of perception. The perceptions themselves may be
static scalar quantities, but the environmental situation they represent
may be highly dynamic. What you say is true up to level 3, but not above
that level.
For example (and not particularly trying to stick with the levels as
proposed in B:CP), consider the simple behavior of beating a drum in a
steady rhythm. What we perceive as one steady rhythm is actually derived
from a periodically changing set of lower-order perceptions, produced by
repetitive actions. We perceive a simple variable called "tempo," which
can become greater (faster) or less (slower): a scalar variable. If
there were a fixed reference level for tempo, the result would not be a
frozen control hierarchy, but a hierarchy that is producing periodic
variations in its actions, those required to produce the steady string
of drumbeats. Of course the output function of this control system has
to be a variable-frequency oscillator which varies the reference signals
for such things as arm or hand position or velocity. The conversion from
tempo error to output frequency might involve an integrator somewhere in
the loop (it would probably have to), but this would just make the
oscillator frequency proportional to the integral of the error. The
actual output signal would not be the integral, but a frequency of
oscillation. And of course the perceptual input function would be a
frequency-to-amplitude converter.
Now consider the relationship level. A control system at this level
might perceive the signal representing tempo, and also a movie of Our
Hero creeping up on an enemy sentry. The purpose of this somewhat far-
fetched control system would be to maintain a constant relationship
between the tempo of the drumbeat and the degree of tension perceived in
the situation on the screen (our subject is involved in making the
musical sound-track for a movie). This relationship would be expressed
quantitatively as (perceived drumming tempo) = k*(perceived tension).
What is perceived, since this is a relationship perception, is k, the
ratio of tempo to tension. When k is too small relative to the reference
level, the error results in raising the drumbeat tempo reference level,
and so forth. The goal is to maintain the right relationship between
drum tempo and perceived tension -- the value of k.
So now maintaining a constant reference level for the relationship k
results not only in the production of a continuing repetitive series of
actions, but a specific rate of change of the reference level for the
frequency of the repetitive actions. The control hierarchy is doubly
"unfrozen."
Let's abandon this unduly strained example. I'll mention it a bit later
because it actually includes a disturbance that is NOT directly opposed
by lower-level systems (this hierarchy is not "complete").
Skipping up a couple of levels, suppose that there is a sequence control
system with a fixed reference level that specifies "sequence A."
"Sequence A" is perceived to be constant as long as one is progressing
through, for example, the steps involved in following a remembered
recipe for baking a cake. If the reference sequence remains the same,
and the control system operates successfully, one will perceive that
Sequence A is occurring all the way from getting the ingredients
together to taking the cake out of the oven an hour later. If asked what
is going on at any point during this sequence, the actor would give the
same answer: I'm baking a cake.
Clearly, this control system with a fixed reference signal creates a
whole series of actions amd varying perceptions of many different kinds,
the actions and perceptual variations required to maintain the
_constant_ perception called "I'm baking a cake."
Now consider the relationship-control system again. There is actually
one component of the relationship that is uncontrolled by anything in
the hierarchy: the rate at which the Hero creeps up on the sentry in the
movie. The hierarchy is now not complete. This perception is derived
from intensities, sensations, configurations, transitions, and events
just as the perception of drum tempo is, but it is not affected by the
actor; it is a disturbance of the relationship. To counteract this
disturbance and maintain a constant k, the actor must _vary_ the
reference level for drumbeat tempo. So the changing scenes on the movie
screen actually result in changing the tempo that is wanted (Peter
Cariani would say that the desired tempo is contingent on the events in
the movie). This is an example of a disturbance affecting a want, the
tempo that is wanted. Notice, however, that the disturbance does not
directly cause the want to change. It only tends to cause the perception
of relationship to change, and it is the relationship-controlling system
that actually varies the wanted tempo as a way of opposing the
disturbance.
Also, the disturbance does not control the want, because if the higher
system that sets the reference level for k were to change that reference
level, the reference-tempo would immediately change, but the events on
the movie screen would not change in such a way as to restore the
reference-tempo to its former value. The actual tempo of drumming would
change its relationship to the action on the screen, independently of
what is happening on the screen. The environment may _influence_ the
want, but it does not control it because there is an equal and
independent influence from the higher-order system.
The effect of independent disturbances is always an _influence_ on a
want, when there is a way for a disturbance to enter at a given level
without being cancelled by lower-order systems. But this is only
influence, not determination or control. A higher system is always able
to cancel the effects of the disturbance on its own perception by
altering the reference level of the lower-level system. To drop down to
a lower-order kind of control, if a weight causes an arm to sag, a
higher system concerned with accuracy of, say, pointing, can raise the
reference signal for the position-control system enough to bring the
actual pointing relationship back to its reference level. There is still
an error in the arm-position control system, but the actual pointing
error is brought to zero by raising the reference signal by the amount
of the error.
The effect of a disturbance on a want is due entirely to the presence of
an active control system at a higher level. If the higher system didn't
care about the disturbance, the want would not change.
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But then either the world must not contain high frequency
disturbances (but it seems it does) or another mechanism is
required, some mechanism which prevents high frequency signals from
penetrating into the hierarchy. A low pass (leaky integrator)
filter, obviously, or something like it. But where could it be
found? Not in the input function, because the combined 180 degrees
phase shift would make the controller into an oscillator. Any
suggestions?
Yes -- it is in the perceptual function, if not in the output function.
There is nothing magical or necessary about making the output function
an integrator. A closed loop can be stabilized if there is a single
integration anywhere in the loop. If it is in the input function, the
output function can be made proportional. If it's in the environment,
the perceptual function and the output function can both be
proportional.
Higher-level systems are generally slower than lower-level systems,
perceptually or on the output side. If one level is detecting the tempo
of a repetitive series of changes in perception, it is perceptually
integrating over at least one cycle. So high-frequency variations in the
events being perceived in terms of tempo simply don't reach the higher
system's perceptions (or they are at least greatly attenuated). If you
try to track a target that is jerking around far faster than you can
move your hand, you simply start tracking a low-pass-filtered version of
the target-cursor relationship. Objectively, the tracking is full of
high-frequency errors, but the tracking system doesn't experience
errors, because its perceptions can vary only slowly. Pilots flying in
turbulent air eventually learn to perceive the moving-average attitude
of the airplane and control that; the high-frequency wobbles, being
uncontrollable, are simply ignored. I'm sure Bruce Gregory or any other
pilot will back me up on that.
Or, shifting to psychology, is it indeed true that sudden changes
in the world that we live in cause lots of changes in what we want,
whereas very slow changes don't?
No, it's the other way around. The higher systems perceive only the
slower effects of disturbances, and alter the lower-level wants to
oppose the slow effects. The rapid effects aren't perceived and aren't
opposed. Don't confuse this with rate feedback, which can exaggerate the
perceptual changes due to rapid input changes. The effect of a rate
component of perception is to help damp the control system AT THE SAME
LEVEL. The result is to advance the phase of the output opposing the
disturbance, and the net effect is to _reduce_ the rate at which the
controlled variable is allowed to change (an overdamped system is very
sluggish).
Also, don't be misled by the fact that some perceptions (like smell or
pressure) adapt very strongly. Higher-level perceptions, like your
perception of your wife, don't adapt away. You can continue to recognize
your wife indefinitely. When you're driving, you continue to perceive
the position of the car in its lane with about the same accuracy all
during the trip. Most perceptions don't adapt noticeably.
The idea that we perceive mainly changes is a myth. The world of
perception is always there; it doesn't occur only in "events." All you
have to do is look around you to see that this is true. What color is
the wall? And what color is it now? Did it have to change color before
you could see what color it is? Just because there are _some_
perceptions of change that stand out is no reason to say that all
perception is of change. Just because microsaccades are necessary to
maintain visual perception is no reason to say that the resulting
perceptions adapt away. The microsaccads see to it that they don't. In
my proposed hierarchy, the transition level is concerned with changes.
But there are 10 other levels.
So, Bill, what seemed to be an insignificant remark to you
initially -- internal goals are modulated by the outside world --
may be a lot more significant, both in terms of understanding of
the hierarchy and in terms of additional questions to be answered,
than you thought.
"Modulated?" You said "determined" or "controlled" before today. There's
a big difference between saying that disturbances in an incomplete
hierarchy have a non-exclusive _influence_ on wants, and saying they
determine or control wants. And keep in mind that even this "modulation"
occurs only because a higher-level system varies the want as a means of
counteracting the disturbance. There is no direct connection between a
disturbance and the ensuing changes in a lower-level want. Those changes
are directly caused by the higher-level system, not by the disturbance.
If the higher-level system reorganizes, or its reference signal changes,
the same disturbance will have a different effect on the same want. The
effect could even reverse. The effect of the disturbance on wants
depends entirely on the organization of higher-level systems. There is
no direct or necessary effect.
We haven't even considered that in HPCT, the reference signal for a
lower-level system is set not by a single higher-level system, but by a
number of higher-level systems pursuing different goals. You have to
consider the effects of a disturbance on many wants, not just one at a
time. That can wait for another day.
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Best,
Bill P.