[From Bill Powers (2004.01.08.1127 MST)]
Bruce Gregory (2004.01.08.1153)–
I still do not understand the
working of the hierarchy well enough to
explain how the goals we are actively pursuing change from minute
to
minute while the upper levels of the hierarchy remain relatively
unchanging.
I’m not sure how “unchanging” the higher goals are. The kinds
of goals we pursue are determined by the kinds of things our various
control systems perceive, and so probably remain the same over relatively
long periods of time. But the level at which the perceptions are
maintained can easily be in continuous flux. When you say
“change”, which kind of change are you referring to? Change of
kind or change of amount? O)f course the one can merge into the other:
controlling for 100 units of A and 1 unit of B can change into
controlling for 1 unit of A and 100 units of B, a quantitative
change. But this could look like first controlling for a lot of A,
and then controlling for a lot of B, as if one system had been switched
of the the other on.
In any of the demonstrations of multi-level control, the kinds of
variables being controlled remain the same, but the reference signals for
each variable are continuously adjusted in magnitude. Even the
highest-level reference signals can be altered in magnitude at any time
by the user of the program. This doesn’t mean bringing different
variables under control, but just changing the target amount of each
controlled variable.
You can see, however, that as the magnitudes of the reference signals
change, the effect can resemble first controlling one variable, then
another, then another. This is particularly true for variables that can’t
go negative, like the truth of a logical proposition, or the repetition
rate of a drumbeat. Setting a zero reference level for such systems is
like turning them off, even though they are still present and
active.
To get the full picture you simply have to examine some of the demos. We
usually talk about just one simple control system at a time, so it’s easy
to get the idea that only one at a time is active. But in Rick’s
spreadsheet demo you can see many control systems at several levels all
acting simultaneously, not taking turns but acting in parallel. I believe
there are 18 altogether. The reference signal for one system is not just
the output of a single higher-level system, but the sum of the outputs
from all the system at the next higher level. So when disturbances
come and go at the lowest level, and reference signals change magnitudes
at the highest level, you see adjustments at all the levels. Sometimes
one system is receiving a high reference signal, and in the next moment a
low or even zero reference signal.
When you say "the goals we are actively pursuing change from minute
to
minute," I’m sure you don’t mean that they change at random. While
there can be shifts of major themes from time to time, most of these
changes are directed by higher-level systems that are engaged in some
process that remains relatively stable for longer periods of time. You
may start picking up newspapers scattered around the living room, then
switch to opening and shutting drawers in a bedroom, then to crawling
around on the floor of the bathroom, which looks like a random series of
different activities, but at a higher level we can see all these
activities as part of the same process: looking for a contact lens, a
search program. Of course that program can be interrupted by a still
higher system: you may decide it’s better to go to your job interview on
time than to find your contact and be late, which decision satisfies a
larger or more important goal, perhaps some sort of general
principle.
The process seems to involve
errors; can I assume that the system with
the greatest error determines what actions will be taken? In other
words, do all goals have the same priority?
Normally it is possible to satisfy a rather large number of different
goals at the same time with a single set of actions. My demonstration of
500 independent control systems (each controlling a perception by acting
on 500 environmental variables that contribute to each perception) is
probably overkill, but it shows how this can work in an extreme case. The
error signals in this collection of control systems are not prioritized,
nor are they put into sequence. They are all corrected simultaneously.
The actions of each control system affect the perceptions of all the
other control systems. Changing any one environmental variable disturbs
the perceptions of all 500 control systems. Yet simultaneous independent
control is achieved.
If you were watching the control actions of these systems, you would see
all the interactions, and as disturbances came and went you would see
first one subset of systems showing the greatest amount of action and
then another. This could easily give the impression of some overall
controlling system that chooses which errors to correct before other
errors. But in fact, all the systems are trying equally hard to correct
their errors all of the time.
I know that this answer is losing its usefulness as it gets longer, but
it’s really necessary to get the feel for how a big complex multileveled
system works before any answer to your question can make sense. It’s hard
even to ask the right questions about such a system: every question has
behind it some assumptions about a model and how it would behave, and if
the assumptions don’t fit the actuality, the answer to the question may
not even be intelligible.
If the above helps, good. Here is one last thing to consider. You’ll
remember we were talking a week or so ago about the size of error
signals, and I pointed out that there can be very large changes in the
output of a control system as a result of very small changes in the
difference between perception and reference. A higher-level system can
seem to be keeping its perceptions almost unchanged, while the reference
signals for the subordinate systems are varying all over the place –
seemingly independently of the higher system, But if there is high gain
in the output function of the higher system, only a very small change in
the perceptual signal will be enough to cause very large changes in the
outputs that set reference levels for lower systems. The large variations
at the lower level faithfully reflect small changes in the perceptual or
reference signals in the higher level, because of amplification taking
place in the output function of the higher system.
When you say that “the upper levels of the hierarchy remain
relatively unchanging,” you may be overlooking the amplification in
the output function. True enough, the perceptual signal may stay close in
value to the reference signal or the reference signal could remain almost
constant, but the small changes that remain could entirely account for
the large changes in reference conditions at the lower level. In fact,
those large changes at the lower levels may be exactly what is required
to maintain the higher-level perception as close as it is to the
reference signal, in spite of the disturbances that are
present.
Best,
Bill P.