[From Bill Powers (980331.1838 MST)]
Bruce Gregory (980331.1617 EST)--
I can see that reference levels are changing. What I cannot see is that they
are being adjusted by higher-level systems. In fact, reference levels are
adjusted so rapidly that high-levels seem unlikely candidates. But I clearly
don't understand HPCT.
A temporary setback -- don't worry.
Let's consider just one low-level control system being used by a higher
system. I ask you to reach out and put your finger on the 't' key. To do
this, you have to use a control system that can move your hand (already
configured to point) to any position anywhere in the reachable local space.
Actually there must be three reference signals involved, one for each
degree of freedom. Consider just the "vertical" dimension (and assume it
_is_ one of the dimensions). When you vary the reference signal for
vertical position, your finger moves up and down. If you vary it at the
normal rate (not as fast as possible), your perception of your finger stays
essentially AT the reference level; the error is never large enough to
matter. While the reference signal is increasing, your (perceived) finger
is rising; while it's decreasing your finger is falling. When the reference
signal becomes constant, your finger becomes motionless.
So how do you raise and lower your finger in order, say, to point at the
't'? By increasing and decreasing the reference signal for perceived
vertical position -- not, as you might have guessed, by changing your
muscle tensions. The muscle tensions are varied by the system that makes
the perceived position match the reference position; the higher system
doesn't know anything about muscle tensions. The higher system that does
the pointing perceives where the finger is and where the thing to be
pointed at is. It sees the relationship, the distance, between them. It is,
we assume, given a reference signal that means "distance of zero". If there
is an error, the error becomes, via the output function, a change in the
reference level for finger position. In three dimensions, there would be
three error signals and three reference signals. As the reference signals
change, the reference position for the finger changes and the finger moves
to keep the perceived position matching the reference position. The
higher-level error signal finally falls to zero when the finger is on the
target, and the position reference signals stop changing (the higher system
must use an integral output function to work this way).
Once the finger is on the 't', only a very small error signal is required
to make the higher system's output begin changing rapidly. If a disturbance
occurs, we would have to look closely to see that the higher system has any
error in it at all; the main effect we would see is that the output of that
system is changing at some rate. That, of course, means that the reference
signal for the position control system is changing at that same rate, and
that the finger is moving at the corresponding speed back toward the 't'.
In fact, the normal state of the whole hierarchy is for all errors at all
levels to remain close to zero, even when the system is acting very
energetically. Only if we could measure very closely would we see that the
perceptions in each system at each level didn't exactly match the reference
signals at all times. Due to the amplification in the output functions, a
small error signal is enough to drive the output through its whole possible
range, thus changing the reference signals at lower levels through their
whole possible range.
The only exceptions to this small-error condition occur when a system first
becomes active, or when a large fast disturbance occurs. Otherwise, the
entire hierarchy is maintaining a state of small error in all systems, and
it is doing so through higher systems varying the reference signals
entering lower systems.
Look at Fig. 6.1 in B:CP, p. 71. There are three levels of control shown.
The output of the third level sets the reference signal for the second
level; the output of the second level sets the reference signal for the
first level. Only the first level operates muscles with its output signals.
Did you look at this diagram and think "Oh, that's too complicated," and