[Martin Taylor 960816 18:40]
Hans Blom, 960729
Nobody seems to have responded to Hans's question, so here's an attempt.
Particularly obsidious is having been brought up in an environment
where it was forbidden to perceive certain things or to act in
certain ways. This results in severely limited models, either the
perceptual side (less perceptions available than possible) or the
motor side (less action patterns available than possible).
Have you met people who cannot
listen? Although they get feedback, they do not use it. Such people
have, earlier in their lives, learned "optimal" behavior which
perfectly suited their situation but that is now, in a "new"
environment, very probably far from optimal.
It is this second meaning
of optimality that is the concern in therapy: how can someone be
brought to relinquish outdated beliefs and habits, which are not
appropriate anymore in his new environment.
Simply said: it has to forget. But what invariably shows
up is a period of "crisis", very bad control behavior; the old model
is being relinquished but the new one is not well tuned yet.
Patients often experience this as being caught on a local maximum.
Every path leads downward, and that is painful and prevents people
from exploration. Yet they know deep down that, somewhere, there must
be a higher mountain where they truly belong. It is this intuitive
"faith" or "hope" that allows some people to endure the crisis, pass
through it, and reach their higher mountain top.
Can a PCT model explain this phenomenon?
I would have thought the answer to be "Yes, it falls out naturally from
the usual statements of HPCT and reorganization." There's no forcing, no
extra assumptions required. But it does require some appreciation of the
interactions in multidimensional spaces.
Where to begin? How about reorganization as a search in a high-dimensional
space of possible perceptual functions and output functions?
Reorganization has several different facets. It can involve a gradient-based
smooth alteration of parameter values in perceptual input functions, output
functions, or link connection weights; or it can involve discrete changes
in what is linked to what (or the sign of a link); or it can involve the
creation of totally new Elementary Control Units (ECUs). Gradient-based
alterations work only when a direction has been found that provides
improvement in the criterion parameter (based on error in intrinsic
variables). When an appropriate direction has been found, continuous
progress can be made, at least until the direction ceases to go downhill.
But before that, random directions must be tried, because there is no way
that the system can determine which directions might be improvements--there
are interactions, remember.
In a one-dimensional space, uphill and downhill are easy to distinguish,
and it if the criterion function is bumpy, there are lots of local minima.
In a two-space, a local minimum exists only if all directions go uphill.
For simplicity, let's ignore interactions and say that a local minimum
exists only if it is uphill in both directions on both axes. Now, think
about a randomly bumpy surface, and imagine that "we" have found a point
that is a minimum insofar as movements in x alone are concerned, and that
the derivative with respect to y is, at that point, zero. What is the
probability that we are at a local minimum? There are four possibilities,
two each for what happens when y increases and when y decreases. In either
direction the criterion might increase or decrease. If it increases in both
directions, we are at a local minimum. If it decreases in both directions,
we are at a saddle point. If it increases in one direction and decreases
in the other, we are at a point like the entrance to a mountain cwm. (And
for those who don't know, the spelling is indeed "cwm"; it's Welsh in
origin, I think).
Each of these four possibilities is equally likely, in the abstract. Only
one represents a local minimum. In the other three, there is a direction
or range of directions toward lower values of the criterion.
Now extend this to movement in a three-space, a four-space, an N-dimensional
space. As N increases, it is ever less likely that a point at which all the
local partial derivatives vanish is a local minimum unless it is a global
minimum. But on the other hand, it becomes ever more likely that a random
direction leads to an increasing value of the criterion. In other words, it
becomes more certain that there exist ways downhill, and more difficult to
find those ways by random moves--at least starting from a point that has
been found by moving persistently downslope.
Back to PCT: so long as there is a reference level for a perception that
is being controlled, the person knows "deep down that, somewhere, there must
be a higher mountain where they truly belong." (Higher mountain = lower
error). Different actions keep getting tried, but most of them just
make matters worse. If the person happens to find the smooth way out
that probably exists, that is lucky, and the "crisis" may be averted.
But what is more likely to happen is that reorganization brings the
person into a worse position from which a different randomly chosen
direction may more easily bring the downslope move to a position better
than previously. This is the "crisis."
Why might things get worse rather than better? Why are they bad in the
first place? The answers to both questions is "conflict." The way the
various perceptual and output functions are arranged may simply not
permit simultaneous good control of all the various perceptions needed
to keep the intrinsic variables where they should be. The "downslope
moves" referred to above mean reductions in internal conflicts. But to
remove one conflict may be to enhance another, and that's why control
overall may get worse before it gets better.
I'm not sure whether this answers the question in the spirit in which it
was asked. It can be approached in different ways, but the basic principle
is that a hierarchy that has gone through substantial reorganization (i.e.
has partly matured) will be fairly rigidly structured, and it will be hard
to find ways of improving control without going through a period in which
control gets substantially worse. And that period will never occur unless
the patient does have faith (i.e. a persisting reference value for a high-
level perception being controlled) that things can get better.