[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brought to relinquish outdated beliefs and habits, which are not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.

Martin