[Martin Taylor 971224 2215]
Tim Carey (972412.0800)
[Martin Taylor 971221 16:00]
Hi Martin,
Thanks for your post ... I'm still trying to understand the concepts you
talk about. I must admit that I've been so concerned with learning the
basics of PCT (and I'm still not sure if I have ... this is such a slippery
thing) that often I have skipped the more technical conversations.
Many of your questions do leave that impression. But if you want to learn
PCT, you _have to_ learn about control. One of the best ways to do that
is to try out Bill Powers' suite of tutorial demonstrations (if you have
a PC-compatible). The demos lead by easy stages through learning what
control is. In deference to the idea that you will attempt Bill's
demos, I will answer only a few of the more basic questions you ask. If
you still have more questions after having gone through Bill's suite, I'll
try answering them then. Go to http://animas.frontier.net/~powers_w/
or ftp://burkep.libarts.wsu.edu/csg/ if you can't do ftp from your
browser. Take the sets of files in "demo1" and "demo2" in "billdemos".
The other demos are for later, after you understand control a bit
better.
What I tried to say was that if you have even a fairly small, simple
network with both positive and negative feedback possibilities
What do you mean by a network?
A network is a number of entities that have some kind of connection
between them. If you prefer mathematical terminalogy instead, it's
a "graph." One kind of graph or network is a road map, in which the
entities are cities and the connections are the roads. In a road map,
the important properties might be the labels for the cities and the
driving time between them--or something else. In my experiment, the
entities were simple sum-and-squash nodes and the connections were
the links between them. The important properties (the "couplings")
were the weights that determined how much of the output of one node
appeared at the input to another. Like the road map, in which the
coupling between two cities might be the inverse of the driving time
between them (closer cities are more tightly coupled).
Is this a group of individual systems?
Yes, including the degree to which each affects another.
Are
they within one person or do you mean control systems in different people?
Yes. Either.
Are there levels in this network as in the HPCT model?
No. And it's not a variant of the HPCT model. I have been using it to
suggest what may happen when several organisms, each a hierarchic
perceptual control system, interact. I have also been using it to
suggest what may happen when several elementary control units within
one hierarchic control system interact. The first is "social psychology,"
the second is an aspect of individual psychology.
What do you mean by
positive feedback possibilities ... I know you explain what positive
feedback _is_ a little later, but I thought the functional unit of a
control system was a negative feedback loop.
It is. But when two control systems interact, the interaction may well
bring a postive feedback loop into being. That's what happens, for instance,
in a direct conflict. If the two control systems have output functions that
are integrating amplifiers, the output of each just keeps growing without
limit, as each output is a disturbance to the other's CEV, and each
requires that the other increase its output if the error is not to
increase.
the entire dynamics followed by the network
What do you mean by this statement? How does a network "follow" dynamics?
What are the dynamics that the network follows?
I find this a hard question to answer, without the necessary foundation.
But I'll try. Quick answer: the dynamics is the way something changes
over time when left to itself. Less quick answer: Think of a child's
swing, hanging from a tree branch. The swing has two dynamic possibilities.
In one, it moves back and forth under the branch; in the other, it swings
over the top and round and round without changing direction. Which
dynamic it follows depends on the energy in its motion when it passes
the bottom of its arc. Now imagine that there's another similar swing
humg from the same branch. These swings are _coupled_. Any motion of one
swing moves the branch and through the branch moves the other swing.
If the first swing is moving back and forth, and the other is initially
stationary, the second swing will start moving back and forth in
synchrony with the first. The _system_ can follow a dynamic in which the
two swings are moving synchoronously (remember, these are _similar_
swings--it won't work if they are much different).
The network follows much more complex dynamics. And under some hardware
conditions (i.e. particular values for the gains and coupling weights
in the network) it can follow a variety of different dynamics, even
of different classes, switching from one to another after slight
disturbances.
Technically, there are three classes of dynamic. The simplest is called
a "fixed point." In a fixed point dynamic, if the system is left to
itself, it comes to rest in some fixed state eventually (as will
the swing because of the air friction I neglected in my description).
The second is called an "oscillator dynamic." The system never comes
to rest, but repeats a series of states over and over again, if it is
left to itself. Often some point in the system is used as an output,
to provide a useful waveform. You can buy boxes that produce sinusoids,
square waves, triangle waves, and the like. Inside the box there is
an oscillator. The third class of dynamic is "chaotic." In a chaotic
dynamic, the system never exactly repeats a state it has been in before,
although most chaotic systems almost repeat themselves. so that they
can look for a long time as if they are oscillators, if you don't look
closely and accurately. One characteristic of chaotic dynamics is that
if you wait long enough, the most infinitesimal difference in initial
conditions will show up eventually as the largest possible difference
in conditions.
Colloquially, small changes in the environment can cause large changes
in the behaviour of the network.
Assuming the changes in the environment cause anything at all, I would
presume that the changes would be on a continuum from "no change" to "lots
of change"?
No. That's the important point about all this. What you say is often true,
but there are important exceptions, sometimes called "bifurcation points".
Think of the swing, but imagine that instead of a rope it has a rigid
suspension rod. Now push the swing a little. It moves back and forth.
Push it a little harder. It moves back and forth over a slightly wider
arc. Push it quite a bit harder. It swings up to nearly vertical, and
back again to nearly vertical on the other side, but it still swings
back and forth. Now push it ever so slightly more than that. This time,
it doesn't come back, but swings right over the top and round and round
for ever (in the absence of friction). That's a bifurcation point, and
the real world in which control systems operate is full of them.
We aren't talking specifically about control systems here.
Actually Martin, control systems are all I'm interested in.
Notice I said "specifically." Control systems are included, but the
discussion is more general.
When I've got a
good enough handle on how they operate I might be interested in considering
other things but if I understand the model of PCT at all, the organisation
of a control system explains the behaviour of _all living things_ .... this
is enough for me to deal with at the moment.
But it is wrong. You said "the organisation of a control system..." But
PCT deals with the organization of a hierarchy of interacting control
systems. The organisation of _a_ control system is simple: one perceptual
input function, one comparator with a reference input, one output to the
environment. If the system is actually to _control_, that output must be
hitched to the environment in some way that allows it to affect the
perceptual input function in such a way that the error is reduced (negative
feedback). If the output is hitched up oppositely, the system will have
positive feedback and won't control. If it is hitched up too strongly,
the system will oscillate, and won't control. And that's only with one
control system. When you have two, there are other problems, and when
you have a whole hierarchy, things get _very_ interesting. That's the
area on which I'm trying to get a handle.
But the implications are valid for
networks in which the elements are control systems that interact because
one's actions disturb another's perceptions, "causing" the other to
resist those disturbances by actions that might disturb the original
control system's perceptions.
Are we speaking about control systems within one person or between people?
Yes.
Aren't one's actions caused _jointly_ by environmental disturbances and the
reference of the control system under consideration? So is it fair to say
that a disturbance is always defined (at least in part) by the reference of
the control system being disturbed?
That's a misreading of the idea of PCT. The word "disturbance" has caused
problems in the past, and may do so again in future. A control loop has
two places where input comes from outside. One is the reference signal
input to the comparator, the other is the disturbance signal influence
on the Complex Environmental Variable defined by the perceptual input
function. The source of the disturbance signal is independent of anything
in the control loop, and is unknowable to anything in the control loop.
Sometimes the word "disturbance" has been taken to mean the disturbance
signal "wire", sometimes the disturbance signal value, and sometimes the
disturbance signal source. Best to use "disturbance signal value," if
I understand your question properly, and the answer is "NO, the reference
signal is irrelevant to the disturbance signal value."
I used the analogy of the feedback squeal you get when a loudspeaker is
too close to the microphone that feeds it. It doesn't matter what is said
into the microphone--the same squeal comes out of the loudspeaker. And it
doesn't matter what frequency the squeal is--the solution is to reduce
the
coupling between microphone and speaker. I propose that the situation is
analogous.
Would you describe the feedback squeal as output? If so it sounds like you
are manipulating what goes in, to get the output that you want (reduced
squeal).
No. The point is that manipulating the input has almost no effect on the
squeal. It is determined by the properties of the loop.
If my speculations are anywhere near correct, Leo's input does matter,
but only insofar as some inputs allow him to alter the feedback dynamics,
and may allow him to regain control. But then, unless there is a hardware
alteration, some other input could equally easily put him back into the
locked-up condition in which control is impossible. Under those
conditions,
it's probably better to fix the hardware than simply to discover which
inputs can kick him out of the lock-up.
I have a lot of questions about this paragraph.
Yes, and I don't think I can answer any of them in a way that will make
much sense to you unless you understand all the foregoing. If you do
understand the foregoing, I think you will not want to ask these
questions. If you understand, and still want to ask them, ask again.
What's an amplifier?
You really do have to know that sort of thing if you are going to try
to understand PCT. An amplifier is something that has an input and an
output, for which the output is larget than the input, but related to
it. A simple amplifier has an output o =, G*i where i is the input. The
factor G is called the gain of the amplifier. There are other types.
The input sinusoid isn't even needed to keep the
oscillation going. The tiniest noise at the input can start the
oscillation
going, and it keeps itself going after that.
Again Martin, in this example it sounds like getting the right output is
the focus.
There's no "right" or "wrong" output. I merely describe what happens
with certain connections. You surely wouldn't want your control systems
connected so that they become an oscillator, would you:-) If you connect
them in some ways, they would, and then they would presumably be
providing the "wrong" output--at least by somebody's criterion.
The experiments were done with simple amplifying nodes. The analogy with
control systems is that a control system's actions disturb other control
systems, and those disturbances "cause" countering actions in the other
control systems.
As I said earlier, to speak of actions being "caused" as well as
considering the disturbances to the system don't you also need to consider
the reference of the system?
Yes, but in this case all you need to assume is that there exists some
reference, which is the case if a control system is actually controlling.
If there is a reference value that changes reasonably slowly, the output
of a control system, as experienced at the CEV, will correlate highly
and negatively with the disturbance value. That's "cause" in the
colloquial sense--and as I said, you can't ever look too closely at the
meaning of that word.
Those actions also disturb yet other control systems,
including the one originally disturbed (with, of course, some delay). It
depends on the gains of all the control systems and their efficiency of
control whether there are any positive feedback loops with gains greater
than unity in the whole structure.
Doesn't it also depend on the references of the control systems?
No. Or rather "no, if the system is linear." But actually the nonlinearities
are important here, and it could easily happen that with some settings
of the reference values in some of the interacting control systems, the
lockup could disappear--at any rather the network dynamics in a simulation
could well change.
I think that's what David
was talking about when he said the drug therapy reduced the coupling,
which is why I intervened originally.
My point is ... how do we know? I'm very wary of applying PCT jargon to
case studies and research that has been conducted from within the paradigms
of conventional psychology.
I'm not talking jargon. I'm talking the results of very simple simulations
of simple networks that show behaviour that looks a bit like what David
described, and which show the same kind of escape from lock-up when the
coupling in the simulation is reduced that David described as happening
"when the coupling is reduced" by Prozac.
I have no idea whether what happens in the simulations is actually what
happens in the biological control structure that is in trouble. I suggest
it as a possibility, though obviously the interaction of the myriads of
control systems in the person is much more complicated.
As an afterthought, you might understand all this a lot better if you were
to look up Stuart Kauffman's "At Home in the Universe" as well as doing
Bill Powers' demos at http://animas.frontier.net/~powers_w/.
Martin