Rick on (off) Shannon

CSGnet Archive CSG1992
1

[Martin Taylor 921217 10:40]
(Rick Marken 921216 sometime)

I really can't let Rick's latest non-sequitur go unchallenged:

Bill P.'s
important observation was that perception is one link in a
causal loop in which we are all locked -- a loop that obviates
Shannon's concerns about reliable transmission since, in living
systems, perception is not the "start" of communication (or the
"end", for that matter); it is both the start and the end at the
same time.

Every piece of the loop is constrained by Shannon's observations/theorems.
If (like Rick) you don't understand them, you are doomed not to uinderstand
PCT.

Martin

2

[From Rick Marken (921221 1300)

Martin Taylor (921216 17:40) --

The argument was roughly (as seen from my side): if there is an intrinsic
variable (i.e. a variable outside the main hierarchy, in a Bill-P-type
reorganization hierarchy) with a reference level R and perceived level P,
giving error E, then I assert that the controlled variable is P. Rick
asserts that it is d(E^^2)/dt.

If this were the argument then there would have been no argument.
Remember, I?m the guy who posted that little proof that the
ERROR VARIABLE IN A CONTROL LOOP is not controlled.
Why the hell would I have argued that error IS controlled?
Unfortunately, I have saved none of our private posts but I
remember the argument quite differently -- I thought that
you were saying that intrinsic error (or some transform thereof)
was controlled in reorganization. Now you say it the perception
of the intrinsic variable that is controlled -- which (of course) is
correct and I agree.

If you have saved the private posts, Martin, then you could post
them and clear this all up. But even without them it is clear from
my post to the net that I NEVER suggested that ?d(E^^2)? was
controlled -- where E (in your comment above) is the error in
the system controlling the intrinsic variable, P. When I said that
d(e^2) is controlled, I made it quite clear that this was a
perceptual variable -- representing perception of error in
OTHER control systems. And I never made a big deal about
what the form of the function was -- it?s a perceptual function
and determining it is best left to research and modelling.

Now what might be an intrinsic variable. I used blood CO2 concentration,
but I'm quite happy with overall error in the main hierarchy. But if
overall error is to be used, Rick's formula won't work.

Well, I won?t conceed that until I see it modelleed. But
I never made an issue of what the damn function is that
transforms overall error into a perceptual measure of error --
I was just saying that ?error in the main hierarchy? can be
a controlled intrinsic variable. Apparently you are happy
with that; if you had written the above paragraph N posts
ago we could have saved all this useless blather.

Rick was talking
about error in the hierarchy AS an intrinsic variable, but using an
expression that couldn't work, whereas when I used the word "error" I
was referring to error IN an intrinsic variable (which might well be
overall error magnitude in the main hierarchy).

Well, then why did you just now (see above) say ?Rick
asserts that it is d(E^^2)/dt.? that is controlled; where E
is error in the control system controlling the intrinsic
variable (according to your notation)? If you don?t
want to have confusion, don?t be confusing.

I find this little misunderstanding (if that?s what it was)
particularly annoying because it led Bill Powers to write:

I think I have to side with Martin Taylor on this one, Rick. In a
simple reorganizing model, e^2 might be a suitable driving signal
for the rate of reorganization. But that isn't the controlled
variable. It's the error signal.

Again -- I?M THE ONE WHO WROTE THE DAMNED PROOF that
error is not controlled; of course e^2 is not controlled -- unless it
is PERCEIVED by another control system which can act in ways that
have systematic effects on that perception. Why in the hell would any-
one imagine that I was arguing that an error signal in a control loop is
controlled??? How could you imagine that this was my argument,
Martin???

Martin Taylor (921217 10:40)

I really can't let Rick's latest non-sequitur go unchallenged:

Every piece of the loop is constrained by Shannon's observations/theorems.
If (like Rick) you don't understand them, you are doomed not to uinderstand
PCT.

Well, you got me there Martin (I think I understand Shannon?s
observations/theorems ok, though not nearly as well as you). But since
you understand PCT so well (thanks to your understanding
of information theory) why haven?t I seen any of your PCT research or
modelling work in the last decade or so,while I?ve been working on PCT?
About the only work I ever found was done by Bill Powers. I did find
some stuff by Carver/Scheier types who didn?t know the difference between
a controlled variable and a reference signal. I also saw lots of tracking
studies by people who?s goal was to figure out how target inputs cause
response outputs. But I never found any research (other than Bill?s) that
was based on a deep understanding (like yours) of PCT. In the last few
years I?ve seen some great stuff done by people like Tom Bourbon (and
his students), Clark McPhail, and Chuck Tucker and a couple others.
But I never ran across anything of yours. Since you REALLY understand
PCT I bet your stuff is great. I?d really like to see it; especially the
stuff
that shows how important information theory is for doing PCT research
and modelling.

Martin, I count a statement like this:

If (like Rick) you don't understand them, you are doomed not to
uinderstand PCT.

as a personal insult. It is a disturbance to the level at which I like
to maintain the perception of my own self esteem. I?m sure you
will say that it was not meant as an personal attack -- and I?m prepared
to believe that; but I don?t really care -- a disturbance is a disturbance,
regarless of the intent of the source; so here is a little compensating
action (in lieu of going up a level):

If (like Martin) you don't undertand PCT, DON'T TRY TO
TEACH IT. Those of us who do understand it -- and
have done the grunt work necessary to grasp the
fundementals -- find condescending tutorials on PCT
to be cloying.

Best regards

Rick (what else would you expect from a loose canon?)
Marken

3

[Martin Taylor 921221 18:00]
(Rick Marken 921221 1300)

Rick ,
Welcome back from your trip. I'm sorry it didn't go well, and left
you in a bad mood, when you saw my little twitting of you. I didn't intend
you to take it as an insult, any more than you presumably intended
your comment to me a couple of weeks ago as an insult, when I took it
badly. Sorry you took it that way.

I think I posted a reasonable summary of the interactions, but you
seem to think I misled the other readership. I had asked you to post
everything, to avoid that kind of problem. Now it seems that to preserve
honour (a rather silly concept, but we tend to have reference levels
for that kind of thing), I have to waste net bandwidth by reposting
the discussion entire.

Either I still misread what you posted, or you misread what I said.
It still seems to me that you were arguing for precisely what I claimed
in my summary, which you now claim is ridiculous.

ยทยทยท

----------------------

If (like Martin) you don't undertand PCT, DON'T TRY TO
TEACH IT. Those of us who do understand it -- and
have done the grunt work necessary to grasp the
fundementals -- find condescending tutorials on PCT
to be cloying.

I have a feeling it is my various attempts to look for the fundamentals
that you (Rick) find cloying (should I guess at threatening?). I know very
well that I don't understand PCT. I don't think anyone on the net claims
to except you, least of all Bill P. I'm sorry that you don't want to
look beyond the behaviour of control hierarchies to see how and why
they work in addition to what they do. I hope that "those of us who do
understand it" is not a large group who find my postings "cloying."

One of the best ways of learning is to try to teach. But I don't think that
I have ever been trying to do that (except locally here at DCIEM). What I
have tried to do is to develop the implications of PCT, to enquire as to
problems that seem to arise, to get at the basics of PCT. If you don't
like it, I'll quit, and just work with our group here at DCIEM. There's
no benefit to me in finding an automatic rejection of my ideas when they
are proposed to the net. It is really Bill P's encouragement more than
anything else that keeps me going--that, and my belief that PCT is the
Newtonian revolution in psychology. But the latter part is something
I can develop on my own, or in private communication with Bill P and my
local collaborators.

------------------------
Here are the postings, so far as I still have them.

Martin

===========================

(I don't seem to have the first mail, to which this is Rick's response)

From Marken@courier4.aero.org Thu Dec 10 14:30:23 1992

Subject: Re: Rick's proof: error not controlled
To: @MVE.AERO.ORG:mmt@ben.dciem.dnd.ca
Status: RO

Martin

You seem to have sent this to me personally -- so I am sending it
back to you personal (I think; it's often hard for me to tell where
mail came from when I'm using this mail system). But I'd be happy
to have the put on the net -- as usual.

I have no complaint about your proof. Different people see things better
from different viewpoints. I thought I was buttressing, not caviling.

OK. What made me think that you disagreed with the proof was the
following:

Where in the world (take the literal meaning of that expression) is the
possibility for disturbing the error in an ECS?

Now you say:

A disturbed error signal is not an error signal as defined.

If you cannot disturb error (and again I point to Bill's diagram to
show that you can) then my proof is invalid because it is based on
the idea that o = k(r-p+de) -- were de is the disturbance to error.

As I mentioned in my post with the equations, if the perceptual signal
were disturbed in the same way (by having a disturbance added to
the neural signal itself) the perceptual signal would still be controlled
(made to equal the reference -- ie. the disturbance would have no effect.
So again, while I agree with your conclusions, I disagree with the
arguments you use to come to them.

I suppose I would agree that error could be controlled if it were to be
provided as input to the perceptual input function of a control system that
maintained the error at some reference level.

As you will see in a reply I plan to make to Greg, there is no
supposing necessary in this case. The error signal (which is now
a perceptual input to a control system) would DEFINITELY be
controlled.

But what on earth would that
do other than enforce a situation in the ECS whose error was being

controlled

that would ordinarily arise only through unresolvable conflict. I can't
see why any hierarchy would include such a mechanism--but I suppose there
might be a reason somewhere.

But this is precisely the way reorganization works. It controls errors by
changing properties of the control system itslef (like its perceptual
function) -- properties which are presumably responsible for the conflict
that is creating the chronic error. Reorganization is control of error
(where error is the input perceptual variable to the reorganization control
system) -- and control is effected by acting on properties of the control
systems themselves. Since there is no way to know HOW to change the
control systems in order to reduce error, there must be a random
componenet to this kind of control -- Bill has modelled as a control
system where the RATE at which random changes occur is inversely
proportional to the perceived value of error.

Best

Rick

From mmt Thu Dec 10 16:45:11 1992

To: Marken@courier4.aero.org
Subject: Re: Rick's proof: error not controlled
Cc: ./marken
Status: RO

Rick,

As usual, we were talking a little at cross purposes. There's no real
argument. You were assuming that there might be some way that a disturbance
could be applied to the error within an ECS, and when you mention electrodes,
that can be true. I was working within the normal hierarchy, in which the
only inputs to an ECS are through its perceptual input function and its
reference inputs, and within that frame, there's no way to apply a "de".
That doesn't argue against your proof at all. If(x) then (y) is the proof.
Not(x) does not say not(y).

On a different topic, you say:

But what on earth would that
do other than enforce a situation in the ECS whose error was being
controlled
that would ordinarily arise only through unresolvable conflict. I can't
see why any hierarchy would include such a mechanism--but I suppose there
might be a reason somewhere.

But this is precisely the way reorganization works. It controls errors by
changing properties of the control system itslef (like its perceptual
function) -- properties which are presumably responsible for the conflict
that is creating the chronic error.

Reorganization may well work this way. (All we know experimentally is that
Bill says that my approach to reorganization is the only one he knows to
work by simulation, and then only in respect to gain functions; even if we
eventually discover various ways in which it COULD work, we won't know
that it DOES work this way). But the thing I was saying was that however
reorganization works, it seems unlikely to develop stable systems that do
useless or obstructionist things.

Reorganization is control of error
(where error is the input perceptual variable to the reorganization control
system) -- and control is effected by acting on properties of the control
systems themselves. Since there is no way to know HOW to change the
control systems in order to reduce error, there must be a random
componenet to this kind of control -- Bill has modelled as a control
system where the RATE at which random changes occur is inversely
proportional to the perceived value of error.

Actually, what Bill has done seems to be a little more complex. He has
found that the derivative of the squared error is a better criterion.
In our experiments, we have been planning to use K1(e^^2)+K2(e*de/dt),
where de/dt is the derivative of error (2e*de/dt is the derivative of
e^^2). We think that both error and the rate of increase of error are
important. It shouldn't matter if the error is momentarily large, provided
it is decreasing well. When I say "criterion" I mean the Poisson rate of
reorganization events.

Does this help to reduce the cross of our purposes?

Martin

From Marken@courier4.aero.org Tue Dec 15 18:54:38 1992

Subject: Re: Rick's proof: error not controlled
To: @MVE.AERO.ORG:mmt@ben.dciem.dnd.ca
Status: RO

Martin

Actually, what Bill has done seems to be a little more complex. He has
found that the derivative of the squared error is a better criterion.

You mean, as the variable controlled by the reorganization system, right?

In our experiments, we have been planning to use K1(e^^2)+K2(e*de/dt),
where de/dt is the derivative of error (2e*de/dt is the derivative of
e^^2). We think that both error and the rate of increase of error are
important. It shouldn't matter if the error is momentarily large, provided
it is decreasing well. When I say "criterion" I mean the Poisson rate of
reorganization events.

Now I don't understand. The "Poisson rate.." is a criterion? It sounds like a
variable. Why would your model be concerned about the "Poisson rate of
reorganization events"? It's not controlling that rate, is it? Bill's model
controls the derivative of the squared error(you are correct about this,
I believe); it controls this variable by changing some parameter of the
systems
that are experiencing the error; the time between such changes increases as
the
difference between the derivative of the squared error and zero decreases. As
a
side effect the Poisson rate of reorganization events changes during the
course
of reorganization.

At least, that was my impression this summer in Durango.

Regards

Rick

From mmt Tue Dec 15 20:34:04 1992

To: Marken@courier4.aero.org
Subject: Re: Rick's proof: error not controlled
Cc: ./marken
Status: RO

Rick,

It's words again getting in the way...

Bill's model doesn't control the derivative of the squared error, in any
normal sense. That derivative has more the function of "error" in a
standard ECS, in that it determines the output of the reorganizing function.
That output is a reorganizing event that occurs from time to time in the
main hierarchy. The higher the value of the derivative of the squared
error, the more likely a reorganization even is to occur. I don't know
whether in Bill's simulations the rate was determinate or Poisson. Ours
is Poisson, which means that the probability of a reorganization event
happenning in a small delta-T is proportional to the value of the criterion
(derivative of squared error in Bill's case, unless he was using a
determinate time-interval between events).

Now what is controlling what? I think what is being controlled is the value
of some intrinsic variable. It has some error, and all this stuff about
derivatives and Poisson rates are attributes of the output function of
the control system for that intrinsic variable. As with any control system,
whether in the main hierarchy or in the reorganizing system, the actual
outputs are not controlled in themselves. Outputs are, shall we say, blind.
So the "criterion" is not controlling the Poisson rate. It is just a
component of the output function of a controller that controls an intrinsic
variable.

(Bill and I have an unresolved, and perhaps unresolvable, disagreement here
as to what might constitute an intrinsic variable, but that disagreement is
minor and not germane to this discussion.)

Martin

PS. It feels great to be back on the air. I hope the link stays in action
for a while.

From Marken@courier4.aero.org Wed Dec 16 11:59:39 1992

Subject: Re: Rick's proof: error not controlled
To: @MVE.AERO.ORG:mmt@ben.dciem.dnd.ca
Status: RO

Martin

Let's put this on the Net.

Bill's model doesn't control the derivative of the squared error, in any
normal sense.

It does. I'll explain on the net.

That derivative has more the function of "error" in a
standard ECS

Because the intrinsic reference (for de^2) is 0.

Now what is controlling what? I think what is being controlled is the value
of some intrinsic variable.

de^2 is the intrinsic variable being controlled relative to an intrinsic
reference which happens to be 0; it could be something else (maybe
evolution wants the system to operate with de^2 at just a tad above
zero -- keeping you on your toes).

de^2 is controlled because it is both a cause and a result of reorganization;
and the sense of the feedback is (or should be) negative.

Regards

Rick

From mmt Wed Dec 16 14:10:23 1992

To: Marken@courier4.aero.org
Subject: Re: Rick's proof: error not controlled
Cc: ./marken
Status: RO

Rick,
I don't mind putting the discussion on the net, but I don't think it worthwhile.
There are too many long wavelength fish involved.

Because the intrinsic reference (for de^2) is 0.

Now what is controlling what? I think what is being controlled is the value
of some intrinsic variable.

de^2 is the intrinsic variable being controlled relative to an intrinsic
reference which happens to be 0;

This makes no sense to me. In words, you are saying that whatever the
error is in the intrinsic variable (say blood CO2 level, for example),
what is controlled is that this error should not change. To me, the
only thing that makes sense is that there is some reference level for
blood CO2, and if this is too high or too low, and particularly if it
is moving in the wrong direction, then the main hierarchy needs reorganizing.
The reason for using the derivative of the squared error in the intrinsic
variable as part of the output function is that it is a short way of
ensuring that the error is both large and increasing, whichever sign it
has. Other functions having the same properties would also be useful.
But e*de/dt is not a controlled variable, any more than (in fact less
than) is the error in a normal ECS.

Another way of seeing that d(e^^2)/dt is not controlled is to note that
zero is not a reference level for it. Negative values are even better,
becasue they show that the intrinsic variable is really being controlled.
A zero value is neutral in this respect, in that the error in the intrinsic
variable may be large but unvarying, or the error may be small while changing
wildly. Neither indicates good control, but both are compatible with good
control (momentarily).

If you want to put it on the net, collect all the postings and send them
out as one. But I don't think it worthwhile. I haven't seen anyone else
that seems to be interested in the matter (except presumably Bill, by
inference)

Martin

4

Sent this last night but got no ACK from CSG-L and
didn't see it on the net this morning -- pardon me
if this shows up twice; I'm possibly still suffering
from results of bad trip (well, the trip was fine,
actually -- the mail waiting on my arrival left some-
thing to be desired, however).

[From Rick Marken (921221 2000)]

Martin Taylor (921221 18:00)

Thanks for posting the correspondance; now I see what happened.

You said:

I suppose I would agree that error could be controlled if it were to be
provided as input to the perceptual input function of a control system that
maintained the error at some reference level.

I replied:

As you will see in a reply I plan to make to Greg, there is no
supposing necessary in this case. The error signal (which is now
a perceptual input to a control system) would DEFINITELY be
controlled.

You said:

But what on earth would that
do other than enforce a situation in the ECS whose error was being
controlled
that would ordinarily arise only through unresolvable conflict. I can't
see why any hierarchy would include such a mechanism--but I suppose there
might be a reason somewhere.

In other words, you were rejecting the idea that perception of error
in the control hierarchy should be the object of control by a reorganizing
control system. But the notion that perceived level of error
is an intrinsic variable controlled in a reorganization loop seems
necessary to explain the many cases of learning where you develop new
control skills even though you still can eat and breath. Dick Robertson
did a nice experiment to show that reorganization can happen for no other
reason than to solve a problem "better" than it's currently being solved;
no obvious "intrinsic" variable is controlled except control skill (low
level of error in the control system) itself.

So the discussion was about whether the reorganization model should
be able to control the quality of control (measured as perceived
level error in one or more control systems) -- and I think it should.
But we seemed to have lost this thread and moved into a discussion of
error and this is where I misinterpreted what you were talking about.
You said:

Actually, what Bill has done seems to be a little more complex. He has
found that the derivative of the squared error is a better criterion.

And I said:

You mean, as the variable controlled by the reorganization system, right?

This was my mistake. When I saw your formula for error, (K1(e^^2)+K2(e*
de/dt), I assumed that this was the PERCEPTUAL FUNCTION,f, which transforms
error in the hierarchical control systems (e) into the perception
controlled by the reorganizing system, P, so that P = f(e). (I will
adopt your convention of using capitol letters to denote variables in
a reorganization loop -- small letters to denote the corresponding
variables in a "regular" control system in the PCT hierarchy). In fact,
your formula is for the OUTPUT function,g, that transforms the error in the
reorganizing control system (E) into the reorganizing system output (O),
so O = g(E). This fooled me because we rarely need to put non-linearities
into the output functions of our models of tracking type data; just
linear amplification. If we did add such non-linearities, they would
be "absorbed" by the control loop (assuming that they are at least
monotonic). But the output of the reorganizing system is not an amount;
rather, like the tumbles of e.coli, the time between reorganizing events
is the output that matters. So a non-linear output function might be just
what the doctor ordered to make reorganization efficient; now I recall
that THIS is what Bill discovered in his studies of reorganization
algorithms that we talked about this summer.

So, Martin, I was not arguing that error is controlled (as you mis-
takenly said in your summary of our exchange -- I'm quite sure,
unintentionally; I don't think you tried to mislead); I just said that one
intrinsic perceptual variable that might be controlled by a reorganizing
system (which is itself a control system controlling perceptions relative
to intrinsic references) is some measure of ambient error in the control
hierarchy itself. So now we can get back to THAT conversation; do
you think that reorganization involves control of perceived error in
the hierarchy (in human control systems)? Why or why not? Can you think
of a behavioral test for such a model? (These are serious questions-- I
don't know the answers but I would appreciate hearing suggestions -- then
maybe we could design some real experiments instead of just blabbering away).

As for Shannon and information theory; could you give me another sample
of this "understanding" of PCT that you get with info theory that you
don't get otherwise? Could it be that info theory is just one of those
comfortable old pieces of wisdom (like reinforcement, statistics,
reflexes, information processing, experimental methodology, decision
theory. etc) that just MUST fit into this (PCT) SOMEWHERE? What if it
doesn't?

Best regards

Rick

5

[Martin Taylor 921223 11:00]
(Rick Marken 921221 2000) (delayed)

Rick,

I think the misunderstanding has been cleared up by your posting.

So now we can get back to THAT conversation; do
you think that reorganization involves control of perceived error in
the hierarchy (in human control systems)?

Yes.

Why or why not?

It seems a very plausible way that the linkages in the hierarchy can be
connected with appropriate signs (and as I mentioned in a posting a few
weeks ago, there seem to be 12 different ways that reorganization of this
kind could be effected, so I'm not plumping for a mechanism).

Can you think of a behavioral test for such a model?

Not offhand. And I think that a good part of this reorganising system
is outside the individual, occurring on an evolutionary time-scale, so
that aspect couldn't be demonstrated behaviourally.

As for Shannon and information theory; could you give me another sample
of this "understanding" of PCT that you get with info theory that you
don't get otherwise? Could it be that info theory is just one of those
comfortable old pieces of wisdom (like reinforcement, statistics,
reflexes, information processing, experimental methodology, decision
theory. etc) that just MUST fit into this (PCT) SOMEWHERE? What if it
doesn't?

I admit the possibility, since we can never know when we are fooling ourselves.
But see the postings to Tom and Bill yesterday. I hope that I will be able
to satisfy you with what I plan to write in a more serious vein than
impromptu net postings.

Happy Xmas.

Martin