Error control (again!!!!)

CSGnet Archive CSG1992
1

[From Rick Marken (921216.1200)]

I'm bringing this to the net from a couple of offline exchanges
with Martin Taylor. Martin said I could and I think it's worth-
while. Maybe by opening this up to other minds we can clarify
things. Here is some background:

Martin said:

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

I said that it does. The derivative of squared error (de^2) is one of the
intrinsic variables controlled in Bill's model of reorganization.

Martin said:

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

And I said

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

And Martin said:

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.

Martin is missing my point. I assume that de^2 is the output of a perceptual
function whose input is error signals from many different control systems in
the hierarchy: de^2 = d(e1+e2+....en)^2 say. This signal (de^2) is compared to
a reference value, r, which is intrinsic because it is set by evolution -- it
is not part of the regular perceptual control hierarchy -- de^2 is a
perceptual
measure of "how well the hierarchy is doing". The error signal that
results from subtracting de^2 from r (r - de^2) is converted into an
output signal whose amplitude determines the probability of a random
change in some parameter of the VERY SAME control systems whose
error signals (e1, e2, etc) contribute to the value of de^2. The change
in parameters might improve the performane of the control systems
(reducing the error in the systems and, hence, bringing de^2 closer to
the reference, 0) or it might make their performance worse (more error,
increased de^2, bigger difference between de^2 and r and greater
probability of another change in parameters soon).

I think this is something like how Bill's reorganization system works -- it
improves performance in a set of perceptual control systems by changing
the parameters of those systems in order to keep a perception of the
ambient error in those systems low. In this case, the measure of ambient
error in the lower level control systems (de^2 -- if that's what Bill is
using)
is the controlled INTRINSIC variable.

There are probabaly MANY intrinsic variables that are controlled -- (like
your example of CO2 level) and they are probably controlled by reorganizing
existing control systems. But it is quite likely that the level of error
in the control systems themselves (what we subjectively experience as stress,
I would guess) -- possibly perceived as de^2 -- is one of those intrinsic
variables.

Martin says:

But e*de/dt is not a controlled variable, any more than (in fact less
than) is the error in a normal ECS.

It may not be a controlled variable in your model -- but in the context
in which I was discussing it (and I'm almost sure in Bill's reorganization
model too) IT IS. At least, it CAN be a controlled variable. I think Tom
Bourbon did some modelling of this kind to. Martin, I think you are
confusing the error signal in a control system (any control system --
regular or reorganizing) -- which IS NOT CONTROLLED -- with
a perceptual signal (in any control system) which might DEPEND on
error signals as INPUTS to the perceptual function which produces
the perceptual signal; this signal CAN BE CONTROLLED.

Martin says:

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).

Well, this is all quite unclear to me.

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)

Here it is on the net. There may, I hope, be others interested who just don't
feel like commenting. But I think it's worth it to discuss this in public
because
it seems like you either have a very different understanding of how
reorganization
(and control) work than I do or we're speaking very different languages. The
language problem could be overcome if you just show me your model.

Regards

Rick

2

[Martin Taylor 921216 17:40]
(Rick Marken 921216.1200)

Rick,

Neither you nor I can talk for Bill. But since you are quoting your
interpretation of what he says, I will, too, since neither of us think
we are altering his model.

When I said it was OK to put our exchanges on the net, I said to put it all
out together, precisely to avoid the kind of selective quotation that you
did put out.

But since you have excluded most of the background and interpretive context,
I guess I have to try to make it intelligible.

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. The output of the control system for this
variable is a stream of events that cause reorganization in the main hierarchy.
I assert that Bill P has simulated reorganization with the rate of this
stream proportional to d(E^^2)/dt if that is greater than zero, and zero
if that is negative. Rick asserts that the control level for d(E^^2)/dt
is zero. I don't understand that, because if the error is decreasing in
absolute magnitude, the variable is probably under control (there could
be a coincidental helpful disturbance, which is why I say "probably").

That's the essence of how I see the issue.

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. The squared sum
of algebraic error is only a measure of the current dynamical disturbance
in the net, and errors introduced by a saturating positive feedback loop
(and they all must in practice saturate) will be swamped by the large
number of actually controlled loops that are responding to current
disturbances. So the derivative of the squared sum of algebraic error
will not even include the effect of the loop that requires reorganization.

I think that Bill and I have previously accepted that the sum of squared
errors (not the derivative of that sum) might well be an intrinsic variable.
We differ, I think mildly, on how localized a chunk of the hierarchy this
kind of sum is likely to be taken over. If the sum of squared error is
an intrinsic variable, its controller may well have a reference value of
zero. But in no way could its derivative be an intrinsic variable to be
controlled, because the only suitable reference value would be minus
infinity (the hierarchy is controlling superbly).

Whatever intrinsic variable might be under consideration, I think we agree
on how Bill sees the reorganization happening. A reorganization event
changes something in the main hierarchy, which may or may not improve the
control of the intrinsic variable. If it does not, then another
reorganization rate is likely to happen relatively soon. If the intrinsic
variable now turns out to be under control, no more reorganization is
likely to happen soon.

So I think that, as I said to Rick in one of the parts he didn't quote,
our disagreement is of words, not models. Only now I realize that the
words at issue were not what I thought they were. 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).

The language problem could be overcome if you just show me your model.

I hope that I have shown it to you, and I hope you see it as the same as
Bill's (and I hope Bill see it that way, too). That's because I was not
trying to discuss MY model (which is a little different) in our private
interchange, but Bill's.

Martin