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Date:         Wed, 16 Dec 1992 12:36:30 -0800
From:         Marken@COURIER4.AERO.ORG
Subject:      Error control (again!!!!)

[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
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