Newsgroups: bit.listserv.csg-l
Date:         Wed, 16 Dec 1992 18:09:49 EST
From:         mmt@BEN.DCIEM.DND.CA
Subject: Re: Error control (again!!!!)

[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
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