A Bomb in the Hierarchy

[From Rick Marken (920719.1300)]

Martin Taylor (920718 12:00) suggested an arrangement of
control systems where one might exist as a "hidden"
positive feedback system just waiting to go off.

The proposal was to have two systems, Y and Z, controlling
different linear combinations of lower level perceptual
variables A, B C and D. The idea was that it would be possible
to hook the outputs of Y and Z to A,B,C and D (or to the
references of the systems controlling these variables) so
that a positive feedback connection from Z would be concealed
through "collaorative" behavior of Y (see Martin's post for
details). Not being a linear algebraicist, I set up Martin's
suggestion as a spreadsheet model. The result was that there
is no "collaborative" way for systems Y and Z to control
their perceptions when system Z has an inappropriate connection
to one of the variables it is controlling. The only collaborative
relationship is the one where system Y is just not controlling
its perception (the one that partially overlaps the one controlled
by system Z). It is true that system Z can control it's perception
even with the wrong output connection to one component of that
perception -- at least over the range of references I investigated.
Actually, now that I think of it, there would be no way for Z to
control for negative reference values. I'll try that in a second
(I don't have multifinder at home dammit).

So modelling shows that Martin's problem is no problem -- at
least for the specific case he proposes. An inappropriate
output connection would lead, quickly, to lack of control
(especially if two systems are controlling two variables that
are not completely independent) and this is something that would
lead to reorganization. So the hierarchy would be strongly biased
against maintaining such systems.

Regards

Rick

ยทยทยท

**************************************************************

Richard S. Marken USMail: 10459 Holman Ave
The Aerospace Corporation Los Angeles, CA 90024
E-mail: marken@aero.org
(310) 336-6214 (day)
(310) 474-0313 (evening)

[Martin Taylor 920720 10:30]
(Rick Marken 920719.1300)

Rick says that his spreadsheet modelling indicates that one can't have
a masked positive feedback loop within the hierarchy. Modelling is certainly
superior to wordsmithing, but I remain unconvinced. Since I came across
the idea, I seem to see it in a lot of apparently inappropriate human behaviour
including suicide, which seems to correspond exactly to this situation.

Rick, I guess I will have to do a little more analysis. But are you absolutely
sure about your spreadsheet analysis? There are issues of computational
order and the gain regime within which masking will happen, aren't there?
In the situation I envisage, if Z acts alone, it will display negative
feedback and be able stably to control its percept, because if B, C, and D
have the same impedance, the effects of Z on b and c will swamp those on D.
You say that your model agrees with this. If the effective impedance of
B and C is reduced by Y, this should make Z more stable, but if it is increased
by Y opposing Z's action on them, then the effect of Z on D should be
relatively more important, and at some point the overall Z loop should go
positive. If this doesn't show up when modelled, I'd like to understand
why not. How is the effective gain of Z affected by the action of Y?

I don't see how you can reconcile:

It is true that system Z can control it's perception
even with the wrong output connection to one component of that
perception -- at least over the range of references I investigated.

with

The result was that there
is no "collaborative" way for systems Y and Z to control
their perceptions when system Z has an inappropriate connection
to one of the variables it is controlling.

You mean Z can control if it acts alone, but never if Y is also acting, even
if Y is affecting B and C in the same sense that Z is?

Martin