Simple bomb in one ECS

[Martin Taylor 920722 11:00]

(Too many references to quote, by myself, Bill and Rick)

It is interesting how understanding evolves. I originally proposed that a
potential bomb existed in a system with 2 ECSs controlling their percepts
through 4 CEVs (complex external variables), of which each controlled one
independently and two in conjunction with the other ECS. One of the ECSs
had a positive feedback loop through one of the CEVs, but this positive
feedback was masked by the negative feedback through the other two CEVs,
until the second ECS opposed the action of the first. Rick showed that this
analysis was faulty, which led me to a deeper understanding that it is the
gain of the second ECS that hides or reveals the bomb, not the direction in
which it controls. The bomb would work with 2 ECSs working through 2 CEVs
with one overlap.

I now see that the bomb can be demonstrated in a system with one ECS acting
on two CEVs, provided that at least one of the CEVs has a non-linear impedance.
I think this is the simplest bomb condition apart from one in which a single
CEV moves into a positive feedback mode. That's a situation that can hardly
be called masked positive feedback, which is what I am getting at.

Consider a CEV with output gain G controlling the percept x+y, where x is
based on the CEV "X" and y on "Y". Disregarding disturbances on "X" and "Y"
the value of x and y depend on the output O of the ECS. x=XO and y=yO. The
percept p=O(X+Y). Let us make the sign of the output such that positive
signs mean negative feedback (i.e. choose the comparator sign appropriately
in the ECS). As described, everything is fine.

Now change the sign of the output relation to Y, so that y=-YO and p=O(X-Y).
Still everything is OK so long as X>Y. Now comes the bomb. Suppose that for
some values of x, dx/dO (i.e. X) is large, whereas for other values it is
small--the ECS has, for example, pushed an object off a slippery surface onto
a sticky one. Then the ECS will control fine so long as x stays in the high
compliance (large X) region, but will go into a positive feedback condition
when "X" becomes stiffer (the object goes onto the sticky surface).

Nonlinearity in the external world can have the same effect as overlapping
control, by reducing the compliance (increasing the impedance) of a CEV
contributing to negative feedback, thus reducing the loop gain. If there
is a CEV contributing positive feedback to the controlled percept, the loop
may as a whole go into positive feedback.

In all the above, a CEV could equally well be a lower-level ECS, and the
relation between the reference sent to it and the percept it returns is
the X and Y in the above.

So, the bomb is there. It can be masked, and my original problem remains
unsolved: What kind of developmental methods can avoid the construction of
masked positive feedback loops? None of the proposed methods of reorganization
seem to accomodate this sort of situation, since an ECS that maintains control
is not going to contribute to the triggering of a reorganization episode
under either Bill's scheme or mine. It is true that an ECS with masked
positive feedback will have a lower gain than it would if the masked loop
were reversed, and perhaps this can be used in some way to detect the existence
of such problems. But unless the positive loops are unmasked, their effects
will be very subtle, affecting mainly the precision and speed of control, not
its success.

When the bomb goes off in one ECS, the situation changes for all ECSs to which
it contributes a percept. For them, the situation is not as if an object had
been pushed from a slippery surface to a sticky one, but more as if the object
had acquired a jet engine to propel it the way it was being pushed. Their
overall loop gains will be reduced and perhaps go positive, and we have a
potential avalanche in which the front of stability moves up the hierarchy,
just as the front of an avalanche moves up the snowfield or sand dune.
Reorganization should then fix the problem, if the organism survives.