Two-level accommodation and conflict

[from Kent McClelland (951129.1445 CST)]

Bill Powers (951128.0805 MST) wrote,

. . . It's never easy to be sure, however; two people can be tossing the
same words around for hours and hours and never realize that the
concepts behind the words, in the two heads, are completely different.
It's much easier to detect disagreements than spurious agreements. The
main sign of a spurious agreement is that one person eventually says
something he fully expects the other to agree with, and meets with a
totally unexpected objection to it. The only way to handle this that I
know of is to hunker down and start going through the details one by
one: just what do you mean by "and?"

I wonder if something I've found in playing with simulated control-system
interactions has a bearing on this phenomenon.

My latest spreadsheet model has two perceptual levels. Lower-order systems
control their perceptions of the position of an environmental variable on
an X-Y grid, with some systems controlling in the X dimension and others in
the Y dimension. Higher-order systems control perceptions based on linear
combinations of signals from one or more lower-order X systems and one or
more lower-order Y systems. A higher-order system, then, will be in
control of its perception when the environmental variable falls somewhere
on a straight line on the X-Y plane, with the slope of the line determined
by the coefficients (weights) for the linear combination of X and Y signals
used by the higher-order system, and the intercept of the line being
determined by the reference level of the higher-order system.

For example, if I set a higher-order system to have weights of 2.0 for X
and 1.0 for Y, and a reference level of 10, so that the system is described
by the equation,

                      2.0 * X + 1.0 * Y = 10,

the system will be "in control" when its perception of the environmental
variable is anywhere on a line that has a slope of -2 and an intercept of
10, including the points (0,10), (2.5,5) or (5,0), as in the diagram below.

                        > \
                        > \
                        > \
                        > \(2.5,5)
                        > \
                        > \
                        > \
                        > \
                        >_________\________ X
                      (0,0) \(5,0)

I've been seeing what happens when I simulate the interaction of two
higher-order systems working at cross purposes, so to speak, in the same
X-Y environment. If the two higher-order systems have different weights
for X and Y and so are controlling different perceptions, their
"satisfaction lines" will cross somewhere on the X-Y plane, and thus there
will always be some point, call it the "accommodation" point (Bob Hintz's
term), where both higher-order systems can be "in control" at the same
time. If the two higher-order systems use exactly the same linear
combination of X and Y but have different reference levels, their
satisfaction lines will be parallel and will never cross--thus the two
systems must always be in conflict, at least until something changes to
realign their reference levels.

In real-life terms, I'm looking at how whether the two systems see the
world in the same way or not. How close do they come to sharing the same
perceptual function? Are they controlling parallel or perpendicular
perceptions? (In other words, are their satisfaction lines highly
correlated or orthogonal?) One of my simulations starts with an X-Y point
that satisfies neither of a pair of higher-order systems and then examines
how quickly they are able to bring their perceptions under control by
reaching their mutual accommodation point.

A finding from these simulations that surprised me was that two
higher-order systems with orthogonal or nearly orthogonal perceptional
functions can reach their accommodation point much more quickly than two
with nearly parallel functions. I guess that if there are enough degrees
of freedom, people can share environments easily provided they're
controlling different perceptions.

However, when the perceptions controlled by the two systems are almost but
not quite parallel, the systems quickly succeed in pulling the
environmental variable to a point somewhere in between their two
satisfaction lines, where they are both more or less satisfied. But then
they get stuck in a state of low-level conflict, with the environmental X-Y
position hovering between the two lines and drifting ever so slowly toward
the mutual accommodation point, which if the two lines are almost parallel
is likely to be a long way off. It's like neither system has enough
leverage to drive things quickly toward the only outcome that would provide
complete satisfaction for both.

I imagine that an analogous state of chronic low-level conflict over
nearly-but-not-exactly-parallel perceptual functions occurs pretty commonly
in human interactions, and perhaps this simulation could serve as a model
for the "spurious agreement" that Bill was talking about in his post.

Another implication: the more alike two people are in their thinking (that
is, the more parallel their perceptual control systems), the more prolonged
(and perhaps fiercer) the conflicts they can engage in, when they adopt
different reference levels. Again to quote Bob Hintz (who has seen the
simulation), "Perhaps the reason Clinton and Congressional leaders can't
resolve their differences more quickly is that they think so much alike!"