[Martin Taylor 980424 20:30]
Rick Marken (980422.2200)
There has been a thread on conflict, in which I think the idea of
conflict has been mixed with the idea of mutual disturbance.
... But I believe conflict becomes less likely the more
dissimilar the perceptions (that is, the more dissimilar
the perceptual functions). If the perceptual functions
are linear (such as p = ax+by) then we can measure dissimilarity
as the orthogonality (linear independence) of the functions. I
forgot the equation that measures the orthogonality of two
linear functions ...
If p1 = a1*x1 + a2*x2 + ... + an*xn
and p2 = b1*x1 + b2*x2 + ...+ bn*xn
p1 and p2 are orthogonal if a1*b1 + a2*b2 + ... an*bn = 0.
I think that the following two perceptual functions are as
different (orthogonal) as two linear functions of two variables
p1 = 1*x+1*y
p2 = 1*x -1*y
These perceptions are functions of the same environmental variables
(x and y). I can build control systems that simultaneously control
these very different perceptions of x an y with no conflict at all.
So you can. But at the same time, any disturbance to p1 will result in
some control action by the p1 control system. That control action will
influence both x and y. Unless its influence is exactly equal on x and on
y, the p1 control action will influence p2. Likewise, a control action
by the p2 control system will influence p1, unless the p2 system acts
equally and oppositely on x and on y.
The control actions of the p1 controller act as disturbances to the
p2 controller, and vice versa, _unless_ the outputs are distributed
to the environmental variables orthogonally to each other's perception.
It is not necessary that the perceptual input functions themselves
Consider the following setup:
p1 = x
p2 = x+y
These are not orthogonal, but they can be controlled without conflict,
and without mutual disturbance, if the output of the p1 controller is
distributed equally and oppositely to x and y, and the output of the
p2 controller affects y alone.
The point here is that you have to consider not only the perceptual
input functions but also, and more importantly, the distribution of
the output signals to the environmental variables of which the
perceptions are functions.
But I will see if I can set up the world so that two systems
that can control orthogonal perceptions are in conflict (so
that they interfere with each other's efforts to control their
Easily done. For the pair of perceptual functions you originally used,
make the output of the p1 controller affect only x and the output of
the p2 controller affect only y. The two will still be able to control,
but each will interfere with the other's efforts to control its own
True conflict occurs when the attempt to control one perceptual signal makes
it inherently impossible for another perceptual signal to be controlled.
There are two ways this can happen: (1) the two perceptual signals are
essentially the same function of environmental variables but are being
controlled to different reference values; (2) the controlling actions
go through a bottleneck so that there are not enough degrees of freedom
available. Case 2 would happen for Rick's two perceptions if each could
affect only the "x" variable, or could affect only "x+2*y", or something
else not orthogonal to either perceptual signal. Israelis wanting to live
in an area without Palestinians while Palestinians want to live in the
same area without Israelis is an example of case 2 conflict.
Mutual disturbance happens any time the control output of one system
influences variables that enter into the perceptual input function of
another--other than the fluky case when the balance of influences
happens to be exactly orthogonal to the other's perceptual input
function. Mutual disturbance isn't conflict, but it does affect the
RMS precision of control in the presence of external disturbances to
Mutual disturbance can, and often does, involve wildly dissimilar
perceptions--my attempt to control for having a taste of chocolate
in my mouth can disturb my attempt to control for not stopping on
an inter-city drive.
Conflict, on the other hand, is likely to involve highly similar
perceptions; in case (1) the conflicting perceptions are identical, and
in case (2) they _must_ use the same control action, so they are likely
to be highly similar (though they need not be).