Conflict and mutual disturbance

[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.

... but
I think that the following two perceptual functions are as
different (orthogonal) as two linear functions of two variables
can be:

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
be orthogonal.

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
own perceptions).

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
perception.

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
both perceptions.

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).

Martin

[From Bruce Gregory (980425.0448 EDT)]

Martin Taylor 980424 20:30

There has been a thread on conflict, in which I think the idea of
conflict has been mixed with the idea of mutual disturbance.

Thanks Martin. Your post clarified what was for me an increasingly murky
exchange.

Best Offer

[From Bill Powers (980425.1008 MDT)]

Martin Taylor 980424 20:30--

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
be orthogonal.

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.

Very nice, Martin. I tend to forget that the output weights can be any
reasonable values, so the orthogonalizing doesn't have to be done entirely
in the input function. Your whole discussion of conflict is very clear.

I have just a few lingering question marks. Using the principle you explain
in this post, would it be possible for all the independent control systems
to use exactly the same input function, and orthogonalize by choosing
different patterns of output weightings? I can't prove it, but my intuition
is that this wouldn't work.

I don't have this all worked out (I'll see what I can do here), but it
seems to me that all you gain from playing with the output weights is the
minimization of the effort needed for controlling all the perceptions
involved. That would be a _different_ controlled variable. Assuming that
the set of systems is "maxed out" in terms of degrees of freedom and number
of perceptions being independently controlled, the set of reference signals
uniquely determines the value of the environmental variables at the inputs
to the systems. Only one pattern of N inputs will create the set of
perceptions that matches all the N reference signals. Thus the _input
functions_ must be orthogonal, regardless of the output weightings. Or
perhaps what I should be saying is that they should be NOT PARALLEL. As
long as the input functions are not pairwise parallel, there is a unique
solution and absolute conflict does not exist.

However, a set of "fully nonparallel" input functions doesn't automatically
determine that the least effort possible is being used to bring all the
input variables to the required values. In order to achieve minimum effort,
the output weights must be optimized to minimize the degree to which one
output vector partially cancels other output vectors. When this mutual
cancellation is minimized, we have the least effort being lost in expending
energy with no result. When the total energy that must be expended (or the
total force that must be generated, etc.) is greater than what the organism
can produce, we have the onset of _effective_ conflict as I defined it
yesterday. The output weights then determine whether there is _effective_
conflict.

So perhaps this will hold up: the input weights of the N control systems
must be such that no two input functions are parallel. That is a very loose
requirement; almost any random collection of input weights would satisfy
it. But at the same time, the output weights must be such that in order to
bring all the N input variables to their required states, no effort greater
that the amount the organism can sustain indefinitely must be required.
This requirement defines a region within which the output weights must be
for effective conflict to be avoided (that is, where there is no decrement
in performance due to some system, or the whole system, hitting its maximum
of output).

Obviously, the outputs will be minimized if the input functions are close
to being mutually orthogonal. As the input functions depart from perfect
orthogonality, the outputs required for control will, to growing degrees,
partially oppose each other and the total amount of effort or force
required will rise. At some point, as the input functions depart further
from orthogonality, one or more output functions will hit a limit, or the
total available energy for generating output will hit a limit. That point
is where effective conflict just starts, producing a decrement in overall
performance.

As Endeavor Morse says to Sergeant Lewis: [Martin], you've done it! We now
have a continuous measure of an N-way conflict, thanks to your remembering
that output weights are also adjustable. The optimum output weightings
depend on the input weightings, and the optimum input weightings can be
measured in terms of some measure of orthogonality.

A very neat and satisfying picture. What's more, it may suggest how we can
set up reorganization to vary both input and output weights based on two
independent criteria, so that the final weights on both sides are related
in some nonrandom way -- perhaps even in a _unique_ way. If there is a
unique determination of optimum weights, we will have a vastly important
epistemological fact: a specific relationship between the experienced world
and the properties of the external reality, such that the organization of
perception converges to a form that is unique to the environment outside
the system. This would be the first way, to my knowledge, of proving that
our internal perceptual organization has some necessary and knowable
relationship to the external reality.

Best,

Bill P.

ยทยทยท

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
own perceptions).

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
perception.

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
both perceptions.

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).

Martin