In the door example, a person’s
left-right degree of freedom for movement is lost as soon as the person
gets into the doorway, whether one person is going easily through the
door or two are getting stuck in it. It’s the front-back df that is lost
when they get stuck. But that’s not the point. The point is that the
ENVIRONMENT (i.e. the doorway) has limited degrees of freedom. Over any
period of s seconds a place on the floor (such as between the door jambs)
can be occupied by only one person or none. If it is occupied by person A
it can not, in that same s-second interval, be occupied by person B. The
doorway permits only one df per s seconds, but T/s df (independent
changes of occupancy) in T seconds.
It’s the same as if there is only one stick and two people each need a
stick to poke at something. There’s only one instantaneous degree of
freedom for stick ownership, and it takes a finite time to change
ownership. If two control systems try to use the same environmental
degree of freedom at the same time, they can’t both
succeed.
[From Bill Powers (2007.12.06.0754 MST)]
Martin Taylor (12/3/2007)–
:
The environment has even more degrees of freedom than perceptions do. You
could break the stick in half, creating two sticks. Or it could occur to
you that there can’t possibly be just one stick in the whole universe, so
you go find another one.
While I agree that conflicts can arise specifically because of lacking
sufficient space-time degrees of freedom of output (sometimes I could use
three hands), it is quite possible and usual for conflicts to exist
because a higher reference condition demands an impossible state of a
perceived variable. I cannot be a pleasant, relaxed, permissive person at
the same time I am being a commanding, assertive, dominating person. Yet
I could become organized so some higher goal requires being each one, and
sometimes both. There’s no problem of bandwidth there. Even with infinite
output capacity and bandwidth of action I still could not perceive
myself, nor would anyone else perceive me, as both things at once. The
emissary cannot convince the Pope of his egalitarian benevolence while
simultaneously or in rapid alternation chastizing his assistant for
insubordination.
By putting the critical degrees of freedom into the environment (that is,
our physical model of the environment), you’re objectifying something
that is basically a subjective problem. The problem with the two people
trying to jam through a door is not just that the door is too narrow; it
is also that the people are too fat. If they lost weight they might both
fit through at once. They could also use a jack to widen the doorway, or
they could dynamite it, if doing that didn’t conflict with some other
reference conditions they hold dear. What the conflicting parties are
trying to do, know how to do, and will allow themselves to do define the
relevant degrees of freedom – the environment does not. It’s the
organisms that create the problem. The environment is just what it is.
The organisms have to change what they are trying to do via the
environment, or how they are doing it, if either one is to be able to
resume normal control.
There’s one more aspect of “PCT conflict” that has to be
considered. The conflicting systems are not two passive organizations
thrust against each other by blind external forces. When the two systems
first come into contact, each experiences an increasing error, which
leads to an increase of output. Both outputs start to increase, and as a
consequence both errors increase even more. This is clearly a positive
feedback situation, and the outcome depends on the product of the
input-to-output loop gains in the two systems. As Kent McClelland showed
with his model of conflict, if the two systems have integrating outputs,
they will act at first like a single system with one virtual reference
level and one net output quantity. But the two output quantities will
continue increasing with time in opposite directions, and eventually one
system or both will run into a limit, and then only one control system
can continue operating – until it, too, reaches its limit (all this can
happen in a fraction of a second). Then there will be no control systems
in working order.
If the combined loop gain is too high, there is no way to stop the
systems from going to the maximum possible level of opposing outputs.
That is what a true conflict involves.
If the loop gains are low enough, and the integrators are leaky (the
normal case for real integrators), the two systems can come to
equilibrium in a state of elevated error, but with room left for changing
the outputs in response to disturbances. Now we have what looks like a
single virtual control system with a single virtual reference level, the
apparent reference level being a little different from the actual
reference levels in both systems. Because part of each output is being
used to counteract the output of the other system, the range of external
disturbances that can be resisted is reduced in the direction that
increases the error in one system (and reduces the error in the other).
Even though the systems are fighting each other, and even though neither
one is experiencing the state of the perception that is desired, they
behave as if they are cooperating to resist disturbances that tend to
alter the status quo. When disturbed, the system that experiences
increased error will try harder, and the other one will start to relax:
the net loop gain is the sum of the loop gains in the two systems. This
is not a case of pure conflict, but a borderline case on the threshold of
true conflict, like a flip-flop just below the point of triggering a
reversal.
In an incipient conflict between two people, it’s remarkable how much
effect there is when one of the parties lowers the gain with which the
disputed variable is being controlled. For a moment, we see one person
starting to be calm and reasonable, while the other is still screaming
insults and lashing out in all directions. But immediately, the other
person finds that the controlled variable has been pushed closer to the
desired state, and begins to relax also. The controlled variable hasn’t
changed much, but now the violence of the opposition has decreased
noticeably.
The critical thing to notice in a dispute is when one’s own actions have
pushed the other party into increasing the loop gain, so the opposing
actions are starting to become extreme. This is a sign that the other
party is losing control and will probably soon take even more extreme
actions. Lowering the disturbance is a sure way of reducing the
opponent’s extremes of output. I see that Jim Wuwert, in his discussion
with Rick Marken, has taken this step, with the expected results.
The traditions in which most of us have been raised – I would say
world-wide – reflect the normal consequences of conflicting goals. If
one experiences a new error, one is starting, even before conscious
reflection, to increase the actions used for control. One feels an
upsurge of emotion as the affected systems spring into action. If the
disturbance then increases, the natural thing to do is to summon up even
more resources and redouble the effort (and the emotions). If nothing
changes on either side – if neither side seems to realize what is
happening and is likely to happen next – the conflict will go quickly to
its maximum level, where the opposing outputs are limited only by
resources, strength, or self-imposed limits on what one is willing to do
to another person ( if survival is threatened, those limits tend to be
removed). I think this in undoubtably the basis of war. Realizing even to
a small degree that this is the basic problem probably accounts for the
existence of diplomacy.
To sum up, Martin, I contend that it is not the environment that limits
our degrees of freedom, or even in most cases our output capabilities,
but our selection of goals that result in trying to accomplish impossible
ends. Behind what seem to be environmental limitations there are, as in
the example of the doorway, unspoken assumptions about what we can do or
are willing to do to gain our ends. The real conflicts come down to
matters of perception and goal-setting.
I also contend that there are normally far more degrees of freedom than
we actually require to achieve all our concurrent goals. The limits of
which you speak come into play when there are almost N controlled
variables in an inner and outer world with N degrees of freedom. As the
number of controlled variables approaches this fixed limit, the
difficulty of finding a solution (N perceptions exactly matching N
reference signals) increases rapidly, because the number of different
states of the variables that is permitted dwindles until only one exact
value is left for all of them. And then, of course, if there is any
conflict due to adding one more controlled variable, the conflict will
simply remain: there is no solution. Finding a way to control the new
variable will mean giving up control of some other variable, if we insist
on an exact solution. Of course if we’re willing to accept a small
amount of error in many systems, the strictly exact solution isn’t
required. But I don’t think we ever get close to that condition. There is
almost always more than one way to correct an error. When we’re in
conflict, internal or external, I guess that almost always we are making
unnecessary assumptions and not seeing alternatives that would work
perfectly well.