[From Bruce Nevin (980709.0923 EDT)]
In the following diagram, the two control systems are Cooperator A and
Cooperator B. For each, there is a higher-level comparator (Ca+ and Cb+)
controlling inputs passed up to it from two lower-level control loops.
ra+
>
pa+ --> Ca+ -->
^ |
>_____________|__
> > \
> _______|____\__________
> > \ |
> ra \ ra'={rb}
> > \ |
pa --> Ca --> pa'--> Ca' -->
···
> > > Cooperator A
sa> >oa> >sa'| |oa'|
--------------------------------------------------------
qia <---- qoa ^ qoa'
^ \ effa |
> \ \
---\ ------>eff(ab)<----\-----------
\ \ | Environment
\______ \_______ |
> > >
> effb | V
qob' V qob ------> qib
--------------------------------------------------------
>ob'| |sb'| |ob| |sb| Cooperator B
> > > >
<--|Cb'|<--pb' <--|Cb|<-----pb
> \ | |
rb'={ra} \ rb |
>_________\__________| |
\ | |
\__|_____________|
> >
> V
<-- Cb+ <-- pb+
>
rb+
Actually only one of the lower loops is completed through the environment
for each control system, through the environment by an environmental
feedback function effa or effb, respectively. Through the other,
incompleted loop, each control system perceives but is unable to control
the environment variable that the other is controlling. There is no
environmental feedback function between any attempts qoa' of Cooperator A
to control qib, the variable controlled by Cooperator B; and conversely.
The actual outputs qoa' and qob' will consequently be small or null, since
they cannot affect the other's controlled variable.
However, there are causal effects through the environment between the two
controlled variables. This is represented by eff(ab). Because of this
influence of qia on qib, and of qib on qia, each cooperator has an
influence on the variable that the other is controlling. This is the
fundamental reason that control systems come to cooperate. The alternative
is conflict because of an environmental interdependency between their
respective controlled variables.
The reference perception for controlling the other's controlled variable
(rb' for qia and ra' for qib) is a replica in imagination of the reference
perception that the other is using for that controlled variable. This is
represented by the notation rb'={ra} and ra'={rb}. The process of imagining
the other's intention is covered by hand-waving in the form of curly braces.
There is no internal connection from the error output of the incomplete
loop over to the loop that is closed through the environment. I believe
that this is not needed. The environmental interdependency eff(ab) provides
one connection, and the higher-level loop provides another. The
higher-level loop adjusts output through the environmentally closed loop
until error in the open loop is reduced. This is why I have labelled the
environmental interdependency of qia and qib as a feedback function, since
it provides environmental feedback helping to close the loop for each of
the cooperators.
Example: A and B are carrying a couch. B, who is taller than A, has a back
problem and is unable to bend over without pain. If the couch is not level
between them, each of them finds it more difficult to grip. B expends more
effort to raise his end to elbow height, or A expends more effort to walk
with knees bent, or both, or both alternating.
Bruce Nevin