[From Bill Powers (981003.0648 MDT)]
For Bruce Abbott: I believe this is what you're trying to say.
Consider the standard PCT diagram for a moment, not as a control system
diagram but just as a map of what we pretty well know is there.
We know that there are certain physical variables to which the organism is
directly sensitive. These variables are indicated by a representative
member of that set, which we call qi, the input quantity: "Input" because
its effects go into the senses of the organism, and "quantity" because we
designate physical variables as quantities.
Receiving the effect of variables like qi is a set of sensory receptors,
connected to the afferent part of the nervous system. A representative
member of this set we designate as an input function, Fi: "Input" because
it receives effects coming into the nervous system, and "function" because
it converts a physical measure outside the nervous system into a neural
signal inside it. This function may be simple or complex.
Inside the nervous system, a signal arises from the input function: we
designate trains of impulses inside the nervous system as signals. These
signals generally travel upward in the brain, toward the cortex, but they
do this via "nuclei", clusters of interconnected neurons. And out of these
nuclei come not only upgoing signals, but "collaterals;" signals that cross
over laterally into motor nuclei. The motor nuclei have a layer that
receives both these collateral signals and signals descending from higher
systems. Where these signals converge, they uniformly have opposite
effects. If one of them is inhibitory, the other is excitatory. As a
result, the remainder of the motor nucleus receives signals representing
the difference between the inhibitory and excitatory effects. We will
follow this path back toward the periphery.
From the motor nucleus there come efferent signals going downward,
eventually reaching the actuators that convert neural signals into physical
effects outside the nervous system. We designate these as output functions:
"Output" because their effects pass out of the nervous system, and
"functions" because they carry out a conversion from neural signals into
physical quantities. A representative of this set of immediately affected
physical quantities we designate as qo, an output quantity: "output"
because it is generated by the nervous system and the actuator, and
"quantity" (rather than signal) because that is the term we use for
physical variables outside the nervous system.
The output quantity affects all other physical variables to which is it
lawfully related. Some of these other variables are closely dependent on
the output quantity; others only remotely. But some of them have effects on
the input quantity, through intervening properties of the environment, a
representative example of which properties we call the environmental
feedback function or EFF: "environmental" because it is part of the world
outside the nervous system, "feedback" because it feeds output effects back
to the input of the nervous system, and "function" because it converts the
state of one physical quantity into the state of a different one. The
remainder of the variables affected by the output quantity we designate as
side-effects.
This bring us back to the input quantity qi. However, we find that the
effects of the output quantity, via the environmental feedback function,
are not the only effects on qi. There are other physical variables on which
qi also depends, so the state of qi is determined by the net effect of all
influences on it: qo, acting through the EFF, and a representative member
of the set of all other influences on the input quantity, which member we
designate as qd, the disturbing quantity. Qd acts on qi via intervening
properties of the environment that we designate as Fd, the disturbance
function.
We therefore have the following diagram:
^ | +
> - v difference signal
+--------->-----------
input | |
signal | v
[Fi] [Fo]
^ |
> v
qi<------[EFF]<----------qo------>side effects
>
[Fd]
>
qd
Notice that we have essentially no choice about how to organize this
diagram. Its organization is given by what we know about the nervous system
and the environment. We could stretch it and distort it and turn it to
various orientations, but its components and internal connections are
givens. It is only a partial diagram of the nervous system and environment,
but it forms a unit that is repeated over and over with variations on the
same theme.
Now the question becomes, what does an organizational unit like this do?
Well, there is no one answer to that. What it does depends on the forms of
the various functions. If they have one kind of forms, we will see all the
variables around the loop oscillating, whether or not there are any inputs
from outside the loop. And of course if they have another kind of form, we
will have a control system that varies its output qo so as to keep the
signal from Fi matching the signal coming down from above.
Any theory of behavior must start with this diagram, because it shows only
the verifiable elements that go into the relationship between nervous
system and environment. The form above is the most general, giving no more
emphasis to one part of the diagram than to any other.
However, depending on the application and the interests of the theorist,
this diagram can be topologically transformed to emphasize certain
relationships while downplaying others. Here we will assume that the
functions are such that this diagram represents a control system.
For example, suppose the theorist has in mind a command structure, in which
the signal coming down from above is the command, and another variable in
the system is the commanded behavior. Since we would prefer that the
commanded behavior have some predictable relation to the command, the only
candidate for it is qi, the variable that corresponds to the signal that is
controlled. The output quantity qo is not a candidate, because it will vary
whenever disturbances occur, independently of the "command" signal, and in
fact will show only a statistical dependence on the command signal. So we
now draw the diagram like this:
> COMMAND
..........v.....................
+-->
> >
> v
> [Fo]
> >
[Fi] v
> qo ---> side effects
> >
> v
> [EFF]
.....|....|.....................
+<--qi COMMANDED BEHAVIOR
^
>
[Fd]
^
>
qd
Since qd has no significant effect on qi, that part of the diagram can
easily be overlooked and omitted.
It strikes me, Bruce, that you may have been writing [CEV] where you meant
[EFF].
This is the "cognitive" form of the diagram: commands higher in the brain
pass through some sort of computing function (between the dotted lines)
that produces the desired result.
Now let's consider the other main version of this diagram. A salient effect
on the actions of this system comes from the disturbance, qd. When the
disturbance changes, the output quantity qo changes so that its effects on
qi, mediated by the EFF, oppose and essentially cancel the effects of qd on
qi mediated by Fd. This can be drawn as follows:
O
O R G A N I S M
S . ........................ R
S T I M U L U S . |bias . R E S P O N S E
. v .
qd --->[Fd]---->qi--->[Fi]----sig-->[ ]--->[Fo]-->qo----> side effects
^ . ^ . |
> . | ....................... |
+<-----------[EFF]-<---------------+
Now we see the causal chain as starting with the remote disturbing
variable, proceeding through the proximal variable qi, entering the sensory
inputs, going through the organism, and ending with the output quantity and
all its various effects on the environment. The only effect of the former
"command" signal is to bias the overall response, changing the value of the
stimulus at which the response just goes to zero.
The feedback connection mediated by [EFF], while almost always present, can
easily be ignored. It can also be deliberately broken, in which case the
effect of S on R will not be the normal one.
In both of these transformations of the basic diagram, exactly the same
diagram is involved, but with its parts moved around to create different
overall visual impressions. In both cases, the feedback connection is
downplayed, with the main trend of the diagram emphasizing an overall
(apparent) lineal causal chain.
Best,
Bill P.