Diagrams

[From Fred Nickols (981002.1725)]

Bill Powers (981001.0538 MDT)

...

My background in diagramming came not from servo analysis or operations
research but from analog computing and circuit design, where diagrams had
to correspond exactly to the physical setup -- in fact, the diagrams were
the "source code" for the actual setup. You couldn't get by with a vague
wave of the arms, or switch randomly back and forth between symbols for
functions and symbols for variables. I have to say this: you could not turn
your diagram into a working system: it simply leaves out too much. I
wouldn't know what kind of physical thing to put between the box you label
CEV and the one you label f=g(o) -- that line you label "output." And I
would have to say the same thing about the diagrams from control
engineering that you're talking about.

Chief Fire Control Technician (FTC) Fred here... :slight_smile:

I can "resonate" with Bill P's post above. While stationed at the White
Sands Missile Range I worked for a while in the Johns Hopkins labs with
the engineers. They would design a "tray" for use in the missile control
computers and express that design in a schematic. From the schematic,
I would build the tray.

Fun work, that...but no ambiguity in the diagrams, please... :slight_smile:

Regards,

Fred Nickols
Distance Consulting
http://home.att.net/~nickols/distance.htm
nickols@worldnet.att.net
(609) 490-0095

[From Bruce Abbott (981003.1015 EST)]

Bill Powers (981003.0648 MDT) --

For Bruce Abbott: I believe this is what you're trying to say.

By Jove, I think you've got it. Different arrangements of the same diagram
tend to emphasize different aspects of the system and its behavior. The
other part of my message is that these different arrangements have also
carried a different set of labels than those of PCT, and this can introduce
confusion if one does not take note of the differences in definition (e.g.,
"input" for "reference").

Regards,

Bruce

[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.

[From Bruce Abbott (981003.1355 EST]

Bill Powers (981003.0648 MDT) --

It strikes me, Bruce, that you may have been writing [CEV] where you meant
[EFF].

No, actually I've been somewhat inconsistent in my thinking about the CEV.
Sometimes I've thought of it as the distal variable "out there" in the
environment and the "input" as that variable's proximal representation at
the sensory receptor. At other times I've thought of it as a name for the
junction point where the effects of the output and disturbance variables
combine, or in other words as a function whose inputs are o and d and whose
output is i. In the conventional diagram this point is represented by
another circle (like that representing the comparator function) divided by
an X into quadrants.

You may recall that some time ago when we were discussing another matter, I
suggested that we could dispense with the CEV in the diagram and just use
qi, and you agreed that the CEV was unnecessary.

I left out the EFF in the interest of simplicity, as if o directly affected
i rather than through the mediation of the physical laws of the environment,
but of course it should be there for completeness. (I hadn't simply
forgotten it.)

                 ^ | +
                 > - v difference signal
                 +--------->-----------
         input | |
         signal | v
               [Fi] [Fo]
                 ^ |
                 > v
                qi<------[EFF]<----------qo------>side effects
                 >
                [Fd]
                 >
                qd

The label "side effects" in the diagram is accurate but may cause some
confusion. In my aircraft example, the change in elevator angle is a side
effect of the change in servo actuator position, but it is exactly what the
pilot intends to bring about by changing the servo's reference input.* Thus
I'm glad to see that the word "irrelevant" has been omitted. Some
side-effects are indeed irrelevant (e.g., the squeak produced as the
elevator moves), but some are the whole reason for controlling the
lower-order variable (perception of servo position as indicated by the
position sensor) in the first place.

[*and, of course, what the pilot _really_ cares about is not the elevator
position but the pitch-attitude of the aircraft, which is controlled by
means of elevator angle.]

Regards,

Bruce

[From Bruce Abbott (981003.1405 EST)]

Bill Powers (981003.1225 MDT) --

You didn't comment on my speculation that you have been confusing "CEV"
with "EFF".

Just did -- see Bruce Abbott (981003.1355 EST).

Bruce

[From Bill Powers (981003.1225 MDT)]

Bruce Abbott (981003.1015 EST)--

For Bruce Abbott: I believe this is what you're trying to say.

By Jove, I think you've got it. Different arrangements of the same diagram
tend to emphasize different aspects of the system and its behavior.

I'm not sure that "emphasize" is the right word. "Conceal" is more like it.
The behavior of the system is exactly the same for all these diagrams, and
the "emphasis" reflects what the viewer is prepared to understand, and what
to ignore. The chief effect of using these distortions of the PCT diagram
is that the viewer can seemingly support an incorrect concept of how
behavior works: that commands are translated into actions, or that stimulus
inputs cause responses. The standard PCT diagram emphasizes nothing; all
aspects of the model are clearly shown and tied consistently to explicit
aspects of the physical systems. When the model is depicted as S-R or
S-O-R, or as Command--->computed output, surely several aspects of the real
system are omitted, as if their absence made no difference (or the author
of the diagram didn't know there was anything missing).

The
other part of my message is that these different arrangements have also
carried a different set of labels than those of PCT, and this can introduce
confusion if one does not take note of the differences in definition (e.g.,
"input" for "reference").

This also is true, but I'll defend the PCT diagram as being the correct
one, and insist that the others are incorrect and confusing. The variable
qi is clearly an input to the controlling system; calling it an output is
not just a matter of choice, especially since there is already clearly an
output, qo, from the organism. The reference signal, because it is not
accessible from outside the organism, is not an "input" to the organism;
its proper name is "reference signal" or "reference variable", and it's
part of the internal operation of the organism. The difficulty that others
may have in translating from their own diagrams to the PCT diagram is their
own fault; it arises chiefly because of their lack of discipline in drawing
system diagrams.

You didn't comment on my speculation that you have been confusing "CEV"
with "EFF".

Best,

Bill P.

[from Autumn Winter (981003.1200 PT)]

[From Bill Powers (981003.0648 MDT)]

I have been wondering why there is just not one environmental function,
with inputs being qo and qd with the one output qi. What's the point in
two separate functions? Is there any harm in drawing the diagram as
follows? Is it a problem with modeling to just have the one function?

                  ^ | +
                  > - v difference signal
                  +--------->-----------
          input | |
          signal | v
                [Fi] [Fo]
                  ^ |
                  > >

                    > >

                  qi |

                    > v
                  [EFF]<------------qo-------------->side effects

                  >
                  >
                  >
                 qd

Cheers,

autumn

[From Bill Powers (981003.1345 MDT)]

Autumn Winter (981003.1200 PT)--

I have been wondering why there is just not one environmental function,
with inputs being qo and qd with the one output qi. What's the point in
two separate functions? Is there any harm in drawing the diagram as
follows? Is it a problem with modeling to just have the one function?

                  ^ | +
                  > - v difference signal
                  +--------->-----------
          input | |
          signal | v
                [Fi] [Fo]
                  ^ |
                  > >

                   > >

                  qi |

                   > v
                 [EFF]<---------------------qo----->side effects

                  >
                  >
                  >
                 qd

This says that the EFF makes qi a function of both qo and qd. This is
perfectly OK, because within that function qdand go can be given the
appropriate weights and functional effects. For example, the expression
qi = EFF(qd,qo) could be

qi = 12*qd^2 + 0.5*qo

As I'm sure you see immediately, this is the same as adding together one
effect of qd (12*qd^2) and an effect of qo (0.5*qo). So the answer to your
question is that it makes no difference at all whether you use two
functions or one, as long as the result is exactly the same.

Best,

Bill P.

ยทยทยท

Cheers,

autumn

[From Bill Powers (981003.1353 MDT)]

Bruce Abbott (981003.1355 EST)--

You may recall that some time ago when we were discussing another matter, I
suggested that we could dispense with the CEV in the diagram and just use
qi, and you agreed that the CEV was unnecessary.

In the simplest cases, yes. But the CEV, or that concept, is needed when
there is no actual external counterpart of the controlled perception.

For example, suppose that the perception is the distance between two
objects. There is one input function that detects the location of one
object, and another input function that detects the location of the other
object. So we have two perceptual signals, each corresponding to a location
(say, position on the x-axis). Now these two signals (each of which might
be under independent control) are fed into a higher-level input function,
where one is subtracted from the other to produce a new perceptual signal,
x3, equal to x2 - x1. This signal represents the distance between x2 and
x1. This new signal can obviously be controlled by varying the reference
signals for x1 and x2, but how do we refer to the external entity that
corresponds to the perception "of" x3? There is no entity outside the
system -- all we can see there are the two variables x1 and x2.

One obvious answer is to say that the observer also perceives the two
positions x1 and x2, and subtracts x1 from x2 to get a distance signal x3.
So to the observer, it appears that there really is a "distance" out there,
which varies according to changes in x1 and x2 in just the way distances
ought to depend on the positions of objects.

But this doesn't answer the question of how we should diagram the
_environment_ between the system and the observer of the system. Should we
simply label the space between x1 and x2 as the distance between them? That
would imply that the distance is really a physical thing in the
environment. For everyday practical purposes, that's probably just fine.
But if we want to remain mindful of this epistemological problem, it might
be better to use some special term for such derived variables. That is
where the CEV comes in. We can say that the distance is a "complex
environmental variable" which is a function of the actual physical
variables x1 and x2, which we are more comforable with saying are "really
there." We can accept that a control system is controlling a CEV even
though we deny that the CEV has any material existence.

Best,

Bill P.