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Newsgroups: bit.listserv.csg-l
Date:         Mon, 14 Dec 1992 02:17:33 -0600
From:         Tom Bourbon <TBOURBON@BEACH.UTMB.EDU>
Subject:      Error; Brains; Lesions

From: Tom Bourbon  (921214 01:30 CST)

IMPORT THIS DOCUMENT WITH HARD CARRIAGE RETURNS INCLUDED

     This is a discussion of simulations I ran to check my
understanding of issues raised in several recent threads on CSG-L:
control systems control error; PCT must "look at the brain" (i.e.,
neuroscience) or die; and deficits in reaching as sequelae of brain
lesions pose a challenge to PCT.  I used the simulations to clarify
my thinking on those issues taken together, not separately.  I do
not refer to specific posts by the various people who contributed
to those threads.  I cannot post graphic output of actual results
of the simulations, each of which includes 1800 data points for
each variable, but I include a stylized rendering in "ASCII
graphics" that in no way misrepresents the results.

     In the simulations I used an old (circa 1985) program in which
a single PCT loop models a person who uses a control handle (H) to
keep a cursor (C) and target (T) in a preselected relationship on
a computer screen, the kind of performance PCT modelers refer to as
intentional or purposive action by the person.  Although I fully
comprehend the logic and algebra of the relationships, as they were
posted by Rick Marken, for example, I am more comfortable when I
see them run in simulation.  In all of the simulations I describe
here, the reference signal calls for the cursor to remain even with
the target which moves uniformly up and down on the screen tracing
a triangular wave of vertical position vs time.  In the program,
ref. sig. = [C - T = 0].

     I modified the old program so that half way through any given
run, I could introduce a disturbance (d) directly to one of the
three signals in the model:  dr for the reference signal, dp for
the perceptual signal, or de for the error signal.  At the
beginning of all simulations, each d was set to 0.  During a given
simulation, half way through the run, one d assumed a value of +3.

     Figure 1 (in ASCII, margins 1", hard returns included) is a
diagram of connections in the model and its simulated environment.
All coefficients are assumed to be 1, except for the "integration
factor," k, which was set to a value estimated from one of my
actual runs on the tracking task.  (Incidentally, the unaltered
model had recreated my run at the familiar correlation > .99)  The
person is modeled as a single control loop, controlling the
perceived spatial relationship between C and T.

************************************************************

Figure 1:  A person modeled as a relationship-level control system,
using a single control handle (H) to affect the position of a
single cursor (C) relative to a target (T) during pursuit tracking.
In the model are three functions (c = comparator, i = input
function, o = output function) and three signals (r = reference
signal, p = perceptual signal, e = error signal).  Also in the
model are three possible disturbances, one for each signal (dr =
disturbance to r, de = disturbance to e, dp = disturbance to p).
Each d adds to its respective signal and the sum conducts
downstream to the next function.  In the simulated data that
accompany this text, all three disturbances are initialized to 0.
In the environment are two independent disturbances, one acting on
the cursor (dC), one on the target (dT).  For the present examples,
dC = 0, and dT is a triangular function of time shown in Figure 2.


                                ref. sig. (r) [C - T]
                                   |
                                   |<------dr
                                   |
                                   | r + dr
                                __\|/__
                    p + dp     |       |   error sig. (p - r)
             .---------------->|   c   |--------------.
             |                 |_______|              |
   dp------->|                                        |<------de
             |                                        |
             | percept. sig. (p) [C - T]              | e + de
          ___|___                                  __\|/__
         |       |                                |       |
         |   i   |                                |   o   |
         |_______|                                |_______|
          /|\ /|\                                     |
           |   |       _______          _______       | -k*(e+de)
           |   |      |       |        |       |      |
           |   |------|   C   |<-------|   H   |<-----|
           |          |_______|        |_______|
           |             /|\
        ___|___           |
       |       |          |
       |   T   |          dC
       |_______|
          /|\
           |
           |
           dT

*********************************************************

     In the computer program (written in Turbo Pascal 3.01) the
following two steps implement the unmodified model used in the
first half of each simulation:

H := H - [k * (p - r)]
C := H + dC

where

p := C - T
r := [(C - T) = 0]
e := p - r.

Half way through the simulation, a disturbance is added to one of
the signals as a constant.  The d remains in effect through the
remainder of the run.  The following program steps implemented the
disturbances:

     For the reference signal:  r := r + dr.
     For the error signal:  e := e + de.
     For the perceptual signal:  p := p + dp.

In every case, d = + 3.

CASE 1:  Disturbance to the reference signal.  The stylized results
are shown in Figure 2.

**********************************************************

Figure 2.  Stylized ASCII representation of simulation of pursuit
tracking by a single PCT model when the reference signal was
disturbed during the second half of the simulation.  The top half
of the figure shows vertical positions of the target (T) and cursor
(C) on the computer screen at successive times (up = toward the top
of the screen); the bottom half, displacements of the control
handle (H) at successive times (up = away from the simulated
person).  During the first half of the simulation, C = T; during
the second half, C = T +3, or C - T = +3.  The position of C
relative to T is explained in the accompanying text.


                             C---->/\        /\
               /\        /\       //\\      //\\
    T & C---->/  \      /  \     //  \\    //  \\
             /    \    /    \   //    \\  //    \\
            /      \  /      \ //      \\//      \\
           /        \/        \/  T---->\/        \



                                   /\        /\
               /\        /\       /  \      /  \
      H------>/  \      /  \     /    \    /    \
             /    \    /    \   /      \  /      \
            /      \  /      \ /        \/        \
           /        \/        \


  Time ----------------------------------------------->


********************************************************

     For the first half of the simulation, r = [(C - T) = 0], and
the model maintained that relationship.  At mid-run, dr = +3.  The
effective reference signal at the comparator became  (C - T = +3).
The model achieved that result -- the handle shifted to a range of
movement centered three equivalent screen units above the middle of
its range and the cursor moved to and remained at a position three
screen units above the moving target:  C = T + 3, or C - T = +3.


CASE 2:  Disturbance to the error signal.  The stylized results are
shown in Figure 3.

**********************************************************

Figure 3.  Stylized ASCII representation of simulations of Case 2
and Case 3, pursuit tracking by a single PCT model when either the
error signal, or the perceptual signal, respectively, was disturbed
during the second half of the simulation.  The top half of the
figure shows vertical positions of the target (T) and cursor (C) on
the computer screen at successive times (up = toward the top of the
screen); the bottom half, displacements of the control handle (H)
at successive times (up = away from the simulated person).  During
the first half of the simulation, C = T; during the second half,
C = T - 3.  The position of C relative to T is explained in the
accompanying text.



               /\        /\   T--->/\        /\
    T & C---->/  \      /  \      //\\      //\\
             /    \    /    \    //  \\    //  \\
            /      \  /      \  //    \\  //    \\
           /        \/        \//      \\//      \\
                               /  C---->\/        \



               /\        /\
      H------>/  \      /  \       /\        /\
             /    \    /    \     /  \      /  \
            /      \  /      \   /    \    /    \
           /        \/        \ /      \  /      \
                               /        \/        \

  Time ----------------------------------------------->


********************************************************


     With de = +3, the effective error signal is e + 3.  When the
product of k*(e + de) is subtracted from the former position of the
handle, the handle moves three units lower in its range of movement
and the cursor is at C = T - 3, or C - T = -3.  The perceptual
signal, p, becomes -3.  (This model treats the entire person as a
relationship controller, so the output of the input function is the
perceived relationship, [C - T].)  The reference signal remains
[C - T = 0], so coming out of the comparator, the error signal is,
p - r = -3 - 0, or, e = -3.  When de is added to e, farther down
stream, the effective error signal into the output function
becomes: e + de = -3 + 3 = 0, and the system no longer changes the
relationship between C and T.  In this case, e + de has become a
virtual reference signal that leads to exactly the same results in
the ENVIRONMENT as would be produced by changing the reference
signal to [C - T = -3], an effect that would also be produced by
disturbing the reference signal with dr = -3.  However, with regard
to the perceptual signal INSIDE the model, dr and de lead to
different results.  When dr is applied, p = r; when  de is applied,
p = r -de, and the perceived relationship [C - T] is NOT as
specified in the reference signal.  More on this later.

CASE 3:  Disturbance to the perceptual signal.  The stylized
results are also shown in Figure 3.

     The effective perceptual signal into the comparator is p + 3,
therefore, e = p - r = +3 - 0 = +3.  When the product of k*e is
subtracted from the former position of the handle, the handle moves
three units lower in its range and the cursor is at C = T - 3, or
C - T = -3.  Coming out of the input function, the perceptual
signal, p, becomes -3.  The disturbed perceptual signal is:
p + dp = -3 + 3 = 0.  Now p = r, or (p - r = 0), the relationship
specified in the reference signal.  The system has eliminated the
effect of dp on p, going into the comparator, but the relationship
between C and T on the screen is not the same as it would be were
there no disturbance on the perceptual signal.

A BRIEF DISCUSSION

     I knew the three disturbances should have DIFFERENT effects on
signals and their relations INSIDE the model, but I did not expect
that all three would have either SIMILAR or IDENTICAL effects on
variables OUTSIDE the control system.  An observer, builder, or
user of control systems could easily observe results in the
environment and conclude there were no differences between the
"treatments" or the effects of the three disturbances.  Inside the
model, that is not true.

     Another surprise was that, if de = +3, then p - r = -3.  The
system never brings the perceived relationship to the value
specified in the "real" reference signal.  Would that happen in
anything but a single-loop system?  Andy Papanicolaou and I
discussed this result and concluded that any system that performed
this way with regard to any critical variable would not survive.
In hierarchical systems with a level above the relationship level,
changes should ensue -- in the error signal from above that sets
the reference signal for relationships; or in the output gain of
the system (k), perhaps via a reorganizing loop that randomly
tinkers with gain.  There may be other possibilities.

     As for whether PCT must "look at the brain" (i.e.,
neuroscience) or die, the reverse seems true.  Simulations like the
ones here ought to provide grist for neurophysiologists.  For
example, what would be the results if someone were to study a
"simple" laboratory preparation, with Aplysia the marine snail for
example, while at least provisionally adopting the idea that the
creature controls the sensed states of certain variables.  In such
a preparation, after the experimenter confirmed that the creature
controls ANY variables, all of the disturbances I described here
could be applied to precisely-mapped neurons and the results
observed.  With the results of the PCT simulations as exact
quantitative predictions, the PCT model would be subjected to the
most rigorous of tests, and neuroscience might benefit from a model
intended to explain how organisms purposefully create and maintain
perceptions.

     On the question of whether deficits in reaching, as sequelae
of brain lesions, pose a challenge to PCT, I will depart from my
stated plan of not mentioning sources from the net.  Gary Cziko
raised the question in a brief account of an interesting clinical
case, and Mark Olson rushed to offer the example as evidence that
PCT must "look at the brain."  I think the reverse is true; brain
science must look at PCT.  In my simulations, all three
disturbances led to the cursor missing the target "by a little
bit:"  In one case, it went beyond the target; in two others, it
"fell just short," a result that sounds a bit like the clinical
report Gary cited.  The clinical "deficit" seemed to have something
to do with "mistakes" in controlling relationships.  Did anyone ask
the man if things looked alright when (outwardly -- where
clinicians and other observers reside) he ended up in the wrong
place?  Wouldn't it be interesting if he said, "yes!"

     Did the man's lesions alter or disturb a reference signal,
making it negative compared to what it was before?  Did the lesions
add positive disturbance to an error signal or a perceptual signal?
Did the lesions destroy one of the functions in a control system,
or modify its workings, or disturb or disrupt a path carrying one
of the signals in a control system?  Knowing that a lesion was in
some general part of the brain, and that outward appearances of the
person's behavior changed, tells us nothing specific about the
reasons for the changes; but the process of modeling and simulating
the control of relationships raises some possible explanations
that, to my knowledge, neuroscientists and neuropsychologists have
not considered.  Until research and theory in the neurosciences
catch up with the science of control by living systems, "looking at
the brain," or looking to the neurosciences, for evidence that will
change the nature of the model in PCT, probably will not be
necessary or fruitful.

Until later,

Tom Bourbon                             e-mail:
Magnetoencephalography Laboratory       TBOURBON@UTMBEACH.BITNET
Division of Neurosurgery, E-17          TBOURBON@BEACH.UTMB.EDU
University of Texas Medical Branch      PHONE  (409) 763-6325
Galveston, TX 77550                     FAX    (409) 762-9961 USA
Comments: Gated by NETNEWS@AUVM.AMERICAN.EDU