Blindmen II

[From Rick Marken (920821.1800)]

In response to popular demand (3 people asked) I am posting
the new version of the Blindmen paper (submitted to Psych
Science, copyright me) -- it's a bit more than 20Kb (sorry Gary).

Here it is:


The Blind Men and the Elephant:
Three Perspectives on the Phenomenon of Control

Richard S. Marken
August 12, 1992

  Abstract - The enthusiasm expressed by Simon
(1992) about current explanations of behavior may be greater
than is warranted by prevailing uncertainties about the nature
of the phenomenon to be explained. Behavior has been
described as a response to stimulation, an output controlled
by reinforcement contingencies and an observable result of
cognitive processes. It seems like these are descriptions of
three different phenomena but they are actually descriptions
of three different aspects of the same phenomenon -- control.
Control is like the proverbial elephant studied by the three
blind men; what one concludes about it, and how one tries to
explain it, depends on where one stands. It is suggested that
the best place to stand is where one has a view of the whole
phenomenon - be it elephant or control.

  In a recent article (Simon, 1992), Nobel Laureate
Herbert Simon asked "what is an 'explanation' of behavior?"
and answered with a tribute to the success of various
computer-based, dynamic simulations of psychological
processes. Simon's enthusiastic answer to his rhetorical
question was most heartening but somewhat optimistic from
the point of view of those, like myself, who believe that
psychology has yet to answer a more fundamental question,
namely, "what is behavior?". The tacit answer to that
question seems to be "behavior is what organisms do". But
it is possible to create circumstances where one can see every
aspect of an organism's behavior and still be unable to tell
what it is up to (Marken, 1989). Results like this suggest
that successful simulation of the appearance of behavior can
still fail to explain what an organism is doing. In order to
understand why this might be the case it is necessary to
examine the possibility that one answer to the question "what
is behavior?" might be "behavior is what organisms control"
(Powers, 1973).

  The behavior of living organisms (and some
artifacts) is characterized by the production of consistent
results in an unpredictably changing environment, a
phenomenon known as control (Marken, 1988). Control
can be as simple as maintaining one's balance on uneven
terrain or as complex as maintaining one's self-esteem in a
dysfunctional family. Control is a pervasive aspect of all
behavior yet it has gone virtually unnoticed in psychology.
What has been noticed is that behavior appears to be a
response to stimulation, an output controlled by
reinforcement contingencies or an observable result of
cognitive processes. Each of these appearances is what
would be expected if people were looking at control from
different perspectives. The situation is similar to that of the
the three blind men who were asked to describe an elephant;
the one near the tail described it as a snake, the one near the
leg described it as a tree trunk and the one near the side
described it as a wall. Each description gives an accurate
picture of some aspects of the elephant, but a false picture of
the elephant as a whole. If behavior involves control then
psychology, too, has given an accurate picture of some
aspects of behavior but a false picture of behavior as a

Closed-Loop Control

  The basic requirement for control is that an organism
exist in a negative feedback situation with respect to its
environment. A negative feedback situation exists when an
organism's response to sensory input reduces the tendency
of that input to elicit further responding. Negative feedback
implies a closed-loop relationship between organism and
environment; sensory input causes responding that
influences the sensory cause of that responding, as shown in
Figure 1. It is hard to imagine an organism that does not
exist in such a closed-loop situation because all organisms
are built in such a way that what they do affects what they
sense. Eyes, for example, are located on heads that move so
that what the eyes see depends on what the head does. To
the extent that what the head does depends on what the eyes
see (such as when the head turns in response to an attractive
passer-by) there is a closed loop; sensory input causes
responding (head movement) which affects the cause of
responding (sensory input). The feedback in this loop must
be negative because behavior is typically stable (organisms,
for example, do not normally exhibit the "run away"
behavior that characterizes positive feedback loops, such as
the "feedback" from a microphone that amplifies its own

Insert Figure 1 About Here

  The fact that organisms exist in a closed negative
feedback loop means that two simultaneous equations are
needed to describe their relationship to the environment.
These are given as equation (1) and equation (2), below.
The terms in these equations are summarized for reference in
the discussion that follows:

  s = sensory input variable
  r = response variable
  s* = reference value for sensory variable such that r = 0
when s = s*
  d = environmental variable
  k.o = organism function relating sensory variable, s, to
response variable, r
  k.e = environmental function relating environmental
variable, d, to sensory variable, s
  k.f = feedback function relating response variable, r, to
sensory variable, s

For simplicity we will assume that all functions are linear
and that all variables are measured in the same units.

  Equation (1) describes the effect of sensory input on
responding so that:

(1) r = k.o (s*-s)

This equation says that responding, r, is a linear function of
sensory input, s. The sensory input is expressed as a
deviation from the value of input, s*, that produces no
responding; s* defines the zero point of the sensory input.
Equation (2) describes the effect of responding on sensory
input. For simplicity it is assumed that responding, r, adds
to the effect of the environment, d, so that:

(2) s = k.f (r)+ k.e (d)

The variables r and d have independent (additive) effects on
the sensory input, s. The nature of the environmental effect
on sensory input is determined by the environmental
function, k.e. The feedback effect of responding on the
sensory cause of that responding is determined by the
feedback function, k.f.

  Equations (1) and (2) must be solved as a
simultaneous pair in order to determine the relationship
between stimulus and response variables in the closed loop
(the derivation is shown in the Appendix). The result is:

(3) r = 1/((1/k.o)+k.f) s* - k.e/((1/k.o)+ k.f) d

Equation (3) can be simplified by noting that the organism
function, k.o, transforms a small amount of sensory energy
into a huge amount of response energy (such as when a
pattern of light on the retina is transformed into the forces
that move the head). In control engineering, k.o is called the
"system amplification factor" or "gain" and it can be quite a
large number. With sufficient amplification (such that k.o
approaches infinity) the (1/k.o) terms in equation (3)
approach zero, so equation (3) reduces to:

(4) r = s*/k.f - (k.e/k.f) d

  Equation (4) is an input-output equation that
describes the relationship between environmental (stimulus)
and response variables when an organism is in a closed-
loop, negative feedback situation with respect to its
environment. The result of being in such a situation is that
the organism acts to keep its sensory input equal to s*,
which is called the reference value of the input. Equation (4)
shows that the organism does this by varying responses, r,
to compensate for variations in the environment, d, that
would tend to move sensory input away from the reference
value; this process is called control.

Three Views of Control

  All variables in equation (4), with the possible
exception of s*, are readily observable when an organism is
engaged in the process of control. The environmental
variable, d, is seen as a stimulus, such as a light or sound.
The response variable, r, is any measurable result of an
organism's actions, such as bar pressing or speaking. The
reference value for sensory input, s*, is difficult to detect
because an observer cannot see what an organism is sensing.
But s* is the central feature of control since everything an
organism does is aimed at keeping its sensory inputs at
reference values. Because these reference values are difficult
to detect it will not be obvious to an observer that an
organism is engaged in the process of control. What will be
obvious is that certain variables, particularly the
environmental and response variables and the relationship
between them, will behave as described by equation (4).
Thus, equation (4) can be used to show what control might
look like if one did not know that it was occurring. It turns
out that there are three clearly different ways of looking at
control depending on which aspect of the behavior described
by equation (4) one attends to.

1. The stimulus - response view. This view of control sees
behavior as a direct or indirect result of input stimulation.
An example of stimulus-response behavior is the so-called
"pupillary reflex" where changes in a stimulus variable
(illumination level) lead to changes in a response variable
(pupil size). The stimulus-response view is the basis of
several current approaches to understanding behavior, such
as the "synergistic" or "coordinative structure" theory of
motor coordination. Warren, Young and Lee (1986), for
example, describe a synergistic model of running in which
"vertical impulse is directly modulated by the optical variable
Ft..." (p.264). The behavior of running is seen in stimulus-
response terms; a stimulus variable, Ft, determines
("modulates") the value of a response variable, vertical
impulse. The stimulus-response view is also the basis of a
recent theory of attention (Cohen, Dunbar and McClelland,
1991) in which connections between printed word stimuli
and verbal responses in the Stroop effect are modulated by
connections in a neural network.

  Equation (4) shows that behavior will look like a
stimulus-response process when the reference value for
sensory input, s*, is a constant; for simplicity assume that it
is zero. Then responding is related to environmental stimuli
as follows:

(5) r = - (k.e/k.f) d

Equation (5) shows that, when there is a fixed reference
level for sensory input, it will look to an observer of
behavior as though variations in an environmental stimulus,
d, cause variations in a response, r. This is what we see in
the pupillary reflex where pupil size, r, is proportional to
illumination level, d. Of course, this relationship between
pupil size and illumination level is precisely what is required
to keep a sensory variable (sensed illumination) at a fixed
reference value (s* = constant).

  One's inclination when looking at an apparent
relationship between stimulus and response is to assume that
the nature of that relationship depends on characteristics of
the organism. Equation (5) shows, however, that when an
organism is engaged in control, this relationship depends
only on characteristics of the environment (the functions k.e
and k.f); the organism function, k.o, that relates sensory
input to response output, is rendered completely invisible by
the negative feedback loop. This characteristic of the
process of control has been called the "behavioral illusion"
(Powers, 1978).

2. The reinforcement view. This view of control sees
behavior as an output that is shaped by contingencies of
reinforcement. A reinforcement contingency is a rule that
relates outputs (like bar presses) to inputs (reinforcements);
in equation (4) this contingency is represented by the
feedback function, k.f, that relates responses to sensory
inputs. The reinforcement view is the basis of at least one
influential theory of generalization and discrimination
(Shepard, 1987). In a connectionist implementation of the
theory, a reinforcement contingency is used to shape the
formation of generalization gradients (Shepard, 1990). The
reinforcement view is also the basis of modern theories of
operant behavior. According to Domjan (1987) the
contemporary perspective on operant behavior focuses on
how contingencies "restrict freedom of action and ... create
redistributions of various types of activities"(p. 562). In
other words, contingencies shape (redistribute) responses

  Equation (4) shows that it will look like
contingencies (the feedback function) control responses
when s*, d and k.e are constants, as they are in the typical
operant conditioning experiment. In these experiments, s* is
the organism's reference value for the sensory effects of the
reinforcement. The environmental variable, d, is the
reinforcement, which, if it is food, is typically a constant
size and weight. The sensory effect of a reinforcement can
be assumed to be directly proportional to its size and weight,
making k.e = 1. So, for the operant conditioning
experiment, equation (4) can be re-written as

(6) r = S*/k.f - D/k.f

where S* is the constant reference value for sensed
reinforcement and D is the constant value of the
reinforcement itself.

  The only variable in equation (6) is the feedback
function, k.f, which defines the contingencies of
reinforcement. One simple contingency is called the "ratio
schedule" in which the organism receives a reinforcement
only after a certain number of responses. The ratio
corresponds to the function k.f in equation (6). When the
ratio is not too demanding it is found that increases in the
ratio lead to increased responding. More demanding ratios
produce the opposite result; increases in the ratio lead to
decreased responding (Staddon, 1979). Either of these
results can be produced by manipulating the relative values
of S* and D in equation (6). The important point, however,
is that the apparent dependence of responding on the
feedback function, k.f, is predicted by equation (6). To an
observer, it will look like behavior (responding) is controlled
by contingencies of reinforcement. In fact, the relationship
between behavior and reinforcement contingencies exists
because the organism is controlling sensed reinforcement;
responding varies appropriately to compensate for changes
in the reinforcement contingency so that sensed
reinforcement is kept at a constant reference value, S*.

3. The cognitive view. This view of control sees behavior
as a reflection or result of mental plans or programs. This
kind of behavior is seen when people produce complex
responses (such as spoken sentences, clever chess moves or
canny investment decisions) apparently spontaneously; there
is often no visible stimulus or reinforcement contingency that
can be seen as the cause of this behavior. The cognitive
view is the basis of numerous psychological theories that
propose mental algorithms to explain the appearance of
cognitive behavior. Examples of such theories include the
ACT (Anderson, 1983) and SOAR (Newell, 1990) models
of cognition, hierarchical models of the generation of
movement sequences (Rosenbaum, Kerry and Derr, 1983),
connectionist models of speech production (Jordan, 1989)
and schema models of expertise in problem solving
(Lesgold, A., Robinson, H., Feltovitch, P., Glaser, R.,
Klopfer, D. and Wang, Y., 1988).

  Cognitive behavior is most obvious when
environmental factors (such as stimulus variables and
environmental and feedback functions) are held constant.
When this is the case, equation (4) becomes

(7) r = s*/F + K

where F is the constant feedback function and K = (k.e/k.f)
d, a constant. Since s* is typically invisible, equation (7)
shows that there will appear to be no obvious environmental
correlate of cognitive behavior. An observer is likely to
conclude that variations in r are the result of mental
processes -- and, indeed, they are. But it is actually
variations in s*, not r, that are caused by these processes;
variations in r being the means used to get sensory inputs
equal to s*. Thus, chess moves are made to keep some
sensed aspect of the game at its reference value. When the
environment is constant, r (the moves) may be a fair
reflection of changes in the reference value for sensory
input. However, under normal circumstances r is only
indirectly related to s*, variations in r being mainly used to
compensate for variations in the environment that would tend
to move sensory input from the reference value, s*.

Looking at the Whole Elephant

  The blind men never got a chance to see the whole
elephant but if they had they would have instantly
understood why it seemed like a snake to one, a tree trunk to
another and a wall to the third. Psychologists, however, can
take a look at control and see why the appearance of
behavior differs depending on one's perspective. What is
common to the three views of behavior discussed in this
paper is the reference for the value of sensory input, s*.
Organisms behave in order to keep sensory inputs at these
reference values (Powers, 1989). They respond to
stimulation in order to keep the sensory consequences of this
stimulation from moving away from the reference value; so it
appears that stimuli cause responses. They adjust to changes
in reinforcement contingencies by responding as needed in
order to keep the sensory consequences of reinforcement at
the reference value; so it appears that contingencies control
responding. And they change their responding in order to
make sensory input track a changing reference value for that
input; so it appears that responding is spontaneous.

  What appear to be three very different ways of
describing behavior can now be seen as legitimate ways of
describing different aspects of one phenomenon -- control.
Each is just a different way of describing what an organism
must do to keep its sensory inputs at their reference values.
Indeed, once you know that the appearances called
"behavior" are merely the visible consequences of an
organism's efforts to control it sensory inputs, the problem
of explaining behavior changes completely, from an attempt
to build models that simulate the appearance of behavior (S-
R, reinforcement or cognitive) to an attempt to build models
that control the same sensory inputs as those controlled by
real organisms. In order to build the latter type of model it is
necessary to learn what sensory variables are actually being
controlled by organisms. This type of investigation cannot
be done by simply looking at the appearance of behavior.
Methods based on control theory can be used to test which
sensory variables an organism might be controlling at any
time (Marken, 1992). These methods make it possible to
take off the blindfolds and see the whole elephant -- the
phenomenon of control.


Given the two system equations:

(1) r = k.o (s*-s) and

(2) s = k.f (r)+ k.e (d)

we want to solve for r as a function of s. First, substitute
equation (2) for s in equation (1) to get:

(A.1) r = k.o (s*-(k.f (r)+ k.e (d)))

Multiply through by k.o to get:

(A.2) r = k.o (s*) - k.o k.f (r) - k.o k.e (d)

Move all terms with r to the left side of the equation to get:

(A.3) r + k.o k.f (r) = k.o (s*) - k.o k.e (d)

Factor r out of the left side of the equation to get:

(A.4) r (1 + k.o k.f ) = k.o (s*) - k.o k.e (d)

Divide both sides of the equation by (1 + k.o k.f ) to get:

(A.5) r = k.o/ (1 + k.o k.f ) s* - k.o k.e/(1 + k.o
k.f ) d

Finally, divide k.o out of the numerators on the right side of
(A.5) to get equation (3):

(3) r = 1/((1/k.o)+k.f) s* - k.e/((1/k.o)+ k.f) d


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Figure Caption

Figure 1. Closed-loop feedback relationship between an
organism, represented by the rectangle, and its environment,
represented by the arrows outside of the rectangle. A
sensory variable, s, influences responding, r, via the
organism function, k.o,. Responding influences the sensory
variable via the feedback function, k.f. The sensory variable
is also influenced by an environmental variable, d, via the
environmental function, k.e.

Figure 1