S-R theory its own self

[From Bill Powers (920328.1030)]

Rick Marken (920328) --

Yes, phenomena first. It's hard to decide what is the phenomenon without
some kind of model in mind, and it's even harder to recognize when you're
unconsciously using a model to define the phenomenon instead of simply
looking at what you can in fact observe as opposed to imagine.

I think we need to clear out a lot of underbrush in this S-R vs. control
argument. We keep getting hung up on "what kind of system is this?" when
the answer to that question doesn't really matter. The basic problems can
be defined without getting inside the organism at all -- that comes later,
when you try to think of the sort of internal organization that could
account for what is seen externally. The most important problems have to do
with the basic naivete of the S-R approach. Prepare for a lecture (Rick,
you don't have to listen).


Greg Williams said "Let's forget about comparators that result in error
signals that influence the actions" of the system. This means not thinking
in terms of a particular implementation of the observed relationships, but
we can't ignore the phenomena that comparators, error signals, and output
functions are intended to explain.

Without a model, we assume that there's some sort of overall response to an
external variable. If the objectively measured state of the stimulus
variable is s, then the response r will be,

     r = A(s - s*)

The s* simply defines that state of the stimulus at which the observed
response is zero. This will depend in part on the measurement scale. We can
say that shivering rate v is a function of skin temperature t, so

   v = A(t - t*).

Clearly, shivering doesn't begin either at 0 Celcius or 0 Fahrenheit, so we
have to use t*, on the appropriate scale, to indicate the shivering
threshold temperature in the units we're using. The rate of shivering grows
as the temperature departs from the effective zero of temperature t*, and A
describes how rapidly shivering increases as temperature increases. The
observations show that A is a negative number, so that shivering will
actually increase only as temperature decreases below t*. Also, observation
shows that this equation only applies for t < t*.

In either S-R theory or control theory, we could refer to s* as the
reference level of the stimulus s. It is that point on the scale of
measurement of the stimulus at which the response just becomes zero. That
is the formal definition of a reference LEVEL in control theory, too: it is
an observational definition. The control model merely proposes a mechanism
for inserting a variable value for s* -- a "comparator" and a reference

Note that for an on-off stimulus, measured as 0 or 1, there is still an s*
-- it is still "that value on the scale of measurement of s at which the
response becomes zero." If the response is to the presence of the stimulus,
then s* is zero. If it is to the disappearance of the stimulus, then s* is

There are types of stimuli and types of responses in S-R theory. With
respect to stimuli, the least attention has been paid to continuous
stimuli. A very common definition of a stimulus is as an event, an impulse
taking place at one instant of time. Another one is "onset" or "offset",
which is defined as the first derivative of a continuous stimulus variable
undergoing a sudden change. Another employs a logical condition of some
sort, for example stimulus greater than (or not greater than) some
threshold value. Even more general concepts of a stimulus are used, such as
the presence of some abstract condition near the organism, like a "threat."
B. F. Skinner introduced rates of occurrance as a type of stimulus.

Responses likewise come in different types. The continuous response is
again neglected in general. Skinner's rates of occurrance are used. Event
responses are also common (first derivatives or changes). There is a
latching response, where the occurrance of a stimulus turns the response
on, and it then stays on regardless of further stimulation. A related type
of response is the "triggered" response, where a stimulus initiates some
series of actions that plays itself out regardless of further stimulation.
There are also switching responses, where the stimulus occasions a change
from one mode of action to another.

All of these modes of stimulation and response can be represented in the
general S-R equation, r = f(s-s*).

A basic question about these kinds of S and R concerns their objective
existence. Event-type stimuli and responses, for example, are almost always
artifacts of definition or experimental conditions. A rat may move toward
the entry of a maze and then start down it, all in one continuous flow, but
the only recorded event is the instant its nose breaks a light-beam. On the
way to the bait, the rat may sniff down side-alleys, pause, move slowly or
rapidly, until it finally enters the goal box, sniffs the bait, and moves
up to it and takes a bite. Only the instant of the bite is recorded as an
event. When I was being taught experimental psychology, it was emphasized
that experimental designs MUST provide for such measurements of critical
events, or else there would be no events to measure! I am therefore
suspicious about S-R relationships expressed in terms of events. I am
equally suspicious of most other ways of defining stimuli and responses,
for reasons that can be deduced from the rest of this lecture.

I have expanded the types of stimuli that can be considered, at least for
human subjects: 11 categories of them.

In modeling behavior from any viewpoint, it's necessary to be much more
careful about measures of either stimuli or responses than when making
armchair judgments. The human observer all too easily and inappropriately
projects human perceptions into the scene, especially for stimuli but
almost equally for responses.

Take the cockroach's "escape" response to a "threatening movement." The
words in quotes represent human interpretations of the situation derived
with human senses and interpreted by a human brain. The human being can go
on, and claim that the reason for this response is to promote survival of
the cockroach. But we'll keep it simple.

A modeler can't take such human interpretations into consideration. To make
a model, one has to provide the model itself with all the capacities needed
to sense the external state of affairs. How do we equip a cockroach to
detect a "threat?" This is impossible to do. Instead, we have to ask "What
would be stimulating the cockroach under the conditions where the human
observer sees a threat to the cockroach?" One answer is that the cockroach
might detect moving air displaced by the approach of a large object. It
might detect infrared radiation. It might detect light patterns on its
retina. It might detect vibrations in the floor.

None of those stimuli, of course, is a "threat." Only the human being would
associate them with such an abstract concept. The cockroach doesn't
classify these stimuli as a human being does. Human logic isn't involved in
the cockroach's response -- it doesn't think "every time stimuli of this
kind have occurred, something bad has (nearly) happened." All such
considerations are irrelevant to the cockroach. The cockroach does not
respond because of a threat. It responds because of wind, infrared, light,
or vibration.

Neither does the cockroach respond by escaping. There can be no "escape
response" in a cockroach -- that is a human classification and has no
relevance to the cockroach. The cockroach can move forward, backward, and
sideways at various speeds, and that is all. None of those movements
inherently constitutes "escape." The same movements are used in approaching
food, avoiding obstacles, and seeking dark damp places.

Escape can't be defined strictly in terms of one of the actions available
to the cockroach. It's a consequence, a relationship between the cockroach
and something else, that's affected by the way the locomotive machinery is
used. Whether these motions amount to "escape" depends partly on the
movements and partly on what is going on independently in the environment.
Escape, as seen by the human observer, is a very particular relationship
between the movements of the cockroach and the spatial relationships
between the cockroach and the "threat." The cockroach must move AWAY from
the threat.

Now "away" is a peculiar word. It seems to define a direction, but in fact
it refers to a relationship; the actual direction remains unspecified. In
order for the cockroach to move reliably "away" from a "threat," it must
somehow know WHERE THE THREAT IS. If we now look back at the proposed
stimuli (wind, infrared,light, and vibration), we can see that they are
inadequately defined. It is not wind, for example, that is the stimulus,
There is no sensory receptor that can report wind velocity AND DIRECTION.
Directional information must somehow be derived from WHICH receptor is
stimulated, not from the information carried in a particular sensory nerve

The escape response of locomoting in a specific direction, therefore, must
be based on sensory information that indicates both the existence and the
direction of the threat. The direction of the threat must translate into a
coordinated set of leg movements that carry the cockroach away from the
sensed direction of the threat. The velocity of movement, presumably, would
depend on the intensity of the stimuli.

By looking carefully at the details, we can see how the cockroach might
respond to various stimuli in a way that takes it in a direction away from
the threat. Stimulation of specific points on its body would generate
specific combinations of locomotive movements aimed toward the side
opposite to the points of stimulation. Thus the cockroach would accomplish
something a human being might classify as "escaping" (or at least
"fleeing") from a "threat", without any stimulus that specifically means
"threat" or any response that specifically means "escaping."

These details tell us that the characterization of actions as an "escape
response" is naive, being loaded with subjective interpretations and hidden
assumptions. By looking at the details in this way, we move much closer to
appreciating the world of stimulus and response that is relevant to the
cockroach, and away from the anthropocentric interpretation of that world.
Even though no model of the cockroach has been proposed, we have approached
the external situation in such a way that we could now begin modeling
without having to figure out how to model such categorical concepts as
"threats" or "escaping" inside a mere cockroach.

There is one final consideration. Having descended to the level of detailed
specific stimulations, we are now in a much smaller world, and we ought to
look at it on a much smaller time scale. To a human being, a puff of air is
simply an event, treated as it if occurred at one instant. But now that
we've shrunk down to the scale of the wind-detecting hairs on a cockroach's
body, we can experience the puff of air as it really occurs. There is first
a slight stir as molecules begin drifting coherently in one direction. The
flow picks up, and the hair bends slightly. A neuron here and there passes
its threshold of stimulation and little ticks begin, like popcorn just
starting to pop. The flow of air becomes stronger and stronger; the hair
leans more and more; the ticking increases to a rattle, then a buzz, then a
roar. Then the flow begins to slacken, the popcorn pops more sporadically,
and the wind gradually tails off to lower and lower levels until it is
still again.

This is the event called a "puff of air." During this event, a number of
responses were getting under way. At a certain level of buzzing of the
sensory receptors, the locomotive machinery began to turn the body of the
cockroach. This, of course, immediately began to alter the direction of
wind-flow around the body, affecting the wind velocity at the sensor beside
our vantage point. This modified the sensor signal, and the response, which
had been aimed at one final state, is now aimed at a slightly different
final state. All through this puff of air, the body is moving and the air
flow is changing as a result.

We can now see that our general equation for a stimulus-response
relationship, r = f(s-s*), is wrong. We have left out the effect of the
response on the stimulus. The equation should read,

             r = f(g(r) + s - s*)

where g is now the function expressing the addition of response effects to
the effective stimulus. While there's no general principle that says g(r)
MUST be a nonzero function, including it in the equation allows the
equation to cover those cases in which s is in fact affected by r.

In those cases where g(r) is not identically zero, the response affects the
stimulus while the response is in progress. This is the situation defined
as "feedback." There's no theory here. Either feedback is present or it's
not. If it's present, the only remaining questions are "how much?" and
"what's the sign?" The question is not "Should we take it into account?"
There is no choice about that if we want a correct characterization of the
S-R relationship.

Now we come to the crucial question in considering S-R theory. The question
is, how common is it for g(r) to be other than zero? This question is not a
theoretical one: it is a factual one. But we have to make sure to ask this
question of the right data.

If we view an S-R relationship as an escape response to a threat, using
naive human categorizations of the observable events and relationships, we
will see no g(r). That is, if I stamp my foot near the cockroach, creating
a threat, the cockroach's escape response will have no effect at all on the
stamping of my foot. The conclusion would be that there is no feedback and
this is a simple S-R phenomenon. That conclusion, as we have seen, would
simply be wrong.

Even if if we used a microanemometer to measure the puff of air itself
instead of the stamping of the foot, we would erroneously conclude that
g(r) = 0. We have to measure the puff of air where the measurement is
relevant: we must mount the anemometer on the cockroach's body next to the
hair in question. The only relevant movement of air is the movement
relative to the hair, in a frame of reference that is attached to the
cockroach. When we make that measurement, we find that g(r) is no longer
zero. There is feedback. In fact, the "escape response" drastically
modifies this relative air velocity while the response is in progress.

Now we are looking at the TRUE stimulus, not just at a human observer's
careless and anthropocentric evaluation of the surrounding environment. We
are seeing the physical process to which the cockroach is actually
responding, and it is quite different from the human observer's
interpretation. We are now looking at the world that the cockroach

In all of this long lecture the only "model" I have proposed was the idea
that sensory nerves response to stimuli. The rest has been concerned only
with information available to an observer outside the behaving system. I am
really talking about thoroughness and care in observing the details of
behavior. I am talking about becoming aware of the way human observers
carelessly impose their interpretations on global phenomena and fail to
think in terms of details that are all-important to arriving at the right

Control theory arises simply from looking carefully at the details of any
stimulus-response situation. It is, if you like, stimulus-response theory
done right.

I don't care in the least whether some responses are indeed unitary and
some stimuli are instantaneous, whether g(r) is zero or nonzero, or what is
found really to be the case. What I'm concerned with is getting away from
the sloppy habits of observation that have led to S-R theory as it now
exists, the projection of inappropriate kinds of interpretation onto the
very act of taking data, so that the wrong processes are noted and the
absolutely critical ones are glossed over as "mere detail." It's simply not
possible to understand behavior correctly if you stand back and generalize
about made-up variables having no proven relationship to the organism. The
reason that behavioral science has come up with such terrible unpredictive
uncertain results is not that behavior is that way, but that behavioral
science is that way. And behavioral science is that way because of sheer
sloppiness of observation.

I claim that in fact, g(r) is nonzero in essentially any kind of behavioral
situation that can be found. Every response alters the very stimuli that
lead to it immediately and strongly. The real stimuli, that is, not the
ones seen through the abstractions of casual and subjective observation.
Given my claim, the remainder of HPCT follows. Make any model you like of
the organism's interior. But it must be able to operate when g(r) is other
than zero.

Bill P.

[From Oded Maler (920331)]

[From Bill Powers (920328.1030)]

Your demonstration of the difference between S-R and Control
is a mixture of two orthogonal dimensions. Now I'm almost
convinced that (in principle) S-R and control are identical
phenomena. Some of the arguments against S-R are not against the
principle but against the practive of S-R psychologists. i'll try
to clarify:

The main argument in your post was a critique of "anthropormpization"
of perception and action, that is, characterization of events from
the point of view of an external observer rather than from the
perspective of the behaving organism itself. I agree with you completely
on this topic, and if behavioral psychologists usually ignore this fact,
this discipline is not worth much. Recall however, that if you climb up
above the most basic sensation, even your models cannot escape from
this problem as long as the categorization problem is unsolved.
When you say that someone controls for being far away from a "dog",
you can say *in principle* that "dog" can be somehow represented by
internal perceptual coordinates of that someone, by you'll never really
have such internal descriptions.

Even in this quote one can find a shadow of anthropormpization:

This modified the sensor signal, and the response, which
had been aimed at one final state, is now aimed at a slightly different
final state.

The second argument was the "essential" difference between

r=f(s,s*) and r=f(g(r),s,s*)

If you just add time indexes (continuous, of course..) to r and s,
and write


then, by assuming that s[t] is somehow influenced by r[t'] for all t'<t,
you can get an S-R formulation. If the organism can tell the difference
between changes in s caused from the outside and the same changes in s
caused by its own actions, it just means that you should replace s by a more
refined perceptual signal that can make these distinctions.