Good topic for Closed Loop. I'm continually amazed at all the things you
do, and so well. You would make a great role model for any 4 people.
ยทยทยท
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Arm model:
I'm putting in a second kinesthetic level of control. This level perceives
the joint angles in such a way as to make radial movements relatively
independent of movements in elevation. Also I'm putting "size constancy"
into the visual perceptions, by making the x and y perceptions proportional
to the distance perception: this will tend to make the gain of visual
control loops constant for objects at various distances, and may help with
the end-point control mode. This second level will provide a place to add
the "artificial cerebellum" which you've already seen, to adapt the
stabilization to various load conditions. I don't think I'll actually add
the A.C. in this version.
Cockroach, SR/Control:
You have deduced that cockroach movement will affect the influence of >the
air- puff on the hairs. But is the loop continuously closed? You >have NOT
deduced that the movement of the cockroach is influenced by >the changes in
influence of the air-puff on the hairs during the >movement. That is the
part of the feedback loop (if it is a loop) >inside the organism.
You're right that verifying the external feedback doesn't prove that the
organism acts continuously. But it's possible to set up a general model
that includes the feedback connection, and deduce the actual input-output
transfer function (guessing, of course at the exact effect of movements on
the wind-sensing hairs). The model of the cockroach's input-output function
that makes the model behave the most like the cockroach, based on the
ACTUAL input, will show whether the response is modified by the effect of
behavior on the input while the response is occurring.
This is what makes the negative feedback control model more general than
the SR model. If all the components of the model are left general, with
parameters to be determined by the data, then in principle the parameters
that result will show whether SR theory is adequate. For example, if the
output-to-input connection is in fact missing, then the best-fit model
should evaluate the feedback connection g(r) as zero. That's in principle,
of course -- in practice that might be difficult.
There are some behavioral experiments that would make matters clearer. For
example, if the puff of air is modulated to prevent the movement of the
body from having the normal effect on relative air speed, then the final
direction of "escaping" should change. Or if an obstacle is placed so that
the escape response would make the cockroach collide with it, we could tell
whether the direction of escaping would be modified to avoid the obstacle.
We could put the cockroach into a passageway too narrow to turn around in
and give it a puff in the face. We could glue a thread to the cockroach and
just as the puff occurs, give it a tug that aids or opposes the initial
turn. We could glue the cockroach's body to a support and watch what the
feet do as the puff of air arrives from various directions. We could use a
strong puff of air from the side applied so it aids or opposes the turning
of the body, and see if the cockroach compensates for the spin induced by
the puff of air. We could put a wall downwind from the cockroach with a
hole through it and see if the cockroach modifies its direction of running
to go through the hole wherever the hole is placed. We could put the
cockroach on a slick Teflon surface and see if it compensates for the
slipping of its feet.
I think that if anyone seriously wanted to test the choice between an open-
loop and a closed-loop escape response, it would not be hard to think of
experiments that would settle the question. Any takers out there among the
bug people?
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There is a potentially good reason why evolution might "just" say "get
away": the neural overhead associated with PCT-circuitry might be more
"costly" than than associated with chain-circuitry.
What overhead? It's no simple matter to arrange for an open-loop behavior
that turns the body by an amount that depends on the direction of the
threat, then institutes running movements with the same legs. You have to
have wind-sensing hairs all around the body. Then you have to connect them
to a central computer so that if the wind is from angle A relative to the
direction of the body, the turning-pattern generator starts lifting and
moving the legs in just right sequences and by just the right amounts to
produce a turn of 180 - A degrees. Then when this sequence of leg movements
is finished, the same computer has to produce signals that cause fast
forward locomotion for some period of time. On a bumpy surface.
All of this would be FAR easier to do with feedback control. No accurate
computations would be needed. The only thing that's less complex about the
"just get away from there" explanation is the thought process of the
explainer. The extra overhead is in the S-R model, not the feedback control
model.
The less-giant leap which actually seems to be the one taken by several
nonPCTers is that actions (I think that is what you meant, not PCT-type
behavior, which would make the "giant leap" simply impossible by
definition!) DO immediately influence the "stimuli," but often that
influence doesn't affect the trajectory (taken generally) of the >action.
"Often" is a pretty giant leap. "Sometimes" I might buy as a possibility.
But considering the defects of observation behind all S-R models, I would
rather approach an unknown situation assuming control by feedback, and let
the experiment show this is wrong. As Mary observed while reading this
morning's posts, you always approach data with some model in mind. The S-R
model is a pretty poor one to assume.
Mary also pointed out that human beings sometimes seek out situations in
which there are trajectories uncontrollable by the actor once they are
started: golf, bowling, baseball, basketball, archery, and skeet-shooting
would be examples. All that can be controlled during the action is the
delivery or initial aim in these cases; long-term control can be achieved
only by repeated tries with small adjustments of reference signals between
them. Controlling in this way is very hard and slow, which seems to be the
appeal -- achieving control is very difficult so that when it's achieved,
the person feels that something worthwhile has been accomplished. If
control were easy there wouldn't be any element of a game or competition in
it. If human beings could make every drive in golf a hole-in-one, nobody
would play golf. On the other hand, if survival depended on playing any of
these games perfectly, the games still wouldn't be played, but for a
different reason. There would be nobody to play them.
If a pre-calibrated chain mechanism contributed to higher-level >control-
of- perception, it wouldn't be resisted. And if there were no >reference
levels at the level of the chain mechanism, it wouldn't act >like a
disturbance.
I don't think you pondered this thought long enough. If a pre-calibrated
act contributed to a higher-level control process, it could do so only with
one setting of the higher-level reference signal. With a different
reference signal, the precalibrated act would be too much, too little, or
in the wrong direction. Remember that ACTS do not have consistent effects
on OUTCOMES. The same act can have opposite effects. On one occasion of
achieving a given outcome, a higher system might increase the output; on
another occasion, it would produce the same outcome by decreasing the
output. A chain mechanism can't do that.
I showed that there ARE reference levels in chain mechanisms: that point on
the measurement scale of the stimulus at which no response is produced. But
with or without reference signals, chain responses disturb things -- what
difference does having a reference signal make?
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No, we should be looking for higher-level loops. And setting aside the
claim that all control is continuous.
I'm still very unhappy with calling anything but negative feedback effects
"control." Control implies a reliable repeatable outcome. In real
environments, outcomes are subject to disturbance independently of the
action of a behaving system. Only a negative feedback system can continue
to produce the same outcome despite these disturbances.
By calling any other mode of action "control" you're throwing away the
central phenomenon and going back to loose qualitative talk of the kind
that has characterized the behavioral sciences for too long. I don't want
to have anything to do with that.
If some organisms respond without feedback, then they must be very simple
organisms living in very protected environments. Without this kind of
limitation on the organism's abilities and this careful protection against
disturbances, such systems would not be sufficient to allow survival to the
age of reproduction. There might be such simple organisms and environments.
I don't know. But if there are, those organisms do not survive by
controlling anything. They survive in spite of not controlling anything.
If higher level control loops exist which modify lower-level open-loop
responses, then control will exist at the higher level, but not at the
lower level. This can work only if the inaccuracies and inappropriateness
of the lower-level responses are unimportant. The vestibular-ocular reflex
is very inaccurate and can't be adjusted very fast. The organism could get
along without it altogether. It doesn't matter if the reflex causes the eye
to miss the target by 20 degrees one way or the other - the oculomotor
control systems will immediately make the eye direction exact. All the
reflex does is make the locking-on slightly quicker.
When the outcome matters, control is continuous. You don't drive a car at
high speed on a mountain road by looking out the windshield and giving the
wheel a twitch once per second or so. If you did that your control
bandwidth would be far too low and you'd go off the road or run into those
Falling Rocks.
The biggest problem with allowing the behavior of open-loop systems to be
called control isn't that there are no open-loop systems. It's that
behaviors that actually couldn't happen without control, true feedback
control, can be conceived of as open-loop behaviors and still be called
controlling. The number of closed-loop phenomena erroneously interpreted as
open-loop greatly exceeds the number of correctly identified open-loop
phenomena.
The observer recognizes control by its effects: some outcome is produced
over and over in a highly variable and uncooperative environment. So the
observer correctly, intuitively, identifies the behavior as control
behavior. But not realizing that feedback is required in order to explain
the observed control behavior, the observer thinks that the same result
could be achieved by an open-loop SR system. So the observer names the
behavior in terms of its outcome: an "orienting response" or a "problem-
solving response," and thinks an explanation has been found. In the
observer's mind there's a notion that SOMEHOW there are stimuli that can
produce the observed controlled outcome just by going through some magical
black box. The observer doesn't see anything wrong with the idea that a
stimulus input simply causes the outcome to occur. After all, the observer
can see the connection. What do we need with all these complicated feedback
loops anyway?
Look how easy it is to say that a threat causes the cockroach to run
"away." Look how easy it is to be SATISFIED with that concept. If you can
see the stomping foot and you can see the turn and the scuttling away, why
isn't that enough to show that there's a simple response to a simple
stimulus? Unfortunately it IS enough for many, many people. They aren't
looking for closed loops. They have in mind some simple fuzzy connection
diagram that goes between input and output, and because they haven't
stopped to ask themselves in detail what those connections would actually
have to accomplish, they don't see any difficulties. They assume that
somehow the necessary circuits would exist and would accomplish what is
observed.
Most of the names we have for behaviors are the names of outcomes, not
actions. Even such a simple word as "walking" names an outcome. All that an
organism with muscles can do is push, pull, twist, and squeeze. Everything
else is outcome. When you realize this, you have to realize that there
can't be any simple connection between an input and an outcome, even though
it's easy to imagine simple connections between a stimulus and push, pull,
twist, or squeeze. So when you imagine a direct connection between a
stimulus and an outcome, you're implying far more complexity in the
intervening processes than is obvious. If you're aware of that complexity,
fine: if you're not, you're just waving your arms.
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Oded Maler (920331) --
Some of the arguments against S-R are not against the principle but
against the practice of S-R psychologists.
True, but I have plenty against the principle, too: see above.
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 used the term "anthropocentrism," which is a little different.
Anthropomorphism is OK when you're trying to understand a human being,
although some might prefer "gynomorphism." It's inappropriate when you're
trying to understand another species, because there's no guarantee that
another species lives in a perceptual world like ours.
Anthropocentrism, on the other hand, means to me being centered in the
observer instead of the behaving system, without realizing it.
... 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.
This is right, and it's always a problem. In principle we can apply The
Test to find out what perceptions another organism is controlling. But
finding candidates for The Test that aren't picked from the confines of
one's own perceptions is very difficult, maybe impossible without aid of
some sort. How would we recognize a controlled variable that we can't
perceive? The only answer I can see, and it's a very long-term one, is to
devise unbiased hypotheses in a random way, using a computer to generate
possibilities. I think the computer would have to be much smarter than the
ones we now have. It would have to be able to generate hypotheses about
perceptions of the type that the organism's nervous system would be capable
of creating through reorganization. Without such guidelines, I think a
truly random search for controllable perceptions would result in, as they
say, an NP-hard problem of the worst sort. I don't know how this problem is
going to be solved, or even if it can be solved. Perhaps we will always
have to be satisfied with approximations to true controlled variables,
particularly in other species, knowing that we can see them only as they
project into human perceptual space (and in particular, our own private
perceptual spaces).
Even in this quote one can find a shadow of anthropormpization:
[I can't spell it either, half of the time]
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.
In control theory, "aiming" isn't anthropomorphizing. It can be modeled in
terms of a control system with a reference signal that specifies the final
state. To say that a system's action is "aiming" at a changing final state
is only to say that the reference signal is changing during the action, and
control is changing the perceptual signal toward the changing reference
signal's value.
If you just add time indexes (continuous, of course..) to r and s,
and write
r[t]=f(s[t],s*)
then, by assuming that s[t] is somehow influenced by r[t'] for all >t'<t,
you can get an S-R formulation.
There is a subtle point here. What you say, strictly speaking, is true: the
current r is always AFTER the previous s. But it makes a difference how
previous the s is and how much r can change in that interval.
The problem with a strict formulation like r[t] == f(s[t-1]) is the
assumption that the response measure is instantaneous and can change by any
amount during one dt. If, however, the response measure can change only by
some amount delta during an interval dt, shrinking dt reduces the amount by
which the response can change, proportionally. The limit is a continuous
dependence of r on s at an INFINITESIMALLY SMALL time in the past, with the
change in r tending to zero.
We're really talking about the fundamental theorem of the calculus here,
which is the difference between a discrete and a continuous picture of
nature. Zeno's Paradox arises from overlooking (or not yet having invented)
this theorem and assuming that the tortoise can move from one position to
another one half as far from the wall IN ZERO TIME. As soon as you think of
the tortoise as moving with some finite velocity, the paradox disappears:
the smaller the distance to be travelled, the faster it will be traversed.
This converts the problem from a discrete, logical problem into an analog
problem.
When responses change on a continuum (and any response involving physical
movement has that property), we then have to ask how much difference there
is between the current stimulus and the stimulus that "occured" dt ago. As
dt shrinks, this difference approaches zero. But the response is still
changing at a finite rate, so the change in the response from one dt to the
next also approaches zero. In the limit, the response and the stimulus
covary.
In real systems, of course, there is always a finite delay. But should we
treat the behavior, then, as a series of closely-spaced stimuli and
responses, or as an approximation to continuous change? Which way of
representing the system, if either, gives the better representation?
In fact, treating the system as an approximation to a continuous one gives
the better representation in almost all cases. The reason is the
implication in the sequential analysis that the response is either present
or not present, and in principle could go from present to not present or
vice versa in ONE delay-time. In real systems, responses take many delay-
times to build up after the stimulus appears, and many more to die out
after the stimulus is gone. This aspect of behavior is missing from the S-R
or discrete representation. The continuous representation, on the other
hand, predicts exactly such gradual changes even if, in the finite-step
approximation, the changes occur in steps.
Another test is to imagine dt going to zero and seeing what effect there is
on the predicted behavior. In the discrete model, the prediction is that
the changes in behavior must go faster and faster as dt is made smaller and
smaller. In the continuous model, the changes in behavior approach a
limiting speed which then stays constant as dt shrinks to zero. When dt is
on the order of normal neural lags, the behavior predicted by a continuous
model is already almost exactly like the real behavior; letting dt shrink
to zero then makes no perceptible difference in the behavior of the model.
These considerations hold true in my model up to about level 6, control of
relationships. At higher levels, however, discrete variables -- symbols --
come into being, and the kinds of behavior that occur are more like the
discrete or sequential kind -- indeed, level 8 is defined as the sequence
level. Now the S-R interpretation becomes more feasible and we have to look
elsewhere than basic mathematics to discriminate SR predictions from
closed-loop predictions.
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.
There isn't any way to make that distinction inside the system doing the
controlling. A change in an input signal is the result of the sum of all
influences on it: in that sum, the contributions of individual sources are
completely lost. Exactly the same change could arise from the action alone,
or from a smaller amount of action and an independent disturbance acting
simultaneously. A higher system could sense the action (proprioceptively,
tactily, or visually, for example) and compare the action with a copy of
the lower-level controlled perception, and deduce the part of the
perception likely to have been caused by independent disturbances. This
would not help the lower-level system doing the controlling to tell which
part of the controlled input was due to its own action. Neither could the
higher-level system deduce how many independent disturbances were acting at
once, assuming that their causes are not available to the senses (as they
are usually not).
Fortunately, control systems do not have to know how much of a given
perception is due to their own actions, or to sense the causes of whatever
disturbances (in any numbers) are acting. The principle of control requires
only sensing the state of the controlled variable itself, and producing
actions that affect it. S-R systems, on the other hand are incapable of
compensating for disturbances if they can't sense the cause of the
disturbance. By definition, open-loop systems don't sense the effects of
the disturbances on the outcome: if they did, they would be control systems
and closed-loop analysis would have to be used.
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Marcos Rodrigues (920331) --
I think the foot-stamping situation is in closed loop. The cockroach
action changes its perception of the environment, surely. My
understanding of your theory is that an action modifying _physically_ >the
environment is not required, provided that our perceptions of the
environment change in direction of correcting the error.
You could be right, but I suggest that to make the cockroach's perception
of foot-stamping into a controlled variable is probably too risky. You're
quite right in reminding us that a controlled variable doesn't have to
exist physically outside the organism (or to have a counterpart that does).
Actually, I've been avoiding that point because the argument tends to drift
off into epistemology, and it's easier to make the cases about S-R vs.
control in terms of visible variables.
But yes, it's conceivable that the cockroach has a perception of a foot
stamping, can recognize it as a significant (visual) event, and has an
internal reference level set very low for such events. On the other hand, I
think it's more plausible that the cockroach has only less advanced
perceptions and has to control for simpler and more proximal variables. At
least, if we can model behavior based on simple variables more directly
connected with processes at the sensory interface, we'll be erring in the
conservative direction, not atttributing higher levels to lower organisms
until the data force us to.
I can't see feedforward or open loop in the escape response.
Goody. Someone else on my side.
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Best to all,
Bill P.