[From Bill Powers (930911.0700 MDT)]
This reminds me, Rick: Avery's date is frequently ahead of ours
by one day because he's across the International Date Line. Note
that I am replying to the following message before it was
written.
Avery Andrews (930911.1519) --
Consider hitting a baseball. There are two possible
conceptions of what this skill involves:
a) the learner develops a Central Pattern Generator (CPG) that
takes as input info about the trajectory of the approach
ball, and produces as output a contour of reference levels
for joint angles, such that ....
b) the learner acquires a control system that controls for a
complex relationship between the location & movement of the
ball and various joint angles, such that ...
... at the appropriate the time, the bat connects with the
ball in the appropriate manner.
PCT'ers presumably would favor (b) over (a), but I'd be happy
to let the choice rest on the outcome of empirical work
I think you're forgetting about disturbances. Choice a) can't
possibly work, because the initial conditions are never the same
twice in a row. In order for the sight of the approaching ball to
be able to operate the muscles to make the bat hit the ball, the
initial stance, footing, bat motion, wind velocity, lighting
conditions, bat weight and moment of inertia, state of laundering
of the uniform, cleanliness of the ball, condition of the arm,
torso, neck, eye, and leg muscles, direction of gaze, degree of
bend of the knees, tightness of the shoelaces, degree of scuffing
of the ground in the batter's box, soil composition of same,
wetness of same, position and friction of grip on the handle of
the bat, and probably several more factors I haven't thought of,
would all have to be identical on every occasion on which the bat
actually contacted the ball.
(I'm actually not entirely convinced that the two are
empirically distinct).
They are quite distinct. Under the assumptions of choice a), two
identical pitches will result in two identical swings of the bat.
The bat will hit the ball only if the batter and bat begin in
exactly the same initial conditions each time, and if the muscle
forces exactly repeat, and if all other conditions are the same.
The bat would have to follow the same trajectory each time; it is
impossible that the bat could be commanded to follow two
different trajectories, given the same inputs to the same CPG,
and highly unlikely that if the initial conditions differed, the
combinations of differences would leave the outcome the same.
Under the PCT proposal, the bat might hit the ball 20 times on 20
identical pitches, and never repeat a trajectory. I predict that
this is what an empirical investigation would find.
My own preference is to propose that the batter converts
kinesthetic positions and velocities, plus ball positions and
velocities, into terms of a common perceptual coordinate system,
and varies the muscle tensions as required to alter the swing as
required to keep the distance between the kinesthetic positions
(adjusted for bat length) and the ball positions continuously
decreasing. This is much more obvious in slow-pitch softball than
in big-league hardball, because the success rate is far higher
and the control systems are operating much farther within their
limits. The actual control task is relatively simple.
What `closed loop' theories of motor learning say is that
acquisition of a skill involves Knowledge of the Results of
attempted actions in order to tune the CPG or whatever that's
producing the action.
This really applies in the context of your example only to
certain skills in which there is a substantial uncontrolled
component or a substantial lag involved. A better example of this
than baseball is bowling, or "bowls" as some underdeveloped
civilizations call it. Bowling success depends entirely on how
precisely the bowler can control the kinesthetic and visual
variables up to the point of release of the ball. Bowlers learn
to focus on repeating initial conditions as precisely as
possible, to minimize the need for corrective actions during the
approach and release. Such corrective actions always occur; the
smaller they need be, the better the long-term result. The
residual inaccuracies of control are reflected in the variations
of ball behavior, in addition to variations due to ball
irregularities and changes in the oiling of the boards on the
alley and irregularities in pin surfaces and placement, and these
factors in turn are reflected in the paucity of 300 games.
Higher-level control necessarily involves a much slower process
because of the long delay between repetitions of the delivery.
The higher system must adjust the reference conditions slowly and
only by small amounts: the visual aiming point, the backswing,
the stride and slide, the cock of the wrist, the twist and lift
on the release. With the exception of the first, these are all
kinesthetic reference signals. In beginners, these changes are
made at random. In professionals they are highly systematic and
parts of higher control systems.
But we shouldn't let these unusual types of control dominate the
discussion. The reason we find them in sports so often is that
behaviors in which control is continuous are too easy to carry
out, and people are just too good at controlling: there's no
sport in having competitor after competitor step up and deliver a
perfect score. This is why Olympic tobogganing is such a boring
sport, except for the possibility of spectacular accidents. When
the top ten finishers' performances are separated by 0.1%, chance
begins to be the main difference. All the major sports have had
their parameters adjusted so that small differences in control
precision are reflected as large differences in outcome. Nobody
can make a hole-in one, sink every free-throw, fire the puck into
the net, hit a home run, roll a perfect 300 game, or even flip
the tiddlywink into the hole on every attempt. The interesting
games force human control capacities near, but not too near, the
limits of what can be controlled. They are deliberately tuned to
achieve this condition.
In most of life, however, control is continuous and easy. The
examples that really show up the difference between the CPG open-
loop model and the closed-loop model are those in which people
have no difficulty in producing the desired result over and over
despite enormous differences in initial conditions and quite
substantial unpredictable disturbances, and in which control is
continuous. This probably covers 99% of observable behavior. Why
switch between models, particular between models that demand
completely different architectures of the nervous system, for
just the few behaviors in which control is difficult --
particular when the difficulties are deliberately introduced to
emphasize differences in performance?
It's probably understandable that we should be most interested in
behaviors in which control is difficult. After all, survival
depends on control, and we become anxious about important things,
or things we are persuaded are important, that prove difficult to
control. We would like to have perfect control over everything
important to us. Even when what we want is to lie back peacefully
and wait for nature to inspire us with love and appreciation, we
very much prefer that nothing is going to attack our relaxed
bellies. That's why monks have monasteries built like fortresses,
and holy beggars let it be known that they own nothing that would
reward a mugger's efforts.
BCP assumes that 2nd order perceptions are linear combinations
of first order ones: if this is true, and all of the first
order perceptions have first order control systems to control
them, then you actually don't need second order *control*
systems at all-you can do calculations to find a combination of
first order perceptual signals that will yield the desired
combination of second order ones (if there is one), and let the
first order control systems do the actual controlling.
But all first order perceptions don't have control systems to
control them: only certain of the kinesthetic perceptions and a
very few others do, and then control is only in the dimension of
intensity. Furthermore, control that requires more than one
first-order control system (such as creating the sound of two
hands clapping) requires control using two kinesthetic position
control systems.
Actually, all control processes COULD be accomplished with a
single, vast, incredibly complex, nonlinear control system. If
you knew the system equations for all the individual control
systems at all the levels, they could (in principle) be solved
and reduced to one expression describing a single control system
with a single one-dimensional perception and reference signal --
and enormously complex input and output functions.
But why would anyone do this, when we know that the real system
is NOT a single control system? The hundreds of spinal control
systems are clearly distinct physical entities; they go right on
working (for a while) after the blade of the guillotine falls. In
decerebrate cats, some coordinated movements persist even when
the cat's head is transected at the level of the midbrain. The
real nervous system is organized into levels of control, and
within levels we can identify distinct control systems. If we
were to reduce this organization to a single equation (assuming
we could), we would be throwing away enormous amounts of useful
information just to satisfy some desire to summarize. And we
would have a picture of behavior only at the highest level.
There's another reason for thinking of many individual control
systems at each level. In any one behavior, the systems at one
level are used in a particular way to accomplish a higher goal.
On different occasions, these SAME control systems, with no
changes in organization, can be used in DIFFERENT ways to achieve
DIFFERENT goals. We don't need a completely different set of
lower-level organizations when the higher-level organization goes
after a different goal. This is the greatest parsimony in the
model in BCP (as opposed, say, to Rodney Brooks' model). Higher-
level systems can be added without any change in the existing
lower-level systems. All that needs to be reorganized is the
manner in which the lower-level systems are used, and that is a
matter that can be accomplished entirely within the higher
levels.
This has implications for evolution. Organisms with only some
small number of levels perceive and control a world in which only
certain variables are known and have preferred states. Evolution
physically adds new levels, which act by varying the previously-
fixed reference levels of the preexisting systems. So the new
level does not have to re-invent all the lower levels of control:
the world to be controlled is already highly controllable in each
of the lower-level respects. Instead of creating a whole new
hierarchy from the bottom up, adding a level simply requires
employing existing systems to control combinations and functions
of variables that have no meaning at the existing levels. The
individual control processes are just the same as before at the
lower levels.
Of course the lower levels too may continue to change, but they
do not change from scratch. They change by small increments from
their former organizations -- from one working control
organization to another one, slightly different, that also works
but perhaps works better for the new higher-level purposes
although no better from the lower-level point of view.
On the other hand, if the second order perceptual functions are
nonlinear, there won't in general be any fixed way to map the
second order error signals onto first order reference signals
that will result in control (I think F&T might have been trying
to say this, if they actually had done so, it would have been a
much better paper).
There might not be a way to map the linear system onto the
nonlinear version of the same system, but that doesn't matter.
What's under control at the higher level isn't any particular
combination (linear or otherwise) of the lower-level perceptions,
but only some function of those perceptions. That function can be
nonlinear or even multiple-valued without preventing second-order
control. Remember that all the second-order system wants is for
its perceptual signal to match its reference signal. If this can
be accomplished by several different sets of lower-level signal
values, that makes no difference to the second-level system.
Try using a cubic form for a perceptual function, one that
provides three ways for the input variable to produce a
perception matching the reference signal. The control system will
alter its output until the reference signal is matched by the
perceptual signal. If you then apply a disturbance big enough or
sudden enough to force the lower variable over the hump in the
cubic equation, the system will quickly change its output to move
the input past the negative-slope solution (where feedback is
positive) and to the other positive-slope solution (if the right
sign of disturbance is used). The lower-level variable will now
be in a totally different state, but the perceptual signal will
still match the reference signal at the second level. And that's
all that the second-level system cares about.
Fowler et. al. made this mistake in criticising the PCT idea of a
two-level kinesthetic control system. They were doing fine until
that point in their analysis. They considered a two-level system
in which the higher perceptual signal was a function of three
lower-level perceptions. Then they showed that a disturbance
which altered one lower-level perception would cause an error
signal in the higher system, but that this error signal couldn't
indicate which of the lower three variables had been disturbed.
So they concluded, quite incorrectly, that the higher system
couldn't correct its error.
What they forgot was that the other two lower-level variables
could still be altered. The action of the higher system would
affect all three lower variables; a disturbance of one variable
would alter the output effects on all three variables, affecting
each in the direction for negative feedback and bringing the
higher perceptual signal to a match with the higher reference
level again. The higher system isn't concerned with restoring the
same lower-level situation as existed before the disturbance. It
is concerned only with maintaining its own perceptual signal at
the reference level it is told to maintain. It couldn't care less
how the environment has to change at the lower level in order to
accomplish this.
So it doesn't make any difference whether second-order systems
are linear or nonlinear.
RE: controlling on a bumpy landscape
If there are multiple bumps on the landscape, the control process
will simply bring the input to a point on the slope of any bump
that has a peak greater than or equal to the required value.
Control systems are not trying to maximize or minimize their
input variables. They are trying to match them to a specific
value. The hill-climbing concept involves an incorrect way of
visualizing the control process. If the highest local bump is not
high enough to match the reference value, the error will persist
and the output will continue. If the output isn't capable of
reaching all available bumps eventually, the error may never be
corrected. If it can reach a sufficiently high bump, the action
will cease the first time the perception matches the reference
signal. The control system doesn't give a hoot that there might
be a higher bump nearby -- not until the reference signal is
raised so much that the current bump won't suffice. Then the
action will continue until a higher bump is found. All this
applies, incidentally, to any control system whether its output
be systematic or e. coli-style random.
The basic error to avoid here is that of casting the control
process in terms of OBJECTIVE requirements that must be
OBJECTIVELY met. The immediate task of any control system is
simply to make its perception match its reference signal. How
that is accomplished at lower levels is completely irrelevant to
that control system. Of course eventually there may be
repercussions of satisfying the reference signal in a particular
lower-level way that cause reorganization to start, but that will
simply result in another control system that still controls only
its own perception relative to its own reference signal.
In the PCT model, the existing control systems plus the
reorganizing system have to accomplish EVERYTHING with no
information except what comes in through the senses and what
affects the physiological state of the organism. The concept of
the "best" or the "optimal" solution is irrelevant to the
hierarchy: the first solution that works is always accepted and
used until it stops working. Then reorganization starts again,
stopping immediately when another solution that works is found.
There is no natural optimizing, maximizing, or minimizing. There
is only control.
RE: group control
.. groups of people and certain other kinds of animals manage
to stabilize (effectively, control) things collectively that
they couldn't control as individuals (as when two stretcher-
bearers keep the stretcher more or less level and moving over
the ground).
If each stretcher-bearer individually intends to keep the
stretcher horizontal as well as hold it off the ground, the
stretcher will become horizontal. This will also be true if one
bearer just holds one end at a convenient height; the other will
adjust the height of the other end to keep the stretcher
horizontal.
An OUTCOME of this is that the stretcher will be horizontal. But
there is no group that has a group perception of levelness or a
group reference signal specifying levelness. There is not, nor
need there be, any group intention about levelness. There is no
need for all people involved to have the same goal, as long as
enough of them do, and as long as the goals of the others don't
interfere. The stretcher bearer who is only concerned about
holding one end at a convenient height makes it possible for the
other to maintain levelness, without in the least intending to do
that. Each bearer can be independently concerned with maintaining
levelness without knowing anything about the other's intention.
If both parties are concerned about maintaining levelness, it
makes no difference whether they think of themselves as
individuals or as half of a team. So the idea of a "shared" or
"group" goal is irrelevant in this example.
The mere fact that people are able to control something only when
others are trying to control a similar thing relative to a
similar goal is not enough to establish the reality of group
control systems. If you have an option as to whether to interpret
the situation in any of several ways, then you're not talking
about something necessary. If you can't explain group behavior in
ANY way but in terms of a specifically group control system, then
you have to accept group control systems. But if there's nothing
going on that can't be handled perfectly well in terms of
independent individual control systems, the group control system
is just a needlessly-multiplied entity, an interpretation by an
observer that has nothing to do with what is actually happening:
a metaphor, not a model.
Not every means of stabilizing something is a control system. If
you drop a marble in a bowl, it will seek the center and return
there after a perturbation, with no control system involved (no
sensor or effector; loop gain less than 1). If you glue dishes to
a tray, no control system is necessary to keep them on the tray
as the tray tilts this way and that. Stabilization against
disturbances is not the only part of the Test: you must also
establish that sensing and acting are required for control to
continue: that control is lost when either sensing or acting is
prevented.
There may be controlled variables that can be controlled only by
a group control system as distinct from a collection of
individual control systems. But so far, nobody has described one.
···
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Best,
Bill P.